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

Praxis Core: Mathematics (5733) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Praxis Core: Mathematics (5733) in Praxis (Praxis Core and Praxis Subject Assessments), not a summary of it.

1. 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. 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. 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. 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 Core: Mathematics (5733) flashcards for Praxis (Praxis Core and Praxis Subject Assessments)

20 of 50 cards from the Praxis Core: Mathematics (5733) deck — real questions with worked 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).

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