PSAT
The PSAT
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PSAT
Revolution Prep PSAT Workbook
This workbook is for the exclusive use of Revolution Prep, LLC and its students and is not legal for resale. © 2015 Revolution Prep, LLC. All rights reserved. Version 8-15. While every effort has been made to ensure the accuracy and correctness of the content in this manual, Revolution Prep assumes no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein. This product is not endorsed by the College Board., nor any other agency or school. Any similarity to other printed material is purely coincidental.
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PSAT
Table of Contents
PSAT Introduction (Page 4)
Critical Reading (Page 8)
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Writing (Page 59)
Mathematics (Page 138)
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PSAT
Introduction
PSAT Introduction
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PSAT
Structure and Scoring
PSAT LENGTH Test 1: Reading = 60 Minutes Test 2: Writing and Language = 35 Minutes Test 3 and Test 4: Math = 70 Minutes o Test 3: No calculator math section = 25 Minutes o Test 4: Calculator permitted math section = 45 Minutes Total = 165 Minutes (2 hours and 45 minutes)
PSAT ORDER OF DIFFICULTY Math questions generally increase in difficulty as you move through a section. o “Obvious” answers are usually correct earlier in a section and incorrect later in a section. Reading and writing questions are of randomly varying difficulty throughout each section.
PSAT SCORING The Math and the combined Reading and Writing tests are each scored from 160 to 760. Your COMPOSITE SCORE is the total of these two scores (320 to 1520).
PSAT SCORING: NATIONAL MERIT SCHOLARSHIP CONSIDERATION Only juniors taking the PSAT are eligible for National Merit Scholarship consideration.
o For COMMENDED status, a junior must receive a PSAT score in the top 96th percentile nationally (~34,000 students each year). o For SEMIFINALIST status, a junior must receive a PSAT score in the top 99th within his or her state. (~16,000 students each year). o For FINALIST status, there are additional criteria that a student must meet beyond his or her PSAT score.
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PSAT
Content
READING If you are reading this, then it’s already clear you can read boring material. Now, you just need to learn how to answer the questions correctly. This has a lot less to do with knowledge than with your ability to survive mind-numbing reading passages.
WRITING AND LANGUAGE What’s scary: it measures your understanding of standard written English. What’s not-so-scary: there’s no spelling, no vocabulary, and no complicated terminology.
MATH All the math you were trying to forget: Pre-Algebra, Algebra, Coordinate & Plane Geometry, and Trigonometry.
**THE BEST NEWS** You will learn what the test will be like EVERY TIME. No surprises on test day.
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PSAT
Guessing and Pacing
GUESSING ON THE PSAT There is NO PENALTY for wrong answers on the PSAT and Every question is worth the SAME POINT VALUE. • FIRST: Answer all the questions you KNOW HOW TO DO. • NEXT: Make educated guesses on questions for which you can ELIMINATE ANSWERS. • LAST: Guess randomly on questions about which you HAVE NO CLUE.
PACING ON THE PSAT DON’T RUSH to answer every question.
• If you’re regularly making careless mistakes, you must SLOW DOWN. • Spend test time working on the problems you KNOW HOW TO DO. • Spend homework time working on the problems you DON’T KNOW HOW TO DO. DON’T HESITATE to cut loose. • If you’re unsure whether you’ve wasted “a lot” of time on a question, you already have! o If you stare at a question and CAN’T figure out anything, MOVE ON! • The LONGER a question takes, the LESS it can help your score.
DON’T WORRY about timing for every single question. • GOOD MOVE: Staying aware of how much time is left in a test. • BAD MOVE: Calculating how much time is left per question in a test. • Develop a sense of test pacing from your practice tests and homework. • Do the math on the test, not on the clock.
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Writing
PSAT Reading: Table of Contents
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PSAT
Reading: Table of Contents PSAT Reading: Table of Contents
PSAT Reading: Introduction (Page 10) Determining Central Ideas, Themes, and Meaning (Page 12) Command of Evidence (Page 28) Analyzing Multiple Texts (Page 35)
PSAT Reading and Writing: Table of Contents Evaluating Quantitative Information (Page 44) Words in Context (Page 52) • •
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Words in Context (Reading) Words in Context (Writing)
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PSAT
Reading
PSAT Reading: Introduction
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PSAT
Reading: Introduction
PSAT Reading Introduction
Test 1: Reading 60 Minutes for 48 Questions • Four single passages and one multiple texts passage Concepts covered on PSAT Reading: • • • •
Understanding main ideas and purpose Applying quantitative information Defining words in context Utilizing textual evidence
Quick Reading Tips • • • • • •
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Read for main ideas. Save time by skimming details. Always anticipate your answer. Always eliminate choices to find the correct answer. Don’t spend too much time on any one question. Don’t make stupid mistakes – stay focused.
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PSAT
Determining Central Ideas, Themes, and Meaning
PSAT Reading: Determining Central Ideas, Themes, and Meaning
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Determining Central Ideas, Themes, and Meaning: Reading for Main Ideas
Reading for Main Ideas When reading on the PSAT, it is important to read for an understanding of what the text is about (as opposed to what happens). We understand what a text is about through its main ideas: • •
Why did the author write this sentence, paragraph, or passage? If I had to quickly describe this sentence, paragraph, or passage to someone else, what would I say?
Facts, lists, and details have little importance for understanding the meaning of a text. Think big picture!
Paragraph Structure: Where Do Main Ideas Live? Main ideas are usually located at the beginning and the end of a paragraph. Details tend to be found in the middle of a paragraph.
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PSAT
Determining Central Ideas, Themes, and Meaning: Effective Reading
Effective Reading: The Two-Track Mind Whenever you read, there are two parts of your brain at work: 1) The part of your brain that reads the words on the page. 2) The part of your brain that thinks about other stuff. These two parts of your brain do not necessarily work together! To ensure focus, periodically stop and ask yourself questions while you read!
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At the end of each paragraph, STOP! What is the main idea? At the end of the passage, STOP! o Who was the author? (Was the author part of the story or just telling the story?) o What was the author’s overall purpose in writing the passage? o How did the author feel about this topic? (What is the tone of the passage?)
Effective Reading: The Two-Track Transmission Once we know how to identify main ideas, we can focus our time and attention on the most important parts of a text. When to accelerate (read more quickly) when reading a text: • • •
When the author lists facts to support a main idea When the author repeats a point that has already been made When the author uses unfamiliar terms/phrases that are unrelated to a main idea
When to slow down (read more slowly) when reading a text: • • •
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At the beginning and end of paragraphs Whenever the author introduces a new idea When the authors uses an adverb (adverbs show how the author feels)
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PSAT
Determining Central Ideas, Themes, and Meaning: Effective Reading
Effective Reading: Sample Paragraph
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Critics argue that since the Apollo missions, little substantial progress has been made in space exploration. NASA missions have been criticized as ineffective and costly, and more than one respected pundit has suggested that the U.S. government drastically reduce funding for the International Space Station and other NASA ventures. Against this backdrop of hostility, policymakers would do well to remember that trailblazing scientific exploration has been the subject of misplaced scrutiny throughout history. Centuries before the founding of NASA, Christopher Columbus faced similar skepticism in funding his maiden – and in retrospect, historic – voyage across the Atlantic.
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Determining Central Ideas, Themes, and Meaning: Effective Reading
Effective Reading: Sample Paragraph
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Critics argue that since the Apollo missions, little substantial progress has been made in space exploration. NASA missions have been criticized as ineffective and costly, and more than one respected pundit has suggested that the U.S. government drastically reduce funding for the International Space Station and other NASA ventures. Against this backdrop of hostility, policymakers would do well to remember that trailblazing scientific exploration has been the subject of misplaced scrutiny throughout history. Centuries before the founding of NASA, Christopher Columbus faced similar skepticism in funding his maiden – and in retrospect, historic – voyage across the Atlantic.
NEW MAIN IDEA (SLOW DOWN): NASA programs have recently been the subject of ridicule. DETAILS (SPEED UP) about the ridicule that NASA has received.
NEW MAIN IDEA (SLOW DOWN): Columbus faced skepticism similar to what NASA is currently facing.
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PSAT
Determining Central Ideas, Themes, and Meaning: Solving Questions
Solving Reading Questions on the PSAT: There are four steps to solving reading questions on the PSAT. 1) Cover the answer choices. Do not look at the answer choices! 2) Anticipate an answer to the question. How would YOU answer the question? Use the notes you took while reading! 3) Eliminate answers that are clearly incorrect. Answers are clearly incorrect because they do not align with your anticipation! 4) Make a decision among whatever choices remain. Avoid answers with absolute language and/or non-relevant information.
Solving Reading Questions on the PSAT: Out of Scope Answers What makes wrong answers wrong can generally be reduced to a few words – the words that make a wrong answer “Out of Scope.” An Answer Choice Is “Out of Scope” if it… 1) …brings in subjects that are not related to the passage 2) …talks about something from a part of the passage outside of the part the question is referring to 3) …is too extreme (unless the author is very extreme) 4) …assumes too much about the author’s viewpoint
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PSAT Questions 1-10 are based on the following passage. This passage is adapted from Ian Wilmut, Keith Campbell, and Colin Tudge, Dolly and the Age of Biological Control. © 2000 by Ian Wilmut, Keith Campbell, and Colin Tudge Line
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Dolly seems a very ordinary sheep – just an amiable Finn-Dorset ewe – yet as all the world has acknowledged, if not entirely for the right reasons, she might reasonably claim to be the most extraordinary creature ever to be born. Mammals are normally produced by the sexual route: an egg joins with a sperm to form a new embryo. But in 1996 Keith Campbell and I, with our colleagues at Roslin Institute and PPL, cloned Dolly from a cell that had been taken from the mammary gland of an old ewe and then grown in culture. We fused that cultured cell with an egg from yet another ewe to “reconstruct” an embryo that we transferred into the womb of a surrogate mother, where it developed to become a lamb. This was the lamb we called Dolly: not quite the first mammal ever to be cloned, but certainly the first to be cloned from an adult body cell. Her birth overturns one of the deepest dogmas in all of biology, for until the moment in February 1997 when we made her existence known through a brief letter in the scientific journal Nature, most scientists simply did not believe that cloning in such a way, and from such a cell, was possible. Dolly’s impact was extraordinary. We expected a heavy response, but nothing could have prepared us for the thousands of telephone calls (literally), the scores of interviews, the offers of tours and contracts, and in some cases the opprobrium, though much less of that than we might have feared. Everyone, worldwide, knew that Dolly was important. Even if they did not grasp her full significance (and the full significance, while not obvious, is far more profound than is generally appreciated), people felt that life would never be quite the same again. And in this they are quite right. Most obviously – and unfortunately, because it is certainly not the most important aspect – commentators the world over immediately perceived that if a sheep can be cloned from a body cell, then so can people. Many hated the idea. But others welcomed human cloning, and some, like
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Sample Reading Passage #1 Dr. Richard Seed, even offered to set up cloning 45 clinics, surely jumping the gun by several decades since very few scientists have the necessary expertise, and even in the best hands, human cloning at this stage would be absurdly risky. I fielded many of the telephone calls that flooded 50 into Roslin Institute in the days after we went public with Dolly, and quickly came to dread the pleas from bereaved families, asking if we could clone their lost loved ones. I have two daughters and a son of my own and know that every parent’s 55 nightmare is to lose a child, and what parents would give to have them back, but I had and have no power to help. I suppose this was my first sharp intimation of the effect that Dolly could have on people’s lives and perceptions. Such pleas are 60 based on a misconception: that cloning of the kind that produced Dolly confers an instant, exact replication – a virtual resurrection. This simply is not the case. But the idea is pervasive and was reflected in articles and cartoons around the world. 65 Der Spiegel’s1 cover showed a regiment of Einsteins, Claudia Schiffers, and Hitlers – the clever, the beautiful, and the not very nice. The prospect of human cloning causes us grave misgivings. It is physically too risky, it could have 70 untoward effects on the psychology of the cloned child, and in the end we see no medical justification for it. For us, the technology that produced Dolly has far wider significance. As the decades and centuries pass, the science of cloning 75 and the technologies that may flow from it will affect all aspects of human life – the things that people can do, the way we live, even, if we choose, the kinds of people we are. Those future technologies will offer our successors a degree of 80 control over life’s processes that will come effectively to seem absolute. Until the birth of Dolly, scientists were apt to declare that this or that procedure would be “biologically impossible” – but now that expression, biologically impossible, 85 seems to have lost all meaning. In the twenty-first century and beyond, human ambition will be bound only by the laws of physics, the rule of logic, and our descendants’ own sense of right and wrong. Truly Dolly has taken us into the age of 90 biological control. 1Germany's
biggest and most influential weekly magazine; the title is German for “The Mirror”
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PSAT
Sample Reading Passage #1
1. The passage is written from the perspective of someone who is
6. Which choice does the author cite as a limitation to the future of scientific research?
A) actively involved in conducting biological research. B) a participant in a recent debate in the field of biology. C) knowledgeable about recent scientific advancements. D) an advocate for further cloning research.
A) Government funding. B) Laboratory techniques. C) Imagination with regard to cloning’s possibilities. D) Morality and logic.
2. The author indicates which of the following about cloning research? A) B) C) D)
Its impact should be thoroughly studied. Its benefits should be widely promoted. Its effects have been fully understood. It will answer previously unconsidered questions
3. The phrase beginning “and unfortunately . . .” (lines 38-39) reflects the author’s response to the fact that A) the successful cloning of Dolly did not prove that people can be cloned. B) in the wrong hands, cloning could bring about dire consequences. C) most people do not grasp the full significance of cloning. D) critics sensationalized the Dolly breakthrough. 4. As used in line 48, “absurdly” most nearly means A) B) C) D)
surreally. unreasonably. ignorantly. purposelessly.
7. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 57-59 (“I suppose…perceptions”) Lines 67-68 (“The prospect…misgivings”) Lines 78-81 (“Those…absolute”) Lines 85-89 (“In…wrong”)
8. As used in line 70, “untoward” most nearly means A) B) C) D)
detrimental. long-lasting. malicious. unforeseen.
9. The author suggests that Dolly’s cloning is A) the pinnacle of his professional career. B) an epoch-defining event. C) most important for its implications for human cloning. D) completely misunderstood. 10. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 25-31 (“Dolly’s…feared”) Lines 38-42 (“Most…people”) Lines 48-53 (“I fielded…ones”) Lines 89-90 (“Truly…control”)
5. The author would most likely agree that the example of the Der Spiegel cover described in lines 65-67 represents A) how the world would be different had cloning existed a century ago. B) a quintessentially German worldview. C) a present-day impossibility. D) the likely negative effects of cloning.
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PSAT Questions 11-19 are based on the following passage. The following passage is an excerpt from an essay on the renowned Swedish scientist Linnaeus. Line
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Without doubt, Carl von Linné, known in the English-speaking world as Linnaeus, is the greatest figure in Swedish natural science. Even during his lifetime he was acclaimed by the whole world, and his writings became peerless books of law. Within the domain of natural history, he reigned supreme, just as Newton did within the exact sciences. Certainly there existed impenitent foreigners who refused to bow before the authority of the Swedish botanist, especially in France, but his influence only increased with the years, and his reformation of the most lovable of the sciences became general property. Even today, several of Linnaeus’s works remain indispensable tools for the biological investigator. But what is remarkable and unique about Linnaeus’s posthumous reputation is the influence he has exercised on his native country. It is without parallel. We know of no other example where a great scientist has become part of a whole people’s national consciousness, a patriotic symbol. There exists, or at least has existed, a Swedish Linnaeus legend, piously tended by those who considered themselves to be the guardians of the memory of Linnaeus. Its founder, it could be claimed, was Linnaeus himself. With his nervous and overwrought self-awareness, he described and commented on the extraordinary destiny of his life and his incomparable greatness as a scientist. But it was not until a little way into the nineteenth century, with the full development of Romanticism, that Linnaeus first became the object of a national cult. His person and work were regarded with reverent awe, and under the sign of the new sensitivity Linnaeus became the Prince of Flowers, pointing the way to the sanctum of the mysteries of Nature. This picture of Linnaeus was bequeathed to coming generations. The delicate Linnaea was made his symbol, soon to be embroidered on the collars of the uniforms worn by members of the medical profession. It was as an incarnation of all the loveliness of the short Nordic summer that Linnaeus gained his prestige. Meadows and groves sang his praises, and Linnaean botany, the science of herbaria, has remained down to our own generation a sort of Swedish national asset, a joy or a vexation to generations of schoolboys. The cult of Linnaeus, the native reverence for Linnaeus and things Linnaean, has naturally
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Sample Reading Passage #2 50 stimulated efforts at research in depth. Modern Swedish research on Linnaeus started in the decades about the turn of this century, during the period of the Linnaean jubilee festivals. An inventory of the extant manuscripts was made and 55 texts were published. In 1903 there appeared Thore Magnus Fries’s monumental biography, and just fifteen years later the Swedish Linnaean Society was founded. Linnaeus’s life, his environment, and aspects of his work were 60 becoming known in the minutest detail. But still, the traditional attitude of awe and wonder was maintained. Linnaeus’s saintly halo shone with greater clarity than ever. He belonged to the Swedish people, and it was not fitting to make a 65 critical evaluation of his person and his scientific accomplishment. Since then, matters have improved. Through the research of the last decades we know that the man Linnaeus was other than the one of the Romantic legend – the sweet and 70 sentimental elements have vanished. His inner world also contained dark tones of depression and despair, at least in his later years. Linnaeus now emerges as more complicated than had previously been suspected. This applies also to his work, 75 primarily his biological view of nature and his religious outlook, which have been the object of increasingly penetrating studies. Thus the revision of the current picture of Linnaeus proceeds. But there still remains much to 80 be done; one is never really finished with a man like Linnaeus. There are great and important questions that research has scarcely touched. And perhaps the Romantic Linnaeus legend still lives on in certain respects, preventing an impartial 85 interpretation of Linnaean botany and the man behind it. We must have the right to invite Linnaeus to step down from his pedestal and to put some searching questions to him; his limitations and failures cast a clearer light over the 90 incomparable quality of his genius. To the best of one’s ability, and with his works as a guide, it is a matter of separating the light from the shadows.
11. The author indicates that Linnaeus was A) B) C) D)
self-effacing. a model for all scientists. superior to all scientists. a conscious cultivator of his own myth.
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PSAT
Sample Reading Passage #2
12. Which choice provides the best evidence for the answer to the previous question?
16. The author would most likely agree with which of the following statements?
A) B) C) D)
A) Linnaeus’s theses will be questioned as more comes to light about his character. B) His stature in Sweden will be adversely affected by new findings. C) Linnaeus the man and Linnaeus the scientist should be considered separately. D) Our admiration for Linnaeus will increase as we better understand his limitations and flaws.
Lines 16-18 (“But…country”) Lines 25-29 (‘Its founder…scientist”) Lines 48-50 (“The cult…depth”) Lines 78-79 (“Thus…proceeds”)
13. The sentence beginning “Certainly there existed . . .” (lines 8-13) primarily serves to illustrate how A) the French disliked the Swedes. B) factors unrelated to science can impede scientific appreciation. C) Linnaeus never transcended national boundaries. D) the opponents of Linnaeus were small in number.
17. The author’s attitude toward current Linnaean scholarship is one of A) B) C) D)
pride and nostalgia. criticism and doubt. approval and encouragement. realism and resignation.
14. The author would most likely characterize the scholarly work described in lines 44-52 (“Modern Swedish . . . detail”) as
18. Which choice provides the best evidence for the answer to the previous question?
A) B) C) D)
A) B) C) D)
important but partial. antiquated and foolish. superficial but seminal. necessary and complete.
15. As used In line 73, “complicated” most nearly means A) B) C) D)
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elaborate. confused. unfathomable. complex.
Lines 16-18 (“But…country”) Lines 22-25 (“There…Linnaeus”) Lines 58-62 (“Linnaeus’s…maintained”) Lines 86-90 (“We must…genius”)
19. The main purpose of the passage is to A) B) C) D)
describe the legend of an influential figure. provide an overview of a scientist’s work. conduct a search for truth. explore the personality flaws of a famous individual.
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Determining Central Ideas, Themes, and Meaning: Notes
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Determining Central Ideas, Themes, and Meaning: Review
Questions 1-10 are based on the following passage. The following passage discusses some aspects – both positive and negative – of a raw food diet. Line
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In recent years, many alternative diets have emerged, each touting itself as the paragon of healthy eating. Many of them – vegan, vegetarian, and fruitarian diets, among others – restrict the ingredients that they claim comprise healthy nutrition. “Raw foodism,” on the other hand, does not necessarily restrict ingredients. Instead, it restricts the methods of food preparation. As its name suggests, raw foodism consists entirely of foods that have not been heated above a certain temperature, usually 116°F, though sometimes as low as 104°F. Its followers generally opt for unprocessed, uncooked fruits, vegetables, nuts, seeds, sprouts, herbs, grains, and legumes, which must comprise at least 70% of their diet in order for them to be considered raw foodists. Often, but not always, raw food dieters are also vegans, who exclude meat, fish, poultry, dairy, and eggs. Both raw foodists and those who oppose the practice agree that applying heat to a food usually, though not always, chemically transforms it, thus changing its flavor, texture, appearance, and nutritional properties. What they disagree on is whether the practice of cooking is positive or negative. Reasons for practicing raw foodism are as diverse as the individuals who support it. Some raw foodists are pragmatists, claiming that the pursuit reduces food and energy costs. They also say it saves time, though some raw food recipes can require considerable advance preparation. Others have been swayed by health arguments. They claim that raw food is the optimal fuel for the human body, since the digestive system evolved before humans started cooking with fire. Benefits are thought to range from lower weight and blood pressure to reduced allergies and cancer risks. Mainstream scientists who oppose raw foodism cite anthropological evidence showing that human beings have been cooking their food for over 250,000 years. Food cooked accidentally, by lightning strikes or brush fires, has been consumed for even longer. These critics claim that widespread use of cooking has changed human anatomy, especially around the jaw, and that the resulting improved nutrition has even led to increased brain size. They recognize that the structure of some foods, like tomatoes and carrots, makes it virtually impossible to access the available nutrients without cooking. Moreover,
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following a raw food diet can make it difficult to get adequate amounts of calcium, vitamin D, vitamin B12, iron, zinc, and protein. In fact, many raw foodists have to rely on supplements in order to maintain good nutritional balance. Additionally, raw food may contain harmful bacteria and parasites, and certain products, such as kidney beans and buckwheat, are unsafe to consume in their raw form. Ignorance on the matter could result in poisoning. Finally, opponents criticize raw food advocates as promoting supporting data that is anecdotal, rather than scientific in nature. Indeed, many raw foodists claim the best support for a raw food diet is personal experience. While mainstream scientists have generally not supported the raw food movement, there is some scientific evidence that can be seen to support raw food claims. Proponents of raw food believe that it contains enzymes that aid its own digestion and help populate the digestive tract with beneficial florae that stimulate the human immune system. Raw food enzymes include amylases, proteases, and lipases, which are enzymes that break down starches, proteins, and fats, respectively. Keeping these and other biological components, such as antibodies, intact helps prevent degenerative diseases, slow the effects of aging, enhance energy, and boost emotional balance. Raw foodists point to several scientific studies that have linked high temperature meat preparation to increased cancer risks. Researchers at the National Cancer Institute have found that human subjects who ate beef rare or medium-rare had less than one-third the risk of stomach cancer than those who ate beef medium-well or well-done. Other research has indicated significant benefits in reducing breast cancer risk when large quantities of raw vegetables are included in the diet. One striking point of contention has involved pasteurization. Depending on the process used, pasteurization heats milk and other liquid products to between 145°F and 280°F in order to reduce or kill dangerous bacteria, such as Salmonella, E. coli, and Listeria. The U.S. Food and Drug Administration (FDA) notes that pasteurization has been highly successful in reducing the prevalence of diseases, including listeriosis, typhoid fever, tuberculosis, diphtheria, and brucellosis. The FDA strongly recommends that children, the elderly, pregnant women, and persons with weakened immune systems avoid raw milk products and other raw liquids, as these diseases can cause serious injury or even death. Raw foodists do not discount the effect of dangerous bacteria, but they claim that the real threat lies in unsanitary dairy and other
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PSAT
Determining Central Ideas, Themes, and Meaning: Review
production conditions. If the milk, for example, is collected and stored cleanly, they believe milkborne diseases will not be a problem. They believe 110 the same holds for other commonly pasteurized products, such as apple juice. More to the point, raw foodists hold that the risk is worth the benefit. Raw milk is claimed to have antibodies that provide resistance to many viruses, bacteria, and 115 bacterial toxins and may help reduce the severity of asthma symptoms. They discount studies that show no significant nutritional difference between pasteurized and nonpasteurized milk. Ultimately, until more hard research is done, mainstream 120 science and raw food advocates will continue to be at odds. 1. The main purpose of the passage is to A) highlight how scientific research overwhelmingly supports raw foodism. B) explain that no scientific research has been found to support raw foodism. C) explain how the benefits of raw foodism are a topic of intense scientific debate. D) allow raw foodists to renounce the dangerous effects of bacteria. 2. The passage indicates that raw foodists view traditional science with A) B) C) D)
scorn. respect. admiration. contempt.
3. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 18-25 (“Both…negative”) Lines 38-41 (“Mainstream…years”) Lines 65-68 (“While…claims”) Lines 86-88 (“Other…diet”)
5. As used In line 32, “swayed” most nearly means A) B) C) D)
authorized. controlled influenced. undermined.
6. Which choice best summarizes the second paragraph of the passage (lines 26-37)? A) Most raw foodists cannot fully comprehend the value of a healthy diet. B) Some raw foodists have better reasons for practicing raw foodism than others. C) There is a diversity among practitioners of raw foodism. D) Raw foodism is an excellent diet for weight loss. 7. It can reasonably be inferred from the passage that raw foodists believe which of the following regarding pasteurization? A) Nonpasteurized nondairy products, like apple juice, do not pose the same risks as nonpasteurized milk. B) Pasteurization is a crutch used by the FDA to avoid enforcing cleaner production conditions. C) There are enough benefits from consuming nonpasteurized products to justify any potential dangers from unsanitary production conditions. D) There has not been enough scientific research regarding the costs and benefits of nonpasteurized liquids. 8. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 33-35 (“They claim…fire”) Lines 65-68 (“While…claims”) Lines 99-103 (“The FDA…death”) Lines 111-116 (“More…symptoms”)
4. The author places the words “Raw foodism” in quotation marks (line 6) most likely to
9. The conclusion that can reasonably be inferred from the fifth paragraph (lines 89-103) is that
A) indicate that she is not quite sure what they mean. B) mark them as a technical term with a specific definition. C) force the reader to pay more attention to the term. D) cast aspersions on raw foodism’s legitimacy as a scientific movement.
A) pasteurization is the only known method of killing E. coli bacteria. B) raw milk is the most dangerous food for children and pregnant women. C) extreme heat can be an effective means of destroying harmful bacteria. D) pasteurization at a lower temperature would make pasteurized milk acceptable to raw foodists.
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PSAT
Determining Central Ideas, Themes, and Meaning: Review
10. When the passage says that raw foodists “discount studies that show no significant nutritional difference between pasteurized and nonpasteurized milk” (lines 116-118), it most nearly means that A) debate over pasteurized milk is irrelevant because most raw foodists do not consume dairy products. B) raw foodists always disagree with FDA findings regarding food processing. C) FDA studies are frequently suspect and cannot be relied upon when making nutritional decisions. D) at times, raw foodists ignore scientific data that does not support their beliefs.
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Determining Central Ideas, Themes, and Meaning: Answers Workbook Answers
Determining Central Ideas, Themes, and Meaning
Review Answers 1) C 2) B
1) A 2) A 3) D 4) B 5) C 6) D 7) D 8) A
3) A 4) B 5) C 6) C 7) C 8) D 9) C 10) D
9) B 10) A 11) D 12) B 13) B 14) A 15) D 16) D 17) C 18) D 19) A
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PSAT
Command of Evidence
PSAT Reading: Command of Evidence
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PSAT
Command of Evidence
Command of Evidence Identifying Command of Evidence Questions on the PSAT: Command of Evidence questions ask for which line(s) “provide the best evidence for the answer to the previous question.” On Command of Evidence questions, pick the lines with the main idea that most-closely aligns with the answer to the previous question. If unsure, eliminate down to as few choices as possible before choosing an answer.
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The Nellie, a cruising ship, swung to her anchor without a flutter of the sails, and was at rest. The tide had come in, the wind was nearly calm, and being bound down the river, the only thing for it was to come to and wait for the turn of the tide. The Director of Companies was our captain and our host. We four affectionately watched his back as he stood in the bows looking toward the sea. On the whole river there was nothing that looked half so nautical. He resembled a pilot, which to a sailor is trustworthiness personified. It was difficult to realize his work was not out there in the luminous estuary, but behind him, within the brooding gloom. Between us there was, as I have already said somewhere, the bond of the sea. Besides holding our hearts together through long periods of separation, it had the effect of making us tolerant of each other’s stories—and even convictions. The Lawyer—the best of old fellows—had, because of his many years and many virtues, the only cushion on deck, and was lying on the only rug. The Accountant had brought out already a box of dominoes, and was toying architecturally with the pieces. Marlow sat cross-legged, leaning against the mast. He had sunken cheeks, a yellow complexion, a straight back, and, with his arms dropped, the palms of his hands outwards, resembled an idol. The Director, satisfied the anchor had good hold, made his way forward and sat down amongst us. We exchanged a few words lazily. Afterwards there was silence on board the yacht. For some reason or another we did not begin that game of dominoes. We felt meditative, and fit for nothing but placid staring.
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1. The passage suggests that the narrator A) regards his fellow sailors with benevolence. B) is concerned that he has been at sea too long. C) believes that the upcoming journey will be unbearable. D) eagerly awaits the stories told by his fellow sailors.
2. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 2-5 (“The…tide”) Lines 6-8 (“The…sea”) Lines 15-18 (“Besides…convictions”) Lines 29-32 (“Afterwards…staring”)
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PSAT
Command of Evidence
Command of Evidence Identifying Command of Evidence Questions on the PSAT: Command of Evidence questions ask for which line(s) “provide the best evidence for the answer to the previous question.” On Command of Evidence questions, pick the lines with the main idea that most-closely aligns with the answer to the previous question. If unsure, eliminate down to as few choices as possible before choosing an answer.
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I spent most of my childhood summers down the road from home at Big Momma’s house. We began each day with the morning ritual she referred to as her labor of love – combing my hair. I would sit on the porch floor with my feet swinging over its edge while my head bobbed back and forth between Big Momma’s legs as she tugged, parted, and braided my long, thick, nappy hair. Big Momma always sat perfectly upright, sucking in her breath with each drag of the comb, then releasing the air from her hollow Cherokee cheeks, never once bending her back. After she finished the job, she’d pat me on the head and say, “Now you beautiful.” I’d rush to the bathroom, stand on the toilet seat, and peer over the sink into the mirror, eager to view this new and beautiful me. Of course, she never materialized. All I ever saw was my chubby face with a crown of lopsided plaits and a mouth full of what my momma teasingly called “beaver teeth” because they looked large enough to saw wood. Besides our grooming, Big Momma and her band of swearing sopranos made sure their offspring got a proper Christian upbringing. Every Sunday there was morning church school and Baptist Training Union. And for one week every August the young ones were herded to Grambling, Louisiana, a small college town, for a gigantic statewide revival called Youth-En-Camp. Although the drive took only a few hours, it had the feel of a great adventure. This was due in part to the parcel of sheets, dresses, and fried chicken that always accompanied me but also because the decreased supervision allowed me to experience free will. It was during one of these revivals that I became hopeful that I would one day look into the mirror and see beauty in myself. I was thirteen at the time – too old to be in one of the crayon classrooms but still too awkward to be cool. Before that summer I’d never thought that I could be beautiful – perhaps cute, on a good day, but never glamorous, radiant, or enchanting. Of course, up to that point, the only form of beauty I
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knew to desire was physical splendor, in which category I was sorely lacking. I was the tallest girl in my eighth-grade class, and when I tried to walk in dress shoes, my heels would slide out, causing me to trip over myself. Naturally, my only concern was ridding myself of awkwardness. Beauty was something I saw only in others. A woman’s evencolored skin and bright white teeth made her beautiful, never the inner peace that sparkled in her eyes. I greatly admired the little girl’s sunny Easter dress, adorned with white bows and ribbons, but gave no thought to the mother – needle in one hand, iron in the other, creating this lovely vision. And Big Momma’s front lawn with its velvet violets, deep purple grape suckers, and yellow sunflowers floating in the air like balloons was beautiful, but never once did I consider the care they were given even as the flowers’ first petals danced indiscriminately in the sunlight. I had always focused on my plainness, and it was this sorry image of myself that I took with me to Youth-En-Camp that summer. Only later would I understand that real beauty emanates from the heart. 3. The author characterizes her time at Youth-EnCamp as a period of A) B) C) D)
adventure. transition. learning. ease.
4. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 16-20 (“All…wood”) Lines 33-35 (“It was…myself”) Lines 36-38 (“I was…cool”) Lines 60-63 (“I had…summer”)
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PSAT
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Command of Evidence Notes
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PSAT
Command of Evidence Review
Questions 1-10 are based on the following passage. This passage discusses the revisionist theory of the origins and outcomes of the French Revolution.
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Edmund Burke first attacked the French Revolution in 1790 with his work the Reflections on the Revolution in France. In his writing, Burke sharply criticized those who claimed that the French Revolution was a necessity. Thomas Paine’s famous work The Rights of Man was written in reply to Burke’s analysis. The Rights of Man was both enormously influential and exceedingly popular in the English working class movements. However, Paine’s work angered the ruling class, and Paine was forced to flee England to France in order to avoid arrest. Until recently, the French Revolution was considered a bourgeois revolution, driven by class conflict, that destroyed the vestigial remnants of feudalism and paved the way for capitalism in France. This narrative is rooted in traditional Marxist interpretations of the social, economic, and political forces at play in France and the rest of Europe in 18th and 19th centuries. Revisionist historians are now challenging this orthodox view of events. Revisionists argue that the French Revolution cannot be seen as a bourgeois revolution that completely terminated feudal political structures. The revisionist theory maintains that class struggle played only a small role in the French Revolution and that the revolt had little or nothing to do with capitalism. The revisionist scholars also argue that the bourgeoisie made up the elite class in society. The bourgeoisie consisted of landowning gentry who tended to agree with each other on political and social issues. Revisionists argue that the elite were generally in favor of the reforms that the common people were demanding, and therefore political reform would have been possible without a violent revolution. While revisionists argue that the French Revolution had little or no correlation to the development of capitalism, critics of the revisionist theory counter that revisionists ignore the tremendous social and economic changes that had been occurring prior to the Revolution. These critics also point out that the significant economic changes did not occur in isolation. The new economic order required new relations
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between classes, a new social hierarchy, and a broader view of the world. Critics of revisionism also argue that while the French Revolution did not create capitalism, the power struggles and structure of pre-revolutionary France were not conducive to capitalism. They argue that it was the elite’s resistance to this new order that caused the Revolution. Revisionists maintain that the French Revolution completed a process of centralization and reconstruction for France that was already materializing prior to the Revolution. They speculate that the process of modernization and reconstruction could have occurred without the violence and upheaval of a revolution. Revisionists argue that some among the French ruling class were already pushing for the same reforms that the Revolution ultimately achieved. Critics have responded to this claim by pointing out that the most famous of these reforms was introduced in 1776 when French aristocrat and economist, A.R. J. Turgot proposed to increase trade, abolish guilds, and reform the tax system. The privileged elite were not supportive of these measures and blocked Turgot’s efforts. Critics of revisionist theory use Turgot’s failure as evidence that the revolution was actually necessary to effectuate change in France. 1. The author of the passage refers to “vestigial remnants” (line 15) in order to A) illustrate the revisionist historians’ assertions about the consequences of the French Revolution B) introduce a flaw in an argument that will be discussed in the subsequent paragraph C) demonstrate a belief formerly held by some monarchists D) provide an example of a traditional Marxist belief 2. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 13-17 (“Until…France”) Lines 17-20 (“This…centuries”) Lines 23-25 (“Revisionists…structures”) Lines 45-48 (“The…world”)
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PSAT
3. The author suggests that the elite members of social class were A) compelled to argue against revisionist thinking. B) unaccustomed to political discord among themselves. C) unaware of the common people. D) uncomfortable in each other’s presence. 4. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 23-25 (“Revisionists…structures”) Lines 31-33 (“The…issues”) Lines 45-48 (“The…world”) Lines 62-64 (“Revisionists…achieved”)
5. In line 39, the phrase “little or no correlation” indicates that revisionists A) were unable to understand the link between the French Revolution and capitalism. B) were uncertain in their belief that capitalism caused political reform. C) ignored major social and economic trends brought about by the French Revolution. D) did not believe that the French Revolution impacted the development of capitalism. 6. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 26-29 (“The…capitalism”) Lines 33-37 (“Revisionists…revolution”) Lines 45-48 (“The…world”) Lines 52-54 (“They…Revolution”)
Command of Evidence Review
7. It can be inferred from the passage that the revisionists A) never accept Marxist interpretations of historical events. B) do not support the traditional interpretation of the French Revolution. C) favor a decentralized system of government over a strongly centralized system. D) think that the French monarchy was actually a strong supporter of the Revolution. 8. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
9. According to the passage, which one of the following statements is most consistent with the view held by revisionists? A) Marxism is a failed ideology. B) Non-violence is the most effective means of achieving social reform. C) There were causes of the French Revolution that cannot be adequately explained by a classical Marxist construction. D) There was no genuine desire among the working class to promote capitalism during the French Revolution. 10. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
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Lines 13-17 (“Until…France”) Lines 17-20 (“This…centuries”) Lines 45-48 (“The…world”) Lines 55-58 (“Revisionists…Revolution”)
Lines 5-9 (“Thomas…movements”) Lines 33-37 (“Revisionist…revolution”) Lines 38-43 (“While…Revolution”) Lines 52-54 (“They…revolution”)
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PSAT
Command of Evidence Answers Workbook Answers
Review Answers
Command of Evidence
1) D
1) A
2) B
2) C
3) B
3) B
4) B
4) C
5) D 6) A 7) B 8) D 9) C 10) B
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PSAT
Analyzing Multiple Texts
PSAT Reading: Analyzing Multiple Texts
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PSAT
Analyzing Multiple Texts
Approaching Multiple Texts Identifying Analyzing Multiple Texts Questions on the PSAT: One PSAT reading portion is comprised of two passages which are followed by questions that relate to both passages. Approaching Multiple Texts on the PSAT: Multiple texts selections always share a common theme/topic, with each passage having a different perspective on that theme/topic. A Venn Diagram can help to organize this information for making anticipations.
Solving Multiple Texts Questions on the PSAT: There are four steps to solving Multiple Texts questions on the PSAT. 1) Cover the answer choices. Do not look at the answer choices! 2) Anticipate an answer to the question. How would YOU answer the question. Use the notes you took while reading! 3) Eliminate answers that are clearly incorrect. Answers are clearly incorrect because they do not align with your anticipation! 4) Make a decision among whatever choices remain. Avoid answers with absolute language and/or non-relevant information.
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PSAT
Analyzing Multiple Texts
Analyzing Multiple Texts Identifying Analyzing Multiple Texts Questions on the PSAT: One PSAT reading portion is comprised of two passages which are followed by questions that relate to the passages. Analyzing Multiple Texts Strategy: After reading each individual passage, stop and answer only the questions that relate to that passage. After answering all questions that relates to one passage, then answer the questions that refer to multiple passages. Passage 1
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Before Lewis and Clark, the territory west of the Mississippi River was about as well understood as outer space – almost as mysterious as the Americas were to Christopher Columbus the day he dropped anchor off El Salvador. It was home to the red nations, yet an enigma to recently arrived whites. French and Spanish traders made inroads along the major waterways, yet little was known of this vast slice of continent other than what could be gleaned from rumors that blended a dash of speculation with boundless exaggeration. It was our very own African heart of darkness, with a handful of men proceeding cautiously upriver to obtain furs from the various native tribes – and courting death in the process. Passage 2
In many histories of the American West, the Lewis and Clark expedition marks the beginning of recorded history; earlier history of the region 20 is relegated to prelude. The Lewis and Clark expedition was a momentous event and a heroic achievement, but it was only a subplot in a historical drama of time, place, and people that had been playing for thousands of years. The 25 “new lands” Lewis and Clark explored were in fact very old. The West they saw had been shaped by many other histories – and ways of understanding history – involving other peoples and recorded not only in writing but in song and 30 story and earth and memory. Lewis and Clark did not bring the West into U.S. history, they brought the United States into western history.
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1. The author of Passage 1 compares Lewis and Clark to Christopher Columbus (lines 3-6) primarily in order to A) B) C) D)
help the reader understand their methods. characterize them as oppressors. highlight their fearlessness. emphasize how little is known about their expedition.
2. Both passages are concerned with A) understanding the truth surrounding Lewis and Clark’s discoveries B) links between the past and the future C) specific discoveries made during Lewis and Clark’s expedition D) perceptions of the regions explored by Lewis and Clark
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PSAT
Words in Context
Analyzing Multiple Texts Identifying Analyzing Multiple Texts Questions on the PSAT: One PSAT reading portion is comprised of two passages which are followed by questions that relate to the passages. Analyzing Multiple Texts Strategy: After reading each individual passage, stop and answer only the questions that relate to that passage. After answering all questions that relates to one passage, then answer the questions that refer to multiple passages.
3. The author of Passage 2 would most likely characterize the “other histories” (line 27) as A) essential to a complete understanding of the American West. B) intentional falsifications of Native American history. C) accurate records based on the journals of Lewis and Clark. D) one-sided.
4. The two passages differ in their views of the Lewis and Clark expedition in that Passage 1 regards it A) through the eyes of a foreigner, while Passage 2 assumes a distinctly American outlook. B) as a major discovery, while Passage 2 diminishes its importance. C) from the perspective of Lewis and Clark’s era, while Passage 2 views it in a broader historical context. D) with complete ignorance of the facts, while Passage 2 approaches it with an informed understanding.
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Analyzing Multiple Texts Notes
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PSAT
The first passage below is an excerpt from a historical survey of early twentieth-century American society; the second is an excerpt from a 1997 article about the Harlem Renaissance. Passage 1
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Hot nights and cool jazz . . . steamy sidewalks and fancy dressers . . . songs of the soul and songs of the body . . . the lilt of laughter and the wail of the blues . . . . That was Harlem in the 1920s – a place that vibrated with excitement, promise, glitter, and joy. If you had visited Harlem in those days, you might have heard bandleader Duke Ellington playing “Take the ‘A’ Train” at the Cotton Club, or Louis “Satchmo” Armstrong shaking up the jazz world with his trumpet at Connie’s Inn. Harlem was also the home of African-American poets, novelists, actors, and philosophers. So great was the cultural explosion of Harlem during the 1920s that the period has since been called the Harlem Renaissance. Harlem has always been measured by a spirit and way of life that have touched all of America and have created a legacy that continues to inspire today. Tens of thousands of black people flocked to Harlem looking for a better life in the 1920s, among them a star-studded group of artists. All were eager to bask in the freedom of city life and the growing excitement of Harlem. Unlike the South’s cities and towns, New York City made African-Americans feel free to express themselves, to create, to fully tell the story of the AfricanAmerican experience in words, pictures, paintings, and, most popularly, music. In the 1920s, African-American music was all the rage. Every night, white people took taxis and subways uptown to Harlem to listen and dance to music by black musicians and singers. White publishers went to Harlem to find black writers and poets. Black people, in Harlem at least, began to feel that they were an important part of the nation’s cultural life. But whatever Harlem did for black people during the 1920s, the Stock Market crash (1929) and the Great Depression (1929-1935) took it away. Suddenly, the money that had supported
Analyzing Multiple Texts Review
African-American artists dried up. The cultural life of Harlem seemed to fade slowly into increasing Line poverty and bleakness. “We were no longer in 45 vogue,” wrote Jervis Anderson in This Was Harlem. Nevertheless, the great legacy of the Harlem Renaissance has continued to enrich and influence American life. The artists who made Harlem their 50 home in the 1920s continue to inspire Americans of all colors today. Passage 2 For some, the Harlem Renaissance evokes the flourishing of intellectual and artistic output exemplified by writers such as Langston Hughes 55 and Zora Neale Hurston. For others, it conjures images of bacchanalia: the long-legged beauties of the Cotton Club and those dark, seedy speakeasies such as the Clam Bake and the Hot Feet. In that postwar environment of social and 60 sexual adventure, Harlem symbolized liberation for black and white alike. In the great migration of African-Americans from the rural South to the cities, the district became a Mecca for streams of black writers, musicians, performers, and 65 filmmakers, a refuge from the all-pervasive racism of American society. But those few city blocks were also a playground for affluent whites. Emboldened by bootleg liquor, they turned this little hamlet of 70 New York into their own exotic laboratory, where they could experiment with what was forbidden in their own world, enjoy what they saw as primal and erotic, then leave it behind a few hours later. The Harlem Renaissance has become so 75 emblematic that it can be hard to separate the myth from the reality. Was this Harlem a place or just a state of mind? Did it really change black cultural life forever, as some historians claim? Or was it simply a handful of privileged black artists 80 patronized by rich, white Afrophiles? Certainly today’s black artists are keen to claim a cultural legacy bridging their work to the heroes of Harlem. But it has also been argued that the Renaissance represented nothing more than a 85 bourgeois playpen, retrospectively endowed with cultural legitimacy by academia and the black
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Analyzing Multiple Texts Review
middle class. Perhaps we celebrate Harlem at the expense of more radical periods, for example, the labor movement of the 1930s that spawned Richard Wright, arguably the greatest AfricanAmerican novelist. Langston Hughes, one of the luminaries of the Harlem Renaissance, admitted at the time: “The ordinary Negro hasn’t heard of the Negro Renaissance. And if they had it didn’t raise their wages any.” Indeed, skeptics argue that the plunging rates of literacy and increasing sense of crisis in America’s black underclass prove the Harlem Renaissance’s influence has been only one class deep. Great novels may have come from Harlem, but how many there now can read them? Part of the energy that fuelled the Harlem Renaissance was the belief that black cultural achievement in the “high” arts would socially and spiritually uplift the race. Manifestly this has not happened. Where the legacy of the Harlem Renaissance remains a profoundly romantic one for the black bourgeoisie, on the streets, where the great majority of black culture is made, its echoes are only faintly heard. 1. The opening paragraph of Passage 1 relies on A) B) C) D)
historical facts. personal anecdotes. sensory details. an extended metaphor.
3. The statement by Jervis Anderson in lines 44-45 implies that A) whites stopped frequenting Harlem altogether. B) the later figures of the Harlem Renaissance were less talented than the earlier ones. C) another, more exciting cultural movement supplanted the Harlem Renaissance. D) the Harlem Renaissance was a fad. 4. The sentence beginning “Emboldened by bootleg liquor” (lines 68-69) suggests that A) Harlem provided whites a temporary refuge from traditional social restrictions. B) social norms were too limiting for most whites. C) whites preferred African-American culture to their own. D) whites did not enjoy themselves in Harlem. 5. According to Passage 1, whites A) took unfair advantage of the talents of Harlem artists. B) offered Harlem artists additional channels for their art. C) were solely responsible for the mainstream success of Harlem artists. D) were opposed to the goals of the Harlem Renaissance.
2. In line 41, “dried up” most nearly means A) B) C) D)
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ran out. hardened. withered. grew brittle.
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Analyzing Multiple Texts Review
6. In line 81, “keen” most nearly means A) B) C) D)
intelligent. sharp. intense. eager.
7. Passage 2 differs from Passage 1 in that A) Passage 2 ignores the racial aspect of the Harlem Renaissance; Passage 1 focuses on it. B) Passage 2 considers the relevance of the Harlem Renaissance today; Passage 1 centers on the actual experience of the Harlem Renaissance. C) Passage 2 underscores the social and historical context of the Harlem Renaissance; Passage 1 assumes the reader has full knowledge of this context. D) Passage 2 praises the legacy of the Harlem Renaissance; Passage 1 examines it critically.
9. The author of Passage 2 would most likely respond to the author’s view in Passage 1 of Harlem’s “spirit and way of life” (line 17) by A) praising the author’s historical insight. B) criticizing the author’s oversimplification. C) lamenting the author’s misinterpretation of Harlem’s spirit and way of life. D) mocking the author’s attempts at flattery. 10. Which choice provides the best evidence for the answer to the previous question? A) B) C) D)
Lines 61-65 (“In…society”) Lines 76-80 (“Was…Afrophiles?”) Lines 102-105 (“Part…race”) Lines 106-110 (“Where…heard”)
8. Both passages suggest which of the following about the major figures of the Harlem Renaissance? A) Many of them were not from Harlem. B) They resented whites encroaching on their territory. C) They wanted to help elevate the black underclass. D) Their art had an immediate impact on all people.
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PSAT
Analyzing Multiple Texts Answers Workbook Answers
Analyzing Multiple Texts 1) C 2) D 3) A 4) C
Review Answers 1) C 2) A 3) D 4) A 5) B 6) D 7) B 8) A 9) B 10) D
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PSAT
Evaluating Quantitative Information
PSAT Reading: Evaluating Quantitative Information
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PSAT
Evaluating Quantitative Information
Evaluating Quantitative Information Identifying Evaluating Quantitative Information Questions on the PSAT: On the PSAT, quantitative information questions assess a student’s ability to understand a chart or graph and connect it to a passage. To solve quantitative information questions, there are two things to keep in mind: 1)
What is the data about?: This can be figured out by answering the question “What does the header of the graphic say?”
2)
What does the data in the graphic show about this topic?: It is important to look for trends in the data (When one thing increases, another thing increases; some things are above average and some are below average, etc.).
To be correct, an answer must be related to the answers to these questions.
Police Percent Increase in Employment, Projected 2015-2025 Total, All Occupations
Police Officers
Fire Fighters 0%
2%
4%
“The United States Bureau of Labor Statistics forecasts job growth in city governments, projecting that 20 percent of new jobs in all occupations will be related to police.”
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8% 10% 12% 14% 16% 18% 20%
1. Which choice completes the sentence with accurate data based on the graph? A) NO CHANGE B) warning, however, that job growth for police will slow to 10 percent by 2025. C) predicting that police employment will increase 20 percent between 2015 and 2025. D) indicating that 10 to 14 percent of police jobs will remained unfilled.
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PSAT
Evaluating Quantitative Information
Evaluating Quantitative Information Identifying Evaluating Quantitative Information Questions on the PSAT: On the PSAT, quantitative information questions assess a student’s ability to understand a chart or graph and connect it to a passage. Questions 2 and 3 refer to the below information
Heart rate beats/minute
Heart rate of five 20 year olds 240 220 200 180 160 140 120 100 80 60 40
maximum desirable level
Walking
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A recent analysis of heart rates was conducted on a group of healthy 20 year old humans. This analysis revealed that for these people, their heart rates in beats per minute increased substantially when running, yet the heart rates remained below the maximum desirable level for 20 year olds. The researchers reported that for these healthy humans, the increase in heart rate was related to the bodily strain caused by the aerobic exercise. “Exercise is highly beneficial for humans,” the study concluded. “It’s an activity which decreases the risk for high blood pressure and other cardiac ailments.”
Running
2. What information discussed in the paragraph is represented by the graph? A) The information in lines 3-7 (“This . . .olds”) B) The information in lines 7-10 (“The . . .exercise”) C) The information in lines 10-12 (“Exercise . . . concluded”) D) The information in lines 12-14 (“It’s . . . ailments”)
3. Which statement about the effect of running on 20 year olds is best supported by the graph? A) Only one of the people did not experience an appreciable change in heart rate when running. B) All of the people remained above the minimum desirable heart rate for humans. C) All of the people remained below the maximum desirable heart rate for humans. D) The person with the lowest walking heart rate had the highest running heart rate.
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PSAT
Evaluating Quantitative Information
Evaluating Quantitative Information Identifying Evaluating Quantitative Information Questions on the PSAT: On the PSAT, quantitative information questions assess a student’s ability to understand a chart or graph and connect it to a passage. Question 4 refers to the below information Table 1: Tiger Woods Major Championships Won By Time Period 1997-2000
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2005-2008
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2009-2012
0 0
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Tiger Woods won the 2008 U.S. Open in sudden death, even while enduring a double stress fracture in his left tibia. He is no stranger to overcoming hurdles as he lives out his basic principle: “If you’re not going forward, you’re going backward.” Tiger will take some time to heal, 4 but will soon be back on the golf course winning major tournaments and doing what comes so naturally.
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4. Which choice best completes the sentence based on the information provided in Table 1? A) NO CHANGE B) and it may be a challenge for Tiger Woods to regain his pre-injury form in major championships. C) and Tiger Woods will never win another major championship after he returns to golf. D) but Tiger Woods will be just as competitive as before his injury.
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PSAT
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Evaluating Quantitative Information Notes
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PSAT
Evaluating Quantitative Information Review Questions 1 and 2 refer to the below information
Number of Users (in millions)
Facebook Users By Month 1500 1200 900 600 300 0 2007
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2013
Year 1. Which statement best summarizes the information presented in the graph?
2. According to the graph, which statement is true about the number of Facebook users in 2013?
A) Far more people around the world used the internet in 2013 than in 2007. B) The number of people using Facebook each month more than tripled from 2010 to 2013. C) The number of people using Facebook each month increased tremendously from 2007 to 2013. D) The number of Facebook users each month is likely to be almost 3 billion in 2015.
A) Growth in the number of Facebook users in 2013 was widely out of proportion to growth during the three years prior. B) The growth in the number of Facebook users began a new upward trend. C) The growth in the number of Facebook users reached its peak. D) The number of Facebook users surpassed 1.2 billion for the first time.
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PSAT
Evaluating Quantitative Information Review Questions 3 and 4 refer to the below information
Mosquito Morality Rate in the United States
Percent Morality Rate
40% 35%
Range of Desired Eradication
30% 25% 20% 15% 10% 5% 0% 2009-2010
2010-2011
2011-2012
2012-2013
2013-2014
2014-2015
Winter Season
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Since 2009, several states have experimented with spraying pesticides during winter months in the hope of reducing the number of mosquitos that emerge during the summer. As a result of this spraying, drops in mosquito populations have 3 exceeded 10 percent of the population each winter. In an attempt to increase the effectiveness of this program, during the winter of 2011–2012, the states changed this chemical used during the process, 4 and the number of insects killed has increased every year since.
3. Which choice offers the most accurate interpretation of the data in the chart? A) B) C) D)
NO CHANGE been below the acceptable range. not changed noticeably from year to year. greatly increased every year.
4. Which choice offers the most accurate interpretation of the data in the chart? A) NO CHANGE B) the percentage of insects killed has been within the range of desired eradication each winter since 2011-2012. C) the percentage of mosquitos killed has exceeded the range of desired eradication each winter since 2011-2012. D) the percentage of mosquitos killed has increased each winter since 2011-2012.
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PSAT
Evaluating Quantitative Information Answers Workbook Answers
Evaluating Quantitative Information
Review Answers 1) C
1) C
2) D
2) A
3) A
3) C
4) D
4) B
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PSAT
Words in Context
PSAT Reading: Words in Context
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PSAT
Words in Context (Reading)
Words in Context (Reading) Identifying Words in Context Questions on the PSAT: On Words in Context questions, students are asked to define a word within the context of the surrounding text. No prior knowledge of the word is necessary. To solve Words in Context questions, first anticipate a word or tone that fits within the surrounding text. Then, use your anticipation to eliminate answers that do not align with your anticipation. Question 1 Refers to the Paragraph Below I am not saying that a good literary education is sufficient to create morally sensitive human beings, but keeping children ignorant of their moral heritage is one way to get ourselves a generation of morally shortchanged human beings. Children who are basically honest but who have not been taught and so don’t know that lying and cheating are wrong or cannot say why they are wrong; children who are compassionate but who aren’t sure that cruelty in exotic societies is just as wrong as it is in our own. Such students are being cheated of their moral heritage that is the glory of our nation. For all our children are rightful heirs to the Judeo-Christian tradition and the European Enlightenment that taught our Founding Fathers their morals and politics.
1. As it is used in the paragraph, “shortchanged” most nearly means A) B) C) D)
penniless robbed deficient underpaid
Question 2 Refers to the Paragraph Below It can be difficult to ask tough questions about immigration when we see nostalgic images of Ellis Island, recall our own families’ coming to America, or encounter a new immigrant who is striving admirably to achieve the American dream. But tough questions about immigration can no longer be avoided as we enter a fourth decade of unprecedentedly high immigration and struggle with its impact on job markets, on the quality of life and social fabric of our communities, and on the state of the environment.
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2. As it is used in the paragraph, “fabric” most nearly means A) B) C) D)
structure cloth weaving surface
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PSAT
Words in Context (Writing)
Words in Context (Writing) Identifying Words in Context Questions on the PSAT: On Words in Context questions, students are asked to define a word within the context of the surrounding text. No prior knowledge of the word is necessary. To solve Words in Context questions, first anticipate a word or tone that fits within the surrounding text. Then, use your anticipation to eliminate answers that do not align with your anticipation. Question 3 Refers to the Paragraph Below I also think she wanted me to go there because she was worried I’d be lost if she sent me south to a historically black college or some big university. I was young and sheltered, and when it came to racial politics, I was largely harmless. I was completely unprepared to play the role people would want me to play as the daughter of an African-American hero. I had not a clue who I was, either as the daughter of Malcolm X or even as simply myself, Ilyasah Shabazz. Mommy probably worried that if I enrolled at a historically black college, the expectations she had so carefully and thoroughly shielded me from my entire life would rise up like a tidal wave and swallow me whole.
3.
A) NO CHANGE B) moral C) innocent D) inexperienced
4.
A) NO CHANGE B) blow C) utter D) perspire
Question 4 Refers to the Paragraph Below Everyone wanted to see the men on the mountain. Gutzon Borglum, who regarded his masterpiece as far more than a tourist attraction, was no doubt reassured when the phrase “Shrine of Democracy” was coined at the 1930 dedication of the Washington head. “A monument’s dimensions,” said Borglum, “should be determined by the importance to civilization of the events commemorated . . . Let us place there, carved high, as close to heaven as we can, the words of our leaders, their faces, to show posterity what manner of men they were. Then send a prayer that these records will endure until the wind and the rain alone shall wear them away.”
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PSAT
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Words in Context Notes
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PSAT
Words in Context Review
Question 1 Refers to the Paragraph Below So, superstitious or not, the Chinese, Muslims, and Babylonians did their scientific duty. Without their records we would not be able to confirm the dates of many key historical events – including the birth of Christ. Where would the millennium celebrations be then?
1.
As it is used in the paragraph, “confirm” most nearly means A) authorize B) state C) demonstrate D) verify
Question 2 Refers to the Paragraph Below It was the week before the school session began. After a long summer, the returning students were enjoying their free time, realizing that there was not a moment to lose. Facing this scene, I was shaken and awed. The reason was simple. Three months before, I had stood in Tiananmen Square. My mind recalled the indignation of the demonstrators, the students on hunger strike, the banners, the slogans, and the loudspeakers.
2.
A) NO CHANGE B) pushed C) abused D) mesmerized
3.
A) NO CHANGE B) frees C) erases D) dismisses
Question 3 Refers to the Paragraph Below Guiding Richie’s hands with her own, she helps him dip the cup into the flour. The cup goes in easily, and through its thin wall he can feel the silkiness and slight grit of the sifted flour. A tiny cloud rises in the cup’s wake. Mother and son bring it up again, heaped with flour. Flour cascades down the silver sides. Laura tells the boy to hold the cup steady, which he nervously manages to do, and with one quick gesture she rejects the grainy little heap on top and creates a flawless white surface exactly level with the lip of the cup. He continues holding the cup with both hands.
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PSAT
Words in Context Review
Question 4 Refers to the Paragraph Below How do I explain my concept of married feminist? I am a woman who feels pulled in two directions – between traditional values and conventions on one hand and a commitment to feminist ideology on the other. A woman who finds custom appealing and comforting, yet despises the patriarchal patterns that make women second-class citizens. I am a woman who wants a loving, long-term relationship with a man but bitterly resents being considered only someone’s other half. A woman who values family life, but deplores the sterile, functional view of man as head of the family and woman as its heart.
4. As it is used in the paragraph, “sterile” most nearly means A) B) C) D)
purified childless uninspired clean
Question 5 Refers to the Paragraph Below Helen picked out a flat fish, pom-pom fish, she called it, only a dollar sixty-nine a pound, bargain bin. And I said, “This kind of bargain you don’t want. Look at his eye, shrunken in and cloudylooking. That fish is already three days old.” But Helen stared at that fish eye and said she saw nothing wrong. So I picked up that fish and felt its body slide between my fingers, a fish that had slipped away from life a long time ago. Helen said it was a good sign – a juicy, tender fish!
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5. As it is used in the paragraph, “slipped away” most nearly means A) B) C) D)
escaped fled departed snuck
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PSAT
Words in Context Answers Workbook Answers
Words in Context 1) C 2) A
Review Answers 1) D 2) A 3) C
3) D 4) C
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4) C 5) C
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PSAT
Writing
PSAT Writing: Table of Contents
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PSAT
Writing: Table of Contents Writing: Table of Contents
PSAT Writing: Introduction (Page 61) Adjectives and Adverbs (Page 63) Parallelism (Page 68) • •
Parallelism Basics Correlative Conjunctions
Passage Analysis (Page 74) • • • •
Adding Precision Introductions and Conclusions Main Idea Analysis Sequence
Prepositions (Page 83) Pronouns (Page 88) • • • • •
Singular vs. Plural Personal Pronouns Possessive Pronouns Pronoun Case Unclear Pronoun Subject
Punctuation (Page 97) • • • • • •
Comma Usage Colon Usage Contractions Dash Usage Possession Run-on Sentences and Sentence Fragments
Transitions (Conjunctions) (Page 107) Verbs (Page 112) • •
Subject-Verb Agreement Verb Tense
Word Choice (Page 118) • •
Frequently Confused Words Inconsistent Tone and/or Style
Wordiness and Redundancy (Page 124) • •
Redundancy Wordiness
Advanced Grammar (Page 130) • • • •
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Affect vs. Effect Logical Comparisons Misplaced Modifiers Who, Whom, That, Which, and Whose
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PSAT
Writing
PSAT Writing: Introduction
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PSAT
Writing: Introduction
PSAT Writing Introduction
Test 2: Writing 35 Minutes for 44 Questions • Four passages Concepts covered on PSAT Writing: •
Basic Grammar and Syntax o
• • •
Prepositions, punctuation, verbs, etc.
Main Idea Analysis Quantitative Analysis Words in Context
Quick Writing Tips • • • • •
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Trust your grammar ear! Stay confident – you know all the grammar you need to know. Identify the grammatical issue that is being tested. Don’t make a problem harder than it is. Don’t make stupid mistakes – stay focused.
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PSAT
Adjectives and Adverbs
PSAT Writing: Adjectives and Adverbs
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PSAT
Adjectives and Adverbs
Adjectives and Adverbs Adjectives are words or phrases that modify nouns and pronouns. Adverbs modify everything but nouns and pronouns (adjectives, verbs, other adverbs). Identifying Adverb Issues on the PSAT: Look for adjectives describing words or phrases that are not nouns or pronouns, or for adverbs describing words or phrases that are not verbs, adjectives, or other adverbs. 1. As developed by Read, the Shaw Alphabet contains 48 letters – each with only one pronunciation – as well as eight different vowel markers. As Shaw had specified, it is essentially a purely phonetic system. A) NO CHANGE B) pure phonetic C) purely phonetically D) pure phonetically
2. Today, people have moved so easy from paper to paperless transactions that swiping a card is the norm. A) NO CHANGE B) so easiest C) so easily D) so easier
3. James approached the test confident and diligent, trusting all of the studying he had done the week before the test. A) NO CHANGE B) approached the test with confidence and diligence C) approached the test confidently and with diligence D) approached the test confidently and diligently
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PSAT
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Adjectives and Adverbs Notes
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PSAT
Adjectives and Adverbs Review
1. Abagail wanted to keep the party a secret, so she had to plan stealthy and talk discreet in order to not let the cat out of the bag. A) NO CHANGE B) plan stealthily and to talk with discreetness C) plan stealthily and to talk discreetly D) plan stealthy and talk discreetly
2. Shamu, a world famous orca whale, was an important factor in the growth of the SeaWorld park in San Diego, California. A) NO CHANGE B) importantly a factor C) an important factor who took part in D) the most importantly factor
3. This year, Americans acted very swift to file their taxes on time and thus avoid fines from the government. A) NO CHANGE B) very swifter C) very swiftly D) very swiftest
4. One worry of walking through tall grass is Lyme Disease, an infectious disorder caused by bacteria. Lyme disease can cause joint pain by the severe swelling joints. A) NO CHANGE B) severe swelling C) the severely swelling of D) severely swelling
5. My tutor said that anxiety is a complete understandable reaction to taking the SAT. However, with proper preparation those worries can be transformed into confidence. A) NO CHANGE B) complete, understandably C) completely understandable D) completely, understandable
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PSAT
Adjectives and Adverbs Answers Workbook Answers
Adjectives and Adverbs
Review Answers 1) C
1) A
2) A
2) C
3) C
3) D
4) D 5) C
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PSAT
Parallelism
PSAT Writing: Parallelism
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PSAT
Parallelism
Parallelism Proper grammar requires that all items in a list or all related clauses be in the same grammatical form (nouns, verbs, correlative conjunctions, etc.). Identifying Parallelism Issues on the PSAT: Look for two or more items or clauses in a list. 1. The local representative considers the new law to be a great success: it improves the quality of roadways, creates many jobs, and it saves the state money.
A) NO CHANGE B) saving C) saves D) will save
2. A green space is set aside in a downtown area. A baseball field is built to encourage youth fitness. To mitigate difficulties in traveling to the field, a new bus stop is established. Which choice best maintains the sentence pattern already established in the paragraph?
A) B) C) D)
NO CHANGE A new bus stop can help mitigate difficulties in traveling to the field. A new bus stop is established to mitigate difficulties in traveling to the field. By a new green space, a new bus stop is established to mitigate travel difficulties.
3. Although we were sitting in last row, the concert was as exciting to us as the people sitting adjacent to the stage. A) B) C) D)
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NO CHANGE people as it was as to the people
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PSAT
Parallelism: Correlative Conjunctions
Parallelism: Correlative Conjunctions Correlative conjunctions are conjunctions that come in pairs, and you have to use both of them to maintain parallelism in a sentence. Identifying Parallelism Issues: Correlative Conjunctions on the PSAT: Look for conjunctions in the below pairs: both … and either … or neither … nor not … but not only … but also 1. The shopping mall’s construction is not going according to plan this morning. Neither the foreman or the building materials has arrived on time. A) NO CHANGE B) Either the foreman or the building materials C) Either the foreman nor the building materials D) Neither the foreman nor the building materials
2. During the early part of the 21st century, companies have increasingly promoted fitness for employees. In light of the resulting benefits not only to employee productivity and again to the bottom line of corporations in the form of reduced health care costs, an expansion of these programs can be expected. A) NO CHANGE B) but it benefits C) as also to D) but also to
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PSAT
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Parallelism Notes
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PSAT
Parallelism Review
1. The tsunami tore through the small ocean-side town, hurling boats and cars, engulfing farmlands, and houses were swept away. A) NO CHANGE B) houses swept away C) sweeping houses away D) swept away houses
2. Renowned for fighting hard, marching hard, and obedience, the Vermont Brigade earned a reputation as one of the finest units in the Army of the Potomac. A) NO CHANGE B) for its obedience C) being obedient D) obedient
3. Lighthouse devotees tend to be passionate: they enjoy decorating their homes with lighthouse memorabilia, putting bumper stickers on their cars, and to wear clothes emblazoned with their favorite lighthouses. A) NO CHANGE B) wearing C) having to wear D) to be wearing
4. Gall and Medek are known for working with builders during the design stages of a project to maximize the economy of materials, to achieve ecological sustainability in construction processes, and building successful working relationships with all the project stakeholders. A) NO CHANGE B) in building C) she built D) to build
5. Edward Abbey’s essays earned him praise and secured his position as a leading American environmentalist during the late 1960s, a period during which he wrote prolifically. A) NO CHANGE B) earn him praise or secure his position to be C) earned him praise and secure his position as D) would earn him praise and secured his position as that of
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PSAT
Parallelism Answers Workbook Answers
Parallelism
Review Answers 1) C
1) C
2) C
2) C
3) B
3) D
4) D
Parallelism: Correlative Conjunctions
5) A
1) D 2) D
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Passage Analysis
PSAT Writing: Passage Analysis
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Passage Analysis: Adding Precision
Passage Analysis: Adding Precision Identifying Passage Analysis: Adding Precision Questions on the PSAT: The question will ask which answer provides the most relevant details. Look for the answer that aligns with the main idea and provides the most vivid imagery through the use of nouns, adverbs, and adjectives. Question 1 Refers to the Paragraph Below There are four categories of specific phobias covering over 350 distinct fears, including arachnophobia (fear of spiders), acrophobia (fear of heights), trypanophobia (fear of needles), and – my favorite – claustrophobia (fear of enclosed spaces). In many cases, persons facing a phobia will show visible signs of panic. Often, people begin to fear the very possibility of a phobic attack. It has happened to me at work. Once, a co-worker found me trembling outside the supply closet, trying to get up the courage to pick up a new ink cartridge; I was immobilized by fear.
1. Which choice best completes the description of phobias if added to the end of the underlined text? A) B) C) D)
NO CHANGE like a rapid heartbeat and shortness of breath. and act frightened. whenever they confront enclosed spaces.
Question 2 Refers to the Paragraph Below Wildlife and livestock are killed, plants are consumed, and hundreds of homes are burned to the ground. Fall means calling friends to see if they need a place to stay or packing up my own things to seek shelter somewhere else. The danger isn’t over once the fires are put out, either. Winter in California means our annual allotment of rain and the potential for landslides. These landslides can pollute water sources and result in the loss of the topsoil necessary to support new growth. Instead, stripped hillsides are extremely unstable. This can also pose a threat to homes in the area.
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2. Which choice provides the most specific information about the devastation brought by wildfires? A) NO CHANGE B) The wildfires kill many plants and animals and also destroy homes. C) Wildfires can be very devastating. D) Raging fires burn out of control.
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PSAT
Passage Analysis: Introductions and Conclusions
Passage Analysis: Introductions and Conclusions Identifying Passage Analysis: Introductions and Conclusions Questions on the PSAT: The question will ask what answer best introduces or concludes a given paragraph or passage. Any introduction or conclusion must connect to the main idea(s) of the paragraph or passage. Question 1 Refers to the Paragraphs Below Garvey’s radical ideas were far from universally popular, even among members of the African American community. His most powerful enemies came due to his controversial stances against the National Association for the Advancement of Colored People (NAACP) and the peaceful Civil Rights Movement. Garvey argued that the NAACP only supported and helped certain members of the African American population. His harsh comments against the popular NAACP and the Civil Rights Movement turned many important people against him. However, it must be remembered that he devoted his life to a cause in which he believed. Garvey’s views never wavered even when he was harshly criticized. Today, there is a United Negro Improvement Association that promotes many of the same values that Garvey preached in the 1920s. Marcus Garvey is dead, but his pride and goals live on in today’s dreamers, and his writings continue to inspire leaders around the world
1. Which choice most effectively sets up the second paragraph? A) Garvey made many people angry. B) History shows that Garvey performed some imprudent actions during his career. C) The NAACP still exists today. D) As a testament to Garvey’s success, his ideas were very bold.
Question 2 Refers to the Paragraph Below Today, thanks in part to the Hart-Cellar Act, the size of these groups has tripled or quadrupled. This increase has allowed the diversity of the immigrant population to be felt in areas that, previously, had not had the experience. In the 1800s, immigrants from Europe tended to settle on the East Coast or in the Midwest. In the 21st century, while immigrants continue to relocate to the traditional areas, they have increasingly decided to settle on the West Coast, in the Southwest, and in the Southeast.
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2. Which of the following offers the best introduction to the paragraph? A) Many people emigrate to the United States in order to achieve personal freedom that may not have been available to them in their country of origin. B) Only 40 years ago, Asians and Hispanics made up an infinitesimal percentage of the American population. C) Birth rates have been increasing in the United States for many reasons. D) The total number of Americans immigrating to other countries has also been recently studied.
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PSAT
Passage Analysis: Main Idea Analysis
Passage Analysis: Main Idea Analysis Identifying Passage Analysis: Main Idea Analysis Questions on the PSAT: The question will ask what meaning will be added or lost if a word or phrase is added, deleted, or modified. Any meaning that is lost must connect to the main idea(s) of the surrounding text. Question 1 Refers to the Paragraph Below The giant panda is one of the most adored animals in the world. Its furry white and black body appears cuddly and soft, while the bear’s round, white head and black eye patches are instantly recognizable. Nevertheless, the giant panda is a very rare creature and is protected by law in its native China, where it lives in the bamboo forests and mountain slopes in the central part of the country. At one time, giant pandas lived at lower altitudes, but farming and land development have pushed the animals high into the mountains. Despite conservation efforts and the panda’s popularity, scientists really know very little about how wild pandas live, since so few people have seen them in their natural habitat.
1. If the writer were to delete the opening sentence of this paragraph (beginning the paragraph with “A giant panda’s furry body . . .”), the paragraph would primarily lose: A) information that sets up a contrast that immediately follows B) an irrelevant but humorous digression C) information that complements the subsequent sentence D) an important description of the setting
Question 2 Refers to the Paragraph Below All living things are made of cells. In fact, the cell is the basic unit of life and is the simplest unit capable of independent existence. Some onecelled organisms can lead independent lives. Others live in loosely organized groups, depending on one another in order to function. In more complex organisms like plants and animals, cells are no longer independent. Instead, they become specialized, with strict organization and specific jobs to perform. Certain cell types are grouped into tissues, and these tissues form organs. Other cell types stay more or less discrete, becoming blood cells or antibodies, for example. Regardless of specialization, cells all work together to form the body of one living thing.
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2. The writer is considering adding the following true statement at the end of the paragraph: In this, they are remarkably similar to their distant, one-celled cousins. Should the writer make this addition here? A) Yes, because all living things are made up of cells. B) Yes, because it provides information necessary to the understanding of cells. C) No, because it will distract the reader from the main idea of the paragraph. D) No, because it contradicts statements made previously in the paragraph.
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PSAT
Passage Analysis: Sequence
Passage Analysis: Sequence Identifying Passage Analysis: Sequence Questions on the PSAT: The question will ask which sequence of sentences within a paragraph, or which sequence of paragraphs within a passage, is most logical. To deduce proper sequencing, look for a topic sentence to use as Sentence 1 or look for connections between ideas to link different sentences. Question 1 Refers to the Paragraph Below [1] While “knocking down” in native forests is still under debate, everyone agrees it is important for residences that border open land. [2] In my neighborhood, homeowners are required to keep their property cleared of anything that might serve as kindling during fire season. [3] Even more, we are told to make our houses as fireproof as possible. [4] This can be accomplished by using special building materials. [5] As some people have learned the hard way, it takes just one spark to burn a house to the ground.
1. For the sake of logic and coherence, Sentence 4 should be placed: A) B) C) D)
where it is now. before Sentence 1. before Sentence 2. before Sentence 3.
Question 2 Refers to the Paragraph Below [1] Although they can be found at such a variety of levels, synchronized swimming still lags behind many other sports in the race for acknowledgment and respect. [2] Perhaps if more people were aware, of the dedication and talent required for success in the sport, it would be taken more seriously. [3] Synchronized swimming teams can be found at the elementary, secondary, collegiate, and Olympic levels
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2. Which of the following sentence sequences will make the paragraph more logical? A) B) C) D)
NO CHANGE 1, 3, 2 2, 3, 1 3, 1, 2
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PSAT
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Passage Analysis Notes
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PSAT
Passage Analysis Review
Question 1 Refers to the Paragraph Below [1] We looked at several more places until we found one that was not only economical, but also perfect for me. [2] It was on the third floor of a stately brick home with a cozy studio apartment. [3] The apartment had hardwood floors throughout and a sizeable walk-in closet lined entirely in cedar. [4] The bathroom was equipped with a claw foot tub and pedestal sink, both of which were original to the house. [5] It didn’t have a fireplace or ornate light fixtures, but it did have a charming bay window. [6] I told my parents that even though the apartment didn’t have everything I wanted, nothing in life was perfect, so I should be happy with what I had found. [7] Of course, they laughed, but I could tell that they were also pleased by my decision. [8] We gave the landlord the deposit and started making plans to move me in the very next weekend.
1. The writer is considering dividing this paragraph into two separate paragraphs. In terms of the logic and coherence of the essay, the best course of action to take would be to: A) B) C) D)
leave the paragraph as it is (NO CHANGE) begin a new paragraph with Sentence 3 begin a new paragraph with Sentence 5 begin a new paragraph with Sentence 7
Question 2 Refers to the Paragraph Below While Dr. Rice’s demeanor throughout her career has often been peace-promoting and diplomacy-oriented, she has also taken strong stances in regard to the country’s ability and responsibility to defend itself and its citizens. She earned a reputation as a decisive leader during her tenure as National Security Advisor because of her work.
2. Which choice best completes the description of Dr. Rice’s attitude toward her position as National Security Advisor? A) B) C) D)
NO CHANGE strength contributions tenacity and boldness
Question 3 Refers to the Paragraph Below [1] Nyman’s most famous achievement was the music for The Piano, winner of the 1993 Cannes Film Festival’s prestigious Palme d’Or award for best picture. [2] In the U.S., the film was nominated for six Academy Awards and won three. [3] Surprisingly, a nomination was not granted to Nyman’s soundtrack for the Best Score award. [4] Its grace is achieved through skillful use of the piano to replace the female lead’s voice, which is absent throughout the film.
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3. The writer wants to add the following sentence to the paragraph: Despite this oversight, the soundtrack remains among the best selling film music recordings of all time. The best placement for the sentence is immediately: A) B) C) D)
before sentence 1 after sentence 2. after sentence 3. after sentence 4.
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PSAT
Passage Analysis Review
Question 4 Refers to the Paragraphs Below Not everyone who comes into contact with toxic mold is so lucky. In the mid 1990s, cases of pulmonary hemorrhage (bleeding in the lungs) occurred in Ohio in infants. Scientists later found that all the homes of these babies had high levels of stachybotrys chartarum. Not every scientist believes that toxic mold was directly responsible for making the Ohio children sick. Still, many researchers point to this case and others to link mold exposure to bleeding in the lungs. I wanted him to hire a professional crew to clean up our basement; I was still curious, however. How did this dangerous fungus get into the building in the first place? Had it been there all along? More research was needed. I discovered that stachybotrys chartarum comes from the soil and generally enters clean buildings through floodwaters, dust, and dirt. Moreover, the fungus is there from the beginning, brought in on the materials when the structure is built. It’s usually only noticed after water damage occurs, like in our basement. Now I knew how the fungus got there – and I was keeping my distance!
4. Which of the following choice would provide the best transition between the paragraphs, guiding the reader from the topic of the first paragraph to the new topic of the second paragraph? A) My boss frequently took my advice about making improvements in the office. B) Armed with this new information, I approached my boss about the subject of toxic mold. C) Although our office was not in Ohio, both my boss and I were concerned about those children. D) Toxic mold appeared to be very dangerous indeed.
Question 5 Refers to the Paragraph Below While most of his fame is due to criticism he received in the 18th century, he was actually highly regarded in his lifetime. Still, despite his reputation, very few detailed records exist about his life, and most of those refer to his career in London. The little information we have suggests that Shakespeare grew up in somewhat prosperous conditions. His father was a glove maker and town official, while his mother came from an affluent family of farmers. There is some indication that his family was Catholic, a crime in England at that time, though there is no proof to support it.
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5. Which introduction most effectively sets up the information that follows? A) There is modern debate about the true scholarship of Shakespeare’s works. B) William Shakespeare was born in 1564 in Stratford-upon-Avon, United Kingdom. C) William Shakespeare produced plays of varying quality during his lifetime. D) William Shakespeare has long been considered the greatest English playwright and poet of all time.
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PSAT
Passage Analysis Answers Workbook Answers
Passage Analysis: Adding Precision
Review Answers 1) A
1) B
2) D
2) A
3) C
Passage Analysis: Introductions and Conclusions
4) B 5) D
1) B 2) B Passage Analysis: Main Idea Analysis 1) C 2) C Passage Analysis: Sequence 1) A 2) D
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PSAT
Prepositions
PSAT Writing: Prepositions
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PSAT
Prepositions
Prepositions Prepositions are words that combine with a noun, noun phrase, or pronoun to show its relationship to another word in the sentence. Ten most common prepositions: of, in, to, for, with, on, at, from, by, about Identifying Preposition Issues on the PSAT: Look for a noun paired with an improper preposition. Use your grammar ear to help determine if the preposition is correct. 1. Death Valley occupies approximately 3,000 square miles, is about 130 miles long, and varies from about six to 14 miles wide. Most of the valley is within an extremely low altitude. A) NO CHANGE B) by C) at D) for
2. Steve just returned from his trip to The Netherlands, a European country dotted with windmills. A) NO CHANGE B) inside C) for D) on
3. During some thunderstorms, the light from lightning bolts can be seen as far as 100 miles away, depending on the height of the bolt, the clarity of the air, and the elevation to the viewer. A) NO CHANGE B) by C) for D) of
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PSAT
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Prepositions Notes
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PSAT
Prepositions Review
1. Streaks of many shades of blue, green, and red run thinly and discretely from the base to the top of the bottles. There are parallels among the action of glassblowing and, say, pulling taffy. And Murano glass does look good enough to eat. A) NO CHANGE B) between C) within D) DELETE the underlined part
2. Some medical research shows that meat actually starts to rot while it is being digested. While this process rarely does harm, vegetarians argue that it proves our long intestines are designed to ensure that we can break down and absorb nutrients within fibrous plant material, not animal flesh. A) NO CHANGE B) that C) by D) from 3. The act of giving out bonuses reflects the value the company places on the work of its employees. This idea was demonstrated by company executives, who took pride in personally congratulating each person for meeting his or her annual goals. A) NO CHANGE B) by C) while D) as if
4. Most online auction companies are very concerned by the security of their systems. Ensuring that neither the seller nor the buyer is going to be jeopardized in any way is an important feature of a good online auctioneer. A) NO CHANGE B) about C) for D) into
5. I learned that tortoises are among the most endangered families in reptiles. That means having a tortoise is a privilege, and I’m proud that my family has entrusted me with Rosie’s care. By caring for Rosie I’ll be able to share something with the grandma I never knew. A) NO CHANGE B) families of C) family in D) family of
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PSAT
Prepositions Answers Workbook Answers
Prepositions
Review Answers 1) B
1) C
2) D
2) A
3) A
3) D
4) B 5) B
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PSAT
Pronouns
PSAT Writing: Pronouns
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PSAT
Pronouns: Singular vs. Plural
Pronouns: Singular vs. Plural Pronouns are words that take the place of nouns. Pronouns are used to reduce the amount of repetition in a sentence. A pronoun error on the SAT is to match a singular subject with a plural pronoun or a plural subject with a singular pronoun. Identifying Singular vs. Plural Pronoun Issues on the PSAT: Look for an underlined pronoun in the sentence. To check for singular vs. plural agreement, find the noun which the pronoun in replacing. Is the word singular or plural? Does the pronoun match? 1. My mother said rationing was important because they helped guarantee supplies for the thousands of military troops overseas. A) B) C) D)
NO CHANGE it she one
2. Many basketball players have started wearing a headband during games. However, other players believe they negatively impact their ability to run up and down the court. A) B) C) D)
NO CHANGE it negatively impacts they’re negatively impact its negatively impacts
3. Powerful music, be it in the form of sixteenth-century operas or modern movie soundtracks, affects listeners because they create distinctive and fresh impressions upon each new listening experience. A) B) C) D)
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NO CHANGE by it having created since they create because it creates
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PSAT
Pronouns: Personal Pronouns
Pronouns: Personal Pronouns Pronouns are words that take the place of nouns. Pronouns are used to reduce the amount of repetition in a sentence. A pronoun error on the SAT is to switch between the types of personal pronouns (1st, 2nd, and 3rd person pronouns). Identifying Personal Pronoun Issues on the PSAT: Look for one or you in the sentence. A sentence can use one (3rd personal pronoun) or you (2nd person pronoun), but cannot switch between them. 1. If you want to store asparagus at home, one should wrap the stalk bottoms in a damp paper towel, cover the towel in foil, and store the foil package in the refrigerator. A) B) C) D)
NO CHANGE one should have wrapped you should wrap they should wrap
2. In the 21st century, you can go to the mall to pick up the latest compact disc, or you can purchase the music online. A) B) C) D)
NO CHANGE or one can or it can or they can
3. The philosopher Epictetus popularized the Stoic doctrine of limiting your desires, believing that one should act in life as at a banquet by taking a polite portion of all that is offered. A) NO CHANGE B) having your desires limited C) having one’s desires limited D) limiting one’s desires
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PSAT
Pronouns: Possessive Pronouns
Pronouns: Possessive Pronouns Pronouns are words that take the place of nouns. Pronouns are used to reduce the amount of repetition in a sentence. A pronoun error on the SAT is to replace a possessive noun with a noncorresponding personal pronoun. Identifying Possessive Pronoun Issues on the PSAT: Look for pronouns that indicate possession in the sentence (my, her, your, their). Are they aligning with the subject correctly?
We, our, and ourselves are only valid when the writer is part of the group being discussed. 1. During the weekend of the wedding, my parents hosted many of our family members. They definitely made themselves at home: eating all of our snacks and moving our clothes into the available closet space. A) B) C) D)
NO CHANGE his or her their one’s
2. Most current hockey players do not wear face masks with their uniforms, so the athletes may find the newly mandated attire to be a burden. A) NO CHANGE B) those C) there D) its
3. Modern medicine does not include traditional Chinese techniques in their procedures, so those practices may seem unusual. A) B) C) D)
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NO CHANGE its those it’s
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PSAT
Pronouns: Pronoun Case
Pronouns: Pronoun Case Pronouns are words that take the place of nouns. Pronouns are used to reduce the amount of repetition in a sentence. A pronoun error on the SAT is to have two pronouns, or a pronoun next to a noun, in a sentence while misusing one, or both, pronouns. Identifying Pronoun Case Issues on the PSAT: Look for two underlined pronouns. To check usage, read the sentence twice and plug in one subject each time. Use your grammar ear to identify errors.
1. Both John and Laura wanted to go to the game, so he and her were willing to pay the exorbitant ticket price. A) B) C) D)
NO CHANGE him and her were he and she were him and she were
2. Other African American musicians and athletes suffered under the same constraints. As a result, Anderson traveled to Europe, where her and other American minorities were able to perform and refine their skills more freely. A) B) C) D)
NO CHANGE she herself they
3. He claims to have paid the contractor on time, but, between you and I, this is hardly the first time he has gotten embroiled in a dispute. A) NO CHANGE B) you and we C) you and me D) yourselves
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PSAT
Pronouns: Unclear Pronoun Subject
Pronouns: Unclear Pronoun Subject Pronouns are words that take the place of nouns. Pronouns are used to reduce the amount of repetition in a sentence. A pronoun error on the SAT is to a have a pronoun without a clear subject. Identifying Unclear Pronouns Subject Issues on the PSAT: Look for an underlined pronoun. Is the pronoun replacing a noun? Is there vagueness about which noun the pronoun is replacing? 1. Panda cubs weigh just a few ounces when they are born, but they will eventually weigh up to 300 pounds and stand five to six feet tall. The cub will stay with its mother for about three years, after which they will be ready to mate again. A) B) C) D)
NO CHANGE it the mother one
2. Sometimes in the afternoon, my grandmother and I would go shopping with my mother at her favorite stores. A) B) C) D)
NO CHANGE its my grandmother’s mine
3. Among the most influential Murano glassmakers was Carlo Scarpa. Scarpa worked with Murano glass from 1933 until 1947, when he turned his full attention to architecture. A) NO CHANGE B) some C) it D) this medium
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PSAT
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Pronouns Notes
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PSAT
Pronouns Review
1. While some vegetarians have cultural or religious reasons for not eating meat, others cite animal cruelty and better health as their reasons for the practice. A) NO CHANGE B) its C) they’re D) such 2. Garvey’s radical idea was that a society benefits most from people acting in their own self-interest, not in the interest of it as a whole. A) NO CHANGE B) them C) himself D) the community 3. Last summer, me and my mother spent a month at my grandmother’s house. A) B) C) D)
NO CHANGE my mother and me my mother and I myself and my mother
4. Margo received a message from the bookstore that the first edition she had ordered had been located, but she would need to come to the store to examine its condition. A) NO CHANGE B) so its condition can be examined C) for the examination of its condition D) to examine the book’s condition 5. Death Valley is located in the east-central part of California, and is part of the larger Mojave Desert. It was named by miners who were heading west in the 1849 California gold rush. Many miners died trying to cross it. A) NO CHANGE B) the valley C) over D) DELETE the underlined portion
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PSAT
Pronouns Answers Workbook Answers
Pronouns: Singular vs. Plural
Review Answers 1) A
1) B
2) D
2) B
3) C
3) D
4) D
Pronouns: Personal Pronouns
5) B
1) C 2) A 3) D Pronouns: Possessive Pronouns 1) C 2) A 3) B Pronouns: Pronoun Case 1) C 2) B 3) C Unclear Pronoun Subject 1) C 2) C 3) A
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PSAT
Punctuation
PSAT Writing: Punctuation
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PSAT
Punctuation: Comma Usage
Punctuation: Comma Usage A PSAT error is to use commas in a way that does not align with their grammatical function. Identifying Comma Usage Issues on the PSAT: If a comma is located in the sentence or the answer choices, check to see if it is performing one of the four functions of commas: separating items in a list; pairing with a conjunction to join two complete sentences; separating an introductory thought; or separating a descriptive phrase. 1. Principals, who have a large role in creating a positive school culture also need to be adept in many other areas: driving high test scores, interacting with parents, and summoning potential donors. A) NO CHANGE B) Principals who have a large role in creating a positive school culture C) Principals who have a large role in creating a positive school culture, D) Principals, who have a large role in creating a positive school culture,
2. In 1863, Abraham Lincoln traveled, to Gettysburg, Pennsylvania and delivered a speech honoring those who had died in battle. These 272 words are now some of the most famous in American history. A) NO CHANGE B) traveled; C) traveled— D) traveled
3. A decrease in newspaper subscriptions has led to a decrease in revenues for publishers, which in turn has caused publishers to turn to more desperate actions in the attempt to boost readership. Some newspapers have resorted to printing more salacious content; when there is a risk of alienating long-time readers this is a risky proposition. A) NO CHANGE B) content, this is a risky proposition when there is the risk of alienating long-time readers. C) content, a risky proposition when there is a risk of alienating long-time readers. D) content; a risky proposition when there is a risk of alienating long-time readers.
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PSAT
Punctuation: Colon Usage
Punctuation: Colon Usage A PSAT error is to use colons in a way that does not align with their grammatical function. Identifying Colon Usage Issues on the PSAT: If a colon is located in the sentence or the answer choices, check to see if it is performing one of the two functions of commas: introducing a list or joining a phrase with additional details about that phrase.
1. During a speech at West Point in 1962, General Douglas MacArthur discussed the three things he believed all graduates should hold most sacred, duty, honor, and country. A) NO CHANGE B) sacred; duty, honor, and country. C) sacred: duty, honor and country. D) sacred: duty, honor, and country.
2. Chris had an idea for an invention that would change the world: a watch that could also be used to answer phone calls. A) NO CHANGE B) world. A watch C) world; a watch D) world, a watch
3. Once the ball is tipped, the jovial attitude of the players dissipates, cheap shots and other underhanded tactics are common occurrences. A) NO CHANGE B) dissipates: because C) dissipates: D) dissipates, that’s when
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PSAT
Punctuation: Contractions
Punctuation: Contractions A PSAT error is to use apostrophes to form contractions whose constituent words do not fit within the sentence. Identifying Contraction Issues on the PSAT: If a contraction is located in the sentence or the answer choices, substitute both of the words in the contraction into the sentence and then check the sentence using your grammar ear.
1. The company decided to stake it’s future on the belief that people would pay for more for songs with higher quality audio. A) NO CHANGE B) their C) its D) its’
2. Although there is debate about the best way to stretch before exercise, most people agree about its importance for avoiding injury. A) NO CHANGE B) it’s C) they’re D) its’
3. They were able to build they’re own theater, The Globe, which gave them some independence. A) B) C) D)
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NO CHANGE there their his
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PSAT
Punctuation: Dash Usage
Punctuation: Dash Usage A PSAT error is to use dashes in a way that does not align with their grammatical function. Identifying Dash Usage Issues on the PSAT: If a dash is located in the sentence or the answer choices, check to see if it is performing one of the three functions of dashes: separating a descriptive phrase, introducing a change in tone, or presenting an explanation. 1. Philanthropists who support the arts like to point out that exposure to art, even to works that are not highly regarded – improves academic outcomes for students of all ages. A) NO CHANGE B) art – even C) art. Even D) art: even
2. Bacteria play an important role in sewage reduction by consuming human waste product. Data has shown that without bacteria's involvement, including consuming various other materials during the water treatment process—rivers and oceans would be much more polluted. A) NO CHANGE B) process: this is C) process, D) process;
3. In 2004, the University of Notre Dame opened the DeBartolo Performing Arts Center. This building includes an organ hall that hosts regular performances of sacred music— compositions that are played during religious ceremonies. A) NO CHANGE B) music. Compositions C) music, compositions D) music; compositions
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PSAT
Punctuation: Possession
Punctuation: Possession A PSAT error is to use apostrophes in a way that do not correctly indicate possession. Identifying Possession Issues on the PSAT: Look for apostrophes in the sentence or in the answers choices. Possession errors on the PSAT include the text missing an apostrophe when there is possession, having an apostrophe when there is no possession, or placing an apostrophe in the incorrect location when indicating possession. 1. Stephanie’s hope of getting home before lunch was quashed as her children’s recital stretched into its fourth hour . A) NO CHANGE B) childrens’s C) childrens’ D) childrens
2. During the 1970s and 1980s, Fleetwood Mac was one of the biggest musical acts in the world. However, the groups internal conflicts led to a breakup of the band in 1995. A) NO CHANGE B) groups’s C) group’s D) groups’
3. Say, for example, a significant hurricane is approaching shore. Citizens need to be evacuated from the city in a prompt and orderly manner. The disaster managers’ job might involve organizing contraflow on the roadways or authorizing broadcasts of the emergency broadcast system. A) NO CHANGE B) manager’s job C) managers job, D) managers job,
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PSAT
Punctuation: Run-on Sentences and Sentence Fragments
Punctuation: Run-on Sentences and Sentence Fragments An SAT error is to either use incorrect punctuation when joining two complete sentences or to use incorrect punctuation when joining two sentence fragments. Identifying Run-on Sentence Issues on the PSAT: Look for two complete thoughts joined by some punctuation. Two complete sentences can only be joined using a period, a semi-colon, or a comma joined with a conjunction. 1. James wanted to take advantage of the new technology to bring education to the masses. His first project – creating digital workbooks – sold barely well enough to cover costs. James then tried again with a technology application for smartphones; this idea is what helped him to strike it rich. A) NO CHANGE B) smartphone, this C) smartphones, this D) DELETE the underlined portion.
2. The spirit of American adventurism was at its peak in the early 19th century, many people packed up their belongings and headed West in search of opportunity. A) NO CHANGE B) century; many C) century, but many D) century, while
3. Vinyl record aficionados try to keep the medium alive through a scattered; but vibrant community of listeners. A) NO CHANGE B) scattered but vibrant C) scattered, but vibrant D) scatted but vibrant,
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PSAT
103
Punctuation Notes
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PSAT
Punctuation Review
1. Conditions like sleep apnea are more common in men, people who snore, overweight people, and the elderly. A person might have a sleep-related breathing disorder if wheezing; grunts; snorts; or other abnormal sounds interrupt his or her breathing. A) NO CHANGE B) wheezing; grunts snorts; or C) wheezing, grunts, snorts, or D) wheezing grunts, snorts or 2. Time Dollars began in 1980 as a means of encouraging and rewarding community involvement. Time Dollars exchange programs recognize that each person is valuable and has something, meaningful, to contribute. A) NO CHANGE B) something – meaningful C) something, meaningful D) something meaningful 3. A portmanteau is a linguistic blend that merges parts of two words into a single phrase. An example of a portmanteau is smog, which combines two parts, “smoke” and “fog.” A) NO CHANGE B) parts: “smoke” and “fog.” C) parts “smoke” and “fog.” D) parts; “smoke” and “fog.” 4. To this day, the Saturday Evening Gazette includes horoscopes based on astrological calendars. The newspapers editor, Karen Finsilver, says, “The information is essential to readers who follow their astrological signs.” A) NO CHANGE B) newspapers’s C) newspaper’s D) newspapers’ 5. Adults who pursue vocations as teachers have a wide array of reasons. These motivations can include a love of working with children or a passion for a particular academic subject. A) NO CHANGE B) Adults, who pursue vocations as teachers, C) Adults who pursue vocations, as teachers, D) Adults who pursue vocations as teachers, 6. Mr. Holmes claims to have a “prairie eye,” he particularly enjoys the magnitude and gracefulness of open grasslands. A) NO CHANGE B) eye,” thus, C) eye” he D) eye.” He
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PSAT
Punctuation Answers Workbook Answers
Workbook Answers
Punctuation: Comma Usage
Punctuation: Run-on Sentences
1) D
1) A
2) D
2) B
3) C
3) B
Punctuation: Colon Usage Review Answers 1) D 2) A 3) C
1) C 2) D 3) B
Punctuation: Contractions
4) C
1) C
5) A
2) A
6) D
3) C Punctuation: Dash Usage 1) B 2) C 3) A Punctuation: Possession 1) A 2) C 3) B
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PSAT
Transitions (Conjunctions)
PSAT Writing: Transitions (Conjunctions)
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PSAT
Transitions (Conjunctions)
Transitions (Conjunctions) A transition is a word or phrase that connects or joins together words, phrases, clauses, or sentences. Conjunctions are the most common type of transition. Conjunctions can indicate agreement (cause and effect), disagreement (contrast), or the order in which events took place. Identifying Transition Issues on the PSAT: Look for an agreeing conjunction joining two disagreeing words, phrases, clauses, or sentences, or a disagreeing conjunction joining two agreeing words, phrases, clauses, or sentences. 1. Due to the lucrative nature of the agricultural industry, notwithstanding the significance of his invention, he struggled to make a profit from it. A) NO CHANGE B) Despite C) As a result of D) Although
2. Books about recent catastrophes may seem like morally bankrupt attempts to profit from the misfortune of others, so they may also inform and educate, thus legitimizing them in some readers’ eyes. A) NO CHANGE B) and they C) moreover they D) but they
3. Some ancient cultures held the belief that the gods controlled the success of the yearly harvest. These societies thus placed a high priority on appeasing the wishes of their deities. Given that, it is not surprising that within these cultures animal sacrifices and other religious ceremonies were common during the planting season. A) NO CHANGE B) However, C) By contrast, D) Thereafter,
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PSAT
108
Transitions (Conjunctions) Notes
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PSAT
Transitions (Conjunctions) Review
1. Because he often blared music while doing his homework, the tumultuous atmosphere in the café posed no impediment to Tyler’s studying. A) NO CHANGE B) Although C) Yet D) Despite the fact that
2. They continued to berate the clumsy worker who had broken the machine, even though their anger had abated somewhat. A) NO CHANGE B) because C) since D) in fact
3. The instructor of the course scheduled weekly quizzes, ostensibly to encourage the students to pay attention, so the class believed the real rationale was to torment them. A) NO CHANGE B) attention, yet C) attention, and D) attention, because
4. Although history is supposed to instruct, some archaeologists believe that their research is rife with evidence that mankind has sometimes repeated the same mistakes by those living in earlier eras. A) NO CHANGE B) Because history C) Since history D) Is it true that
5. During their family reunion in Vermont, the Johnsons met a distant cousin who was the most unemotional individual they had ever known, yet when he wept as they boarded the airplane to depart, they were surprised. A) NO CHANGE B) so C) though D) hence
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PSAT
Transitions (Conjunctions) Answers Workbook Answers
Transitions (Conjunctions)
Review Answers 1) A
1) B
2) A
2) D
3) B
3) A
4) A 5) B
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PSAT
Verbs
PSAT Writing: Verbs
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PSAT
Verbs: Subject-Verb Agreement
Verbs: Subject-Verb Agreement Verbs are words that convey actions, occurrences, or states of being. In proper grammar, singular subjects are paired with singular verbs and plural subjects are paired with plural verbs. Identifying Subject-Verb Agreement Issues on the PSAT: Look for an underlined verb in the sentence. To check for subject and verb agreement, place the verb and its subject directly next to each other, read together, and check using your grammar ear. 1. Since the economic slow-down, retail sales has been plummeting across the country. A) NO CHANGE B) plummets C) have been plummeting D) has plummeted
2. Legal regulations aimed at protecting the innocent requires districts to provide lawyers for every accused criminal. A) NO CHANGE B) require districts to provide C) require districts providing D) that requires districts to provide
3. The grim realities of street life belies the traditional romantic notions of adventure found in the novels of Mark Twain or Charles Dickens. A) NO CHANGE B) are belied by C) belie D) have been belied by
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PSAT
Verbs: Tense
Verbs: Tense Verbs are words that convey actions, occurrences, or states of being. In proper grammar, verb tense must align with the tense of the surrounding text. Identifying Verb Tense Issues on the PSAT: Look for an underlined verb in the sentence. When checking tense alignment, look for descriptive text (“ending in 1994”) and the tense of surrounding verbs to indicate the tense of the sentence.
1. Isaac Newton may have discovered gravity when he saw an apple fall from a tree, but he did not really know what he had discovered; gravity remains a mystery to him until his death. A) NO CHANGE B) has remained C) remained D) remaining
2. The documentary of the 2010 championship shows the final, tense moments of the game. The rabid fans cheer as the captain walked to the free throw line to attempt the winning shots. A) NO CHANGE B) had walked C) would walk D) walks
3. Edward Abbey’s essays earned him praise as a leading American environmentalist during the late 1960s, a period during which he wrote prolifically. A) NO CHANGE B) earn him praise C) have earned him praise D) would earn him praise
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PSAT
114
Verbs Notes
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PSAT
Verbs Review
1. The minutes the average American child spend playing outside have decreased dramatically over the last decade. A) NO CHANGE B) has spent C) spends D) are spent
2. The enigmatic smile that graces the face of the woman portrayed in Leonardo da Vinci’s Mona Lisa has been attributed to her knowing a mysterious secret. A) NO CHANGE B) is being attributed C) have been attributed D) has had its attribution
3. When the committee revised the judging standards in 2004, it believed it had created a set of guidelines that will ensure fairness at the Olympic Games. A) NO CHANGE B) would have ensured C) had ensured D) would ensure
4. The particles in Dr. Jones’ experimental sample appear to have changed in an unusual way. A) NO CHANGE B) appears C) have appeared D) DELETE the underlined portion
5. The success of George Washington’s program for reforming weights and measures, Andro Linklater and Tom Smith argue, were essential to the eventual emergence of a consumer economy. A) NO CHANGE B) was C) have been D) being
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PSAT
Verbs Answers Workbook Answers
Verbs: Subject-Verb Agreement
Review Answers 1) C
1) C
2) A
2) B
3) D
3) C
4) A
Verbs: Tense
5) B
1) C 2) D 3) A
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PSAT
Word Choice
PSAT Writing: Word Choice
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PSAT
Word Choice: Frequently Confused Words
Word Choice: Frequently Confused Words An error on the SAT is to use a word that sounds similar to a word that works in the context of the sentence, but has a different meaning. Identifying Frequently Confused Words Issues on the PSAT: Look for words that have homophones which may confuse your grammar ear. Examples: • Affect vs. Effect • Accept vs. Except • Farther vs. Further 1. From there, we would take the train to my mother’s house, spend the night, than return home the following day. A) NO CHANGE B) then return C) than returning D) then be returned
2. The government suggested to tribal leadership that it would be in its best interest to own real property and pay taxes on it like all property owners. The Native American leadership did not accept the offers of land ownership. They believed that it would cause reservation territory to recede. A) NO CHANGE B) except C) with the exception of D) have an acceptance of
3. One significant affect of the law’s passage was that traffic accidents decreased by 20% when compared to the year prior. A) NO CHANGE B) A significant affect C) One effect significantly D) One significant effect
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PSAT
Word Choice: Inconsistent Tone and/or Style
Word Choice: Inconsistent Tone and/or Style An error on the SAT is to use diction/tone/style that is inconsistent with the surrounding text. Identifying Inconsistent Tone and/or Style Issues on the PSAT: Inconsistencies can include the use of vague language, overly informal language, colloquialisms, or jargon (vocabulary of a particular group).
1. As a general rule, temperature increases when altitude decreases. Thus, the low altitude of deserts is one of the reasons for their ridiculously scorching temperatures. A) NO CHANGE B) steel melting temperatures. C) insanely asinine temperatures. D) extremely hot temperatures.
2. A big reason for the passage of the bill was the fear that the invasive species would soon overrun the wetland.
A) NO CHANGE B) main thing causing C) huge thing about D) primary cause of
3. Following the American Revolution, George Washington resigned his commission and returned home to Virginia. During this time he assiduously superintended the plantation in the hope of developing goods for sale. A) NO CHANGE B) oversaw C) fastidiously directly D) diligently administrated
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PSAT
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Word Choice Notes
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PSAT
Word Choice Review
1. Dunbar’s breakthrough came at the age of 20, when he gave his first public reading before the Western Association of Writers. The praise he gathered attracted the attention of other writers, whom began to take an interest in his career. A) NO CHANGE B) writers, that C) writers, who D) writers
2. Most people had little interest in the merger of the two companies, but for the employees of those organizations it was a pretty big deal. A) NO CHANGE B) could not be put on the backburner. C) was nothing to shake their tails at. D) was an important occurrence.
3. When politicians are in need of extra exposure – for example, near election season – one guaranteed way to gain attention is to get on their soapboxes and talk directly to the public. A) NO CHANGE B) invest some sweat equity C) give a speech D) DELETE the underlined portion 4. Even though movies usually do not effect Jeremy, for some reason he could not stop crying when he left the theater. A) NO CHANGE B) have an effect on C) affect D) create an affect for 5. Jim wanted Tom to go farther into the distance: He had just purchased some new Frisbees and he wanted to give them a good throw. A) NO CHANGE B) farther by C) further into D) further along
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PSAT
Word Choice Answers Workbook Answers
Word Choice: Frequently Confused Words 1) B 2) A 3) D
Review Answers 1) C 2) D 3) C 4) C 5) A
Word Choice: Inconsistent Tone and/or Style 1) D 2) D 3) B
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PSAT
Wordiness and Redundancy
PSAT Writing: Wordiness and Redundancy
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123
PSAT
Wordiness and Redundancy: Wordiness
Wordiness and Redundancy: Wordiness Wordiness occurs when an underlined phrase uses more words than it needs. Identifying Wordiness on the PSAT: Look for the use of passive voice, the presence of several two or three letter words, or the inclusion of an unnecessary ‘–ing’ verb. On the PSAT, if you are stuck between two or more choices, pick the answer that has the fewest number of words.
1. The Statute of Frauds was enacted in 1679 and required that all contracts for the purchase and sale of any land be in writing and signed “by the party to be charged” in order to be enforceable. With some modifications by someone making changes, the same rule is in place today. A) NO CHANGE B) changes made by modifying, C) modifications, D) DELETE the underlined portion.
2. Garvey was born in Jamaica in 1887 and went to be in college in London just before World War I. During the war, he moved to the United States to begin working on his dream of political unity for all people with African ancestry. A) NO CHANGE B) would have been in C) attended D) went to attend
3. Yoga has ardent practitioners. These people find that the strength and mental clarity provided by yoga cannot be replicated by any other exercises. A) NO CHANGE B) practitioners, who will go to the studio at least once a day. C) practitioners, who fully believe in its benefits. D) practitioners—lovers of the exercise.
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PSAT
Wordiness and Redundancy: Redundancy
Wordiness and Redundancy: Redundancy Redundancy occurs when an underlined word or phrase repeats an idea that is already in the sentence. Identifying Redundancy on the PSAT: Look for common redundancies. Examples: • • • • •
6:30 p.m. at night And also Close proximity Manually by hand Repeat again
1. The next day, we walked out to one of the spectacular view sites overlooking the Grand Canyon. While my husband took more photos of the sprawling vista, I again looked down at my feet. This time, there was no confusion or doubt. A) NO CHANGE B) doubt by which to be confused C) confusing doubt D) DELETE the underlined portion. 2. Last year, Samantha Johnson, alumna of Dedham High School, donated twelve million dollars to the school for the construction of a new gymnasium and athletic fields. Because of the generosity of Johnson’s contribution to the school, Dedham students will have access to world class facilities for years to come. A) NO CHANGE B) the generous donation of so much money to the school, C) the substantial donation of resources, D) Johnson’s generosity,
3. The government suggested to tribal leadership that it would be in the tribe’s best interest to own real property and pay taxes on it like all property owners. Legally, the government owned tribal lands but offered to donate it to the tribe without charge. A) NO CHANGE B) free of charge C) without charging them D) DELETE the underlined portion
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PSAT
126
Wordiness and Redundancy Notes
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PSAT
Wordiness and Redundancy Review
1. While reflux can often usually be controlled during the daytime by swallowing and sitting in an upright position, during the night, people suffering from acid reflux do not swallow as frequently, and their reclined position causes more reflux to occur. A) NO CHANGE B) typically C) quite possibly D) DELETE the underlined portion.
2. Ever since switching their business from selling lumber to selling mechanical equipment, Jim and Steve have lost a yearly sum of $1.2 million annually due to the fact they have entered a more competitive market. A) NO CHANGE B) experienced an annual loss of $1.2 million each year C) lost $1.2 million annually D) have a yearly loss of $1.2 billion annually
3. The Statue of Liberty was brought to America in 1886. France gave the statue to the United States as a sign of friendship, and it was dedicated on October 28. French artist Frederic Bartholdi sculpted the statue; engineer Maurice Koechlin, the man who designed the Eiffel Tower, created the statue’s internal structure. A) B) C) D)
NO CHANGE designer of the Eiffel Tower, who was also a designer of the Eiffel Tower who was the man that designed the Eiffel Tower
4. Dr. Condoleezza Rice has lived a life of great accomplishment and achievement. She was an avid scholar, graduating from high school at the age of 15. At only 19 – a very young age – she graduated from the University of Denver with a degree in political science. A) B) C) D)
NO CHANGE – which is quite young – – not yet in her twenties – DELETE the underlined portion.
5. John was not accustomed to waking up at 5:00 a.m. in the morning, but taking his first trip to Europe was worth the early rise. A) B) C) D)
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NO CHANGE 5:00 a.m. 5:00 a.m. during the mornings DELETE the underlined portion.
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PSAT
Wordiness and Redundancy Answers Workbook Answers
Wordiness and Redundancy: Wordiness 1) C 2) C 3) A
Review Answers 1) D 2) C 3) B 4) D 5) B
Wordiness and Redundancy: Redundancy 1) D 2) D 3) D
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PSAT
Advanced Grammar
PSAT Writing: Advanced Grammar
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PSAT
Advanced Grammar: Affect vs. Effect
Advanced Grammar: Affect vs. Effect An error on the PSAT is to misuse the words affect and effect Identifying Affect vs. Effect Issues on the PSAT: Looks for the word affect or effect underlined in a sentence. Affect means “to produce a change” or “to act in a way you do not feel” (used as a verb). • The weather affected Jeremy’s plans. Effect means “a result” (used as a noun). • The weather had no effect on Jeremy’s plans. 1. One of the primary causes for the financial crisis of 2008 was the effect of banks granting loans to people who could not pay them back. A) NO CHANGE B) the affect of C) an effect of D) an affect of
2. Tom had no idea of the immediately positive affect that would result from switching the part in his hair. A) NO CHANGE B) immediately positive effect C) immediate positive effect D) immediate positive affect
3. The presidential election had a major affect on the country’s policies. A) NO CHANGE B) effect on C) affecting on D) effect
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PSAT
Advanced Grammar: Logical Comparisons
Advanced Grammar: Logical Comparisons An error on the PSAT is to set up a comparison (words linked by like, than, or as) where the items being compared are not of the same type. Identifying Logical Comparison Issues on the PSAT: Look for a comparison being made in the sentence. Are the items of the same type? 1. As an avid mystery reader, Patrick felt that novels by John Grisham were more enjoyable than other authors. A) NO CHANGE B) enjoyable, more so than other authors. C) more enjoyable than books by other authors. D) more enjoyable, particularly when compared to other authors.
2. The average cost of a student’s yearly education in private school is several times a student in public school. A) NO CHANGE B) what it is for a student being in public school C) that of a student’s yearly education in public school D) like for a student in public school
3. Begun during the Great Depression, Woman’s Day magazine had an effect on the American family that was greater than any other magazine. A) NO CHANGE B) as greater as any other magazine C) greater than those of any other magazine D) greater than that of any other magazine
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PSAT
Advanced Grammar: Misplaced Modifiers
Advanced Grammar: Misplaced Modifiers An error on the PSAT is to have a descriptive word or phrase that is NOT next to what it is describing. Identifying Misplaced Modifier Issues on the PSAT: Look for a descriptive phrase that is next to a comma. What is being described (the subject of the sentence) must come directly after the comma. 1. First sighted in the 17th century, the moons of Jupiter contradicted much of the traditional thinking about Earth’s place in the cosmos. A) NO CHANGE B) In the 17th century, C) Galileo first sighted them in the 17th century, D) They were first sighted in the 17th century,
2. Born one hundred years ago in St. Petersburg, the peaceful childhood of choreographer George Balanchine was disrupted by World War I.
A) NO CHANGE B) choreographer George Balanchine had his peaceful childhood C) World War I disrupted the peaceful childhood of choreographer George Balanchine D) choreographer George Balanchine’s peaceful childhood
3. Thumbing through Sonnets from the Portuguese, it wasn’t difficult to find more than one poem that spoke to Richard. A) NO CHANGE B) Richard realized it wasn’t difficult to find more than one poem that spoke to him C) Richard realized that more than one poem spoke to him without difficulty D) more than one poem spoke to Richard, which wasn’t difficult to realize
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PSAT
Advanced Grammar: Who, Whom, That, Which, and Whose
Advanced Grammar: Who, Whom, That, Which, and Whose An error on the PSAT is to misuse the words who, whom, that, which, and whose. Identifying Who, Whom, That, Which, and Whose Issues on the PSAT: Look for the word(s) who, whom, that, which, or whose in a sentence. Use the following rules to identify correct usage. Who and Whom are used with sentence subjects or objects that are a person. •
•
Who is used with a sentence subject (We all know who was responsible for the prank). Whom is used with a sentence object (You gave the card to whom?).
That and which are used with sentence subjects or objects that are not a person. • •
That is used to introduce a clause that is essential to the sentence. Which is used to introduce a clause that is not essential to the sentence.
Whose is used to indicate possession (Whose jacket is this?). 1. Moreover, the chemical has been severely criticized by people that believe it is having a negative impact on the environment. A) NO CHANGE B) who C) whom D) which 2. Benches, that are found at many bus stops, are often uncomfortable to sit on. A) NO CHANGE B) which C) who D) of that 3. Emily Dickinson, one of America’s great nineteenth-century poets, was a prolific letter writer. Although her physical contact with the world was limited by caring for her invalid mother and by her own poor health, whose correspondence was extensive A) NO CHANGE B) their C) Dickinson’s D) who’s 133
133
PSAT
134
Advanced Grammar Notes
134
PSAT
Advanced Grammar Review
1. Brightly lit stations welcomed the public, many of them were skeptical of traveling underground. It didn’t take long for New Yorkers to adapt, however. A) NO CHANGE B) of whom C) of who D) DELETE the underlined portion 2. In 1998, dust from the Gobi Desert crossed the Pacific Ocean and sent dust-pollution levels on the West Coast much higher than the East Coast. A) NO CHANGE B) higher than those on C) more high than what they were on D) as higher than on 3. With great enthusiasm, they added on a year every New Year’s Day. By contrast American society has often been described as one that values the vibrant energy of youth over the wisdom and experience gained with age. A) NO CHANGE B) whose C) this D) whom 4. The vowel sounds in English are more numerous than Spanish. A) NO CHANGE B) numerous in Spanish C) numerous than that in Spanish D) numerous than those in Spanish
5. Studying for a test can affect a student’s final grades. A) NO CHANGE B) effect C) have the effect on D) be affecting on 6. Although criticized by a few for his daredevil stunts, most people viewed Evel Knievel as a skillful motorcyclist. A) NO CHANGE B) Evel Knievel was viewed by most people as a skillful motorcyclist C) most people viewed Evel Knievel to be a skillful motorcyclist D) Evel Knievel, a skillful motorcyclist in the view of most people
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PSAT
Advanced Grammar Answers Workbook Answers
Advanced Grammar: Affect vs. Effect
Advanced Grammar: Who, Whom, That, Which, and Whose 1) B
1) A
2) B
2) B
3) C
3) B Advanced Grammar: Logical Comparisons 1) C 2) C 3) D
Review Answers 1) B
2) B 3) A 4) D 5) A
Advanced Grammar: Misplaced Modifiers
6) B
1) A 2) B 3) B Advanced Grammar: Parallelism 1) C 2) C 3) D
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PSAT
Math
PSAT Math: Table of Contents
137
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PSAT
Math: Table of Contents
Math: Table of Contents PSAT Math: Introduction (Page 142)
Arithmetic and Algebra Foundations of Arithmetic and Algebra (Page 144) • • • •
Absolute Value Exponents Percentage Terms and Operations
Average, Median, and Mode (Page 152) • Average • Median and Mode
Functions (Page 159) • • • •
f(x) f(x ± a) Function Graphs Function Tables
Quadratics and Polynomials (Page 167) • • • • • •
Higher-Order Equations Quadratics Polynomial Division Polynomial Factors Solving Polynomials: Completing the Square Solving Polynomials: Quadratic Formula
Ratio, Proportion, and Unit Conversion (Page 176) • • • •
Probability Ratio and Proportional Relationships Ratio and Proportional Relationships (Colons) Unit Conversions
Solving Linear Equations (Page 184) • Distance and Midpoint Formulas • Slope • Slope-Intercept Form
Solving Non-Linear Equations (Page 190) • Rewriting Equations • Single Equations Questions (Non-Quadratic) • Systems of Equations
Translating Word Problems (Page 197) • Linear Equations • Non-Linear Equations • Systems of Equations
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PSAT
Math: Table of Contents
Math: Table of Contents Geometry Circles (Page 205) • • • •
Arc and Sector Circumference and Area Chords Inscribed Circles
Geometry in Three Dimensions (Page 213) • • • • • •
Cones Cylinders Rectangular Prisms Spheres Triangular Prisms Triangular Pyramids
Graphing (Page 220) • Circles • Parabolas
Lines and Angles (Page 226) • Intersecting Lines • Rule of 180
Quadrilaterals and Polygons (Page 232) • Polygons • Rhombuses • Trapezoids
Triangles (Page 239) • • • • •
139
Area Pythagorean Theorem Rule of 180 Similar Triangles Special Right Triangles
139
PSAT
Math: Table of Contents
Math: Table of Contents Additional Topics Advanced Topics (Page 248) • • • • •
Complex Numbers Compound Interest Radians Trigonometry: Sine, Cosine, and Tangent Unit Circle
Interpreting Equations (Page 257) • Interpreting Linear Equations • Interpreting Non-Linear Equation
Plug and Chug & Backsolving (Page 263) • Backsolving • Plug and Chug
Statistics (Page 269) • • • •
140
Exponential Growth Interpreting Charts and Graphs Line of Best Fit Margin of Error
140
PSAT
Math
PSAT Math: Introduction
141
141
PSAT
Math: Introduction
PSAT Math Introduction
70 Minutes for 48 Questions Test 3: Math (No Calculator) • •
25 minutes for 17 questions Multiple choice questions and student-produced responses
Test 4: Math (Calculator) • •
45 minutes for 31 questions Multiple choice questions and student-produced responses
Concepts covered on PSAT Math: •
Algebra o
•
Data analysis o
•
Ratios, proportions, and percentages
Advanced math o
•
Formulas, expressions, and equations
Quadratics and polynomials
Additional topics o
Geometry and trigonometry
Quick Math Tips • • • • •
142
Stay confident – you know all the math you need to know. Identify the concept that is being tested. Don’t make a problem harder than it is. Don’t make stupid mistakes – stay focused. Answer the question that is being asked (variables/units/etc.).
142
PSAT
Foundations of Arithmetic and Algebra
PSAT Math: Foundations of Arithmetic and Algebra
143
143
PSAT
Foundations of Arithmetic and Algebra: Terms and Operations Factor vs. Multiple Term
Definition
Whole Number
A number with no factional or decimal part.
Integer
Any whole number (–400, 0, 2, 1000).
Factor
An integer that divides evenly into another integer.
Multiple
An integer that can be divided by a smaller integer with no remainder.
Prime vs. Composite Term
Definition
Prime
A number with only 1 and itself as factors. 1 is NOT a prime number.
Composite
A number with factors other than 1 and itself. 1 is NOT a composite number.
Even vs. Odd Term
Definition
Even
An integer which divided by 2 yields a whole number (0 is an even number).
Odd
An integer which divided by 2 does not yield a whole number.
1. Which of the following is a multiple of 90 ? A) B) C) D)
1,120 1,530 1,720 2,230
2. If x is an even integer, then which of the following could be the value of (x + 1)(x + 2) ? A) B) C) D)
20 30 40 50
3. If a is the greatest prime factor of 34 and b is the greatest prime factor of 96, what is the value of a + b?
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PSAT
Foundations of Arithmetic and Algebra: Exponents Term
Definition
Example
Positive powers
Multiply the base by itself as many times as the exponent tells you to.
35 =
Negative powers
Put a one over the base and multiple the base by as many times as the exponent tells you to.
3–5 =
0 as a power
Any number raised to the power of zero equals 1.
30 =
1 as a power
Any number raised to the power of 1 equals itself
31 =
Powers on fractions
Multiply the fraction by itself as many times as the exponent tell you to.
( 3 )3 =
Powers on negative numbers
It a negative number is raised to an even power, it becomes positive, if it is raised to an odd power, it stays negative.
(–3)2 =
Multiplying powers
When multiplying similar bases with powers, add the powers together
Dividing powers
When dividing similar bases with powers, subtract the powers
Raising a power to another power
When raising a power to another power, multiply the powers
(35)3 =
Fractional powers
The numerator of the fractional power represents the power and the denominator of the fractional power represents the root.
30.5 =
1
33 x 34 = (
35 )= 34
2 1. (NO CALCULATOR) Which of the following is equal to 𝑡 9 for all values of t ? A) 𝑡9 B) 𝑡2 C) D)
2 9
t9 𝑡2
2. (NO CALCULATOR) Which real number satisfies (2n)(8) = 163 ?
2
3. If
145
xa 12 2 = x , x > 1, and a – b = 4, what is the value of a + b ? xb
145
PSAT
Foundations of Arithmetic and Algebra: Absolute Value
Foundations of Arithmetic and Algebra: Absolute Value Absolute value is a number’s distance from zero. As such, absolute values are never negative. Identify: Any problem that uses absolute value bars … Set Up: Create two equations and solve for the two values of the given variable. 1. What are the values for which 2x – 3 < 7 ? A) x < –2 B) x > 5 C) – 5 < x < 2 D) –2 < x < 5
2. If |7a – 10| > 4, then which of the following CANNOT be a value of a ? A) B) C) D)
–5 –3 2 4
3. (NO CALCULATOR) For what value of a is |a – 2| + 3 equal to 0 ? A) 0 B) 1 C) 2 D) There is no such value of a
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146
PSAT
Foundations of Arithmetic and Algebra: Percentage
Foundations of Arithmetic and Algebra: Percentage A percentage is a number or ratio expressed as a fraction of 100. Identify: Questions that involves percentages, or give “before and after numbers.” Set Up: To determine percent change, plug any elements you know into the percent change formula.
Percent Change Formula Percent Change =
Final – Original x 100% Original
1. What number is 45 percent less than 600 ?
2. Janet goes to the store to buy herself a new dress, and she finds that there is a 20% off sale going on. Additionally, Janet has a 20% discount coupon. If Janet buys the dress that is on sale and also uses her coupon, what will her total discount be? A) 20% B) 38% C) 36% D) 40%
3. Steven works for a company that mines copper and iron. Last year, his company mines 1200 tons of copper and 1000 tons of iron. This year, the yield, by tonnage, of copper declined by 20 percent, and the yield, by tonnage, of iron increased by 40 percent. What percent of the original tonnage is represented by the amount of copper and iron mined this year? (Round to the nearest tenth of a percent.) A) B) C) D)
147
92.7% 106.8% 107.3% 112.7%
147
PSAT
148
Foundations of Arithmetic and Algebra Notes
148
PSAT
Foundations of Arithmetic and Algebra Review
1. (NO CALCULATOR) If (x2)n = x14 , what is the value of n ?
2. (NO CALCULATOR) What is the greatest common factor of 6y, 12y2, and 81y3 ? A) B) C) D)
3.
3y 3y2 6y2 9x3
2x + 4 < 8 is equivalent to which of the following expressions? 5 A) –15 < x < 15 B) –30 < x < 10 C) − D)
15 35
16 < x < 10 5
4. Tom’s factory produces toothpicks and coasters. Last month, his factory produced 1,200 pounds of toothpicks and 800 pounds of coasters. This month, the production, by weight, of toothpicks declined by 40 percent, and the production, by weight, of coasters increased 40 percent. What was the percent decline in the total weight of the two items produced by the factory?
5. If 2a – b = 6, what is the value of
4a 2b
A) 26 B) 44 C) 8 D) The value cannot be determined from the information given.
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SAT
Foundations of Arithmetic and Algebra Answers Workbook Answers
Terms and Operations
Review Answers 1) 7
1) B
2) A
2) B
3) B
3) 20
4) 8%
Exponents
5) A
1) D 2) 9 3) 3 Absolute Value 1) D 2) C 3) D Percentage 1) 330 2) C 3) C
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PSAT
Average, Median, and Mode
PSAT Math: Average, Median, and Mode
Important Formulas Average (Arithmetic Mean) Formula Average =
Sum Total Number
Weighted Average Formula Weighted Average =
151
Sum of Weighted Terms Total Number
151
PSAT
Average, Median, and Mode: Average (Arithmetic Mean)
Average, Median, and Mode: Average (Arithmetic Mean) Identify: If you see the term average (arithmetic mean) in a math question, it is an average question. Set Up: Immediately write down the average formula. Plug whatever information is given in the question into the formula and solve for whatever is missing in the equation. Repeat as necessary.
Average Formula Average =
Sum Total Number
Weighted Average Formula Weighted Average =
Sum of Weighted Terms Total Number
1. Allen and three friends play in a softball league. This season, Allen struck out 45 times, Bob struck out 72 times, Chad struck out 23 times, and Derek struck out 61 times. What is the average number of strikeouts for these players, to the nearest 0.1 strikeouts?
2. The local city orchestra has 11 violin players. The five male violin players average 73 inches tall and the six female violin players average 67 inches tall. What is the average height, in inches, of the 11 violin players? (Rounded to the nearest tenth of an inch.)
3. If a is the average (arithmetic mean) of 3n and 6, b is the average of 4n and 6, and c is the average of 5n and 18, what is the average of a, b, and c in terms of n ? A) 2n + 5 B) 2n + 10 C) 3n + 8 D) 6n + 15
152
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PSAT
Average, Median, and Mode: Median and Mode
Average, Median, and Mode: Median and Mode Identify: You see the term median or mode. Set Up: Median is the middle number in a set arranged from least to greatest. Mode is/are the number(s) that appear(s) most frequently in a set. 1. A researcher chose 240 students at random from each of two high schools and asked each student how many cousins he or she has. The results are shown in the table below. What is the median number of cousins for all students surveyed? Cousins Survey Number of Cousins
Dedham High School
Norwood High School
2
80
70
3
40
60
4
65
45
5
55
65
A) 2 B) 3 C) 3.5 D) 4
2. (NO CALCULATOR) The median of a set of data containing five items was found. Six data items were added to the set. Three of these items were greater than the original median, and the other three items were less than the original median. Which of the following statements must be true about the median of the new data set? A) It is the average of the three new lower values. B) It is the same as the original median. C) It is the average of the three new higher values. D) It is greater than the original median.
153
153
PSAT
154
Average, Median, and Mode Notes
154
PSAT
Average, Median, and Mode Review Questions 1 and 2 relate to the below data
The histogram below shows the distribution of players in a local euchre league. 25
Frequency
20 15 10 5 0 20-29
30-39
40-49
50-59
60-69
70-79
Age (years) 1. Which of the following could be the median age of the 71 players in the league? A) 22 years old B) 41 years old C) 50 years old D) 63 years old
2. (NO CALCULATOR) Which of the following could NOT be the mode of the 71 players in the league? A) 26 years old B) 32 years old C) 55 years old D) 64 years old
3. (NO CALCULATOR) In Taylor’s karate class, the mean age of all the female members is 7 years, and the mean age of all male members is 9 years. Which of the following must be true about the mean age y of the combined group of male and female members of the karate club? A) y = 7 B) y = 9 C) 7 < y < 9 D) y > 9
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PSAT
Average, Median, and Mode Review Questions 4 and 5 relate to the below data
The histogram below shows the distribution of players in the Page Turners book club. 5
Frequency
4 3 2 1 0 18
19
20
21
22
23
24
25
26
27
28
Age (years) 4. What is the average (arithmetic mean) age of the members of the book club? A) 21.9 years old B) 22.7 years old C) 23.9 years old D) 25.1 years old
5. What is the median age of the 28 members of the book club? A) 22.5 years old B) 23 years old C) 23.5 years old D) 24 years old
6. A student receives grades on tests of between 0 and 100, inclusive. In the first five grades the student received, the average (arithmetic mean) of the scores was 95. What is the least grade the student can receive for the sixth test and still be able to have an average of at least 90 for the first 10 tests?
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PSAT
Average, Median, and Mode Answers Workbook Answers
Average (Arithmetic Mean)
Review Answers 1) C
1) 50.3
2) A
2) 69.7
3) C
3) A
4) C
Median and Mode
5) D
1) B
6) 25
2) B
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PSAT
Functions
PSAT Math: Functions
158
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PSAT
Functions: f(x)
Functions: f(x) Identify: Any question that includes function notation with numbers or variables such as f(4), g(t), or h(6). Set Up: The number in the parentheses is the number to plug in to the function wherever you see a variable. 1. (NO CALCULATOR) If h(x) = 3x + 20, what is the value of h(4)?
2. (NO CALCULATOR) If f(x) = x2 + x + 5 and g(x) = x , then what is the value of
g(4) ? f(1)
1 f(x) = 3x + a 3. In the function above, a is a constant. If f(6) = 12, what is the value of f(–9) A) –12 B) –16 C) 1 D) 7
4. (NO CALCULATOR) A function y satisfies y(3) = 6 and y(6) = 12. A function z satisfies z(6) = 3 and z(12) = 3. What is the value of z(y(6)) ? A) 3 B) 6 C) 9 D) 12
159
159
PSAT
Functions: f(x ± a)
Functions: f(x ± a) Identify: Any question that includes function notation with a variable AND a number and/or a second variable in the original function such as f(x – 3), g(t + 4), or h(a + b) Set Up: If the original input is an equation (for example, x – 1), first solve for the variable by setting the two values in parentheses equal to one another and then input the new value into the equation.
1. (NO CALCULATOR) If the function f is defined by f(x + 7) = 4x + 10, what is the value of f(7)? A) B) C) D)
2.
7 10 14 38
If the function h is defined by h(z – 2) = 2z2 – 100, what is the value of h(7)?
A) –34 B) –2 C) 0 D) 62
3. If the function z is defined by z(θ – 2) = 4θ + 54, what is the value of z(10)?
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PSAT
Functions: Graphs
Functions: Graphs Identify: Problems involving a graph of variables (x) and functions f(x). Set Up: The input to the function (what is inside the parentheses) is also an xcoordinate on the graph. The output of the function is the corresponding ycoordinate on the graph. y
2
y = f(x)
1
y = g(x) -2
-1
O
1
2
x
Questions 1, 2 and 3 relate to the above graph 1. (NO CALCULATOR) The graph of y = f(x) is shown above. What is f(–1) ? A) –1 B) 0 C) 1 D) 2 2. (NO CALCULATOR) The graph of y = g(x) is shown above. If g(q) = 1, which of the following is a possible value of q? A) –1.5 B) –0.5 C) 0 D) 1.5 3. (NO CALCULATOR) Graphs of the functions f and g are shown in the xy-plane above. For which of the following values of x does f(x) + g(x) = 2 A) –2 B) –1 C) 1 D) 2 161
161
PSAT
Functions: Tables
Functions: Tables Identify: Problems involving a table of variables (x) and functions f(x). Set Up: Pick a variable (x) from the table and plug it into each of the answer choice functions. The output value should equal the corresponding f(x) from the table.
x
2
4
6
8
f(x)
–2
0
2
4
1. (NO CALCULATOR) The table above gives values of the linear function f(x) for selected values of x. Which of the following defines f(x) ? A) B) C) D)
f(x) = –x + 4 f(x) = x – 4 f(x) = 2x – 8 f(x) = 4x – 16
x
1
2
3
4
y
3
4
5
6
2. (NO CALCULATOR) The table above gives values of the linear function f(x) for selected values of x. Which of the following defines y ? A) B) C) D)
162
y = x3 y = 2x y = 3x y=x+2
162
PSAT
163
Functions Notes
163
PSAT
Functions Review
1. (NO CALCULATOR) If f(x) = 7x – 12, then f(7) =
r(p) = p2 + p s(p) = p2 – p 2. (NO CALCULATOR) Which of the following is equivalent to s(t + 1) ? A) B) C) D)
r(t) r(t) + 1 r(t) – 1 s(t) + 1 y 15 10 5 –15 –10 –5 O –5
5 10 15
x
–10 –15
3. (NO CALCULATOR) The figure above shows the graph of the function f. If f(q) = 5, which of the following is closest to q ? A) B) C) D)
–13 –7 1 11
4. (NO CALCULATOR) If f(x + 5) = x + 4, then f(4) =
5. Consider the function c(t) = 2t3 + 3. What is the value of c(c(–2)) ?
164
164
SAT
Functions: Answers Workbook Answers
Functions: f(x)
Review Answers 1) 37
1) 32
2) A
2 2) 7
3) A
3) D
4) 3 5) –4,391
4) A Functions: f(x ± a) 1) B 2) D 3) 102 Functions: Graphs 1) D 2) B 3) A Functions: Tables 1) B 2) D
165
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PSAT
Quadratics and Polynomials
PSAT Math: Quadratics and Polynomials
Important Formulas Quadratic Formula
x=
166
–b ±
2 b – 4ac 2a
166
PSAT
Quadratics and Polynomials: Quadratics
Quadratics and Polynomials: Quadratics Identify: Look for a quadratic equation or binomials (two things in parentheses being multiplied together). Set Up: Keep the FOIL rules in mind: First, Outer, Inner, Last. Look for patterns, like these three commonly tested quadratics: (x + y)2 = (x +y)(x + y) = x2 + 2xy + y2 (x – y)2 = (x – y)(x – y) = x2 – 2xy + y2 (x + y)(x – y) = x2 – y2
1. (NO CALCULATOR) If x2 – y2 = 36 and x + y = 9, what is the value of (x – y) ?
2. (NO CALCULATOR) 16a4 + 24a2b2 + 9b4 Which of the following is equivalent to the expression shown above? A) (4a2 + 3b2)2 B) (2a + 3b)4 C) (2a2 + 3b2)2 D) (4a + 3b)4
3. (NO CALCULATOR) If (ax + 4)(bx + 5) = 8x2 + cx + 20 for all values of x, and a + b = 6, what are the two possible values for c ?
A) 6 and 20 B) 12 and 20 C) 26 and 28 D) 28 and 38
167
167
PSAT
Quadratics and Polynomials: Polynomial Division and Polynomial Factors
Quadratics and Polynomials: Polynomial Division Identify: A question has a polynomial divided by a second algebraic equation. Set Up: When dividing, focus on the left-most part of the divisor. This is the part of the equation that will go into the dividend.
1. (NO CALCULATOR)
7x2 – 3x – 4 =? x+ 2
22 A) 7x – 17 + x + 2 22 B) 7x – 17 + x + 2 30 C) 7x – 17 – x + 2 30 D) 7x – 17 + x + 2
Quadratics and Polynomials: Polynomial Factors Identify: A question references the factor(s) of a polynomial equation. Set Up: For a number and/or equation to be a factor of a polynomial, it must divide the polynomial evenly (divide the polynomial with no remainder). 1. (NO CALCULATOR) The function f is defined by a polynomial. Some values of x and f(x) are shown in the table above. Which of the following must be a factor of f(x) ? x
1
3
5
7
f(x)
4
2
1
0
A) x – 1 B) x – 3 C) x – 5 D) x – 7
168
168
PSAT
Quadratics and Polynomials: Polynomial Solving - Quadratic Formula
Quadratics and Polynomials: Polynomial Solving – Quadratic Formula Identify: A question that requires finding the solutions to a polynomial equation or asks for the zero of a polynomial function. Set Up: If possible, convert the equation into the form ax2 + bx + c = 0 and then plug the given information into the Quadratic Formula.
Quadratic Formula x=
–b ±
2 b – 4ac 2a
A zero (or root) of a polynomial function is a number that, when plugged in for the variable, makes the function equal to zero. 1. (NO CALCULATOR) Which of the following is a zero of the function f(y) = y2 + 6y – 6 ? A) 3 + 15 B) –3 + 15 C) 6 + 15 D) 6 – 15
3x2 + 2x – 8 = 0 2. If a and b are two solutions of the equation above, and a > b, which of the following is the value of a – b ?
169
169
PSAT
Quadratics and Polynomials: Polynomial Solving - Completing the Square
Quadratics and Polynomials: Polynomial Solving – Completing the Square Identify: A question which requires finding the solutions to a polynomial equation with complex factors. Set Up: Polynomials can be solved by completing the square. Completing the square steps: Step 1: Divide all terms by the coefficient of x2. Step 2: Move the number term to the right side of the equation. Step 3: Take half of the coefficient of the x-term, and square it. Add this square to both sides of the equation. Convert the left-hand side to squared form, and simplify the right-hand side. Step 4: Take the square root on both sides of the equation. Step 5: Subtract the number that remains on the left side of the equation to find x.
x2 + y2 + 8x + 10y – 215 = 0 1. The equation of a circle in the xy-plane is shown above. What is the diameter of the circle? A) B) C) D)
170
32 64 90 128
170
PSAT
Quadratics and Polynomials: Higher-Order Equations
Quadratics and Polynomials: Higher-Order Equations Identify: A question will involve the solution to a polynomial formula where the highest power is greater than 2. Set Up: If the highest power is even, let x2 = a, solve for a, then replace a with x2 and solve to get the answers to the original equation. If the highest power is odd, factor out an x, and then follow the steps for an even power. A zero (or root) of a polynomial function is a number that, when plugged in for the variable, makes the function equal to zero. A polynomial of degree n will have n roots, some of which may be multiple roots (they repeat). 1. (NO CALCULATOR) What are the roots of the equation x4 = 20x2 – 64 ? A) B) C) D)
x = 0, x = ±4 x = 0, x = ±2 x = ±4, x = ±8 x = ±2, x = ±4
2. What are the zeroes of the equation 3x5 = 36x3 – 96x ? A) B) C) D)
171
x = 0, x = ±2 2, x = ±2 x = 0, x = ±2 2, x = ± 2 x = 0, x = ± 2, x = ± 3 x = 0, x = ±2, x = ±3
171
PSAT
172
Quadratics and Polynomials Notes
172
PSAT
Quadratics and Polynomials Review
1. If x2 – y2 = 100 and x + y = 4, what is the value of (x – y) ?
2. What are the solutions of 7a – 34 = –a2 ?
3. (NO CALCULATOR) What is the sum of the zeroes of the function (F(x) = 0) when F(x) = (x2 + 6x + 5)(x + 10) ?
x3 – 1 4. (NO CALCULATOR) x + 2 = ? A) x2 – 2x + 4 +
–9 x–2
–9 B) x2 – 2x – 4 + x + 2 C) x2 + 2x + 4 +
9 x+2
D) x2 – 2x + 4 +
–9 x+2
x2 + y2 – 4x + 12y = 41 5. The equation of a circle in the xy-plane is shown above. What is the diameter of the circle? A) B) C) D)
173
6 9 18 36
173
PSAT
Quadratics and Polynomials Answers Workbook Answers
Quadratics
Review Answers 1) 25
1) 4 2) A 3) C Polynomial Division
2) a =
−7 ± 185 2
3) –16 4) D 5) C
1) D Polynomial Factors 1) D Quadratic Formula 1) B 10 2) 3 Completing the Square 1) A Higher-Order Equations 1) D 2) A
174
174
PSAT
Ratio, Proportion, and Unit Conversion
PSAT Math: Ratio, Proportion, and Unit Conversion
Important Formulas Ratio Formula Ratio =
Direct Proportional Relationship One Part One Part = Whole Thing Whole Thing
One Part Another Part
Probability Probability =
175
Desired Outcomes Total Outcomes
175
PSAT
Ratio, Proportion, and Unit Conversion: Ratios and Proportional Relationships
Ratios and Proportional Relationships Identify: If you see a question that defines a ratio and/or a proportional relationship. Set Up: Write down the ratio and/or proportional relationship formulas and fill in the provided information to solve the question. For proportional relationships, cross multiply to solve for the unknown variable. Make sure your units are consistent.
Ratio Formula Ratio =
One Part Another Part
Direct Proportional Relationship One Part One Part = Whole Thing Whole Thing
1. (NO CALCULATOR) Kate’s parents will allow her to buy six cookies for every 4 times she takes out the trash this month. If Kate takes out the trash 10 times this months, how many cookies will she be able to purchase?
2. A tennis instructor charges $70 per lesson, plus an additional fee for the use of the court. The additional fee varies directly with the square root of the amount of time, in minutes, the court is used. If a lesson plus 120 minutes of court time costs $150, approximately what is the total amount charged for a lesson with 90 minutes of court usage? (Round to the nearest cent.)
A survey of 33,443 randomly selected teenagers aged 13 through 16 in the United States was conducted to gather data on social media usage. The data are shown in the table below. Use Social Media
Do Not Use Social Media
Total
Ages 13 and 14
12,145
8,232
20,377
Ages 15 and 16
8,545
4,521
13,066
Total
20,690
12,753
33,443
3. Based on the data, how many times more likely is it for 13 year old or a 14 year old to use social media than it is for a 15 year old or a 16 year old to use social media? (Round to the nearest hundredth.)
176
176
PSAT
Ratio, Proportion, and Unit Conversion: Ratios and Proportional Relationships
Ratios and Proportional Relationships (Colons) Identify: If you see a question that defines a ratio and/or proportional relationship between two or more things expressed with a colon. Set Up: Represent each number in the ratio as the coefficient of a variable. Each coefficient represents a portion of the overall total:
Proportion of Overall Total Relationship Proportion =
An individual coefficent The sum of the coefficents
1. If the degree measures of the angles of a quadrilateral are in the ratio 1:2:3:4, by how many degrees does the measure of the largest angle exceed the measure of the smallest angle?
2. Triangle ABC above is isosceles with AB = AC and BC = 120. The ratio of ED to FD is 4:6. What is the length of BD ?
177
177
PSAT
Ratio, Proportion, and Unit Conversion: Probability
Probability Identify: The question will mention “probability,” often in reference to data presented in a chart or graph. Set Up: List the elements you know, and plug them into the probability formula:
Probability Probability =
Desired Outcomes Total Outcomes
1. In a survey of 1,000 drivers, all but 350 claimed that they always wear a seat belt while driving. If one of the survey’s participants is randomly chosen, what is the probability that this person claimed to always wear a seat belt while driving?
Ages 20 to 24 Ages 25 to 29 Total
Listen to Podcasts
Do Not Listen to Podcasts
Total
11,145 4,673 18,818
5,232 3,950 9,182
16,377 8,623 24,000
2. A survey of 24,000 randomly selected American aged 20 through 29 in the United States was conducted to gather data on podcast listenership. The data are shown in the table above. Based on the data, if a person from the survey is picked at random, what is the probability that the person will either be a person of ages 20-24 who listens to podcasts or a person of ages 25-29 who does not listen to podcasts A) B) C) D)
178
0.39 0.47 0.63 0.74
178
PSAT
Ratio, Proportion, and Unit Conversion: Unit Conversion
Unit Conversion Identify: You are being asked a question which asks for a conversion between different units. Set Up: Use relevant conversions to cancel units between the provided unit(s) and the desired unit(s).
1. (NO CALCULATOR) A certain juice drink carton contains 5 pints. What is the total volume, in gallons, of the contents of a crate that contains 56 of these juice drink cartons? (8 pints = 1 gallon) A) 12 B) 20 C) 27 D) 35
2. A local restaurant serves soda to customers by the pint. Each week, the restaurant receives a 20 gallon shipment of soda syrup. How many customers can be served which this shipment? (1 gallon = 128 ounces; 1 pint = 16 ounces) A) 100 B) 128 C) 144 D) 160
3. A typical image taken by Jim’s digital camera is 12.5 megabits in size. Jim can upload his photo to the internet at a rate of 15 kilobits per second for a maximum of 8 hours each day. If 1 megabit equals 1,024 kilobits, what is the maximum number of typical images that Jim can upload to the internet each day? (Round to the nearest whole number.)
179
179
PSAT
180
Ratio, Proportion, and Unit Conversion Notes
180
PSAT
Ratio, Proportion, and Unit Conversion Review
1. In her last two track meets, Heather has run 800 meters and 1500 meters. How many inches did Heather run during those two meets? (Round to the nearest inch.) (1 meter ≈ 39.37 inches)
2. (NO CALCULATOR) A bowl is filled with jellybeans of three colors: orange, purple, and green. Suppose that if John reaches into the bowl and picks a jellybean at random, the probability that he chooses a green jellybean 1 is 4 . Which of the following could NOT be the total number of jellybeans in the bowl? A) 20 B) 36 C) 42 D) 56
3. According to a certain mixture, 45 pounds of mulch are needed to cover 60 square feet of a flower bed. At this rate, how many pounds of mulch are needed to cover 780 square feet of a flower bed?
4. In a mixture of cake and ice cream, the ratio by weight of cake to ice cream is 3:11 per pound of mixture. How many pounds of cake will there be in 2 pounds of this mixture?
5. Ryan traveled in his car at an average speed of 55 kilometers per hour for 12 hours and consumed fuel at a rate of 40 kilometers per gallon. How many gallons of fuel did the car use for the entire 12-hour trip? A) B) C) D)
16.5 18 20.5 24
6. There are 150 green marbles and 100 yellow marbles in a bag that contains 250 marbles. If only yellow marbles are added to the bag so that the probability of randomly drawing a yellow marble from the bag becomes 3 5 , how many yellow marbles are in the bag? A) 125 B) 175 C) 225 D) 250
181
181
PSAT
Ratio, Proportion, and Unit Conversion Answers Workbook Answers
Ratios and Proportional Relationships
Review Answers 1) 90,551
1) 15
2) C
2) $139.28
3) 585
3) 0.91 Ratios and Proportional Relationships (Colon) 1) 108°
3 4) 7 5) A
6) C
2) 48 Probability 13 1) 20 2) C Unit Conversion 1) D 2) D 3) 34
182
182
PSAT
Solving Linear Equations
PSAT Math: Solving Linear Equations
183
183
PSAT
Solving Linear Equations: Slope-Intercept Form
Solving Linear Equations: Slope-Intercept Form Identify: The question will give you at least one point, a slope, and/or a y- or xintercept of a line. Set Up: Write down the slope-intercept form and use it to solve the question. Parallel lines have the same slope. Perpendicular lines have slopes which are negative reciprocals.
Slope-Intercept Form y = mx + b m = slope b = y-intercept 1. (NO CALCULATOR) In the standard (x, y) coordinate plane, what is the y-intercept of the line given by the equation 4x + 7y = 14 ?
1 2. In the (x, y) coordinate plane, a line passes through the point (–4, 6) and has a slope of –3. What is the x-coordinate of a point on the line having a y-coordinate of 3?
Solving Linear Equations: Slope-Intercept Form Application Identify: The question asks for an interpretation of an equation in slope-intercept form (y = mx + b). Set Up: The slope of a line (m) represents average (arithmetic mean) rate of change. The y-intercept (b) represents the value of y when x equals 0. 1. (NO CALCULATOR) The mean height of trees (in feet), y, at a local park can be estimated using the equation y = 63.232x + 13.435, where x represents the number of years since 2010 and x ≤ 5. Which of the following statements is the best interpretation of the number 13.435 in the context of this problem? A) The estimated mean height of trees (in feet) in 2010. B) The estimated mean height of trees (in feet) in 2015. C) The estimated yearly decrease in the mean height of trees (in feet). D) The estimated yearly increase in the mean height of trees (in feet).
184
184
PSAT
Solving Linear Equations: Distance, Midpoint, and Slope
Solving Linear Equations: Distance and Midpoint Formulas Identify: You are asked to find the distance between two points, or the midpoint of two points. Set Up: Immediately write down the distance or midpoint formula. Plug whatever information is given in the question into the formula and solve for whatever is missing in the equation.
Distance Formula Distance =
x2 ˗ x1 2 + y2 ˗ y1
Midpoint Formula 2
Midpoint =
x1 + x2 y1 + y2 2 , 2
1. What is the distance, in units, between the points with standard (x, y) coordinates (˗2, 3) and (˗6, 6) ? 2. (NO CALCULATOR) What is the midpoint of the points with standard (x, y) coordinates (5, 7) and (˗9, 3) ? A) (˗2, 5) B) (˗4, 4) C) (4, ˗4) D) (5, ˗2)
Solving Linear Equations: Slope Identify: You will be given two points on a line in the xy-coordinate plane and be asked about the slope.
Set Up: Write down the slope formula and use it to solve for the missing information.
Slope Equation change in y (rise) y2 − y1 slope (m) = = change in x (run) x2 − x1 1. A line in a coordinate plane has points of (−1, w) and (3, 8). The slope of the line is 1.5. What is the value of w?
185
185
PSAT
186
Solving Linear Equations Notes
186
PSAT
Solving Linear Equations Review
1. (NO CALCULATOR) In the standard (x, y) coordinate plane, what is the slope of the line given by the equation –5x + 4y = 17 ?
2. In the xy-coordinate plane, what is the distance between the points with coordinates (–4, 2) and (–2, 6)?
3. What is the slope of a line perpendicular to the line that passes through (–2, 5) and (7, –9) in the standard (x, y) coordinate plane?
9 4. (NO CALCULATOR) A line in the xy-plane passes through the origin and has a slope of 2. Which of the following points lies on the line? A) (0, 9) B) (0, 2) C) (2, 12) D) (4, 18)
5. (NO CALCULATOR) The amount of time it takes students at a local elementary school to run one mile (in minutes), y, can be represented by the equation y = –0.642x + 18.125, where x represents the age of the student and 6 < x < 10. Which of the following statements is the best interpretation of the number –0.642 in the context of this problem? A) The estimated mile time of students (in minutes) in 2005. B) The estimated mile time of students (in minutes) in 2009. C) The estimated yearly decrease in the mile time of students (in minutes). D) The estimated yearly increase in the mile time of students (in minutes).
6. (NO CALCULATOR) In the system of linear equations below, d is a constant. If the system has infinite solutions, what is the value of d ? 1 1 3x – 8y = 5 5 dx – 8y = 25
187
187
SAT
Solving Linear Equations Answers Workbook Answers
Review Answers
Slope-Intercept Form 1) 2 2) 5
5 1) 4 2) 20
Slope-Intercept Form Application
9 3) 14
1) A
4) D
Distance and Midpoint Formulas
5) C
1) 5
5 6) 3
2) A Slope Formula 1) 2
188
188
PSAT
Solving Non-Linear Equations
PSAT Math: Solving Non-Linear Equations
189
189
PSAT
Solving Non-Linear Equations: Single Equation Questions
Solving Non-Linear Equations: Single Equation Questions Identify: A question (before or after translation from a word problem) has one equals sign and/or inequality or you are solving for the value of an equation. Set Up: Follow the below steps (where necessary): 1) Group like terms (variables with the same exponent and/or whole numbers). 2) Multiply by a common denominator and/or cross-multiply to remove fractions. 3) Solve for the variable.
1. (NO CALCULATOR) The inequality 5(x – 3) < 7(x + 1) is equivalent to which of the following inequalities? A) B) C) D)
x > –11 x > –8 x > –2 x > 11
7b2 + 2 – x = 0 2. If b > 0 and x = 4 in the equation above, what is the value of b ? A) B) C) D)
1 2 2 2 2 s = 80 + 10.5x
3. One end of a spring is attached to a ceiling. When an object of mass x kilograms is attached to the other end of the spring, the spring stretches to a length of s centimeters as shown in the equation above. What is x when s is 290 ? A) 14.8 B) 20.0 C) 37.0 D) 75.2
190
190
PSAT
Solving Non-Linear Equations: Systems of Equations Questions
Solving Non-Linear Equations: Systems of Equations Questions Identify: There are two or more equals signs and/or inequalities. Set Up: Follow the below steps (where necessary): 1) Group like terms (variables with the same exponent and/or whole numbers). 2) Add or subtract given equations (if possible). 3) If you cannot add or subtract, then substitute between equations. 1. (NO CALCULATOR) If g = 2, h = –5, i = 7, and j = –4 what is the value of gi + hj ?
2. (NO CALCULATOR) If
a 8b = 4, what is the value of a ? b
3. If k = 5 4 and 2k = 4x2 , and x > 0, what is the value of x ?
2x – 2y = y + 4 6y + 8x = 4x x 4. Solve for y: .
191
191
PSAT
Solving Non-Linear Equations: Rewriting Equations
Solving Non-Linear Equations: Rewriting Equation Questions Identify: A question that relates to manipulating equations to create new expressions. These questions will often ask for one variable “in terms of” another. Set Up: Use algebraic operations and/or substitution to convert the provided expression into the desired equation. The phrase “in terms of” translates to “solve for the first variable.” Thus, if a question asks to “solve a in terms of b,” you should solve the equation for a. The b variable will appear on the right side of the equation. 1. (NO CALCULATOR) If 2b + 1 = 2x – 2, what is x in terms of b ? 1 A) x = b + 2 b+3 B) x = 2 3 C) x = b + 2 D) x = 2b 2. (NO CALCULATOR) A circle has area D and radius t. Which of the following represents t in terms of D ? D A) t = 2 D B) t = D C) t = 2 D D) t = 3. (NO CALCULATOR) If a–1 = gives x in terms of a ? 1 A) x = a 1 B) x = a3
4 3
𝑥
, were a > 0 and x > 0, which of the following equations
C) x = a3 D) x = 64a3
192
192
PSAT
193
Solving Non-Linear Equations Notes
193
PSAT
Solving Non-Linear Equations Review 4x x + 8 = 3 4
1. (NO CALCULATOR) In the equation above, what is the value of x ?
2. (NO CALCULATOR) If
2 = 5d where d ≠ 0 and c ≠ 1, what is d in terms of c ? c–1
A) d = 5c – 5 B) d =
2 5c – 5
1 C) d = 2c – 2 2 D) d = 5 c + 2
2 4 3. If a – b = 6, what is the value of 14a – 20b ? 5 7 A) 41 B) 72 C) 120 D) 210
2y 4. (NO CALCULATOR) Which of the following is equivalent to (x – 2y) (2xy) 2y A) 1 – x B)
y2 + 2xy x
x x C) y + y2 D) 2xy
194
194
PSAT
Solving Non-Linear Equations Answers Workbook Answers
Review Answers
Single Equation Questions
24 1) 13
1) A
2) B
2) B
3) D
3) B
4) A
Systems of Equations 1) 34 2) 2 3) 10 3 4) –2 Rewriting Equations 1) C 2) B 3) D
195
195
PSAT
Translating Word Problems
PSAT Math: Translating Word Problems
196
196
PSAT
Translating Word Problems: Translation Table
Translating Word Problems: Translation Table Use the following chart to assist in translating word problems into algebra: .
197
Term
Translation
“Each,” “Groups of (a number)” “Number of Times,” “Per,” “Some”
Variable (x , y, etc.)
“Equals,” “Is”
=
“And,” “Plus,” “Sum”
+
“Difference”
–
“Product”
x
“For every,” “Per (ratio)”
÷
“Exceed(s)” “Greater Than”
>
“Meet or exceed” “Greater Than or Equal To”
≥
“Less Than”
<
“Less Than or Equal To”
≤
197
PSAT
Translating Word Problems: Linear Equations
Translating Word Problems: Linear Equations Identify: A word problem that mentions a linear model. A linear model relates to the formula y = mx + b, where m is the slope (the rate of change) and b is the yintercept (the amount when x = 0). Set Up: Plug the given information into slope intercept form (y = mx + b) and then solve for the requested information.
1. (NO CALCULATOR) Yesterday, Daniel ran a half marathon. At 11 a.m., Daniel had finished four miles and at 1 p.m. Daniel had finished 10 miles. What was Daniel’s speed in miles per hour from 11 a.m. to 1 p.m.?
2. (NO CALCULATOR) Tammy is a member of a sorority which has a yearly membership fee of $500 plus the requirement to donate $15 for each social function that is held during the year. Which of following functions gives Tammy’s cost, in dollars, for a year in which the sorority holds f social functions? A) S(f) = 500 + 15f B) S(f) = 500f + 15 C) S(f) = 15f D) S(f) = 515f
3. As Nathan traveled into the Sahara desert, the air temperature increased at a constant rate. If at 10 miles into the desert the temperature was 97 degrees Fahrenheit, and at 210 miles into the desert the temperature was 107 degrees Fahrenheit, which of the following linear models best describes the relationship between temperature t and distance traveled into the desert d ? A) t = 0.05d + 96.5 B) t = 0.05d + 97 C) t = 10d + 96.5 D) t = 10d + 200
198
198
PSAT
Translating Word Problems: Non-Linear Equations
Translating Word Problems: Non-Linear Equations Identify: After translating a word problem equation there is one equation and/or you are solving for the value of a variable. Set Up: Follow the below steps after translation (where necessary): 1) Group terms into a single equation with an equals or inequality sign. 2) Plug any information provided in the question into the equation. 3) Solve for the equation and/or for the requested variable.
1. A local store charges $2.50 for one loaf of bread and $8.25 for a pound of roast beef. If Jim bought two loaves of bread and three pounds of roast beef, how much money did Jim spend?
2. (NO CALCULATOR) The number of boys that played lacrosse in a local town this year is three times the number of boys that played lacrosse in the same town last year. If 150 boys played lacrosse this year and y boys played last year, which of the following equations is true? A) 150y = 3 B) 3y = 150 y C) 3 = 150 D) y + 150 = 3
3. (NO CALCULATOR) Sean is renting a car for a cross country road trip. The car rental company charges a one-time flat fee of $20.00 plus $49.99 per day. A tax of 11% is also applied to the daily cost for insurance. Which of the following represents Sean’s total cost, in dollars, for renting a car for x days?
A) 1.11(49.99x) + 20x B) 1.11(69.99x) C) 1.11(49.99x + 20) D) 1.11(49.99x) + 20
199
199
PSAT
Translating Word Problems: System of Equations
Translating Word Problems: System of Equations Identify: After translating a word problem equation there are multiple equations and/or inequalities. Set Up: Follow the below steps (where necessary): 1) Group like terms (variables with the same exponent and/or whole numbers). 2) Add, subtract, or substitute between the given equation. 3) Solve for the equations and/or for the requested variable
1. (NO CALCULATOR) John exercises by doing sit ups, a, in groups of ten and push ups, b, in groups of 20. If last week John did 20 total groups of exercise for a total of 450 completed movements, which system of equations would yield the number of push ups John completed? A)
a + b = 450 20a + 10b = 20
B)
a + b = 20 20a + 10b = 450
C)
a + b = 450 10a + 20b = 20
D)
a + b = 20 10a + 20b = 450
2. The sum of three numbers is 930. One of the numbers, x, is 50% less than the sum of the other two numbers. What is the value of x ?
3. Mr. Hoffman has a beaker containing q milliliters of solution to distribute to the students in his chemistry class. If he gives each student 4 milliliters of solution, he will have 30 milliliters left over. In order to give each student 6 milliliters of solution, he will need an additional 8 milliliters. How many students are in the class?
200
200
PSAT
201
Translating Word Problems Notes
201
PSAT
Translating Word Problems Review
1. (NO CALCULATOR) In a number game, players receive points in increments of either three or five. If a player scores 47 total points, and 35 of those points come in increments of 5, how many increments of three did the player score?
2. (NO CALCULATOR) Thomas subscribes to a magazine that charges a yearly fee of $25 plus $2 extra for each special issue that is released during the year. Which of the following functions gives Thomas’s cost, in dollars, for a year in which the magazine releases m special issues? A) F(m) = 25m B) F(m) = 25m + 2 C) F(m) = 25+ 2m D) F(m) = 25m + 2m 3. (NO CALCULATOR) A homeowner purchased 5,000lbs. of stone to build a new walkway. Some of the stones weighed 25lbs. and some of the stones weighed 10lbs. The 25lbs. stones were ordered at a ratio of 3:2 to the 10lbs. stones. Solving which of the following equations yields the number of 25lbs. stones. A) 25x + 10y = 5000 3x = 2y B) 25x + 10y = 5000 2x = 3y C)
3x + 2y = 5000 25x = 10y
D)
2x + 3y = 5000 10x = 25y
4. A local city has two jugglers that perform at birthday parties. Julio charges a flat $250 fee plus $10 per minute spent performing and Erin charges a flat $130 fee plus $25 per minute spent performing. If j represents the number of minutes performed, what are all values of j for which Erin’s total charge is greater than Julio’s total charge? A) j > 8 B) 6 ≤ j ≤ 8 C) 4 ≤ j ≤ 6 D) j < 4
5. In Blueberry City, houses are built to accommodate groups of 2 and 4 people. This year, 1,200 people live in Blueberry City in a total of 500 homes. In Blueberry City, how many people live in houses of 2 people?
202
202
PSAT
Translating Word Problems Answers Workbook Answers
Linear Equations 1) 3 mph 2) A 3) A
Review Answers
1) 4 2) C 3) B 4) A 5) 800
Non-Linear Equations 1) $29.75 2) B 3) D System of Equations 1) D 2) 310 3) 11
203
203
PSAT
Circles
PSAT Math: Circles
Important Formulas
204
Area Formula
Circumference Formula
Area = r2
Circumference = 2r
Sector Formula
Arc Formula
Central Angle Sector = Area( ) 360
Central Angle Arc = Circumference( ) 360
204
PSAT
Circles: Circumference and Area
Circles: Circumference and Area Identify: Any question that provides a circumference and/or area of a circle. Set Up: Write down the responding formula to find missing information (often the radius). Repeat as necessary.
Circumference Formula
Area Formula
Circumference = 2r
Area = r2
1. A certain circle has an area of 16 square inches. How many inches long is its diameter?
2. If circle A has a circumference of 120, and circle B has a circumference equal to the length of a 30° arc of circle A, what is the area of circle B ? A) B) C) D)
10 12 25 50
A
120°
O
B
C
3. In the figure above, point O is the center of the circle, line segments AB and BC are tangent to the circle at points A and C, respectively, and the segments intersect at point B as shown. If the circumference of the circle is 36, what is the length of minor arc AC ?
205
205
PSAT
Circles: Arc and Sector
Circles: Arc and Sector Identify: Any question with a sector, a central angle, or an arc. Set Up: Use the arc and sector formulas.
Arc Formula Arc = Circumference(
Central Angle ) 360
Sector Formula Central Angle Sector = Area( ) 360
1. In a circle with a radius of 30 inches, what is the length, in inches, of an arc on the circle with a central angle measure of 120°? A) B) C) D)
4 10 20 30
2. In a circle with a diameter of 10 inches, what is the area, in square inches, of a sector of the circle with a central angle measure of 72°? A) B) C) D)
5 10 20 30
2 3. In a circle with center O, central angle AOB has a measure of 3 radians. The area of the sector formed by central angle AOB is what fraction of the area of the circle?
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Circles: Chords
Circles: Chords Identify: Any question with a chord. A chord is a line segment whose endpoints both lie on a circle. Set Up: Use the Pythagorean Theorem to solve for the missing information.
1. In the circle above, F is the center. Chord DE is 24 feet long and is 5 feet from G. What is the distance from point G to point D ?
2. The area of the above circle is 64, the distance from point C to point D is 6, and AB is the circle’s longest chord. What is the distance from point D to point A ? A) B) C) D)
6 6 2 10 10 2
3. A circle has a radius of r inches, and chord CD is parallel to the diameter AB. If the length of CD is 49 of the length of AB, what is the distance between the chord and the diameter in terms of r? (round to the nearest hundredth.) A) 0.43r B) 0.57r C) 0.76r D) 0.90r
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Circles: Inscribed Circles
Circles: Inscribed Circles Identify: Any question which references an inscribed circle. Set Up: A length of a square is the same as the diameter of an inscribed circle. The diameter of a circle is the same length as the diagonal of an inscribed square. .
1. A circle is inscribed within a square. The square has an area of 144 square units. What is the circumference of the inscribed circle? A) B) C) D)
6 12 36 144
2. A circle is inscribed in a square. If the area of the inscribed circle is 81, what is the area of the square?
A) B) C) D)
81 81 324 324
3. A square is inscribed in a circle. If the area of the inscribed square is 16, what is the area of the circle? A) B) C) D)
208
8 8 2 16 16 2
208
PSAT
209
Circles Notes
209
PSAT
Circles Review
1. In a circle with a radius of 12 inches, what is the length, in inches, of an arc on the circle with a central angle measure of 180° ?
2. In a circle with a diameter of 20 inches, what is the length, in inches, of a sector of the circle with a central angle measure of 90° ?
3. A circle is inscribed within a square. The circle has an area of 400 square units. What is the perimeter of the square? A) B) C) D)
40 80 160 1,600
4. The area of circle A is four times greater than of the area of circle B. If the circumference of circle B is 8, what is the circumference of circle A? A) B) C) D)
4 8 16 32
5. In the circle below, B is the center. Chord AD is 800 feet long and is 300 meters from C. What is the distance from point A to point C ?
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PSAT
Circles: Answers Workbook Answers
Circles: Circumference and Area
Review Answers 1) 12
1) 13
2) 25
2) C
3) C
3) 6
4) C
Circles: Arc and Sector
5) 500
1) C 2) A 1 3) 3 Circles: Chords 1) 13 2) C 3) D Circles: Inscribed Circles 1) B 2) C 3) A
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PSAT
Geometry in Three Dimensions
PSAT Math: Geometry in Three Dimensions Important Formulas Cone Volume
Sphere Volume
1 Volume = 𝜋r2 h 3
4 Volume = 𝜋r3 3
Cylinder Surface Area
Cylinder Volume
Surface Area = 2𝜋r2 + 2𝜋rh
Volume = 𝜋r2 h
Rectangular Prism Surface Area
Rectangular Prism Volume
Surface Area = 2wl + 2hl + 2hw
Volume = lwh
Rectangular Pyramid Volume 1 Volume = 3lwh
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PSAT
Cones and Cylinders
Cones Identify: Any question that references the volume of a cone or the distance from the apex of a cone to a point along the base. Set Up: Write down the cone volume formula to find the missing information for a volume question. The distance from the apex of the cone to a point along the base is the hypotenuse of a right triangle.
Cone Volume Formula 1 Volume = 𝜋r2 h 3 1. A cone has a height of 60 and a base diameter of 30. What is the volume of this cone? A) 1,500𝜋 B) 4,500𝜋 C) 9,000𝜋 D) 18,000𝜋
Cylinders Identify: Any question that references the surface area or volume of a cylinder. Set Up: Write down the appropriate formula to find the missing information. Repeat as necessary.
Cylinder Surface Area Formula
Cylinder Volume Formula
Surface Area = 2𝜋r2 + 2𝜋rh
Volume = 𝜋r2 h
1. A cylinder has a volume of 2,160𝜋 and a height of 15. What is the radius of this cylinder?
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PSAT
Rectangular Prisms and Spheres
Rectangular Prisms Identify: Any question that references the surface area or volume of a rectangular prism. Set Up: Write down the appropriate formula to find the missing information. Repeat as necessary.
Rectangular Prism Surface Area Formula
Rectangular Prism Volume Formula
Surface Area = 2wl + 2hl + 2hw
Volume = lwh
1. A rectangular prism has a height of 25, a width of 8, and a length which is twice as long as its height. What is the volume of this rectangular prism? A) 2,500 B) 3,200 C) 5,000 D) 10,000
Spheres Identify: Any question that references the volume of a sphere. Set Up: Write down the sphere volume formula to find the missing information. Repeat as necessary.
Sphere Volume Formula 4 Volume = 𝜋r3 3 1. A sphere has a volume of 7,776𝜋. What is the diameter of the sphere?
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PSAT
Rectangular Pyramids
Rectangular Pyramids Identify: Any question that references the volume of a rectangular pyramid or the distance from the apex of a rectangular pyramid to a point along the base. Set Up: Write down the appropriate formula to find the missing information for a volume question. The distance from the apex of a rectangular pyramid to a point along the base is the hypotenuse of a right triangle.
Rectangular Pyramid Volume Formula 1 Volume = lwh 3 1. A rectangular pyramid has a height of 10, a length of 20, and a volume of 1,800. What is the width of this rectangular pyramid?
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PSAT
216
Geometry in Three Dimensions Notes
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PSAT
Geometry in Three Dimensions Review
1. A sphere has a diameter is 42. What is the volume of the sphere?
2. The height h of a certain cylinder is equal to its radius, If the diameter of the cylinder is 30, then what is the volume of this cylinder?
3. A local town is building both a new science museum and a new library with walls each made out of stone. Each building is using stones that are 1 foot by 1 foot by 6 inches. The dimensions of the walls of the science museum are 80 feet by 60 feet by 3 feet, and the dimensions of the walls of the library are 60 feet by 60 feet by 2 feet. If each building has four walls, by what factor will the number of stones for the walls of the library be greater than the number of stones for the walls of the science museum?
4. What is the volume of the largest sphere that can be inscribed inside a cube of volume 1,728 ? A) B) C) D)
144𝜋 288𝜋 576𝜋 2,304𝜋
5. A cone with height h sits inside a cube of the same height. If the sides of the cylinder touch each of the four sides of the box, what is the volume of the cone in terms of r ? 1 A) 2 h2 B) 2h2 C)
h3 4
h3 D) 12
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PSAT
Geometry in Three Dimensions Answers Workbook Answers
Cones
Review Answers 1) 12,348𝜋
1) B
2) 3,375𝜋
Cylinders
3) 0.5
1) 12
4) B 5) D
Rectangular Prisms 1) D Spheres 1) 36 Rectangular Pyramids 1) 27
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PSAT
Graphing
PSAT Math: Graphing
Important Formulas Circle Graphing Formula Circle Graphing Formula: (x – h)2 + (y – k)2 = r2 Center: (h, k) Radius: r
Parabola Graphing Formulas Graphing Formula: y = ax2 + bx + c Vertex form: y = a(x – h)2 + k, where (h, k) is the vertex If: a > 0; parabola opens up (u-shaped). If: a < 0; parabola opens down (n-shaped) b x-coordinate of the vertex (highest or lowest point of the curve): –2a A parabola’s “axis of symmetry” passes vertically through the vertex.
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PSAT
Graphing: Circles
Graphing: Circles Identify: Look for questions that reference the graphing formula of a circle. Set Up: Plug in the elements from the question into the circle equation.
Circle Graphing Formula Circle Graphing Formula: (x – h)2 + (y – k)2 = r2 Center: (h, k) Radius: r
1. What is the radius of a circle with the equation (x – 4)2 + (y + 8)2 – 36 = 0?
2. The Santa Monica carnival recently purchased a new Ferris Wheel. The wheel has a diameter of 220 feet. Which of the following is the equation of the circle formed by a rider traveling along the circumference of the Ferris Wheel? A) B) C) D)
220
x2 + y2 = 2202 (x + y)2 = 220 x2 + y2 = 1102 x + y = 1102
220
PSAT
Graphing: Parabolas
Graphing: Parabolas Identify: Look for questions that have a diagram of a parabola or reference the graphing formula(s) of a parabola. Set Up: Plug in the elements from the question into the relevant parabola equation(s).
Parabola Graphing Formulas Graphing Formula: y = ax2 + bx + c Vertex form: y = a(x – h)2 + k, where (h, k) is the vertex
If: a > 0; parabola opens up (u-shaped). If: a < 0; parabola opens down (n-shaped) b x-coordinate of the vertex (highest or lowest point of the curve): – 2a A parabola’s “axis of symmetry” passes vertically through the vertex. 1. The graph of y = (3x – 3) (x + 3) is a parabola in the xy-plane. In which of the following equivalent equations do the x- and y-coordinates of the vertex of the parabola appear as constants or coefficients? A) B) C) D)
y = 3x2 + 12x – 9 y = 3(x + 1) + 6 y = 3(x + 1)2 + (–12) y = (x – 3)(3x – 3)
2. The xy-plane above shows one of the two points of intersection of the graphs of a linear function and a quadratic function. The shown point of intersection has coordinates (a, b). If the vertex of the graph of the quadratic function is at (–2, 0), what is the value of a? (Round to the nearest thousandth.) A) B) C) D)
221
0.432 1.076 1.576 2.458
221
PSAT
222
Graphing Notes
222
PSAT
Graphing Review
1. (NO CALCULATOR) What is the diameter of the circle represented by the below equation? (x + 8)2 + (y – 11)2 = 432
y = x2 − 2x + 24 2. The equation above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the x-intercepts of the parabola as constants or coefficients? A) B) C) D)
y − 6 = x2 − 6x y + 4 = (x − 2)2 y = x(x − 4) + 8 y = (x + 4)(x − 6)
3. (NO CALCULATOR) Which of the following is an equation of a circle in the xy-plane with center (0, 2) and a radius with endpoint (4, 5)? A) B) C) D)
x2 + (y – 2)2 = 25 x2 + (y – 5)2 = 25 (x – 2)2 + y2 = 5 (x – 4)2 + y2 = 5
4. The graph of y = (2x + 2) (x – 4) is a parabola in the xy-plane. In which of the following equivalent equations do the x- and y-coordinates of the vertex of the parabola appear as constants or coefficients? 3 50 A) y = 2(x – )2 + (– ) 2 4 3 50 B) y = 2(x – ) + (– ) 2 4 3 50 C) y = 2(x – 2)3 + (– 2 ) D) y = (x – 2)(2x – 8)
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Graphing Answers Workbook Answers
Graphing – Circles
Review Answers 1) 86
1) 6
2) D
2) C
3) A
Graphing – Parabolas
4) B
1) C 2) B
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PSAT
Lines and Angles
PSAT Math: Lines and Angles
Important Formulas Rule of 180 Sum of the angles in any triangle = 180 degrees Sum of the angles on a straight line = 180 degrees
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PSAT
Intersecting Lines
Lines and Angles: Intersecting Lines Identify: A question has two parallel lines intersected by a third line. Set Up: For parallel lines intersected by a third line, the formed acute angles are congruent, the formed obtuse angles are congruent, and acute and obtuse angles are supplementary.
1. In the figure above, x||y and a = 110°. What is the value of b ?
2. (NO CALCULATOR) Lines w, x, y, and z are shown below, and y║z. Which of the following is the set of all angles that must be supplementary to angle a ? A) {9, 10} B) {2, 3, 9, 10} C) {9, 10, 13, 14} D) {2, 3, 5, 7, 9, 10, 13, 14}
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PSAT
Rule of 180
Lines and Angles: Rule of 180 Identify: If you see angles on a straight line, and you are being asked for an angle measurement. Set Up: Use the Rule of 180 to solve for the unknown information.
1. Given the triangle shown below with exterior angles that measure a˚, b˚, and c˚ as shown, what is the sum of a, b, and c?
2. (NO CALCULATOR) In the figure above, lines a, b, and c intersect at a point. If j + k = x + y, which of the following must be true? I. j = l II. k = z III. l = z A) I and II only B) I and III only C) II and III only D) I, II, and III
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PSAT
228
Lines and Angles Notes
228
PSAT
Lines and Angles Review
1. In the figure above, XWY measures 35°, WXY measures 105°, and points X, Y, and Z are collinear. What is the measure of WYZ ?
2. In the figure above, if r is parallel to s and b = 96, then a + c = A) B) C) D)
168 180 192 Cannot be determined
3. The measure of NOP in the figure above is 150°. The measures of the three angles are given in terms of x, in degrees. What is the measure of QOP ?
4. In the figure above, line m is parallel to line n. Transversals u and v intersect at point B on m and intersect n at points R and S, respectively. Point Z is on n, the measure of BSZ is 130°, and the measure of RBS is 80°. How many of the angles formed by rays of m, n, u, and v have a measure of 50°?
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229
SAT
Lines and Angles Answers Workbook Answers
Intersecting Lines
Review Answers 1) 140
1) 70
2) A
2) B
3) 120
Rule of 180
4) 8
1) 360 2) B
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PSAT
Quadrilaterals and Polygons
PSAT Math: Quadrilaterals and Polygons Important Formulas Rhombuses Area Formula
Perimeter Formula
Area = bh
Perimeter = 2b + 2h
(In a square, b and h are equal)
(In a square, b and h are equal)
Angle Relationship
Trapezoids Area Formula Area = (
Angle Relationship
b1 + b2 2 )h
Polygons Sum of Interior Angles = 180° (n – 2) n = number of sides
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PSAT
Quadrilaterals and Polygons: Rhombus Questions
Quadrilaterals and Polygons: Rhombus Questions Identify: A question references the area, angles, and/or perimeter of a non-trapezoid quadrilateral. Set Up: Write down the appropriate formula(s) and/or relationship(s) to find the missing information.
Area Formula
Perimeter Formula
Area = bh
Perimeter = 2b + 2h
(In a square, b and h are equal)
(In a square, b and h are equal)
Angle Relationship
1. In the above parallelogram, if x = 140, what is 2y ?
2. Jan is planning to fence a 6-foot by 9-foot rectangular plot of ground to use as a garden. She intends to plant a 1-foot-wide border of flowers along the inside of the entire perimeter. What is the minimum number of feet of fence Jan would need to enclose the garden if there will be a 2foot-wide opening on one side of the plot for people to enter the garden?
A) B) C) D)
13 15 28 30
3. Tammy puts a fence around her rectangular garden. The garden has a width that is 4 feet more than 2 times its length. What is the perimeter of Tammy’s fence if the area of her garden is 1,550 square feet? (round to the nearest foot)
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PSAT
Quadrilaterals and Polygons: Trapezoid Questions
Quadrilaterals and Polygons: Trapezoid Questions Identify: Any question that references the area and/or angles of a trapezoid. Set Up: Write down the appropriate formula and/or relationship to find the missing information.
Area Formula Area = (
Angle Relationship
b1 + b2 2 )h
1. What is the area of a trapezoid with bases of length 8 and 6 and a height of 20 ?
2. In the above parallelogram, if x = 120, what is y + 100 ?
3. (NO CALCULATOR) In quadrilateral ABCD above, BC is parallel to AD, and AB = CD. If BC and AD were each halved and BE was decreased by 50 percent, how would the area of ABCD change? A) B) C) D)
233
The area of ABCD would be decreased by 75 percent. The area of ABCD would be decreased by 50 percent. The area of ABCD would not change. The area of ABCD would be multiplied by 2.
233
PSAT
Quadrilaterals and Polygons: Polygons
Quadrilaterals and Polygons: Polygons Identify: Look for regular shapes with greater than four sides. Regular shapes have sides that are all equal and interior (inside) angles that are all equal. Set Up: For area problems, try to break the polygon into smaller figures such as triangles. For angle problems, use the Sum of Interior Angles formula.
Sum of Interior Angles Formula Sum of Interior Angles = 180° (n – 2) n = number of sides
1. In the diagram above, ABCDE is a regular polygon. What is the value of x ?
2. The figure above shows a regular hexagon with sides of length z and a square with sides of length z. If the area of the hexagon is 60 3 square inches, what is the area, in square inches, of the square? A) 40 B) 32 C) 16 3 D) 8 3
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PSAT
235
Polygons and Quadrilaterals Notes
235
PSAT
Polygons and Quadrilaterals Review Questions 1 and 2 relate to the below information
A local town is currently constructing a new park that is 80 feet by 100 feet. This park will be all grass, except for a rectangular track that runs along the inside border of the park and is 15 feet wide. 1. What is the area, in square feet, of the park’s grassy area?
2. What is the minimum number of feet of fence the city would need to enclose the park (which includes the track) if there will be two separate openings for access that are each four feet wide?
Questions 3 relates to the below information The perimeter of a rectangle is P units, the area is A units, and the width is w units. The length of the rectangle is x units longer than the width. 3. (NO CALCULATOR) Which of the following equations expresses x in terms of P and w ? p A) 2 − 2w B)
p − 4w 2
C) P − 2w D) P − 4w
4. A circular fountain with a diameter of 30 meters is to be placed entirely within a rectangular plaza that is 40 meters by 60 meters. Bricks will be laid on the entire plaza around the fountain (but not under it), making it accessible to pedestrians. What is the approximate area, in square meters, of the plaza that will be brick? A) B) C) D)
236
400 square feet 1,400 square feet 1,700 square feet 2,300 square feet
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PSAT
Polygons and Quadrilaterals Answers Workbook Answers
Rhombus Questions
Review Answers 1) 3,500
1) 80
2) 352
2) C
3) A
3) 169
4) C
Trapezoid Questions 1) 140 2) 160 3) A Polygon Questions 1) 126 2) A
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PSAT
Triangles
PSAT Math: Triangles
Important Formulas Area Formula
Pythagorean Theorem
1 Area = bh 2
a2 + b2 = c2
Rule of 180 Sum of the angles in any triangle = 180 degrees Sum of the angles on a straight line = 180 degrees
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PSAT
Triangles: Angles (Rule of 180)
Triangles: Angles (Rule of 180) Identify: If you see a triangle or intersecting lines, and you are being asked for an angle measurement. Set Up: Use the Rule of 180 to solve for the unknown angle(s).
Rule of 180 Sum of the angles in any triangle = 180 degrees Sum of the angles on a straight line = 180 degrees
1. Two angles of a triangle are 23° and 71°. What is the other angle in this triangle?
2. In the circle above with center O, if w = 54, what fraction of the circle’s total circumference is minor arc AB ?
3. Two isosceles triangles are show above. If 180 – b = 3a and a = 30, what is the value of c ?
239
239
PSAT
Triangles: Area
Triangles: Area Identify: If the area of a triangle is referenced, you are being asked a triangle area question. Set Up: Immediately write down the triangle area formula. Plug whatever information is given in the question (triangle area, base, and/or height) into the formula and solve for whatever is missing in the equation. Repeat as necessary.
Triangle Area Formula 1 Area = 2bh 1. A right isosceles triangle has an area of 162. What is the length of each of its legs?
2. In the figure above, XY = YZ, and XZ is a diameter of the circle, having a length of 10 inches. What is the area of ΔXYZ, in square inches?
3. In the figure above, the circle has a center O and radius r. Segments NL and NM are tangent to the circle. If P is the midpoint of segment NL and the measure of angle LOP equals the measure of angle OPL, what is the combined area, in terms of r, of the triangles MNO and LNO ? A) r 5 B) 2r 5 C) r2 D) 2r2
240
240
PSAT
Triangles: Side Lengths (Pythagorean Theorem)
Triangles: Side Lengths (Pythagorean Theorem) Identify: If you are solving for the side of a right triangle or need to find the length of any diagonal line, you are being asked a right triangle side length question. Set Up: Immediately write down the Pythagorean Theorem. Plug whatever information is given in the question (hypotenuse and/or legs) into the formula and solve for whatever is missing in the equation. Repeat as necessary.
Pythagorean Theorem a2 + b2 = c2 1. Consider a right triangle with a hypotenuse of length 13, and legs (9 – x) and 12. What is the value of x?
2. In pentagon FGHIJ above, what is the value of a2 + b2 ?
3. A right triangle has legs of lengths j and k and a hypotenuse of length l. If j2 + k2 + l2 = 1058, what is the value of 3l ?
A) 24 B) 33 C) 48 D) 69
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PSAT
Triangles: Special Right Triangles
Triangles: Special Right Triangles Identify: If you see a right triangle with the angles 30º-60º-90º or 45º-45º-90º. Set Up: Use special right triangle ratios to solve the problem.
30º-60º-90º
45º-45º-90º
1. In the figure above, RSTV is a square and UV = 7. What is the area of RSTV ?
2. In quadrilateral MNOP above, the bisector of
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PSAT
Triangles: Similar Triangles
Triangles: Similar Triangles Identify: If you see triangles with similar angle measures. Set Up: If triangles have similar angle measures, then their side lengths are proportional. .
If: a=d b=e c =f
Then:
And:
A B C = = D E F
∆ABC ~ ∆DEF
1. The sides of a triangle are 11, 14, and 19. What is the length of the longest side of a similar triangle whose shortest side is 15 ? (Round your answer to the nearest tenth.)
2. The lengths represented by AB, EB, BD, and CD in the above diagram are 600 feet, 800 feet, 450 feet, and 550 feet, respectively. Segments AC and DE intersect at B, and ∠AEB and ∠CDB have the same measure. What is the value of x ?
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PSAT
244
Triangles Notes
244
PSAT
Triangles Review
1. To get to the bookstore from his house, Jacob must drive his car 12 miles north and then 5 miles west. What is the shortest distance, in miles, between the bookstore and Jacob’s house?
2. If a triangle has a height of 15 and a base of 40, what is the area of the triangle?
3. In the above triangle, if ABO is 34°, what is v ?
4. (NO CALCULATOR) In the circle shown above, E is the center and lies on AD and BC. Which of the following statements is true? A) B) C) D)
EDC measures 76° ED is perpendicular to CD AB ≈ BE CD ≈ AE
5. (NO CALCULATOR) In the figure above ∆STU ~ ∆VUW. Which of the following must be true? A) STU = VUW B) ST | SU C) SU ∥ UV D) STU = UVW
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PSAT
Triangles Answers Workbook Answers
Triangles: Angles (Rule of 180)
Review Answers 1) 13
1) 86
2) 300
1 2) 5
3) 112
3) 135
4) A 5) D
Triangle: Area 1) 18 2) 25 3) D Triangles: Sides Lengths (Pythagorean Theorem)
1) 4 2) 21 3) D Triangles: Special Right Triangles 1) 147 2) D Triangles: Similar Triangles 1) 25.9 2) 978
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PSAT
Advanced Topics (Math)
PSAT Math: Advanced Topics
Important Formulas Compound Interest Formula r Compound Interest: A = P(1 + n)nt A = Amount accumulated P = Principal r = Interest rate n = Compounding per period t = Number of periods
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PSAT
Advanced Concepts (Math): Complex Numbers
Advanced Concepts (Math): Complex Numbers (i) Identify: The question will include the complex number i. Set Up: Use i = −𝟏 to solve the question.
1. (NO CALCULATOR) What value is equivalent to 14 – 8i2 ?
2. Which of the following is equal to (5 – 2i)(7 + 4i) = ? (Note: i = A) B) C) D)
−1)
27 43 27 + 6i 43 + 6i
3. Which of the following complex numbers is equivalent to
4 – 6i ? (Note: i = 6 – 3i
−1)
14 8i A) 15 + 15 14 8i B) 15 – 15 2 24i C) 3 + 33 2 24i D) 3 – 33
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PSAT
Advanced Concepts (Math): Compound Interest
Advanced Concepts (Math): Compound Interest Identify: The question will ask about compound interest. Set Up: Use the compound interest formula to solve the question.
Compound Interest Formula r Compound Interest: A = P(1 + n)nt A = Amount accumulated P = Principal r = Interest rate n = Compounding per period t = Number of periods 1. Eric opened a bank account that earns 4 percent interest compounded annually. His initial deposit was $100 and he uses the expression $100(x)t to find the value of the account after t years. What is the value of x in the expression?
2. Eric’s friend Nathan found an account that earns 6 percent interest compounded annually. Nathan made an initial deposit of $200 into his account and at the same time Eric made a deposit of $100 into his account. After ten years, how much more money will Nathan’s initial deposit have earned than Eric’s initial deposit? A) B) C) D)
$114.45 $178.76 $210.15 $305.34
3. If you deposit $2,500 into an account paying 8% annual interest compounded quarterly, how much money will be in the account after 4 years? (Round your answer to the nearest dollar and ignore the dollar sign when gridding in your response.)
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PSAT
Advanced Concepts (Math): Radians
Advanced Concepts (Math): Radians Identify: Question with angles determined in terms of . Set Up: Use radians = 180 degrees to solve the question.
1. What degree measurement is equivalent to 15.5 ?
2. If two interior angles of a triangle have measures of 15 and 45 degrees respectively, then what is the measure of the third angle, in radians? 2 A) 3 B) 2 C) 3 D) 6
3. If two interior angles of a triangle have measures of 9 and 12 radians respectively, then what is the measure of the third angle, in degrees?
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PSAT
Advanced Concepts: Trigonometry: Sine, Cosine, and Tangent
Trigonometry: Sine, Cosine, and Tangent Identify: Look for references to sine, cosine, or tangent in the question. Set Up: Use the SOH-CAH-TOA relationships to solve the question.
SOH-CAH-TOA sin Θ =
opposite hypotenuse
cos Θ =
adjacent hypotenuse
tan Θ =
opposite adjacent
1. (NO CALCULATOR) For the above right triangle, what is cos B ?
2. (NO CALCULATOR) Given the triangle ABC above, which of the following is equal to
a ? b
A) cos A B) cos B C) tan A D) tan B
3. In triangle LMN, the measure of ∠M is 90°, MN = 8, and LN = 10. Triangle QRS is similar to triangle QRS, where vertices Q, R, and S correspond to vertices L, M, and N, respectively, and each side of triangle QRS is four times the length of the corresponding side of triangle LMN. What is the value of tan Q ?
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PSAT
Advanced Concepts (Math): Unit Circle
Advanced Concepts (Math): Unit Circle Identify: Look for trigonometric identities (sine, cosine, or tangent) and radian measures in the question. Set Up: Use unit circle values or draw a unit circle and graph the information provided in the question to solve the question. Cosine and sine are co-functions of each other. This mean that complementary angles of cosine and sine are equal.
First number: Cosine Second number: Sine Tangent = sine/cosine
a°
b° 1 1. (NO CALCULATOR) In the above right triangle sin a° = 3. What is cos (90° − a°) ?
2. (NO CALCULATOR) In the xy-plane above, O is the center of the circle, and the measure of ∠AOB is radians. What is the value of b ? b
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Advanced Concepts (Math): Notes
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Advanced Concepts (Math): Review
1. (NO CALCULATOR) What is the value of cos() ?
2. At a time when the sun’s rays are striking the level ground at an angle of 35°, a statue casts a shadow that is 81 feet long. To the nearest foot, how many feet tall is the statue? (Note: sin 35° ≈ 0.57, cos 35° ≈ 0.82, tan 35° ≈ 0.70)
3. For i = −1 , (3 – i)2 = ? A) B) C) D)
3i 10i 8 – 6i 10 – 6i
4. (NO CALCULATOR) What is the value of (sin(4))((cos(3)) ? A) 1 B) – 2 2 C) 2 2 D) 4
5. (NO CALCULATOR) In a triangle, one angle measures 90°, and the other angles measure x 2 and y. If sin x° = 3 , What is cos y° ?
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Advanced Concepts (Math): Answers Workbook Answers
Unit Circle
Complex Numbers 1) 22 2) D
1 1) 3 2) 3
3) B
Review Answers 1) –1
Compound Interest 2) 57 1) 1.04
3) C
2) C
4) D
3) 3,432
2 5) 3
Radians 1) 2,790 2) A 3) 145 Trigonometry: SOH-CAH-TOA
3 1) 5 2) C 4 3) 3
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PSAT
Interpreting Equations
PSAT Math: Interpreting Equations
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PSAT
Interpreting Equations: Linear Equations
Interpreting Equations: Linear Equations Identify: A question asks about an equation model that can be rewritten in the form y = mx + b . Set Up: Identify the units represented by x and y (the answer must relate to these units) and then plug numbers in for x to identify trends in the data. W = 450 + 20m 1. (NO CALCULATOR) The equation above is used to model the relationship between weight, W, of a grizzly bear and the bear’s age, m, in months. According to the model, what is the meaning of the 450 in the equation? A) For every increase in one month of age, a grizzly bear weighs an additional 450 pounds. B) For every increase in twenty months of age, a grizzly bear weighs an additional 450 pounds. C) At birth, a grizzly bear weighs 450 pounds. D) A grizzly bear gains 20 pounds of weight each month until it weighs 450 pounds.
s = 1,000 – 40x 2. (NO CALCULATOR) A radio station is running a promotion where a number of songs are given away each day. The equation above can be used to model the number of songs, s, that remain to be given away x days after the promotion began. What does it mean that (25, 0) is a solution to this equation? A) During the promotion, 40 songs are given away each day. B) It takes 40 days during the promotion to give away 1,000 songs. C) There are 40 songs available at the start of the promotion. D) The song promotion will last for 1,000 days. .
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Interpreting Equations: Non-Linear Equations
Interpreting Equations: Non-Linear Equations Identify: An equation model that CANNOT be rewritten in the form y = mx + b . Set Up: Translate the information in question into a formula on your own and then compare your equation to the one given. If there are two things performing a task at rates that are different magnitudes (one thing is twice as fast as the other, for example), then the faster thing is represented by a variable and the slower thing is represented by a multiple of that variable. 1 1 1 6+8=p 1. (NO CALCULATOR) A father and son are painting a shed together. The father can complete the paint job in six hours, and the son can complete the paint job in eight hours. The 1 equation above describes the situation described. Which the following describes what 8 represents in this equation?
A) The portion of the shed completed by the father. B) The portion of the shed completed by the father and son. C) The portion of the shed completed by the son in one hour. D) The portion of the shed completed by the father and son in one hour.
1 2 1 x+x=5 2. (NO CALCULATOR) John and Jim are working together to move a pile of mulch onto their mother’s flower bed. John can shovel half as fast as Jim, and together they can complete the job in 5 hours. The equation above represents the situation described. Which of the 1 following describes what the expression x represents in the equation? A) The time, in hours, it takes Jim to complete the job alone. B) The portion of the job that John would complete in one hour. C) The portion of the job that Jim would complete in one hour. D) The portion of the job that John would complete in two hours. .
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Interpreting Equations Notes
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Interpreting Equations Review
1. (NO CALCULATOR) Sam’s Shoe Emporium has volunteered to make a contribution to charity. The contribution will include a flat donation and a matching amount for each additional business that donates. The overall contribution of Sam’s Shoe Emporium is modeled by the equation C = 1,000m + 50,000, where m represents the number of additional companies that donate. Which of the following statements is true? A) For every additional business that contributes, Sam’s Shoe Emporium will contribute an additional 50,000 dollars. B) Each additional business will contribute 1,000 dollars. C) For every additional business that contributes, Sam’s Shoe Emporium will contribute an additional 1,000 dollars. D) Sam’s Shoe Emporium will donate at least 1,000 dollars.
2. (NO CALCULATOR) A construction company estimates the price of a job, in dollars, using the expression 400 + 25xy, where x is the number of builders who will be working and y is the total number of days the job will take using x builders. Which of the following is the best interpretation of the number 25 in the expression? A) B) C) D)
A minimum of 25 builders will work on each job. The price of every job increases by $25 every day. Each builder works 12 hours a day. The company charges $25 per day for each builder.
3. (NO CALCULATOR) Robert paints houses during the summer. If Robert’s payment for each house painted is modeled by the equation H = 500 – 8p , where p represents time spent painting, in hours, which of the following statements is true? A) For every increase in painting of eight hours, Robert receives 500 more dollars in payment. B) For every increase in painting of eight hours, Robert receives 8 less dollars in payment. C) For every increase in painting of one hour, Robert receives 500 more dollars in payment. D) For every increase in painting of one hour, Robert receives 8 less dollars in payment.
1 1 1 + = 4 7 w 4. (NO CALCULATOR) Rose and Edith are working together to create a quilt. Rose could knit the quilt in seven hours and Edith could knit the quilt in four hours. The equation above describes the situation 1 described. Which the following describes what 7 represents in this equation? A) The portion of the quilt completed by Edith. B) The portion of the quilt completed by Rose. C) The portion of the quilt completed by Edith in one hour. D) The portion of the quilt completed by Rose in one hour.
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Interpreting Equations Answers Workbook Answers
Interpreting Linear Equations
Review Answers 1) C
1) C
2) D
2) A
3) D
Interpreting Non-Linear Equations
4) D
1) C 2) B
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PSAT
Plug and Chug & Backsolving
PSAT Math: Plug and Chug & Backsolving
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Plug and Chug & Backsolving: Plug and Chug
Plug and Chug & Backsolving: Plug and Chug Identify: Problems with variable(s) in the question and variable(s) in the answer choices. The phrase “in terms of” often indicates a plug and chug question. Set Up: Pick number(s) for the variable(s) and solve the question as though the variable(s) is/are your number(s). Plug your number(s) into the answer choices and look for the same value. If more than one answer choice works, pick different number(s) to eliminate the remaining choice(s).
1. (NO CALCULATOR) If 2a – 4 = 2b, then 4b – 11 = A) B) C) D)
a+6 3a 4a – 11 4a – 19
2. (NO CALCULATOR) Katrina went to the food store to buy her cereal for the week. All brands of cereal were discounted 42% off the marked price. Which of the following is an expression for the discounted price on a marked price of y dollars? A) B) C) D)
0.42y y – 42y y – 0.42 y – 0.42y
3. (NO CALCULATOR) If 6x = 3n – 3 and y = 4 – n, which of the following expresses y in terms of x? A) y =
4–x 3
B) y =
18 – 2x 3
C) y = 4 – 3x D) y = 3 – 2x
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PSAT
Plug and Chug & Backsolving: Backsolving
Plug and Chug & Backsolving: Backsolving Identify: Problems with variable(s) in the question and numbers in the answer choices. Set Up: Plug the answer choices into the question as the variable(s). Look for the answer that generates the desired value.
1. If │x + 24│ = 40, what are the possible values for x? A) B) C) D)
–64 and 16 –64 and –16 –16 and 26 18 and 64
2. A town committee recently voted for whether or not to expand a local park. It was revealed that 60 percent of the committee voted for the expansion. Which of the following could be the total number of committee members? A) B) C) D)
82 94 110 162
3. (NO CALCULATOR) Which ordered pair (x, y) satisfies the system of equations shown below? 2x + 4y = 10 4x – 2y = 20 A) B) C) D)
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(−5, 0) (5, 0) (0, 2.5) (2.5, 0)
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Plug and Chug & Backsolving Notes
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Plug and Chug & Backsolving Review
1. (NO CALCULATOR) If
11 x = , what does x equal? x2 121
A) 1 B) 11 C) 11 D) 121
2. Which ordered pair (x, y) satisfies the system of equations shown below? 3x + 2y = 12 5x – 4y = 42 A) B) C) D)
(4, 0) (0, 4) (6, −3) (−3, 6)
3. The students at Hawthorne Elementary School are either right-handed or lefthanded. A survey reveals that exactly 15 percent of the students at Hawthorne are left-handed. Which of the following could be the total number of left-handed students at Hawthorne Elementary School? A) B) C) D)
70 84 92 120
4. (NO CALCULATOR) If x ≠ 0, y is a real number, y3 = 4x, and y2 = 8x, then y = ? 1 A) 2 B) 1 C) 2 D) 4
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Plug and Chug & Backsolving Answers Workbook Answers
Plug and Chug
Review Answers 1) C
1) D
2) C
2) D
3) D
3) D
4) A
Backsolving 1) A 2) C 3) B
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Statistics
PSAT Math: Statistics
Important Formulas Exponential Growth x
y = a(2) b
y = Final Amount x = Duration a = Original Amount b = Doubling Time
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Statistics: Exponential Growth
Statistics: Exponential Growth Identify: A question which references exponential growth (periodic doubling). Set Up: Write down the exponential growth formula and plug in the given information to solve for the unknown quantity.
Exponential Growth x
y = a(2) b
y = Final Amount x = Duration a = Original Amount b = Doubling Time 1. A scientist set up a one year experiment to study the mitosis of cells. The cells in the experiment doubled in number every 6 months. If at the end of the experiment there were 80 cells, how many cells were there at the beginning of the experiment?
2. From 1770 to 1850, the population of a country doubled in size every twenty years. If the population of the country was 320,000 in 1850, what was the population of the country in 1770?
3. (NO CALCULATOR) From 2000 to 2010, a city worker measured the amount of pollution in a local river every 24 months. The pollution of pollution in January 2000 was 150 ppm, and had doubled at every subsequent measuring. If Z represents the pollution at the end of 2010, then which of the following equations models pollution over time (in ppm)? 24 A) Z = 150(2)120 5 B) Z = 150(2)120
C) Z = 150(2)24(5) D) Z = 150(2)105
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Statistics: Interpreting Charts and Graphs
Statistics: Interpreting Charts and Graphs Identify: The question will describe a survey, poll, experiment, or other situation, using a chart, table, and/or graph. Set Up: Review the titles of any tables, and the headings of any axes. Make sure that you are using data from the correct location(s). Questions 1 and 2 relate to the below data The table below shows how 2,461 residents of three different cities voted in a recent election. Candidate A 234 156 343 733
City A City B City C Total
Candidate B 232 453 123 808
Candidate C 123 454 343 920
Total 589 1,063 809 2,461
1. What percentage of all votes cast in City A went to Candidates A and C? (Round to the nearest whole number.) 2. What percentage of all votes cast in the three cities did Candidate C receive? (Round to the nearest tenth of a percent.)
100 90 Guests
80 70 60 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM Time
3. The line graph above shows the hourly numbers of guests from 4PM to 11PM at a local restaurant. According to the graph, what was the greatest change (in absolute value) in hourly guests between two consecutive hours? A) B) C) D)
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7 guests 10 guests 16 guests 21 guests
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PSAT
Statistics: Line of Best Fit
Statistics: Line of Best Fit Identify: A question will reference the line of best fit for a given collection of data (usually arranged in a scatter plot). Set Up: The line of best fit is a line on a graph shows the general direction that a group of points seems to be heading. The slope (rise divided by run) of a line of best fit describes the trend of the collected data. Questions 1, 2, and 3 relate to the below data The below scatterplot shows the relationship between the ages and weights of 15 dogs in a local neighborhood. Weight (kilograms)
60 50 40 30 20 10 0 2
4
6
Age
8
10
12
1. (NO CALCULATOR) Based on the line of best fit, which of the below answers is closest to the predicted weight for a dog that is 11 years old? A) 27 kilograms B) 35 kilograms C) 45 kilograms D) 50 kilograms 2. (NO CALCULATOR) Based on the line of best fit, which of the below answers is the closest to the predicted age for a dog that weighs 25 kilograms? A) 6 years old B) 7 years old C) 8 years old D) 9 years old
3. (NO CALCULATOR) What is the approximate slope of the line of best fit for the above data? A) –4 B) 1 C) 2 D) 4 271
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Statistics: Margin of Error
Statistics: Margin of Error Identify: A question will reference some form of data collection and the terms “margin of error,” “sample/sample error” or “association.” Set Up: To decrease the margin of error (the amount of random sampling error) or increase the association (the strength of the connection between different data points) in the results of a survey, additional information must align with the population in the original survey. 1. (NO CALCULATOR) Jason surveyed 100 Massachusetts lawyers about their opinions on tort reform. Which of the below actions will most likely result in a lower margin of error for the survey? A) Asking 200 lawyers from around the world about their opinions on tort reform. B) Asking 500 people from across all professions about their opinions on tort reform. C) Asking 200 Massachusetts lawyers about their opinions on tort reform. D) Asking 500 lawyers from across the United Stated about their opinions on tort reform.
2. (NO CALCULATOR) A researcher wanted to know if there is an association between the amount of rain and the number of daffodils in California. She studied rainfall and daffodil data for 10 years and found convincing evidence of a positive association between rainfall and daffodils in California. Which of the following conclusions is well supported by the data? A) There is a positive association between the amount of rainfall and the number of daffodils in the United States. B) There is a positive association between the amount of rainfall and the number of daffodils in California. C) Using the number of daffodils and the amount of rain as defined in the study, an increase in the number of daffodils is caused by an increase in the amount of rain in the United States. D) Using the number of daffodils and the amount of rain as defined in the study, an increase in the number of daffodils is caused by an increase in the amount of rain around the world.
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Statistics Notes
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Statistics Review Questions 1 and 2 relate the following scenario
A student at a local university created a program to double a given number at a regular interval of two hours. The student then input 12 as the initial number and set the experiment to run for 3 days. 1. (NO CALCULATOR) If N represents the number at the end of the experiment, then which of the following equations models the experiment? (1 day = 24 hours.) A) N = 12(12)36 B) N = 12(2)36 C) N = 12(2)12 D) N = 12(12)12
2. If the student ran the experiment again for 2 days and ended with the number 117,440,512, what was the original number for this experiment (1 day = 24 hours)?
3. (NO CALCULATOR) Ms. Douglas asked fifteen students in her tenth grade French class what activity they would like to do for a field trip. Which of the below actions will most likely result in a more accurate sample of the preferred field trip of her students? A) Asking 25 students in all of her classes what activity they would like to do for a field trip. B) Asking 25 of her tenth grade French students what activity they would like to do for a field trip. C) Asking 35 of her fellow teachers what activity they would like to do for a field trip. D) Asking 35 of her ninth, tenth, and eleventh grade French students what activity they would like to do for a field trip.
4. (NO CALCULATOR) A recent study of the commute times for 2,500 people around the world showed that as people live closer to a downtown area, their commute time increases. Which of the following conclusions is supported by the data? A) There is a positive association between proximity to a downtown area and commute time in the United States. B) There is a positive association between proximity to a downtown area and commute time around the world. C) There is a negative association between proximity to a downtown area and commute time in the United States. D) There is a negative association between proximity to a downtown area and commute time around the world.
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Statistics Review Questions 5 and 6 relate to the below data
The below scatterplot shows the growth and achievement percentiles of Ms. Frazee’s second grade class on a recent standardized assessment. 100 80 60 40 20 0 0
20
40
60
80
100
5. (NO CALCULATOR) Based on the above data, which of the following would be the most accurate statement? A) The data shows a positive association that is linear. B) The data shows a positive association that is not linear. C) The data shows a negative association that is linear. D) The data shows a negative association that is not linear. 6. Which linear equation most accurately represents the line of best fit for this data (not shown)? A) y = –1.5x + 135 B) y = –1.5x + 160 C) y = 1.5x + 180 D) y = 1.5x + 135
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Statistics Review Questions 7, 8, 9, and 10 relate to the below data
The table below shows how 2,461 residents of three different cities voted in a recent national election.
Blue Red Green Total
1st Graders 7 12 23 42
2nd Graders 14 24 21 59
3rd Graders 31 17 8 56
Total 52 53 52 157
7. What percentage of 1st and 2nd graders chose blue or red as their favorite color? (Round to the nearest tenth.)
8. What percentage of 1st and 3rd graders chose green as their favorite color? (Round to the neatest tenth.)
9. How many times as likely is it for blue to be a 1st grader’s favorite color than for blue to be a 2nd grader’s favorite color? A) 0.70 times as likely B) 0.87 times as likely C) 1.30 times as likely D) 1.42 times as likely
10. How many times as likely is it for red to be a 2nd grader’s favorite color than for red to be a 3rd grader’s favorite color? A) 0.71 times as likely B) 0.89 times as likely C) 1.02 times as likely D) 1.34 times as likely
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Statistics Answers Workbook Answers
Statistics: Exponential Growth 1) 20
Review Answers 1) B 2) 7
2) 20,000
3) B
3) A
4) D
Statistics: Interpreting Charts and Graphs
5) C 6) A 7) 56.4
1) 61
8) 31.6
2) 37.4
9) A
3) C
10) D
Statistics: Line of Best Fit 1) C 2) A 3) D Statistics: Margin of Error 1) C 2) B
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