Resources tagged with: Functions and their inverses

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Broad Topics > Coordinates, Functions and Graphs > Functions and their inverses

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.

Readme

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.

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.

PCDF

Age 16 to 18 Challenge Level:

When can a pdf and a cdf coincide?

Inverting Rational Functions

Age 16 to 18 Challenge Level:

Consider these questions concerning inverting rational functions

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?

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?

Pitchfork

Age 16 to 18 Challenge Level:

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

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?

Curve Match

Age 16 to 18 Challenge Level:

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

Equation Matcher

Age 16 to 18 Challenge Level:

Can you match these equations to these graphs?

Rational Request

Age 16 to 18 Challenge Level:

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

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