Mathematics: Core Skills and Exam Traps
What the Kankor mathematics section rewards
The exam tests speed and precision on school-level material: arithmetic and number properties, algebra (linear and quadratic equations, inequalities, exponents, logarithms), functions and their graphs, sequences and series, basic trigonometry, coordinate geometry, mensuration, and elementary probability and statistics. You are not expected to prove theorems; you are expected to compute correctly under time pressure.
Concepts you must own
- Quadratics: discriminant, sum and product of roots, factoring, completing the square.
- Exponents and logarithms: laws of indices, change of base, domain restrictions (logarithm arguments must be positive).
- Trigonometry: exact values at 30°, 45°, 60°, the Pythagorean identity, and the sine/cosine rules for triangles.
- Geometry: area and volume formulas, similar triangles, circle theorems (inscribed angle = half central angle).
- Sequences: the nth term and sum formulas for arithmetic and geometric progressions.
Traps that appear
- Sign errors when expanding or moving terms; always substitute your answer back.
- Extraneous roots from squaring both sides or from multiplying by an expression that can be zero.
- Units in rate and mensuration problems (cm vs m, minutes vs hours).
- "At least one" probability: use 1 − P(none).
- Order of operations with negative bases and fractional exponents.
Rule of thumb
For a quadratic ax² + bx + c = 0, check the discriminant b² − 4ac first: if it is negative there are no real roots and any "real solution" option is wrong. Worked example: solve x² − 5x + 6 = 0. Discriminant = 25 − 24 = 1, so roots are (5 ± 1)/2 = 3 and 2. Sum of roots = 5 = −b/a, product = 6 = c/a - a quick consistency check.