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Rationals Between...

What fractions can you find between the square roots of 65 and 67?

F'arc'tion

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.

Tiny Nines

What do you notice about these families of recurring decimals?

Circuit Training

Age 14 to 16 Challenge Level:

Running Clockwise

Why do runners always run around the track in an anticlockwise direction?

Do they develop a clinical lean?

Mike and Monisha meet at the race track, which is $400 \; \text{m}$ round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise, normally Mike can complete a circuit of the track in two thirds of the time Monisha takes.

They agree to stop when they both meet at the start again. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?