Mathematics
This domain covers number and operations (integers, fractions, decimals, percents, factors and multiples), algebraic reasoning (expressions, equations, patterns, the coordinate plane), geometry and measurement (perimeter, area, volume, angles, similarity), and data and probability (mean, median, mode, range, graph reading, simple probability). Expect multi-step computation and word problems rather than formal proofs.
Operation rules that appear constantly
- Order of operations: grouping symbols, exponents, multiply/divide left to right, add/subtract left to right. A fraction bar groups the entire numerator and denominator.
- Dividing by a fraction means multiplying by its reciprocal: 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2.
- Percent means per hundred: part = percent × whole; percent change = change ÷ original amount.
- Ratios scale by multiplying both terms; solve proportions by cross-multiplying: 3/4 = x/12 gives 4x = 36.
- The mean shifts when an outlier is added; the median does not. Range = maximum − minimum.
Formulas to memorize
Triangle area ½bh; parallelogram bh; circle area πr² and circumference 2πr; rectangular prism volume lwh; a² + b² = c² applies only to right triangles; complementary angles total 90°, supplementary 180°, triangle interior angles 180°.
Worked example
An $80 jacket is marked down 25%, then an extra 10% is taken off the sale price. Successive discounts compound, they do not add: 80 × 0.75 = $60, then 60 × 0.90 = $54. Computing 80 × 0.65 = $52 by adding the percents is the classic error.
Traps that cost marks
Adding percents across stages; reporting perimeter when area is requested (linear vs square units); forgetting that squaring a negative yields a positive; reading “increased by 20%” as “is 20% of”; rounding mid-problem and then selecting a distractor that matches the rounded figure.