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Applications of Derivatives - I

ICSE · Class 12 · Mathematics

Practice quiz for Applications of Derivatives - I — ICSE Class 12 Mathematics. MCQs and questions with answers to test your preparation.

55 questions37 flashcards5 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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Quick Quiz: Applications of Derivatives - I

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Tap an answer to check it instantly. No sign-up needed for these 4.

1

dy/dx represents the:

2

The side of a square is increasing at 2 cm/s. The rate of increase of area when side = 4 cm is:

3

If A = πr², then dA/dt equals:

4

If V = (4/3)πr³ (sphere), then dV/dr equals:

55 Questions·
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Sample Questions

1multiple choice

The approximate change in y = f(x) for a small change Δx in x is:

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f'(x)·Δx

Δy ≈ dy = f'(x)·Δx. The differential dy is the approximate change in y.

2multiple choice

For f(x) = √x and x = 25, Δx = 0.5, the approximate value of √25.5 is:

Show answer

5.05

f(x)=√x, f'(x)=1/(2√x)=0.1 at x=25. f(25.5)≈5+0.1×0.5=5+0.05=5.05.

3multiple choice

A function f is strictly increasing on interval I if:

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x₁ < x₂ ⟹ f(x₁) < f(x₂) for all x₁,x₂ ∈ I

Strictly increasing means a larger x always gives a strictly larger f(x).

4multiple choice

If f'(x) < 0 for all x ∈ (a,b), then f is:

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Strictly decreasing on (a,b)

f'(x) < 0 means the function is falling — it is strictly decreasing.

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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 First Derivative Test for Monotonicity, Important Geometric Problems. These are the concepts ICSE Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Applications of Derivatives - I — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 55 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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