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GED (General Educational Development) Mathematical Reasoning Syllabus

The Mathematical Reasoning syllabus for GED (General Educational Development) in full: 6 chapters, 22 topics and 30 sub-topics, every one listed below, plus 51 Mathematical Reasoning flashcards with answers.

6Chapters
22Topics
30Sub-topics
51Flashcards

Mathematical Reasoning syllabus: all 6 chapters

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

  1. Number Sense and Operations

     4 topics
    • Operations With Integers and Rational Numbers
      • Order of operations (PEMDAS)
      • Absolute value and the number line
    • Fractions, Decimals, and Percents
      • Converting among forms
      • Percent of a number, percent change, and discounts
    • Ratios, Rates, and Proportions
      • Setting up and solving proportions
      • Unit rates and scaling
    • Exponents, Roots, and Scientific Notation
      • Laws of exponents
      • Square and cube roots

  2. Algebraic Expressions and Equations

     4 topics
    • Evaluating and Simplifying Expressions
      • Combining like terms
      • Distributive property and factoring
    • Solving Linear Equations and Inequalities
      • One- and two-step equations
      • Multi-step and variables on both sides
      • Graphing and interpreting inequalities
    • Polynomials and Quadratics
      • Multiplying binomials and factoring trinomials
      • Solving quadratics by factoring and the quadratic formula
    • Systems of Linear Equations
      • Solving by substitution and elimination
      • Solving by graphing

  3. Functions and Graphing on the Coordinate Plane

     4 topics
    • The Coordinate Plane and Plotting Points
    • Slope and Linear Equations
      • Slope-intercept and point-slope form
      • Finding slope from points and graphs
    • Interpreting and Comparing Functions
      • Function notation and inputs/outputs
      • Linear versus nonlinear functions
    • Reading Tables, Graphs, and Word Problems

  4. Geometry and Measurement

     4 topics
    • Perimeter, Area, and Circumference
      • Triangles, quadrilaterals, and circles
      • Composite and irregular figures
    • Volume and Surface Area
      • Prisms, cylinders, cones, pyramids, spheres
    • The Pythagorean Theorem and Right Triangles
    • Units, Conversions, and Scale

  5. Data Analysis, Statistics, and Probability

     3 topics
    • Measures of Center and Spread
      • Mean, median, mode, and range
      • Weighted averages
    • Interpreting Data Displays
      • Bar graphs, line graphs, histograms
      • Scatter plots and dot plots
    • Basic Probability
      • Simple and compound events
      • Counting outcomes

  6. Test Strategy and the Calculator

     3 topics
    • Using the TI-30XS Onscreen Calculator
    • The Provided Formula Sheet
    • Estimation and Reasonableness Checks

GED (General Educational Development) Mathematical Reasoning flashcards — 51 questions with answers

  1. When multiplying or dividing two integers, how do you determine the sign of the result?

    Same signs give a positive result; different signs give a negative result (e.g., (-6)(-3)=18, (-6)(3)=-18).

  2. What is the rule for adding 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., -8 + 5 = -3).

  3. What is the order of operations (PEMDAS), and how are multiplication/division and addition/subtraction handled?

    Parentheses, Exponents, Multiplication/Division (left to right), then Addition/Subtraction (left to right). M/D have equal priority; A/S have equal priority.

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

    Find a common denominator, rewrite each fraction with it, add or subtract the numerators, keep the denominator, then simplify.

  5. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal of the second (invert the divisor and multiply): a/b ÷ c/d = a/b × d/c.

  6. How do you convert a decimal to a percent and a percent to a decimal?

    Decimal to percent: multiply by 100 (move decimal 2 places right). Percent to decimal: divide by 100 (move decimal 2 places left).

  7. What is the percent-change formula?

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

  8. How do you find a percent of a number, e.g., 15% of 80?

    Convert the percent to a decimal and multiply: 0.15 × 80 = 12.

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

    A ratio compares two quantities of the same kind (e.g., 3:2 boys to girls); a rate compares two quantities with different units (e.g., 60 miles per hour).

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

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

  11. What is a unit rate and how do you find it?

    A unit rate is a rate with a denominator of 1; find it by dividing the numerator quantity by the denominator quantity (e.g., $12 for 3 lb = $4 per lb).

  12. What does a negative exponent mean, as in x⁻ⁿ?

    A negative exponent means the reciprocal: x⁻ⁿ = 1/xⁿ (for x ≠ 0).

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

    Product: xᵃ · xᵇ = xᵃ⁺ᵇ. Quotient: xᵃ / xᵇ = xᵃ⁻ᵇ.

  14. What is the power rule for exponents, (xᵃ)ᵇ?

    (xᵃ)ᵇ = xᵃᵇ (multiply the exponents).

  15. What does any nonzero number raised to the power of 0 equal?

    x⁰ = 1 for any x ≠ 0.

  16. What is the standard form of a number written in scientific notation?

    a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer; positive n means a large number, negative n means a small (fractional) number.

  17. What does the square root of a number represent, and what is √144?

    A square root is a value that, when multiplied by itself, gives the original number; √144 = 12.

  18. How do you evaluate an algebraic expression for given variable values?

    Substitute the given numbers for the variables, then follow the order of operations to simplify.

  19. What are like terms, and how are they combined?

    Like terms have the same variables raised to the same powers; combine them by adding or subtracting their coefficients (e.g., 3x + 5x = 8x).

  20. What does the distributive property state?

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

Show the other 31 Mathematical Reasoning flashcards

  1. What is the general process for solving a linear equation in one variable?

    Simplify each side, use inverse operations to isolate the variable term, then divide by the coefficient; whatever you do to one side, do to the other.

  2. What must you do to the inequality symbol when multiplying or dividing both sides by a negative number?

    Reverse (flip) the inequality symbol (e.g., -2x < 6 becomes x > -3).

  3. What is a polynomial, and what is the degree of a polynomial?

    A polynomial is a sum of terms made of variables with whole-number exponents and coefficients; its degree is the highest exponent of the variable.

  4. How do you factor a quadratic of the form x² + bx + c?

    Find two numbers that multiply to c and add to b; write it as (x + m)(x + n) using those numbers.

  5. What is the quadratic formula for ax² + bx + c = 0?

    x = [−b ± √(b² − 4ac)] / (2a).

  6. In the quadratic formula, what does the discriminant b² − 4ac tell you?

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

  7. What does it mean to solve a system of two linear equations?

    Find the (x, y) value pair that satisfies both equations simultaneously — the point where the two lines intersect.

  8. Describe the substitution method for solving a system of equations.

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

  9. Describe the elimination (addition) method for solving a system of equations.

    Multiply equations as needed so one variable's coefficients are opposites, add the equations to eliminate that variable, solve, then back-substitute.

  10. How many solutions does a system have if the lines are parallel versus identical?

    Parallel lines: no solution. Identical (same) lines: infinitely many solutions.

  11. In the coordinate plane, what does the ordered pair (x, y) represent?

    x is the horizontal distance from the origin (right positive, left negative); y is the vertical distance (up positive, down negative).

  12. In which quadrant are both coordinates positive, and how are the quadrants numbered?

    Quadrant I has both positive (upper right); quadrants are numbered I–IV counterclockwise starting from the upper right.

  13. What is the slope formula given two points (x₁, y₁) and (x₂, y₂)?

    slope m = (y₂ − y₁) / (x₂ − x₁), i.e., rise over run.

  14. What is the slope-intercept form of a line, and what do its parts mean?

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

  15. What are the slopes of horizontal and vertical lines?

    A horizontal line has slope 0; a vertical line has an undefined slope.

  16. How do the slopes of parallel lines compare to those of perpendicular lines?

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

  17. What is the definition of a function in terms of inputs and outputs?

    A function assigns exactly one output (y) to each input (x); no input value may have more than one output.

  18. What is the vertical line test?

    If any vertical line crosses a graph more than once, the graph is not a function.

  19. How can you compare the rate of change of two linear functions given as a table and an equation?

    Find each function's slope (change in y over change in x for the table; the coefficient of x for y = mx + b) and compare those values.

  20. What is a key first step when solving a math word problem?

    Identify what is being asked and the relevant given information, translate words into a mathematical expression or equation, then solve and check units.

  21. What are the formulas for the perimeter and area of a rectangle?

    Perimeter P = 2l + 2w; Area A = l × w.

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

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

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

    A = ½ × base × height.

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

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

  25. What is the formula for the volume of a cylinder?

    V = πr²h (area of the circular base times the height).

  26. What is the difference between volume and surface area of a solid?

    Volume measures the space inside (cubic units); surface area measures the total area of all outside faces (square units).

  27. State the Pythagorean theorem and what its variables represent.

    a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse (the side opposite the right angle).

  28. How do you convert between units, such as feet to inches, using a conversion factor?

    Multiply by a fraction equal to 1 that cancels the unwanted unit (e.g., 5 ft × 12 in/1 ft = 60 in).

  29. 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 of two middle values if even count). Mode: the most frequently occurring value.

  30. What does the range of a data set measure, and how is it calculated?

    Range measures spread; it equals the largest value minus the smallest value.

  31. What is the basic probability formula for a single event?

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

GED (General Educational Development) Mathematical Reasoning FAQ

What is in the GED (General Educational Development) Mathematical Reasoning syllabus?

GED (General Educational Development) Mathematical Reasoning is split into 6 chapters: Number Sense and Operations, Algebraic Expressions and Equations, Functions and Graphing on the Coordinate Plane, Geometry and Measurement, Data Analysis, Statistics, and Probability and Test Strategy and the Calculator. Together they contain 22 topics and 30 sub-topics.

How many chapters are in GED (General Educational Development) Mathematical Reasoning?

6 chapters, containing 22 topics and 30 sub-topics. The largest chapter is Number Sense and Operations, with 4 topics.

Are there flashcards for GED (General Educational Development) Mathematical Reasoning?

Yes — a 51-card Mathematical Reasoning 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.