Working through this module will help you to consolidate your existing knowledge before extending your thinking. For more details about the Advanced Problem Solving programme, READ THIS.
In this second calculus module, we share some of the theory behind certain calculus techniques and offer you the opportunity to practise some of the calculus skills you will need to be successful in STEP and other advanced mathematics examinations.
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Chain rule
Read a derivation of the chain rule for differentiation, and then use our Mathmo app to practise.
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The Product Rule
Read a derivation of the Product Rule for differentiation, and then use our Mathmo app to practise.
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Integration and Differentiation Practice Questions
Age
16 to 18
Challenge level
Try this selection of differentiation and integration questions to practise choosing an appropriate technique.
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Favourite
Curved square
Age
16 to 18
Challenge level
Can you find the area of the central part of this shape? Can you do it in more than one way?
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Towards Maclaurin
Age
16 to 18
Challenge level
Build series for the sine and cosine functions by adding one term
at a time, alternately making the approximation too big then too
small but getting ever closer.
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Prepare for university - pure mathematics
Helpful preparation for those intending to study a course involving pure mathematics at university.
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Prepare for university - applied mathematics
Helpful preparation for university for those intending to study a
course involving applied mathematics at university.
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NRICH and Olympiads
A useful entry point into the NRICH site for those students interested in Mathematical Olympiad problems or the Maths Challenges.