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Broad Topics > Functions and Graphs > Functions and their inverses

Equation Matcher

Age 16 to 18 Challenge Level:

Can you match these equations to these graphs?

PCDF

Age 16 to 18 Challenge Level:

When can a pdf and a cdf coincide?

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?

Spaces for Exploration

Age 11 to 14

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

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?

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?

Rational Request

Age 16 to 18 Challenge Level:

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

Inverting Rational Functions

Age 16 to 18 Challenge Level:

Consider these questions concerning inverting rational functions

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

Curve Match

Age 16 to 18 Challenge Level:

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

Pitchfork

Age 16 to 18 Challenge Level:

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

Double Time

Age 16 to 18 Challenge Level:

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

Age 16 to 18 Challenge Level:

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.

Machines

Age 7 to 11 Challenge Level:

What is happening at each box in these machines?

Modular Fractions

Age 16 to 18 Challenge Level:

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.

The Number Crunching Machine

Age 7 to 11 Challenge Level:

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?