Vector journeys
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?
Factorising with multilink
Double trouble
Salinon
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?
Spotting the loophole
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?
Which is bigger?
Kite in a square
Can you make sense of the three methods to work out what fraction of the total area is shaded?
Square number surprises
Picture story
Three cubes
Triangle midpoints
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Doesn't add up
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Triangles and petals
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
The spider and the fly
A question of scale
Immersion
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Partly painted cube
Fit for photocopying
Explore the relationships between different paper sizes.
Dating made easier
Areas and ratios