# Advanced Problem Solving Module 4

### Advanced Problem Solving Module 4

##### 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.
##### Age 16 to 18 Challenge Level:

Consider these analogies for helping to understand key concepts in
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.

##### Age 16 to 18 Challenge Level:

Find the relationship between the locations of points of inflection, maxima and minima of functions.

##### Age 16 to 18 Challenge Level:

Can you hit the target functions using a set of input functions and a little calculus and algebra?

##### Age 16 to 18 Challenge Level:

Can you match the charts of these functions to the charts of their integrals?