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### There are 17 results

Broad Topics > Sequences, 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.

### Changing Places

##### Age 14 to 16 Challenge Level:

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. . . .

### 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?