Mathematics: Algebra, Geometry, and Data Reasoning
What the section tests
Mathematics items cover arithmetic and percentages, algebraic manipulation and equations, functions and graphs, geometry and measurement, and interpretation of data and probability. Many questions are word problems, so translation from text to equation is a core skill.
Concepts to master
- Linear equations and systems: isolate variables; solve two-variable systems by substitution or elimination.
- Percent change: percent change = (new − old) / old × 100; distinguish increase from decrease and from percent of a number.
- Ratios and proportions: set up equivalent fractions and cross-multiply.
- Geometry: area and perimeter of rectangles, triangles, and circles; Pythagorean theorem; angle sums (180° in a triangle, 360° around a point).
- Functions: slope = rise/run; interpret intercepts in context.
- Data and probability: read tables and graphs carefully; probability = favorable outcomes / total outcomes.
Common traps
- Mixing units (minutes vs. hours, cm vs. m) before calculating.
- Confusing percent increase with the new value.
- Forgetting that a negative slope means the line falls left to right.
- Using diameter where radius is required in circle formulas.
- Answering the wrong quantity (e.g., solving for x when the question asks for 2x).
Worked example
A jacket costs 80 and is discounted 25%, then taxed 10% on the sale price. Sale price = 80 × 0.75 = 60. Final price = 60 × 1.10 = 66. Rule of thumb: apply successive percentage changes by multiplying factors (0.75 then 1.10), not by adding or subtracting percents.
Strategy
Estimate the answer before computing, check units, and substitute your result back into the original equation.