FREE SHSAT Study Guide 2026: ELA, Math & Admission

This free SHSAT study guide teaches to the Specialized High Schools Admissions Test — the single exam the NYC Department of Educationuses to admit students to eight of the city’s specialized high schools.^[1] It covers every skill on the test, organized the way the exam is built: an English Language Arts section and a Math section, 57 questions each.

It’s interactive, not a wall of text: every module has a built-in checkpoint quiz, hover-able glossary terms, worked math examples, and concept questions, so you learn by doing.

Read it module by module, test yourself at each checkpoint, then round out your free SHSAT prep with our practice questions and flashcards.

SHSAT Exam Snapshot

The SHSAT has no passing score. Your ELA and Math results combine into one composite scaled score, and admission is decided by competitive rank order — seats fill from the highest scores down.^[2] That makes every question matter, and because there is no guessing penalty, you should never leave one blank. Here is roughly how the 114 questions break down across the four content areas this guide teaches:

The two sections are equal in weight — 57 questions each — but within them the Math section leans heavily on multiple-choice computation and word problems, and the ELA section leans on reading. This guide teaches all four content areas, in exam order: ELA Revising/Editing, then Reading Comprehension, then Math word problems and computation, then Math grid-ins and the scoring that ties it all together.

1 · ELA — Revising/Editing

The Revising/Editing part of the ELA section is the most learnable on the whole test, because the rules are finite. Part A gives you standalone sentences to fix; Part B asks you to improve sentences inside a short passage.^[2] Master a handful of grammar and punctuation rules and these become fast, reliable points.

Sentence Boundaries & Punctuation

Most punctuation questions come down to one test: is each side of the mark an independent clause (a complete sentence)? If both halves can stand alone, you need a period, a semicolon, or a comma plus a FANBOYS conjunction — never a comma by itself, which creates a comma splice.

Agreement, Verbs & Pronouns

Subject-verb agreement means the verb matches the true subject in number. The classic SHSAT trap puts a phrase between the subject and the verb so you agree with the wrong noun.

Modifiers & Parallel Structure

A modifiermust sit next to the word it describes. An opening modifier describes the noun right after the comma — when it doesn’t, it “dangles.” Parallel structure keeps items in a series in the same grammatical form.

Word Choice & Organization

Part B also tests transitions and organization: choosing the word that signals the right logical relationship, and placing or removing a sentence so a paragraph flows. Transitions test logic, not vocabulary — decide the relationship first, then pick the word:

2 · ELA — Reading Comprehension

Reading Comprehension uses informational, literary, and poetry passages.^[2] Every correct answer is supported by the passage in front of you — never by outside knowledge. The skill is reading closely and matching the choice the text actually backs.

Main Idea & Supporting Details

The main ideais the central point the whole passage makes — broad enough to cover every paragraph. A supporting detail is one specific fact or example. A wrong “main idea” choice is often true but too narrow (really just a detail) or too broad (beyond what the passage says).

Inference & Evidence

An inference is a conclusion the passage impliesbut doesn’t state. Pick the choice the text most directly supports — not the most dramatic one. When a question asks for the best evidence, find the single sentence that most directly backs the stated claim.

Vocabulary in Context

Vocabulary-in-contextquestions give a word as it’s used in the passage and ask for its meaning there— not its most common definition. Reread the full sentence, predict your own meaning, then match. A choice can be a real definition of the word and still be wrong if it doesn’t fit the passage.

Poetry & Figurative Language

Poetry passages ask about tone, mood, theme, and figurative devices. Personificationgives human actions to nonhuman things; other devices include metaphor, simile, and imagery. When a question asks about a device’s effect, explain how it shapes the poem’s mood or meaning.

3 · Math — Word Problems & Computation

The Math section’s 52 multiple-choice questions cover arithmetic, ratios and percentages, algebra, geometry, statistics, and probability — no calculator.^[2] Most are word problems, so translating the words into an equation is half the battle.

Ratios, Rates & Percentages

A ratio compares quantities; a proportion sets two ratios equal. For parts-of-a-whole problems, add the parts, divide the total by that sum, and multiply. Percent change is the change divided by the original value, times 100.

Algebra & Equations

Solve a linear equation by isolating the variable — do the same operation to both sides, undoing addition/subtraction first, then multiplication/division. When the variable appears on both sides, collect the variable terms on one side first.

Exponents & Number Sense

Know the exponent laws cold: multiplying powers of the same base adds exponents, dividing subtracts them, and a power of a power multiplies them. Any nonzero base to the zero power is 1. Scientific notation writes a number as a value between 1 and 10 times a power of 10. And remember order of operations (PEMDAS).

Geometry, Statistics & Probability

Geometry questions cover area, perimeter, volume, angles, and the Pythagorean theorem. For statistics, know mean versus median; for probability, it’s favorable outcomes divided by total outcomes.

4 · Math Grid-Ins & the Composite Score

Five of the 57 Math questions are grid-ins — student-produced responses with no answer choices.^[2]They’re worth the same as a multiple-choice question, and this module also explains how your section scores combine into the one composite that decides admission.

How Grid-Ins Work

Because there are no choices to work backward from, grid-ins reward exact arithmetic. You enter a whole number, a fraction, or a decimal exactly — no rounding unless the question asks for it. There is no penalty, so never leave one blank, but a careless slip costs the full point.

Composite Score & Rank-Order Admission

Your raw scores on the 47 scored questions in each section are converted to scaled scores (so different test forms are comparable), then added into one composite score.^[2] Admission is by rank order: you list up to all eight schools in order of preference, and the match places you in the highest-ranked school whose cutoff your composite meets.

How to Use This Study Guide

A study guide is a map, not the whole territory — use it alongside official NYC DOE practice tests and our free tools. Because there is no passing score, the goal is to maximize your composite, so steady, mixed practice across all four content areas beats one long cram.

SHSAT Glossary

Quick definitions for the terms you’ll see most across the SHSAT:

Comma splice

An error in which two independent clauses (complete sentences) are joined by only a comma. Fix it with a period, a semicolon, or a comma plus a conjunction.

Composite score

Your ELA and Math scaled scores added together into one number (max about 800). This single composite is the only score used for admission.

Dependent clause

A group of words with a subject and verb that cannot stand alone because it begins with a subordinating word like 'because' or 'although.'

Exponent

A small raised number showing how many times a base is multiplied by itself; 2 to the 5th power means 2 × 2 × 2 × 2 × 2 = 32.

FANBOYS

The seven coordinating conjunctions — for, and, nor, but, or, yet, so — that can join two independent clauses after a comma.

Field-test question

An unscored question embedded in the test to try out new items. You can't tell which questions are field-test, so you must answer every one.

Grid-in

A student-produced-response Math question with no answer choices; you enter an exact numeric answer in a grid.

Independent clause

A group of words with a subject and a verb that can stand alone as a complete sentence.

Inference

A logical conclusion a passage strongly implies but does not state outright; the correct inference is the one the text most directly supports.

Main idea

The central point a whole passage makes — broad enough to cover the entire text, not just one detail.

Mean

The average of a data set — the sum of the values divided by how many there are.

Median

The middle value of an ordered data set; it resists outliers, unlike the mean.

Modifier

A word or phrase that describes another part of a sentence. A misplaced or dangling modifier sits next to the wrong noun.

Parallel structure

Using the same grammatical form for items in a series, such as three infinitives ('to stretch, to drink, to rest').

Percent change

The change in a quantity divided by its original value, times 100. Always divide by the starting amount.

Personification

A figure of speech that gives human qualities or actions to something nonhuman, such as 'the wind whispered.'

Pronoun-antecedent agreement

The rule that a pronoun must match the noun it refers to (its antecedent) in number and gender.

Pythagorean theorem

For a right triangle with legs a and b and hypotenuse c, a² + b² = c².

Rank-order admission

The SHSAT admission method: students are placed in the highest-ranked school whose cutoff their composite score meets, with seats filled from the highest scores down.

Ratio

A comparison of two quantities, such as 3 to 4. A proportion sets two ratios equal to each other.

Reading Comprehension

The ELA part with informational, literary, and poetry passages, testing main idea, inference, vocabulary in context, structure, and tone.

Revising/Editing

The ELA part that tests how well you correct grammar, punctuation, sentence structure, and organization — in standalone sentences (Part A) and within a passage (Part B).

Run-on sentence

Two or more independent clauses joined with no punctuation or conjunction between them.

Scaled score

A converted score that adjusts for slight differences between test forms, so scores from different versions of the SHSAT can be compared fairly.

Scientific notation

Writing a number as a value between 1 and 10 times a power of 10, such as 6,400,000 = 6.4 × 10 to the 6th power.

Sentence fragment

A group of words punctuated as a sentence but missing a subject, a verb, or a complete thought.

SHSAT

The Specialized High Schools Admissions Test — the single exam used to admit students to eight of New York City's specialized high schools, administered by the NYC Department of Education.

Specialized high school

One of NYC's selective public high schools (such as Stuyvesant, Bronx Science, and Brooklyn Tech) that admits students through the SHSAT.

Subject-verb agreement

The rule that a verb must match its subject in number — a singular subject takes a singular verb, a plural subject a plural verb.

Vocabulary in context

A skill that asks you to choose the meaning of a word based on how it is used in a passage, not its most common dictionary definition.

Free SHSAT Study Materials & Resources

Everything you need to prepare for the SHSAT is free here — no paywall, no sign-up. This guide is the foundation; pair it with the rest of our free SHSAT study materials for active recall, timed practice, and last-minute review:

• SHSAT Practice Test — exam-style ELA and Math questions, with explanations.
• SHSAT Flashcards — active-recall decks for grammar rules, reading skills, and math formulas.

SHSAT Study Guide FAQ

References

1. 1.NYC Department of Education. “Specialized High School Admissions Test (SHSAT).” NYC Public Schools. ↑
2. 2.NYC Department of Education. “Specialized High Schools Student Handbook.” NYC Public Schools. ↑
3. 3.NYC Department of Education. “High School Admissions — Specialized High Schools.” NYC Public Schools. ↑

Sources for the concept answers

Every answer in the SHSAT concept questions above is drawn from an official primary source:

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