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.
In this article
šĀ Hint:Ā Do not skip this article, you will findĀ FREE Digital SAT Math Prep resources throughout the article.
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!
š”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 (ā75%) and student-produced response (SPR) (ā25%)
|
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 āadaptsā to present questions that are more appropriate to a studentās performance level. Going through several SAT Math Exercises and Practices will improve your scores. The following figure depicts the Digital SAT adaptive testing model.
š”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.
Now, let’s go through the SAT Math Exercises!
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.
š”Weāve 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:
- Linear equations in one variable
- Linear equations in two variables
- Linear functions
- Systems of two linear equations in two variables
- Linear inequalities in one or two variables
š”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 
Exercise II.Ā 
Exercise III.Ā 
Exercise IV.Ā 
Exercise V.Ā 
Exercise VI.Ā Ethan has $15. He gets 
dollars from his grandfather. If Ethan has $35 now, what is the value of ?
š”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!
. First, subtract 2 from both sides;
. Then, divide both sides by 3.
. Add 7 to both sides;
. Divided both sides by 5.
. Subtract 7 from both sides.
. Divide both sides by 7.
. Add 7 to both sides.
. Divide both sides by 5.
. Subtract 
from both sides.
. This equation yields;
. If we multiply both sides by 2;
. This yields;
.
dollars.Ā If Ethan has $35 now;
. If we subtract 15 from both sides;
. This yields;
.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 Math Prep Course
SFBS offers aĀ Free Digital SAT Math PrepĀ course. The course goes through a particular skill and knowledge testing point and improvesĀ 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 
. What is the y-intercept of this graph?
Exercise II.Ā 
. What is the x-intercept of this graph?
Exercise III.Ā 
. 
and 
are two possible solutions to the equation. What is the value of 
?
Exercise IV.Ā 
. Grapf of line m is given. A line k is parallel to line m. What is the slope of line k?
Exercise V.Ā 
. 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?
.
.
. If we divide both sides by 5;
–> (0, 3) is the y-intercept of this graph.
.
.
. If we divide both sides by 2;
–> (7, 0) is the x-intercept of this graph.
. This yields;
. If we subtract 35 from both sides;
. This yields;
If we divide both sides by 7;
.
. This yields;
. If we subtract 35 from both sides;
. This yields;
If we divide both sides by 5;
.
. Subtract 
from both sides. This yields;
. If we divide both sides by 3;
. This equation yields;
. This equation is in the slope-intercept form y = mx + b.
. Since the line k is parallel to this line, it will have the same slope as well.
. Subtract 
from both sides. This yields;
. If we divide both sides by 4;
. This equation yields;
. This equation is in the slope-intercept form y = mx + b.
. If line h is perpendicular to this line, the products of the slopes of these two lines will be -1. If we say 
for the slope of line h;
. If we divide both sides by 
;
. This yields;
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.
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 
. What is the value of f(x) when 
?
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 
. What is the y-intercept of the graph of 
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 
. If 
, write the y=h(x) function.
Exercise VI. The function 
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?
. If we substitute the x and y coordinates of the two points (1, 4) and (3, 10);
. This yields;
.
. We substituted (1, 4). x = 1, y = 4. Solving this equation yields;
. Now, we can write the equation;
. If we divide both sides by 3;
. If we substitute x = 2 in the function equation;
. This yields;
. It is in slope-intercept form of y = mx + b. Therefore;
. If we say the slope of y=h(x) is 
;
. If we divide both sides by 2;
. It’s given that 
. This yields;
. If we add 3 on both sides;
. We found 
. This yields;
feet.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 
The solution to the given system of equations is (x, y). What is the value of y)
Exercise II.Ā 
For the given system of equations, what is the value of y ?
Exercise III.Ā 
The solution to the given system of equations is (x, y). What is the value of x + y?
Exercise IV.Ā Ā 
In the given system of equations, k is a constant. If the system has no solution, what is the value of k?
. This yields;
. In the second equation, we can substitute 6x for -9y
. This yields;
. Dividing both sides by 2;
and this yields;
.
. This yields;
. Now, we can substitute x = 4 in the second equation;
. This yields;
. If we open the parentheses; and combine the like terms;
. This yields;
. If we use the common factor of 3 on the left side of the equation;
. If we divide both sides by 3; we will find the value of x + y.
. This yields;
, and
and for these lines to be distinct;
ā 
and 
. If we do cross-multiplication;
. Dividing both sides by 2 yields;
. Note that, when k=15, these two lines are parallel. For them to be distinct;
ā 
–> This is true. And
–> this is true as well.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 
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. 
(2, p) is a solution to the given system of inequalities. What is the maximum integer value for p?
= Total cost of basketballs
= Total cost of baseballs.
= Total cost of all balls Ryan can purchase.
.
. If we subtract 3 from both sides of the inequality;
. This yields;
. This yields;
.
. This yields;
.
. This yields;
.
.
. This yields;
, or 
.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:
-
- Equivalent expressions
- Nonlinear equations in one variable and systems of equations in two variables
- Nonlinear functions
š”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. 
The given equation relates the positive numbers p, x, and y. Write the p-value in terms of x and y.
Exercise II. 
What is the value of 
?
Exercise III. 
What is the value of x?
Exercise IV.Ā 
Simplify the given expression.
. This equation yields;
. We need to isolate p to write the p-value in terms of x and y. Divide both sides of the equation by 221x;
. This yields;
.
;
. This yields;
. If we substitute the x value;
.
, and;
. With the help of these two, we can rewrite the left side of the equation as follows;
. This is the left side of the equation.
. This yields;
. This yields;
. This is the right side of the equation.
. The bases of the right and left sides of the equation are the same now. Therefore, powers must be the same as well.
. If multiply both sides by 3;
. This yields;
. If we subtract 5x+3 from both sides;
. This yields;
. Therefore, the first fraction can be rewritten as;
. There are (x-2) both in the numerator and denominator, so we can eliminate them, and the first fraction yields;
. This is the simplified expression for 1st fraction.
. Therefore the numerator can be rewritten as follows;
.
as 
. Therefore, we can rewrite the denominator of the 2nd fraction as follows;
. If we rewrite the 2nd fraction with the expressions we found;
. We see that (x-2)(x+2) are present both in the numerator and denominator of the 2nd fraction. Therefore, we can eliminate them.
. This is the simplified expression for 2nd fraction.
. The result yields;
.Free Digital SAT Math Prep Course
SFBS offers aĀ Free Digital SAT Math PrepĀ course. The course goes through a particular skill and knowledge testing point and improvesĀ 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. 
.
One solution to the given equation can be written as 
, where k is a constant. What is the value of k?
Exercise III. 
.
In the given equation, p is a constant. The equation has exactly one solution. What is the value of p?
Exercise IV. 
.
A solution to the given system of equations is (x, y), where x>0. What is the value of x?
. a is a constant. Let’s test this.
5 times 5a equals to 25a. Therefore, the equation is correct.
. The zero power of a number is equal to 1. Therefore;
. This yields;
, the solution to the equation is as follows;
.
and 
values.
. This yields;
. This is in the form of 
. This yields;
. This yields;
. This yields;
Ā± 
. Therefore;
and 
.
is called discriminant. If the discriminant of an equation;
. There are two 
. There is exactly one solution x.
. There are no real solutions.
. This yields;
. If we add 144 on both sides;
. If we apply the square root on both sides;
. This yields;
. This yields;
. If we substitute this in the second equation for y;
. If we subtract 
from both sides;
. This yields;
.
as 
. Therefore, we can rewrite the equation as;
.
, then 
. This yields;
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. 
The given equation defines the function f. What is the minimum value of f(x)?
Exercise II.Ā The function f is defined by 
. What is the value of f(6)?
Exercise III.Ā The function 
gives a spring’s length, in feet, when an object of w kilograms is hung, where 
. What is the best interpretation of 15 in this context?
, if a > 0, then the graph is upward. In the given equation, a = 3. So, the minimum value of the f(x) will be its vertex.
where a, h, and k are constants, (h,k) is the vertex point.
. We can rewrite as 
. Therefore;
. If we expand the parenthesis;
. This is in the form of 
. This yields x = 2. If we substitute x = 2 in the function equation;
. This yields;
. This yields;
.
. So, when there are no objects, the length of the spring is 15 feet. We can conclude that the initial length of the spring when no object is hung is 15 feet.SFBS Online Digital SAT Math Prep Through Questions Program
San Francisco Business School offers a comprehensiveĀ Digital SAT Math Prep Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain and 19 skills and knowledge testing points through 322 realistic Digital SAT Math 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:
-
- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures of center and spread
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims: observational studies and experiments
š”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
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?
. If we add 3x to both sides and subtract 20 from both sides of the equation;
. This yields;
. If we divide both sides by 3;
. This yields;
. The smallest integer greater than 26.66 is 27. Therefore, in 27 days, the number of tea bags in Alisa’s tea box will drop below 20.
= Discount Amount.
= Discount Amount.
. If we substitute the values;
If we divide both sides by p, this yields;
. If we substitute the values;
. This yields;
. We found the median.
. If we substitute the values;
. This yields;
. We found the mean.
, or 
of Grade 12 students do not attend French club. There are 72 Grade 12 students. Therefore;
54 Grade 12 students do not attend the French club.
. The difference between the supporters and non-supporters in the sample group is;
. If we do cross-multiplication;
. If we divide both sides by 60;
. We can conclude that the number of supporters will be around 2,501 greater than the number of non-supporters.Free Digital SAT Math Prep Course
SFBS offers aĀ Free Digital SAT Math PrepĀ course. The course goes through a particular skill and knowledge testing point and improvesĀ 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:
-
- Area and Volume
- Lines, angles, and triangles
- Right triangles and trigonometry
- Circles
š”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.
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 
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
. If we divide both sides by w;
. This yields;
. We found the relationship between the length and width of the rectangle.
. We can substitute 
and this yields;
. This yields;
. If we subtract 2l from both sides;
. This yields;
. For an isosceles right triangle, the angles will be 45Ā°-45Ā°-90Ā°.
. Therefore;
. If we do cross-multiplication;
. If we divide both sides by 
;
. This yields;
. This yields;
. If we isolate the 
;
. This yields;
. If we apply square root on both sides;
. This yields;
.
. If we substitute the value of a;
where (h,k) is the center of the circle and r is the radius. Therefore, we should rewrite the given equation in the standard circle form to find its radius, r.
as 
. Therefore, we can rewrite;
. If we subtract 
from both sides;
.
part as follows;
.
. This yields;
. This yields;
. This is now in the standard form of a circle 
, 
and 
.
. This yields;
.
. If we substitute the values in this formula;
. This yields;
. (You can round this to 254.47.)š”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!
SFBS Online Digital SAT Math Prep Through Questions Program
San Francisco Business School offers a comprehensiveĀ Digital SAT Math Prep Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain and 19 skills and knowledge testing points through 322 realistic Digital SAT Math questions. You will see all the different types of questions that may appear in Digital SAT.