SAT Math Exercises – 50 SAT Math Exercises on All Domains

After teaching thousands of SAT exam students, we’ve revealed that a high SAT Math score strongly depends on students’ practice on SAT Math exercises. We’ve seen many students increase their SAT Math scores by around 200 points. This is a huge increase, and it is only possible by doing as many SAT Math exercises and practices as possible.


šŸ“ŒĀ Hint:Ā Do not skip this article, you will findĀ FREE Digital SAT Math Prep resources throughout the article.


SAT Math Exercises 800 Score

Ethan is one of our thousands of successful SAT students.Ā He perfectly scored 1600 on the SAT, the highest score a student can get! We were with thousands of students, like Ethan, in their SAT Math Prep journey. We’ve witnessed how they approach SAT Math Exercises and practices and that is why created this SAT Math Exercices post to help many others!

šŸ’”You might be interested in reading the Digital SAT Math Prep post.

Digital SAT Math Structure

Before diving into SAT Math Exercises, you must understand the SAT Math structure, question types, and how to approach different types of questions.

The SAT exam consists of two modules, Module I and Module II.Ā Each module consists of 22 questions, and there will be a total of 44 questions. You will have 35 minutes for each module. Going through comprehensive SAT Math Exercises will help you to get a higher score on SAT Math. We prepared the following table to summarize the structure of theĀ  SAT Math sections.

Format Question Types Stimulus Topics Test Length Time Per Module Number of Questions
Module 1
Two-stage adaptive test design: one Math section administered via two separately timed modules
Discrete; four-option multiple-choice (ā‰ˆ75%) and student-produced response (SPR) (ā‰ˆ25%)
Science, social science, real-world topics
20 operational questions and 2 pretest questions 35 minutes 22
Module 2 20 operational questions and 2 pretest questions 35 minutes 22
Total 40 operational questions and 4 pretest questions 70 minutes 44

The most critical aspect of the Digital SAT is being adaptive.Ā In SAT Math Module I, you will be asked a broad mix of easy, medium, and hard questions. Then, the difficulty of the SAT Math Module II will depend on your score in the SAT Math Module I. This means that the test ā€œadaptsā€ to present questions that are more appropriate to a studentā€™s performance level. Going through several SAT Math Exercises and Practices will improve your scores. The following figure depicts the Digital SAT adaptive testing model.

Digital SAT Adaptive Testing
Source: College Board

šŸ’”You might be interested in reading theĀ Digital SAT Math Ultimate Guide post. We have provided further details about the SAT Math structure, examples of easy, medium, and hard questions, answers, rationales, and frequently asked questions about the SAT Math.

Anna B. Scored 800 on SAT Math!

Anna B. is one of our thousands of successful SAT students. She scored 800 on SAT Math. You can watch her SAT story.

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Now, let’s go through the SAT Math Exercises!

šŸ—Ž Download the 15-page Digital SAT Math Formula Sheet.

Digital SAT Math Exercises

We’ve created these SAT Math Exercises to provide exercises for the commonly tested concepts on the SAT exam. You can consider enrolling in our Online Digital SAT Math Prep Course for a comprehensive SAT Math Prep.

We’ve listed the SAT Math Exercises for each content domain and skills and knowledge testing points respectively. There are a total of 50 SAT Math Exercises in 10 sets. We do not recommend using a calculator for many of the questions. In case a question needs complex calculations, we mentioned as a note that you can use a calculator for that particular SAT Math Exercise.

šŸ’”Weā€™ve prepared aĀ 7-Step Digital SAT Math Study GuideĀ helping students to prepare their unique SAT Math Study Guide.

SAT Math Exercises for Algebra

Algebra is the first content domain in the SAT Math.Ā The SAT exam will haveĀ around 13 to 15 questions from the Algebra content domain. There are 5 skills and knowledge testing points in the Algebra content domain:

  1. Linear equations in one variable
  2. Linear equations in two variables
  3. Linear functions
  4. Systems of two linear equations in two variables
  5. Linear inequalities in one or two variables

šŸ’”You might be interested in seeing our SAT Algebra post. It covers the hack points you should know and 31 SAT Algebra Practice Questions!

Let’s review each skill and knowledge point and see some SAT Math Exercises for each.

SAT Math Exercise Set 1: Linear Equations in One Variable

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I.Ā  3x + 2 = 17

Exercise II.Ā  5x - 7 = 3

Exercise III.Ā  7x + 7 = 0

Exercise IV.Ā  5x - 7 = -13

Exercise V.Ā  1/2x + 5/4Ā  = 1/4

Exercise VI.Ā  Ethan has $15. He gets x dollars from his grandfather. If Ethan has $35 now, what is the value of x?

šŸ’”You might be interested in seeing ourĀ Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!

šŸ“š San Francisco Business School offers a vast amount of FREE Digital SAT Prep Online materials. See it on the Free Digital SAT Prep Online Library.

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Math Exercise Set 2:Ā Linear Equations in Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I.Ā  3x + 5y = 15. What is the y-intercept of this graph?

Exercise II.Ā  2x + 3y = 14. What is the x-intercept of this graph?

Exercise III.Ā  5x + 7y = 70. (7, k) and (l, 5) are two possible solutions to the equation. What is the value of k+l?

Exercise IV.Ā  2x + 3y = 12. Grapf of line m is given. A line k is parallel to line m. What is the slope of line k?

Exercise V.Ā  3x + 4y = 24. If the line h is perpendicular to the given equation’s graph, what is the slope of line h?

Exercise VI.Ā A line passes through (0, 4) and the slope of the line is 2. What is the equation of this line?

Watch SAT Math Prep Online Course – Sample Lecture on YouTube

We have a sample 8-minute video lecture from our SAT Math Prep Online Course on YouTube. You can watch below.

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SAT Math Exercise Set 3: Linear Functions

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I.Ā  Ā The graph of y = f(x) passes through the points (1, 4) and (3, 10). What is the function f ?

Exercise II.Ā Ā The function f is defined by the equation f(x) = 7x + 9. What is the value of f(x) when 3x = 6?

Exercise III. An electrician charges a $40 fixed fee plus $25 per hour. If the function h models the total fee for the electrician for t hours of work, write the function h.

Exercise IV. The function f is defined by f(x) = 3x - 7. What is the y-intercept of the graph of y = f(x) in the xy-plane?

Exercise V. The graph of y =Ā f(x) and y=h(x)Ā are perpendicular to each other in the xy-plane. Function f is defined by f(x) = 2x +13. If h(6)=2, write the y=h(x) function.

Exercise VI. The function a(m) = 300 + 950m models the altitude of an airplane m minutes after takeoff. According to the model, what is the altitude of the airport where the airplane took off?

SAT Math Exercise Set 4:Ā Systems of Two Linear Equations in Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I.Ā  2x = -3y
6x + 11y = 22

The solution to the given system of equations is (x, y). What is the value of y)

Exercise II.Ā x + 7 = 11
(x + 3)^2 = y

For the given system of equations, what is the value of y ?

Exercise III.Ā  7x + 9 = 19
-4x + 3y - 9 = 2

The solution to the given system of equations is (x, y). What is the value of x + y?

Exercise IV.Ā  Ā 2x + 5y = 12
6x + ky =33

In the given system of equations, k is a constant. If the system has no solution, what is the value of k?

SAT Math Exercise Set 5:Ā Linear Inequalities in One or Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I. Ryan has $100 and wants to purchase balls. A store sells basketballs and baseballs. Basketballs are $15 each and baseballs are $20 each.Ā  If x represents the number of basketballs and y represents the number of baseballs Ryan can purchase, what is the inequality representing this situation?

Exercise II.Ā The maximum value of x+3 is 13 greater than another number k. What is the inequality for x in terms of k?

Exercise III. A High School has students whose height is between 160 cm to 186cm. If h represents the height of a student in this High School, what is the inequality representing the height of a student?

Exercise IV. -5y le -x - 3
2y le 3x + 5

(2, p) is a solution to the given system of inequalities. What is the maximum integer value for p?

SAT Math Exercises for Advanced Math

Advanced Math is the second content domain in SAT Math. In the SAT exam, there will be around 13 to 15 questions from the Advanced Math content domain. There are 3 skills and knowledge testing points in the Advanced Math content domain:

    1. Equivalent expressions
    2. Nonlinear equations in one variable and systems of equations in two variables
    3. Nonlinear functions

šŸ’”You might be interested in seeing our SAT Advanced Math post. It covers the hack points you should know and 27 SAT Advanced Math Practice Questions!

Let’s go through each skill and knowledge point and see some SAT Math Exercises for each one.

SAT Math Exercise Set 6:Ā Equivalent Expressions

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I. 3/(13p) = (17x)/(5y)

The given equation relates the positive numbers p, x, and y. Write the p-value in terms of x and y.

Exercise II. (3x)/4 = 3/16

What is the value of 3/x?

Exercise III. root{3}{a^(5x+3)} = sqrt{a^x . a^(3x+2)}

What is the value of x?

Exercise IV.Ā (2x^2 -x -6)/(x-2) + ((3x^2 - 5x -2)(x+2))/(x^2-4)

Simplify the given expression.

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SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Math Exercise Set 7:Ā Nonlinear Equations in One Variable and Systems of Equations in Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I. Two variables, x, and y are related such that for each increase of 1 in the value of x, the value of y increases by a factor of 5. When x=0, y=10. Write the y in terms of x.

Exercise II. 2x^2 - 8x = 11.

One solution to the given equation can be written as 2+ sqrt{k}/2, where k is a constant. What is the value of k?

Exercise III. -3x^2 + px - 12 = 0.

In the given equation, p is a constant. The equation has exactly one solution. What is the value of p?

Exercise IV. 2y = 5x
y = x^2 + 25/16.

A solution to the given system of equations is (x, y), where x>0. What is the value of x?

SAT Math Exercise Set 8:Ā Nonlinear Functions

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I. f(x) = 3x^2 - 6x + 15

The given equation defines the function f. What is the minimum value of f(x)?

Exercise II.Ā The function f is defined by f(3x) = 5x^3 - 11. What is the value of f(6)?

Exercise III.Ā The function l(w) = 15 + w^2 + w gives a spring’s length, in feet, when an object of w kilograms is hung, where w le 20. What is the best interpretation of 15 in this context?

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San Francisco Business School offers a comprehensiveĀ Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

SAT Math Exercises for Problem-Solving and Data Analysis

Problem-solving and Data Analysis is the third content domain in SAT Math. In the SAT exam, there will be around 5 to 7 questions from the Problem-solving and Data Analysis content domain. There are 7 skills and knowledge testing points in the Problem-solving and Data Analysis content domain:

    1. Ratios, rates, proportional relationships, and units
    2. Percentages
    3. One-variable data: distributions and measures of center and spread
    4. Two-variable data: models and scatterplots
    5. Probability and conditional probability
    6. Inference from sample statistics and margin of error
    7. Evaluating statistical claims: observational studies and experiments

šŸ’”You might be interested in seeing our SAT Problem-Solving and Data Analysis post. It covers the hack points you should know and 15 SAT Problem-Solving and Data Analysis Practice Questions!

We’ve listed one SAT Math Exercise for each skill and knowledge testing below. To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

SAT Math Exercise Set 9: Problem-Solving and Data Analysis

Exercise I. Alisa purchased a box of 100 tea bags. She uses one tea bag for each cup of tea. If Alisa drinks 3 cups of tea every day, in how many days will the number of tea bags in the box drop below 20?

Exercise II.Ā A store offers a 20% discount on a certain bag. During the Black Friday promotion, an additional 10% discount is applied on all products in the store. If the final price of the bag is x % of the initial price, what is the value of x?

Exercise III.Ā 1, 3, 7, 7, 8, 5, 2, 11

What is the sum of the median and mean of the data set shown?

Exercise IV.Ā 

SAT Math Exercises

The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. What is the difference between the y-coordinate of the data point with x = 4 and the y-value predicted by the line of best fit at x = 4?

Exercise V.Ā The following table shows the number of students in each grade in a High School.

Grades Number of Students
9 105
10 101
11 100
12 72

25% of the Grade 12 students attend French club. If a student is picked randomly, what is the probability of selecting a Grade 12 student not attending the French club?

Exercise VI.Ā A random sample of 60 people from a town with a population of 18,756 were asked for their opinion on a recent government policy. If 34 people in the sample support the government policy, what is the expected number difference between the supporters and non-supporters in the town?

Note: You can use a calculator in this SAT Math Exercise

Exercise VII.Ā A study is conducted in the state of Utah. A sample of people over 50 years old are asked how many times they visit a doctor each year. What is the largest population to which the result of the survey can be generalized?

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Math Exercises for Geometry and Trigonometry

Geometry and Trigonometry is the fourth and last content domain in SAT Math.Ā The SAT exam will haveĀ around 5 to 7 questions from the Geometry and Trigonometry content domain. There are 4 skills and knowledge testing points in the Geometry and Trigonometry content domain:

    1. Area and Volume
    2. Lines, angles, and triangles
    3. Right triangles and trigonometry
    4. Circles

šŸ’”You might be interested in seeing our SAT Geometry and Trigonometry post. It covers the hack points you should know and SAT Geometry Practice Questions!

We’ve listed one SAT Math Exercise for each skill and knowledge testing below. To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

SAT Math Exercise Set 10: Geometry and Trigonometry

Exercise I.Ā One side of a rectangle and square are common. The area of the rectangle is two times the area of the square. If the perimeter of the rectangle is 10 units greater than the perimeter of the square, what is the length of the rectangle in units?

Exercise II.

SAT Math Exercises Geometry
Note: Figure not drawn to scale.

In the figure, line m is parallel to line n, and line k intersects both lines. What is the value of x + y ?

Exercise III.Ā One leg of an isosceles right triangle A is common with the shortest leg of another right triangle B. The length of the longest side of the triangle B is 17, and longer leg length is 15. What is the length of the longest side of triangle A?

Exercise IV. The graph of x^2 + x + y^2 + y = 161/2 in the xy-plane is a circle. What is the area of the circle?

Note: You can use a calculator in this SAT Math Exercise

šŸ’”You might be interested in seeing ourĀ Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!

Digital SAT Prep Online Course Program

San Francisco Business School offers a comprehensiveĀ Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

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