All CD Heaven stores were given the same number of a popular CD to
sell for £24. In their two week sale each store reduces the
price of the CD by 25% ... How many CDs did the store sell at. . . .
There are lots of different methods to find out what the shapes are worth - how many can you find?
If a sum invested gains 10% each year how long before it has
doubled its value?
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?
Five children went into the sweet shop after school. There were
choco bars, chews, mini eggs and lollypops, all costing under 50p.
Suggest a way in which Nathan could spend all his money.
If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G =
F and A-H represent the numbers from 0 to 7 Find the values of A,
B, C, D, E, F and H.
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
The clues for this Sudoku are the product of the numbers in adjacent squares.
There is a particular value of x, and a value of y to go with it,
which make all five expressions equal in value, can you find that
x, y pair ?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Use the differences to find the solution to this Sudoku.
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Take any prime number greater than 3 , square it and subtract one.
Working on the building blocks will help you to explain what is
special about your results.
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
What is the same and what is different about these circle
questions? What connections can you make?
A circle of radius r touches two sides of a right angled triangle,
sides x and y, and has its centre on the hypotenuse. Can you prove
the formula linking x, y and r?
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
If the hypotenuse (base) length is 100cm and if an extra line
splits the base into 36cm and 64cm parts, what were the side
lengths for the original right-angled triangle?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Can you find the area of a parallelogram defined by two vectors?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
Which set of numbers that add to 10 have the largest product?
Two motorboats travelling up and down a lake at constant speeds
leave opposite ends A and B at the same instant, passing each
other, for the first time 600 metres from A, and on their return,
400. . . .
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
What is the area of the quadrilateral APOQ? Working on the building
blocks will give you some insights that may help you to work it
This shape comprises four semi-circles. What is the relationship
between the area of the shaded region and the area of the circle on
AB as diameter?
Find the sum of the series.
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
Can you describe this route to infinity? Where will the arrows take you next?
Your school has been left a million pounds in the will of an ex-
pupil. What model of investment and spending would you use in order
to ensure the best return on the money?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
A napkin is folded so that a corner coincides with the midpoint of
an opposite edge . Investigate the three triangles formed .
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?