Quick answer: SAT math questions come from four domains: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. The 12 practice questions below cover all four. Try each one before reading the solution, then practice your weakest skill with a full set.
The fastest way to see where you stand in SAT Math is to try a few questions from every domain and notice which ones slow you down. These 12 SAT math practice questions are written in the style of the Digital SAT, and every answer was checked by code before publishing. Each solution shows the steps and names the wrong answer that the question is designed to catch, because on the SAT the wrong choices are rarely random.
Work each question on paper first. Cover the solution, pick an answer, then check.
Algebra questions
1. Linear equation in one variable
If 3x + 9 = x + 25, what is the value of x?
A) −8
B) 4
C) 17
D) 8
Answer: D. Move the x terms to one side and the numbers to the other: 3x − x = 25 − 9, so 2x = 16 and x = 8. Check it: 3(8) + 9 = 33 and 8 + 25 = 33. Plugging your answer back in takes ten seconds and catches most slips.
2. Linear function from two points
A linear function f satisfies f(−1) = −11 and f(4) = 9. What is the value of f(5)?
A) 20
B) 13
C) −27
D) 27
Answer: B. The slope is (9 − (−11)) / (4 − (−1)) = 20 / 5 = 4. Since 5 is one step past 4, add one slope to f(4): f(5) = 9 + 4 = 13. You can also write the full function, f(x) = 4x − 7, and get the same answer. Choice A is the change in output (20), not a value of the function.
3. System of linear equations
x − 5y = −36
2x + 5y = 48
If (x, y) is the solution to the system, what is the value of x + y?
A) 4
B) 12
C) −4
D) 8
Answer: B. The y terms are −5y and +5y, so add the equations: 3x = 12 and x = 4. Substitute into the first equation: 4 − 5y = −36, so −5y = −40 and y = 8. The question asks for x + y = 12. Choices A and D are x and y alone, which is the most common trap on systems questions: answering for the wrong quantity.
4. Linear inequality
Which of the following values of x satisfies the inequality −2x + 1 > −3?
A) −1
B) 2
C) 4
D) 3
Answer: A. Subtract 1: −2x > −4. Divide by −2 and flip the sign, because you divided by a negative number: x < 2. Only −1 is less than 2. Choice B is the boundary value; at x = 2 the two sides are equal, so it doesn’t satisfy a strict inequality.
Advanced Math questions
5. Quadratic equation
x² − 6x − 16 = 0
What is the positive solution to the equation above?
A) −8
B) −2
C) 2
D) 8
Answer: D. Find two numbers that multiply to −16 and add to −6: −8 and 2. So (x − 8)(x + 2) = 0, and the solutions are x = 8 and x = −2. The positive one is 8. Choices A and C come from reading the factors’ numbers as the solutions without flipping their signs.
6. Exponent rules
Which expression is equivalent to (2x⁴)³?
A) 2x¹²
B) 8x⁷
C) 6x¹²
D) 8x¹²
Answer: D. The exponent applies to every factor inside the parentheses. 2³ = 8, and (x⁴)³ = x¹² because a power of a power multiplies the exponents. Choice A forgets to cube the 2, choice B adds the exponents instead of multiplying, and choice C multiplies 2 × 3 instead of cubing.
7. Exponential function
The function f is defined by f(x) = 6·3^x. What is the value of f(2)?
A) 15
B) 324
C) 54
D) 36
Answer: C. Exponents come before multiplication: 3² = 9, then 6 × 9 = 54. Choice B is (6 × 3)², which multiplies first. This order-of-operations trap shows up in nearly every exponential growth question.
Problem-Solving and Data Analysis questions
8. Percent increase
The price of an item changed from $180 to $198. By what percent did the price increase?
A) 9.1%
B) 18%
C) 20%
D) 10%
Answer: D. Percent change = (new − old) / old × 100 = 18 / 180 × 100 = 10%. Choice A divides by the new price ($198) instead of the original. Choice B treats the $18 change as if it were already a percent. Percent questions are a whole skill on their own; the percentages practice set drills them.
9. Probability from a two-way table
A survey asked students in two grades whether they prefer art or music.
| Art | Music | Total | |
|---|---|---|---|
| 9th grade | 28 | 38 | 66 |
| 10th grade | 10 | 8 | 18 |
| Total | 38 | 46 | 84 |
If a student who prefers art is chosen at random, what is the probability that the student is in 9th grade?
A) 14/19
B) 1/3
C) 14/33
D) 5/19
Answer: A. “A student who prefers art” sets the group: the 38 students in the Art column. Of those, 28 are 9th graders, so the probability is 28/38 = 14/19. Choice B uses all 84 students (28/84), and choice C uses the 9th-grade row (28/66). Finding the right denominator is the whole question.
Geometry and Trigonometry questions
10. Circle area from circumference
A circle has a circumference of 22π. What is the area of the circle?
A) 22π
B) 484π
C) 11π
D) 121π
Answer: D. Circumference = 2πr, so 2πr = 22π and r = 11. Area = πr² = 121π. Choice B uses 22 as the radius, which is the most common slip: 22 is the diameter.
11. Right-triangle trigonometry
In right triangle ABC, angle C is the right angle, BC = 15, AC = 36, and AB = 39. What is the value of sin(A)?
A) 12/13
B) 12/5
C) 5/12
D) 5/13
Answer: D. From angle A, the opposite side is BC = 15 and the hypotenuse is AB = 39. sin(A) = 15/39 = 5/13. Choice A is cos(A) (36/39), and choice C is tan(A) (15/36). Label opposite, adjacent, and hypotenuse from the angle in the question before you write a ratio.
12. Scaling area
A triangle has an area of 12 square centimeters. Each side of the triangle is multiplied by 2 to make a larger, similar triangle. What is the area of the larger triangle, in square centimeters?
A) 96
B) 24
C) 48
D) 14
Answer: C. When lengths are multiplied by 2, areas are multiplied by 2² = 4, so the new area is 12 × 4 = 48. Choice B doubles the area, and choice A multiplies by 2³ = 8, which is the rule for volume.
How to use your results
Count your misses by domain, not just your total. Two misses in Problem-Solving and Data Analysis and none elsewhere tells you exactly where to spend the next week. Then look at why you missed each one:
- Didn’t know the rule (for example, flipping the inequality sign): read the lesson at the top of that skill’s practice page, then do a full set.
- Answered the wrong quantity (x instead of x + y): underline what the question asks for before you start solving.
- Arithmetic slip: plug your answer back in on every question where it’s fast to do so.
Every skill on the SAT Math practice page has a lesson, a worked example, and sets of 10 questions with new numbers every time, so you can repeat a weak skill until it’s automatic. If you’d rather see these skills inside a timed, full-length test first, the SAT practice test guide explains how to set one up.
Frequently asked questions
What kinds of questions are on the SAT Math test?
SAT Math questions come from four domains: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. Most are multiple choice with four options; the rest ask you to type in your own answer.
How many math questions are on the SAT?
The Math section has 44 questions in two modules of 22, with 35 minutes for each module.
Can I use a calculator on SAT math practice questions?
On the real test you can use a calculator for every Math question, including the built-in Desmos graphing calculator. For practice, solve by hand first so you understand each step, then use the calculator to check.
Are these official SAT math questions?
No. These are original practice questions written in the style of the Digital SAT. This site is independent and not affiliated with College Board.
What is the best way to practice SAT math?
Find your weakest skills with a mixed set like this one, then practice those skills one at a time with full sets, reading the explanation for every answer, including the ones you got right.