Study Pure Mathematics revision pack on Differentiation for A-Level. Useful for revision, homework, and exam preparation in Zimbabwe.
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This is the ZIMSEC A-Level Pure Mathematics revision pack from 2022. It is a free revision pack for revision. Time allowed: 1 hour.
A' LEVEL
PURE MATHEMATICS
DIFFERENTIATION TEST 1
TIME: 1 hour
45 marks
Answer all questions.
[If a numerical answer cannot be given exactly, and the accuracy required is not specified in the question, then in the case of an angle it should be given correct to the nearest degree, and in other cases it should be given to 2 significant figures.]
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Sharewell B. C
1. Find by differentiating from first principle the derivative of each of the following expressions. Hence find the gradient of the curve $y=f(x)$ at the given point.
a) $x^{2}-x(1,0)$
[4]
b) $x^{4}(2,16)$
[6]
2. Find by differentiating from first principle the derivative of $\frac{1}{x^{2}}$.
[6]
3. Differentiate each of the following function with respect to $x$.
a) $\frac{4}{x}+\frac{5}{x^{2}}-\frac{6}{x^{3}}$
[3]
b) $\frac{1}{\sqrt{x}}-\frac{6}{x}$
[3]
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