
problem
Beelines
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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

problem
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?

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

problem
How old am I?
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?

problem
Where to land
Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

problem
Matchless
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 ?

problem
The legacy
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?

problem
Partly painted cube
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?

problem
Training schedule
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?

problem
Difference of two squares
What is special about the difference between squares of numbers adjacent to multiples of three?


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

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

problem
Napkin
A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.

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