ACT math practice test 54

1. For i2 = -1, (3 - i)2 = ?

F. 16
G. 2i
H. 4i
J. 10 - 6i
K. 8 - 6i

2. The volume of a sphere is determined by the equation imgπR3, where R is the radius of the sphere. In a given model of the solar system, all of the planets are perfect spheres. If the radius of Mars is exactly 4 times greater than the radius of Venus, how many times the volume of Venus is the volume of Mars?

A. 81
B. 64
C. 16
D. 12
E. 4

3. Which of the following is equivalent to img

F. 4R3
G. 4R4
H. 8R3
J. 8R4
K. 32R12

4. If 2 is a solution of the equation x2 + kx + 12 = 0, what does k equal?

A. -12
B. -8
C. -2
D. 6
E. 8

5. In the standard (x, y) coordinate plane, the center of the circle shown below lies on the y-axis at y = 3. If the circle is also tangent to the x-axis, then what is the equation of the circle?

img

F. x2 + (y - 3)2= 6
G. x2 + (y - 3)2= 9
H. x2 + (y + 3)2 = 9
J. (x - 3)2 + y2 = 6
K. (x + 3)2 + y2 = 9

6. Which of the following equations summarizes the data listed below?

img

A. y = -2x - 2
B. y = 2x - 4
C. y = 2x + 3
D. y = 3x - 2
E. y = 3x + 2

7. The law of sines states that for any triangle, the ratio between the sine of an angle and the length of the side opposite that angle is the same for all of the interior angles in the triangle. In imgXYZ shown below, image = 22 cm, imagez = 32°, and imagey = 44°. What is the length of image?

img

F. img
G. img
H. img
J. img
K. img

8. Which of the following is the graph of the equation 3x - 2y = 6?

A. mg alt=img src=/image/tests/6/00948.jpg />
B. mg alt=img src=/image/tests/6/00949.jpg />
C. mg alt=img src=/image/tests/6/00950.jpg />
D. mg alt=img src=/image/tests/6/00951.jpg />
E. mg alt=img src=/image/tests/6/00952.jpg />

9. For img to be an integer, with m and n representing positive prime numbers, the sum of m + n must equal which of the following?

F. 8
G. 10
H. 12
J. 15
K. 21

10. Cam is going into business selling umbrellas. He pays $25,000 for a building and machinery, and each umbrella costs $4.00 to manufacture. If Cam sells x umbrellas for $6.50 each, which of the following equations best represents his net profit in dollars?

A. 10.50x - 25,000
B. 6.50x - 25,000
C. 4.00x + 25,000
D. 4.00x - 25,000
E. 2.50x - 25,000

11. In the circle shown below, O lies on the center of the circle and on chords image and image. The measure of img = 100°. Which of the following statements is NOT true?

img

F. m imagePLN = 50°
G. m imagePOL = 80°
H. imagePON imgimageNOM
J. imagePOL imgimageNOM
K. image

12. For all real numbers m and n, when is the equation |m - n| = |m + n| true?

A. Never
B. Always
C. Only when m = n
D. Only when m = 0 and n = 0
E. Only when m = 0 or n = 0

13. What is the value of log4 16?

F. 2
G. 4
H. 12
J. 20
K. 64

14. Television screen sizes are measured on the diagonal. Joshua bought a new television with a 24-inch screen and gave his old 21-inch television to his younger brother. If Joshua is watching a soccer ball that appears to be 4 inches in diameter on his new screen, how long does the diameter of the same ball, to the nearest tenth of an inch, appear to his brother watching on the smaller screen?

A. 3
B. 3.5
C. 4.6
D. 3π
E. 3.5π

15. When 0° < x < 90°, which of the following is NOT equal to tan x?

F. img
G. (sin2x + cos2x)(tan x)
H. img
J. img
K. img