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
Equation matcher

Age

16 to 18

Challenge level

Can you match these equations to these graphs?
problem
PCDF

Age

16 to 18

Challenge level

When can a pdf and a cdf coincide?
problem
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
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?