ACT Math Practice Test 1 (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 3x − 7 = 20, what is the value of x?- A) 133
- B) 9
- C) 27
- D) 81
2 Question 2
A jacket costs $60. The sales tax is 5%. What is the total cost?- A) $3
- B) $57
- C) $63
- D) $65
3 Question 3
Which expression is equivalent to √50?- A) 2√5
- B) 5√2
- C) 10√5
- D) 25√2
4 Question 4
A bag has 3 red, 5 blue and 4 green marbles. One marble is picked at random. What is the probability that it is blue?- A) 112
- B) 512
- C) 57
- D) 712
5 Question 5
Two angles form a straight line. One of them measures 128°. What is the measure of the other angle?- A) 52°
- B) 128°
- C) 232°
- D) 308°
6 Question 6
A car travels 195 miles in 3 hours at a steady speed. How many miles does it travel in 1 hour?- A) 65
- B) 192
- C) 198
- D) 585
7 Question 7
If 6(x − 2) = 4x + 10, what is the value of x?- A) −1
- B) 2.2
- C) 6
- D) 11
8 Question 8
The function f is defined by f(x) = 3x2 − 2x + 4. What is the value of f(−1)?- A) 3
- B) 5
- C) 9
- D) 15
9 Question 9
For i = √−1, what is (4 + 3i) − (1 − 2i)?- A) 3 + i
- B) 3 + 5i
- C) 5 + i
- D) 5 + 5i
10 Question 10
Ravi's test scores are 78, 84, 81 and 85. What score on the next test makes his mean 83?- A) 4
- B) 83
- C) 84
- D) 87
11 Question 11
A circle has a radius of 7 inches. Using 3.14 for π, what is its area, in square inches?- A) 21.98
- B) 43.96
- C) 153.86
- D) 615.44
12 Question 12
What is the solution (x, y) of the system 2x + y = 11 and x − y = 1?- A) (3, 4)
- B) (4, 3)
- C) (4, 5)
- D) (12, 11)
13 Question 13
How many inches are in 3.5 feet?- A) 10.5
- B) 15.5
- C) 35
- D) 42
14 Question 14
What is the 20th term of the arithmetic sequence 5, 8, 11, 14, ...?- A) 57
- B) 62
- C) 65
- D) 100
15 Question 15
A right triangle has legs of length 8 and 15. What is the length of the hypotenuse?- A) 7
- B) 17
- C) 23
- D) 289
16 Question 16
What is (3 × 104)(2.5 × 103)?- A) 7.5 × 101
- B) 5.5 × 107
- C) 7.5 × 107
- D) 7.5 × 1012
17 Question 17
A café offers 4 sandwiches, 3 soups and 2 drinks. A lunch is one sandwich, one soup and one drink. How many different lunches are there?- A) 6
- B) 9
- C) 12
- D) 24
18 Question 18
If 5x = 1524, what is the value of x?- A) 3
- B) 8
- C) 14
- D) 72
19 Question 19
What is the value of log_2(32)?- A) 5
- B) 16
- C) 30
- D) 64
20 Question 20
What is the distance between the points (2, 1) and (8, 9) in the standard (x, y) coordinate plane?- A) 10
- B) 10√2
- C) 14
- D) 100
21 Question 21
21 is 35% of what number?- A) 7.35
- B) 56
- C) 60
- D) 735
22 Question 22
What are the solutions of x2 + 3x − 28 = 0?- A) −14 and 2
- B) −7 and 4
- C) −4 and 7
- D) 4 and 7
23 Question 23
In a survey, 12 juniors chose art and 18 chose music; 20 seniors chose art and 10 chose music. A student who chose art is picked at random. What is the probability that the student is a senior?- A) 13
- B) 38
- C) 58
- D) 23
24 Question 24
In a right triangle, one angle measures 35° and the hypotenuse is 20 cm. What is the length of the side opposite the 35° angle, to the nearest tenth of a centimeter?- A) 11.5
- B) 14.0
- C) 16.4
- D) 34.9
25 Question 25
If f(x) = x2 − 2 and g(x) = 3x + 1, what is f(g(1))?- A) −4
- B) −2
- C) 14
- D) 16
26 Question 26
What is the determinant of the matrix [3 2; 5 4]?- A) −2
- B) 2
- C) 7
- D) 22
27 Question 27
A can is a cylinder with radius 3 cm and height 8 cm. Using 3.14 for π, what is its volume, in cubic centimeters?- A) 75.36
- B) 150.72
- C) 226.08
- D) 602.88
28 Question 28
What are all the solutions of- A) 5 only
- B) −2 and 5
- C) −5 and 2
- D) 2 and 5
29 Question 29
The function f is defined by f(x) = 2x − 1 for x < 3 and f(x) = x2 for x ≥ 3. What is f(3)?- A) 5
- B) 6
- C) 9
- D) 14
30 Question 30
A bag has 5 red and 7 blue marbles. Two marbles are picked at random, without replacement. What is the probability that both are red?- A) 533
- B) 25144
- C) 512
- D) 103132
31 Question 31
What is the midpoint of the segment with endpoints (−3, 4) and (5, 10)?- A) (1, 7)
- B) (2, 14)
- C) (4, 3)
- D) (8, 6)
32 Question 32
What is the slope of the line through (1, −2) and (4, 7)?- A) 13
- B) 53
- C) 3
- D) 9
33 Question 33
A rectangular garden is 10 m by 7 m. A 3 m by 2 m rectangle inside it is a pond. What is the area of the garden without the pond, in square meters?- A) 6
- B) 64
- C) 70
- D) 76
34 Question 34
$1,500 is invested at 2% interest compounded yearly. To the nearest cent, how much is in the account after 3 years?- A) $1530.00
- B) $1590.00
- C) $1591.81
- D) $2592.00
35 Question 35
In a game, you win $10 with probability 14 and lose $2 otherwise. What is the expected value of one game?- A) $1
- B) $2
- C) $2.50
- D) $8
36 Question 36
In triangle ABC, side a = 5, side b = 8 and angle C = 60°. What is the length of side c?- A) 7
- B) √89
- C) √129
- D) 13
37 Question 37
Two cars start 420 km apart and drive toward each other, one at 65 km/h and the other at 75 km/h. After how many hours do they meet?- A) 3
- B) 6
- C) 6.5
- D) 42
38 Question 38
If 3x − 1 = 81, what is the value of x?- A) 3
- B) 4
- C) 5
- D) 28
39 Question 39
For i = √−1, which of the following equals (3 + 2i)(1 − i)?- A) 1 − i
- B) 5 − i
- C) 5 − 5i
- D) 5 + 5i
40 Question 40
What is the measure of each interior angle of a regular octagon?- A) 45°
- B) 135°
- C) 157.5°
- D) 1080°
41 Question 41
What is the median of 12, 7, 15, 9, 20, 11?- A) 11.5
- B) 12
- C) 12.33
- D) 13.5
42 Question 42
What is the ones digit of 347?- A) 1
- B) 3
- C) 7
- D) 9
43 Question 43
What is the 7th term of the geometric sequence 2, 6, 18, 54, ...?- A) 26
- B) 486
- C) 1458
- D) 4374
44 Question 44
In triangle ABC, angle A = 40°, angle B = 65° and side a = 12. What is the length of side b, to the nearest tenth?- A) 8.5
- B) 10.9
- C) 16.9
- D) 19.5
45 Question 45
A class of 18 students has a mean score of 75. A class of 12 students has a mean score of 85. What is the mean score of all 30 students?- A) 79
- B) 80
- C) 81
- D) 2370
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