List

Functions & Graphs: Age 14-16

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

Parabolic Patterns
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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.

Doesn't add up
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Doesn't add up

Age
14 to 16
Challenge level
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In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Exploring cubic functions
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Exploring cubic functions

Age
14 to 18
Challenge level
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Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Perpendicular lines
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Perpendicular lines

Age
14 to 16
Challenge level
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Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
Negatively Triangular
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Negatively Triangular

Age
14 to 16
Challenge level
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How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

At right angles
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At right angles

Age
14 to 16
Challenge level
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Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
Back fitter
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Back fitter

Age
14 to 18
Challenge level
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10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Surprising Transformations
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Surprising Transformations

Age
14 to 16
Challenge level
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I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

What's that graph?
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Favourite

What's that graph?

Age
14 to 18
Challenge level
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Can you work out which processes are represented by the graphs?

Tangled Trig Graphs
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Favourite

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?



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Functions & Graphs - Stage 4 STEM footer
 

You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.