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Class 12 Continuity and Differentiability worksheet
CBSE Mathematics. Continuity, chain rule, implicit, logarithmic and parametric derivatives, second derivatives. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
f(x) = kx + 9 for x ≤ −1, and f(x) = x² + 8 for x > −1. f is continuous at x = −1 when k equals:
- 0
- −18
- 2
- 1
Answer
(a) 0
k(−1) + 9 = 9
- 2.
The derivative of sin(6x − 8) with respect to x is:
- −6 cos(6x − 8)
- 6 sin(6x − 8)
- cos(6x − 8)
- 6 cos(6x − 8)
Answer
(d) 6 cos(6x − 8)
chain rule: differentiate the outside, then multiply by the derivative of the inside
- 3.
If y = (x + 5)³, then dy/dx at x = 0 is:
- 76
- 125
- 75
- 375
Answer
(c) 75
dy/dx = 3(x + 5)² = 3 × 5²
Section B · short answer
- 4.
Is f continuous at x = 1, where f(x) = 5x + 9 for x ≤ 1 and f(x) = 2x + 13 for x > 1?
Answer
No: LHL = 14 but RHL = 15
left limit and f(1) from 5x + 9, right limit from 2x + 13
- 5.
Find k so that f(x) = (x⁵ + 1024)/(x + 4) for x ≠ −4, and f(−4) = k, is continuous at x = −4.
Answer
k = 1,280
lim (xⁿ − aⁿ)/(x − a) = naⁿ⁻¹ = 5 × (−4)⁴
Section C · long answer
- 6.
Find a and b so that f is continuous: f(x) = 18 for x ≤ −3, f(x) = ax + b for −3 < x < 3, and f(x) = −6 for x ≥ 3.
Answer
a = −4, b = 6
(−3)a + b = 18 and 3a + b = −6
Fresh sheets for your child
In the app, every Continuity and Differentiability sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
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