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Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

What can you say about the common difference of an AP where every term is prime?

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.

Use the logarithm to work out these pH values

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

A colourful cube is made from little red and yellow cubes. But can you work out how many of each?

Use the grids to draw pictures to different scales.