ACT Math Practice Test 68

1. The art teacher at Valley High School is decorating her classroom by reproducing famous pictures on her walls. She has a picture 8 inches wide and 10 inches tall that she wants to replicate to scale on the wall. If the painting on the wall will be 6 feet tall, then approximately how wide will the painting be, in feet?

F. 5
G. 7
H. 9
J. 11
K. 13

2. The formula for line l in standard form is 5x - y = 2. Which of the following gives the formula for line l in slope-intercept form?

A. y = 5x + 2
B. y = 5x - 2
C. y = 2x - 5
D. y = -5x - 2
E. y = -5x + 2

3. The expression |2-14| - |-25| is equal to:

F. 41
G. 37
H. 13
J. -13
K. -37

4. In ΔJKL the measure of ∠J is exactly 37° , and the measure of ∠K is less than or equal to 63°. Which of the following phrases best describes the measure of ∠L ?

A. Exactly 120°
B. Exactly 100°
C. Exactly 80°
D. Greater than or equal to 80°
E. Less than or equal to 80°

5. If 3x - 1 > 26, then which of the following is the smallest possible integer value of x ?

F. 6
G. 7
H. 8
J. 9
K. 10

6. Paul is tying red and white ribbons around a gift box. He begins by tying the white ribbon and one red ribbon around the box. These two ribbons intersect on one face of the box at a 62° angle, as shown in the figure below. Now Paul wants to tie a second red ribbon onto the box so that the two red ribbons are parallel. What is the degree measure of the angle, indicated below, between the white ribbon and the bottom red ribbon?

A. 62°
B. 76°
C. 90°
D. 104°
E. 118°

7. In right triangle ΔPRS shown below, Q is the midpoint of PR. What is the length of QR, to the nearest inch?

F. 2
G. 3
H. 4
J. 6
K. 36

8. Katie notices that the textbooks for her past 3 math courses have the same length and width, but each year's textbook has more pages and weighs more than the previous year's textbook. Katie weighs the textbooks, to the nearest 0.1 ounce, for her past 3 math courses and wonders about the relationship between the number of pages in math textbooks and the weights of those textbooks. She graphs the number of pages and corresponding weights of her 3 math textbooks in the standard (x,y) coordinate plane, as shown below, and discovers a linear relationship among these 3 points. She concludes that the equation of the line that passes through these 3 points is y = 0.1x + 2.2.

How much more, in ounces, does a math textbook with 1,056 pages weigh than one with 868 pages?

A. 18.8
B. 19.8
C. 54.1
D. 77.3
E. 107.8

9. Katie notices that the textbooks for her past 3 math courses have the same length and width, but each year's textbook has more pages and weighs more than the previous year's textbook. Katie weighs the textbooks, to the nearest 0.1 ounce, for her past 3 math courses and wonders about the relationship between the number of pages in math textbooks and the weights of those textbooks. She graphs the number of pages and corresponding weights of her 3 math textbooks in the standard (x,y) coordinate plane, as shown below, and discovers a linear relationship among these 3 points. She concludes that the equation of the line that passes through these 3 points is y = 0.1x + 2.2.

According to Katie's equation, how much would a math textbook with 1,338 pages weigh, in pounds? (Note: 16 ounces = 1 pound)

F. 7.4
G. 8.5
H. 10.2
J. 13.6
K. 14.1

10. All line segments that intersect in the polygon below do so at right angles. If the dimensions given are in centimeters, then what is the area of the polygon, in square centimeters?

A. 168
B. 176
C. 184
D. 192
E. 200

11. Mr. Baylor spent 6 days grading 996 essays. He averaged 178 essays per day for the first 3 days. Which of the following is closest to his average speed, in essays graded per day, for the final 3 days?

F. 154
G. 157
H. 160
J. 163
K. 166

12. For all values of y, which of the following is equivalent to (y + 1)(y2 - 3y + 2)?

A. y3 + y2 - y - 2
B. y3 + y2 + 2y + 2
C. y3 - 2y2 - y + 2
D. y3 - 2y2 + y - 2
E. y3 - 2y + 2

13. For ∠D in ΔDEF below, which of the following trigonometric expressions has value ?

F. sin D
G. tan D
H. cos D
J. sec D
K. csc D

14. Over the weekend, Shawn bought 22 songs from an online music store. He spent a total of $17.90 on contemporary and classical songs. If contemporary songs cost $0.95 each and classical songs cost $0.75 each, then how many contemporary songs did Shawn buy? (Note: There is no sales tax charged on these songs because they were purchased online.)

A. 7
B. 9
C. 10
D. 13
E. 15

15. If the operation # is defined as x # y = , where x and y are real numbers such that x ≠ -y, then what is the value of (-3)#(-7)?

F. 10
G. 4
H. 1
J. -4
K. -10