Mathematics: Arithmetic, Algebra, Geometry, and Data
What the Mathematics section tests
Math items cover number operations, fractions and decimals, ratios and proportions, percents, basic algebra, geometry, measurement, and data interpretation from tables and graphs. Most problems are multi-step, so planning matters as much as computation.
Concepts to master
- Order of operations: Parentheses, exponents, multiplication and division left to right, then addition and subtraction.
- Fractions and percents: Convert among fractions, decimals, and percents. Percent change equals the amount of change divided by the original amount.
- Ratios and proportions: Set up a proportion and cross-multiply; keep units aligned.
- Linear equations: Isolate the variable by performing the same operation on both sides. For slope, use rise over run.
- Geometry: Area of a rectangle is length times width; a triangle's area is half base times height; a circle's area uses pi times radius squared. The angles of a triangle total 180 degrees.
- Data: Read axis labels and units before comparing values; distinguish mean (average) from median (middle value).
Traps to watch
- Unit mismatches: Minutes versus hours, or centimeters versus meters, cause wrong answers.
- Answering the wrong question: You may solve for x but be asked for 2x or for a total.
- Percent increase versus percent of: "20% more than 50" is 60, not 10.
- Estimation: Rounding first can eliminate impossible choices quickly.
Worked example
A shirt costs $40 and is discounted 25%, then taxed 10% on the sale price. Sale price: 40 times 0.75 equals $30. Tax: 30 times 0.10 equals $3. Total: $33. A common error is applying the discount and tax to the original price, giving $34.