# Number and Functions - May 2005, Stage 4&5

## Problems

##### Stage: 3 and 4 Challenge Level:

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

### Triangles Within Triangles

##### Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

### Triangles Within Squares

##### Stage: 4 Challenge Level:

Can you find a rule which relates triangular numbers to square numbers?

### Triangles Within Pentagons

##### Stage: 4 Challenge Level:

Show that all pentagonal numbers are one third of a triangular number.

### Slide

##### Stage: 5 Challenge Level:

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

### Loch Ness

##### Stage: 5 Challenge Level:

Draw graphs of the sine and modulus functions and explain the humps.

### Squareness

##### Stage: 5 Challenge Level:

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?