ACT math practice test 33

1. In the hiking trail shown below, X marks the trail's halfway point. If measures 24 kilometers and is the length of , what is the total length, in kilometers, of the trail?

A. 144
B. 104
C. 96
D. 72
E. 48

2. What is the value of x when + 7 = 6?

G. -
H. -1
J. -
K. -5

3. Cyclist A averages 80 pedal revolutions per minute, and Cyclist B averages 61 pedal revolutions per minute. At these rates, how many more minutes does Cyclist B need than Cyclist A to make 9,760 pedal revolutions?

A. 19
B. 38
C. 122
D. 141
E. 160

4. The perimeter of a square is 36 inches. What is the area of the square, in square inches?

F. 6
G. 9
H. 18
J. 36
K. 81

5. For the rectangle shown in the standard (x,y) coordinate plane below, what are the coordinates of the unlabeled vertex?

A. (4,5)
B. (4,7)
D. (6,7)
E. (10,4)

6. Carla has 5 times as many notebooks as her brother does. If they have 42 notebooks between them, how many notebooks does Carla have?

F. 30
G. 33
H. 35
J. 37
K. 47

7. If G is in the interior of right angle DEF, then which of the following could be the measure of GEF?

A. 85°
B. 95°
C. 105°
D. 115°
E. 125°

8. Susie has three T-shirts: one red, one blue, and one black. She also has three pairs of shorts: one red, one blue, and one black. How many different combinations are there for Susie to wear exactly one T-shirt and one pair of shorts?

F. 3
G. 6
H. 8
J. 9
K. 27

9. 20% of 20 is equal to 50% of what number?

A. 2
B. 4
C. 8
D. 10
E. 200

10. There are 45 musicians in an orchestra, and all play two instruments. Of these musicians, 36 play the piano, and 22 play the violin. What is the maximum possible orchestra members who play both the piano and the violin?

F. 9
G. 13
H. 22
J. 23
K. 36

11. What is the largest value of m for which there exists a real value of n such that m2 = 196 – n2?

A. 14
B. 98
C. 182
D. 196
E. 392

12. Phil earned $800 at his summer job and saved all of his earnings. He wants to buy a deluxe drum kit that is regularly priced at $925 but is on sale for off. The drum kit is subject to 5% sales tax after all discounts are applied. If Phil buys the kit on sale and gives the sales clerk his entire summer earnings, how much change should he receive?

F. $23
G. $37
H. $40
J. $77
K. None; Phil still owes $171.25.

13. Which of the following numbers is an imaginary number?

C. -
D. -
E. -

14. Which of the following correctly factors the expression 25x4 - 16y8?

F. (25 - 16)(x2 - y4)(x2 + y4)
G. (5x2 - 4y4)(5x2 + 4y4)
H. (25x2 - y4)(x2 + 16y4)
J. (5x4 - 4y8)(5x4 + 4y8)
K. (5x4 - 8y8)(5x4 + 2y8)

15. The figure below shows a portion of a tile floor from which the shaded polygon will be cut in order to make a repair. Each square tile has sides that measure 1 foot. Every vertex of the shaded polygon is at the intersection of 2 tiles. What is the area, in square feet, of the shaded polygon?

A. 9.5
B. 10
C. 10.5
D. 11
E. 11.5