Mathematics
What this subtest measures
Mathematics covers high-school arithmetic and number sense, algebra, geometry, trigonometry, and basic statistics and probability. Items reward clean setup more than lengthy computation: translate words into equations, use properties to simplify, and check whether the answer is reasonable.
Core rules to apply
- Follow order of operations; distribute negatives carefully: −(x − 3) = −x + 3.
- For quadratics, try factoring first; otherwise use x = [−b ± √(b² − 4ac)]/(2a).
- Exponent rules: a^m a^n = a^(m+n); (a^m)^n = a^(mn); a^0 = 1 for a ≠ 0.
- Coordinate geometry: slope = (y₂ − y₁)/(x₂ − x₁); distance = √[(x₂ − x₁)² + (y₂ − y₁)²].
- Right triangles: a² + b² = c²; sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
- Statistics: the mean is affected by outliers; the median is the middle value; probability = favorable outcomes / total equally likely outcomes.
Worked example
A right triangle has legs 5 and 12. Find sin θ, where θ is opposite the side of length 5. First find the hypotenuse: c² = 5² + 12² = 25 + 144 = 169, so c = 13. Then sin θ = opposite/hypotenuse = 5/13. The trap is using 5/12, which is tan θ, not sin θ.
Traps that cost marks
- Dropping the negative sign when distributing or moving terms.
- Forgetting the ± case in quadratic solutions.
- Using degrees and radians interchangeably on a calculator.
- Rounding too early; keep exact values until the final step.
- Misreading “not,” “except,” or “least possible.”