Find the point on the line segment AB that is twice as far from B as it is from A.

Can you fill this square so that the number in the middle of each line is the mean of the two numbers on either side of it?

How many questions did Sarah answer correctly in this multiple choice exam?

Prove that the angle marked $a$ is half the size of the angle marked $b$.

How far from the finishing line should these runners start to make the race 'fair'?

If the shape on the inside is a rectangle, what can you say about the shape on the outside?

Prove that the angle bisectors of a triangle can never meet at right angles.

Draw another line through the centre of this rectangle to split it into 4 pieces of equal area.

What length of candy floss can Rita spin from her cylinder of sugar?

Two similar cylinders are formed from a block of metal. What is the volume of the smaller cylinder?

When the roll of toilet paper is half as wide, what percentage of the paper is left?

What proportion of each of these pendants will be made of gold?

This square piece of paper has been folded and creased. Where does the crease meet the side AD?

Prove that these two lengths are equal.

Can you find the distance from the well to the fourth corner, given the distance from the well to the first three corners?

The horizontal red line divides this equilateral triangle into two shapes of equal area. How long is the red line?

A property developer sells two houses, and makes a 20% loss on one and a 20% profit on the other. Overall, did he make a profit or a loss?

Can you find the area of the yellow part of this snake's eye?

If you take two dominoes from a set at random, what is the probability that they 'match'?

Cutting a rectangle from a corner to a point on the opposite side splits its area in the ratio 1:2. What is the ratio of a:b?

A semicircle is drawn inside a right-angled triangle. Find the distance marked on the diagram.

When you pull a boat in using a rope, does the boat move more quickly, more slowly, or at the same speed as you?

If two friends run in opposite directions around a track, and they pass each other every 24 seconds, how long do they take to complete a lap?

How do these measurements enable you to find the height of this tower?