# 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.

### Calculus Analogies

##### Stage: 5 Challenge Level:

Consider these analogies for helping to understand key concepts in calculus.

### Turning to Calculus

##### Stage: 5 Challenge Level:

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

### Patterns of Inflection

##### Stage: 5 Challenge Level:

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

### Calculus Countdown

##### Stage: 5 Challenge Level:

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

### Integration Matcher

##### Stage: 5 Challenge Level:

Match the charts of these functions to the charts of their integrals.