---
title: "PSAT Math Prep: PSAT/NMSQT Math and National Merit"
description: "PSAT math prep for the PSAT/NMSQT: 44 questions in two 35-minute modules, the four domains, the Selection Index and National Merit entry, with original practice."
canonical: https://learn.modernagecoders.com/psat-math-prep
source: src/pages/psat-math-prep.html
---
> PSAT math prep for the PSAT/NMSQT: 44 questions in two 35-minute modules, the four domains, the Selection Index and National Merit entry, with original practice.

In short

The PSAT/NMSQT is College Board's digital test, cosponsored by National Merit Scholarship Corporation (NMSC). Its Math section has 44 questions in two 35-minute adaptive modules, scored 160 to 760, with a Desmos calculator allowed throughout. Juniors' scores feed the NMSC Selection Index (48 to 228). Our SAT Math Prep course teaches this section live online, so the same lessons carry a student from PSAT to SAT, in a batch or 1-on-1.

One preparation, two tests

## Three courses for PSAT/NMSQT math

The PSAT and SAT share one math blueprint, so our SAT course is the core; the other two strengthen the algebra and functions beneath it.

[![SAT Math 800 Prep course thumbnail](/images/sat-math-prep.webp)  PSX / 01 SAT and PSAT math The digital SAT Suite math domains, Desmos and pacing. Open the syllabus →](/courses/sat-math-prep-course)[![Algebra Foundations course thumbnail](/images/algebra-foundations.webp)  PSX / 02 Algebra foundations Linear equations and inequalities, the largest PSAT domain. Open the syllabus →](/courses/algebra-foundations-masterclass)[![High School Mathematics course thumbnail](/images/high-school-maths.webp)  PSX / 03 High school math Nonlinear functions, data and trigonometry in depth. Open the syllabus →](/courses/complete-high-school-mathematics-mastery)

The Math section

## How long is the PSAT math section, and how many questions are on it?

Seventy minutes and 44 questions, split into two equal modules. College Board says the whole PSAT/NMSQT takes 2 hours and 14 minutes.

| Section | Minutes | Questions |
| --- | --- | --- |
| Reading and Writing | 64 | 54 |
| Math | 70 | 44 |
| Total | 134 | 98 |

| Feature | What College Board says |
| --- | --- |
| Modules | Two, each with 20 operational questions and 2 pretest questions |
| Time per module | 35 minutes (about 1 minute 35 seconds per question) |
| Order | Within each module, questions run from easiest to hardest |
| Adaptive | The second module depends on how you did in the first |
| Question types | Multiple choice and student-produced response |
| In context | Approximately 30% of questions are word problems in science, social studies or real-world settings |
| Calculator | An acceptable calculator, or the built-in Desmos calculator, on the entire section |
| Pretest questions | Do not count toward the score |

Sources: [The PSAT/NMSQT Math Section](https://satsuite.collegeboard.org/in-school-assessments/whats-on-the-test/psat-nmsqt/math), [How the PSAT/NMSQT Is Structured](https://satsuite.collegeboard.org/in-school-assessments/whats-on-the-test/psat-nmsqt/structure) and the [Fall 2026 PSAT/NMSQT Student Guide](https://satsuite.collegeboard.org/media/pdf/psat-nmsqt-student-guide.pdf), read 31 October 2026. PSAT/NMSQT is a registered trademark of College Board and National Merit Scholarship Corporation; we are not connected with either.

### The calculator rule changes the strategy

College Board's SAT Suite calculator policy allows the Desmos calculator in the Bluebook app, with graphing and scientific options, or an approved handheld calculator. Calculators with a computer algebra system (CAS) are not allowed.

Graphing both sides of an equation and reading the intersection is legitimate on every PSAT math question. Students who practise this in Bluebook beforehand save real time.

### Easiest to hardest, twice

Because each module climbs from easier to harder questions, the last few in a module are usually the most demanding. A student who spends four minutes on question 5 is spending time the hard questions at the end will need.

College Board also says it is better for most students to guess than leave a question blank, especially after ruling out one or two options.

Four domains

## What math is on the PSAT/NMSQT?

Four content domains. Algebra and Advanced Math are the two largest in College Board's question distribution; geometry is the smallest.

| Domain | Questions | Skills College Board lists |
| --- | --- | --- |
| Algebra | 13 to 15 | Linear equations in 1 and 2 variables; linear functions; systems of 2 linear equations; linear inequalities |
| Advanced Math | 12 to 14 | Equivalent expressions; nonlinear equations and systems; nonlinear functions |
| Problem-Solving and Data Analysis | 7 to 9 | Ratios, rates and units; percentages; 1-variable data; 2-variable data and scatterplots; probability and conditional probability; inference from sample statistics |
| Geometry and Trigonometry | 4 to 6 | Area and volume; lines, angles and triangles, including right triangle trigonometry |

### Why grade 10 and grade 11 feel different

Advanced Math, at 12 to 14 questions, covers quadratic, exponential, polynomial, rational and radical equations. A sophomore still in Geometry may not have met some of it in class yet; a junior in Algebra 2 usually has.

So a grade 10 result is best read as a baseline: some of the Advanced Math on it may simply not have been taught yet.

### Geometry is small but not optional

Geometry and Trigonometry is 4 to 6 questions. That is too few to build a plan around but too many to ignore, because each one is a full question in a short section.

A list of common formulas is available in the Math section, so the work is in knowing which formula applies, not in memorising it.

National Merit

## Does the PSAT count for National Merit, and in which grade?

Only the PSAT/NMSQT counts, and for most students only the one taken in grade 11. The NMSC section of College Board's fall 2026 student guide spells out the rules.

### Which test, which year

The guide says "The 2026 PSAT/NMSQT is the qualifying test for entry to the 2028 National Merit Program," and that the PSAT 10 and PSAT 8/9 "will NOT be considered for entry."

For a student spending the usual four years in high school, the guide says "you must take the qualifying test in your third year of high school (grade 11, junior year)." Sophomores who sit the 2026 test and plan four years "must take the PSAT/NMSQT again in 2027" to enter.

### Who can enter

Entrants must be enrolled as a high school student, traditional or homeschooled, progressing normally toward graduation, and planning to accept admission to college no later than the fall after they finish. They must attend high school in the United States, DC or a US commonwealth or territory, or meet citizenship rules if studying abroad.

College Board says you cannot opt out of sending PSAT/NMSQT scores to NMSC; a student who does not want to be considered contacts NMSC directly.

| Stage | About how many | When |
| --- | --- | --- |
| Entrants who meet requirements | 1.3 million | October 2026 test |
| High scorers identified by Selection Index | 50,000 | Names sent to principals in April 2027 |
| Semifinalists, the highest-scoring entrants in each state | 16,000 | Notified early September 2027 |
| Commended Students | 34,000 | Notified late September 2027 |
| Finalists | 15,000 | Notified February 2028 |
| Scholarships offered | 7,320 | Winners notified from March 2028 |

Source: the National Merit Scholarship Program section of College Board's [Fall 2026 PSAT/NMSQT Student Guide](https://satsuite.collegeboard.org/media/pdf/psat-nmsqt-student-guide.pdf), provided by NMSC, read 31 October 2026. nationalmerit.org refused our request (HTTP 403), so state-by-state Semifinalist cutoffs are not quoted here; NMSC publishes its own figures. We are not connected with NMSC and make no claim about any student's chance of recognition.

The Selection Index

## How is the PSAT Selection Index calculated?

College Board gives the formula: double the Reading and Writing score, add the Math score, and divide by 10. The result runs from 48 to 228.

| Score | Range |
| --- | --- |
| Total score | 320 to 1520 |
| Reading and Writing section | 160 to 760 |
| Math section | 160 to 760 |
| NMSC Selection Index (PSAT/NMSQT only) | 48 to 228 |

| Step | Calculation |
| --- | --- |
| 1. Reading and Writing score | 690 |
| 2. Double it | 690 x 2 = 1,380 |
| 3. Add the Math score | 1,380 + 710 = 2,090 |
| 4. Divide by 10 | 2,090 / 10 = 209 |
| 5. Check the range | 209 sits inside 48 to 228 |

### What the formula means for math

Because Reading and Writing is doubled, each Math point moves the index by 0.1 and each Reading and Writing point by 0.2: our arithmetic from College Board's formula. Math still matters, but for National Merit it counts at half weight.

A student whose math is already strong and whose reading is not may help their index more by working on Reading and Writing, even on a math page. We say so because it is true.

### What it does not mean

The index is a screening number, not a scholarship. College Board says NMSC uses Selection Index scores "to screen students who enter its scholarship programs", and NMSC sets the qualifying levels, which vary by state for Semifinalists.

For most students, the PSAT's main value is the practice it gives for the SAT and the score report that shows which skills to work on next.

Worked examples

## Three PSAT-level math problems, worked by reasoning

Our own problems in three of the four domains. They are not College Board items, and the official practice is in Bluebook.

| Step | Reasoning |
| --- | --- |
| 1. Complete the square | x^2 - 6x + 9 - 9 + 5 = (x - 3)^2 - 4 |
| 2. Read the vertex | The minimum is at (3, -4), since (x - 3)^2 is never negative |
| 3. Find the zeros | (x - 3)^2 = 4, so x - 3 = 2 or -2, giving x = 5 or x = 1 |
| 4. Cross-check by factoring | x^2 - 6x + 5 = (x - 1)(x - 5), the same zeros |
| 5. Desmos check | Graph it: the vertex and both intercepts appear when you tap the curve |

|   | Plays a sport | No sport | Total |
| --- | --- | --- | --- |
| Takes a bus | 18 | 30 | 48 |
| No bus | 42 | 30 | 72 |
| Total | 60 | 60 | 120 |

Question (ours): a student is chosen at random from those who take a bus. What is the probability they play a sport? Restrict to the bus row only: 18 of 48, so 18/48 = 3/8. The trap is dividing by 120 or by 60. Conditional probability always shrinks the denominator to the group named after "given" or "from those who".

| Step | Reasoning |
| --- | --- |
| 1. Write the inequality | 7 + 3n <= 40, where n is the number of games |
| 2. Subtract the fixed part | 3n <= 33 |
| 3. Divide | n <= 11 |
| 4. Interpret | At most 11 games, since games come in whole numbers |
| 5. Check | 7 + 3 x 11 = 40 exactly; a 12th game would need 43 credits |

Practice and a plan

## An original PSAT math practice set and a junior-year plan

Ten problems we wrote across the four domains, with answers, then a plan for the months before an October test.

| # | Domain | Problem | Answer |
| --- | --- | --- | --- |
| 1 | Algebra | Solve 4(x - 2) = 2x + 10 | x = 9 |
| 2 | Algebra | A line has slope 3 and passes through (1, 5). Its y-intercept? | 2 |
| 3 | Algebra | Solve x + 2y = 10 and x - y = 1 | x = 4, y = 3 |
| 4 | Advanced | Expand (2x - 3)^2 | 4x^2 - 12x + 9 |
| 5 | Advanced | A value of 800 halves every 5 years. Value after 15 years? | 100 |
| 6 | Advanced | Solve x^2 = 5x | x = 0 or x = 5 |
| 7 | Data | 36 is what percent of 48? | 75% |
| 8 | Data | A car uses 6 gallons for 192 miles. Miles per gallon? | 32 |
| 9 | Geometry | Right triangle legs 9 and 12: hypotenuse? | 15 |
| 10 | Geometry | Circle with area 49 pi: circumference? | 14 pi |

1. **Spring of grade 10: baseline.** Take a full-length official practice test in Bluebook and note which domain each miss belongs to.
2. **Summer: Advanced Math.** Quadratics, exponentials and equivalent expressions, the 12 to 14 questions most sophomores have seen least.
3. **September: Algebra fluency and Desmos.** Linear equations and systems quickly and accurately, plus graphing to check.
4. **Early October: rehearsal.** A second practice test under real timing: two 35-minute modules with a break between sections.
5. **After scores arrive: read the report.** College Board's score report shows performance in each content area; that, not the total alone, sets the SAT plan.

Dates: College Board's 2026-27 calendar lists the fall 2026 PSAT/NMSQT testing window as October 1 to 30, 2026, and says schools may also offer it on Saturday, October 17, 2026. Students testing in school do not register themselves; the school handles it. Homeschooled students must contact a participating school at least four weeks before the window begins. At the time of writing, the 2027 PSAT/NMSQT window had not been published on the dates page we read.

Where your student is

## Four PSAT situations and the sensible next step

Our guide for families, based on the rules College Board and NMSC publish.

| Situation | Sensible next step |
| --- | --- |
| 1. Grade 10, first PSAT/NMSQT | Treat it as practice; it does not enter National Merit for a four-year student |
| 2. Grade 11, aiming at National Merit | Balance Reading and Writing and Math, since RW counts double |
| 3. Grade 11, focused on the SAT | Use the score report's content areas to plan SAT practice |
| 4. Homeschooled | Find a participating school at least four weeks before the window |

### For students

Practise in Bluebook with Desmos so the tools are familiar on the day.

In each module the hardest questions come last. Keep time for them.

### For parents

Ask the school whether it gives the PSAT/NMSQT on a weekday in the window or on the Saturday option.

National Merit recognition depends on NMSC's published levels; no class can promise it.

The catalogue

## Math courses for high school students

From Algebra 1 to AP Calculus, with the SAT Suite course at the center.

I

### Core high school math

Grades 9 and 10

PSX / H / 01

#### Algebra foundations

Algebra 1 in depth.

[Open the syllabus](/courses/algebra-foundations-masterclass)

PSX / H / 02

#### High school math

Through precalculus.

[Open the syllabus](/courses/complete-high-school-mathematics-mastery)

PSX / H / 03

#### Statistics and probability

For the data domain.

[Open the syllabus](/courses/statistics-probability-maths-course)II

### Tests

Grades 10 to 12

PSX / T / 01

#### SAT and PSAT math

The digital SAT Suite.

[Open the syllabus](/courses/sat-math-prep-course)

PSX / T / 02

#### ACT math

If you sit the ACT too.

[Open the syllabus](/courses/act-math-prep-course)

PSX / T / 03

#### Competition math

AMC and beyond.

[Open the syllabus](/courses/olympiad-competition-mathematics-mastery)III

### Advanced

AP level

PSX / A / 01

#### AP Precalculus

Functions in depth.

[Open the syllabus](/courses/ap-precalculus-exam-prep-course)

PSX / A / 02

#### AP Calculus

AB and BC.

[Open the syllabus](/courses/ap-calculus-exam-prep)

PSX / A / 03

#### AP Statistics

Data and inference.

[Open the syllabus](/courses/ap-statistics-maths-exam-prep-course)

How lessons run

## PSAT math lessons around the school week

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

Weekdays

After school, alongside class math.

Weekends

Practice modules under real timing.

1-on-1

Planned to your school's test day.

### Four domains

Weighted as College Board weights them.

### Desmos fluency

Graph, intersect, check.

### Module pacing

Time saved early for the hard end.

### Score report reading

We plan from your content areas.

### SAT continuity

The same blueprint, one plan.

### Group or private

Fifteen to twenty, or one to one.

Student work

## Work from our students

Some students take their algebra into code and data projects. See [student labs](/student-labs).

![NutriLife AI nutrition coach project screenshot](/images/projects/nutrilife.webp)

AI and ML

#### NutriLife

An AI nutrition coach that reads what you eat and works you toward a target.

by Bhavya · [Open it](https://nutrilife-bhavya.lovable.app)

![Misti AI chatbot for maths and coding screenshot](/images/projects/misti.webp)

AI and ML

#### Misti

A chatbot that answers mathematics and programming questions, built and deployed by a student.

by Harshit · [Open it](https://misti.modernagecoders.com)

![GuardianX AI internet safety assistant screenshot](/images/projects/guardianx.webp)

AI and ML

#### GuardianX

An assistant that helps a young person recognise unsafe situations online.

by Vivaan · [Open it](https://guardianx-cybersaver.lovable.app)

![SkyCast weather forecast application screenshot](/images/projects/skycast.webp)

Web app

#### SkyCast

A weather forecasting site with live conditions for any location.

by Krish

Fees

## Fees

A monthly fee in US dollars covers PSAT math classes. Families can stop after the October test, or carry straight on into SAT preparation; neither needs a contract.

Free first class

USD 0

no card required

- A free first class
- Bring a practice score report
- No card details

Book it

Group batch

USD 100

a month, billed in US dollars

- Fifteen to twenty learners
- One regular teacher
- Choose your batch
- Monthly

Start here

One to one

USD 150

a month, billed in US dollars

- A teacher to yourself
- Planned to your test window
- Flexible times

Enquire

What families say

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Parents' Google reviews, as they wrote them.

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Questions families ask

## PSAT/NMSQT math: common questions

### How many math questions are on the PSAT?

The PSAT/NMSQT Math section has 44 questions in two modules of 22. In each module, 20 questions are scored and 2 are unscored pretest questions.

### How long is the PSAT math section?

Seventy minutes: two modules of 35 minutes each. College Board says the whole PSAT/NMSQT takes 2 hours and 14 minutes.

### Can you use a calculator on the PSAT math?

Yes, on the entire Math section. You can use the Desmos calculator built into Bluebook or an approved handheld calculator; CAS calculators are not allowed.

### What math is on the PSAT?

Four domains: Algebra (13 to 15 questions), Advanced Math (12 to 14), Problem-Solving and Data Analysis (7 to 9), and Geometry and Trigonometry (4 to 6), according to College Board's fall 2026 student guide.

### How is the PSAT Selection Index calculated?

Double your Reading and Writing score, add your Math score, and divide by 10. The index runs from 48 to 228; for example, 690 and 710 give 209.

### Does the sophomore PSAT count for National Merit?

Not for a student spending four years in high school. The NMSC section of College Board's guide says such students must take the PSAT/NMSQT in grade 11 to enter, and the PSAT 10 never counts.

### When is the PSAT in 2026?

College Board lists the fall 2026 PSAT/NMSQT window as October 1 to 30, 2026, and schools could also offer it on Saturday, October 17, 2026. Schools register their own students.

### Is PSAT math harder than SAT math?

No. College Board gives both Math sections 44 questions in two 35-minute modules across the same four domains, and the PSAT/NMSQT section scale tops out at 760 rather than the SAT's 800. Good PSAT preparation is good SAT preparation.

### When are your PSAT math classes?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

### Are you connected with College Board or National Merit?

No. We are an independent online school, not connected with College Board or National Merit Scholarship Corporation, and we cannot promise any score or recognition.

Elsewhere on this site

## Related pages

More math help for US high school students.

### [SAT math tutoring](/sat-math-tutoring-online)

The test the PSAT prepares for.

### [ACT math tutoring](/act-math-tutoring-online)

For students sitting both.

### [Tenth grade math](/online-math-tutor-10th-grade)

The first PSAT/NMSQT year for many.

### [Eleventh grade math](/online-math-tutor-11th-grade)

The National Merit year.

### [Algebra 2 tutoring](/algebra-2-tutoring-online)

Where Advanced Math is taught.

### [Math tutor cost](/online-math-tutor-cost)

How tutoring is usually priced.

## Related pages in this guide

Part of the guide: [US math placement and college readiness tests](/us-math-placement-and-college-readiness-tests)

### PSAT and PreACT

- [PSAT 8/9 and PSAT 10 math prep](/psat-8-9-math-prep)
- [PreACT math prep](/preact-math-prep)
- [SAT math tutoring online](/sat-math-tutoring-online)
- [ACT math tutoring online](/act-math-tutoring-online)

### School placement and growth tests

- [MAP Growth math test prep](/map-growth-math-test-prep)
- [i-Ready math help](/i-ready-math-help)
- [Middle school math placement test prep](/middle-school-math-placement-test-prep)
- [Accelerated math program online](/accelerated-math-program-online)

### High school math courses

- [Integrated Math 1 tutoring](/integrated-math-1-tutoring)
- [Integrated Math 2 tutoring](/integrated-math-2-tutoring)
- [Integrated Math 3 tutoring](/integrated-math-3-tutoring)
- [Trigonometry tutoring online](/trigonometry-tutoring-online)
- [Statistics tutoring online](/statistics-tutoring-online)
- [AP Precalculus tutoring online](/ap-precalculus-tutoring-online)

### College placement and credit

- [ACCUPLACER math prep](/accuplacer-math-prep)
- [ALEKS math placement test prep](/aleks-math-placement-test-prep)
- [TSIA2 math prep](/tsia2-math-prep)
- [CLEP College Algebra prep](/clep-college-algebra-prep)
- [CLEP Calculus prep](/clep-calculus-prep)
- [Dual enrollment math help](/dual-enrollment-math-help)

More guides: [US state math tests by state](/us-state-math-tests-by-state) · [US gifted and selective school tests](/us-gifted-and-selective-school-tests-guide) · [Homeschool and school math curricula guide](/homeschool-math-curriculum-guide-usa) · [US math and coding competitions guide](/us-math-and-coding-competitions-guide)

Start here

## Book a free first class

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See [how we teach](/how-we-teach), or look at [our courses](/courses).

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## Keep exploring Modern Age Coders

### More maths tuition

- [PSSA Math Practice, Grades 3 to 8: The May 2027 Test](/pssa-math-practice)
- [Queensland Academies Entrance Test Maths Practice](/queensland-academies-entry-maths-practice)
- [Primary Maths Challenge Practice](/primary-maths-challenge-practice)
- [Quest 11 Plus Maths Practice](/quest-assessments-11-plus-maths-practice)
- [Precalculus Tutoring Online](/precalculus-tutoring-online)
- [SA Ignite Assessment Maths Practice](/sa-ignite-entry-maths-practice)
- [CLEP Calculus Prep and CLEP Precalculus Prep: Exam Guide](/clep-calculus-prep)
- [ESAT Maths Preparation: Mathematics 1 and 2, 2026 to 2027](/esat-maths-preparation)
- [Geometry Regents Prep: Proofs, Tools and the June 2027 Exam](/geometry-regents-prep)

### Learn more

- [Middle School Math Competitions: MATHCOUNTS](/courses/middle-school-math-competitions-course)
- [Computer Applications ICSE Class 10: Java BlueJ Tuition](/computer-applications-icse-class-10)
- [Modern Age Coders vs Spirit of Math: 2026 Comparison](/modern-age-coders-vs-spirit-of-math)
- [Waterloo Math Contests: Gauss to Euclid](/courses/waterloo-math-contests-gauss-to-euclid-course)

### From the blog

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- [How to Learn Times Tables Fast: The 21-Fact Method](/blog/how-to-learn-times-tables-fast)
- [AP Computer Science A Changes for 2026: A Parent's Guide](/blog/ap-computer-science-a-changes-2026)

### Start here

- [Modern Age Coders pricing, one honest price per plan](/pricing)
- [How Modern Age Coders teaches, small batches and real projects](/how-we-teach)

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