Ratio and proportion

problem

Why Multiply When You're About to Divide?

Age

16 to 18

Challenge level

A brief introduction to PCR and restriction mapping, with relevant calculations...
problem

Tennis Club

Age

14 to 16

Challenge level

Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?
problem

How Big?

Age

11 to 14

Challenge level

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?
problem

Pent

Age

14 to 18

Challenge level

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
problem

Off the Cuff

Age

11 to 14

Challenge level

Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?
problem

Slippage

Age

14 to 16

Challenge level

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?
problem

Square Ratio

Age

14 to 16

Challenge level

A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?
problem

Double Cover

Age

11 to 14

Challenge level

Weekly Problem 3 - 2007
What is the ratio of the area of the table covered twice, to the uncovered area?
problem

Pythagoras' Comma

Age

14 to 16

Challenge level

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.
problem

Eight Ratios

Age

14 to 16

Challenge level

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.