CBSE Grade 12 Mathematics Exam Survival Guide

Window: Board Exam | Core Units: Algebra, Calculus, Vectors, Probability

Must-do topics

• Relations & Functions (domain/range, inverse, composition)
• Matrices & Determinants (properties, adjoint/inverse, solution of equations)
• Calculus: limits, continuity/differentiability, applications of derivatives (tangent/normals, maxima–minima)
• Integrals (definite/indefinite; substitution, parts, partial fractions)
• Applications of Integrals (area under curves)
• Differential equations (order/degree, general vs particular solution, standard forms)
• Vectors & 3D Geometry (dot/cross products, lines, planes, angle between)
• Probability (Bayes theorem, binomial distribution, independent events)

Top traps (avoid)

• Determinant cofactor sign errors
• Skipping domain restrictions in inverse trig
• Wrong choice of integration method → wasted time
• Confusing order vs degree in differential eqs

Study split
35% Calculus | 20% Algebra | 20% Vectors/3D | 25% Probability/Stats

Last-48h checklist

• 2 full integrals sets (20 Qs mixed)
• 10 determinant/matrix problems
• 10 vector + 3D angle/plane Qs
• Formula sheet skim: derivatives/integrals, binomial/probability

Quick facts/frames

• ddx(ex)=ex,ddx(ln⁡x)=1/x\frac{d}{dx}(e^x)=e^x, \frac{d}{dx}(\ln x)=1/xdxd​(ex)=ex,dxd​(lnx)=1/x
• ∫exdx=ex+C\int e^x dx = e^x+C∫exdx=ex+C, ∫11+x2dx=tan⁡−1x+C\int \frac{1}{1+x^2} dx = \tan^{-1}x+C∫1+x21​dx=tan−1x+C
• Bayes: P(A∣B)=P(A)P(B∣A)ΣP(Ai)P(B∣Ai)P(A|B)=\frac{P(A)P(B|A)}{\Sigma P(A_i)P(B|A_i)}P(A∣B)=ΣP(Ai​)P(B∣Ai​)P(A)P(B∣A)​

Speed tactics

• Show step-wise → box final answer
• For integrals, test substitution first → parts second
• For probability, list sample space cleanly before formula

Exam-day mini-plan
Start with Calculus (while fresh) → Algebra → Vectors/3D → Probability last
Keep 15 min for graph/diagram/units check