Mathematics: Algebra, Functions, and Calculus
What to master
ECAT mathematics tests algebra (quadratics, simultaneous equations, inequalities), functions and graphs, sequences and series, trigonometry (identities, equations, triangles), coordinate geometry (lines, circles), matrices and determinants, complex numbers, differentiation and integration, and basic probability and statistics.
Traps that catch candidates
- Losing a root when dividing by a variable - always factor, never cancel blindly.
- Sign errors in the quadratic formula and in the discriminant.
- Forgetting the chain rule in composite functions.
- Mixing degrees and radians in trigonometric equations.
- Confusing permutations (order matters) with combinations (order does not).
- Ignoring domain restrictions, especially for logarithms and square roots.
Rule of thumb
When stuck, substitute a simple value to test an identity or simplify a limit. For integration, always add the constant of integration for indefinite integrals and check by differentiating the result.
Worked example
Solve x² − 5x + 6 = 0. Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3. Verify with the discriminant: b² − 4ac = 25 − 24 = 1 > 0, confirming two real distinct roots. If the discriminant were negative, the roots would be complex conjugates.