Challenge Level

What are the possible perimeters of the larger triangle?

Challenge Level

Can you find the shortest distance between the semicircles given the area between them?

Challenge Level

Which of these is the best approximation for this square root?

Challenge Level

Put these expressions in order, from smallest to largest.

Challenge Level

If the base and height of a triangle are increased by different percentages, what happens to its area?

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6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?

Challenge Level

A square has area 72 cm$^2$. Find the length of its diagonal.

Challenge Level

Work your way through these right-angled triangles to find $x$.

Challenge Level

What is the ratio of the areas of the squares in the diagram?

Challenge Level

Can you work out the radius of a circle from some information about a chord?

Challenge Level

Can you find Dolly Dolphin's average speed as she swims with and against the current?

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There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?

Challenge Level

Find the missing distance in this diagram with two isosceles triangles

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What is the largest that the mean of these numbers could be?

Challenge Level

A palm tree has snapped in a storm. What is the height of the piece that is still standing?

Challenge Level

A circle of radius 1 is inscribed in a regular hexagon. What is the perimeter of the hexagon?

Challenge Level

What will the scale on this map be after it has been photocopied?

Challenge Level

Can you find the radius of the circle inscribed inside a '3-4-5 triangle'?

Challenge Level

Can you find the length and width of the screen of this smartphone in inches?

Challenge Level

If you take a number and add its square to its cube, how often will you get a perfect square?

Challenge Level

Yesterday, at Ulaanbaatar market, a white elephant cost the same amount as 99 wild geese. How many wild geese cost the same amount as a white elephant today?

Challenge Level

If some of the audience fell asleep for some of this talk, what was the average proportion of the talk that people heard?

Challenge Level

What average speed should Ms Fanthorpe drive at to arrive at work on time?

Challenge Level

Can you find the value of this expression, which contains infinitely nested square roots?

Challenge Level

What is the largest number of intersection points that a triangle and a quadrilateral can have?

Challenge Level

Find the value of $m$ from these statements about a group of numbers

Challenge Level

How much of the inside of this triangular prism can Clare paint using a cylindrical roller?

Challenge Level

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

Challenge Level

Two trains started simultaneously, each travelling towards the other. How long did each train need to complete the journey?

Challenge Level

Can you find the perimeter of the pentagon formed when this rectangle of paper is folded?

Challenge Level

Two ribbons are laid over each other so that they cross. Can you find the area of the overlap?

Challenge Level

Can you find the total number of students in the school, given some information about ratios?

Challenge Level

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

Challenge Level

What power of 27 is needed to get the correct power of 3?

Challenge Level

What are the possible lengths for the third side of this right-angled triangle?

Challenge Level

If the numbers in this news article have been estimated, then what is the largest number of gorillas that there could have been 10 years ago?

Challenge Level

The top square has been rotated so that the squares meet at a 60$^\text{o}$ angle. What is the area of the overlap?

Challenge Level

On which of the hare's laps will she first pass the tortoise?

Challenge Level

Can you find the radius of the larger circle in the diagram?

Challenge Level

How much money did the pensioner have before being robbed?

Challenge Level

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

Challenge Level

From the information given, can you work out how long Roberto drove for after putting petrol in his car?

Challenge Level

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?

Challenge Level

What percentage of students who graduate have never been to France?