Gradients

problem
Parallel lines

Age

11 to 14

Challenge level

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
problem
Up and across

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.
problem
How far does it move?

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.
problem
Towards Maclaurin

Age

16 to 18

Challenge level

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.
problem
Walls

Age

16 to 18

Challenge level

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.
problem
Climbing

Age

16 to 18

Challenge level

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

Age

14 to 18

Challenge level

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?
problem
Mediant madness

Age

14 to 16

Challenge level

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

Age

16 to 18

Challenge level

This is a beautiful result involving a parabola and parallels.
problem
Lying and cheating

Age

11 to 14

Challenge level

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!