ACT math practice test 24

1. If a is a factor of 32 and b is a factor of 45, the product of a and b could NOT be which of the following?

F. 1,440
G. 288
H. 80
J. 54
K. 1

2. For each positive integer k, let ko be the sum of all positive odd integers less than k. For example, 6o = 5 + 3 + 1 = 9 and 7o = 5 + 3 + 1 = 9. What is the value of 17o × 4o?

A. 16
B. 144
C. 256
D. 324
E. 816

3. If (a,-3) is on the graph of the equation x - 4y = 14 in the standard (x,y) coordinate plane, then a =?

F.
G. -2
H. 2
J. 17
K. 26

4. For all t > 0, f(t) = . Which of the following is true about f(t) ?

A. It increases in proportion to t.
B. It increases in proportion to t2.
C. It decreases in proportion to t.
D. It decreases in proportion to t2.
E. It remains constant.

5. In the figure below, X is on . If the angle measures are as shown, what is the degree measure of YXZ?

F. 25°
G.
H.
J.
K.

6. Points (2, - 2) and (3,10) lie on the same line in the standard (x,y) coordinate plane. What is the slope of this line?

A. 12
B. 8
C.
D. -8
E. -12

7. What is the degree measure of an angle that measures radians?

F.
G.
H. 252°
J. 84°
K. 12°

8. Which of the following gives the equation for the circle in the standard (x,y) coordinate plane with a center at (4,-8) and a circumference of 10π square coordinate units?

A. (x - 4)2 + (y + 8)2 = 25
B. (x - 4)2 + (y + 8)2 = 100
C. (x + 8)2 + (y - 4)2 = 25
D. (x + 8)2 - (y - 4)2 = 100
E. (x + 8)2 + (y - 4)2 = 100

9. For some x and y that satisfy the equation xy = -x2, which of the following is FALSE?

F.
G.
H. x2 + y2 = -2xy
J. x2 = y2
K. x3 - y3 = 0

10. Rectangle ABCD lies in the standard (x,y) coordinate plane with corners at A(4,2), B(6,-1), C(1,-4), and D(-1,-1), and is represented by the 2 × 4 matrix . ABCD is then translated, with the corners of the translated rectangle represented by the matrix . What is the value of n?

A. 0
B. -1
C. -2
D. -3
E. -4

11. Whenever a > 0, which of the following real number line graphs represents the solutions for x to the inequality |x - a|≤?

F.
G.
H.
J.
K.

12. Three different functions are defined in the table below.

The diagram below uses three functions. The only values for p, q, r, s, and t are 1 and 0. Which of the following inputs (p, q, r, s, t) will produce the output 0?

A. (0,1,1,0,1)
B. (0,1,1,1,1)
C. (0,0,1,0,1)
D. (1,0,1,0,0)
E. (1,0,1,0,1)

13. Whenever x and y are both integers, what is (6.0 × 10x)(5.0y × 10y)expressed in scientific notation?

F. 30.0 × 100xy
G. 30.0 × 100xyy
H. 30.0 × 10xy
J. 3.0 × 10x + y + 1
K. 3.0 × 10xy

14. The points P, Q, R, and S lie in that order on a straight line. The midpoint of is R and the midpoint of is Q. The length of is x feet and the length of is 4x - 16 feet. What is the length, in feet, of ?

A. 32
B. 20
C. 16
D. 8
E. 4

15. The circle below has an area of 64π cm2. A central angle with measure 24° intercepts minor arc . What is the length of minor arc , in centimeters?

F. π
G. π
H.
J. π
K. 192π