Mathematics
What you actually need to know
The paper draws on Class 11–12 core: sets, relations and functions; complex numbers and quadratic equations; matrices and determinants; permutations, combinations and the binomial theorem; sequences and series; limits, continuity and differentiability; applications of derivatives (tangents and normals, rates of change, maxima–minima); indefinite and definite integration with simple differential equations; 2D and 3D coordinate geometry (straight lines, circles, conic sections, planes, vectors); and statistics with probability. Questions are short, so recall of standard results - distance of a point from a line, the condition for a line to touch a circle, sum and product of roots, number of terms in an expansion - decides your score far more than long derivations.
Where marks leak away
Sign slips in integration by parts; dropping the constant when the answer is an indefinite integral; ignoring domain restrictions (logarithm of a positive number only, square roots, non-zero denominators); confusing permutations with combinations in "arrangements of letters" items; and misreading "at least one" as "exactly one" in probability. In coordinate geometry, check whether the question wants a length, a slope or a point. In maxima–minima on a closed interval, always compare critical points with the endpoints.
Worked example
Evaluate ∫₀¹ (3x² + 2x) dx. The antiderivative is x³ + x². At x = 1 it gives 1 + 1 = 2; at x = 0 it gives 0. The answer is 2. Rule of thumb: integrate term by term and substitute both limits immediately - most errors come from substituting only the upper limit.