Year 11 Being resilient

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?

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Two ladders are propped up against facing walls. At what height do the ladders cross?

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?

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?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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?

Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

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.

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Explore the relationships between different paper sizes.

Can you make sense of the three methods to work out what fraction of the total area is shaded?

Do you have enough information to work out the area of the shaded quadrilateral?