ACT math practice test 15

1. The kinetic energy, KE, of an object travelling at v velocity can be modeled by the equation KE = mv2, where m is the mass of the object. If an object is moving at a velocity of 9, and it has a kinetic energy of 120, about how great is the object's mass?

A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. 6
E. 13

2. Let x, y, and z be distinct positive integers. What is the fourth term of the geometric sequence below?

2xz, 2x2yz, 2x3y2z,…

F. 2x2yz
G. 2x4y3z
H. 2x3yz2
J. 4x3y2z
K. 4x4y3z2

3. A recent survey of book critics asked 30 critics how many stars out of a possible 5 they gave to a recent novel from a popular author. The 30 critics' responses are summarized by the histogram below.

What fraction of the critics gave the book a one-star review?

A.
B.
C.
D.
E.

4. A recent survey of book critics asked 30 critics how many stars out of a possible 5 they gave to a recent novel from a popular author. The 30 critics' responses are summarized by the histogram below.

The group that took the survey wants to show the data in a circle graph (pie chart). What should be the measure of the central angle of the portion for one-star reviews?

F. 15°
G. 24°
H. 30°
J. 48°
K. 60°

5. A recent survey of book critics asked 30 critics how many stars out of a possible 5 they gave to a recent novel from a popular author. The 30 critics' responses are summarized by the histogram below.

To the nearest hundredth, what is the average star review for the 30 reviews?

A. 2
B. 2.33
C. 2.5
D. 2.63
E. 3

6. For all x > 8, = ?

F.
G.
H.
J.
K. 1

7. A rock band, The Young Sohcahtoans, is trying to design a t-shirt logo. The measurements they have chosen are represented on the figure below. The angle to the right of the logo "TYS" has a degree measure of 35°, and the side of the figure has a measure of 10 in. Which of the following expressions gives the measure, in inches, of the diagonal top side of the figure?

A. 10 tan 35°
B. 10 cos 35°
C. 10 sin 35°
D.
E.

8. The endpoints of the diameter of a circle O are A and C. In the standard (x,y) coordinate plane, A is at (4,3) and C is at (-9,-2). What is the y-coordinate of the center of the circle?

F. -5
G. -
H.
J. 1
K. 2

9. On a sonar map in the standard (x,y) coordinate plane, the Yellow Submarine and the Sandwich Submarine are located at the points (-7,4) and (-2,6), respectively. Each unit on the map represents an actual distance of 5 nautical miles. Which of the following is closest to the distance, in nautical miles, between the two submarines?

A. 5
B. 19
C. 27
D. 30
E. 67

10. All of the following statements about rational and/or irrational numbers must be true EXCEPT:

F. the sum of any two rational numbers is rational.
G. the product of any two rational numbers is rational.
H. the sum of any two irrational numbers is irrational.
J. the product of a rational and an irrational number may be rational or irrational.
K. the product of any two irrational numbers is irrational.

11. For the imaginary number i, which of the following is a possible value of in if n is an integer less than 5?

A. 0
B. -1
C. -2
D. -3
E. -4

12. The table below gives the values of f(x) for selected values of x in the function f(x) = (x + 4)2 - 1, where x and y are both real numbers.

xf(x)
-78
-50
-30
-18
015
124

For the equation above, which of the following values of x gives the greatest value of f(x)?

F. -4
G. -5
H. -6
J. -7
K. -8

13. The volume of the right circular cylinder shown below is 64π cubic inches. If its height is 4 in., what is its radius in., what is its radius in inches?

A. 2
B. 4
C. 8
D. 10
E. 16

14. Line segments , , and are parallel and intersect line segments and as shown in the figure below. The ratio of the perimeter of ΔFJK to the perimeter of ΔFLM is 3:5, and the ratio of to is 1:5. What is the ratio of to ?

F. 1:05
G. 1:03
H. 1:02
J. 2:01
K. 5:03

15. Avi is trying to draw a map of his most recent bike ride. He chose to place Market Street on the x-axis and Broad Street on the y-axis. He rode 60 m at an angle of 60° relative to Market Street, then rode 100 m at an angle of 45° relative to Market Street, and finally rode 35 m directly north on Broad Street. How many meters north of Market Street did Avi ride?

A. 35
B. 115
C. 195
D. 50 + 30
E. 35 + 50 + 30