Functions and Graphs - Stage 4

Doesn't Add Up

Age 14 to 16
Challenge Level

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Parabolic Patterns

Age 14 to 18
Challenge Level

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.

Exploring Cubic Functions

Age 14 to 18
Challenge Level

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Perpendicular Lines

Age 14 to 16
Challenge Level

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Negatively Triangular

Age 14 to 16
Challenge Level

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

Curve Fitter

Age 14 to 18 Short
Challenge Level

This problem challenges you to find cubic equations which satisfy different conditions.

At Right Angles

Age 14 to 16
Challenge Level

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

Tangled Trig Graphs

Age 16 to 18
Challenge Level

Can you work out the equations of the trig graphs I used to make my pattern?

Back Fitter

Age 14 to 18
Challenge Level

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

Age 14 to 16
Challenge Level

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?

Age 14 to 18
Challenge Level

Can you work out which processes are represented by the graphs?

Functions and Graphs - Short Problems

Age 11 to 16

A collection of short problems on straight line graphs.

Inside a Parabola

Age 14 to 16 Short
Challenge Level

A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.

Triangular Slope

Age 14 to 16 Short
Challenge Level

Can you find the gradients of the lines that form a triangle?

Graph Triangles

Age 14 to 16 Short
Challenge Level

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

Closer to Home

Age 14 to 16 Short
Challenge Level

Which of these lines comes closer to the origin?