Free PSAT/NMSQT Math Course: Lessons, Practice Questions and Full Tests
Learn every topic on the PSAT/NMSQT Math section with this free course: 23 step-by-step lessons, 715 practice questions, 67 topic quizzes, 23 timed mini-exams and 11 full-length practice tests. Every question comes with a worked explanation, and you can start right now without creating an account.
A complete, free PSAT/NMSQT Math course
The PSAT/NMSQT is more than a practice SAT. For 11th graders, it is the qualifying test for the National Merit Scholarship Program, so every math point can matter. This free course is built to help you earn those points. Each of the 23 lessons explains one skill in plain language with worked examples, then links to a matching quiz so you can practice right away. When a topic feels solid, timed mini-exams and full-length practice tests build the speed and accuracy you need on test day.
The lessons follow the four official College Board math domains, so your study time lines up with what actually appears on the test. Everything you learn here also carries straight over to the SAT, which uses the same domains and question styles. Whether you are a sophomore getting a first look or a junior aiming for National Merit recognition, you can work at your own pace and target your weakest topics.
PSAT/NMSQT Math format at a glance
The PSAT/NMSQT is digital and adaptive, just like the SAT. Here is what to expect on the Math section:
| Who takes it | Mostly 10th and 11th graders; only the 11th grade test counts for National Merit |
|---|---|
| Number of questions | 44, in two modules of 22 |
| Time limit | 70 minutes (35 minutes per module, about 1.6 minutes per question) |
| Calculator | Allowed on every question; the built-in Desmos graphing calculator is available |
| Question types | About 75% multiple choice (4 options), about 25% student-produced response (you type the answer) |
| Content domains | Algebra about 35%, Advanced Math about 32.5%, Problem-Solving and Data Analysis about 20%, Geometry and Trigonometry about 12.5% |
| Adaptive testing | Your Module 1 performance decides whether Module 2 is easier or harder |
| Scoring | Math: 160 to 760 (total test: 320 to 1520); no penalty for wrong answers |
Algebra and Advanced Math together make up about two-thirds of the section, which is why most of the lessons below focus on them. A strong first module also unlocks the harder second module, where the highest scores, and National Merit-level results, come from.
All 23 free PSAT/NMSQT Math lessons
The lessons are grouped by the official PSAT/NMSQT Math domains. Each one pairs a clear explanation with matching quizzes in the question bank.
Foundations
Algebra (about 35% of the test)
Advanced Math (about 32.5%)
Problem-Solving and Data Analysis (about 20%)
Geometry and Trigonometry (about 12.5%)
Ready to test yourself?
Jump into 715 free PSAT/NMSQT Math questions with full explanations.
Try 5 free PSAT/NMSQT Math sample questions
These original questions show the style and level of the course, with at least one from each official domain. Pick an answer to see whether you are right, then read the step-by-step explanation.
The line y = −2x + 3 passes through which of the following points?
Correct answer: C. (2, −1)
Substitute each x-value and check the y-value. For x = 2: y = −2(2) + 3 = −1, so (2, −1) is on the line. For x = −1 the line gives y = 5, and for x = 3 it gives y = −3, so choices B and D fail. Choice A drops the negative sign on the slope.
The value of a phone, in dollars, t years after purchase is modeled by V(t) = 800(0.9)t. What is the value of the phone after 2 years?
Correct answer: B. $648
Substitute t = 2: V(2) = 800(0.9)2 = 800(0.81) = $648. Choice A subtracts 10% of the original price twice, which treats exponential decay as linear. Choice C is the value after just 1 year.
What is the vertex of the parabola y = x2 − 6x + 5?
Correct answer: A. (3, −4)
The x-coordinate of the vertex is −b/(2a) = 6/2 = 3. Substitute to find y: 32 − 6(3) + 5 = 9 − 18 + 5 = −4. The vertex is (3, −4). Choice B has the wrong sign on the x-coordinate, and choice C uses the y-intercept instead.
A bag contains 4 red, 6 blue and 5 green marbles. One marble is chosen at random. What is the probability that it is not blue?
Correct answer: D. 3/5
There are 4 + 6 + 5 = 15 marbles, and 4 + 5 = 9 of them are not blue. The probability is 9/15 = 3/5. Choice A is the probability that the marble is blue, 6/15 = 2/5.
A circle in the xy-plane has the equation (x − 2)2 + (y + 1)2 = 25. What are the coordinates of its center?
Correct answer: B. (2, −1)
The standard form of a circle is (x − h)2 + (y − k)2 = r2, with center (h, k). Here h = 2, and y + 1 means y − (−1), so k = −1. The center is (2, −1) and the radius is 5. Choice A flips both signs, the most common mistake.
How to study for PSAT/NMSQT Math with this course
- Find your starting point. Take one timed mini-exam and note which domains cost you the most points.
- Learn the topic. Open the matching lesson above and work through the examples before trying the quiz.
- Practice by topic. Take the topic quizzes and read every explanation, including the ones you got right.
- Build speed. Use the 23 timed mini-exams to practice the pace of about 1.6 minutes per question.
- Simulate test day. Take full 44-question practice exams in one sitting, using Desmos the way you will on the real test.
- Review and repeat. Go back to the lessons for any topic where you still miss questions, then retest.
If you are a junior aiming for National Merit, start early. A few focused sessions each week over the summer and early fall, with careful review of every explanation, does far more than cramming the week before the October test.
PSAT/NMSQT Math course: frequently asked questions
Is this PSAT/NMSQT Math course really free?
Yes. All 23 lessons, 67 quizzes, 715 practice questions, 23 timed mini-exams and 11 full practice exams are free, and you do not need an account to start.
How many questions are on the PSAT/NMSQT Math section?
The Math section has 44 questions split into two modules of 22. You get 35 minutes per module, 70 minutes in total. About 75% are multiple choice and about 25% ask you to type in your own answer.
Can I use a calculator on the PSAT/NMSQT Math section?
Yes. A calculator is allowed on every math question. The built-in Desmos graphing calculator is available in the testing app, and you may also bring an approved calculator.
How is the PSAT/NMSQT scored?
The Math section is scored from 160 to 760, and the total score ranges from 320 to 1520. The test is adaptive, so your first module decides the difficulty of the second, and there is no penalty for wrong answers.
Does the PSAT/NMSQT count for National Merit?
Yes, but only the test you take in 11th grade. The National Merit Scholarship Corporation converts your junior-year scores into a Selection Index, which decides who is recognized. Taking it earlier is valuable practice but does not count toward the program.
How should I use this PSAT/NMSQT Math course?
Work through a lesson, take its topic quiz, and review every explanation you miss. Then build speed with timed mini-exams, and finish with full 44-question practice exams under real timing.
Start your free PSAT/NMSQT Math course today
23 lessons, 715 questions, 11 full practice exams. No sign-up required.