Ratio and proportion

problem

Eight Ratios

Age

14 to 16

Challenge level

2 out of 3

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.
problem

Shepherd's Flock

Age

14 to 16

Challenge level

2 out of 3

Does Joseph have too many sheep in his flock...
problem

The Fastest Cyclist

Age

14 to 16

Challenge level

2 out of 3

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?
problem

Golden Thoughts

Age

14 to 16

Challenge level

3 out of 3

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
problem

From All Corners

Age

14 to 16

Challenge level

3 out of 3

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.
problem

Same Height

Age

14 to 16

Challenge level

3 out of 3

A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium?
problem

Televisual Technology

Age

14 to 16

Challenge level

3 out of 3

If a new and an old television have screens of the same area, what is the ratio of their widths?
problem

Orbiting Billiard Balls

Age

14 to 16

Challenge level

3 out of 3

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
problem

The Rescaled Map

Age

14 to 16

Challenge level

3 out of 3

We use statistics to give ourselves an informed view on a subject of interest. This problem explores how to scale countries on a map to represent characteristics other than land area.
problem

Points in Pairs

Age

14 to 16

Challenge level

3 out of 3

Move the point P to see how P' moves. Then use your insights to calculate a missing length.