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High School Equivalency Test (HiSET) Mathematics Syllabus

The Mathematics syllabus for High School Equivalency Test (HiSET) in full: 4 chapters, 18 topics and 39 sub-topics, every one listed below, plus 55 Mathematics flashcards with answers.

4Chapters
18Topics
39Sub-topics
55Flashcards

Mathematics syllabus: all 4 chapters

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

  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. 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. 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. 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

High School Equivalency Test (HiSET) Mathematics flashcards — 55 questions with 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).

Show the other 35 Mathematics flashcards

  1. 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).

  2. What must you do to an inequality when multiplying or dividing by a negative number?

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

  3. What is the slope-intercept form of a linear equation, and what does each part mean?

    y = mx + b, where m is the slope (rate of change) and b is the y-intercept (the y-value where the line crosses the y-axis).

  4. How do you calculate the slope between two points (x1, y1) and (x2, y2)?

    slope m = (y2 − y1)/(x2 − x1), the change in y divided by the change in x (rise over run).

  5. What do positive, negative, zero, and undefined slopes look like on a graph?

    Positive slopes rise left to right; negative slopes fall; a zero slope is a horizontal line; an undefined slope is a vertical line.

  6. What are the slopes of parallel and perpendicular lines?

    Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (their product is −1).

  7. What does it mean to evaluate a function f(x) at a given input?

    Substitute the input value for x everywhere in the rule and simplify; the result is the output f(x). Example: if f(x)=2x+1, then f(3)=7.

  8. What are the three possible solution outcomes for a system of two linear equations?

    One solution (lines intersect at a point), no solution (parallel lines), or infinitely many solutions (same line).

  9. How do you solve a system of equations by substitution?

    Solve one equation for a variable, substitute that expression into the other equation, solve for the remaining variable, then back-substitute to find the first.

  10. How do you solve a system of equations by elimination?

    Add or subtract the equations (after scaling if needed) so one variable cancels, solve for the remaining variable, then substitute back to find the other.

  11. What is the standard form of a quadratic equation and its graph?

    ax^2 + bx + c = 0 (a ≠ 0); its graph is a parabola, opening up if a > 0 and down if a < 0.

  12. What is the quadratic formula?

    x = (−b ± sqrt(b^2 − 4ac)) / (2a), used to find the solutions of ax^2 + bx + c = 0.

  13. What does the discriminant b^2 − 4ac tell you about a quadratic's solutions?

    If positive, two real solutions; if zero, one real (repeated) solution; if negative, no real solutions.

  14. How does a linear relationship differ from an exponential relationship?

    A linear relationship changes by a constant amount (added) each step; an exponential relationship changes by a constant factor (multiplied) each step.

  15. How do you convert between units using a conversion factor?

    Multiply by a fraction equal to 1 that has the desired unit on top and the original unit on the bottom, so the unwanted units cancel (dimensional analysis).

  16. How many inches are in a foot, feet in a yard, and how many milliliters in a liter?

    12 inches = 1 foot; 3 feet = 1 yard; 1,000 milliliters = 1 liter (and 1,000 grams = 1 kilogram).

  17. What is the formula for the perimeter of a rectangle and the circumference of a circle?

    Rectangle perimeter P = 2l + 2w; circle circumference C = 2πr = πd.

  18. What are the area formulas for a rectangle, triangle, and circle?

    Rectangle A = l·w; triangle A = (1/2)·b·h; circle A = πr^2.

  19. What is the area formula for a parallelogram and for a trapezoid?

    Parallelogram A = b·h; trapezoid A = (1/2)(b1 + b2)·h, the average of the two parallel bases times the height.

  20. What is the formula for the volume of a rectangular prism and of a cylinder?

    Rectangular prism V = l·w·h; cylinder V = πr^2·h (base area times height).

  21. What is the formula for the volume of a sphere and of a cone?

    Sphere V = (4/3)πr^3; cone V = (1/3)πr^2·h.

  22. What is surface area, and how does it differ from volume?

    Surface area is the total area of all outer faces of a 3D object (measured in square units); volume is the space inside it (measured in cubic units).

  23. What is the Pythagorean theorem and when does it apply?

    In a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse (the side opposite the right angle) and a, b are the legs. It applies only to right triangles.

  24. What is the sum of the interior angles of any triangle, and how are triangles classified by angles?

    The angles always sum to 180°. By angle: acute (all < 90°), right (one = 90°), obtuse (one > 90°).

  25. How are triangles classified by their side lengths?

    Equilateral (all three sides equal), isosceles (two sides equal), and scalene (no sides equal).

  26. What are the four basic geometric transformations and how do they affect a figure?

    Translation (slide), reflection (flip), and rotation (turn) preserve size and shape (rigid/congruent); dilation (resize) changes size, producing a similar figure.

  27. How do you find the distance between two points and the midpoint of a segment on the coordinate plane?

    Distance = sqrt((x2−x1)^2 + (y2−y1)^2); midpoint = ((x1+x2)/2, (y1+y2)/2).

  28. When should you use a bar graph versus a line graph?

    Use a bar graph to compare amounts across separate categories; use a line graph to show how a quantity changes continuously over time.

  29. What does a scatter plot show, and what does its correlation indicate?

    A scatter plot shows the relationship between two variables as points; an upward trend is positive correlation, a downward trend is negative correlation, and no pattern means no correlation.

  30. How do you find the mean, median, and mode of a data set?

    Mean = sum of values ÷ number of values; median = the middle value when ordered (average the two middle values if even count); mode = the most frequently occurring value.

  31. What is the range and the interquartile range (IQR) of a data set?

    Range = maximum − minimum; IQR = Q3 − Q1, the spread of the middle 50% of the data.

  32. How is the probability of a single event calculated?

    P(event) = (number of favorable outcomes)/(total number of equally likely outcomes), a value between 0 (impossible) and 1 (certain).

  33. How do you find the probability of two independent events both occurring?

    Multiply their individual probabilities: P(A and B) = P(A) × P(B).

  34. What is the fundamental counting principle?

    If one choice can be made m ways and a second n ways, the number of combined outcomes is m × n (multiply the options for each stage).

  35. What is the difference between a permutation and a combination?

    A permutation counts arrangements where order matters; a combination counts selections where order does not matter.

High School Equivalency Test (HiSET) Mathematics FAQ

What is in the High School Equivalency Test (HiSET) Mathematics syllabus?

High School Equivalency Test (HiSET) Mathematics is split into 4 chapters: Numbers and Operations, Algebraic Concepts, Measurement and Geometry and Data Analysis, Probability, and Statistics. Together they contain 18 topics and 39 sub-topics.

How many chapters are in High School Equivalency Test (HiSET) Mathematics?

4 chapters, containing 18 topics and 39 sub-topics. The largest chapter is Algebraic Concepts, with 5 topics.

Are there flashcards for High School Equivalency Test (HiSET) Mathematics?

Yes — a 55-card Mathematics 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.