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PRAXISCode: 5733Core Mathematics๐Ÿ“ CCSS Math Aligned๐Ÿ–ฉ Calculator Provided

Praxisยฎ Core Academic Skills
for Educators: Mathematics (5733)
Practice Test & Study Guide

Comprehensive preparation for prospective teachers โ€” covering all 3 official content categories aligned to Common Core State Standards for Mathematics. An on-screen four-function calculator is provided throughout.

56
Questions
90 min
Time limit
Varies
Passing score*
3
Content categories
$90
Individual fee
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A four-function on-screen calculator is provided for the entire exam. It performs addition, subtraction, multiplication, and division only โ€” no square roots, exponents, trig functions, or graphing. You must handle more complex computations by hand. The calculator is built into the testing interface; you cannot bring your own. Review the ETS Calculator Use page before test day to familiarize yourself with the interface.

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The live page shows 4 domains at NaN% โ€” this exam has 3 content categories. The correct structure per the ETS Study Companion is: Number and Quantity (36%, ~20 questions), Data Interpretation and Representation, Statistics, and Probability (32%, ~18 questions), and Algebra and Geometry (32%, ~18 questions). Three question formats also appear โ€” including numeric-entry where you type an exact number, not multiple choice.

๐Ÿ“‹

Source: All exam details are drawn from the official ETS Praxis Core Academic Skills for Educators: Mathematics (5733) Study Companion. The exam is aligned to the Common Core State Standards for Mathematics. Passing scores vary by state โ€” always confirm at ets.org/praxis/states.

Praxis Core Mathematics (5733) โ€” Test at a Glance

Key facts directly from the official ETS test specifications.

Test name
Core Academic Skills: Math
Praxis Core Subtest
Test code
5733
Computer-delivered
Total questions
56
3 question types
Time limit
90 min
~96 seconds per question
Calculator
Provided
On-screen four-function
Question types
3 formats
SR, select-all, numeric
Individual fee
$90
Or $150 combined (5752)
Score reporting
~5 wks
After test date

About the Praxis Core Academic Skills: Mathematics (5733)

What you need to know before you register.

The Core Academic Skills for Educators: Mathematics (5733) measures academic skills in mathematics needed to prepare successfully for a career in education. All skills assessed have been identified as needed for college and career readiness, in alignment with the Common Core State Standards for Mathematics. The focus is on key mathematical concepts and the ability to solve problems and to reason in a quantitative context.

The test covers three major content areas: Number and Quantity; Data Interpretation and Representation, Statistics, and Probability; and Algebra and Geometry. Many problems require the integration of multiple skills to achieve a solution โ€” not just recall of isolated facts. Students are expected to read and solve word problems, interpret data displays, and apply geometric formulas in real-world contexts.

The test uses three question formats: standard selected-response (select one of five choices), selected-response with multiple correct answers (select one or more โ€” marked with square boxes, not ovals), and numeric-entry (type an integer, decimal, or fraction). An on-screen four-function calculator is provided throughout the 90-minute test. No personal calculators are permitted.

This subtest can be taken independently ($90) or as part of the Core Combined (5752) with Reading and Writing for $150 total. Scores are reported separately for each subtest. Some questions are unscored pretest items that cannot be identified โ€” treat every question equally.

Three Question Types on This Exam

Understanding all three formats before test day prevents confusion and lost time on non-standard question types.

๐Ÿ”ต
Selected-Response โ€” One Answer
Select exactly one answer from five choices. Marked with ovals. The most common format. Standard "best answer" multiple choice.
Select exactly ONE โ€” selecting more than one invalidates the answer.
โ˜‘
Selected-Response โ€” One or More Answers
Select ALL correct answers. Marked with square boxes, not ovals. The question may or may not say how many answers to select. At least one answer is always correct.
You must select ALL correct choices โ€” partial credit is NOT awarded.
๐Ÿ”ข
Numeric-Entry Questions
Type your answer directly: as an integer or decimal in one box, or as a fraction in two boxes (numerator and denominator separately). Equivalent correct forms (e.g., 2.5 and 2.50) are all accepted.
Enter the EXACT answer unless told to round โ€” rounding an exact answer may be marked wrong.

Official Exam Blueprint: 3 Content Categories

The official ETS blueprint defines 3 content categories. Number and Quantity is the largest at 36%; Data/Statistics/Probability and Algebra/Geometry are each 32%.

Category I
Number and Quantity
Operations with integers, decimals, and fractions; ratios, proportions, and percent; constant rates (miles per hour, gallons per mile); place value and ordering of numbers; properties of whole numbers (factors, multiples, even/odd, prime numbers, divisibility); counterexamples to arithmetic statements; real-life problem solving; units and measurement, including U.S. customary and metric conversions.
36%
~20 questions
Category II
Data Interpretation and Representation, Statistics, and Probability
Reading and interpreting data displays (tables, bar graphs, line graphs, circle graphs, histograms, scatterplots, stem-and-leaf plots, boxplots, pictographs); measures of central tendency (mean, median, mode) and spread (range); drawing inferences from samples; identifying positive and negative linear relationships in scatterplots; using linear models for predictions; distinguishing correlation from causation; computing simple and compound probabilities.
32%
~18 questions
Category III
Algebra and Geometry
Algebraic properties (commutative, associative, distributive); following arithmetic or algebraic procedures step by step; generating equivalent algebraic expressions; writing equations or expressions that model real-life problems; solving word problems and Venn diagram problems; solving linear equations in one variable; solving simple quadratic equations; properties of 2D shapes; angles (vertical, supplementary, complementary, parallel lines cut by a transversal); congruence and similarity; area, perimeter, circumference (circle), and volume of rectangular prism.
32%
~18 questions

Formulas Provided During the Exam

These formulas are given in the test itself โ€” you do not need to memorize them. You do need to know when and how to apply them correctly.

Official Formulas Reference Sheet (provided in test booklet)

Circle (radius r)
Area = ฯ€rยฒ Circumference = 2ฯ€r
Use ฯ€ โ‰ˆ 3.14 unless told otherwise
Rectangle (length โ„“ ร— width w)
Area = โ„“ ร— w
Also applies to squares (โ„“ = w)
Triangle (base b ร— height h)
Area = ยฝ ร— b ร— h
Height must be perpendicular to base
Rectangular Box (โ„“ ร— w ร— h)
Volume = โ„“ ร— w ร— h
Same as rectangular prism volume
Notation Symbols
โŠฅ = perpendicular โˆฅ = parallel โˆŸ = right angle
Used in geometry questions
Not Provided โ€” Memorize
Pythagorean theorem: aยฒ + bยฒ = cยฒ Slope: (yโ‚‚โˆ’yโ‚)/(xโ‚‚โˆ’xโ‚) Distance, rate, time: d = rt
These are NOT in the formula sheet

Key Topics by Content Category

Specific competencies drawn directly from the official ETS content specifications and discussion questions.

I

Number and Quantity

~20 questions ยท 36%
Operations with integers, fractions, and decimals: addition, subtraction, multiplication, division; mixed numbers and improper fractions; computing fractions of fractions (e.g., ยผ of โ…œ)
Ratios and proportions: setting up and solving ratios of 2 and 3 quantities; ratio notation; proportional reasoning in real-life contexts
Percent: converting between fractions, decimals, and percents; percent of a whole; percent change; compound percent problems
Constant rates: identifying and using a constant rate of change (e.g., miles per hour); calculating rate from two data points; using rate to project future values
Place value: reading multi-digit decimal numbers; identifying the digit in a specific place; effect of multiplying or dividing by powers of 10
Properties of whole numbers: identifying factors, multiples, even/odd numbers, prime numbers, and composite numbers; divisibility rules; GCF and LCM; prime factorization
Number ordering: sorting positive and negative decimals and fractions; placing values on a number line; comparing fractions and decimals
Counterexamples: given a general statement about arithmetic, identifying a specific pair of numbers that disproves it
Real-life problem solving: identifying relevant numbers and operations from a word problem; rounding to appropriate precision; Venn diagram problems involving sets
Units and measurement: U.S. customary and metric systems; converting units within and between systems; solving measurement problems using conversion factors
Exponents and roots: adding/subtracting/multiplying/dividing numbers with integer exponents; approximating square roots to nearest whole number or tenth
Estimation and approximation: recognizing when an approximation is an underestimate vs. overestimate; rounding strategies
II

Data Interpretation, Statistics, and Probability

~18 questions ยท 32%
Data displays: reading and interpreting tables, bar graphs, line graphs, circle graphs, histograms, stem-and-leaf plots, boxplots, pictographs, frequency tables, and timelines
Circle graph interpretation: determining dollar values from percentages; identifying which categories exceed a threshold
Measures of central tendency: mean (arithmetic average), median, mode โ€” computing each; knowing which measure is most appropriate for a given data set
Effect of data changes on statistics: understanding how adding a constant, multiplying by a constant, or adding/removing data points affects mean, median, mode, and range
Measures of spread: range; understanding standard deviation conceptually; identifying outliers; analyzing data distributions
Sampling and inference: using data from a random sample to draw inferences about a population; scaling a sample statistic to the full population size
Scatterplots: identifying positive vs. negative linear relationships; identifying outliers; describing behavior in a scatterplot
Linear models and prediction: using a line of best fit to make predictions; interpreting what the equation of a line means in context
Correlation vs. causation: identifying whether two variables are correlated or whether one causes the other
Simple probability: P(event) = favorable outcomes / total outcomes; computing probability for real-world problems
Compound probability: computing probability for two independent events; identifying all possible outcomes; using probability to evaluate decisions
Choosing appropriate graphs: selecting the most effective graph type for a given data set; justifying conclusions based on data display information
III

Algebra and Geometry

~18 questions ยท 32%
Algebraic properties: applying commutative, associative, and distributive properties; simplifying expressions using these properties
Following algebraic procedures: carrying out a step-by-step procedure or evaluating a flowchart; applying a simple recurrence sequence
Equivalent expressions: identifying or generating equivalent algebraic expressions (e.g., multiplication by 0.1 gives the same result as division by 10)
Translating to algebra: writing an equation or expression that models a real-life or mathematical problem (e.g., "2 less than 3 times x" โ†’ 3x โˆ’ 2)
Word problems: solving real-world problems involving linear relationships; solving problems representable by Venn diagrams
Linear equations: solving linear equations in one variable; graphing lines in the xy-plane; determining slope; finding x- and y-intercepts
Quadratic equations: solving simple quadratic equations such as xยฒ = 49; recognizing when a solution is positive vs. negative
Order of operations: correctly applying PEMDAS in multi-step expressions; knowing the order your calculator uses
Properties of 2D shapes: classifying triangles by sides and angles; classifying quadrilaterals (parallelogram, rectangle, square, rhombus, trapezoid)
Angle relationships: vertical angles, supplementary angles, complementary angles; angles formed when two parallel lines are cut by a transversal
Congruence and similarity: identifying congruent triangles to find missing sides or angles; properties of similar figures; triangle inequality property
Area, perimeter, and volume: using provided formulas for circles, rectangles, triangles, and rectangular prisms; finding the radius given circumference; solving for an unknown dimension given area or perimeter

Registration, Test Day & Scoring

Everything you need to know before and on exam day.

Registration

Where to registerpraxis.ets.org
Individual fee$90
Combined fee (5752)$150 (all 3 subtests)
Testing formatsIn-person or remote
Arrive (in-person)30 min early

Scoring

Score typeScaled score
Raw score basisCorrect answers only
Passing scoreVaries by state
Results available~5 weeks post-test
State requirementsets.org/praxis/states

Test Day โ€” Calculator & Tools

Calculator typeFour-function (on-screen)
Personal calculatorNot permitted
FormulasProvided in test
Scratch paperProvided at test center
All numbersReal numbers

Remote Testing

Browser requiredETS Secure Test Browser
DeviceLaptop or desktop only
Calculator (Math)On-screen in test interface
Proctor typeLive remote proctor

Passing Score Requirements by State

Passing scores for the Mathematics (5733) subtest are set independently by each state.

Important: Passing score requirements for the Core Academic Skills: Mathematics (5733) are set individually by each state or licensing agency. A score that meets requirements in one state may not meet requirements in another. Always verify the exact passing score for your state at ets.org/praxis/states before registering.

Your raw score (number of correct answers across all three question formats) is converted to a scaled score that accounts for minor difficulty differences between test editions. There is no penalty for incorrect answers on selected-response questions โ€” always answer every question. For numeric-entry questions, enter your best answer even if uncertain; an unanswered numeric-entry question is simply scored as incorrect. Some questions are unscored pretest items that you cannot identify, so treat every question equally.

How to Prepare for the Praxis Core Mathematics Exam

Strategies aligned to the three question formats, the provided four-function calculator, and the exam's emphasis on integrated, real-world reasoning.

  • Number and Quantity (36%) is the largest category โ€” master it first. With approximately 20 questions, Category I covers fractions, decimals, percents, ratios, rates, properties of whole numbers, place value, and unit conversion. These topics require fluency with arithmetic โ€” even with a calculator provided, knowing how to set up ratio and proportion problems, convert between fraction/decimal/percent forms, and apply percent change formulas correctly is essential. Systematic arithmetic mistakes (not calculator errors) are the most common source of wrong answers in this category.
  • Know how to identify and answer โ€œselect one or moreโ€ questions. These questions are marked with square boxes instead of ovals โ€” a critical visual distinction. You must select ALL correct answer choices to receive credit; partial answers receive zero points. Before submitting, ask yourself: "Is there any other answer that is also correct?" Sample question 15 in the ETS Study Companion (the parallel streets/angles problem) is a perfect example โ€” three statements are presented and you must evaluate each independently.
  • For numeric-entry questions, enter the exact answer โ€” donโ€™t round unless told to. The exam explicitly states: โ€œIf a question does not ask you to round your answer, you should be able to enter the exact answer. If you are unable to do so, this may indicate that your answer is incorrect.โ€ Fraction questions have two separate boxes (numerator and denominator) โ€” make sure you enter the value in the correct box. Equivalent fractions (1/2 and 6/12) are both accepted.
  • The four-function calculator is not a substitute for number sense. While a calculator is provided throughout, it only does basic arithmetic. It will not factor expressions, compute square roots, or tell you which operations to apply. The exam tests whether you can set up problems correctly โ€” choosing the right operations, interpreting what a word problem asks, and reasoning about whether an answer is plausible. Strong number sense and problem-setup skills matter more than computation speed.
  • Category II (Data/Statistics/Probability, 32%) heavily emphasizes interpretation over computation. Questions in this category rarely require complex math โ€” they test whether you can read a graph accurately, identify a trend in a scatterplot, distinguish correlation from causation, compute a simple probability, or extend a sample statistic to a population. Practice reading all 9+ types of data displays (bar graphs, circle graphs, histograms, scatterplots, boxplots, stem-and-leaf, pictographs, frequency tables, line graphs) quickly and accurately before test day.
  • For Geometry, know which formulas are provided and which are not. The exam provides: Circle area and circumference, Rectangle area, Triangle area, and Rectangular box volume. What is NOT provided but may be needed: the Pythagorean theorem (aยฒ + bยฒ = cยฒ), slope formula, distance-rate-time formula (d = rt), and angle relationships (vertical angles, supplementary angles, parallel lines). Know angle relationships for parallel lines cut by a transversal โ€” corresponding angles are equal, alternate interior angles are equal, co-interior angles are supplementary.
  • Work through all 15 sample questions in the official ETS Study Companion with explanations. The companion contains 15 authentic questions spanning all three categories and all three question formats, with detailed answer explanations. Sample questions include a Venn diagram intersection question, a circle geometry proof, a percent reduction word problem, a circle graph interpretation, a place value question, an algebraic equivalence question, a mean calculation, a percent of percent question, a linear equation, a counterexample question, a number ordering question, a fraction of a budget calculation, a numeric-entry parts problem, and a parallel lines geometry multi-select. Each is representative of actual exam difficulty.

Frequently Asked Questions

Answers sourced directly from the official ETS Praxis Core Mathematics (5733) Study Companion.

How many questions are on the Praxis Core Mathematics (5733)?
The exam contains 56 questions with a 90-minute time limit. Questions span 3 content categories: Number and Quantity (36%, ~20 questions), Data Interpretation/Statistics/Probability (32%, ~18 questions), and Algebra and Geometry (32%, ~18 questions). The exam uses three question types: single-answer selected-response, one-or-more selected-response, and numeric-entry.
Is a calculator provided on the Praxis Core Mathematics exam?
Yes. An on-screen four-function calculator (addition, subtraction, multiplication, division) is provided throughout the entire 90-minute exam. No personal calculators are permitted. Review the ETS calculator use guide at praxis.ets.org before test day to practice with the on-screen interface.
What formulas are provided during the exam?
The following formulas are provided in the test: Circle (Area = ฯ€rยฒ, Circumference = 2ฯ€r), Rectangle (Area = length ร— width), Triangle (Area = ยฝ ร— base ร— height), and Rectangular box (Volume = length ร— width ร— height). Notation symbols (โŠฅ, โˆฅ, right angle) are also provided. Formulas not provided include the Pythagorean theorem, slope formula, and distance-rate-time formula.
What content categories are on the Praxis Core Mathematics (5733)?
Three categories: Number and Quantity (36%, ~20 questions) โ€” integers, fractions, decimals, ratios, percents, rates, place value, whole number properties, measurement; Data Interpretation, Statistics, and Probability (32%, ~18 questions) โ€” data displays, central tendency, scatter plots, linear models, probability; Algebra and Geometry (32%, ~18 questions) โ€” expressions, equations, word problems, linear relationships, shapes, angles, congruence, area/perimeter/volume.
How do the โ€œselect one or moreโ€ questions work?
Select-one-or-more questions are marked with square boxes (not ovals). You must select all correct answer choices โ€” a question may have one, two, or three correct answers. Partial credit is not awarded: if a question has three correct choices and you only select two, you receive zero points. Always evaluate each answer choice independently.
How do numeric-entry questions work?
Type your answer directly into a box as an integer, decimal, or fraction. For fraction questions, there are two separate boxes โ€” one for the numerator and one for the denominator. Equivalent correct forms (e.g., 2.5 and 2.50, or 1/2 and 6/12) are all accepted. Enter the exact answer unless told to round โ€” if you cannot enter the exact answer in the box, your answer may be incorrect.
Can I take Mathematics (5733) as part of the Combined test?
Yes. The Mathematics (5733) can be taken independently ($90) or as part of the Praxis Core Combined (5752) with Reading (5713) and Writing (5723) for $150. The Combined test saves $120 vs. taking all three separately. Scores are reported separately for each subtest regardless of how you register.
When will I receive my Praxis Core Mathematics scores?
Official score reports are typically available approximately five weeks after your test date. Scores are posted to your ETS account and sent to any institutions you designated at registration.

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Sources: ETS Praxis Core Academic Skills for Educators: Mathematics (5733) Study Companion (official PDF, praxis.ets.org); ETS official test page for 5733; Common Core State Standards for Mathematics; ETS Praxis fee schedule 2025โ€“26. Praxisยฎ is a registered trademark of Educational Testing Service (ETS). This site is not affiliated with or endorsed by ETS. Passing score requirements vary by state โ€” always verify at ets.org/praxis/states.
Last Updated: May 10, 2026