Free Resources
Start With a Free SAT Math Practice Test
Build a useful study habit with free practice and clear explanations. Start with our original questions below, or take a free full-length test through College Board’s Bluebook resources.
Free practice: four skills, four questions
These original MathTestHub questions are a short skill check, not a full-length test or a score predictor. Try each question before opening its solution.
1. Algebra: linear equations
A club pays a $\$24$ setup fee plus $\$6$ per notebook. The total cost is $\$90$. How many notebooks does the club buy?
Show solution: 11 notebooks
Let n be the number of notebooks. The cost equation is . Subtract 24 to obtain , then divide by 6: n = 11. Check: .
2. Advanced Math: quadratic structure
What is the minimum value of $f(x) = x² − 6x + 14$ for real $x$?
Show solution: 5
Complete the square: . Since a square is nonnegative, the smallest possible value is 5, reached when $x = 3$.
3. Problem Solving & Data Analysis: percentages
A jacket costs $\$72$ after a $20\%$ discount. What was its original price, before tax?
Show solution: $\$90$
After the discount, $80\%$ of the original price remains. Let p be that original price. Then $0.80p = 72$, so $p = 72 ÷ 0.80 = 90$. Check: $20\%$ of $\$90$ is $\$18$, and $\$90 − \$18 = \$72$.
4. Geometry & Trigonometry: right triangles
A right triangle has legs of length 9 and 12. What is the sine of the acute angle opposite the leg of length 9?
Show solution: 3/5
The hypotenuse is $\sqrt{9^2 + 12^2} = \sqrt{225} = 15$. Sine equals opposite divided by hypotenuse, so $\sin \theta = 9/15 = 3/5$.
SAT Math Study Checklist
- Take a timed practice test and record your answers.
- Review each missed or guessed question before starting another test.
- Classify the mistake: concept, setup, calculation, or time management.
- Practice the same skill with fresh questions.
- Use your calculator deliberately and check answers in context.
- Keep a written error log and revisit it weekly.
SAT Math Topic Guide
Review the four domains and build a topic-by-topic study plan. Our topic guide is available online; separate downloadable formula sheets and checklists are not yet available.
Sample Step-by-Step Solutions
Open the solutions above to see how we define variables, choose a method, and check the result. Use the reasoning to solve a new problem, rather than memorizing an answer.
More free practice
Use the official Student Question Bank for targeted practice by test, domain, skill, and difficulty.