Mathematics (Math Skills)
What to master
Build fluency in arithmetic with fractions, decimals, and percents; ratio and proportion; linear equations; unit conversions; averages; and basic geometry (perimeter, area, volume, right-triangle relationships). Most questions are word problems, so translation skill matters as much as computation.
Traps to expect
- Percent change base: a 20% increase followed by a 20% decrease does not return to the original value. Always apply each percent to the new amount.
- Unit mismatch: minutes versus hours, inches versus feet, or dollars versus cents. Convert before calculating.
- Order of operations: simplify parentheses and exponents first, then multiply/divide left to right, then add/subtract.
- Averaging rates: average speed for equal distances is not the simple average of the two speeds unless times are equal.
- Answering the wrong quantity: the question may ask for the remaining amount, not the amount used.
Worked example
A jacket costs $80 and is discounted 25%, then taxed 10% on the sale price. Sale price = 0.75 × 80 = $60. Tax = 0.10 × 60 = $6. Final = $66. A common wrong path is to combine 25% off and 10% tax as a 15% reduction, which gives $68-incorrect because the tax applies after the discount.
Rule of thumb
Write a one-line equation or proportion before computing, label every unit, and estimate the answer first. If your result is far from the estimate, recheck the setup rather than the arithmetic.