ACT Math Practice Test 66

1. As shown in the figure below, ΔXYZ is a right triangle with legs of length x units and y units and hypotenuse of z units, such that 0 < x < y. Quadrilaterals ABYX, CDZY, and EFXZ are squares.

If 2x = z, then what is the value of cos(∠XYZ) ?

F.
G.
H.
J.
K. 2

2. The sum of 4 consecutive even integers is t. What is the sum, in terms of t, of the 2 larger of these integers?

A. - 4
B.
C. + 4
D. t + 2
E. t + 4

3. Figure 1 below shows the graph of y = x2 in the standard (x, y) coordinate plane. Which of the following is the equation for the graph in Figure 2 ?

F. y = (x - 4)2 -1
G. y = (x - 4)2 + 1
H. y = (x + 1)2 - 4
J. y = (x + 4)2 - 1
K. y = (x + 4)2 + 1

4. In a piggy bank, there are pennies, nickels, dimes, and quarters that total $5.29 in value. If there are 3 times as many dimes as there are pennies, 1 more dime than nickels, and 2 more quarters than dimes, then how many nickels are in the piggy bank?

A. 11
B. 13
C. 17
D. 21
E. 23

5. The mean of 5 numbers is 87. The smallest of the 5 numbers is 75. What is the mean of the other 4 numbers?

F. 72
G. 87
H. 88
J. 90
K. 108

6. "If Jenny is home, then her car is in the driveway." If the previous statement is true, then which of the following must also be true?

A. "If Jenny's car is in the driveway, then she is home."
B. "If Jenny is not home, then her car is in the driveway."
C. "If Jenny is not home, then her car is not in the driveway."
D. "If Jenny's car is not in the driveway, then she is home."
E. "If Jenny's car is not in the driveway, then she is not home."

7. If (y0.2)a2-20 = y and y ≠ 0, then what is the solution set of a ?

F. {1}
G. {-, }
H. {5}
J. {-5,5}
K. {25}

8. If g(x) = csc x tan x, then which of the following trigonometric functions is equivalent to g(x) ? (Note: csc x = , sec x = , and cot x = )

A. g(x) = sin x
B. g(x) = cos x
C. g(x) = tan x
D. g(x) = csc x
E. g(x) = sec x

9. A particular linear equation includes the (x, y) pairs below. What is the value of b ?

x y
11
-2b
3-3
-39

F. -8
G. -5
H. -1
J. 0
K. 7

10. If the volume of a sphere is 288π cubic inches, then which of the following is the surface area, in square inches, of the same sphere? (Note: For a sphere with radius r, the volume is πr3 and the surface area is 4πr2.)

A. 6π
B. 8π
C. 24π
D. 36π
E. 144π

11. When x > 1, 3logxx-2 = ?

F. -6
G. -
H.
J. 1
K.

12. Jamie drew a triangle bounded by the lines y = -x, x = -2, and y = 8 and shaded the interior, as shown in the figure below. Then Jamie decided to reflect this triangle across the y-axis and shade the interior of the new triangle. Which of the following would describe the shaded region of Jamie's new triangle?

A. x ≥ 2, y ≤ 8, yx
B. x ≥ 2, y ≤ 8, yx
C. x ≥ 2, y ≤ -8, yx
D. x ≥ -2, y ≤ 8, yx
E. x ≤ -2, y ≤ -8, yx

13. An angle with vertex at the origin and measure θ is shown in the standard (x,y) coordinate plane below. If one side of the angle includes the positive x-axis and the other side passes through (-12, -5), then what is the sine of θ ?

F. -
G. -
H. -
J.
K.

14. Side AB of parallelogram ABCD is shown in the figure below. If the coordinates of A are (7,6) and those of B are (5,1), then CD could lie on which of the following lines?

A. y = x + 9
B. y = x + 5
C. y = x - 4
D. y = -x + 4
E. y = -x - 9

15. If the function f(x,y) is defined as f(x,y) = (x-y)2 + (x+y)2, then, for all values of c and d, f(c2, d2) = ?

F. 4c2d2
G. 2c4 + 2d4
H. 2c4 - 2d4
J. 1
K. -4c2d2