This free Praxis Core study guide covers everything the three Praxis Core subtests measure — Reading (5713), Writing (5723), and Mathematics (5733) — organized to the current ETS content for each subtest.[1]
It’s interactive, not a wall of text: every subtest module has built-in checkpoint quizzes, flashcards, and practice questions, so you learn by doing — not just reading.
The Praxis Core is three separate subtests, each scored on a 100–200 scale and passed independently. You can take them one at a time or all together as the Combined test (5752).
Either way you study and conquer one subtest at a time: read a module, test yourself at each checkpoint, then drill gaps with our free practice test and flashcards. This guide is a high-yield overview of what each subtest tests — not a full textbook.
Praxis Core Exam Snapshot
| Detail | Praxis Core |
|---|---|
| Subtests | 3 separate tests: Reading (5713), Writing (5723), Mathematics (5733) |
| Combined option | Combined test (5752) covers all three in one session |
| Format | Computer-based; test at home (online proctored) or at a test center |
| Questions | Reading 56 · Writing 40 + 2 essays · Math 56 (154 total, mostly selected-response) |
| Score scale | 100–200 per subtest (no combined average) |
| Passing score | ETS qualifying: Reading 156 · Writing 162 · Math 150 (states/programs may differ) |
| Time | Reading 85 min · Writing 100 min · Math 90 min |
| Calculator | On-screen four-function calculator on Math; notation reference provided |
| Cost | ≈$90 per subtest; ≈$150 for the Combined test (5752) |
| Used for | Admission to teacher-preparation programs and some state licensure requirements |
Reading
#571356 selected-response · 85 min
Key ideas & details, craft/structure/language, and integrating evidence across sources.
Writing
#572340 selected-response + 2 essays · 100 min
Grammar, mechanics, and research skills, plus one argumentative and one source-based essay.
Mathematics
#573356 selected-response · 90 min
Number & quantity, algebra & functions, geometry, and statistics & probability.
You don’t need an “overall” Praxis Core score — you need to clear the required score on each of the three subtests.[6] Here’s how the scoring works:
Reading (#5713)
Scaled 100–200. ETS qualifying score is 156 — but your state or teacher-prep program may require a different number.
Writing (#5723)
Scaled 100–200. ETS qualifying score is 162 — but your state or teacher-prep program may require a different number.
Mathematics (#5733)
Scaled 100–200. ETS qualifying score is 150 — but your state or teacher-prep program may require a different number.
Module 1 · Reading (5713)
56 selected-response questions; 85 minutes. The Reading subtest measures how well you understand, analyze, and evaluate written passages — short and long, single and paired, including charts and graphs.[3] You don’t need outside knowledge; every answer is supported by the text in front of you.
Key Ideas & Details (~35%)
Main ideas, supporting details, direct & inferred meaning, summarizing, and the author's purpose.
Craft, Structure & Language (~30%)
Vocabulary in context, text structure, tone, point of view, fact vs. opinion, and figurative language.
Integration of Knowledge & Ideas (~35%)
Evaluating arguments and evidence, comparing sources, and interpreting graphs, tables, and quantitative information.
1.1 Key Ideas & Details
About a third of the test. Every question here comes back to two skills: finding the and tracing the that develop it. From there you draw — logical conclusions the passage implies but doesn’t state — and identify the .
| Skill | What it asks you to do |
|---|---|
| Main idea & summary | Identify the central point and restate it concisely |
| Supporting details | Find the facts/examples that develop the main idea |
| Inference | Draw a logical conclusion the text implies but doesn't state |
| Author's purpose | Decide why the text was written — to inform, persuade, or explain |
| Direct vs. inferred | Tell what the text states outright from what you must reason to |
1.2 Craft, Structure & Language
About 30% of the test. Here you work with how a passage is built and worded: , (cause/effect, compare/contrast, sequence), and , the difference between , and .
| Skill | What to do |
|---|---|
| Vocabulary in context | Use surrounding clues, not the word's most common meaning |
| Text structure | Recognize cause/effect, compare/contrast, sequence, problem/solution |
| Tone & point of view | Infer the author's attitude and perspective from word choice |
| Fact vs. opinion | Tell provable statements from beliefs and judgments |
| Figurative language | Interpret metaphor, simile, personification, and idiom |
1.3 Integration of Knowledge & Ideas
The final third — and the most analytical. You evaluate arguments and evidence, compare and synthesize two passages, and interpret quantitative information in charts, tables, and graphs.[3] The test wants to know whether an author’s claim is actually supported by sufficient, relevant evidence.
| Skill | What it asks you to do |
|---|---|
| Evaluate an argument | Judge whether evidence is sufficient and relevant to the claim |
| Compare two sources | Find points of agreement, disagreement, and differing emphasis |
| Interpret graphics | Read data from charts, tables, and graphs and connect it to the text |
| Distinguish evidence | Separate strong, relevant support from weak or off-topic claims |
Checkpoint · Reading (5713)
Question 1 of 10
The decline of honeybee colonies has alarmed scientists and farmers alike. Bees pollinate roughly a third of the crops humans eat, so their loss threatens the food supply. Researchers point to a combination of pesticides, parasites, and habitat loss as the likely causes. No single factor fully explains the collapse, and solutions will require addressing all of them at once. Which of the following best states the main idea of the passage?
Module 2 · Writing (5723)
40 selected-response questions plus 2 essays; 100 minutes (a 40-minute and a 60-minute block). The selected-response questions test standard English conventions and research skills; the two essays test your writing directly.[4] Most points come from grammar and mechanics, so master those first.
Argumentative essay
Take a clear position on an issue and defend it.
How to score well: State a thesis, support it with reasons and examples, address the other side, and conclude.
Source-based (informative/explanatory) essay
Synthesize two provided sources on a topic.
How to score well: Draw on BOTH sources, cite them, and explain the topic objectively — don't just give your opinion.
2.1 Grammar, Usage & Sentence Structure
The biggest selected-response area. The highest-yield rules: , consistent , and clarity, , correct placement, and fixing and fragments. You edit sentences within a passage rather than recall grammar trivia.
| Rule | What to check |
|---|---|
| Subject-verb agreement | Singular subject → singular verb; ignore words between them |
| Verb tense | Keep tense consistent unless the time frame actually changes |
| Pronoun agreement & clarity | Pronouns match their nouns in number; each refers to one noun |
| Parallel structure | Items in a list or comparison share the same grammatical form |
| Modifiers | Place describing phrases next to the word they modify (no danglers) |
| Run-ons & fragments | Every sentence needs a subject, a verb, and a complete thought |
2.2 Punctuation & Mechanics
Punctuation, capitalization, and spelling round out the conventions tested. Know how commas separate items and set off introductory and nonessential phrases, how to avoid a , when to use semicolons and colons, and how apostrophes show possession or contraction.
| Mark | Use it to… |
|---|---|
| Comma | Separate items, set off intro/nonessential phrases, join clauses with a conjunction |
| Semicolon | Join two closely related independent clauses without a conjunction |
| Colon | Introduce a list, explanation, or quotation after a complete clause |
| Apostrophe | Show possession (dog's) or contraction (it's) — never a plain plural |
| Comma splice fix | Replace the lone comma with a period, semicolon, or comma + conjunction |
2.3 Research Skills
A distinctive Praxis Core feature: some questions test research skills — evaluating sources, integrating evidence, and avoiding with proper .[8] You judge which source is most relevant or credible and how to use it honestly.
| Skill | Key idea |
|---|---|
| Evaluate a source | Prefer relevant, credible, current, and unbiased sources |
| Primary vs. secondary | Primary = firsthand/original; secondary = analyzes primary sources |
| Integrate evidence | Blend quotation or paraphrase smoothly and cite it |
| Avoid plagiarism | Quote exact words, paraphrase in your own words and structure, always credit |
| Cite a source | Identify author, title, and location so a reader can find it |
2.4 The Two Essays
The Writing subtest includes an (take and defend a position) and a (synthesize and cite two provided sources). Both reward a clear , organized paragraphs with specific support, and correct standard English.
- 1
Read both provided sources
Two short sources address the same topic. Read for each one's main points and key evidence.
- 2
Plan a focused thesis
Decide the central idea you'll explain — informative and objective, not a personal opinion piece.
- 3
Draw on BOTH sources
Use specific information from each source; an essay that ignores one source scores lower.
- 4
Cite as you go
Reference the sources (e.g., 'Source 1 notes…') so the reader can tell which idea came from where.
- 5
Organize, then proofread
Intro, body paragraphs with evidence, conclusion — then check grammar, spelling, and clarity.
For the argumentative essay, state your position in the introduction, give 2–3 reasons with examples, briefly acknowledge the other side, and conclude. For the source-based essay, build a focused thesis and draw on both sources, citing each.
Checkpoint · Writing (5723)
Question 1 of 10
Choose the underlined portion that contains an error. If there is no error, choose 'No error.' Neither the manager nor the employees (A) was (B) willing to accept the new policy without first (C) discussing its (D) potential effects.
Module 3 · Mathematics (5733)
56 questions (selected-response and numeric-entry); 90 minutes. The Math subtest covers four areas with an on-screen four-function calculator and a notation reference provided.[5] So the Praxis Core rewards knowing which method to apply and translating word problems into math — not memorizing every formula.
Number & Quantity (~36%)
Fractions, decimals, percents, ratios & proportions, order of operations, integers, exponents & roots, units.
Algebra & Functions (~24%)
Linear equations & inequalities, expressions, slope, functions, patterns, and word problems.
Geometry (~16%)
Perimeter, area & volume, angles, the Pythagorean theorem, similarity, and coordinate geometry.
Statistics & Probability (~24%)
Mean, median, mode & range, reading data displays, simple probability, and comparing data sets.
3.1 Number & Quantity
The largest area (~36%). Master fractions, decimals, and and how to convert among them; and (solve by cross-multiplying); , exponents and roots; and the .
- P
Parentheses
Do everything inside grouping symbols first.
- E
Exponents
Then evaluate powers and roots.
- MD
Multiplication & Division
Left to right — they share one level.
- AS
Addition & Subtraction
Left to right — they share the lowest level.
| Topic | Key move |
|---|---|
| Percent of a number | Convert to a decimal and multiply: 20% of 80 = 0.20 × 80 = 16 |
| Percent change | (new − old) ÷ old × 100 |
| Ratio / proportion | Set two ratios equal and cross-multiply to solve |
| Fractions | Common denominator to add/subtract; multiply straight across |
| Order of operations | PEMDAS: parentheses, exponents, ×/÷, then +/− |
| Integers | Track signs carefully: a negative times a negative is positive |
3.2 Algebra & Functions
About 24% of the test. Solve and inequalities, work with the slope-intercept form , and find the of a line as rise over run. You’ll also evaluate functions, simplify expressions, and translate word problems into equations.
| Concept | What to remember |
|---|---|
| Slope | Rise over run = (y₂ − y₁)/(x₂ − x₁); the m in y = mx + b |
| Y-intercept | Where the line crosses the y-axis (x = 0); the b in y = mx + b |
| Linear equation | Isolate the variable using inverse operations on both sides |
| Inequality | Solve like an equation, but flip the sign when multiplying/dividing by a negative |
| Function | Each input has exactly one output; f(x) is the output for input x |
| Word problems | Define the variable, translate the words, then solve |
3.3 Geometry
About 16% of the test. Know perimeter, area, and volume of common shapes; angle relationships; the for right triangles; and basic coordinate geometry. The notation reference supplies the formulas — your job is to choose the right one and substitute carefully.
| Shape / measure | Formula |
|---|---|
| Rectangle area | Area = length × width |
| Triangle area | Area = ½ × base × height |
| Circle area / circumference | Area = πr² ; circumference = 2πr |
| Rectangular solid volume | Volume = length × width × height |
| Pythagorean theorem | a² + b² = c² (right triangles) |
| Angles | Angles on a straight line sum to 180°; a full turn is 360° |
3.4 Statistics & Probability
About 24% of the test. Read graphs and tables, find the measures of center, and compute simple probability. Know the difference between the , , and , plus the . is favorable outcomes divided by total outcomes, from 0 to 1.
| Measure | How to find it |
|---|---|
| Mean (average) | Add all values, divide by how many there are |
| Median | Middle value when data are in order (average the two middle if even count) |
| Mode | The value that appears most often |
| Range | Highest value minus lowest value |
| Probability | Favorable outcomes ÷ total outcomes (a number from 0 to 1) |
| Reading data | Use the title, axes, legend, and units of a graph or table |
Checkpoint · Mathematics (5733)
Question 1 of 8
A shirt costs $40 and is marked down 25%. What is the sale price?
How to Use This Praxis Core Study Guide
Because the Praxis Core is three subtests passed independently, the smartest plan is to conquer them one at a time:
- Pick one subtest. Start with the one you find hardest (often Math or the Writing essays) so you give it the most runway.
- Read the module, then check yourself. Take the end-of-module checkpoint to see exactly which sub-topics need another pass.
- Check off as you go. Mark each section done in the Study Guide Contents — it raises your exam-readiness score.
- Drill weak spots. Send shaky topics into the flashcards and a practice test until you clear the required score comfortably.
- Schedule that subtest — then repeat. Pass it, move to the next, or sit all three at once as the Combined test (5752).
Praxis Core Concept Questions
Common Praxis Core concepts students search while studying — each answered briefly and backed by an official source. Test yourself, then drill them as flashcards.
Praxis Core Glossary
The high-yield Praxis Core terms across all three subtests in one place — hover any dotted term in the guide, or flip the whole deck here as a self-grading flashcard set.
- Argumentative essay
- An essay that takes a clear position on an issue and defends it with reasons and evidence.
- Author's purpose
- The reason a text was written — to inform, persuade, entertain, or explain.
- Citation
- A reference that credits a source so readers can identify and locate it.
- Comma splice
- An error joining two independent clauses with only a comma.
- Fact vs. opinion
- A fact can be verified or proven; an opinion is a belief or judgment that cannot be proven.
- Figurative language
- Language that means something beyond the literal — metaphor, simile, personification, and idiom.
- Inference
- A logical conclusion the reader draws from text evidence plus reasoning — implied but not stated outright.
- Integer
- A whole number and its negatives, including zero (…, −2, −1, 0, 1, 2, …).
- Linear equation
- An equation whose graph is a straight line, with variables to the first power (e.g., y = 2x + 1).
- Main idea
- The central point or message a passage conveys — what the whole text is mostly about.
- Mean
- The average — the sum of all values divided by the number of values.
- Median
- The middle value of a data set arranged in order.
- Mode
- The value that appears most often in a data set.
- Modifier
- A word or phrase that describes another; a misplaced or dangling modifier attaches to the wrong word.
- Order of operations
- The sequence for evaluating expressions — Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS).
- Parallel structure
- Items in a list or comparison share the same grammatical form.
- Percent
- A part per hundred; convert to a decimal by dividing by 100 (25% = 0.25).
- Plagiarism
- Using another's words or ideas without credit; avoided by quoting, paraphrasing properly, and citing.
- Point of view
- The perspective from which a text is written and the author's stance toward the subject.
- Probability
- The likelihood of an event, from 0 (impossible) to 1 (certain), as favorable outcomes ÷ total outcomes.
- Pronoun agreement
- A pronoun must match its antecedent in number and gender, and must clearly refer to one noun.
- Proportion
- An equation stating that two ratios are equal; solved by cross-multiplying.
- Pythagorean theorem
- In a right triangle, a² + b² = c², where c is the hypotenuse.
- Range
- The difference between the highest and lowest values in a data set.
- Ratio
- A comparison of two quantities by division (e.g., 3 to 4, or 3:4).
- Run-on sentence
- Two independent clauses joined incorrectly without proper punctuation or a conjunction.
- Slope
- The steepness of a line: rise over run — the change in y divided by the change in x; the m in y = mx + b.
- Source-based essay
- An informative/explanatory essay that synthesizes and cites two provided sources on a topic.
- Subject-verb agreement
- A grammar rule requiring a singular subject to take a singular verb and a plural subject a plural verb.
- Supporting detail
- A fact, example, statistic, or reason that explains, proves, or develops the main idea.
- Text structure
- How a passage is organized — e.g., cause/effect, compare/contrast, sequence, or problem/solution.
- Thesis
- A single sentence stating the central claim or focus of an essay.
- Tone
- The author's attitude toward the subject, revealed through word choice (e.g., formal, critical, hopeful).
- Verb tense
- The form of a verb that shows when an action happens; keep it consistent unless the time frame changes.
- Vocabulary in context
- The meaning of a word as it is used in a specific sentence, found from surrounding context clues.
- Y-intercept
- The point where a line crosses the y-axis (where x = 0); the b in y = mx + b.
Praxis Core Study Guide FAQ
Praxis Core has three separate subtests — Reading (5713), Writing (5723), and Mathematics (5733). Each is scored on a 100–200 scale and passed independently; there is no combined average. ETS's qualifying scores are 156 for Reading, 162 for Writing, and 150 for Math, but your state or program may require different scores.
Reading (5713) has 56 selected-response questions, Writing (5723) has 40 selected-response questions plus 2 essays, and Mathematics (5733) has 56 questions (a mix of selected-response and numeric-entry). The Combined test (5752) covers all three in one session — 154 questions total plus the 2 essays.
Reading (5713) is 85 minutes, Writing (5723) is 100 minutes (split into a 40-minute and a 60-minute block), and Mathematics (5733) is 90 minutes. Taken together as the Combined test (5752), the three run back-to-back in a single appointment.
ETS lists qualifying scores of 156 (Reading), 162 (Writing), and 150 (Math) on the 100–200 scale, and you must clear the required score on each subtest separately. Many states and teacher-preparation programs set their own cut scores, so always confirm the exact requirement where you'll teach.
Yes — an on-screen four-function calculator is provided for the Mathematics subtest (5733), and you may not bring your own. A notation and formula reference is also available on-screen, so understanding which method to use matters more than memorizing every formula.
No. You can take each subtest separately on different days, in any order, and retake just the one you don't pass — or you can sit all three together as the Combined test (5752). Studying one subtest at a time works well because each is passed independently.
The Writing subtest includes two essays: one argumentative essay, where you take and defend a position, and one source-based (informative/explanatory) essay, where you synthesize and cite two provided sources. Both are scored for a clear thesis, organized support, and correct standard English.
Each subtest (Reading, Writing, or Math) costs about $90, and the Combined test (5752) is about $150 — cheaper than three separate sittings, with four free score recipients. Fees can change, so verify the current amount on the ETS website before you register.
The Praxis Core measures the reading, writing, and math skills aspiring teachers need. Many teacher-preparation programs require it for admission, and some states require it for teacher licensure. This study guide, practice test, and flashcards are 100% free with no account required.
References
- 1.Educational Testing Service. “Praxis Core Academic Skills for Educators.” ets.org. ↑
- 2.Educational Testing Service. “Core Combined (5752).” ets.org. ↑
- 3.Educational Testing Service. “Praxis Core Reading (5713).” ets.org. ↑
- 4.Educational Testing Service. “Praxis Core Writing (5723).” ets.org. ↑
- 5.Educational Testing Service. “Praxis Core Mathematics (5733).” ets.org. ↑
- 6.Educational Testing Service. “Praxis Passing Scores.” ets.org. ↑
- 7.Purdue University. “Subject/Verb Agreement (Purdue OWL).” owl.purdue.edu. ↑
- 8.Purdue University. “Avoiding Plagiarism (Purdue OWL).” owl.purdue.edu. ↑
- 101.Purdue University. “Thesis Statements (Purdue OWL).” owl.purdue.edu, accessed 19 June 2026. ↑
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