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Index Numbers

Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce

Quick revision notes for Index Numbers — Maharashtra Board Class 12 Mathematics & Statistics -Commerce. Key concepts, formulas, and definitions for last-minute revision.

44 questions20 flashcards5 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 Notes

Key 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?
Index Numbers covers several key topics that are frequently asked in Maharashtra Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Index Numbers — Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Understand the core concepts first, then work through the 44 practice questions available for this chapter. Revise formulas and 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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