GED (General Educational Development) Mathematical Reasoning Syllabus

Mathematical Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematical Reasoning in GED (General Educational Development), not a summary of it.

1. 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. 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. 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. 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. 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. 6

   Test Strategy and the Calculator

   3 topics

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

Mathematical Reasoning flashcards for GED (General Educational Development)

18 of 51 cards from the Mathematical Reasoning deck — real questions with worked 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.

See more Mathematical Reasoning flashcards →

Planning Mathematical Reasoning for GED (General Educational Development)

Mathematical Reasoning (GED (General Educational Development)) FAQ