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Continuity and Differentiability

ICSE · Class 12 · Mathematics

Practice quiz for Continuity and Differentiability — ICSE Class 12 Mathematics. MCQs and questions with answers to test your preparation.

105 questions29 flashcards5 concepts

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A graph of a continuous function at a specific point, showing the limit approaching the function value, illustrating that the function is unbroken and defined at that point.
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Quick Quiz: Continuity and Differentiability

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1

If f(x) = (x² - 9)/(x - 3) for x ≠ 3, and f(3) = k, then the value of k that makes f continuous at x = 3 is:

2

The function f(x) = |x - 2| is:

3

For the function f(x) = {kx² if x ≤ 2, 3 if x > 2} to be continuous at x = 2, the value of k is:

4

Which of the following functions is NOT continuous at x = 0?

105 Questions·
MCQmultiple choice

Sample Questions

1MCQ

The value of lim_{x→0}(sin x / x) is:

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B

lim_{x→0}(sin x / x) = 1 is a standard limit. This is Theorem 8.1(i).

2MCQ

The value of lim_{x→0}(eˣ − 1) / x is:

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C

lim_{x→0}(eˣ−1)/x = 1 is a standard exponential limit (Theorem 8.1(iii)).

3MCQ

lim_{x→0}(tan x / x) equals:

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A

lim_{x→0}(tan x/x) = 1. Since tan x = sin x/cos x and cos x→1 as x→0.

4MCQ

A function f is continuous at x = c if:

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B

The complete definition: f is continuous at c if lim_{x→c}f(x) = f(c), which requires f(c) defined, limit exists, and limit = f(c).

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Frequently Asked Questions

What are the important topics in Continuity and Differentiability for ICSE Class 12 Mathematics?
Key topics in Continuity and Differentiability include Decision Tree: Is a Function Continuous at Point c?, Continuity and Differentiability - Complete Overview, Flowchart showing how limits are determined by comparing left and right limits. These are the concepts ICSE Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Continuity and Differentiability — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 105 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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