# Differentiation and Integration

### Mind Your Ps and Qs

##### Stage: 5 Short Challenge Level:

Sort these mathematical propositions into a series of 8 correct statements.

### Implicitly

##### Stage: 5 Challenge Level:

Can you find the maximum value of the curve defined by this expression?

### Integration Matcher

##### Stage: 5 Challenge Level:

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

### Brimful

##### Stage: 5 Challenge Level:

Can you find the volumes of the mathematical vessels?

### Brimful 2

##### Stage: 5 Challenge Level:

Which of these infinitely deep vessels will eventually full up?

### The Right Volume

##### Stage: 5 Short Challenge Level:

Can you rotate a curve to make a volume of 1?

### Calculus Countdown

##### Stage: 5 Challenge Level:

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

### Weekly Challenge 25: Trig Trig Trig

##### Stage: 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

##### Stage: 5 Short Challenge Level:

What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?

### 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.

### Curvy Catalogue

##### Stage: 5 Challenge Level:

Make a catalogue of curves with various properties.

### Calculus Analogies

##### Stage: 5 Challenge Level:

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

### Weekly Challenge 30: the Sign of the Times

##### Stage: 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

### Patterns of Inflection

##### Stage: 5 Challenge Level:

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