Mathematics
Core skills and where points are lost
The Mathematics section covers arithmetic with fractions, decimals, and percents; ratios and proportions; order of operations; algebraic expressions and linear equations; geometry (perimeter, area, volume); measurement and unit conversion; and data interpretation (mean, median, mode, range, reading tables and graphs). Word problems are common, so translation matters: 'of' usually means multiply, 'per' signals a rate, and 'is' often marks the equals sign.
Traps:
- Percent change: always divide by the original (base) amount, not the new amount. A price that rises from $50 to $60 is a 20% increase ($10/$50), not a 16.7% decrease.
- Chained percents: a 20% discount followed by 8% tax is not a 12% change. Apply each factor in order: price x 0.80 x 1.08.
- Unit mismatch: convert before computing; keep units in your setup.
- Order of operations: parentheses, exponents, multiply/divide left to right, then add/subtract left to right.
- Rounding early: keep full precision until the final step.
Rule of thumb: for any proportion, set up two equal ratios with matching units in the same positions and cross-multiply.
Worked example: An $80 jacket is discounted 25%, then 8% tax is added. Final price = 80 x 0.75 = $60; 60 x 1.08 = $64.80. Adding 25% and 8% to get 33% is the classic wrong answer.