What happens to the area and volume of 2D and 3D shapes when you enlarge them?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Which of these games would you play to give yourself the best possible chance of winning a prize?
Here are two games you can play. Which offers the better chance of winning?
A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
Can you find the hidden factors which multiply together to produce each quadratic expression?
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 each price?
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
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?
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?
Can you work out the probability of winning the Mathsland National Lottery?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.
Use the differences to find the solution to this Sudoku.
A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?
The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
