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Resources tagged with Functions and their inverses similar to Hyperbolic Thinking:

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

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Area L

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Draw the graph of a continuous increasing function in the first quadrant and horizontal and vertical lines through two points. The areas in your sketch lead to a useful formula for finding integrals.

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Changing Places

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Equation Matcher

Stage: 5 Challenge Level: Challenge Level:1

Can you match these equations to these graphs?

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Inverting Rational Functions

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Consider these questions concerning inverting rational functions

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Rational Request

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Maths Shop Window

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Function Pyramids

Stage: 5 Challenge Level: Challenge Level:1

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?

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Curve Match

Stage: 5 Challenge Level: Challenge Level:1

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

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Real-life Equations

Stage: 5 Challenge Level: Challenge Level:1

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

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Readme

Stage: 5 Challenge Level: Challenge Level:1

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.

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Modular Fractions

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Double Time

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Pitchfork

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Spaces for Exploration

Stage: 3 and 4

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

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PCDF

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When can a pdf and a cdf coincide?


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