Khan Math 41 practices
Solving linear equations
Solving linear equations
1.
Solve for k : k
+ 22 = 29
k
=
Correct answer: 7 2.
Difficulty level: 1
Solve for n: -8 + n = 23 n
=
Correct answer: 31 3.
Solve for x: x – x
9=1
=
Correct answer: 10 4.
n
n
- 18
=
Correct answer: 36
k
+ 10 = 27
k
= Difficulty level: 1
Solve for t : t
+ 25 = 26
t
=
Correct answer: 1 7.
Difficulty level: 1
Solve for k :
Correct answer: 17 6.
Difficulty level: 1
Solve for n: 18 =
5.
Difficulty level: 1
Difficulty level: 1
Solve for k : -30 + k = 22 k
=
Correct answer: 52 8.
Solve for k :
Difficulty level: 1
Solving linear equations
1.
Solve for k : k
+ 22 = 29
k
=
Correct answer: 7 2.
Difficulty level: 1
Solve for n: -8 + n = 23 n
=
Correct answer: 31 3.
Solve for x: x – x
9=1
=
Correct answer: 10 4.
n
n
- 18
=
Correct answer: 36
k
+ 10 = 27
k
= Difficulty level: 1
Solve for t : t
+ 25 = 26
t
=
Correct answer: 1 7.
Difficulty level: 1
Solve for k :
Correct answer: 17 6.
Difficulty level: 1
Solve for n: 18 =
5.
Difficulty level: 1
Difficulty level: 1
Solve for k : -30 + k = 22 k
=
Correct answer: 52 8.
Solve for k :
Difficulty level: 1
19 = 14 + k k= Correct answer: 5 9.
Difficulty level: 1
Solve for q: 3 = -8 + q q= Correct answer: 11
Difficulty level: 1
10. Solve for p for p:: 10 = -19 + p + p p = Correct answer: 29
Difficulty level: 1
11. Solve for r: -12 + r = 7 r= Correct answer: 19
Difficulty level: 1
12. Solve for p: p + 12 = 30 p = Correct answer: 18
Difficulty level: 1
13. Solve for p: p – 18 = 3 p = Correct answer: 21
Difficulty level: 1
14. Solve for k: 30 = k + 23 k= Correct answer: 7 15. Solve for y: 25 = -14 + y y=
Difficulty level: 1
Correct answer: 39
Difficulty level: 1
16. Solve for r: 20 = r + 11 r= Correct answer: 9
Difficulty level: 1
17. Solve for z: -26 + z = 15 z= Correct answer: 41
Difficulty level: 1
18. Solve for p: 29 = p + 20 p = Correct answer: 9
Difficulty level: 1
19. Solve for y: 24 = y + 19 y= Correct answer: 5
Difficulty level: 1
20. Solve for n: 27 = 15 + n n= Correct answer: 12
Difficulty level: 1
21. Solve for k: 2 = -30 + k k= Correct answer: 32
Difficulty level: 1
22. Solve for n: 19 + n = 30 n= Correct answer: 11
Difficulty level: 1
23. Solve for k: 18 + k = 30 k= Correct answer: 12
Difficulty level: 1
24. Solve for r: 25 = 7 + r r= Correct answer: 18
Difficulty level: 1
25. Solve for p: 2 = -1 + p p = Correct answer: 3
Difficulty level: 1
26. Solve for r: 17 = r +10 r= Correct answer: 7 27.
!"! ! !!!
Difficulty level: 1
! !!
Which of the following best describes the solutions to the inequality shown above? A.
!
!
!!
B.
!
!
!
C.
!
!
!!
D.
!
! !
!
!
!
Correct answer: A 28.
Difficulty level: 2
!! ! ! ! !! ! !
Which of the following best describes the solutions to the inequality shown above? A. All real numbers B.
!
C.
!
!
! !
!
! !
D. No solution
Correct answer: D 29. If
! ! !! ! ! ,
Difficulty level: 2
which inequality represents the possible range of values of
A.
!"! ! ! ! !"
B.
!"! ! ! ! !"
C.
!"! ! ! ! !"
D.
!"! ! ! ! !"
Correct answer: D 30.
!
!
Difficulty level: 2
!! ! !!
Given the above equation, what is the value of
! ! !!!!
! ! !?
A. -739 B. -29 C. 31 D. 741 Correct answer: C 31. If
Difficulty level: 2
! !! ! ! !" ! !!, what is the value of A. ! ! ! !! !"
!
!
B.
!! C. ! ! ! D. ! ! ! !
!
!
!
!
!
!!
Correct answer: B
32. If
!
!
!
!
!
!
!
!
!
!
!
!
what is the value of s?
!
A.
!
B.
!
C.
!
!
! !"
D.
!
!
!
!
!
!" !
!"
!"
! !
Correct answer: B 33.
Difficulty level: 2
!"!!" ! !!
!
Difficulty level: 2
!""# ! !""#
What is the value of ! in the equation above?
!
! !?
!"! ! !?
Correct answer: 3/2 34. !! ! !"
Difficulty level: 2
!! ! !""""
!
In the equation above, h is a constant. If p=10 is a solution to the equation, what is the value of h? Correct answer: 9950 35.
!"!
!!
!
Difficulty level: 2
!! ! !
Which of the following is the solution to the equation shown above? !
A.
!
B.
!
!
C.
!
!
D.
!
!
!
!
!! !
!
!
!
Correct answer: C 36.
! ! !!
!
Difficulty level: 2
!! ! ! !
!
Which of the following best describes the solution set to the equation shown above? A. The equation has exactly one solution, m=0. B. The equation has exactly one solution, m=1. C. The equation has no solutions. D. The equation has infinitely many solutions. Correct answer: C 37. If
!"!"
Difficulty level: 2
! !" ! !" where b is a positive constant, what is the possible range of values of !
4!3bx? A. Any value less than !7 B. Any value greater than !7 C. Any value less than !
!!
!!"
D. Any value greater than
Correct answer: A 38. If !! ! !"
!
!"
Correct answer: 0
!!
!!"
Difficulty level: 2
! !", then what is the value of k ? Difficulty level: 3
39.
!!!!!!!
!
!!!"!
!
!
Which of the following best describes the solutions to the inequality shown above? !"
A. p
!
!
B. p
!
!
C. p
!
!
D. p
!
!!
!
!" !
! !
!
Correct answer: D 40. !! ! !"
!
Difficulty level: 3
! ! ! ! !! ! ! !
In the equation shown above, b is a constant. For what value of b does the equation have no solutions? A. 3 B. 4 C. 5 D. 6 Correct answer: 5
41.
! !
! !
! !
!
Difficulty level: 3
! !"
Which of the following best describes the solutions to the inequality shown above? A. q
!
3
B. q
!
3
C. q
!
6
D. q
!
6
Correct answer: D 42. If of
! ! !"#$ ! !
Difficulty level: 3
! ! ! !", where m is a positive constant, what is the possible range of values
! !!" ?
A. Any value greater than !3 or less than !9 B. Any value greater than !9 and less than !3 C. Any value greater than ! D. Any value greater than !
!
!!
!"
!"!
or less than !
!"
!"!
and less than !
!
!!
Correct answer: B 43. !!!! ! !! ! !
Difficulty level: 3 !
!
! !!
Which of the following is the solution to the equation shown above? A.
x
= 17
B.
x
= -23
C.
x
= 23
D.
x
= 11
Correct answer: C !!! ! !""!
44. If
!
!,
Correct answer: 0
45.
! !!!
Difficulty level: 3 then what is the value of
!
! !""
! !?
Difficulty level: 3
!
!
! ! !! !
Which of the following best describes the solution set to the equation shown above? A. The equation has no solutions. B. The equation has exactly one solution,
!
C. The equation has exactly one solution,
!
! !
!
!
!
!"
! !
D. The equation has infinitely many solutions. Correct answer: B 46. If !
Difficulty level: 3
! !! ! ! ! !!,
what is the possible range of values of !!! ! !?
A. Any value greater than !10 or less than !22 B. Any value greater than !22 and less than !10 C. Any value greater than 1 and less than 4 D. Any value greater than 4 or less than 1 Correct answer: B
47.
!
!
!
!
!
!
Difficulty level: 3
!!! ! !
Which of the following is the solution to the equation shown above? !
A.
!
!
B.
!
!
C.
!
!
!"
!
! !" !
!"
D.
!" !
!
!
Correct answer: A 48. If !"#
! !! !
!
Difficulty level: 3
! , then what is the value of
! !
! ! !! ! !
! !"#?
A. -113 B. -40 C. 40 D. 113 Correct answer: B 49.
!!! ! !! !
Difficulty level: 3
! !" ! !!
Which of the following best describes the solutions to the inequality shown above? A. !!" B. !! C.
!
!
!
!
!
! !
or
! !
! !
!
! !
D. No solution Correct answer: B 50.
!! ! !
!
Difficulty level: 4
!!" ! !
In the equation shown above, a is a constant. Which of the following values of
a results
in an
equation with exactly one solution? A. 4 B. -4 C. Neither value D. Both values Correct answer: A 51.
!!!" !
!
!
!
Difficulty level: 4
! !! ! !
In the equation above,
k is
a constant. For what value of
k are
there no solutions to the
equation? Correct answer: 4/3 52.
!
!!
!
!!
!
!"
Difficulty level: 4 !!
In the equation shown above, a is a constant. Which of the following values of equation with exactly one solution? A. 9 B. 8 C. Neither value
a
results in an
D. Both values Correct answer: D 53.
!! !
! !! ! !
!
!"
Difficulty level: 4
!!
In the equation shown above, a is a constant. Which of the following values of
a
results in an
a
results in an
a
results in an
equation with exactly one solution? A. 4 B. 5 C. Neither value D. Both values Correct answer: A 54. !!!! ! !!
!
!
Difficulty level: 4
! !"
In the equation shown above, a is a constant. Which of the following values of equation with exactly one solution? A. -2 B. 2 C. Neither value D. Both values Correct answer: A 55.
!!
!!
!
Difficulty level: 4
!! ! !"
In the equation shown above, a is a constant. Which of the following values of equation with exactly one solution? A. 2 B. 3 C. Neither value D. Both values Correct answer: B 56.
!
! !!
!
!! ! !
Difficulty level: 4
! !!
Which of the following best describes the solution set to the equation shown above? A. The equation has no solutions. B. The equation has exactly one solution,
!
!
C. The equation has exactly one solution,
!
!
D. The equation has infinitely many solutions. Correct answer: D
Difficulty level: 4
!. !
.
!
57.
!" ! !"
!
!!!
Given the above equation, what is the value of Correct answer: 1330
!"!!!"! ! !!?
Difficulty level: 4
SAT
Part II
Interpreting linear functions
1. The expression 1.08s+1.02b predict the end of year value of a financial portfolio where s is the value of stocks and b is the value of bonds in the portfolio at the beginning of the year. What is the predicted end-of-year value of a portfolio that begins the year with $200 in the stocks and $100 in bonds?
$ Correct answer: 318
Difficulty level: 1
Tag: Data collection and
conclusions
2.
The graph above shows the results of a controlled experiment designed by a scientist to determine the effect of magnetic field strength on the growth of sunflower plants. 500 young sunflower plants were randomly assigned to the control or experimental group. In the control group, the scientist grew 250 sunflower plants under normal local geo-magnetic field conditions ( 30 microteslas). In the experimental group, the scientist grew 250 sunflower plants identically except under a lower geomagnetic field ( 20 microteslas). Based on the results of this experiment, which conclusion is NOT valid? A. Sunflower plants grown under lower magnetic field conditions were more likely to weigh more than sunflower plants grown under normal magnetic field conditions. B. There is evidence of an association between the strength of magnetic field and height in sunflower plants. C. Sunflower plants grown under lower magnetic field conditions were more likely to be taller than sunflower plants grown under normal magnetic field conditions.
D. Members of the control group were more likely to grow to less than100 inches than members of the experimental group. Correct answer: A
Difficulty level: 2
Tag: Data collection and conclusions
3. A researcher wants to conduct a survey to gauge United States (U.S.) voters’ opinions about the U.S. Congress. Which of the following should NOT be a component of this survey?
A. The researcher collects data from the survey takers. B. The researcher analyzed data from the survey takers. C. The researcher distributes the survey to 10,1000 randomly selected U.S. citizens aged 18 and older. D. The researcher distributes the survey to 10,000 residents of a Washington D.C. neighborhood. Correct answer: D
Difficulty level: 2
Tag: Data collection and conclusions
4. A scientist wants to collect data about the effects of gravity on the growth of soybean plants. To test her hypothesis that soybeans grow better in a zero-gravity setting, she randomly assigns the plants into one of two groups. The first group is grown in typical soybean growing conditions in a greenhouse on earth, and the second group is grown in a zero-gravity, yet otherwise identical greenhouse in a space station. Which of the following is the best description of the research design for this study? A. Controlled experiment B. Observational study C. Sample survey D. None of the above Correct answer: A
Difficulty level: 2
Tag: Data collection and conclusions
5. A researcher representing a city government wants to measure public opinion about recycling by asking 1,000 randomly selected residents a series of questions on the subject. Which of the following is the best description of the research design for this study? A. Observational study B. Sample survey C. Controlled experiment D. None of the above Correct answer: B
Difficulty level: 2
Tag: Data collection and conclusions
6. In order to determine whether children who have just watched cartoons will perform better on cognitive tasks than children who have not just watched cartoons, researchers randomly divided 60 preschoolers into three groups. For nine minutes, one group watched a rapid-paced cartoon,
one group watched a slower-paced educational program, and one group colored. They then administered standardized tests to determine the immediate impact of the children’s previous nine minutes of activity. Which of the following is the best description of this type of research design? A. An observational study, a study in which investigators observe subjects and measure variables of interest without assigning treatments to the subjects. B. A controlled experiment, a study in which an investigator separates subjects into a control group that does not receive a treatment and an experimental group that receives a treatment, and then observes the effect of the treatment on the experimental group. C. A sample survey, a study that obtains data from a subset of a population, usually through a questionnaire or interview, in order to estimate population attributes. D. None of the above Correct answer: B
Difficulty level: 2
Tag: Data collection and conclusions
7.
A player at point A passes a ball to a player at point B. What is the distance, in yards, between point A and point B? ( Round your answer to the nearest tenth of a yard.)
Correct answer: 45.5
Difficulty level: 2
Tag: Right triangle word
problems
8. Wanahton’s rectangular baking sheet is 9
! !
inches (in) by 13 in. To the nearest inch, what is the
longest breadstick Wanahton could bake on his baking sheet? A. 13 in B. 16 in C. 124 in D. 259 in Correct answer: B
Difficulty level: 2
Tag: Right triangle word problems
9.
Due to weather, a barge captain decides to reach her destination in two legs: one due north and one due west. On a direct route, her destination is about 1,830 miles (mi) away; see the figure above. If after traveling 605 mi due north the captain determines it is time to head due west, how many more miles are left in the trip? (Round your answer to the nearest mile.)
Correct answer: 1727
Difficulty level: 2
Tag: Right triangle word
problems
10. Abby is buying a widescreen TV that she will hang on the wall between two windows. The windows are 36 inches apart, and wide screen TVs are approximately twice as wide as they are tall. Of the following, which is the longest that the diagonal of a widescreen TV can measure and still fit between the windows? A. 32 inches B. 42 inches C. 55 inches D. 60 inches Correct answer: A
Difficulty level: 2
Tag: Right triangle word problems
18 11. Bilal was assembling a set of bunkbeds and wanted to make sure the support posts were perpendicular to the floor. He measured that the posts were 165 centimeters ( cm) tall and 220 cm apart. How long should the diagonal measurement be if the support posts are perpendicular to the floor? A. 75cm B. 130cm C. 275cm D. 385cm Correct answer: C
12.
!
!
!
!!
3
Difficulty level: 2
Tag: Polynomial factors and graphs
! ! !!
Given the polynomial function P defined above, what are its zeros?
A. {-9, -6, 2, 3} B. {-9, 0, 2} C. {-3.3} D. {-3,0,3} Correct answer: D
Difficulty level: 2
Tag: Polynomial factors and graphs
13.
Which of the following gunctions could represent the graph at left in the !
!
!" -plane,
where
! !! !?
"#
!
!
!
!
$#
!
!
!
!
%#
!
!
!
!
&#
!
!
!
2
3
! !! ! ! 2
! !! ! !!
2
! !! ! ! 2 3 ! ! !! ! !!
Correct answer: D
Difficulty level: 2
Tag: Polynomial factors and graphs
14. A polynomial has zeros at -9, 2, and 0. Which of the following could be the polynomial? A.
2
! !! ! !" 2 B. ! ! !! ! !"! 2 3 C. ! ! !! ! !!! ! !" 2 3 D. ! ! !! ! !! ! !" !
3
Correct answer: B
15.
!
!!
!
!!
Difficulty level: 2 !!
!!
Given the polynomial above, what are its zeros? A. {-7,5, -3} B. {7, -5, 3} !
C. {-7, 5, - } !
!
D. {7, -5, } !
Tag: Polynomial factors and graphs
Correct answer: D
16.
Difficulty level: 2
Tag: Polynomial factors and graphs
2!! ! !!!!! ! !"!
Given the polynomial above, what are its zeros? A.
!
!
B.
!
!
C.
!
!
D.
!
!
!!! !"# ! !" !!! ! !! !"# ! !!" !"# ! !! !!" ! ! !"# ! !
!
!
!
!
!"
!
!
!
!
Correct answer: A
!
!!
Difficulty level: 2
Tag: Polynomial factors and graphs
17. 0.2B+ 0.1S = C Rhia is using the above equation to investigate the carbon footprint, C, in kilograms of carbon dioxide (CO 2) emissions, for her morning commute, during which S miles are by subway and B miles are by bus. How many kilograms of CO 2 per mile does the bus portion contribute to Rhia’s carbon footprint?
Correct answer: 0.2
Difficulty level: 2
18. V=2.5(6.4 !t) Salma is filling her water jugs with spring water at the supermarket. The above equation gives the empty space in her jugs, V, in US gallons, after t minutes at a constant fill rate. How many minutes will it take to fill the jugs?
Correct answer: 6.4
Difficulty level: 2
19. T=0.25q+87 Manon's statistics professor puts a bonus question on every test, which adds 0.25 points to a student's overall grade at the end of the term. The above equation gives Manon's current overall grade, T , after taking into account q extra credit questions answered correctly. What does the 87 mean in this equation? A. Manon must get an 87 or above to pass. B. Manon's average is an 87 before adding the extra credit. C. After adding in her extra credit, Manon’s average is an 87. D. Manon's professor gave 87 opportunities for extra credit this term. Correct answer: B
20. T=10m+40
Difficulty level: 2
