ACT math practice test 4

1. In the following figure, the line passes through the origin and through P= (1, 3). If you were to draw a new line perpendicular to the first that also passes through P,what would be the equation of this new line?

F. y= 3x+ 4
G.
H.
J.
K.

2. If

A. 4
B. 5
C. 6
D. 7
E. 8

3. What is the area of the trapezoid in the following figure?

F. 7
G.
H.
J.
K.

4. The following graph shows the number of new bank accounts that eight account executives have opened so far this week. Which of the following answer choices is the median number of accounts opened among these eight people?

A. 9.5
B. 10
C. 10.5
D. 11
E. 12

5. If x2x– 2 > 0, which of the following is the solution set for x?

F. x> –1
G. x> 2
H. –1 < x < 2
J. x< –1 or x> 2
K. No solutions are possible.

6. If you plot the equation x2+ (y– 2)2= 4 as a circle on a standard xy-graph, what is the area of the circle’s region that will lie in Quadrant 1, as shown in the following figure?

A. 0
B. π
C. 2π
D. 4π
E. 16π

7. If a+ 2b= 2, what is the value of ?

F. –6
G. 8
H. 10
J. –12
K. 14

8. On an xy-graph, three corners of a parallelogram are located at (3, 3), (4, – 4), and (–2, –1). Which of the following points could be the remaining corner?

A. (8, 0)
B. (8, –1)
C. (–1, 9)
D. (–3, 6)
E. (–5, 7)

9. Doug, who runs track for his high school, was challenged to a race by his younger brother, Matt. Matt started running first, and Doug didn’t start running until Matt had finished a quarter-mile lap on the school track. Doug passed Matt as they both finished their sixth lap. If both boys ran at a constant speed, with Doug running 2 miles an hour faster than Matt, what was Matt’s speed?

F. 10.5 miles per hour
G. 10 miles per hour
H. 9 miles per hour
J. 8 miles per hour
K. 7.5 miles per hour

10. When calculating a certain tax, Simone found that no tax is due for all income up to pdollars, with p > 0. Income greater than pdollars is taxed at a rate of 15%. Which of the following graphs accurately represents this tax?

A.
B.
C.
D.
E.

11. The following figure shows the graph of . Which of the answer choices are the correct amplitude and period of this function?

F. amplitude = 5, period = π
G. amplitude = 5, period = 2π
H. amplitude = 5, period = 4π
J. amplitude = 10, period = 2π
K. amplitude = 10, period = 4π

12. If the equation x2+ mx+ n= 0 has two solutions, x = kand x = 2k,what is the value of mnin terms of k?

A. 2k2
B. –2k2
C. –2k3
D. 6k3
E. –6k3

13. When she chooses a password, Eloise always uses exactly ten different characters: five letters (A, B, C, D, and E) and five numbers (2, 3, 4, 5, and 6). Additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive. How many different passwords conform to these rules?

F. fewer than 1,000
G. between 1,000 and 10,000
H. between 10,000 and 100,000
J. between 100,000 and 1,000,000
K. more than 1,000,000

14. If the least common multiple of 9, 10, 12, and vis 540, which of the following could be v?

A. 18
B. 24
C. 27
D. 36
E. 45

15. The equation y= axb+ cproduces the following (x, y) coordinate pairs: (0, 2), (1, 7), and (2, 42).What is the value of abc?

F. 10
G. 20
H. 30
J. 40
K. 60