Mathematics: Algebra, Calculus and Coordinate Geometry for AEEE
Mathematics carries the largest question share in AEEE and is where ranks are most often decided. Questions are single-correct MCQs drawn from Class 11–12 scope: quadratic equations and complex numbers, sequences and series, permutations and combinations, binomial theorem, matrices and determinants, trigonometric identities, straight lines and conics, limits, continuity, differentiation (including logarithmic and parametric), integration, definite integrals and areas, differential equations, vectors, 3D geometry, probability and statistics.
Rules worth memorising
- For ax² + bx + c = 0: sum of roots = −b/a, product = c/a, discriminant D = b² − 4ac.
- Standard limits: lim(x→0) sin x/x = 1, lim(x→0) (1 − cos x)/x² = 1/2, lim(x→0) (eˣ − 1)/x = 1, lim(x→0) ln(1+x)/x = 1. All require x in radians.
- Integration by parts: ∫u dv = uv − ∫v du; choose u by the ILATE order.
- Definite integral areas below the x-axis come out negative; take the modulus for geometric area.
- Matrix product is not commutative: AB ≠ BA in general, and AB = 0 does not imply A = 0 or B = 0.
Worked example
If α and β are the roots of x² − 5x + 6 = 0, find α³ + β³. Here α + β = 5 and αβ = 6. Use the identity a³ + b³ = (a + b)³ − 3ab(a + b). α³ + β³ = 5³ − 3(6)(5) = 125 − 90 = 35. Check directly: roots are 2 and 3, and 8 + 27 = 35. The identity route is faster under time pressure.
Traps that cost marks
- Doing calculus limits with the calculator in degree mode.
- Dropping the constant of integration, or forgetting to change limits after substitution.
- Squaring both sides of an equation and keeping extraneous roots without checking.
- Using combinations when order matters (arrangements of letters, seating).
- Probability without replacement: the denominator shrinks after each draw.