Mathematics - Highest-Weight Section of the IOE Entrance
What the paper tests
Mathematics is the heaviest section of the IOE entrance paper and the main separator of ranks. Questions come from the grade 11–12 syllabus: sets and functions, algebra (quadratic equations, sequences, binomial theorem, complex numbers, matrices), trigonometry, coordinate geometry (straight lines, circles, conics), vectors, calculus (limits, derivatives, integration, differential equations) and statistics with probability. Items are short numerical one- or two-step problems, not long proofs, so speed with standard results matters more than derivation skill.
Rules worth memorising cold
- Standard limits: lim x→0 (sin x)/x = 1 and lim x→0 (tan x)/x = 1; apply these before reaching for L'Hôpital.
- Derivatives: (xⁿ)′ = nxⁿ⁻¹, (eˣ)′ = eˣ, (ln x)′ = 1/x, plus the chain and product rules for composites.
- Integration by parts: ∫u dv = uv − ∫v du, with u chosen by LIATE (log, inverse trig, algebraic, trig, exponential).
- Conics: circle x² + y² = a²; parabola y² = 4ax with focus (a, 0); ellipse x²/a² + y²/b² = 1 with e = √(1 − b²/a²).
- Probability: P(A∪B) = P(A) + P(B) − P(A∩B); binomial term P(X = r) = ⁿCᵣ pʳ qⁿ⁻ʳ.
Worked example
Evaluate ∫ x eˣ dx. Set u = x and dv = eˣ dx, giving du = dx and v = eˣ. Then ∫ x eˣ dx = x eˣ − ∫ eˣ dx = x eˣ − eˣ + C = eˣ(x − 1) + C. Verify by differentiating: d/dx[eˣ(x − 1)] = eˣ(x − 1) + eˣ = x eˣ, which returns the integrand.
Traps that cost marks
- A wrong answer is penalised by 20% of that question's marks, so guessing among four options is only sensible after eliminating at least two.
- Mixing degrees and radians inside limit or derivative formulas.
- Dropping the constant of integration, or the minus sign in ∫x⁻² dx = −1/x.
- Dividing an equation by a variable and silently losing the root x = 0.
- Confusing ⁿPᵣ with ⁿCᵣ, and forgetting that matrix multiplication is not commutative.