Year 11 Visualising and representing

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?

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?

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

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

Simple additions can lead to intriguing results...

Infographics are a powerful way of communicating statistical information. Can you come up with your own?

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Can you work out the dimensions of the three cubes?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

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?

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

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?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

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

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

There are unexpected discoveries to be made about square numbers...

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

If a sum invested gains 10% each year how long before it has doubled its value?

Explore the relationships between different paper sizes.

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