Mathematics
The Mathematics domain tests arithmetic, fractions and decimals, percentages, ratios and proportions, basic algebra, geometry, measurement, and word-problem setup. It rewards clean setup and estimation more than calculator speed. Most missed questions are setup errors, not arithmetic errors.
Core rules
- Order of operations: parentheses, exponents, multiply/divide left to right, then add/subtract left to right.
- Fractions: use a common denominator to add or subtract; multiply straight across; divide by multiplying by the reciprocal.
- Percent: part = percent × whole. A 20% increase is ×1.20, not ×0.20.
- Proportions: place corresponding units in the same positions, then cross-multiply.
- Unit conversion: multiply by fractions equal to 1 and cancel units.
- Linear equations: undo addition or subtraction first, then multiplication or division.
- Geometry: rectangle area = lw; triangle area = ½bh; circle area = πr²; circumference = 2πr; Pythagorean theorem a² + b² = c².
Worked example
An $80 item is discounted 25%, then 8% tax is added to the sale price. Find the total. Sale price = 80 × 0.75 = $60. Tax = 60 × 0.08 = $4.80. Total = $64.80. Do not apply tax to $80; the tax base is the discounted price.
Traps that cost marks
- Adding percent changes directly: 25% off plus 8% tax is not 17% off.
- Using the new value as the base for a percent increase.
- Mixing milliliters and liters in one proportion.
- Rounding before the final step.
- Solving for x but answering a different quantity.
Check whether the question asks for a rate, a total, or a remaining amount before you choose an answer.