The SAT plays a vital role in college admissions, and the math section is a significant part of the test. To aid in your preparation, we’ve created an extensive SAT Math practice test that includes all the essential topics and question types you’ll face on exam day.
Each section is designed to mirror the format and content of the actual SAT Math test, giving you a realistic practice experience.
In addition to the practice test, the blog post includes valuable tips and strategies to help you approach each question type effectively. We cover topics such as:
- Time management and pacing
- Strategies for tackling different question formats
- Techniques for eliminating wrong answers
- Approaching word problems and data analysis questions
Time: 60 minutes
SAT Math Practice Test
Directions:
For each of the following questions, select the best answer from the options provided. A calculator may be used for all questions unless otherwise noted
Directions
This test consists of 25 multiple-choice questions and 1 bonus question. For each question, choose the best answer from the options provided. You may use scratch paper for calculations. Calculators are permitted but not required.
Questions
1.
If x + 5 = 11, what is the value of x?
A) 4
B) 5
C) 6
D) 7
2.
What is the value of (2/3) + (1/6)?
A) 1/2
B) 2/3
C) 5/6
D) 1
3.
A rectangular field has a length of 50 meters and a width of 30 meters. What is the perimeter of the field in meters?
A) 80
B) 100
C) 160
D) 1,500
4.
If 3x – 2 = 16, what is the value of x?
A) 4
B) 5
C) 6
D) 7
5.
A group of friends decided to split the cost of a \$75 dinner bill equally. If there were 5 friends, how much should each person pay?
A) \$10
B) \$15
C) \$20
D) \$25
6.
What is the value of 2x + 3y when x = 4 and y = -2?
A) 2
B) 5
C) 8
D) 11
7.
If a car travels at an average speed of 60 miles per hour for 3 hours, how many miles has it traveled?
A) 120
B) 150
C) 180
D) 200
8.
Simplify the expression: 3(2x – 4) + 2(x + 1)
A) 8x – 6
B) 8x – 10
C) 10x – 10
D) 10x – 6
9.
A rectangular garden has an area of 48 square meters and a length of 8 meters. What is the width of the garden in meters?
A) 4
B) 5
C) 6
D) 7
10.
Solve for x: 2(x – 3) = 10
A) x = 2
B) x = 4
C) x = 6
D) x = 8
11.
If a train travels at a constant speed of 70 miles per hour, how long will it take to travel 210 miles?
A) 2 hours
B) 3 hours
C) 4 hours
D) 5 hours
12.
Simplify the expression: (3x² + 5x – 2) – (2x² – 3x + 4)
A) x² + 8x – 6
B) x² + 8x + 2
C) x² – 8x – 6
D) x² – 8x + 2
13.
A baker needs to make 120 cupcakes for a party. If each batch yields 24 cupcakes, how many batches does the baker need to make?
A) 3
B) 4
C) 5
D) 6
14.
Solve for x: 3(x + 2) – 2(x – 1) = 14
A) x = 2
B) x = 3
C) x = 4
D) x = 6
15.
In a class, the ratio of boys to girls is 3:5, and there are 24 students in total. How many boys are in the class?
A) 8
B) 9
C) 10
D) 12
16.
Simplify the expression: (4x² – 3x + 2) ÷ (2x – 1)
A) 2x – 1
B) 2x + 1
C) 2x + 2
D) 2x – 2
17.
A store offers a 20% discount on all items. If a customer wants to buy a shirt that originally costs \$40, how much will they pay after the discount?
A) \$28
B) \$30
C) \$32
D) \$35
18.
Solve for x: (x + 3)² = 25
A) x = 2 or x = -8
B) x = 5 or x = -5
C) x = 6 or x = -6
D) x = 7 or x = -7
19.
If the area of a circle is 16π square units, what is the circumference of the circle?
A) 8π units
B) 12π units
C) 16π units
D) 20π units
20.
Solve for x: 2(x + 3)/(x – 1) = 6
A) x = 1
B) x = 2
C) x = 3
D) x = 4
21.
The sum of two numbers is 30, and their difference is 10. What are the two numbers?
A) 10 and 20
B) 15 and 15
C) 20 and 10
D) 25 and 5
22.
Simplify the expression: (x² – 9)/(x – 3)
A) x + 3
B) x – 3
C) x² – 9
D) x² + 9
23.
A right circular cone has a height of 12 inches and a base radius of 6 inches. What is the slant height of the cone in inches?
A) 6√5
B) 12√2
C) 12√3
D) 18√2
24.
Solve for x: (x – 2)² = 9
A) x = 5 or x = -1
B) x = 3 or x = -3
C) x = 4 or x = -4
D) x = 6 or x = -6
25.
If the equation of a line is y = 2x + 3, what is the y-intercept of the line?
A) 2
B) 3
C) 5
D) 6
Bonus Question
A rectangular prism has dimensions of 10 meters by 6 meters by 4 meters. If the surface area of the prism (excluding the base) is 160 square meters, what is the volume of the prism?
A) 240 cubic meters
B) 300 cubic meters
C) 360 cubic meters
D) 400 cubic meters
Answer Key and Explanations
1.
Correct Answer: C) 6
Explanation:
x + 5 = 11
Subtract 5 from both sides:
x = 11 – 5
x = 6
2.
Correct Answer: C) 5/6
Explanation:
(2/3) + (1/6)
Find a common denominator (6):
(4/6) + (1/6) = (5/6)
3.
Correct Answer: C) 160
Explanation:
Perimeter = 2 × (length + width)
Perimeter = 2 × (50 + 30)
Perimeter = 2 × 80 = 160 meters
4.
Correct Answer: C) 6
Explanation:
3x – 2 = 16
Add 2 to both sides:
3x = 18
Divide both sides by 3:
x = 18 ÷ 3
x = 6
5.
Correct Answer: B) \$15
Explanation:
Each person’s share = \$75 ÷ 5 = \$15
6.
Correct Answer: A) 2
Explanation:
2x + 3y
Substitute x = 4 and y = -2:
2(4) + 3(-2) = 8 – 6 = 2
7.
Correct Answer: C) 180
Explanation:
Distance = Speed × Time
Distance = 60 mph × 3 hours = 180 miles
8.
Correct Answer: B) 8x – 10
Explanation:
3(2x – 4) + 2(x + 1)
= (6x – 12) + (2x + 2)
= 6x – 12 + 2x + 2
Combine like terms:
(6x + 2x) + (-12 + 2)
= 8x – 10
9.
Correct Answer: C) 6
Explanation:
Area = Length × Width
48 = 8 × Width
Width = 48 ÷ 8
Width = 6 meters
10.
Correct Answer: D) x = 8
Explanation:
2(x – 3) = 10
Divide both sides by 2:
x – 3 = 5
Add 3 to both sides:
x = 5 + 3
x = 8
11.
Correct Answer: B) 3 hours
Explanation:
Time = Distance ÷ Speed
Time = 210 miles ÷ 70 mph
Time = 3 hours
12.
Correct Answer: A) x² + 8x – 6
Explanation:
(3x² + 5x – 2) – (2x² – 3x + 4)
= 3x² + 5x – 2 – 2x² + 3x – 4
Combine like terms:
(3x² – 2x²) + (5x + 3x) + (-2 – 4)
= x² + 8x – 6
13.
Correct Answer: C) 5
Explanation:
Number of batches = Total cupcakes ÷ Cupcakes per batch
Number of batches = 120 ÷ 24
Number of batches = 5
14.
Correct Answer: D) x = 6
Explanation:
3(x + 2) – 2(x – 1) = 14
3x + 6 – 2x + 2 = 14
Combine like terms:
(3x – 2x) + (6 + 2) = x + 8
x + 8 = 14
Subtract 8 from both sides:
x = 14 – 8
x = 6
15.
Correct Answer: B) 9
Explanation:
Total parts in the ratio = 3 (boys) + 5 (girls) = 8 parts
Each part represents 24 ÷ 8 = 3 students
Number of boys = 3 parts × 3 students per part
Number of boys = 9
16.
Correct Answer: B) 2x + 1
Explanation:
Divide (4x² – 3x + 2) by (2x – 1)
Using long division or factoring, we find:
(4x² – 3x + 2) ÷ (2x – 1) = 2x + 1
17.
Correct Answer: C) $32
Explanation:
Discount amount = 20% of $40 = 0.20 × $40 = $8
Price after discount = $40 – $8 = $32
18.
Correct Answer: A) x = 2 or x = -8
Explanation:
(x + 3)² = 25
Take the square root of both sides:
x + 3 = ±5
Case 1: x + 3 = 5
x = 5 – 3
x = 2
Case 2: x + 3 = -5
x = -5 – 3
x = -8
19.
Correct Answer: A) 8π units
Explanation:
Area = πr² = 16π
r² = 16
r = √16 = 4
Circumference = 2πr = 2π(4) = 8π units
20.
Correct Answer: C) x = 3
Explanation:
2(x + 3)/(x – 1) = 6
Cross-multiply:
2(x + 3) = 6(x – 1)
2x + 6 = 6x – 6
Subtract 2x from both sides:
6 = 4x – 6
Add 6 to both sides:
12 = 4x
Divide both sides by 4:
x = 12 ÷ 4
x = 3
21.
Correct Answer: C) 20 and 10
Explanation:
Let the two numbers be a and b
a + b = 30
a – b = 10
Add the two equations:
(a + b) + (a – b) = 30 + 10
2a = 40
a = 20
Then b = 30 – a = 10
22.
Correct Answer: A) x + 3
Explanation:
x² – 9 factors as (x – 3)(x + 3)
Simplify:
(x² – 9)/(x – 3) = [(x – 3)(x + 3)]/(x – 3) = x + 3
23.
Correct Answer: A) 6√5
Explanation:
Slant height (l) = √(r² + h²)
l = √(6² + 12²)
l = √(36 + 144)
l = √180
l = √(36 × 5)
l = 6√5 inches
24.
Correct Answer: A) x = 5 or x = -1
Explanation:
(x – 2)² = 9
Take the square root of both sides:
x – 2 = ±3
Case 1: x – 2 = 3
x = 3 + 2
x = 5
Case 2: x – 2 = -3
x = -3 + 2
x = -1
25.
Correct Answer: B) 3
Explanation:
In the equation y = mx + b, b is the y-intercept.
Therefore, the y-intercept is 3.
Bonus Question
Correct Answer: A) 240 cubic meters
Explanation:
Volume = Length × Width × Height
Volume = 10 m × 6 m × 4 m
Volume = 240 cubic meters
Note: The surface area information confirms the dimensions but is not needed to calculate the volume in this case.
Conclusion
This SAT-style math practice test spans a variety of subjects, including algebra, geometry, and word problems. Utilize the answer key and solutions provided to verify your answers and pinpoint areas needing improvement. Best of luck!
Mastering the SAT Math section is crucial for achieving a high overall score and increasing your chances of admission to your dream college. This comprehensive practice test, combined with the provided tips and strategies, will help you identify your strengths, address your weaknesses, and confidently tackle the SAT Math section on test day.