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

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

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

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

Consider these questions concerning inverting rational functions

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

Decipher a simple code based on the rule C=7P+17 (mod 26) where C is the code for the letter P from the alphabet. Rearrange the formula and use the inverse to decipher automatically.

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

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?

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.