Mathematics
Mathematics tests accuracy under time pressure: sets and relations, quadratics and inequalities, sequences and series, permutations and combinations, binomial theorem, matrices and determinants, trigonometry, coordinate geometry, differential and integral calculus, vectors, probability and statistics.
Core rules
- Quadratic ax² + bx + c: sum of roots = −b/a, product = c/a; discriminant b² − 4ac decides the nature of roots.
- AP: tₙ = a + (n−1)d, Sₙ = n/2[2a + (n−1)d]; GP: Sₙ = a(rⁿ − 1)/(r − 1).
- nPr counts arrangements (order matters), nCr counts selections, and nCr = nPr ÷ r!.
- Differentiation: d/dx(xⁿ) = nxⁿ⁻¹, product rule (uv)' = u'v + uv', chain rule for composites.
- Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); multiply for independent events.
Worked example
Two fair dice are rolled; find P(sum = 9 or both faces even). Total outcomes = 36. Sum 9: (3,6), (4,5), (5,4), (6,3) → 4 outcomes. Both even: 3 × 3 = 9 outcomes, of which (4,6) and (6,4) are already counted in the sum-9 set. So P = 4/36 + 9/36 − 2/36 = 11/36. List the overlap explicitly - that is where marks are lost.
Traps
Working in degrees where calculus needs radians; dropping the constant of integration; assuming AB = BA for matrices; reading 'at least one' as 'exactly one'; using nPr when the question asks for groups; ignoring domain restrictions in log and inverse-trigonometry questions.