Challenge Level

A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell.

Challenge Level

If two of these unusually numbered dice are thrown, how many different sums are possible?

Challenge Level

Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.

Challenge Level

What is the smallest possible area that this rectangle could have?

Challenge Level

What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?

Challenge Level

Use 2 straight lines to split the clock face into 3 parts so that the sums of the numbers in each of the parts are equal.

Challenge Level

Which of these can be obtained by rotating this shape?

Challenge Level

Can you find the volume of a cuboid, given the areas of its faces?

Challenge Level

Can you work out how many brothers and sisters are in the family?

Challenge Level

Can you find the missing digits in this calculation?

Challenge Level

Find these 4 numbers, given their mode, median and range.

Challenge Level

The net shown is folded up to form a cube. What is the largest possible vertex product?

Challenge Level

The water is being drained from a pool. After how long will the depth of the pool be 144 cm?

Challenge Level

How fast is the train travelling as it goes over the bridge?

Challenge Level

Can you find the area of the overlap when these two beer mats are placed on top of each other?

Challenge Level

When is the next time that Brian's age will be the reverse of his father's age?

Challenge Level

Three numbers add up to 100. The difference between the larger two is 12 and the difference between the smaller two is 2. What are the numbers?

Challenge Level

How many cubes would be visible in a 12 by 12 by 12 Rubik’s cube?

Challenge Level

77 is multiplied by another two-digit number with identical digits. What is the product?

Challenge Level

Amy misread a question and got an incorrect answer. What should the answer have be?

Challenge Level

How many hot dogs did this hot dog lover eat on the first day of her binge?

Challenge Level

What fraction of this square is shaded?

Challenge Level

Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?

Challenge Level

What is the largest possible number of yellow tiles in this pattern?

Challenge Level

A square is divided into three shapes which all have equal areas. Can you find the length of this side?

Challenge Level

Given this information about averages, find the ages of these teachers.

Challenge Level

How many different bunches of flowers can this class buy for their teacher?

Challenge Level

Find the area of the triangle enclosed by these lines.

Challenge Level

Can you find the height of the water in this tilted tank when it is flat?

Challenge Level

Can you find the area between this graph and the x-axis, between x=3 and x=7?

Challenge Level

How many small boxes will fit inside the big box?

Challenge Level

These are the results when 3 numbers were added in pairs. What were the numbers?

Challenge Level

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

Challenge Level

This tiled floor has 109 purple tiles. How many tiles are there altogether?

Challenge Level

How many students are in the maths club and the science club?

Challenge Level

At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?

Challenge Level

Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?

Challenge Level

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

Challenge Level

Can you work out the area of a square drawn on a diagonal?

Challenge Level

Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day

Challenge Level

What happens to the average if you subtract 8 from all of the numbers?

Challenge Level

The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?

Challenge Level

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

Challenge Level

Can you work out what fraction of this grid is shaded?

Challenge Level

Can you arrange the red and blue cards so that the rules are all followed?

Challenge Level

Find the sum of all of the angles denoted by letters in this diagram

Challenge Level

Can you find the next time that the 29th of February will fall on a Monday?

Challenge Level

What is the probability that the next person you meet has an above average number of arms?

Challenge Level

Every member of the club is a member of two committees. How many members are there in the club?

Challenge Level

What is the angle between the the hands of a clock at 8:24?

Challenge Level

What is the last digit in this calculation involving powers?

Challenge Level

How long will it take Mary and Nigel to wash an elephant if they work together?

Challenge Level

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...

Challenge Level

Choose the digits $a$ and $b$ so that this number is divisible by 55.

Challenge Level

Use this series of fractions to find the value of x.

Challenge Level

Which faces are opposite each other when this net is folded into a cube?

Challenge Level

Given information about the mean, can you work out the missing numbers?

Challenge Level

A coin is flipped 4 times. What is the probability of getting heads at least 3 times?

Challenge Level

Find the perimeter of this shape made of semicircles

Challenge Level

What is the ratio of the area of the hexagon to the area of the triangle?

Challenge Level

If two girls each take a sweet from each other's bags, what is the probability that they end up with what they started with?

Challenge Level

The area of a rectangle is 225 square units. Find its width.

Challenge Level

Can you find the sum of all of the numbers in the table?

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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'?