ACT math practice test 42

1. For i2 = -1, (5 - i)2= ?

F. 24
G. 26
H. 24 - 5i
J. 24 - 10i
K. 26 + 10i

2. If x and y are integers such that y > 12 and 2x + y = 19, which of the following is the solution set for x?

A. x ≥ 4
B. x ≥ 3
C. x ≤ 4
D. x ≤ 3
E. x ≤ 0

3. If pq3T4 > 0, which of the following products must be positive?

F. pq
G. pt
H. qt
J. pqt
K. pq2

4. If log3 81 = x + 1, then x = ?

A. 3
B. 4
C. 5
D. 6
E. 243

5. In imageRST below, imageS is a right angle, image = 7 units, and image = 2 units. What does csc imageT equal?

image

F. image
G. image
H. image
J. image
K. image

6. A flight instructor charges $75 per lesson, plus an additional fee for the use of his plane. The charge for the use of his plane varies directly with the cube root of the time the plane is used. If a lesson plus 27 minutes of plane usage costs $120, what is the total amount charged for a lesson involving 64 minutes of plane usage?

A. $195
B. $180
C. $157
D. $135
E. $60

7. In ΔABD shown below, c is on image, imageimage, the length of image is 6 inches, the length of image is 10 inches, and sin d = 0.8. What is the area of ΔABD in square inches?

image

F. 6
G. 12
H. 24
J. 30
K. 60

8. For real numbers x and y, when is the equation |2x + 3y| = |2x - 3y| true?

A. Never
B. Always
C. Only when 2x = 3y
D. Only when x = 0 and y = 0
E. Only when x = 0 or y = 0

9. In the figure below, all line segments that intersect are perpendicular. Using only the segments and vertices in the figure, how many distinct rectangles are there with areas less than the area of ADLI?

(Note: If 2 rectangles have all four vertices in common, then they are not distinct.)

image

F. 7
G. 8
H. 17
J. 18
K. 19

10. For some real number a, the graph of y = (a + 3)x + 5 in the standard (x, y) coordinate plane passes through the point (3, 11). What is the slope of this line?

A. -5
B. -2
C. -1
D. 2
E. 5image

11. In the figure below, image is a line segment and all distances are given in inches. What is the ratio of the area of quadrilateral RBCS to the area of quadrilateral SCFT?

image

F. 9:7
G. 7:9
H. 11:13
J. 11:39
K. 11:50

12. When graphed in the standard (x, y) coordinate plane, the graphs of y = x2 - 5 and y = x + 1 intersect at which of the following points?

A. (-3, 2) and (2, 3)
B. (-3, 4) and (2, -1)
C. (3, -4) and (-2, 1)
D. (3, 4) and (-2, -1)
E. The graphs do not intersect.

13. In septagon ABCDEFG shown below, imagea = 115° and imageg = 70°. What is the sum of the measures of the other 5 interior angles?

image

F. 585°
G. 595°
H. 655°
J. 690°
K. 715°

14. For all real numbers x and y such that the product of y and 4 is x, which of the following expressions represents the sum of y and 4 in terms of x?

A. x + 4
B. 4x + 4
C. 4(x + 4)
D. image
E. image

15. What is cos image given that image = image + image and that cos (a+b) = cos a (cos b) - sin a (sin b)?

(Note: You may use the following table of values.)

image

F. image
G. - image
H. image
J. 0.999
K. image