I85PREP
⌘ K
GED study materials
GED study resources

GED: Mathematical Reasoning

GED · Work through your exam, one topic at a time.

All guide sections

Mathematical Reasoning

What the Mathematical Reasoning test covers

The GED Mathematical Reasoning domain measures quantitative and algebraic problem solving. You have 115 minutes for about 46 questions. The first segment is calculator-free; after that, an on-screen TI-30XS MultiView calculator and a formula sheet are available. Questions ask you to compute, model, interpret graphs, and solve real-world problems-not just memorize procedures.

Core rules and concepts

  • Order of operations: simplify parentheses, exponents, multiplication/division left to right, then addition/subtraction.
  • Percents: part = percent × whole. For percent change, divide the change by the original amount.
  • Proportional reasoning: set up ratios with matching units; cross-multiply only when the ratios are equivalent.
  • Geometry: use the formula sheet for area, volume, and the Pythagorean theorem; keep units consistent.
  • Algebra: isolate a variable by doing the same operation to both sides; when multiplying or dividing an inequality by a negative number, reverse the inequality sign.
  • Linear functions: slope = (y₂ − y₁)/(x₂ − x₁); slope-intercept form is y = mx + b.
  • Data: mean is the sum divided by the count; median is the middle value in order; mode is most frequent. A line of best fit summarizes a scatter plot but does not prove causation.

Worked example

A jacket regularly costs $80. It is marked down 25%, and then 6% sales tax is added to the sale price. What is the total? Sale price = 80 × (1 − 0.25) = 80 × 0.75 = $60. Tax = 60 × 0.06 = $3.60. Total = $60 + $3.60 = $63.60. Notice that the tax is calculated on the reduced price, not the original $80; using $80 would give $64.80 and is a common error.

Traps that cost marks

  • Applying a percent discount and then a percent tax to the wrong base.
  • Forgetting to reverse an inequality when dividing by a negative.
  • Mixing units (for example, inches and feet) before computing area or volume.
  • Answering the wrong quantity-perimeter instead of area, or slope instead of intercept.
  • Trusting the calculator segment for arithmetic that is faster by hand, then running out of time.