Chapter 10 of 16
Revision Notes
Index Numbers — Revision Notes
Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce
Index Numbers revision notes for Maharashtra Board Class 12 Mathematics & Statistics -Commerce: 4 topics in quick points.
44 questions20 flashcards11 formulas & key relations5 concepts
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Key Topics to Revise
1
Area Under a Single Curve
- The definite integral ∫ᵇₐ f(x) dx gives the area under the curve y = f(x) from x = a to x = b
- If f(x) ≥ 0 in [a,b], then area = ∫ᵇₐ f(x) dx
- If f(x) ≤ 0 in [a,b], then area = |∫ᵇₐ f(x) dx|
2
Area Between Two Curves
- Area between curves y = f(x) and y = g(x) is |∫ᵇₐ [f(x) - g(x)] dx|
- Find intersection points by solving f(x) = g(x)
- Determine which curve is upper and which is lower in the given interval
3
Special Curves and Their Areas
- Parabolas: y² = 4ax, area with latus rectum = 32a²/3
- Circles: x² + y² = r², total area = πr²
- Ellipses: x²/a² + y²/b² = 1, total area = πab
4
Problem-Solving Strategies
- Step 1: Identify the curves and region
- Step 2: Find intersection points
- Step 3: Determine limits of integration
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Full NotesKey Concepts
For a continuous curve y =For curves y = f(x)When f(x) ≤ 0 in [aSometimes it's easier to integrateUse symmetry to simplify calculations
Frequently Asked Questions
What are the important topics in Index Numbers for Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Key topics in Index Numbers include Area Under a Single Curve, Area Between Two Curves, Special Curves and Their Areas, Problem-Solving Strategies. Study these first, then practise questions on each for the Maharashtra Board Class 12 board exam.
How should I revise Index Numbers for the Maharashtra Board Class 12 board exam?
Learn the core ideas first, then work through the 44 practice questions on Index Numbers. Revise definitions regularly and use flashcards for quick recall before the exam.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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