ACT math practice test 28

1. A rectangular solid consisting of 18 smaller cubes that are identical is positioned in the standard (x,y,z) coordinate system, as shown below. Vertex M has coordinates of (-1,3,0) and point O on the y-axis has coordinates of (0,3,0). What are the coordinates of vertex N?

F. (3,0, 2)
G. (2,2, 0)
H. (3,0,-1)
J. (0,2, 2)
K. (2,0, 2)

2. What is the median of the data given below?

18, 25, 19, 41, 23, 29, 35, 19

A. 32
B. 26
C. 25
D. 24
E. 19

3. Let ab = (-2a - b)2 for all integers a and b. Which of the following is the value of ?

F. -15
G. -2
H. 49
J. 91
K. 109

4. For all negative even integers x, which of the following is a correct ordering of the terms x, xx, ((–x)!)x, and ((–x)!)(–x)!?

A. ((-x)!)(-x)! ≥ ((-x)!)xxxx
B. ((-x)!)(-x)!xx ≥ ((-x)!)xx
C. xxx ≥ ((-x)!)(-x)! ≥ ((-x)!)x
D. xx ≥ ((-x)!)xx ≥ ((-x)!)(-x)!
E. x ≥ ((-x)!)xxx ≥ ((-x)!)(-x)!

5. What is the perimeter of quadrilateral STUR if it has vertices with (x,y) coordinates S(0,0), T(2,-4), U(6,-6), R(4,-2) ?

F. 2
G. 2 + 2
H. 8
J. 80
K. 400

6. The line with equation 5y - 4x = 20 does NOT lie in which quadrant(s) of the standard (x, y) coordinate plane below?

A. Quadrant I only
B. Quadrant II only
C. Quadrant III only
D. Quadrant IV only
E. Quadrants I and III only

7. The figure below shows representations of the first 4 triangular numbers, through . What is the value of ?

F. 144
G. 168
H. 288
J. 300
K. 600

8. The four midpoints of the sides of a square represent four points on a circle. Line segments connect the opposing corners of the square. This circle and these line segments divide the square into how many individual, non-overlapping regions of nonzero area?

A. 4
B. 5
C. 10
D. 12
E. 24

9. The circumference of a circle is 50 inches. How many inches long is its radius?

J. 50π
K. 100π

10. In the (x,y) coordinate plane, what is the diameter of the circle having its center at (-6,1) and (0,9) as one of the endpoints of a radius?

A. 10
B. 14
C. 20
D. 28
E. 100

11. The graph of the function f(x) = is shown in the standard (x,y) coordinate plane below. Which of the following, if any, is a list of each of the vertical asymptotes of f(x)?

F. This function has no vertical asymptote.
G. y = x + 1
H. y = 2x – 1
J. x = -1 and x = 2
K. x = 1

12. The product of 2 distinct positive prime numbers is an even number, and one less than the product is a prime number. All of the following prime numbers could be one of the original prime numbers EXCEPT:

A. 2
B. 3
C. 5
D. 7
E. 19

13. Connecting the midpoints of opposite sides of any quadrilateral to the midpoints of the adjacent sides must always create which of the following?

F. Point
G. Line
H. Circle
J. Square
K. Parallelogram

14. If a(x) = b(x) + c(x), where b(x) = 3x2 - 8x + 113 and c(x) = - 3x2 + 18x + 7 and x is an integer, then a(x) is always divisible by which of the following?

A. 6
B. 7
C. 10
D. 12
E. 15

15. Isosceles triangle T1 has a base of 12 meters and a height of 20 meters. The vertices of a second triangle T2 are the midpoints of the sides of T1. The vertices of a third triangle, T3, are the midpoints of the sides of T2. Assume the process continues indefinitely, with the vertices of Tk+1 being the midpoints of the sides of Tk for every positive integer k. What is the sum of the areas, in square meters, of T1, T2, T3, …?

F. 30
G. 40
H. 120
J. 144
K. 160