Mathematics: Algebra, Calculus, and Problem Discipline
Core concepts
BHSEC Mathematics tests fluency across algebra, trigonometry, coordinate geometry, calculus, and vectors. You must handle quadratic equations (discriminant, roots, factorisation), sequences and series (AP and GP formulas), binomial expansion, and matrices. In calculus, know derivative rules (product, quotient, chain) and integration as the reverse process, including definite integrals for area. Trigonometry demands identities, radian measure, and solution of triangles.
Traps in questions
- Domain and range traps: dividing by zero, square roots of negatives, and log of non-positive values.
- Sign errors in the chain rule and when expanding $(a-b)^2$.
- Units of angle: a calculator in degree mode when the question uses radians.
- Definite integrals: forgetting the constant disappears, or mis-ordering limits and missing the negative sign.
- "Hence" questions: the word means use the previous part; starting fresh often wastes time.
Worked example
Differentiate $y = x^2 \sin x$. Use the product rule with $u = x^2$, $v = \sin x$: $u' = 2x$, $v' = \cos x$. So $\frac{dy}{dx} = 2x\sin x + x^2\cos x$. Check: both terms carry $x$, so $y'(0)=0$, which matches $y$ having a repeated root at $x=0$.
Rule of thumb
After solving, substitute your answer back into the original equation or check a limiting case. For quadratics, verify the sum and product of roots against the coefficients.