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Applications of Derivatives - I — Syllabus

ICSE · Class 12 · Mathematics

What Applications of Derivatives - I covers in ICSE Class 12 Mathematics: 4 topics, for the 2026-27 session. Topics include Rate of Change.

55 questions37 flashcards23 formulas & key relations5 concepts

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A graph of a function y=f(x) with a tangent line at a point (x, y), illustrating dy/dx as the slope of the tangent.
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4 Topics · ICSE Class 12 Mathematics · 2026-27

Topics in Applications of Derivatives - I

1

1. Rate of Change and Differentials

  • Average rate of change is Δy/Δx.
  • Instantaneous rate of change is dy/dx = lim(Δx→0) (Δy/Δx).
  • dy/dx is the instantaneous rate of change of y with respect to x.
2

2. Approximation by Differentials

  • Choose a nearby value of x that makes calculation easy.
  • A helping note trick is used for powers with fractional exponents.
  • For exponent 1/q, choose a nearby perfect qth power.
3

3. Increasing and Decreasing Functions

  • Strictly increasing means x1 < x2 implies f(x1) < f(x2).
  • Increasing means x1 < x2 implies f(x1) ≤ f(x2).
  • Strictly decreasing means x1 < x2 implies f(x1) > f(x2).
4

4. Tangent and Normal to a Curve

  • dy/dx at x = a gives the slope of the tangent to y = f(x) at (a, f(a)).
  • The tangent touches the curve at the given point and has the same slope there.
  • The normal is perpendicular to the tangent.

Key Concepts

Central concept: Applications of derivatives in rate of change, approximation, monotonicity, tangents, normals, and angle of intersection

Rate of Change of QuantitiesApproximation by DifferentialsIncreasing and Decreasing FunctionsTangent and Normal to a CurveAngle of Intersection of CurvesLogarithmic Function MonotonicityWorked Applications and Standard Question Types

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Frequently Asked Questions

What are the important topics in Applications of Derivatives - I for ICSE Class 12 Mathematics?
Key topics in Applications of Derivatives - I include Rate of Change and Differentials, Approximation by Differentials, Increasing and Decreasing Functions, Tangent and Normal to a Curve. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How should I revise Applications of Derivatives - I for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 55 practice questions on Applications of Derivatives - I. 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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