Mathematics
Core concepts
Mathematics questions sample number and operations, fractions and decimals, proportional reasoning, algebraic thinking, geometry and measurement, and data and probability. Strong place-value understanding underlies regrouping, rounding, and decimal comparison. For fractions, expect equivalence, ordering, and all four operations; for ratios, expect unit rates and scaling. Geometry includes angle relationships, area and perimeter, volume, and coordinate-plane work in all four quadrants. Data questions often ask about mean, median, mode, range, and misleading graphs.
Traps
Follow order of operations: parentheses, exponents, multiply and divide left to right, then add and subtract left to right. "Of" usually means multiply, as in 1/3 of 90. Percent change uses the original amount as the base; a percent increase followed by the same percent decrease does not return to the starting value. Do not confuse area (square units) with perimeter (linear units). When dividing by a fraction, multiply by its reciprocal. In data sets with outliers, the median is more resistant than the mean.
Worked example
3/4 ÷ 1/2. Keep the first fraction, change division to multiplication, and flip the second: 3/4 × 2/1 = 6/4 = 3/2, or 1 1/2. Check by reasoning: how many halves fit in three-quarters? One full half plus half of a half, so 1 1/2.
Rule of thumb
Estimate first, label units, and ask whether the answer is reasonable.