Gradients

problem
Favourite

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?
problem
Favourite

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?
problem
Favourite

Which Is Bigger?

Age

14 to 16

Challenge level

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

Ladder and Cube

Age

14 to 16

Challenge level

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?
problem
Favourite

Parabella

Age

16 to 18

Challenge level

This is a beautiful result involving a parabola and parallels.
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

Power Up

Age

16 to 18

Challenge level

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
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!
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

From All Corners

Age

14 to 16

Challenge level

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.