Functions and their inverses

problem

Maths shop window

Age

16 to 18

Challenge level

Make a functional window display which will both satisfy the manager and make sense to the shoppers
problem

Function pyramids

Age

16 to 18

Challenge level

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
problem

Rational request

Age

16 to 18

Challenge level

Can you make a curve to match my friend's requirements?
problem

Inverting rational functions

Age

16 to 18

Challenge level

Consider these questions concerning inverting rational functions
problem

Curve match

Age

16 to 18

Challenge level

Which curve is which, and how would you plan a route to pass between them?
problem
Favourite

Equation matcher

Age

16 to 18

Challenge level

Can you match these equations to these graphs?
problem
Favourite

PCDF

Age

16 to 18

Challenge level

When can a pdf and a cdf coincide?
problem
Favourite

Real-life equations

Age

16 to 18

Challenge level

Here are several equations from real life. Can you work out which measurements are possible from each equation?
problem

Pitchfork

Age

16 to 18

Challenge level

Plot the graph of x^y = y^x in the first quadrant and explain its properties.
problem
Favourite

Area L

Age

16 to 18

Challenge level

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?