Mathematics for the REE Board: Algebra, Trigonometry, Calculus, and Probability
What the exam actually tests
Mathematics in the REE board is applied, not abstract. Expect algebra (quadratics, binomial expansion, exponents and logarithms), trigonometry (identities, law of sines and cosines, radian measure), analytic geometry (lines, circles, parabolas, ellipses, distance and midpoint formulas), differential and integral calculus (limits, product/quotient/chain rules, maxima-minima, areas, integration by parts), simple first-order differential equations, complex numbers in rectangular and polar form, matrices and determinants, and probability and statistics (permutations, combinations, binomial probability, mean, median, standard deviation).
Traps that cost points
- Calculator mode. Items mixing degrees and radians are the most common silent error. Convert first: θ_rad = θ_deg × π/180.
- Permutation versus combination. "Committee," "selection," "group" means combination; "arrangement," "ranking," "password" means permutation.
- Extraneous roots. Squaring both sides or clearing logs can create answers that fail the original equation. Always substitute back.
- "At least one" items. Use 1 − P(none); direct casework wastes time and invites double counting.
- Area between curves. Integrate (upper − lower) over the intersection interval; a negative result means the curves were reversed.
- Rounding drift. Keep π and radicals symbolic until the final step.
Worked example
Evaluate ∫ x ln x dx. Integrate by parts with u = ln x and dv = x dx, so du = dx/x and v = x²/2:
∫ x ln x dx = (x²/2)ln x − ∫ (x²/2)(1/x) dx = (x²/2)ln x − x²/4 + C.
Rule of thumb: whenever an integrand contains a lone logarithm multiplied by a power of x, choose u = ln x - the logarithm differentiates away and the remaining integral is elementary.