ACT math practice test 34

1. The percent P of a population that has completed 4 years of college is given by the function P(t) = -0.001t2 + 0.4t where t represents time, in years. What percent of the population have completed four years of college after 20 years, to the nearest tenth?

F. 0.1
G. 7.6
H. 8
J. 8.4
K. 160

2. At Fatima's Fruits, a bag of eight grapefruits costs $4.40. At Ernie's Edibles, a bag of three grapefruits costs $1.86. How much cheaper, per grapefruit, is the cost at Fatima's Fruits than at Ernie's Edibles?

A. $0.07
B. $0.35
C. $0.59
D. $1.17
E. $2.54

3. Which of the following is equivalent to (x4 - 4)(x4 + 4)?

F. 2x4
G. x8 - 16
H. x8 + 16
J. x16 - 16
K. x8 - 8x4 - 16

4. Wade is making a tile mosaic. He begins the project by laying tile at a speed of 50 pieces per hour for 3.5 hours. He is then interrupted from his work for 60 minutes. He resumes working and lays tile at a speed of 35 pieces per hour, until he has laid 280 pieces of tile total. How many hours did Wade spend working on the mosaic after he was interrupted?

A. 2.5
B. 3
C. 3.5
D. 4
E. 4.5

5. Point C (1,2) and point D (7,-10) lie in the standard coordinate plane. What are the coordinates of the midpoint of ?

F. (1, 8)
G. (3,-6)
H. (4,-4)
J. (4,-6)
K. (7,-4)

6. Michael is planning to put fencing along the edge of his rectangular backyard, which is 22 yards by 16 yards. One long side of the backyard is along his house, so he will need to fence only 3 sides. How many yards of fencing will Michael need?

A. 38
B. 54
C. 60
D. 76
E. 352

7. What is the y-intercept of the line given by the equation 7x – 3y = 21?

F. -7
G. -
H.
J. 7
K. 21

8. On April 8th, a flower at Blooming Acres Florist was 15.0 centimeters tall. On April 16th, the flower was 17.4 centimeters tall. If the flower grew at a constant rate, on what day was the flower 16.5 centimeters tall?

A. April 11th
B. April 12th
C. April 13th
D. April 14th
E. April 15th

9. Which of the following expressions is equivalent to the expression given below?

(2x3x - 1) - 3(x4 + 2x3 - 2x2x + 3)

F. x14 - 3
G. -3x14
H. -3x4 + 8x3 - 6x2 - 4x + 8
J. -3x4 + 4x3 - 2x2 - 2x - 3
K. -3x4 - 4x3 + 6x2 + 2x - 10

10. The playground equipment shown below has a ladder that is 6 feet tall and a diagonal slide that is 7 feet long. If the ladder makes a right angle with the ground, approximately how many feet is the base of the slide from the base of the ladder?

A. 2
B. 4
C. 6
D. 8
E. 10

11. In a data set of 5 points, the mean, median, and mode are each equal to 8. Which of the following could be the data set?

F. {5, 7, 8, 8, 12}
G. {7, 7, 8, 8, 12}
H. {7, 8, 8, 8, 12}
J. {7, 8, 8, 10, 12}
K. {7, 8, 8, 12, 12}

12. In a certain sequence of numbers, each term after the 1st term is the result of adding 2 to the previous term and multiplying that sum by 3. If the 4th term in the sequence is 186, what is the 2nd term?

A. 2
B. 4
C. 18
D. 60
E. 174

13. Which of the following values of x does NOT satisfy the inequality |x-3|≥12?

F. -15
G. -12
H. -9
J. 9
K. 15

14. For all real numbers s, t, u, and v, such that s + t + u = 29 and s < v, which of the following statements is true?

A. s + t + v < 29
B. t + u + v > 29
C. s + t + v = 29
D. s + u + v = 29
E. s + t + v > 29

15. In the figure below, rectangle ABCD shares with CDE, diagonal of the rectangle extends in a straight line beyond D to E to create , and the measure of CDE is 155°. What is the measure of CBD?

F. 25
G. 55
H. 65
J. 90
K. 155