Mathematics
The Mathematics domain of MP PAT tests algebra, trigonometry, calculus, coordinate geometry, and basic probability. The exam favors direct formula application, so write the rule first, then substitute.
Algebra and trigonometry
- Quadratic ax² + bx + c = 0: roots = [−b ± √(b² − 4ac)]/2a; discriminant b² − 4ac decides real/equal/complex roots.
- Know AP/GP sums and standard identities: sin²θ + cos²θ = 1.
- Use sine rule a/sin A = b/sin B = c/sin C and cosine rule a² = b² + c² − 2bc cos A.
Calculus and coordinate geometry
- Power rule d/dx(xⁿ) = nxⁿ⁻¹; product rule (uv)′ = u′v + uv′; quotient and chain rules.
- Maxima/minima: solve f′(x) = 0, then check f″(x).
- Straight line: y = mx + c; distance formula and circle equation.
Probability
- P(E) = favourable outcomes ÷ total outcomes; 0 ≤ P(E) ≤ 1.
Worked example
Differentiate f(x) = x³ sin x. Let u = x³ and v = sin x. Then u′ = 3x² and v′ = cos x. Product rule: f′(x) = 3x² sin x + x³ cos x. No further simplification is required unless the question asks for it.
Traps that cost marks
- Forgetting the product/chain rule or dropping the negative sign in cosine derivatives.
- Using degrees when calculus requires radians; omitting +C in indefinite integrals.
- Squaring only part of a binomial; ignoring domain restrictions.