Praxis Math
study guide
Every chapter of the course summarized, with each section linked to its lesson.
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This free Praxis Math study guide summarizes all 3 chapters of Achievable's Praxis Math course: what each covers, the points to remember, and its 17 sections in order. Read each chapter after you study it, or work through the whole guide before exam day.
Each section links to its full lesson in Achievable, with the review quizzes and full-length practice exams.
Chapter 1: Number and quantity
6 sections
- Integers and decimals: Same signs combine, different signs compare magnitudes, and decimals require aligned points, decimal places, and shifted divisors for arithmetic.
- Fractions and percents: Use common denominators, multiply straight across, divide using Keep-Change-Flip, identify the unknown with , and decide whether you need the part, whole, or percent.
- Place value order: Each digit's value depends on its position and a power of , so moving left multiplies by and moving right divides by .
- Whole numbers and operations: Factors, GCF or GCD, LCM, sequences, units, inverse operations, the distributive property, exponent rules, and square roots help simplify, compare, and check results.
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Chapter 2: Data analysis, statistics, and probability
5 sections
- Central tendencies: Always order data before computing median or quartiles, use mean for balanced average with caution for extreme values, and use median when distribution is skewed or contains extreme values.
- Spread measures: Mode is useful for categorical or discrete data, range gives quick sense of total spread but is sensitive to extremes, IQR focuses on central spread ignoring extremes, and standard deviation quantifies average deviation from the mean.
- Reading displays: Always read titles and labels carefully, understand the scale, look for patterns and outliers, and choose graphs based on the type of data, including stem-and-leaf plots and scatterplots.
- Interpreting data: Use the five-number summary and rule, anchor conclusions in specific numeric changes, interpret scatterplots and line of best fit carefully, and compute probabilities from clear events and tables.
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Achievable Praxis Core: Math
The Praxis Math (5733) exam is part of the Praxis Core, a set of tests used for teacher certification in about 20 states, plus Washington, D.C. and several U.S. territories. Achievable's interactive online Praxis Math prep course makes complex topics simple and engaging. Our adaptive platform and AI tutor personalize your study plan, while memory science ensures effective teacher prep that gets results.
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Chapter 3: Algebra and geometry
6 sections
- Algebraic manipulation: Combine like terms, use the distributive property, FOIL, and GCF factoring, then verify factoring by expanding back to the original expression.
- Equations and functions: Solve equations by isolating the variable, reverse an inequality sign when multiplying or dividing by a negative, and use function rules, substitutions, and set operations correctly.
- Geometry relationships: Use triangle inequality, slopes, distances, angle relationships, congruence tests, and similarity rules, including scale factor changes to perimeter, area, and volume.
- Measurement formulas: Use the correct formulas for perimeter, area, and volume, convert radius and diameter, apply to sectors and arcs, and solve reverse problems algebraically.
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Praxis Math exam at a glance
- Questions
- 56 selected-response and numeric-entry questions
- Time
- 90 minutes
- Passing score
- 150 in many states (varies by state)
- Exam fee
- $90
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