Some of these problems are designed to help you think about fundamental skills and build your mathematical fluency and speed, so don't be put off if you think they're too easy!
On most STEP and other advanced mathematics examinations papers, there are several questions requiring a good understanding of integration and differentiation. This module is intended to help you to develop your intuition for calculus, and we hope that by working through the problems you will gain a deeper understanding of the ideas behind integration and differentiation. The next module will focus on calculus techniques.
problem
Calculus analogies
Age
16 to 18
Challenge level
Consider these analogies for helping to understand key concepts in
calculus.
problem
Turning to calculus
Age
16 to 18
Challenge level
Get started with calculus by exploring the connections between the
sign of a curve and the sign of its gradient.
problem
Patterns of inflection
Age
16 to 18
Challenge level
Find the relationship between the locations of points of inflection, maxima and minima of functions.
problem
Calculus countdown
Age
16 to 18
Challenge level
Can you hit the target functions using a set of input functions and a little calculus and algebra?
problem
Integration matcher
Age
16 to 18
Challenge level
Can you match the charts of these functions to the charts of their integrals?
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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.