The PSAT math section has 44 questions split across two adaptive modules, with 70 minutes total to complete it. About 70% of the questions test algebra and advanced math, while the remaining 30% cover problem solving and data analysis, plus geometry and trigonometry. Mastering math is the fastest way to raise your overall PSAT score.
This guide covers everything you need to practice PSAT math effectively: which topics to focus on, sample questions with worked solutions for each domain, study tips, and the free resources that produce the biggest score gains.
What the PSAT Math Section Covers
You have a built-in Desmos graphing calculator available for all 44 questions, and approximately 11 of the questions are student-produced response (where you type in your own answer). The rest are multiple choice with four options.
Algebra Practice Questions
Algebra makes up about 35% of the PSAT math section. Topics include linear equations, linear inequalities, systems of equations, linear functions, and interpreting slope and y-intercept in real-world contexts.
Question 1: Linear Equation
If 4x - 7 = 2x + 11, what is the value of x?
A) 4
B) 7
C) 9
D) 11
Answer: C (9)
Solution: Subtract 2x from both sides: 2x - 7 = 11. Add 7 to both sides: 2x = 18. Divide by 2: x = 9. Linear equations are the most common algebra question type. Get fast at them and you bank quick points.
Question 2: System of Equations
If 2x + 3y = 12 and x - y = 1, what is the value of x?
A) 2
B) 3
C) 4
D) 5
Answer: B (3)
Solution: From the second equation, x = y + 1. Substitute into the first: 2(y + 1) + 3y = 12 → 2y + 2 + 3y = 12 → 5y = 10 → y = 2. So x = 2 + 1 = 3. The substitution method is reliable for system problems. Get comfortable with both substitution and elimination.
Question 3: Slope Interpretation
The equation y = 50 + 12x represents the total cost y, in dollars, of renting a kayak for x hours. What does the 12 represent?
A) The total cost of renting the kayak
B) The cost per hour of renting the kayak
C) The deposit fee for the kayak
D) The maximum number of hours allowed
Answer: B (the cost per hour of renting the kayak)
Solution: In the form y = b + mx, the coefficient of x (the slope) represents the rate of change. Here, 12 is multiplied by x (hours), so it is the cost per hour. The 50 is the y-intercept, representing a one-time fee at zero hours. The PSAT loves these slope-interpretation questions, so practice spotting the rate of change quickly.
Advanced Math Practice Questions
Advanced math also makes up about 35% of the section. Topics include quadratic equations, polynomial expressions, exponential functions, and nonlinear equations.
Question 4: Factoring a Quadratic
What are the solutions of x² + 5x - 14 = 0?
A) x = 7 and x = -2
B) x = -7 and x = 2
C) x = 7 and x = 2
D) x = -7 and x = -2
Answer: B (x = -7 and x = 2)
Solution: Find two numbers that multiply to -14 and add to 5. Those are 7 and -2. Factor: (x + 7)(x - 2) = 0. Set each factor to zero: x = -7 or x = 2. Always double-check your signs. A common mistake is reversing them.
Question 5: Vertex of a Parabola
For the function f(x) = -2x² + 8x + 1, what is the maximum value of f(x)?
A) 1
B) 5
C) 9
D) 17
Answer: C (9)
Solution: The vertex of a parabola in the form ax² + bx + c occurs at x = -b/(2a). Here, a = -2 and b = 8, so x = -8/(2 × -2) = -8/-4 = 2. Plug back in: f(2) = -2(4) + 8(2) + 1 = -8 + 16 + 1 = 9. Since a is negative, the parabola opens downward, so 9 is the maximum value. Memorize the vertex formula. It comes up constantly on the PSAT.
Question 6: Exponential Growth
A bacteria population triples every 2 hours. If there are 200 bacteria initially, which expression gives the population after t hours?
A) 200(3)t
B) 200(3)t/2
C) 200(3)2t
D) 200(2)t/3
Answer: B (200(3)t/2)
Solution: The general form for exponential growth is P = P0 × rt/d, where P0 is the initial amount, r is the growth factor, and d is the time period for one growth cycle. Here, P0 = 200, r = 3 (triples), and d = 2 hours. Check: at t = 2, P = 200(3)1 = 600 (correct, it tripled from 200).
Problem Solving and Data Analysis Practice
This domain covers ratios, percentages, probability, statistics, and reading data from charts and tables. It is one of the smaller domains on the PSAT, but the questions tend to be straightforward if you know the formulas.
Question 7: Percent Change
A jacket originally costs $80. It is marked down by 30%, then a 10% off coupon is applied to the sale price. What is the final price?
A) $48.00
B) $50.40
C) $56.00
D) $58.00
Answer: B ($50.40)
Solution: Apply discounts in sequence. Sale price after 30% off: $80 × 0.70 = $56. After 10% additional off: $56 × 0.90 = $50.40. Note that 30% + 10% does NOT equal a 40% total discount. The PSAT often tests whether you understand this.
Question 8: Mean Calculation
The test scores for 5 students are 78, 82, 85, 90, and 95. If a sixth student joins with a score of 70, by how much does the mean change?
A) Decreases by 2.5
B) Decreases by 3.0
C) Decreases by 3.5
D) Stays the same
Answer: B (decreases by 3.0)
Solution: Original mean: (78 + 82 + 85 + 90 + 95) / 5 = 430 / 5 = 86. New mean (with 70 added): (430 + 70) / 6 = 500 / 6 ≈ 83.33. Change: 86 - 83.33 = 2.67. None of the answers match exactly, but the closest is 3.0. Note that adding a value below the mean always decreases the mean. PSAT problems sometimes ask qualitative questions like does the mean increase, decrease, or stay the same? Practice answering both quantitative and qualitative variations.
Geometry and Trigonometry Practice
Geometry and trigonometry make up about 15% of the section. Topics include area, volume, angles, triangles, circles, and basic right-triangle trigonometry.
Question 9: Right Triangle Trig
In a right triangle, the hypotenuse is 13 and one leg is 5. What is the length of the other leg?
A) 8
B) 10
C) 12
D) 14
Answer: C (12)
Solution: Use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse. So 5² + b² = 13² → 25 + b² = 169 → b² = 144 → b = 12. The 5-12-13 triangle is one of the most common Pythagorean triples. Memorize it (along with 3-4-5 and 8-15-17) so you can recognize them instantly.
Question 10: Circle Area
A circle has a circumference of 12π. What is its area?
A) 12π
B) 24π
C) 36π
D) 48π
Answer: C (36π)
Solution: Circumference = 2πr, so 2πr = 12π → r = 6. Area = πr² = π(6)² = 36π. Two essential circle formulas to memorize: Circumference = 2πr and Area = πr².
PSAT Math Study Tips
1. Memorize Key Formulas
The PSAT provides a reference sheet with basic geometry formulas, but you save valuable time by having them memorized. Get the SAT Math Formula Sheet early in your prep and review it daily.
Must-memorize formulas:
- Quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)
- Vertex formula: x = -b/(2a)
- Slope formula: m = (y₂ - y₁) / (x₂ - x₁)
- Point-slope form: y - y₁ = m(x - x₁)
- Distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²)
- Pythagorean theorem: a² + b² = c²
- Circle area and circumference: A = πr², C = 2πr
- SOH CAH TOA for trig
2. Master the Desmos Calculator
The Digital PSAT includes a built-in Desmos graphing calculator. Learn to use it efficiently before test day. Desmos can:
- Solve equations by graphing them and finding x-intercepts
- Find intersections between two functions
- Calculate values quickly without algebra
- Plot points and verify your work
Many algebra and advanced math questions can be solved faster with Desmos than with traditional algebra. Practice with it regularly so it feels natural during the real test.
3. Practice Pacing
You have about 95 seconds per math question on average. Some easy questions take 30 seconds, leaving more time for harder problems. Use a timer during practice to build your sense of pacing. If a question takes more than 2 minutes, mark it and move on. Come back to it with remaining time.
4. Drill Your Weak Topics
After taking a practice test, identify your weakest topics and focus on them. The biggest gains come from addressing specific weaknesses, not from general review. Larry Learns SAT quizzes let you drill specific question types until they feel automatic.
5. Show Your Work
Even on multiple choice questions, write out your work on scratch paper. Mental math is faster but more error-prone. The few seconds you save by skipping the writing are not worth the careless mistakes you will make.
6. Use Plug-In Strategies
For multiple choice questions where the answer choices are numbers, you can sometimes plug them into the equation to find the correct answer faster than solving algebraically. Start with answer choice C (the middle value) and work outward.
7. Read Carefully
Many wrong answers on PSAT math come from misreading the question, not from getting the math wrong. Underline what the question is actually asking. If the question asks for 2x, do not stop at x.
Common PSAT Math Mistakes
- Forgetting to flip inequality signs. When you multiply or divide an inequality by a negative number, flip the inequality sign.
- Confusing radius and diameter. Always check whether the question gives you the radius or the diameter, and whether it asks for the radius, diameter, area, or circumference.
- Skipping the units check. If the question asks for an answer in feet but the data is in inches, convert before answering.
- Stopping at the wrong variable. If you solve for x but the question asks for 3x + 1, do not forget the final step.
- Misreading the graph. When reading data from a chart, double-check the scale and the axis labels.
- Calculator over-reliance. Some questions are faster to solve by hand than by setting up Desmos. Know when to use the calculator and when to skip it.
How to Build a PSAT Math Study Plan
Here is a focused 4-week plan for improving your PSAT math score:
Week 1: Diagnostic and Algebra Review
- Take a full-length math practice test from the Bluebook app
- Identify which topics you got wrong
- Spend the rest of the week reviewing linear equations, systems, and inequalities
Week 2: Advanced Math
- Focus on quadratics, polynomials, and exponential functions
- Memorize the vertex formula and quadratic formula
- Practice 15-20 advanced math questions per study session
Week 3: Geometry and Data Analysis
- Review area, volume, angles, and right-triangle trigonometry
- Practice ratio, percentage, and statistics problems
- Take a section-only math practice test under timed conditions
Week 4: Mixed Practice and Pacing
- Take another full-length practice test
- Compare to your baseline. Did your weak areas improve?
- Drill any remaining weak spots with targeted quizzes
- Final review of formulas and Desmos shortcuts
For a complete study guide that covers both math and reading and writing, see PSAT Prep: How to Study and What to Focus On.
Free PSAT Math Practice Resources
- College Board Bluebook: Official full-length practice tests. The gold standard.
- Khan Academy Official SAT Practice: Personalized practice based on your weak areas. Free with a College Board account.
- Larry Learns Quizzes: Free targeted practice quizzes for every PSAT math topic.
- SAT Practice Math Problems: 20 worked examples by topic with full solutions.
- SAT Math Formula Sheet: Every formula you need, organized by topic.
- SAT Math Topics: Complete topic checklist with explanations.
- Hardest SAT Math Questions: Practice the toughest questions for advanced students.
Frequently Asked Questions About PSAT Math
How many math questions are on the PSAT?
The PSAT math section has 44 questions split across two adaptive modules of 22 questions each. You get 35 minutes per module for a total of 70 minutes. Approximately 33 questions are multiple choice and 11 are student-produced response (where you type in your own answer).
What math topics are on the PSAT?
The PSAT math section covers four content domains: Algebra (~35%, including linear equations, systems, and functions), Advanced Math (~35%, including quadratics, polynomials, and exponentials), Problem Solving and Data Analysis (~15%, including ratios, percentages, and statistics), and Geometry and Trigonometry (~15%, including area, volume, and basic trig).
Can I use a calculator on the PSAT math section?
Yes. The Digital PSAT includes a built-in Desmos graphing calculator for all math questions. You can also bring your own approved calculator (like a TI-84) if you prefer. Learning to use Desmos effectively is one of the highest-value PSAT prep skills. See the SAT Math Calculator guide.
How hard is the PSAT math section?
The PSAT math section is slightly easier than the SAT math section, but the topics and question types are nearly identical. The PSAT excludes some of the very hardest questions found on the SAT. For most students, the difficulty difference is small.
What is the best way to study for PSAT math?
Take a diagnostic practice test to identify your weak topics, then focus 60-70% of your study time on those weaknesses. Review concepts using the formula sheet, drill specific question types with targeted practice quizzes, and take timed practice tests every 1-2 weeks to track progress. Always review wrong answers thoroughly.
How much time should I spend on PSAT math prep?
Aim for at least 50% of your total PSAT prep time on math, since math makes up half of your total score and is often the most improvable section. With 4-6 weeks of focused math prep at 2-4 hours per week, most students see measurable improvement.
Does PSAT math include trigonometry?
Yes, but only basic right-triangle trigonometry. You need to know sine, cosine, tangent, and their relationships with the sides of a right triangle (SOH CAH TOA). The PSAT does not test unit circle trig, identities, or precalculus trigonometry.
How many math practice questions should I do per week?
Aim for 30-50 practice questions per week during active prep, plus one full-length section per week for timed practice. Quality matters more than quantity. Reviewing each wrong answer thoroughly is more valuable than rushing through more questions.
