High School Equivalency Test (HiSET) Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in High School Equivalency Test (HiSET), not a summary of it.

1. 1

   Numbers and Operations

   4 topics

   • Real Number System
     • Integers, rational and irrational numbers
     • Ordering and comparing numbers
     • Absolute value and number line
   • Fractions, Decimals, and Percents
     • Operations with fractions and decimals
     • Converting between forms
     • Percent increase, decrease, and applications
   • Ratios, Proportions, and Rates
     • Setting up and solving proportions
     • Unit rates and scaling
   • Exponents, Roots, and Order of Operations
     • Powers and square roots
     • Scientific notation
     • Estimation and reasonableness of answers
2. 2

   Algebraic Concepts

   5 topics

   • Expressions and Polynomials
     • Evaluating and simplifying expressions
     • Adding, subtracting, and multiplying polynomials
     • Factoring
   • Linear Equations and Inequalities
     • Solving one- and multi-step equations
     • Solving and graphing inequalities
   • Linear Functions and Graphs
     • Slope and rate of change
     • Slope-intercept and point-slope forms
     • Interpreting graphs of lines
   • Systems of Equations
     • Substitution and elimination methods
     • Graphical solutions
   • Quadratics and Nonlinear Relationships
     • Solving quadratic equations
     • Function notation and patterns
3. 3

   Measurement and Geometry

   5 topics

   • Units and Measurement
     • U.S. customary and metric units
     • Unit conversions
   • Perimeter, Area, and Circumference
     • Polygons and composite figures
     • Circles
   • Surface Area and Volume
     • Prisms, cylinders, and cones
     • Spheres and pyramids
   • Triangles and the Pythagorean Theorem
     • Right-triangle relationships
     • Distance between points
   • Transformations and Coordinate Geometry
4. 4

   Data Analysis, Probability, and Statistics

   4 topics

   • Interpreting Data Displays
     • Bar, line, and circle graphs
     • Tables and scatterplots
   • Measures of Center and Spread
     • Mean, median, and mode
     • Range and outliers
   • Probability
     • Simple and compound events
     • Independent and dependent events
   • Counting and Data Reasoning
     • Combinations and basic counting
     • Drawing conclusions and predictions from data

Mathematics flashcards for High School Equivalency Test (HiSET)

21 of 55 cards from the Mathematics deck — real questions with worked answers.

1. What are the subsets of the real number system, from most to least inclusive?

   Real numbers contain rational and irrational numbers; rationals contain integers; integers contain whole numbers; whole numbers contain natural (counting) numbers.

2. What distinguishes a rational number from an irrational number?

   A rational number can be written as a fraction a/b of two integers (its decimal terminates or repeats); an irrational number cannot, and its decimal is non-terminating and non-repeating (e.g., pi, sqrt(2)).

3. How do you convert a fraction to a decimal, and a decimal to a percent?

   Divide the numerator by the denominator to get a decimal; multiply the decimal by 100 (move the point two places right) and add % to get a percent.

4. How do you convert a percent to a fraction in lowest terms?

   Write the percent over 100, then simplify. Example: 25% = 25/100 = 1/4.

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

   Find a common denominator (the LCD), rewrite each fraction with that denominator, add or subtract the numerators, keep the denominator, then simplify.

6. How do you multiply and divide fractions?

   To multiply, multiply numerators and multiply denominators. To divide, multiply the first fraction by the reciprocal of the second (invert and multiply).

7. What is the formula relating part, whole, and percent?

   part = percent × whole (as a decimal), so percent = part/whole and whole = part/percent.

8. How do you find percent increase or percent decrease?

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

9. What is the difference between a ratio and a rate?

   A ratio compares two quantities of any kind (e.g., 3:2); a rate compares two quantities with different units (e.g., miles per hour). A unit rate has a denominator of 1.

10. How do you solve a proportion a/b = c/d for an unknown?

    Cross-multiply: a·d = b·c, then solve the resulting equation for the unknown variable.

11. What is a unit rate and how is it found?

    A unit rate is a rate per single unit of the second quantity; find it by dividing the first quantity by the second so the denominator equals 1 (e.g., $6 for 3 lb = $2/lb).

12. What are the product and quotient rules for exponents with the same base?

    Product: x^a · x^b = x^(a+b). Quotient: x^a / x^b = x^(a−b).

13. What do a zero exponent and a negative exponent mean?

    x^0 = 1 (for x ≠ 0); x^(−n) = 1/x^n, the reciprocal raised to the positive power.

14. What is the power of a power rule for exponents?

    (x^a)^b = x^(a·b); multiply the exponents.

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

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

16. What is the relationship between a square root and a square?

    The square root of x is the nonnegative number that, when multiplied by itself, gives x; sqrt(a^2) = |a|. Squaring and taking the principal square root are inverse operations for nonnegative numbers.

17. How do you combine like terms in an algebraic expression?

    Add or subtract the coefficients of terms that have exactly the same variable(s) raised to the same power(s); the variable part stays unchanged (e.g., 3x + 5x = 8x).

18. How do you multiply two binomials (FOIL)?

    Multiply the First, Outer, Inner, and Last terms, then combine like terms. Example: (x+2)(x+3) = x^2 + 5x + 6.

19. What is the distributive property?

    a(b + c) = ab + ac; multiply the outside factor by each term inside the parentheses.

20. What is the degree of a polynomial?

    The degree is the highest exponent of the variable in the polynomial (e.g., 4x^3 + 2x − 1 has degree 3).

21. How do you solve a two-step linear equation like 3x + 5 = 20?

    Undo addition/subtraction first (subtract 5 to get 3x = 15), then undo multiplication/division (divide by 3 to get x = 5).

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