Mathematics
Core concepts
Mathematics on the state exam rewards fluency across algebra, functions, geometry, and probability. Be able to solve linear and quadratic equations, factor polynomials, apply the quadratic formula, and work with exponents and logarithms. Know function behavior: domain, range, monotonicity, and graphing transformations (shifts, reflections, stretches). In geometry, memorize area and volume formulas for triangles, circles, prisms, cylinders, cones, and spheres, plus the Pythagorean theorem and similarity ratios. In trigonometry, know the unit circle, sine/cosine values at standard angles, and the identity sin²x + cos²x = 1. For probability and statistics, distinguish permutations from combinations and compute expected value.
Traps
- Sign errors when expanding or moving terms across the equals sign.
- Forgetting that dividing by a variable can lose solutions (check x = 0 separately).
- Confusing area and perimeter, or radius and diameter.
- Mixing up permutations (order matters) and combinations (order does not).
- Ignoring the domain restriction on logarithms and square roots.
Rule of thumb
When a quadratic does not factor cleanly, go straight to the discriminant D = b² − 4ac; the sign of D tells you the number of real roots before you solve.
Worked example
Solve x² − 5x + 6 = 0. D = 25 − 24 = 1 > 0, so two real roots. x = (5 ± 1)/2, giving x = 3 or x = 2. Always substitute back to verify.