Calculus

Topic overview

MM6/MM7: differentiation and integration of rational powers and their sums and differences, trapezium rule; differentiation of exponentials/trigonometric functions and general differential equations are not required.

Key concepts

Limits of rational powers in calculus and sums and differences after simplification; differentiation of exponential/trigonometric functions, variance, distributions of random variables, or mathematical induction are not required. Basic expected frequencies remain within the syllabus.

Key points

◆Follow the prerequisite knowledge requirements given by the examination body; new concepts may only be used when the question provides sufficient guidance.
◆The examples on this site are training with a limited scope and do not represent full syllabus coverage or official difficulty.

Worked examples

Try each example yourself before checking the explanation.

1Basic examples within scope

For $y=x^3-6x^2+9x$ , the value of $\dfrac{dy}{dx}$ at $x=1$ is:

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