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. . . .
If a sum invested gains 10% each year how long before it has doubled its value?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
The sums of the squares of three related numbers is also a perfect square - can you explain why?
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.
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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 out.
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?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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?
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?
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 ?
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?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
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?
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?
What is the same and what is different about these circle questions? What connections can you make?
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 golden ratio.
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?
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.
Can you find the area of a parallelogram defined by two vectors?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Find the sum of this series of surds.
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?
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. . . .
If you move the tiles around, can you make squares with different coloured edges?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?
Can you maximise the area available to a grazing goat?
Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?
Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Can you describe this route to infinity? Where will the arrows take you next?
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?