Mathematics: Algebra, Trigonometry, Calculus, and Probability
JENPAS-UG Mathematics tests algebra, trigonometry, coordinate geometry, calculus, and probability at the Class 11–12 level. The exam favors direct application and formula recall over lengthy proofs.
Core rules and concepts
- Quadratic equations: the discriminant D = b² − 4ac classifies roots. D > 0 gives real distinct roots, D = 0 gives equal real roots, and D < 0 gives complex roots.
- Trigonometric identities: sin²θ + cos²θ = 1; sin(A ± B) expansions; the range of sin θ and cos θ is [−1, 1].
- Coordinate geometry: distance formula, section formula, slope, and the circle equation (x − h)² + (y − k)² = r².
- Calculus: d/dx(x^n) = nx^{n−1}; use the chain rule for composites; f'(x) = 0 locates stationary points, and a sign change in f' classifies extrema.
- Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); for independent events, P(A ∩ B) = P(A)P(B).
Worked example
Find the maximum value of f(x) = −x² + 4x + 1. Set f'(x) = −2x + 4 = 0, giving x = 2. Since f''(x) = −2 < 0, this is a maximum. Then f(2) = −4 + 8 + 1 = 5. Completing the square gives −(x − 2)² + 5, confirming the maximum is 5.
Traps that cost marks
- Forgetting domain restrictions when solving trigonometric equations.
- Using permutations when order does not matter - combinations are required.
- Losing the negative root when taking a square root.
- Misreading the sign of f'' when classifying a stationary point.
- Adding probabilities of non-mutually exclusive events without subtracting the intersection.