Calculus · Class 12 Applied Mathematics · Chapter 3
🔢 Calculus — Differentiation, Applications & Integration
CBSE Class 12 Humanities & Commerce · Applied Mathematics · Chapter 1
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📖Notes Deck
Full lecture deck with teaching paragraphs, misconception red-boxes, and glossary. Read this first.
Download PDF →📝Quick Drill
15 pattern-tagged MCQs with per-Q time budget. Drill under a 20-min timer.
Download PDF →📄Exam Paper
Full exam-pattern paper with sections. Sit it closed-book before checking the marking scheme.
Download PDF →✅Marking Scheme + Topper Templates
Model answers + topper-template structures examiners reward with full credit.
Download PDF →⚡Cheat Sheet
1-page exam-day card: key points, top question patterns, 90-minute revision flow.
Download PDF →👨👩👧For Parents
1-page plain-language parent guide: what's being learned + questions to ask your child.
Download PDF →Top question patterns · CBSE annual / SQP aggregate
| 90% | Marginal cost / marginal revenue at a given output — Differentiate C(x) or R(x) · substitute the given x · interpret as 'cost/revenue of one more unit'. | 3 MARKS |
| 95% | Profit / revenue maximisation (maxima-minima) — Form P(x) = R − C · solve P'(x) = 0 · confirm with P''(x) < 0 · compute P at that x · state the optimal output. | 5 MARKS |
| 70% | Increasing / decreasing intervals — Find f'(x) · solve f'(x) = 0 for boundary points · test the sign of f' in each interval · state increasing where f'>0, decreasing where f'<0. | 3 MARKS |
| 85% | Definite integral (often by substitution) — Choose substitution u=g(x) · change the limits · integrate · evaluate F(upper) − F(lower). No +C on a definite integral. | 3 MARKS |
| 75% | Consumer / producer surplus — Find equilibrium x₀ from price · CS = ∫₀^{x₀}[D(x)−p₀]dx (or PS = ∫₀^{x₀}[p₀−S(x)]dx) · integrate · state with ₹ units. | 4 MARKS |
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