ACT Math Practice Test 2 (free, online, with answers)
45 questions · 50 minutes · 4 choices · calculator on screen · estimated score 1-36 · step-by-step answers
How it works
- Like the ACT math test: 45 questions in 50 minutes, about a minute each. The questions get harder as you go. Solve it right here on the screen: no sign-up.
- Every question has 4 choices (A to D). A wrong answer costs nothing, so answer every question.
- One question at a time. Use Back and Next, or the question list at the bottom. Mark for review the ones you want to look at again.
- A timer counts down (you can hide it; it shows again in the last 5 minutes). At 0:00 the test ends. Before you submit, Check your work shows what is answered.
- A calculator is allowed for the whole test, as on the ACT. There is no formula sheet: the ACT does not give one either (our formula sheets help you learn them).
- At the end: your estimated ACT math score (1-36), your result in each area, and every question marked right or wrong, with the right answer, why your choice was wrong, and its step-by-step solution.
Your answers are kept in this browser, so you can close the page and come back.
1 Question 1
If 5x + 8 = 43, what is the value of x?- A) 7
- B) 515
- C) 35
- D) 175
2 Question 2
A pair of shoes costs $80. It is on sale for 25% off. What is the sale price?- A) $20
- B) $55
- C) $60
- D) $100
3 Question 3
Which expression is equivalent to √72?- A) 2√6
- B) 6√2
- C) 6√12
- D) 36√2
4 Question 4
A bag has 6 red, 2 blue and 4 yellow marbles. One marble is picked at random. What is the probability that it is yellow?- A) 112
- B) 13
- C) 12
- D) 23
5 Question 5
Three angles meet on a straight line. Two of them measure 40° and 65°. What is the measure of the third angle?- A) 75°
- B) 105°
- C) 115°
- D) 255°
6 Question 6
Six pens cost $4.80. Each pen costs the same. What is the cost of one pen?- A) $0.80
- B) $1.25
- C) $10.80
- D) $28.80
7 Question 7
If x4 + 3 = 7, what is the value of x?- A) 1
- B) 16
- C) 25
- D) 40
8 Question 8
The function f is defined by f(x) = −2x2 + 5x. What is the value of f(3)?- A) −33
- B) −3
- C) 33
- D) 51
9 Question 9
For i = √−1, what is the value of i14?- A) −1
- B) −i
- C) 1
- D) i
10 Question 10
The mean of 6 test scores is 80. What score on the next test makes the mean 82?- A) 12
- B) 82
- C) 84
- D) 94
11 Question 11
A rectangle is 12 cm long and 7.5 cm wide. What is its area, in square centimeters?- A) 19.5
- B) 39
- C) 90
- D) 180
12 Question 12
What is the solution (x, y) of the system x + 3y = 13 and 2x − 3y = 8?- A) (2, 7)
- B) (7, 2)
- C) (7, 6)
- D) (7, 203)
13 Question 13
How many meters are in 2.5 kilometers?- A) 0.0025
- B) 25
- C) 250
- D) 2500
14 Question 14
What is the 15th term of the arithmetic sequence 7, 4, 1, −2, ...?- A) −42
- B) −38
- C) −35
- D) 49
15 Question 15
A right triangle has a hypotenuse of length 25 and one leg of length 7. What is the length of the other leg?- A) 18
- B) 24
- C) √674
- D) 576
16 Question 16
What is 0.00072 written in scientific notation?- A) 7.2 × 10−5
- B) 7.2 × 10−4
- C) 7.2 × 10−3
- D) 7.2 × 104
17 Question 17
A club of 10 students chooses 3 of them to plan a trip. How many different groups of 3 are possible?- A) 30
- B) 120
- C) 720
- D) 1000
18 Question 18
y varies inversely with x. y = 12 when x = 3. Find y when x = 9.- A) 4
- B) 18
- C) 36
- D) 108
19 Question 19
What is the value of log_5(125)?- A) 3
- B) 25
- C) 120
- D) 625
20 Question 20
Two parallel lines are cut by a transversal. Two alternate interior angles measure (5x − 15)° and (3x + 25)°. What is the value of x?- A) 5
- B) 20
- C) 21.25
- D) 85
21 Question 21
A price goes from $80 to $92. What is the percent increase?- A) 12%
- B) 13%
- C) 15%
- D) 115%
22 Question 22
What are the solutions of 2x2 + 5x − 3 = 0?- A) −3 and 12
- B) −3 and 1
- C) −32 and 1
- D) −12 and 3
23 Question 23
15 freshmen come to school by bus and 25 by car; 18 sophomores come by bus and 12 by car. A sophomore is picked at random. What is the probability that the sophomore comes by car?- A) 635
- B) 1237
- C) 25
- D) 35
24 Question 24
In a right triangle, one angle measures 28° and the side adjacent to it is 15 m. What is the length of the side opposite the 28° angle, to the nearest tenth of a meter?- A) 7.0
- B) 8.0
- C) 13.2
- D) 28.2
25 Question 25
If f(x) = 3x − 6, which of the following is the inverse function f−1(x)?- A) (x − 6)/3
- B) (x + 6)/3
- C) 3x + 6
- D) 1/(3x − 6)
26 Question 26
What is the dot product of the vectors <3, −1> and <2, 4>?- A) 2
- B) 6
- C) 8
- D) 10
27 Question 27
A cone has radius 6 cm and height 10 cm. Using 3.14 for π, what is its volume, in cubic centimeters?- A) 62.8
- B) 376.8
- C) 1130.4
- D) 1507.2
28 Question 28
What are all the solutions of- A) −13 and 5
- B) −5 and 13
- C) 5 only
- D) −9 and 9
29 Question 29
What is the remainder when x3 − 2x2 + 4x − 5 is divided by x − 2?- A) −29
- B) 1
- C) 3
- D) 8
30 Question 30
A bag has 2 green and 8 yellow marbles. Two marbles are picked at random, without replacement. What is the probability that both are yellow?- A) 145
- B) 2845
- C) 1625
- D) 45
31 Question 31
Triangle ABC is similar to triangle DEF, with AB = 4, BC = 6, CA = 8 and DE = 10, EF = x, FD = 20. What is the value of x?- A) 2.4
- B) 12
- C) 15
- D) 60
32 Question 32
What is the slope of the line through (−2, 5) and (4, −1)?- A) −6
- B) −1
- C) 1
- D) 2
33 Question 33
A floor is a 10 m by 6 m rectangle with a semicircle on one 6 m end. Using 3.14 for π, what is its area, in square meters?- A) 60
- B) 74.13
- C) 88.26
- D) 116.52
34 Question 34
$2,000 is invested at 5% interest compounded yearly. How much is in the account after 2 years?- A) $2100
- B) $2200
- C) $2205
- D) $4500
35 Question 35
In a game, you win $12 with probability 16 and lose $3 otherwise. What is the expected value of one game?- A) -$0.50
- B) $0.50
- C) $2
- D) $9
36 Question 36
What is the exact value of sin 135°?- A) −√22
- B) 12
- C) √22
- D) √32
37 Question 37
Ana can paint a fence in 12 hours. Ben can paint the same fence in 4 hours. Working together, how many hours will it take them?- A) 13
- B) 3
- C) 8
- D) 16
38 Question 38
If 52x = 125, what is the value of x?- A) 32
- B) 3
- C) 12.5
- D) 25
39 Question 39
For i = √−1, which of the following equals 3 + i1 − i?- A) 1 + 2i
- B) 2 + 2i
- C) 2 + 4i
- D) 3 − i
40 Question 40
Each interior angle of a regular polygon measures 150°. How many sides does the polygon have?- A) 6
- B) 12
- C) 15
- D) 30
41 Question 41
What is the mean of 14, 9, 22, 17, 13, 9?- A) 9
- B) 13.5
- C) 14
- D) 16.8
42 Question 42
What is the 60th digit after the decimal point of 57?- A) 1
- B) 5
- C) 7
- D) 10
43 Question 43
What is the sum of the first 6 terms of the geometric sequence 3, 6, 12, ...?- A) 96
- B) 189
- C) 192
- D) 381
44 Question 44
In triangle ABC, side a = 8, side b = 11 and angle C = 50°. What is the area of the triangle, to the nearest tenth?- A) 28.3
- B) 33.7
- C) 44
- D) 67.4
45 Question 45
A class of 24 students has a mean score of 70. A class of 16 students has a mean score of 80. What is the mean score of all 40 students?- A) 74
- B) 75
- C) 76
- D) 2960
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