Number and Functions - May 2005, Stage 4&5

Problems

problem icon

More Number Pyramids

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

problem icon

Triangles Within Triangles

Stage: 4 Challenge Level: Challenge Level:1

Can you find a rule which connects consecutive triangular numbers?

problem icon

Triangles Within Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Triangles Within Pentagons

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Slide

Stage: 5 Challenge Level: Challenge Level:1

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.

problem icon

Loch Ness

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Squareness

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?