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Praxis (Praxis Core and Praxis Subject Assessments) Praxis Core: Mathematics (5733) Syllabus

The Praxis Core: Mathematics (5733) syllabus for Praxis (Praxis Core and Praxis Subject Assessments) in full: 4 chapters, 17 topics and 19 sub-topics, every one listed below, plus 50 Praxis Core: Mathematics (5733) flashcards with answers.

4Chapters
17Topics
19Sub-topics
50Flashcards

Praxis Core: Mathematics (5733) syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

  1. Number and Quantity

     5 topics
    • Operations with Integers, Fractions, and Decimals
      • Order of operations
      • Fraction-decimal-percent conversions
    • Ratios, Proportions, and Rates
      • Setting up and solving proportions
      • Unit rates and scaling
    • Percents and Percent Change
      • Percent increase and decrease
      • Simple interest applications
    • Place Value, Exponents, and Roots
    • Number Sense and Estimation

  2. Algebra and Functions

     4 topics
    • Linear Equations and Inequalities
      • Solving one-variable equations
      • Translating words into expressions
    • Systems of Equations
    • Functions and Relations
      • Evaluating functions
      • Linear relationships and slope
    • Patterns and Sequences

  3. Geometry and Measurement

     4 topics
    • Perimeter, Area, and Volume
      • Common 2D figures
      • Surface area and volume of solids
    • Properties of Angles and Triangles
      • Pythagorean theorem
      • Congruence and similarity
    • Coordinate Geometry
      • Distance and midpoint
    • Units of Measurement and Conversion

  4. Statistics and Probability

     4 topics
    • Measures of Center and Spread
      • Mean, median, mode, range
    • Data Representation and Interpretation
      • Reading bar graphs, line graphs, and box plots
      • Interpreting scatterplots
    • Basic Probability
      • Simple and compound events
    • Drawing Inferences from Data

Praxis (Praxis Core and Praxis Subject Assessments) Praxis Core: Mathematics (5733) flashcards — 50 questions with answers

  1. What is the result of adding two integers with the same sign?

    Add their absolute values and keep the common sign (e.g., -3 + -5 = -8).

  2. How do you add two integers with different signs?

    Subtract the smaller absolute value from the larger, and keep the sign of the number with the larger absolute value (e.g., -7 + 3 = -4).

  3. What is the rule for the sign when multiplying or dividing two integers?

    Same signs give a positive result; different signs give a negative result.

  4. What is the order of operations (PEMDAS)?

    Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

  5. How do you add or subtract fractions with unlike denominators?

    Convert to a common denominator (the least common denominator), then add or subtract the numerators and keep the denominator.

  6. How do you multiply two fractions?

    Multiply the numerators together and the denominators together, then simplify (e.g., 2/3 × 4/5 = 8/15).

  7. How do you divide one fraction by another?

    Multiply by the reciprocal of the divisor (e.g., 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6).

  8. How do you convert a fraction to a decimal?

    Divide the numerator by the denominator (e.g., 3/4 = 3 ÷ 4 = 0.75).

  9. When multiplying decimals, how do you place the decimal point in the answer?

    Count the total number of decimal places in both factors; the product has that many decimal places.

  10. What is a ratio?

    A comparison of two quantities by division, written as a:b, a/b, or 'a to b'.

  11. What is a proportion and how do you solve one?

    A proportion is a statement that two ratios are equal (a/b = c/d). Solve it by cross-multiplying: a×d = b×c.

  12. What is a unit rate?

    A rate expressed with a denominator of 1 (e.g., 60 miles in 2 hours = 30 miles per hour).

  13. If 3 pens cost $1.50, what is the unit price per pen?

    $1.50 ÷ 3 = $0.50 per pen.

  14. How do you convert a percent to a decimal?

    Divide by 100 (move the decimal point two places left), e.g., 45% = 0.45.

  15. How do you find a percent of a number?

    Convert the percent to a decimal and multiply (e.g., 20% of 80 = 0.20 × 80 = 16).

  16. What is the formula for percent change?

    Percent change = (new value − old value) / old value × 100. A positive result is an increase; negative is a decrease.

  17. A shirt's price rises from $40 to $50. What is the percent increase?

    (50 − 40)/40 × 100 = 10/40 × 100 = 25% increase.

  18. What does the place value of a digit represent in the decimal system?

    Its value based on position; each place is 10 times the place to its right (e.g., in 352, the 3 means 300).

  19. What does a positive integer exponent mean, as in a^n?

    Multiply the base a by itself n times (e.g., 2^4 = 2×2×2×2 = 16).

  20. What is the value of any nonzero number raised to the power of 0?

    1 (e.g., 7^0 = 1).

Show the other 30 Praxis Core: Mathematics (5733) flashcards

  1. What does a square root (√) of a number represent?

    A value that, when multiplied by itself, gives the original number (e.g., √49 = 7 because 7×7 = 49).

  2. What is the rule for multiplying powers with the same base?

    Add the exponents: a^m × a^n = a^(m+n) (e.g., 2^3 × 2^2 = 2^5).

  3. What does it mean to estimate by rounding to make a calculation easier?

    Replace numbers with nearby convenient values (e.g., 297 + 412 ≈ 300 + 400 = 700) to find an approximate answer.

  4. When rounding a number, what determines whether you round up or down?

    Look at the digit to the right of the rounding place: 5 or greater rounds up, less than 5 rounds down.

  5. How do you solve a one-variable linear equation like 3x + 5 = 20?

    Isolate the variable using inverse operations: subtract 5 (3x = 15), then divide by 3 (x = 5).

  6. What must you do to an inequality when you multiply or divide both sides by a negative number?

    Reverse the direction of the inequality sign (e.g., -2x < 6 becomes x > -3).

  7. What is the slope-intercept form of a linear equation?

    y = mx + b, where m is the slope and b is the y-intercept.

  8. What does the slope of a line measure?

    The rate of change: rise over run, or (change in y) / (change in x) between two points.

  9. What are the methods for solving a system of two linear equations?

    Substitution, elimination (addition/subtraction), and graphing to find the point of intersection.

  10. What does the solution to a system of two linear equations represent graphically?

    The point (or points) where the lines intersect; parallel lines give no solution, identical lines give infinitely many.

  11. What defines a function?

    A relation in which each input (x-value) is paired with exactly one output (y-value).

  12. What is the vertical line test?

    A graph represents a function if no vertical line crosses it more than once.

  13. What are the domain and range of a function?

    Domain is the set of all possible input (x) values; range is the set of all possible output (y) values.

  14. In an arithmetic sequence, how do you find the next term?

    Add the common difference to the previous term (e.g., 3, 7, 11, 15... adds 4 each time).

  15. In a geometric sequence, how do you find the next term?

    Multiply the previous term by the common ratio (e.g., 2, 6, 18, 54... multiplies by 3 each time).

  16. What is the formula for the perimeter of a rectangle?

    P = 2(length + width), or P = 2l + 2w.

  17. What is the formula for the area of a rectangle?

    A = length × width (A = lw).

  18. What is the formula for the area of a triangle?

    A = ½ × base × height.

  19. What are the formulas for the circumference and area of a circle?

    Circumference C = 2πr (or πd); Area A = πr².

  20. What is the formula for the volume of a rectangular prism (box)?

    V = length × width × height (V = lwh).

  21. What is the sum of the interior angles of any triangle?

    180 degrees.

  22. What is the Pythagorean theorem?

    For a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle).

  23. What are complementary and supplementary angles?

    Complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees.

  24. How do you find the distance between two points on a coordinate plane?

    Use the distance formula: d = √[(x₂−x₁)² + (y₂−y₁)²].

  25. What is the midpoint formula for two points on a coordinate plane?

    Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).

  26. How many feet are in a mile, and how many inches are in a foot?

    There are 5,280 feet in a mile and 12 inches in a foot.

  27. How do you convert kilometers to meters and meters to centimeters?

    Multiply by 1,000 for km to m, and by 100 for m to cm (the metric system is base 10).

  28. What are the mean, median, and mode of a data set?

    Mean is the average (sum ÷ count); median is the middle value when ordered; mode is the most frequently occurring value.

  29. What is the range of a data set, and how is it found?

    The range measures spread: it equals the maximum value minus the minimum value.

  30. What is the formula for the probability of a single event?

    Probability = (number of favorable outcomes) / (total number of possible outcomes), giving a value from 0 to 1.

Praxis (Praxis Core and Praxis Subject Assessments) Praxis Core: Mathematics (5733) FAQ

What is in the Praxis (Praxis Core and Praxis Subject Assessments) Praxis Core: Mathematics (5733) syllabus?

Praxis (Praxis Core and Praxis Subject Assessments) Praxis Core: Mathematics (5733) is split into 4 chapters: Number and Quantity, Algebra and Functions, Geometry and Measurement and Statistics and Probability. Together they contain 17 topics and 19 sub-topics.

How many chapters are in Praxis (Praxis Core and Praxis Subject Assessments) Praxis Core: Mathematics (5733)?

4 chapters, containing 17 topics and 19 sub-topics. The largest chapter is Number and Quantity, with 5 topics.

Are there flashcards for Praxis (Praxis Core and Praxis Subject Assessments) Praxis Core: Mathematics (5733)?

Yes — a 50-card Praxis Core: Mathematics (5733) deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.