ACT Math Practice Questions with Answers & Step-by-Step Solutions

Correct Answer: B. 5

Step-by-step solution:

Start with: 3x+7=22

Subtract 7 from both sides:

3x=15

Divide both sides by 3:

x=5

Correct Answer: C. $50

Step-by-step solution:

Find 25% of $40:

0.25 × 40 = 10

Add the increase to the original price:

40 + 10 = 50

So the new price is $50.

Correct Answer: C. 26

Step-by-step solution:

Substitute a = 4 and b = 6:

2a + 3b = 2(4) + 3(6)

= 8 + 18

= 26

Correct Answer: B. 2

Step-by-step solution:

Use the slope formula:

Slope = (y₂ − y₁) ÷ (x₂ − x₁)

= (11 − 3) ÷ (6 − 2)

= 8 ÷ 4

= 2

So the slope is 2.

Correct Answer: B. 30

Step-by-step solution:

Use the triangle area formula:

A = ½bh

Where

• b = base
• h = height
  

Shortcut: Multiply the base and height first, then divide by 2.

Correct Answer: C. 40

Step-by-step solution:

The ratio is: 3:5

3 parts represent 24 boys.

One part is:

24 ÷ 3 = 8

Girls are 5 parts:

5 × 8 = 40

So there are 40 girls.

Correct Answer: A. x⁷

Step-by-step solution:

When multiplying powers with the same base, add the exponents:

x³ · x⁴ = x³⁺⁴

= x⁷

Correct Answer: B. 87.5

Step-by-step solution:

Add the scores:

80 + 85 + 90 + 95 = 350

Divide by the number of scores:

350 ÷ 4 = 87.5

So the mean is 87.5.

Correct Answer: B. 3/12

Step-by-step solution:

Total marbles:

4 + 3 + 5 = 12

Blue marbles: 3

Probability = 3/12

This can also simplify to ¼, but the exact matching answer is 3/12.

Correct Answer: A. 10

Step-by-step solution:

For any right triangle, use the Pythagorean Theorem: a²+b²=c²

where:

• a and b are the legs
• c is the hypotenuse (the longest side)

So:

a²+b²=c²
6² + 8² = c²
Calculate the squares:
36 + 64 = c²
100 = c²
Take the square root of both sides:
c = √100
c = 10
Therefore:
The hypotenuse is 10 units long.

Shortcut: Recognize the common 3–4–5 triangle pattern.

Since:
3 : 4 : 5
and
6 : 8 : 10 = (3×2) : (4×2) : (5×2)
the hypotenuse must be 10.

Correct Answer: B. (x + 2)(x + 3)

Step-by-step solution:

Find two numbers that multiply to 6 and add to 5.

Those numbers are 2 and 3.

So:

x² + 5x + 6 = (x + 2)(x + 3)

Correct Answer: C. (6,4)

Step-by-step solution:

Add the two equations:

x + y = 10

x - y = 2

Adding gives:

2x = 12

x = 6

Substitute into x + y = 10:

6 + y = 10

y = 4

So the solution is (6,4).

Correct Answer: C. 29

Step-by-step solution:

Substitute x = 4:

f(4) = 2(4)² - 3

= 2(16) - 3

= 32 - 3

= 29

Correct Answer: C. x > 7

Step-by-step solution:

Add 5 to both sides:

2x > 14

Divide by 2:

x > 7

Correct Answer: D. x = 9 or x = -9

Step-by-step solution:

Absolute value means distance from 0.

Both 9 and -9 are 9 units away from 0.

So:

x = 9 or x = -9

Correct Answer: C. 49π

Step-by-step solution:

Use:

A = πr²

The radius is 7:

A = π(7)²

A = 49π

Correct Answer: C. 5

Step-by-step solution:

Find the change in x:

4 - 1 = 3

Find the change in y:

6 - 2 = 4

Use the Pythagorean Theorem:

3² + 4² = c²

9 + 16 = 25

c = 5

Correct Answer: B. y = 3x + 2

Step-by-step solution:

Slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

Here:

m = 3

b = 2

So:

y = 3x + 2

Correct Answer: B. $60

Step-by-step solution:

Use:

I = Prt

Where:
·  I = Interest earned
·  P = Principal (the original amount invested or borrowed)
·  r = Annual interest rate (written as a decimal)
·  t = Time (usually in years)

I = 500(0.06)(2)

I = 60

So the interest earned is $60.

Correct Answer: B. 10

Step-by-step solution:

The numbers are already in order.

The middle number is:

10

So the median is 10.

Correct Answer: C. 12

Step-by-step solution:

Let the number be x.

"Increased by 7" means:

x + 7

So:

x + 7 = 19

Subtract 7 from both sides:

x = 12

Correct Answer: B. 8

Step-by-step solution:

Cross multiply:

3x = 6 × 4

3x = 24

Divide by 3:

x = 8

Correct Answer: B. 4.5 × 10⁴

Step-by-step solution:

Move the decimal so the number is between 1 and 10:

45,000 = 4.5

The decimal moved 4 places.

So:

45,000 = 4.5 × 10⁴

Correct Answer: B. 9

Step-by-step solution:

9 × 9 = 81

So:

√81 = 9

Correct Answer: A. y = 4x + 3

Step-by-step solution:

Parallel lines have the same slope.

The slope of:

y = 4x - 1

is 4.

The equation with slope 4 is:

y = 4x + 3

Correct Answer: C. 26

Step-by-step solution:

Use:

P = 2l + 2w

P = 2(9) + 2(4)

P = 18 + 8

P = 26

Correct Answer: D. 60

Step-by-step solution:

Use:

V = lwh

V = 5 × 3 × 4

V = 60

Correct Answer: B. 70°

Step-by-step solution:

The angles in a triangle add to:

180°

Add the known angles:

50 + 60 = 110

Subtract from 180:

180 - 110 = 70

So the third angle is 70°.

Correct Answer: A. 3/5

Step-by-step solution:

Sine is:

sin θ = opposite ÷ hypotenuse

sin θ = 6/10

Simplify:

6/10 = 3/5

Correct Answer: C. 25

Step-by-step solution:

Take half of the coefficient of x:

10 ÷ 2 = 5

Square it:

5² = 25

So add 25.

x² + 10x + 25 = (x + 5)²

Correct Answer: C. 24

Step-by-step solution:

Find the pattern:

9 - 4 = 5

14 - 9 = 5

19 - 14 = 5

Each term increases by 5.

Next:

19 + 5 = 24

Correct Answer: D. 48

Step-by-step solution:

Each term is multiplied by 2:

3 × 2 = 6

6 × 2 = 12

12 × 2 = 24

Next:

24 × 2 = 48

Correct Answer: B. (5,7)

Step-by-step solution:

Use the midpoint formula:

((x₁ + x₂)/2, (y₁ + y₂)/2)

Substitute the values:

((2 + 8)/2, (4 + 10)/2)

= (10/2, 14/2)

= (5,7)

Correct Answer: A.

[6 4]
[2 10]

Step-by-step solution:

Add matching positions:

1 + 5 = 6

3 + 1 = 4

2 + 0 = 2

4 + 6 = 10

So:

[6 4]
[2 10]

Correct Answer: B. 7 - 3i

Step-by-step solution:

Add the real parts:

3 + 4 = 7

Add the imaginary parts:

2i + (-5i) = -3i

So:

(3 + 2i) + (4 - 5i) = 7 - 3i

Correct Answer: B. 3

Step-by-step solution:

log₂ 8 = x means:

2^x = 8

Since:

2³ = 8

x = 3

Correct Answer: B. x = 2, 3

Step-by-step solution:

Factor:

x² - 5x + 6 = (x - 2)(x - 3)

Set each factor equal to 0:

x - 2 = 0

x = 2

x - 3 = 0

x = 3

So:

x = 2, 3

Correct Answer: C. 20

Step-by-step solution:

Direct variation means:

y = kx

Use y = 12 and x = 3:

12 = 3k

k = 4

Now use x = 5:

y = 4(5)

y = 20

Correct Answer: B. 6

Step-by-step solution:

There are 3 choices for the first position.

After that, 2 choices remain for the second position.

Then 1 choice remains for the last position.

3 × 2 × 1 = 6

So there are 6 ways.

Correct Answer: B. C = 2m + 4

Step-by-step solution:

The taxi charges $2 for each mile, so the mileage cost is:

2m

There is also a flat fee of $4.

Add them:

C = 2m + 4