ACT Math Practice Test 102

1. If log₄ x = 3, then x = ?

• A.
• B. 4 log³
• C. 12
• D. 64
• E. 81

2. If a system of 2 linear equations in 2 variables has NO solution, and 1 of the equations is graphed in the (x,y) coordinate plane below, which of the following could be the other equation?

• F. y = -2
• G.
• H. y = -2x - 4
• J.
• K. y = 4x - 4

3. A certain resort has 60 rooms. Based on many previous years' occupancy rates, the manager created the table below showing the daily occupancy rates and their probability of occurring for the next tourist season. Based on the probability distribution in the table, to the nearest whole number, what is the expected number of rooms that will be occupied on any day during the next tourist season?

• A. 25
• B. 38
• C. 45
• D. 52
• E. 60

4. In the standard (x,y) coordinate plane, what is the equation of the line that passes through the origin and the point (3,4)?

• F.
• G.
• H.
• J.
• K.

5. The measure of the vertex angle of an isosceles triangle is (a + 30)°. The base angles each measure (2a - 15)°. What is the measure in degrees of one of the base angles?

• A. 36°
• B. 45°
• C. 57°
• D. 66°
• E. 90°

6. What is the smallest possible value for the product of 2 integers that differ by 7?

• F. 8
• G. 0
• H. -6
• J. -10
• K. -12

7. Three distinct lines, all contained within a plane, separate that plane into distinct regions. What are all of the possible numbers of distinct regions of the plane that could be separated by any such three lines?

• A. 4, 6, 7
• B. 4, 5, 6
• C. 3, 5, 7
• D. 3, 5, 6
• E. 3, 4, 5

8. Given the vertices of parallelogram QRST in the standard (x, y) coordinate plane below, what is the area of triangle QRS, in square units?

• F. 24
• G. 28
• H. 48
• J. 60
• K. 80

9. The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?

• A. (ab)⁶⁴²
• B. (ab)⁶⁴³
• C. a⁶⁴²b
• D. a⁶⁴³b
• E. ab⁶⁴²

10. Points A, B, and C are three distinct points that lie on the same line. If the length of AB is 19 meters and the length of BC is 13 meters, then what are all the possible lengths, in meters, for AC?

• F. 6 only
• G. 32 only
• H. 6 and 32 only
• J. Any number less than 32 or greater than 6
• K. Any number greater than 32 or less than 6