New SAT Math Multiple Choice Practice Test 42

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Question 15 questions

Time 22 minutes

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1. A jar contains only red, white, and blue marbles. It contains twice as many red marbles as white marbles and three times as many white marbles as blue marbles. If a marble is chosen at random, what is the probability that it is not red?

  • A. Images
  • B. Images
  • C. Images
  • D. Images

2. y = -3(x - 2)2 + 2

In the xy-plane, line l passes through the point (-1, 3) and the vertex of the parabola with equation above. What is the slope of line l?

  • A. Images
  • B. Images
  • C. Images
  • D. Images

3. A certain function takes an input value and transforms it into an output value according to the following three-step procedure:

Step 1: Multiply the input value by 6.

Step 2: Add x to this result.

Step 3: Divide this result by 4.

If an input of 7 to this function yields an output of 15, what is the value of x?

  • A. 12
  • B. 16
  • C. 18
  • D. 24

4. The variables x and y are believed to correlate according to the equation y = ax2 + bx + c, where a, b, and c are constants. Which of the following scatterplots would provide the strongest evidence in support of the hypothesis that a < 0?

  • A. Images
  • B. Images
  • C. Images
  • D. Images

5. On a number line, the coordinates of points P and R are p and r, respectively, and p < r. If the point with coordinate x is closer to p than to r, then which of the following statements must be true?

  • A. Images
  • B. Images
  • C. |x - p|< r
  • D. |x + p|< r - p

6. Let function f(x) be defined by the equation Images. If m is a positive integer, then Images

  • A. Images
  • B. Images
  • C. Images
  • D. 2 - m

7. The value of y varies with x according to the equation y = a(x - 2)(x + 1), where a < 0. As the value of x increases from 0 to 5, which of the following best describes the behavior of y?

  • A. It increases and then decreases.
  • B. It decreases and then increases.
  • C. It increases only.
  • D. It decreases only.

8. If the expression Images is equivalent to the expression Images for all values of n, what is the value of k?

  • A. -12
  • B. -6
  • C. 6
  • D. 12

9. An online trading company charges a 3% commission for all stock purchases. If a trader purchases 200 shares of a stock through this company and is charged $3,399 including commission, what is the cost per share for this stock?

  • A. $16.45
  • B. $16.48
  • C. $16.50
  • D. $16.52

10. For nonzero numbers w and y, if w is 50% greater than y, then what is the ratio of w-2 to y-2?

  • A. 4 to 9
  • B. 2 to 3
  • C. 9 to 4
  • D. 4 to 1

11. Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?

  • A. This group contains 40 soccer players.
  • B. This group contains 20 athletes who play soccer but do not run track.
  • C. This group contains 20 athletes who play both track and soccer.
  • D. The number of soccer players in this group is 15 greater than the number of track team members in this group.

12. Images

A portion of the graph of the quadratic function y = f(x) is shown in the xy-plane above. The function g is defined by the equation g(x) = f(x) + b. If the equation g(x) = 0 has exactly one solution, what is the value of b?

  • A. -2
  • B. -1
  • C. 1
  • D. 2

13. If cos x = a, where Images, and cos y = - a, then which of the following could be the value of y?

  • A. x + 2π
  • B. x + π
  • C. Images
  • D. - x + 2π

14. Images

Of those surveyed who expressed an opinion on Proposal 81a, approximately what percentage are under 40 years of age?

  • A. 30%
  • B. 38%
  • C. 68%
  • D. 72%

15. Images

If the data in the table above are assumed to be representative of the general voting population, which of the following statements is most directly justified by these data?

  • A. The approval rate for Proposal 81a generally decreases with the age of the voter.
  • B. The disapproval rate for Proposal 81a generally increases with the age of the voter.
  • C. Those who express an opinion on Proposal 81a are more likely to be over 64 than they are to be under 40.
  • D. In all three age categories, voters are more than twice as likely to approve of Proposal 18a than to have no opinion about it.