Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

This is a beautiful result involving a parabola and parallels.

Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x

If you plot these graphs they may look the same, but are they?

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.

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

Can you find the lap times of the two cyclists travelling at constant speeds?

Kyle and his teacher disagree about his test score - who is right?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Explore the relationship between resistance and temperature

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

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

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?

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

Collect as many diamonds as you can by drawing three straight lines.

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

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

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

Looking at the graph - when was the person moving fastest? Slowest?

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.