PSAT/NMSQT, PSAT 10 & PSAT 8/9 Math

PSAT Math Practice Test: Free Practice, Lessons & Study Guide

PSAT Math is the same four-domain digital test at three levels: PSAT/NMSQT, PSAT 10 and PSAT 8/9. Each practice test here has 44 questions and a 70-minute timer, with an estimated score and full explanations. A free formula sheet and topic lessons help you fix what you missed.

PSAT/NMSQT MATH ONLINE CENTER — original handwritten comic illustration.

What is the PSAT/NMSQT?

The PSAT/NMSQT and PSAT 10 are College Board tests taken at school on the Bluebook app. The PSAT/NMSQT is given in October, mostly to 11th graders, and is the qualifying test for the National Merit Scholarship Program. The PSAT 10 is given to 10th graders in spring. Both have 98 questions in 2 hours 14 minutes, including a 44-question, 70-minute Math section, scored 320 to 1520.

Math section
44 questions, 70 minutes, 2 adaptive modules
Total test
98 questions, 2 hours 14 minutes
Score range
320-1520 total; Math 160-760
Math benchmark
480 (grade 10), 510 (grade 11)
Calculator
Allowed on the entire Math section; Desmos built into Bluebook

Source: College Board official information. Rules and dates can change, so confirm with the official site or your test center.

PSAT Math Test Outline

PSAT 8/9, PSAT 10, and PSAT/NMSQT share a two-module Math section. Explore the level that matches your test, then use its practice and topic resources.

PSAT LEVEL 01 · GRADES 8–9

PSAT 8/9 Math

70 minutes · 44 questions

Build the math foundations assessed in the PSAT 8/9, with all four content domains appearing across its two timed modules.

Topics covered
  • Algebra
  • Advanced Math
  • Problem-Solving and Data Analysis
  • Geometry
PSAT LEVEL 02 · GRADE 10

PSAT 10 Math

70 minutes · 44 questions

Practice algebra, advanced math, problem-solving and data analysis, and geometry and trigonometry across two modules.

Topics covered
  • Algebra
  • Advanced Math
  • Problem-Solving and Data Analysis
  • Geometry and Trigonometry
PSAT LEVEL 03 · NATIONAL MERIT

PSAT/NMSQT Math

70 minutes · 44 questions

Review the PSAT/NMSQT Math section and connect practice to the same four domains used on PSAT 10.

Topics covered
  • Algebra
  • Advanced Math
  • Problem-Solving and Data Analysis
  • Geometry and Trigonometry

6 Free Full-Length PSAT Math Practice Tests

Using Digital PSAT Math Complete Prep? Your book includes access to 50 full-length interactive practice tests. Use the QR codes in your book to open those tests. The six free tests below are a separate collection.

Take a complete PSAT Math simulation online. Each test has 44 questions, a 70-minute timer, two module labels, 33 multiple-choice items, 11 student-produced responses, an estimated PSAT Math score, topic breakdowns, and full explanations.

PSAT Math Practice Test 1

44 questions, 70 minutes, 33 multiple-choice items, 11 student-produced responses, instant score report, explanations, and topic review.

Start Test 1

PSAT Math Practice Test 2

44 questions, 70 minutes, 33 multiple-choice items, 11 student-produced responses, instant score report, explanations, and topic review.

Start Test 2

PSAT Math Practice Test 3

44 questions, 70 minutes, 33 multiple-choice items, 11 student-produced responses, instant score report, explanations, and topic review.

Start Test 3

PSAT Math Practice Test 4

44 questions, 70 minutes, 33 multiple-choice items, 11 student-produced responses, instant score report, explanations, and topic review.

Start Test 4

PSAT Math Practice Test 5

44 questions, 70 minutes, 33 multiple-choice items, 11 student-produced responses, instant score report, explanations, and topic review.

Start Test 5

PSAT Math Practice Test 6

44 questions, 70 minutes, 33 multiple-choice items, 11 student-produced responses, instant score report, explanations, and topic review.

Start Test 6

Free interactive practice

PSAT Study Lab: Flashcards, Question of the Day and Study Plan

Short, active practice for the digital PSAT: flip PSAT Math flashcards for formulas, key concepts and Desmos moves, learn the grammar rules behind Reading and Writing questions, quiz yourself on vocabulary in context, answer a new question every day and build a week-by-week plan for your test date.

54 math cards23 grammar rules1,000 words

PSAT Math flashcards

Formulas, concepts, quick “solve it” problems and Desmos tips, grouped by the four PSAT Math content domains. Mark each card “Got it” or “Review again”; cards you miss collect in your review list.

Keys: Space flip · ← → move · 1 review again · 2 got it

See all 54 cards as a list
What is the slope of the line through (x1, y1) and (x2, y2)?
m = (y2 − y1) / (x2 − x1). Example: through (2, 5) and (6, 13), m = 8/4 = 2.
In y = mx + b, what do m and b tell you?
m is the slope (change in y for each 1-unit increase in x). b is the y-intercept, the value of y when x = 0. In a word problem, b is usually the starting amount and m the rate.
How are the slopes of parallel and perpendicular lines related?
Parallel lines have equal slopes. Perpendicular slopes are negative reciprocals, so their product is −1. A line perpendicular to y = −(1/3)x + 2 has slope 3.
When does a system of two linear equations have no solution? Infinitely many?
No solution: same slope, different y-intercepts (parallel lines). Infinitely many: the equations describe the same line (one is a multiple of the other).
For what value of k does the system 2x + 3y = 6 and kx + 9y = 18 have infinitely many solutions?
k = 6. Multiplying the first equation by 3 gives 6x + 9y = 18, which must match the second equation exactly.
Solve 3(x − 4) = 2x + 5.
x = 17. Distribute: 3x − 12 = 2x + 5, then subtract 2x and add 12.
How do you find the slope of Ax + By = C?
Slope = −A/B. Example: 4x + 2y = 10 has slope −4/2 = −2. (Solve for y if you forget: y = −2x + 5.)
Solve the system x + y = 10 and x − y = 4.
Add the equations: 2x = 14, so x = 7 and y = 3.
A phone plan costs $25 plus $8 per month. What linear model fits, and what does 8 mean?
C = 25 + 8m, where m is months. The 8 is the slope: the cost increases by $8 for each additional month. The 25 is the cost when m = 0.
Solve |x − 3| < 5.
−5 < x − 3 < 5, so −2 < x < 8.
How do you graph y > 2x + 1?
Draw y = 2x + 1 as a dashed line (the line itself is not included) and shade above it. Use a solid line for ≥ or ≤.
What is the quadratic formula?
For ax2 + bx + c = 0: x = (−b ± √(b2 − 4ac)) / (2a).
What does the discriminant b2 − 4ac tell you?
Positive: two real solutions. Zero: exactly one real solution. Negative: no real solutions. Example: x2 + 4x + 7 = 0 has 16 − 28 < 0, so no real solutions.
Where is the vertex of y = a(x − h)2 + k?
At (h, k). The parabola opens up if a > 0 and down if a < 0.
Find the vertex of y = x2 − 6x + 5.
x = −b/(2a) = 6/2 = 3, and y = 9 − 18 + 5 = −4. Vertex: (3, −4).
For ax2 + bx + c = 0, what are the sum and product of the solutions?
Sum = −b/a, product = c/a. For 2x2 − 8x + 6 = 0: sum = 4, product = 3 (the solutions are 1 and 3).
How does a2 − b2 factor?
(a + b)(a − b). Example: x2 − 49 = (x + 7)(x − 7).
Name three exponent rules you will use most.
xa · xb = xa+b; (xa)b = xab; xm/n = the nth root of xm. Also x−a = 1/xa and x0 = 1 (x ≠ 0).
What are the exponential growth and decay models?
Growth: y = a(1 + r)t. Decay: y = a(1 − r)t. $500 growing 4% per year: 500(1.04)t. The base tells you the rate: 0.85 means a 15% decrease each period.
If f(x) = 2x2 − 3, what is f(−2)?
f(−2) = 2(4) − 3 = 5. Square first, then multiply.
If f(x) = x + 3 and g(x) = 2x, what is f(g(4))?
Work inside out: g(4) = 8, then f(8) = 11.
How does y = f(x − h) + k move the graph of f?
Right h units and up k units. y = −f(x) reflects across the x-axis; y = f(−x) reflects across the y-axis.
If p(3) = 0, what do you know about the polynomial p(x)?
3 is a zero (an x-intercept), and (x − 3) is a factor of p(x). More generally, the remainder when p(x) is divided by (x − a) equals p(a).
Solve x2 − 5x − 14 = 0.
(x − 7)(x + 2) = 0, so x = 7 or x = −2.
Solve √(x + 7) = x − 5.
Square: x + 7 = x2 − 10x + 25, so x2 − 11x + 18 = 0 and x = 9 or x = 2. Check: x = 2 gives 3 = −3, which is false. Only x = 9 works.
How do you find percent change?
(new − old) / old × 100%. From 80 to 92: 12/80 = 15% increase.
A price rises 20% and then falls 20%. What is the overall change?
1.20 × 0.80 = 0.96, so the final price is 4% lower than the original. Percent changes multiply; they do not cancel.
Which is affected more by an outlier: the mean or the median?
The mean. One very large or small value pulls the mean toward it, while the median (the middle value) barely moves.
What does standard deviation measure?
How spread out the data are around the mean. A data set whose values cluster tightly near the mean has a smaller standard deviation.
How do you read a conditional probability from a two-way table?
Restrict to the given group first. P(A given B) = (number in both A and B) / (number in B). Watch the word “of” or “given” to find the right total.
Convert 60 miles per hour to feet per second (1 mile = 5,280 feet).
60 × 5,280 / 3,600 = 88 feet per second. Line up units so the ones you do not want cancel.
A recipe uses 3 cups of flour for 4 servings. How much flour for 10 servings?
3/4 = x/10, so x = 7.5 cups.
When can a survey result be generalized?
Only to the population the random sample was drawn from. A random sample of one school’s students supports conclusions about that school, not all teenagers. Random assignment (in an experiment) is what supports cause-and-effect claims.
How do you interpret the slope of a line of best fit?
It is the predicted change in y for each 1-unit increase in x, in the units of the problem. Example: slope 2.5 in a hours-vs-score plot means about 2.5 more points per extra hour.
The mean of five numbers is 12. Four of them are 10, 11, 14 and 15. What is the fifth?
Total = 5 × 12 = 60. The four known numbers add to 50, so the fifth is 10.
Area and circumference of a circle?
Area = πr2; circumference = 2πr. Both are on the reference sheet, but knowing them saves time.
How do you find arc length and sector area from a central angle in degrees?
Arc length = (θ/360) × 2πr. Sector area = (θ/360) × πr2. Radius 9, angle 40°: arc = 2π.
How do degrees and radians convert?
180° = π radians. Multiply degrees by π/180 to get radians. In radians, arc length is simply s = rθ.
Find the center and radius of x2 + y2 − 6x + 4y − 12 = 0.
Complete the square: (x − 3)2 + (y + 2)2 = 12 + 9 + 4 = 25. Center (3, −2), radius 5.
What are the side ratios of the special right triangles?
45-45-90: x, x, x√2. 30-60-90: x (opposite 30°), x√3 (opposite 60°), 2x (hypotenuse).
Which Pythagorean triples are worth memorizing?
3-4-5, 5-12-13, 8-15-17 and 7-24-25, plus their multiples (6-8-10, 9-12-15). a2 + b2 = c2 covers everything else.
What do sine, cosine and tangent equal in a right triangle?
SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
How are sin x and cos(90° − x) related?
They are equal: sin x = cos(90° − x). So sin 30° = cos 60°. Questions often hide this in the two acute angles of a right triangle.
If two similar figures have a side ratio of k, how do their areas and volumes compare?
Areas scale by k2 and volumes by k3. Doubling every side makes the area 4 times as large.
What is the sum of the interior angles of an n-sided polygon?
(n − 2) × 180°. A hexagon: 4 × 180° = 720°. A triangle’s angles always add to 180°.
Volumes of a cylinder, cone and sphere?
Cylinder πr2h; cone (1/3)πr2h; sphere (4/3)πr3. These are on the reference sheet you get during the test.
A right triangle has legs 6 and 8. What is the hypotenuse, and what is the sine of the angle opposite the side of length 6?
Hypotenuse = 10 (a 3-4-5 triangle doubled). sin = 6/10 = 0.6.
How can Desmos solve a one-variable equation like 3x + 7 = x2 − 5?
Type each side as its own line (y = 3x + 7 and y = x2 − 5) and tap the intersection points. Their x-values are the solutions.
How do you solve a system of equations in Desmos?
Enter both equations exactly as written (no need to solve for y) and tap where the graphs cross.
How do you find a line or curve of best fit in Desmos?
Add a table with your data in x1 and y1, then type y1 ~ mx1 + b (use the tilde). Desmos returns m and b.
How can a slider help when a question has an unknown constant?
Type the equation with the constant as a letter (for example y = x2 + kx + 9), add the slider and move it until the graph meets the condition, such as touching the x-axis once.
About how much time do you have per question in each Math module?
Each module is 35 minutes for 22 questions, roughly 1 minute 35 seconds per question. Mark a slow question, move on and come back.
Should you guess if you are unsure?
Yes. There is no penalty for wrong answers, so never leave a question blank. Eliminate what you can first.
What are the rules for student-produced (grid-in) answers?
You can enter up to 5 characters for a positive answer and up to 6 for a negative one (the minus sign counts). Fractions or decimals are fine; if a fraction does not fit, enter its decimal form. No mixed numbers.

Jump into PSAT Math

A friendly place to start

See it. Understand it. Try it.

PSAT Math Quick Review turns each idea into a picture, a clear explanation, and a worked example. Start with the basics, or jump to the skill you want to learn.

Open Quick Review

6 topic areas · 96 short lessons · learn at your own pace
Pick a direction

Six ways into PSAT Math

Every lesson starts with a visual explanation and ends with a chance to practice.

01 · Number sense
Fractions & decimalsSee how a part of a whole becomes a number.
02 · Everyday math
Percent word problemsMake sense of discounts, tax, tips, and change.
03 · Visual patterns
Slope & graphingTurn points and lines into a story you can read.
04 · Algebra
Multi-step equationsUndo one step at a time to find the unknown.
05 · Shapes & space
Geometry formulasConnect the shape to its area, perimeter, or volume.
06 · Data stories
Data & averagesRead charts, find typical values, and judge chance.
How it worksOne small step at a time
Read the ideaStart with a short, friendly explanation.
See it workFollow the picture and worked example.
Try it yourselfCheck your answer, then take the quiz.
Practice, learn, then review formulas. Start with a printable worksheet, open the matching lesson when a skill needs support, then use the PSAT Math formula guide below for final review.

PSAT Math Skill Quizzes

Short, focused quizzes, pick one skill, answer 10 questions, get instant scoring and full step-by-step solutions. Each opens right here in a popup.

Quick checks for selected Math skills.Built from the Grade 7 and Algebra 1 math skills that match PSAT Math foundations.

PSAT Math Topics: Learn, Practice, and Quiz

Choose a topic, open its worksheet for printable practice, then take a short quiz from the same row.

96 topics · worksheets · quizzes

PSAT Math Mistakes to Watch For

Use a missed or guessed question to choose your next review. Open a worked check, then follow the link to the matching topic. These examples explain the method and are not official test questions.

1

Negative signs and powers

Parentheses decide whether a negative sign is part of the base. Copy the expression carefully before evaluating it.

See a worked check

(-2)² = 4 because the base is -2. In -2², square 2 first, then apply the negative sign: -4.

Review the matching topic →

2

Adding fractions

Adding denominators does not create a common unit. Rewrite the fractions with the same denominator, then add their numerators.

See a worked check

1/3 + 1/4 = 4/12 + 3/12 = 7/12. The denominator stays 12.

Review the matching topic →

3

Distributing to a whole expression

Multiplication outside parentheses applies to each term. Keep the minus sign attached to its term as you expand.

See a worked check

2(3x – 4) = 6x – 8. Expanding only the first term would leave an incorrect constant.

Review the matching topic →

4

Confusing area and perimeter

Sketch the shape and write the unit next to the requested measurement. A boundary length and the space inside a figure use different formulas.

See a worked check

A square with side 12 cm has perimeter 4 × 12 = 48 cm and area 12 × 12 = 144 cm².

Review the matching topic →

5

Reading the full data set

Count every value when finding a mean, and read graph scales before comparing heights. A missing zero can change the result.

See a worked check

The mean of 0, 4, and 11 is (0 + 4 + 11)/3 = 5. There are three values, even though one is zero.

Review the matching topic →

Choose The Right PSAT Math Book

Use a study guide when you need explanations; choose a workbook when you need more practice with individual topics. The two options below make those starting points easy to compare.

PSAT Math FAQ

How many math questions are on the PSAT?

The PSAT/NMSQT and PSAT 10 Math section has 44 questions in two modules, with 70 minutes total. The first module has a mix of easy, medium and hard questions. The second module adapts and is harder or easier based on your performance. Some questions ask you to type in an answer.

What math topics are on the PSAT?

PSAT math covers Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. Expect linear equations, systems and inequalities, quadratic and exponential functions, ratios, percentages, statistics and probability, plus area, volume, triangles, circles and right-triangle trigonometry. Algebra and Advanced Math make up the largest share.

What is a good PSAT math score?

PSAT math scores range from 160 to 760. College Board's grade-level math benchmark is 480 for 10th graders and 510 for 11th graders. Meeting the benchmark means you are on track for college readiness. National Merit qualifying cutoffs are set by the National Merit Scholarship Corporation and vary by state and year.

Is the PSAT/NMSQT different from the PSAT 10?

The two tests have the same content, format and score scale. The difference is timing and purpose. The PSAT/NMSQT is given in October, mostly to 11th graders, and it is the qualifying test for National Merit. The PSAT 10 is given to 10th graders in spring and is not used for National Merit.

How should I practice for PSAT math?

Start with a free full-length practice test in the Bluebook app to see the adaptive format and the built-in Desmos calculator. Then work on your weakest skill areas with targeted practice questions, such as linear equations or data analysis. Finish with another timed practice test to check your progress.

What should I practice first for PSAT Math?

Begin with a short mixed set for your PSAT level. Review the skills behind your missed or guessed questions; if basic arithmetic slows you down, work on that foundation before returning to algebra and the other tested domains.

How should I use this PSAT Math Online Center?

Begin with the main starting resource, choose one weak skill from the map, practice it, then return to the online center for the next topic or a timed review.

Are there free resources on this page?

Yes. The online center links to free Effortless Math resources such as PSAT Math Course, Free PSAT Math Practice Test, PSAT Math Study Guide.

Which PSAT Math skills matter most?

Use the four tested domains to organize review: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry for PSAT 10/NMSQT (Geometry for PSAT 8/9). Use missed questions to choose a specific skill within a domain, rather than assuming every student needs the same starting topic.

When should I use a book or workbook?

Use a book when the student needs a structured sequence, repeated practice, or a printed path that is easier to follow than scattered online links.

Related Online Centers

Make This Your PSAT Math Starting Point

Bookmark this online center, choose one weak area, and use the linked practice pages and books to move from scattered review to a clear study path.

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Why trust Effortless Math?

How this PSAT Math Online Center supports your review

This test prep online center is part of the Effortless Math library for PSAT Math. We connect lessons, worksheets, practice tests, books, and tools so students can study with a clearer next step.

Last updated: October 5, 2026
Students working together on math practice
Since 2014Helping students build math confidence and prepare for exams.
Topic-focused resourcesMove from a missed skill to its lesson, practice links, and review tools.
Study at your paceChoose a topic, check your method, and return to mixed review when ready.
Free first stepsWorksheets, flashcards, practice tests, and topic lessons.
Authored for learnersResources are written in student-friendly language, with examples before heavier practice whenever possible.
Reviewed for usefulnessPages are checked for topic fit, internal links, answer support, product relevance, and learning sequence.
Commercial links are separatedBooks and paid resources are recommended as next steps after free practice paths, not as the only way forward.

This is an independent Effortless Math PSAT Math preparation online center. Official exam, standards, or curriculum owners do not endorse this page.


Test-first path

Start With A Practice Test

Choose the PSAT level your school has scheduled, then use mixed practice to identify a review target. Note whether a miss came from a concept, setting up an equation, interpreting data, or checking an answer; review that skill before a fresh attempt.

Start the timed test

1

Take a diagnostic first

Start with mixed practice. Mark every missed question by topic instead of only looking at the score.

Start PSAT Math practice

2

Know what is tested

Use the outline or official structure to see which skills matter most before adding more study time.

See what is tested

3

Fix one weak skill

Choose one target, such as Number sense, and practice it before returning to a full mixed set.

Find weak-skill fixes

4

Move into lessons or books

After the first test, use lessons, flashcards, worksheets, or the recommended book path for structure.

Open the full course

A USEFUL NEXT STEP

PSAT Math: study questions

How is the PSAT/NMSQT structured?

The digital PSAT/NMSQT has Reading and Writing and Math sections. Reading and Writing has 54 questions in 64 minutes; Math has 44 questions in 70 minutes. Standard testing time is 2 hours and 14 minutes, excluding breaks.

Official source ↗
Which PSAT level should I choose?

Use the resources for the test your school has scheduled: PSAT/NMSQT, PSAT 10, or PSAT 8/9. This Online Center links to Math preparation for each level. Check with your school if you are unsure which version you will take.

Official source ↗
Are these official PSAT preparation materials?

Effortless Math is an independent publisher. Its original materials are preparation resources, and practice results are study feedback rather than official scores. Use the test provider’s website for registration, policies, and official practice.

Official source ↗

Resources from Effortless Math · Editorial standards · Test details checked October 5, 2026