practice questions are a great way to get started on studying for the SAT and testing your quantitative skills. The SAT math test primarily tests your ability in algebra, problem solving, data analysis as well as your knowledge of more advanced foundational concepts in math. Remember that depending on which SAT test version you’re writing, you may or may not have the use of a calculator for some questions! In this blog, we’ve included SAT math practice questions in every content area to test your skills, plus our top tips for preparing for the SAT math test.
Listen to the blog!
SAT Math Practice Questions: Heart of Algebra
Question 1: Solve for x: 2(x - 3) + 4 = 3(2x + 1).
A) x = 4
B) x = 5
C) x = 6
D) x = 7
Question 2: If 4x - 2y = 10 and 2x + 5y = 1, what is the value of y?
A) y = -2
B) y = 1
C) y = 2
D) y = 3
Question 3: Simplify the expression: 3(2x - 4) - 2(3x + 1).
A) 3x - 8
B) 6x - 5
C) 2x - 11
D) 6x - 10
Question 4: Solve the inequality: 2x - 3 > 7.
A) x < 5
B) x > 5
C) x > 6
D) x < 6
Question 5: The equation y = 2x - 3 represents a linear function. What does the coefficient 2 represent in the context of this function?
A) The x-intercept
B) The slope of the line
C) The y-intercept
D) The constant term
Question 6: A local bakery charges a fixed fee of $5 for a delivery plus $2 per mile. Write a linear function, f(d), that models the cost in dollars for a delivery of d miles.
A) f(d) = 2d + 5
B) f(d) = 5d + 2
C) f(d) = 2d - 5
D) f(d) = 5d - 2
Question 7: Solve the system of equations: 2x - 3y = 7 5x + 2y = 16
A) x = 2, y = 1
B) x = 1, y = 2
C) x = 3, y = 2
D) x = 4, y = 3
SAT Math Practice Questions: Problem Solving and Data Analysis
Question 1: In a charity event, the number of adults attending was three times the number of children. If the total number of attendees was 120 and each adult ticket costs $20, and each child ticket costs $10, how much money was raised from ticket sales?
Question 2: A company's sales increased by 15% each year for three consecutive years. If their sales were $1,000,000 at the end of the third year, what were their initial sales at the beginning of year one?
Question 3: The average of five numbers is 25. If one of the numbers is removed from the group, the average becomes 30. What is the value of the removed number?
Question 4: A car travels at a constant speed for the first 3 hours at 60 miles per hour. It then travels at another constant speed for the next 2 hours at 40 miles per hour. What is the car's average speed for the entire journey?
A) 44 mph
B) 48 mph
C) 50 mph
D) 55 mph
Question 5: A survey of 300 people found that 40% prefer tea, 30% prefer coffee, and the rest had no preference. If 60 people had no preference, how many people prefer coffee?
Question 6: A rectangular room is 5 meters long, 3 meters wide, and 2.5 meters high. What is the volume of the room in cubic meters?
A) 12.5 cubic meters
B) 37.5 cubic meters
C) 50 cubic meters
D) 75 cubic meters
Question 7: A scatterplot shows the relationship between study hours and test scores. What type of relationship is likely depicted if the points form a linear pattern with a positive slope?
A) As study hours increase, test scores decrease.
B) As study hours increase, test scores increase.
C) There is no clear relationship between study hours and test scores.
D) As study hours increase, test scores remain constant.
SAT Math Practice Questions: Advanced Math
Question 1: Factor completely: 3x^2 - 12x.
A) 3x(x - 4)
B) 3(x - 4)
C) x(3x - 4)
D) (3x - 4)(x - 4)
Question 2: Solve the quadratic equation for x: x^2 + 5x + 6 = 0.
A) x = -6 or x = -1
B) x = -3 or x = -2
C) x = -6 or x = 1
D) x = -5 or x = -6
Question 3: Simplify the expression: √(9x^2).
Question 4: Determine the most suitable form of the expression to reveal the maximum area of a rectangular garden with a fixed perimeter of 40 meters. What is the area of the garden in this case?
A) 100 square meters
B) 120 square meters
C) 150 square meters
D) 200 square meters
Question 5: Sketch the graph of the quadratic function y = -2x^2 + 4x - 1 and identify its vertex and axis of symmetry.
A) Vertex: (1, 3); Axis of Symmetry: x = 1
B) Vertex: (2, 3); Axis of Symmetry: x = 2
C) Vertex: (1, -3); Axis of Symmetry: x = -1
D) Vertex: (-2, 1); Axis of Symmetry: x = -2
Question 6: Create a quadratic function to model the following scenario: A ball is thrown from a height of 10 meters above the ground. The ball reaches its highest point and starts to descend after 1 second. The ball's height h (in meters) can be represented by the quadratic function h(t) = -5t^2 + 10t + 10, where t is the time in seconds. What is the maximum height the ball reaches?
A) 10 meters
B) 12 meters
C) 15 meters
D) 20 meters
Question 7: Create an equivalent form of the expression (2x + 3)^2 by expanding and simplifying it.
A) 4x^2 + 12x + 9
B) 4x^2 + 6x + 9
C) 4x^2 + 12x + 6
D) 4x^2 + 9
SAT Math Practice Questions: Additional Topics in Math
Question 1: In a right triangle, the length of the hypotenuse is 10 units, and one of the acute angles is 30 degrees. What is the length of the shorter leg?
A) 3 units
B) 4 units
C) 5 units
D) 6 units
Question 2: A regular hexagon is inscribed in a circle with a radius of 6 inches. What is the perimeter of the hexagon?
A) 18 inches
B) 24 inches
C) 36 inches
D) 48 inches
Question 3: Find the area of a trapezoid with a height of 8 units, a base of 10 units, and a shorter parallel side of 4 units.
A) 32 square units
B) 40 square units
C) 48 square units
D) 64 square units
Question 4: If sin(θ) = 3/5 and θ is an acute angle, what is the value of cos(θ)?
Question 5: In triangle ABC, ∠A is congruent to ∠D, and ∠B is congruent to ∠E. If AB = 6 inches, BC = 9 inches, and DE = 4 inches, what is the length of AC?
A) 4 inches
B) 6 inches
C) 9 inches
D) 12 inches
Question 6: A cylindrical tank with a radius of 5 meters is filled with water to a height of 8 meters. What is the volume of water in the tank?
A) 100π cubic meters
B) 200π cubic meters
C) 250π cubic meters
D) 400π cubic meters
Question 7: Simplify the complex number: (2 + 3i) - (5 - 4i).
A) -3 + 7i
B) -3 - 7i
C) 7 - 3i
D) 7 + 3i
Acing the SAT math test is about more than being a math whiz. Since the SAT math covers a concrete set of content areas, this section of the test is very coachable and is something you can learn to improve. Here are a few tips for you as you begin studying for the test and prepare to take the SAT:
1. Review the test content
As we’ve said, the math on the SAT is coachable. The subjects you’ll be tested on are algebra, problem solving, complex mathematical equations and additional topics like trigonometry and algebra. All of the math tested on the SAT is covered in your high school math courses, so it won’t be anything you haven’t seen before.
It’s a good idea to review what concepts are tested on the SAT math and what types of problems you’ll encounter. However, it’s also wise to review math section, and how this part of the test is structured. This will give you a complete view of the SAT math test and help you plan your .
2. Create a good study schedule
A good SAT schedule is essential! Some students may want more time to study for the test, dedicating more hours to math study. Others may not need as much SAT math practice but still want to review the foundational concepts. Give yourself enough time to both review the math concepts on the SAT and practice them regularly until you’re scoring high on your practice tests or answering tricky questions correctly.
Remember to include in your study schedule your and make note of , in case you decide to re-test ahead of college application deadlines. If you’re not sure , look at your college application schedule and aim to take your first SAT in the spring of your junior year.
3. Practice your skills
Practice tests and SAT math practice questions like the ones included above are important to test your knowledge of foundational mathematical concepts. You should aim to take regular practice tests, or practice questions as part of your study schedule.
It’s best to take both timed and untimed practice tests, especially in the math section where the time limits can be tough and the use of a calculator is not always permitted. Practice solving problems both with and without your calculator so you can get used to solving problems in your head, fast. Your calculator may be necessary to solve some problems, but it can slow you down, too, so use it wisely.
4. Get extra help
An SAT tutor can be very helpful for students who struggle in math. A tutor can prepare a personalized study schedule and walk you through math question strategies to help you improve your skills on certain questions. A tutor can also help you define which questions are the toughest for you and how to approach them.
Of course, if you’re not sure and would rather take the ACT, or neither. This is an option. There are some schools that do not require either standardized test for admissions. For those who choose to take the ACT instead, there is still math tested, but your math section score accounts for a smaller percentage of your overall score.
5. Master your calculator
The calculator is permitted for parts of your SAT math test, but not knowing how to use this valuable tool can slow you down. Or, inputting every single equation from every question can take away valuable time. If you don’t need to use the calculator, it’s recommended that you skip it and calculate in your head. If a question requires the use of your calculator, it’s better to be familiar with is functionality so you don’t use up time trying to find the right function.
Keep in mind the SAT only permits certain types of calculators! Check the list of permitted calculators to make sure you have the right one.
1. How can I practice for the SAT math section?
One of the best ways to math section is to use practice questions and take regular practice tests. These will allow you to get more comfortable with the level and difficulty of math questions on the SAT, check your test timing and determine which are your weakest or strongest skills in math. This way, you can focus on improving your weakest skills in math and improve your score.
2. Where can I find more SAT math practice questions?
3. What is the hardest type of math on the SAT?
The hardest type of math on the SAT is usually found in the “advanced math” section, which tests your knowledge of more complex mathematical equations. However, each student may find different sections of the SAT math most difficult.
4. Does the ACT or SAT have more math?
The type of math tested is roughly the same as on the , and the tests are comparable in terms of difficulty. However, your SAT math score accounts for a larger percentage of your overall score than on the ACT.
5. Can I still ace the SAT if I’m not good at math?
Yes, it is still possible to get a good even if math is not your strongest subject. You can improve your SAT math score with the help of good study strategies or the help of an to walk you through SAT math practice questions.
6. What kind of math is on the SAT?
The SAT Math test includes three different content areas: Heart of Algebra, Problem Solving and Data Analysis, and Advanced Math, which includes questions on advanced mathematical equations. You may also be tested on “Additional topics in math” such as trigonometry and geometry.
7. How many math questions are on the SAT?
There are 58 questions on the SAT math test, and you are given 80 minutes total to complete it. The test is divided into a calculator-allowed portion and a no-calculator portion. The no-calculator section has a time limit of 25 minutes and includes 15 multiple-choice questions and 5 grid-in questions. The calculator section includes 30 multiple-choice questions and 8 grid-in questions. You’re given 55 minutes to complete this section.
8. Are you allowed a calculator on the SAT math?
The paper version of the SAT includes both a calculator-permitted section and a no-calculator allowed section. The portion that needs to be completed with a calculator contains problems and questions that can be solved without the use of a calculator, although it’s important to practice solving problems both with and without a calculator. Be sure to check .
The digital SAT version allows the use of a calculator throughout the math section, although it’s recommended that you learn how to compute without the benefit of a calculator so you don’t rely on it too heavily during the test and use up valuable time.