The SAT is a critical component of the college admissions process, and the math section is a crucial part of the exam. To help you prepare, we’ve put together a comprehensive SAT Math practice test that covers all the key topics and question types you’ll encounter on test 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
Directions:
For each of the following questions, choose the best answer from the given options.
- If x + 5 = 11, what is the value of x?
- a) 4
- b) 5
- c) 6
- d) 7
- What is the value of 2/3 + 1/6?
- a) 1/2
- b) 2/3
- c) 3/4
- d) 1
- If 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
- If 3x – 2 = 16, what is the value of x?
- a) 4
- b) 5
- c) 6
- d) 7
- 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
- What is the value of (2x + 3y) when x = 4 and y = -2?
- a) 2
- b) 5
- c) 8
- d) 11
- 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
- Simplify the expression: 3(2x – 4) + 2(x + 1)
- a) 8x – 6
- b) 8x – 10
- c) 10x – 10
- d) 10x – 6
- If 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
- Solve for x: 2(x – 3) = 10
- a) x = 2
- b) x = 4
- c) x = 6
- d) x = 8
- 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
- Simplify the expression: (3x^2 + 5x – 2) – (2x^2 – 3x + 4)
- a) x^2 + 8x – 6
- b) x^2 + 8x + 2
- c) x^2 – 8x – 6
- d) x^2 – 8x + 2
- A baker needs to make 120 cupcakes for a party. If each batch of cupcakes yields 24 cupcakes, how many batches does the baker need to make?
- a) 3
- b) 4
- c) 5
- d) 6
- Solve for x: 3(x + 2) – 2(x – 1) = 14
- a) x = 2
- b) x = 3
- c) x = 4
- d) x = 5
- If the ratio of boys to girls in a class 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
- Simplify the expression: (4x^2 – 3x + 2) / (2x – 1)
- a) 2x – 1
- b) 2x + 1
- c) 2x + 2
- d) 2x – 2
- 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 have to pay after the discount?
- a) $28
- b) $30
- c) $32
- d) $35
- Solve for x: (x + 3)^2 = 25
- a) x = ±4
- b) x = ±5
- c) x = ±6
- d) x = ±7
- 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
- Solve for x: 2(x + 3)/(x – 1) = 6
- a) x = 1
- b) x = 2
- c) x = 3
- d) x = 4
- If 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
- Simplify the expression: (x^2 – 9)/(x – 3)
- a) x + 3
- b) x – 3
- c) x^2 – 9
- d) x^2 + 9
- 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
- Solve for x: (x – 2)^2 = 9
- a) x = ±3
- b) x = ±4
- c) x = ±5
- d) x = ±6
- 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
Answers and Step-by-Step Solutions:
- c) 6
x + 5 = 11
x = 11 – 5
x = 6 - c) 3/4
2/3 + 1/6 = (4/6) + (1/6) = 5/6 = 3/4 - c) 160
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (50 + 30)
Perimeter = 2 × 80
Perimeter = 160 meters - b) 5
3x – 2 = 16
3x = 16 + 2
3x = 18
x = 18/3
x = 6 - b) $15
Total bill = $75
Number of friends = 5
Each person’s share = $75/5 = $15 - d) 11
(2x + 3y) when x = 4 and y = -2
= (2 × 4 + 3 × -2)
= 8 – 6
= 2 - c) 180
Distance = Speed × Time
Distance = 60 miles/hour × 3 hours
Distance = 180 miles - a) 8x – 6
3(2x – 4) + 2(x + 1)
= 6x – 12 + 2x + 2
= 8x – 10 - b) 6
Area of a rectangle = Length × Width
48 = 8 × Width
Width = 48/8
Width = 6 meters - c) 6
2(x – 3) = 10
2x – 6 = 10
2x = 16
x = 8 - b) 3 hours
Time = Distance / Speed
Time = 210 miles / 70 miles per hour
Time = 3 hours - a) x^2 + 8x – 6
(3x^2 + 5x – 2) – (2x^2 – 3x + 4)
= 3x^2 + 5x – 2 – 2x^2 + 3x – 4
= x^2 + 8x – 6 - d) 5
Total cupcakes needed = 120
Cupcakes per batch = 24
Number of batches = 120/24 = 5 - b) 3
3(x + 2) – 2(x – 1) = 14
3x + 6 – 2x + 2 = 14
x + 8 = 14
x = 6 - c) 10
Total students = 24
Ratio of boys to girls = 3:5
Let x be the number of boys and y be the number of girls.
x/y = 3/5
x = 3y/5
24 = x + y
24 = 3y/5 + y
24 = 8y/5
120 = 8y
y = 15
x = 3 × 15/5 = 9 - b) 2x + 1
(4x^2 – 3x + 2) / (2x – 1)
= (2x(2x – 1) – x + 2) / (2x – 1)
= (2x^2 – 2x – x + 2) / (2x – 1)
= (2x^2 – 3x + 2) / (2x – 1)
= 2x + 1 - a) $32
Original cost = $40
Discount = 20% of $40 = 0.2 × $40 = $8
Cost after discount = $40 – $8 = $32 - b) x = ±5
(x + 3)^2 = 25
(x + 3)(x + 3) = 25
x^2 + 6x + 9 = 25
x^2 + 6x – 16 = 0
(x + 8)(x – 2) = 0
x = -8 or x = 2
x + 3 = -5 or x + 3 = 5
x = ±5 - b) 12π units
Area of a circle = πr^2
16π = πr^2
r^2 = 16
r = 4
Circumference = 2πr = 2π(4) = 8π units - d) 4
2(x + 3)/(x – 1) = 6
2x + 6 = 6x – 6
-4x = -12
x = 3 - c) 20 and 10
Let x and y be the two numbers.
x + y = 30 (Sum is 30)
x – y = 10 (Difference is 10)
Adding the two equations:
2x = 40
x = 20
Substituting x = 20 in the first equation:
20 + y = 30
y = 10 - a) x + 3
(x^2 – 9)/(x – 3)
= (x – 3)(x + 3)/(x – 3)
= x + 3 - c) 12√3
In a right circular cone:
Slant height^2 = height^2 + base radius^2
Slant height^2 = 12^2 + 6^2
Slant height^2 = 144 + 36
Slant height^2 = 180
Slant height = √180
Slant height = 12√3 inches - a) x = ±3
(x – 2)^2 = 9
(x – 2)(x – 2) = 3^2
x – 2 = ±3
x = 2 ± 3
x = 5 or x = -1 - b) 3
y = 2x + 3
When x = 0, y = 2(0) + 3 = 3
The y-intercept is 3.
Bonus Question: Difficulty level: hard
Problem: A rectangular prism has dimensions of 10 meters by 6 meters by 4 meters. 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
Solution:
- First, let’s find the surface area of the rectangular prism. The surface area of a rectangular prism (excluding the base) is given by: [ \text{Surface Area} = 2lw + 2lh + 2wh ] where (l) is the length, (w) is the width, and (h) is the height. Plugging in the given dimensions: [ 160 = 2(10)(6) + 2(10)(4) + 2(6)(4) ] [ 160 = 120 + 80 + 48 ] [ 160 = 248 ]
- Now, let’s find the volume of the rectangular prism: [ \text{Volume} = lwh ] Plugging in the given dimensions: [ \text{Volume} = (10)(6)(4) = 240 ]
- The correct answer is A) 240 cubic meters.
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.
