List

Extension Conjecturing and Generalising

Parabolic Patterns
problem
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Parabolic Patterns

Age
14 to 18
Challenge level
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The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

Summing geometric progressions
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Summing geometric progressions

Age
14 to 18
Challenge level
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Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Expenses
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Expenses

Age
14 to 16
Challenge level
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What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Why 24?
problem
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Why 24?

Age
14 to 16
Challenge level
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Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Areas of parallelograms
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Areas of parallelograms

Age
14 to 16
Challenge level
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Can you find the area of a parallelogram defined by two vectors?
Tangled Trig Graphs
problem
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Tangled Trig Graphs

Age
16 to 18
Challenge level
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Can you work out the equations of the trig graphs I used to make my pattern?