Mathematics: Algebra, Calculus, Coordinate Geometry and Probability
Mathematics is the highest-scoring BVP CET section for a prepared candidate because answers are exact and often verifiable by substitution. Coverage: sets and functions, complex numbers and quadratic equations, sequences and series, permutations and combinations, binomial theorem, matrices and determinants, trigonometry and inverse trigonometry, straight lines and conics, limits, continuity, differentiation with applications, integration and area, differential equations, vectors and 3D geometry, probability and statistics.
Strategy that pays
Check the domain before solving-a logarithm, square root or denominator narrows the valid answers. When a question asks for the number of solutions, a rough graph usually beats algebra.
Worked example
Evaluate ∫₀¹ x·e^(x²) dx. Let u = x², du = 2x dx, so x dx = du/2. Limits: x = 0 → u = 0; x = 1 → u = 1. The integral becomes (1/2)∫₀¹ e^u du = (1/2)[e^u]₀¹ = (e − 1)/2 ≈ 0.859. Sign check: the integrand is positive on [0,1] and the answer is positive, so the result is consistent.
Conic quick-reference
Circle x²+y²+2gx+2fy+c=0: centre (−g,−f), radius √(g²+f²−c). Parabola y²=4ax: focus (a,0), directrix x=−a. Ellipse x²/a²+y²/b²=1: e = √(1−b²/a²). Hyperbola: e = √(1+b²/a²).
Traps
- Squaring an equation without testing for extraneous roots.
- Assuming AB = BA, or taking an inverse when |A| = 0.
- Sampling without replacement changes the denominator in probability.
- Substituting degrees where a limit or derivative needs radians.
- Reporting only one solution for sin θ = 1/2 over a stated interval.