ETS's catalog lists Core Combined (5752) alongside its three subtests — reading 5713, writing 5723, and mathematics 5733 — as measuring academic skills in reading, writing, and mathematics for a career in education, with a $150 fee for the combined test. Which registration your state accepts varies, so confirm your state's requirements before registering. Then prepare by sorting every practice question into the standard it applies: textual evidence, language correctness or fitness, or quantitative reasoning — and log the decision you got wrong, not just the topic. The sections below teach each standard with complete worked exercises.
What the Praxis Core Covers — Combined 5752 or Separate Subtests?
ETS lists Core Combined (5752; subtests 5713, 5723, 5733) as measuring academic skills in reading, writing, and mathematics for a career in education, at a $150 fee, taken at home or at a test center. The official Study Companions give each subtest's format: reading (5713) runs 85 minutes for 56 questions, writing (5723) runs 100 minutes with 40 selected-response questions plus two 30-minute essays, and mathematics (5733) runs 90 minutes for 56 questions. Each state sets its own passing score, so confirm the tests and scores your state accepts before you register.
The catalog entry is a purpose statement, not a syllabus. The detailed picture comes from the free Study Companion for each subtest, which publishes the timing, question counts, question types, and content-category percentages shown above. The preparation sections of this guide follow those official breakdowns.
State acceptance is the decision that actually changes your registration. ETS tells candidates that each state has its own certification requirements and directs you to its state-requirements checker before you register. There is also no single ETS passing score: the Praxis technical manual states that each state ultimately sets its own passing score, so confirm both the test code and the score your target state requires.
Practice exercise
You are applying for licensure in a state you have not yet researched. ETS lists Core Combined (5752) and also sells the reading, writing, and mathematics subtests (5713, 5723, 5733) individually. Which registration should you choose?
Show answer
Neither one yet. First confirm which option your state accepts using ETS's state-requirements checker; then register for the combined test if it is accepted, or for exactly the subtests your state names.
The choice between combined and subtest registration is a state policy question, not a study-preference question. ETS's catalog lists both routes and tells candidates to verify state requirements before registering because acceptance differs by state. Passing scores are also set state by state, so choosing based on convenience or on what another candidate did risks registering for a test or score your state does not recognize.
- Before you register, complete three checks: confirm your state's requirements with ETS's state-requirements tool; choose Core Combined (5752) or the specific subtests your state names; and, if you need testing accommodations, review ETS's requirements and apply early.
| Registration option | Test codes | Format | What to confirm first |
|---|---|---|---|
| Core Combined (one session) | 5752 | All three subtests in one sitting; $150 | That your state accepts the combined test and its score |
| Separate subtests | 5713, 5723, 5733 | 85, 100, and 90 minutes respectively | Which subtest codes and scores your state requires |
| Accommodations request | Applies to any option above | ETS review of eligibility documentation | Review requirements and apply early |
Official sources: Core Combined (5752; subtests 5713, 5723, 5733) — ETS Praxis test page; ETS Praxis Core Reading Study Companion 5713; ETS Praxis Core Writing Study Companion 5723; ETS Praxis Core Mathematics Study Companion 5733; ETS Praxis (catalog and state requirements) — praxis.ets.org; Technical Manual for the Praxis Tests and Related Assessments (October 2025)
Reading: Literal Comprehension vs. Inference
Literal questions ask what the passage states; inferential questions ask what it implies. For literal items, locate the exact sentence each choice paraphrases. For inference items, allow yourself one step beyond the text — never more.
For a literal question, the correct answer is a paraphrase of a specific sentence, and the distractors are usually plausible real-world claims the text simply never makes. Practice by pointing to the sentence each choice restates. If you cannot put your finger on it, treat that choice as unsupported, no matter how sensible it sounds. This converts reading questions from a memory task into a matching task you can verify.
For an inferential question, the correct answer is one step from the text: a comparison, a cause, or a prediction grounded in the author's own wording. The characteristic error is over-inferring — importing outside knowledge or extending a trend further than the passage licenses. Hold yourself to a two-line rule: every inference answer should let you name the two pieces of text it bridges.
One official reassurance: every question can be answered from information in the passage alone. If a passage conflicts with something you know about the subject, answer on the basis of what the passage states or implies, not your outside knowledge.
Practice exercise
Practice passage: (1) Lincoln Middle School moved its start time from 7:30 to 8:45 last September. (2) The following semester, first-period attendance rose from 91 percent to 96 percent. (3) The school nurse reported fewer visits for headaches and fatigue. (4) Some parents objected because the later bell pushed after-school sports past 6 p.m. (5) The district responded by shifting practice schedules rather than shortening them. (6) A nearby district that made no schedule change recorded no attendance improvement over the same period. (7) The school board will review the policy next spring. — Literal item: How did the district respond to parents' objections? Inferential item: What does sentence 6 suggest about the attendance gain?
Show answer
Literal: it shifted practice schedules rather than shortening them. Inferential: the attendance gain is unlikely to be merely a district-wide trend, because a comparable district that changed nothing saw no improvement.
The literal answer restates sentence 5. The trap is stopping at sentence 4, which matches the topic (parents) but is not the response. For the inference, the single step is comparing the two districts; anything further — such as 'later start times cause better attendance' — over-reaches, because one school's before-and-after numbers plus one contrast case do not establish causation. A choice like 'later starts eliminate fatigue' would fail the two-line rule twice over: it needs outside research knowledge and it outruns what the nurse's report shows.
Official sources: ETS Praxis Core Reading Study Companion 5713
Reading Analysis: Matching Evidence and Naming Rhetorical Moves
Analysis questions test whether a quoted sentence actually supports a stated claim, and whether you can name a rhetorical move — an appeal, a concession, an illustration — by its function rather than its topic.
Evidence questions reward matching the variables in the claim, not recognizing a familiar topic. Restate the claim's exact variables first, then test each candidate sentence against them. Topic-matching is precisely the decision that feels right while being wrong: a sentence can be true, related, and quotable, and still support nothing.
For strategy questions, label each paragraph's function before reading the choices — support, concede, define, contrast. 'The author cites one district's results' is empirical illustration; 'the author acknowledges the cost concern' is a concession; 'the author repeats the same phrase' may be emphasis. Once every paragraph has a function label, a strategy question becomes a lookup instead of a judgment call made under time pressure.
Practice exercise
Using the same seven-sentence passage above: (a) Which sentence most directly supports the claim that moving the start time improved attendance — sentence 2 (attendance rose from 91 to 96 percent) or sentence 3 (fewer nurse visits for headaches and fatigue)? (b) What is the rhetorical function of sentence 4, the one about parents' objections?
Show answer
(a) Sentence 2. (b) It is a concession — the author acknowledges a counterpoint before answering it in sentence 5.
The claim's variables are start time and attendance, and sentence 2 repeats both. Sentence 3 is true, on-topic, and quotable, but its variable is health complaints, not attendance — a classic topic-match distractor. For (b), naming the move as a concession before looking at the choices prevents mislabeling it as mere background or as evidence; the author is not disputing the parents' concern, only showing how the district addressed it.
Official sources: ETS Praxis Core Reading Study Companion 5713
Writing: Editing for Standard English Conventions
Conventions questions ask which version is grammatically correct. They usually turn on a small set of decision points — subject-verb agreement, tense consistency, pronoun case, and punctuation between clauses — and the efficient technique is subtraction: reduce the choices to the elements that differ and judge only those.
The official writing outline splits the selected-response section into four parts — usage, sentence correction, revision-in-context, and research skills — and notes that you are not required to know formal grammatical terminology. Naming rules is still worth doing for your own error log; the test just will not ask you to recite them.
Use subtraction on every conventions item. In 'The list of supplies (is/are) on the desk,' the subject is 'list,' so 'of supplies' is decoration designed to pull you off the agreement. Strip the shared wording away until only the differing element remains, then apply a rule you can name. Diffing the choices turns a vague 'which sounds right' feeling into a checkable decision.
The same subtraction works for tense and punctuation. For tense, find the time anchor in the sentence — 'after the workshop ended' — and make every verb agree with that anchor. For clauses, ask whether two independent statements are joined by only a comma; if so, the fix is either a coordinating conjunction, a semicolon, or splitting the sentence. Naming the deciding rule out loud is the reusable skill: when you miss an item, your error-log entry should name the rule, not just the sentence.
Practice exercise
Choose the correct rendering in each sentence and name the deciding rule. (1) The display of photographs (was / were) donated by the alumni association. (2) After the workshop ended, the participants filled out surveys and (leave / left) for the parking lot. (3) Which version is correct: (a) 'Attendance doubled, the board approved a second year.' or (b) 'Because attendance doubled, the board approved a second year.'?
Show answer
(1) was. (2) left. (3) Version (b).
(1) Subtract the prepositional phrase: the subject is 'display,' singular, so 'was.' The 'of photographs' wording is a distraction from the agreement. (2) The anchor 'after the workshop ended' sets past time; both verbs must match it, so 'filled ... left.' Judging each verb against the anchor, not against its neighbor alone, keeps long compound sentences consistent. (3) Version (a) joins two independent clauses with only a comma — a comma splice. Version (b) converts the first clause into a dependent 'because' clause, which is correctly separated from the following main clause by a comma.
Official sources: ETS Praxis Core Writing Study Companion 5723
Writing: Revising for Purpose and Audience
Text-production questions apply a different standard from conventions: a sentence can be grammatically perfect and still wrong for the paragraph. Read the stated purpose in the stem first, then test each candidate against focus, economy, and transition logic. The two 30-minute essays apply the same standard at full length.
The usual disqualifiers are a shift away from the paragraph's stated purpose, redundancy, a register that breaks the tone, or a transition word claiming a logical relationship the ideas do not have. Practice with paired sentences that are all correct and ask which better serves the purpose the stem announces. When you miss one, record which fitness criterion — focus, economy, or transition — you overlooked, because that criterion is the reusable lesson.
Keep the two standards separate in your head while practicing. If you apply correctness to a fitness question you will accept a grammatical off-task sentence; if you apply fitness to a correctness question you will talk yourself into a stylish error. The stem tells you which test you are running — read it before the choices.
The two essays make this standard concrete. The argumentative essay gives you 30 minutes to take a position and support it from your own reading, experience, or observations. The source-based essay gives you two short passages and 30 minutes to write an informative essay that draws on both, citing each source whether you paraphrase or quote. Official scoring descriptors reward a clear thesis, logical organization, relevant support, and control of grammar and mechanics — and an essay that uses only one of the two sources cannot reach the top score bands.
Practice exercise
Paragraph: 'Recycling bins were installed in every hallway last fall. During the first month, the weight of collected paper doubled. The student council now plans to add bins to the cafeteria.' Which sentence best continues it, given that all three candidates are grammatically correct? (A) Paper recycling has existed in various forms since the nineteenth century. (B) Placing paper-recycling bins in the cafeteria would extend the program beyond the hallways. (C) Adding the hallway bins was a totally awesome move by an amazing team.
Show answer
(B).
The paragraph describes expanding a school recycling program. (B) continues that topic by explaining how the planned cafeteria bins extend its reach. (A) shifts to recycling history; (C) changes the informational tone to unsupported praise. Nothing in the passage establishes the amount of food waste or future recycling gains, so those claims would require additional evidence.
Official sources: ETS Praxis Core Writing Study Companion 5723
Mathematics: Translating Words, Sequencing Percents, and Managing Units
Math items reward accurate translation before computation: define the variable, write the relationship, apply percent changes to the current base in sequence, and keep units consistent from the first substitution.
Worked example: a jacket priced at $80 is discounted 25%, and the sale price is then reduced by a further 20%. The tempting error is combining the percents — 25% plus 20% seems like a 45% discount, so $80 × 0.55 = $44. Apply the changes in sequence instead: $80 × 0.75 = $60, then $60 × 0.80 = $48. Percent change always operates on the current base, and the second discount applies to the new price, not the original. Combining percents is valid only when both apply to the same base — a conditional shortcut, so check the base before you merge anything.
Build a small translation vocabulary and use it deliberately: 'of' signals multiplication, 'per' signals division, and 'less than' reverses the order — 'seven less than x' is x − 7, not 7 − x. Verify the translation rather than the arithmetic: substitute a simple value like 2 into both the written relationship and your equation and confirm they agree. When an answer comes out strange, re-translate before re-computing, because the error usually entered at the sentence level.
Geometry and measurement reduce to two habits: choosing the right formula and keeping a unit plan. 'How much fencing' is a perimeter question; 'how much paint' is an area question — the same figure supports both. Write the formula in symbols, substitute with units labeled, convert everything to one unit system before multiplying, and decompose composite figures into rectangles and triangles. If your answer's units do not match the units requested — square feet versus feet, minutes versus hours — stop and re-solve; that mismatch is a diagnostic, not a rounding problem.
Two test-day facts shape math practice: an on-screen four-function calculator is provided, and the Study Companion prints the formulas you will have — circle area and circumference, rectangle and triangle area, and rectangular-box volume. Spend your rehearsal on knowing when each applies, not on rote recall.
Practice exercise
(a) A laptop priced at $600 is discounted 20%, and the new price is then reduced by a further 10%. What is the final price, and why is it not $600 × 0.70 = $420? (b) A garden plot is a 10 m × 6 m rectangle with a semicircular bed (diameter 6 m) attached along one 6 m side. How much fencing encloses the entire plot, and what is the total area? Use π ≈ 3.14.
Show answer
(a) $600 × 0.80 = $480; then $480 × 0.90 = $432. (b) Fencing = 10 + 6 + 10 + (3.14 × 3) = 26 + 9.42 = 35.42 m. Area = (10 × 6) + (3.14 × 3² ÷ 2) = 60 + 14.13 = 74.13 m².
(a) Each percent applies to its own base. The 20% discount leaves $480, and the 10% discount operates on $480, not on $600 — so the answer is $432, not $420. Merging the percents would only be valid if both applied to the same base, which they do not. (b) The shared 6 m edge becomes interior once the semicircle is attached, so the boundary is two 10 m sides, one remaining 6 m side, and the semicircular arc (half of 2πr = π × 3 ≈ 9.42 m) replacing the shared edge. The fencing answer is in meters because perimeter is a length; the area answer is in square meters. Both numbers come from the same figure, which is exactly why labeling units at every step prevents swapping them.
Official sources: ETS Praxis Core Mathematics Study Companion 5733
Data Interpretation: Read Tables as Claims, Not Pictures
Data questions ask you to extract rates, totals, and comparisons, then judge which stated conclusion the numbers actually support — the same evidence-matching skill from reading, now wearing units. Read labels, units, groups, and time periods before any question.
Start every table or graph by reading the axis labels, units, and the group and time period each column represents. Then compute exactly what the stem asks: a rate is not a count, and a change from one period is not a trend. Many wrong choices are arithmetically true numbers attached to the wrong group, wrong year, or wrong unit.
Conclusion questions apply the evidence standard: two variables moving together does not establish causation. If a choice says one thing 'causes' another, check whether the data present a controlled comparison that could support it; often they show only correlation over time. Treat each choice as a claim and ask which cell, bar, or row is its evidence.
The official content list names these skills explicitly: interpreting visual displays of quantitative information, computing and interpreting measures of central tendency such as mean and median, working with spread such as range, and distinguishing correlation from causation. Treat that list as your coverage checklist for this block.
Practice exercise
Using the table above: (a) What was the average number of items checked out per visit in June? (b) Which conclusion does the table support: (i) visits held steady while checkouts rose 25 percent; (ii) the steady visit count caused the extra checkouts; or (iii) June was the library's busiest month?
Show answer
(a) 1,500 ÷ 400 = 3.75 items per visit. (b) Only conclusion (i) is supported.
(ii) claims causation the two rows cannot establish — the table alone provides no evidence for that causal explanation. (iii) fails because 'busiest' is undefined and visits were equal in both months; only the checkout count differs. This is the same variable-matching discipline as the reading items: every accepted conclusion must point to specific cells, and causal language demands more than the table provides.
| Month | Items checked out | Library visits |
|---|---|---|
| January | 1,200 | 400 |
| June | 1,500 | 400 |
Official sources: ETS Praxis Core Mathematics Study Companion 5733
Preparation, Accommodations, and Next Steps
Start with administration: confirm your state's accepted tests and scores, choose combined or separate registration, and apply for accommodations early if you need them. Then prepare by rotation — one reading, one writing, and one math block per cycle, logging the decision behind each miss — and finish with mixed timed sets that practice switching between the three standards.
A workable shape for the middle phase is one reading, one writing, and one math block per rotation, with an error-log entry for each miss that names the concept and the wrong decision — for example, 'combined percent changes with different bases' or 'picked the topic-match sentence instead of the variable-match.' Mixed timed sets at the end rehearse the switching the combined test demands.
Two administrative facts anchor the start. ETS tells candidates that each state has its own certification requirements and to check them before registering, and the technical manual adds that each state ultimately sets its own passing score. On accommodations, ETS states that testing accommodations are available for test takers who meet its requirements, with extended time possible if English is not your primary language; start that process early and check ETS's accommodations pages for current processing timelines.
For free preparation, ETS provides an interactive practice test free with each test registration, and the Study Companions for 5713, 5723, and 5733 are free downloads containing sample questions with explanations. One optional readiness check: take a fresh mixed set and write a one-sentence justification for every answer before looking at the key — reading justifications name lines or cells, writing justifications name a rule or fitness criterion, and math justifications name the translation. Entries you cannot justify are your re-study targets, not predictions of your official result, which comes only from ETS after you test.
On career relevance, keep the claims narrow: ETS positions the Core as measuring academic skills for a career in education, and many states use the Core tests alongside Praxis Subject Assessments in the licensing process. Whether and how the Core counts for you is set by your target state, so verify current requirements directly. For practice against these skills, use the site's free Praxis Core practice set, and compare your error log against the broader library of study guides.
- Check your state's accepted tests and scores with ETS's state-requirements tool.
- Choose Core Combined (5752) or the specific subtests your state names.
- If you need accommodations, review ETS's requirements and start the application early.
- Download the free Study Companion for each code you register for, and use the free interactive practice test included with registration.
Official sources: Core Combined (5752; subtests 5713, 5723, 5733) — ETS Praxis test page; ETS Praxis Core Reading Study Companion 5713; ETS Praxis Core Writing Study Companion 5723; ETS Praxis Core Mathematics Study Companion 5733; ETS Praxis (catalog and state requirements) — praxis.ets.org; Technical Manual for the Praxis Tests and Related Assessments (October 2025)
Official sources
Exam facts checked against official ETS pages:
- Core Combined (5752; subtests 5713, 5723, 5733)
- ETS Praxis Core Reading Study Companion 5713
- ETS Praxis Core Writing Study Companion 5723
- ETS Praxis Core Mathematics Study Companion 5733
- ETS Praxis (catalog and state requirements)
- Technical Manual for the Praxis Tests and Related Assessments (October 2025)