HOW I CAN KICK BUTT IN THE HSC IN 4U MATHS!!! By : Khiet Hoang – World’s craziest teacher
WARNING This book may be considered by some as offensive, insensitive and politically incorrect ……..and if you do then go and tell someone who cares! ……..uhh and it also contains lots of speling and grematical erors……and the odd maths error! Footnote: (should really be at the bottom of the page but who cares…….) The author of this book has about 500808 different split personalities so sometimes he (she/it/they/we) uses the first person (often “I”) to refer to himself. Other times he uses third person such as “the author”. I believe he uses perpendicular pronouns too…..so if you are confused already before you even read the rest of this book then he has succeeded! I can tell you that one of the author’s favourite sayings to his students is “are you scarred for life yet?” and then laugh very loudly in an infectious manner! You’d have to be one of my students to understand the joke! The man is crazy!!!! Acknowledgements: I would like to thank my Mum, my Dad for bringing me into this world, my wife, my kids, my dog…… No seriously, I’d like to thank all of my students and ex-students at Kellyville High and at the various coaching institutions in Sydney. By teaching you I have learnt a great deal about how the NSW 4U syllabus should be taught. Thank you for putting up with me and my eccentricities. I’d also like to thank my colleagues and friends who have read this and have given feed back and support. This humble grass hopper owes you. Most of all I must thank my wife, Vanessa for being so understanding about me writing this during the wee hours of the mornings in my “spare” time……….
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Content Page
Why I wrote this book
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4
Most Important Procedure for HSC
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4U course overview
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4U syllabus content
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9
Chapter 1 – GRAPHS :Sketch a curve
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Chapter 2 – GRAPHS :Do something to a curve
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Chapter 3 – COMPLEX NO: locus
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Chapter 4 - COMPLEX NO: Geometry
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Chapter 5 - COMPLEX NO: nth Roots and proofs
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Chapter 6 – CONICS -
Rectangular Hyperbolas
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Chapter 7 – CONICS -
Ellipse
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Chapter 6 – CONICS -
Hyperbolas
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Chapter 6 – INTEGRATION
- Special properties
Chapter 14 – INTEGRATION - partial fractions Chapter 8 – INTEGRATION - reduction/recurrence formulas Chapter 9 – INTEGRATION
- By Parts
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Chapter 12 – VOLUMES - cross-section
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Chapter 13 – VOLUMES - shell
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Chapter 15 – MECHANICS – Projectile and SHM
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Chapter 15 – MECHANICS – Resisted Motion
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Chapter 15 – MECHANICS – Circular Motion
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Chapter 16 – POLYNOMIALS – transformation + roots and coeffs ------------
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Chapter 16 – POLYNOMIALS – Solve and factorise
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Chapter 16 – POLYNOMIALS – Multiple Roots
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Chapter 18 – HARDER 3U – Permutation and Combination
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Chapter 18 – HARDER 3U – Inequality
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Chapter 18 – HARDER 3U – Circle Geometry
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Chapter 18 – HARDER 3U – Induction
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Chapter 18 – HARDER 3U – Other
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Chapter 23 – Integration Table
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Why I wrote this book. This book was compiled by an experienced teacher who has taught this course from as early as 1989. He was NOT a terribly good student at 2U/3U/4U maths (….who also refuses to recognise the new course names as the names are the only things that changed. The syllabus content has NOT) and had to teach himself these courses again during 1990-1991 using this book below. This book was written with the 1982 syllabus in mind and is only good until 2010 because the syllabus is due to be changed then and who knows what will become of the new syllabus. If there are only cosmetic changes then this book will still be useful. Else, if you’re ever short on toilet paper then………. This book explains the whole 4U course in easy to understand language and it is intended to be used as a self help guide for students as well as teachers. 90% of 2U/3U and especially 4U is about following certain procedures to obtain the answers. This book is just that. You can easily get over 90% for 2, 3 and 4U maths just by following the procedures in this book alone. Students often find 3U/4U (and even 2U) hard. This is the case NOT because the content is hard. I can teach my 10 year old son (in 2007) some 4U maths concepts! Will he be able to remember it is another story?!!! Will he want to learn?!!!! Maths IS hard though for the following reasons: 1)
There is TOO MUCH to REMEMBER. From the formula perspective alone, can you REMEMBER about 15 pages of typed up formulas, let alone know which one to use? If you cannot remember, then do General maths because 90% of the formulas are given to you. Somewhere in this book you’ll find all the formulas you’ll need to know.
2)
People fear and RESIST any CHANGE in their lives ………..and hence they do NOT REMEMBER new definitions or concepts given to them. When a new theory or formula is given to students the first thing they often ask is why? Or say “That’s too hard. How am I going to remember that” (cast your mind back to the quadratic formula…..Oh sorry you don’t remember that one? ………my point exactly. For those who do remember, that’s the one with a, b and c in it. How about the distance formula from a point to a line……..what you didn’t know there was such a formula? ......... Uhh yeah there is and that one is not even 3U maths. It is 2U maths !!!!!).
3)
Students DON’T UNDERSTAND the CONCEPTS ……..and hence do NOT REMEMBER them. Unfortunately maths is often typically taught by teachers putting a few QUESTIONS on the board, showing how the QUESTIONS ARE TO BE SOLVED. They then ask the students to do a million (or thereabout) questions for homework which the students, of course, find difficult to
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do because they didn’t understand the CONCEPTS of the topic. Then the teacher puts some more questions on the board the next day, again showing the students how to solve those questions and again ask the students to do another million (or more) questions for homework ………..and the vicious cycle goes on…………meanwhile the students fall behind. And the text book also “teaches” the same way. They show how two or three questions are done and hardly show the concepts behind it, or if they do it is not explicitly shown. One of the text books I’ve seen shows a couple of questions with solutions in one chapter and then the concepts are shown in the NEXT chapter. I think the rationale there was to show “Oh do you see how hard it is for you to do the question this way but with this formula it is so much easier!!!” Well, why wasn’t it shown in the same chapter at the beginning of the chapter in the first place? 4)
Students PONDER upon the beauty of THE QUESTION. This is the biggest problem of all. This happens in not only maths but in all subjects. This is the main reason why HSC students do not do as well as they should in the HSC. What is the problem? Simply put, students, when sitting an exam, spend far too much time on questions they CAN’T do and very little or no time on questions they CAN do and hence run out of time. Many of my students often say “Oh, I didn’t have time to do the last question and it was the easiest question of the exam!!!” My response is always: “Well then why didn’t you do that question first?” which is often met with another of the student’s question: “Oh can you do that?” “Uhh……yeah you can….” I often say to my 4U maths students that you can suck at 4U maths but the idea is to make others suck at it worse than you. That is unfortunately how the UAI works. It simply ranks you in order from highest to lowest. The aim of any HSC exam is NOT to finish the paper but to finish AS MUCH AS YOU CAN. So if you ponder upon the beauty of the questions that you could not do and “accidentally” ignore questions that you can do, than you will suck worse then your HSC peers. The rule of thumb is if you read the question and you do not understand or have a mental blank you count to 3 and if you still do not know then go onto the next question. Don’t sit there and ponder upon its beauty. That is the real secret behind the HSC!!! There is an actual procedure on how to attack an HSC paper also somewhere in this book…… I’ll give you two actual real life everyday situations and one of my personal experiences where people ponder upon the beauty of the questions: Situation 1 2 DAY FM (and other radio stations) often has a contest where they ask the contestants 10 questions in a minute. You answer all 10 correctly you get $1000 otherwise you get $10 (or $100 depending on the radio station) per question. If the contestant does not know the answer they are allowed to say “pass” and the next question is asked. All questions are always asked until they answer all the questions correctly or run out of time.
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Not many contestants get $1000!!! Most often get $50 or even $60. A lot get $30 - $40. Some even get $10 or nothing!!! This is NOT because they do not know a lot of the answers. It’s simply because they ponder upon the beauty of one or two questions and before you know it, the minute is up. Instead of saying “pass” STRAIGHT AWAY when they do not know the answer, typical contestants say “Uhh can you read the question again?” or “Uhhh…… I read that in Cosmopolitan the other day…..what was his name again?......Uhh, what was the question again?” Of course I am exaggerating here a little but you get the idea. Situation 2 Students often claim that they study 3-4 hours some say even 6 hours a day after school and still their marks do not reflect their efforts!!! Why is this so? It’s because they ponder upon the beauty of the questions!!! This happens for ALL subjects not just for maths. When students come across a difficult question or concept or theme or theory or a certain place in their essay etc they often sit and ponder sometimes for hours (sometimes on just one question - I know because I myself have done it!!!!) because if they leave the question then it means in their mind that they have failed and so they must do that particular question before they can do the next one. It’s quite a funny psychological thing! The right thing to do is of course to move onto something else or ask your teacher or friend or tutor etc the next day so that you can carry on your study in a productive and effective manner. If you ponder upon the beauty of one or two questions then you will never finish the million or so question for maths that were set for homework. Remember the teacher asked you to do the million questions but they did not say that you have to do them in any order. That means that you finish as many as you can in the time set. This approach of “skipping” questions should be done not just for homework but for class work and particularly for exams (especially HSC exams). Make sure you come back to the ones you skipped and attempt them when you have done all the others that you can do. One of my own personal experiences. In writing this book the author pondered upon the beauty of this section alone ……..sitting there thinking and thinking some more and so far for the last 2 pages spent 3 hours pondering what to write. What he should have done is he should have stood up. Go and make a cup of coffee and write it the next day……But no, he must finish this section otherwise he cannot write the next section……..that funny psychological bs…remember? ………Sorry got to go….got other things I must write for this book…..the pages of formulas for example which is much easier to write then the pages above….... I think I made my point………..NEVER
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Most Important Procedure for HSC. Out of all of the procedures in this book this is by far the most important one. Here it is: 0) Take a few (10) deep breaths so you can relax and also get some brain food (oxygen) into the brain. 1) Read the whole paper in 2 minutes (you WILL be given at least 5 minutes reading time in the HSC regardless of how crappy your school is in NOT giving you reading time in the trials or in any test. I give reading time for EVERY single exam I give to my students from year 7 to year 12 even if it’s just for a minute or 10 seconds – for my one minute exam!). Of course you are not to read word for word question for question in the 2 minutes (you just don’t have time for that unless you are a very good speed reader). Instead you glance at the whole paper to see what you can do and plan to do those first. Trust me, this is the most productive 2 minutes of the exam. 2) Write down the formulas next to each question when you are asked to start writing since your mind is still fresh at the start of the exam. There’s nothing worse then you not remembering the formulas mid-way through the exam even though you know the topic. And don’t stress if you don’t remember at the start. You’ll dig it out later out of that brain of yours during the exam. The idea is not to stress your self but to remain calm…easier said then done. Remember it’s just a STUPID test (all tests are stupid believe me and you’ll unfortunately go through a lot of tests in your lifetime). It does not change the fact that you are a wonderful person! (pay me later for that one later!!!) 3) Do the exam in the order that you can skipping the ones that you can’t. If question 1 is the hardest question for you then skip it straight away and go to question 2. If question 2 is also not obvious to you then go to Q3. I often deliberately put question 1 as the hardest question in my exams to train my students to skip. Remember if you have read the question and for some reason it’s not obvious to you then don’t sit there and ponder upon its beauty. Go onto the next question straight away. Don’t be afraid to do this because even though you consciously leave the question your mind subconsciously works at the solution to try and find the answer. Your mind is a wonderful machine for that very reason. And I can prove it to you. All of us have problems of our own. But how often do we CONSCIOUSLY think about our problems during the course of the day. We still carry on with our busy lives but our brain continues to work on the problem and then somehow the solution presents itself!!! Just make sure though that you make a marking on the questions that you skipped so you can come back to do them later. 4) When you get to the end of the paper go back to the beginning of the exam and repeat steps 2 to 4 until you finish every question in the exam or when time is up, whichever is sooner. 5) Check the exam for silly mistakes or check whether you have answered what they asked for. They may have asked you to factorise for example and you gave them the roots instead! If you do finish the whole paper then don’t just sit there and show off “oh look at me I’m a smart ar…I finished the paper first before yous all!!!” Remember the idea of any HSC paper is NOT to finish the whole paper but to FINISH CORRECTLY AS MUCH AS YOU CAN.
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Graphs:
sketch a curve
usual do something to a curve including composite curves
Complex:
Roots and proofs
geometry
Integration:
By parts
reduction/recurrence
Volumes:
slice
shell
Conics:
Ellipse tangents and normals etc and the 4 proofs
locus partial fractions
substitution
special property
cross section
Hyperbola tangents and normals etc and the 4 proofs Rectangular Hyperbola tangents and normals etc Mechanics:
Projectile and SHMotion
Polynimials: multiple roots Harder 3 U:
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locus
Resisted motion transformation of roots
inequality
circle geo
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induction
and the 2 proofs circular motion solve + factorise other
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Topic1 GRAPHS – sketch a curve Year question 1990
marks comment Q1/Q1
1991
Q2
1992
Q4/Q3
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GRAPHS – sketch a curve 1992
Q4
1993
Q5
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GRAPHS – sketch a curve 1994
Q6
1995 1996
Q4/Q7
Q6/Q8
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GRAPHS – sketch a curve 1997
Q3/Q9
1998 1999
Q4/Q10
2000 2003 2004
Q3/Q11
2005
Q3/Q12
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Topic1 GRAPHS- do something to a curve including composite Year question 1990 1991
marks comment Q13
1992 1993 1994 1995
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GRAPHS- do something to a curve including composite 1996
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1997 1998
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GRAPHS- do something to a curve including composite 1999
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GRAPHS- do something to a curve including composite 2000
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GRAPHS- do something to a curve including composite 2001
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GRAPHS- do something to a curve including composite 2003
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GRAPHS- do something to a curve including composite 2006
Q3/Q24
2007 2010
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Topic2 COMPLEX NUMBERS – locus Year question 1990 1991 1992
marks comment Q2/Q25
1993
Q26
1994
Q2/Q27
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COMPLEX NUMBERS – locus 1995
5
1996
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Q2/Q29
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COMPLEX NUMBERS – locus 1996
Q2/Q30
1997
Q2/Q31
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COMPLEX NUMBERS – locus 1998
Q2/Q32
1999
Q2/Q33
2000
Q2/Q34
2001
Q2/Q35
2002
Q2/Q36
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COMPLEX NUMBERS – locus 2003
Q2/Q37
2004
Q2/Q38
2005
Q2/Q39
2006
Q2/Q40
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Topic2 COMPLEX NUMBERS – geometry rotate vectors etc Year question 1990
marks Comment Q1/Q41
1991
Q2/Q42
1992
Q43
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Q2/Q44
Q45
1994
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COMPLEX NUMBERS – geometry rotate vectors etc 1995
Q46
1996
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COMPLEX NUMBERS – geometry rotate vectors etc 1998
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COMPLEX NUMBERS – geometry rotate vectors etc 1999
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COMPLEX NUMBERS – geometry rotate vectors etc 2000
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COMPLEX NUMBERS – geometry rotate vectors etc 2001
Q2/Q51
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COMPLEX NUMBERS – geometry rotate vectors etc 2004
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Q2/Q53
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Topic2 COMPLEX NUMBERS – nth roots of unity and their proofs Year question 1990 1991 1992
marks comment Q7/Q54
1993
Q55
1994
Q56
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COMPLEX NUMBERS – nth roots of unity and their proofs 1995
Q4/Q57
1996
Q8/Q58
1997 1998
Q2/Q59
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COMPLEX NUMBERS – nth roots of unity and their proofs 1999
Q8/Q60
2000
Q2/Q61
2001
Q2/Q62
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COMPLEX NUMBERS – nth roots of unity and their proofs 2003
Q8/Q64
2004
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COMPLEX NUMBERS – nth roots of unity and their proofs 2005
Q6/Q65
2006
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Topic2 COMPLEX NUMBERS – algebra including square roots Year question 1990
marks comment Q67
1991
Q68
1992
Q2/Q69
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Q2/Q70
1994
Q71 a
Q71b
1995
Q2/Q72 1
3
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COMPLEX NUMBERS – algebra including square roots 1996
2
1997
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Q2/Q76
1999
Q2/Q77
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Q2/Q78
Q8/Q79
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Q2/Q80
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Topic2 COMPLEX NUMBERS – complex conjugate root theorem and proofs Year question 1990 1991 1992
marks comment Q89
1993 1994 1995 1996
Q90
1997 1998
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Q2/Q91
2000 2001 2002
Q2/Q92
2003 2006
Q3/Q93
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Topic3 CONICS- rectangular hyperbola Year question 1990 1991
marks comment Q94
1992 1993
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CONICS- rectangular hyperbola Q5/Q96
1997 1998 1999
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Topic3 CONICS Ellipse Year question 1990 1991
marks comment Q3/Q101
1992
Q102
1993 1994
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Q5/Q107
2003
Q3/Q108
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Q4/Q110
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Topic3 CONICS Hyperbola Year question 1990
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Q112
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CONICS Hyperbola Q3/Q115
2002
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Topic4 Year 1990
INTEGRATION – special properties question
marks comment
1991 1992
Q119
1993 1994
Q120
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INTEGRATION – special properties 1996
Q3/Q122
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INTEGRATION – special properties Q7/Q124
1999
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6
Q6/Q126
2001 2002 2003
Q6/Q127
2004
Q6/Q128
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INTEGRATION – special properties 2005
Q5/Q129
2006 2007 2010
286283476.doc
- 112 -
K Hoang 2007
Topic4 Year 1990
INTEGRATION – partial fractions question
marks Comment Q1/Q130
1991
Q1/Q131
1992
Q1/Q132
1993
Q1/Q133
1994
Q1/Q134
1995
4
Q1/Q135
1996
3
Q1/Q136
1997
4
Q1/Q137
286283476.doc
- 113 -
K Hoang 2007
INTEGRATION – partial fractions 1998
Q1/Q138
1999
4
2000
286283476.doc
Q1/Q139
Q1/Q140
- 114 -
K Hoang 2007
INTEGRATION – partial fractions 2001
Q1/Q141
2002
3
2003
286283476.doc
Q1/Q142
Q1/Q143
- 115 -
K Hoang 2007
INTEGRATION – partial fractions 2004
Q1/Q144
2005
Q1/Q145
2006
Q1/Q146
2007 2010
286283476.doc
- 116 -
K Hoang 2007
Topic4 Year 1990
INTEGRATION – reduction formula question
marks comment Q2/Q147
1991 Q1c/Q148
1992 1993 1994
286283476.doc
- 117 -
K Hoang 2007
INTEGRATION – reduction formula 1995
Q7/Q149
1996 1997 1998
Q3/Q150
1999 286283476.doc
- 118 -
K Hoang 2007
2000 2001 2002
286283476.doc
INTEGRATION – reduction formula Q6/Q151
- 119 -
K Hoang 2007
INTEGRATION – reduction formula 2003
286283476.doc
Q8/Q152
- 120 -
K Hoang 2007
INTEGRATION – reduction formula 2004
286283476.doc
Q8/Q153
- 121 -
K Hoang 2007
INTEGRATION – reduction formula 2005
286283476.doc
Q6/Q154
- 122 -
K Hoang 2007
INTEGRATION – reduction formula 2006
Q7/Q155
2007 2010
286283476.doc
- 123 -
K Hoang 2007
Topic4 Year 1990
INTEGRATION – by parts question
marks comment
1991 1992
Q1/Q156
1993
Q1/Q157
1994
Q1/Q158
1995
2
Q1/Q159
1996
3
Q1/Q160
1997
4
Q1/Q161
1998
3
Q1/Q162
1999
4
Q1/Q163
2000
3
Q1/Q164
286283476.doc
- 124 -
K Hoang 2007
INTEGRATION – by parts 2001
3
Q1/Q165
2002
4
Q1/Q166
2003
3
Q1/Q167
2004
2
Q1/Q168
2005
3
Q1/Q169
2006
3
Q1/Q170
2007 2010
286283476.doc
- 125 -
K Hoang 2007
Topic4 Year 1990
INTEGRATION – substitution, complete the square or using integration table question
marks comment Q2a/Q171
Q2b/Q172
1991 Q1a/Q173
Q1b/Q174 1992
Q175
1993
Q176
1994
Q177
1995
286283476.doc
2
- 126 -
K Hoang 2007
Q1/Q178
INTEGRATION – substitution, complete the square or using integration table 1995
3
1996
Q1/Q179
Q1/Q180 2
2
1997
Q1/Q181 2
3
2
286283476.doc
- 127 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table 1998
2
1999
286283476.doc
Q1/Q182
Q1/Q183
- 128 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table 2000
Q1/Q184 2
2
4 2001
Q1/Q185 2
2
4
286283476.doc
- 129 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table 2002
Q1/Q186 2
2
4
286283476.doc
- 130 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table 2003
2
Q1/Q187
2
4
2004
Q1/Q188 3
2
4
286283476.doc
- 131 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table 2005
Q1/Q189 2 2
2006
2
2
3
2007 2010
286283476.doc
- 132 -
K Hoang 2007
Q1/Q190
Topic5 VOLUMES - slice Year question 1990 1991 1992 1993 1994 1995
286283476.doc
marks comment
Q3/Q191
- 133 -
K Hoang 2007
VOLUMES - slice 1996
286283476.doc
Q3/Q192
- 134 -
K Hoang 2007
VOLUMES - slice 1997
Q3/Q193
1998 1999 2000 2001 2002
286283476.doc
- 135 -
K Hoang 2007
VOLUMES - slice 2003
Q3/Q194
2004 2005 2006 2007 2010
286283476.doc
- 136 -
K Hoang 2007
Topic5 VOLUMES – cross-section Year question 1990 1991
286283476.doc
marks comment Q5/Q195
- 137 -
K Hoang 2007
VOLUMES – cross-section 1991
286283476.doc
Q5 cont’/Q195
- 138 -
K Hoang 2007
VOLUMES – cross-section 1992
286283476.doc
Q196
- 139 -
K Hoang 2007
VOLUMES – cross-section 1993
Q197
1994 1995 286283476.doc
- 140 -
K Hoang 2007
1996 1997 1998
VOLUMES – cross-section Q5/Q198
1999
286283476.doc
- 141 -
K Hoang 2007
VOLUMES – cross-section 2000
286283476.doc
Q3/Q199
- 142 -
K Hoang 2007
VOLUMES – cross-section 2001
286283476.doc
Q4/Q200
- 143 -
K Hoang 2007
VOLUMES – cross-section 2002
286283476.doc
Q8/Q201
- 144 -
K Hoang 2007
2003 2004
286283476.doc
VOLUMES – cross-section Q3/Q202
- 145 -
K Hoang 2007
VOLUMES – cross-section 2005
286283476.doc
Q5/Q203
- 146 -
K Hoang 2007
VOLUMES – cross-section 2006
Q4/Q204
2007 2010
286283476.doc
- 147 -
K Hoang 2007
Topic5 VOLUMES - shell Year question 1990
marks Comment Q205
1991 1992 1993
286283476.doc
- 148 -
K Hoang 2007
VOLUMES - shell 1994
Q3/Q206
1995 1996 1997
Q5/Q207
1998
286283476.doc
- 149 -
K Hoang 2007
VOLUMES - shell 1999
Q4/Q208
2000 2001
Q3/Q209
286283476.doc
- 150 -
K Hoang 2007
VOLUMES - shell 2002
286283476.doc
Q4/Q210
- 151 -
K Hoang 2007
VOLUMES - shell 2003
Q7/Q211
2004
Q5/Q212
286283476.doc
- 152 -
K Hoang 2007
VOLUMES - shell 2005
Q4/Q213
2006
Q5/Q214
2007 2010
286283476.doc
- 153 -
K Hoang 2007
Topic6 MECHANICS – Motion including projectile and SHM Year question 1990 1991 1992
marks Comment Q5/Q215
1993 1994 1995
286283476.doc
- 154 -
K Hoang 2007
MECHANICS – Motion including projectile and SHM 1996
Q7/Q216
1997
286283476.doc
- 155 -
K Hoang 2007
MECHANICS – Motion including projectile and SHM 1998
Q7/Q217
1999 2000 286283476.doc
- 156 -
K Hoang 2007
2001 2002 2003 2004 2005
286283476.doc
MECHANICS – Motion including projectile and SHM
Q7/Q218
- 157 -
K Hoang 2007
MECHANICS – Motion including projectile and SHM 2006
Q6/Q219
2007 2010 286283476.doc
- 158 -
K Hoang 2007
Topic6 MECHANICS – Resisted motion Year question 1990
marks comment Q220
1991
Q6/Q221
1992 286283476.doc
- 159 -
K Hoang 2007
1993 1994
MECHANICS – Resisted motion Q4/Q222
1995 1996
286283476.doc
- 160 -
K Hoang 2007
MECHANICS – Resisted motion 1997
Q6/Q223
1998
286283476.doc
- 161 -
K Hoang 2007
MECHANICS – Resisted motion 1999
Q6/Q224
2000 286283476.doc
- 162 -
K Hoang 2007
MECHANICS – Resisted motion 2001
Q5/Q225
2002
286283476.doc
- 163 -
K Hoang 2007
MECHANICS – Resisted motion 2003
286283476.doc
Q5/Q226
- 164 -
K Hoang 2007
MECHANICS – Resisted motion 2004
Q6/Q227
2005 2010 286283476.doc
- 165 -
K Hoang 2007
Topic6 MECHANICS – circular motion Year question 1990 1991 1992
286283476.doc
marks comment Q228
- 166 -
K Hoang 2007
MECHANICS – circular motion 1993
Q229
1994
286283476.doc
- 167 -
K Hoang 2007
MECHANICS – circular motion 1995
286283476.doc
Q8/Q230
- 168 -
K Hoang 2007
MECHANICS – circular motion 1996
286283476.doc
Q6/Q231
- 169 -
K Hoang 2007
MECHANICS – circular motion 1997
286283476.doc
Q5/Q232
- 170 -
K Hoang 2007
MECHANICS – circular motion 1998
286283476.doc
Q4/Q233
- 171 -
K Hoang 2007
MECHANICS – circular motion 1999
286283476.doc
Q5/Q234
- 172 -
K Hoang 2007
MECHANICS – circular motion 2000
286283476.doc
Q5/Q235
- 173 -
K Hoang 2007
MECHANICS – circular motion 2001
286283476.doc
Q6/Q236
- 174 -
K Hoang 2007
MECHANICS – circular motion 2002
286283476.doc
Q6/Q237
- 175 -
K Hoang 2007
MECHANICS – circular motion 2003
286283476.doc
Q4/Q238
- 176 -
K Hoang 2007
MECHANICS – circular motion 2004
286283476.doc
Q5/Q239
- 177 -
K Hoang 2007
MECHANICS – circular motion 2005
286283476.doc
Q3/Q240
- 178 -
K Hoang 2007
MECHANICS – circular motion 2006
Q5/Q241
2007 2010
286283476.doc
- 179 -
K Hoang 2007
Topic7 POLYNOMIALS – transformation + relationship bwt roots and coefficients +others Year question 1990
1991 1992 1993 1994 1995
Q5/Q243
1996 1997
286283476.doc
marks Comment Q242
- 180 -
K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others 1998
Q6/Q244
1999
Q5/Q245
2000
286283476.doc
- 181 -
K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others 2001
Q3/Q246
2002
Q5/Q247
286283476.doc
- 182 -
K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others 2003
Q5/Q248
2004
Q4/Q249
286283476.doc
- 183 -
K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others 2005
2006 2007 2010
286283476.doc
- 184 -
K Hoang 2007
Q4/Q250
Topic7 POLYNOMIALS – solve and factorise Year question 1990 1991
marks comment Q251
1992 1993 1994
286283476.doc
Q8/Q252
- 185 -
K Hoang 2007
POLYNOMIALS – solve and factorise 1995 1996 1997 1998
Q7/Q253
1999 2000
Q5/Q254
286283476.doc
- 186 -
K Hoang 2007
POLYNOMIALS – solve and factorise 2001
Q7/Q255
2002 2003 2006 2007 2010
286283476.doc
- 187 -
K Hoang 2007
Topic7 POLYNOMIALS – multiple roots Year question 1990 1991
marks comment Q7/Q256
1992 1993
Q257
1994
Q258
1995 1996
286283476.doc
- 188 -
K Hoang 2007
POLYNOMIALS – multiple roots 1997
286283476.doc
Q5/Q259
- 189 -
K Hoang 2007
POLYNOMIALS – multiple roots 1998
Q4/Q260
1999
Q4/Q261
2000 2001 2002
Q5/Q262
2003 2004 2005 2006
Q4/Q263
2007 2010 286283476.doc
- 190 -
K Hoang 2007
Topic8 HARDER 3U- permutation and combination and probability Year Question 1990
marks comment Q5/Q264
1991
286283476.doc
Q265
- 191 -
K Hoang 2007
Topic8 HARDER 3U- permutation and combination and probability 1992
Q266
1993
Q267
286283476.doc
- 192 -
K Hoang 2007
Topic8 HARDER 3U- permutation and combination and probability 1994
286283476.doc
Q5/Q268
- 193 -
K Hoang 2007
HARDER 3U- permutation and combination and probability 1995
286283476.doc
- 194 -
Q7/Q269
K Hoang 2007
HARDER 3U- permutation and combination and probability 1996
286283476.doc
- 195 -
Q4/Q270
K Hoang 2007
HARDER 3U- permutation and combination and probability 1997
Q3/Q271
1998
Q4/Q272
286283476.doc
- 196 -
K Hoang 2007
HARDER 3U- permutation and combination and probability 1998
286283476.doc
Q6/Q273
- 197 -
K Hoang 2007
HARDER 3U- permutation and combination and probability 1999
286283476.doc
- 198 -
Q7/Q274
K Hoang 2007
HARDER 3U- permutation and combination and probability 2000
Q8/Q275
2001
Q5/Q276
286283476.doc
- 199 -
K Hoang 2007
HARDER 3U- permutation and combination and probability 2002
Q4/Q277
2003
Q4/Q278
2004
Q5/Q279
286283476.doc
- 200 -
K Hoang 2007
HARDER 3U- permutation and combination and probability 2005
Q5/Q280
2006
Q5/Q281
2007 2010 286283476.doc
- 201 -
K Hoang 2007
Topic8 HARDER 3U - inequalities Year question 1990 1991 1992
marks comment Q8/Q282
1993
286283476.doc
Q8/Q283
- 202 -
K Hoang 2007
HARDER 3U - inequalities 1994
Q284
1995 1996
286283476.doc
- 203 -
K Hoang 2007
HARDER 3U - inequalities 1997
286283476.doc
Q6/Q285
- 204 -
K Hoang 2007
HARDER 3U - inequalities 1998
Q8/Q286
1999 2000
286283476.doc
- 205 -
K Hoang 2007
HARDER 3U - inequalities 2001
Q8/Q287
2002 2003
Q6/Q288
286283476.doc
- 206 -
K Hoang 2007
HARDER 3U - inequalities 2003
Q7/Q289
2004
286283476.doc
- 207 -
K Hoang 2007
HARDER 3U - inequalities 2005
286283476.doc
Q8/Q290
- 208 -
K Hoang 2007
HARDER 3U - inequalities 2006
Q8/Q291
2007 2010
286283476.doc
- 209 -
K Hoang 2007
Topic8 HARDER 3U- circle geometry Year question 1990
marks comment Q6/Q292
1991
286283476.doc
Q293
- 210 -
K Hoang 2007
Topic8 HARDER 3U- circle geometry 1992
Q3/Q294
1993
Q6/Q295
286283476.doc
- 211 -
K Hoang 2007
HARDER 3U- circle geometry 1994
286283476.doc
Q6/Q296
- 212 -
K Hoang 2007
HARDER 3U- circle geometry 1995
286283476.doc
Q6/Q297
- 213 -
K Hoang 2007
HARDER 3U- circle geometry 1996
286283476.doc
Q8/Q298
- 214 -
K Hoang 2007
HARDER 3U- circle geometry 1997
286283476.doc
Q7/Q299
- 215 -
K Hoang 2007
HARDER 3U- circle geometry 1997
286283476.doc
Q7/Q300
- 216 -
K Hoang 2007
HARDER 3U- circle geometry 1997
286283476.doc
Q8/Q301
- 217 -
K Hoang 2007
HARDER 3U- circle geometry 1998
286283476.doc
Q8/Q302
- 218 -
K Hoang 2007
HARDER 3U- circle geometry 1999
286283476.doc
Q8/Q303
- 219 -
K Hoang 2007
HARDER 3U- circle geometry 2000
286283476.doc
Q6/Q304
- 220 -
K Hoang 2007
HARDER 3U- circle geometry 2001
286283476.doc
Q6/Q305
- 221 -
K Hoang 2007
HARDER 3U- circle geometry 2002
286283476.doc
Q4/Q306
- 222 -
K Hoang 2007
HARDER 3U- circle geometry 2003
286283476.doc
Q7/Q307
- 223 -
K Hoang 2007
HARDER 3U- circle geometry 2004
286283476.doc
Q4/Q308
- 224 -
K Hoang 2007
HARDER 3U- circle geometry 2005
286283476.doc
Q7/Q309
- 225 -
K Hoang 2007
HARDER 3U- circle geometry 2006
Q4/Q310
2007 2010 286283476.doc
- 226 -
K Hoang 2007
Topic8 HARDER 3U- induction Year question 1990
marks Comment Q7/Q311
286283476.doc
- 227 -
K Hoang 2007
HARDER 3U- induction 1991
Q8/Q312
1992
Q6/Q313
1993
Q7/Q314
286283476.doc
- 228 -
K Hoang 2007
286283476.doc
- 229 -
K Hoang 2007
HARDER 3U- induction 1994
286283476.doc
Q7/Q315
- 230 -
K Hoang 2007
HARDER 3U- induction 1995
Q4/Q316
1996 1997 1998 1999
Q6/Q317
2000
286283476.doc
- 231 -
K Hoang 2007
HARDER 3U- induction 2001
Q8/Q318
2002
Q2/Q319
286283476.doc
- 232 -
K Hoang 2007
HARDER 3U- induction 2003
Q6/Q320
2004
Q7/Q321
2005
286283476.doc
- 233 -
K Hoang 2007
HARDER 3U- induction 2006
Q7/Q312
2007 2010
286283476.doc
- 234 -
K Hoang 2007
Topic8 HARDER 3U - other Year question 1990
286283476.doc
marks comment Q313
- 235 -
K Hoang 2007
Topic8 HARDER 3U - other 1990
Q314
1991 1992
286283476.doc
- 236 -
K Hoang 2007
HARDER 3U - other 1993
Q3/Q315
1994 1995
286283476.doc
4
- 237 -
K Hoang 2007
Q5/Q316
HARDER 3U - other 1995
286283476.doc
Q5/Q317
- 238 -
K Hoang 2007
HARDER 3U - other 1995
Q6/Q318
1996
Q4/Q319
286283476.doc
- 239 -
K Hoang 2007
HARDER 3U - other 1996
286283476.doc
Q6/Q320
- 240 -
K Hoang 2007
HARDER 3U - other 1997
Q4/Q321
1998
Q3/Q322
286283476.doc
- 241 -
K Hoang 2007
HARDER 3U - other 1998
286283476.doc
Q5/Q323
- 242 -
K Hoang 2007
HARDER 3U - other 1999
286283476.doc
Q5/Q324
- 243 -
K Hoang 2007
HARDER 3U - other 2000
286283476.doc
Q3/Q325
- 244 -
K Hoang 2007
HARDER 3U - other 2000
286283476.doc
Q4/Q326
- 245 -
K Hoang 2007
HARDER 3U - other 2000
Q7/Q327
2001
Q4/Q328
286283476.doc
- 246 -
K Hoang 2007
HARDER 3U - other 2002
286283476.doc
Q7/Q329
- 247 -
K Hoang 2007
2003 2004 2005
286283476.doc
HARDER 3U - other Q5/Q330
- 248 -
K Hoang 2007
HARDER 3U - other 2006
Q5/Q331
Q6/Q332
286283476.doc
- 249 -
K Hoang 2007
HARDER 3U - other 2006
286283476.doc
Q7/Q333
- 250 -
K Hoang 2007
286283476.doc
- 251 -
K Hoang 2007
HARDER 3U - other 2006
Q8/Q334
2007 2010
286283476.doc
- 252 -
K Hoang 2007
286283476.doc
- 253 -
K Hoang 2007
