ACT math practice test 19

1. What is the slope of the line given by the equation 8 = 3y - 5x?

A. -5
B. -
C. -
D.
E.

2. When adding fractions, a useful first step is to find the least common denominator (LCD) of the fractions. What is the LCD for these fractions?

F. 3 · 5 · 7 · 11
G. 32 · 52 · 7 · 11
H. 32 · 52 · · 113
J. 32 · 52 · 7 · 113
K. 33 · 53 · 7 · 114

3. = ?

A.
B.
C.
D.
E. 1

4. Dave is in Pikeston and needs to go to Danville, which is about 110 miles due south of Pikeston. From Danville, he'll head east to Rocketville, about 200 miles from Danville. As he sets out on his trip, a plane takes off from the Pikeston airport and flies directly to Rocketville. Approximately how far, in miles, does the plane fly?

F. 310
G.
H.
J.
K.

5. The figure below is a pentagon (5-sided figure). Suppose a second pentagon were overlaid on this pentagon. At most, the two figures could have how many points of intersection?

A. 1
B. 2
C. 5
D. 10
E. Infinitely many

6. MicroCorp will hold its annual company picnic next week and will assign 3 planning duties to its employees. One person selected will reserve a venue, another will arrange catering, and a third will plan activities. There are 10 employees eligible to fulfill these duties, and no employee can be assigned more than one duty. How many different ways are there for duties to be assigned to employees?

F. 73
G. 93
H. 103
J. 9 · 8 · 7
K. 10 · 9 · 8

7. In the (x,y) coordinate plane below, points P (6,2) and Q (1,4) are two vertices of ΔPQR. If PQR is a right angle, then which of the following could be the coordinates of R?

A. (4,-3)
B. (3, 0)
C. (2, 1)
D. (2, 4)
E. (3, 9)

8. If y = 0.25(100 - y), then what is the value of y?

F. 200
G. 75
H. 25
J. 20
K. 18

9. If 0° ≤ x° ≤ 180° and 4cos2x = 1, then x= ?

A. 0°
B. 60°
C. 90°
D. 150°
E. 180°

10. Danielle's living room is a rectangle with the dimensions 16 feet by 18 feet. If she partially covers the bare floor with a circular throw rug with a diameter of 12 feet, what is the approximate area of bare floor, in square feet, that remains exposed?

(Note: Assume the rug lies completely flat and does not touch any wall.)

F. 113
G. 144
H. 175
J. 288
K. Cannot be determined without knowing the exact position of the rug

11. In the standard (x,y) coordinate plane, which of the following is the equation of the line perpendicular to the line y = -2x + 2 and that passes through the point (0,-3)?

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

12. In the figure given below, what is sin θ?

F.
G.
H.
J. 1
K.

13. If a = 5 and b = -, which of the following expressions will be the greatest?

A. a + b
B. a - b
C. a × b
D. a ÷ b
E. |a × b|

14. When , which of the following must be true?

F. -12 < x < -3
G. -3 < x < 0
H. 0 < x < 3
J. 3 < x < 4
K. 4 < x

15. Which choice below is the complete solution set of |2z - 3| ≥ 7?

A. z ≥ 5
B. z ≤ -2 or z ≥ 5
C. -5 ≤ -6 or z ≥ 2
D. z ≤ -6 or z ≥ 2
E. z ≤ -5 or z ≥ 2