Ratio and proportion

problem

Ratio Sudoku 2

Age

11 to 16

Challenge level

A Sudoku with clues as ratios.
problem

Ratio Sudoku 3

Age

11 to 16

Challenge level

A Sudoku with clues as ratios or fractions.
problem

Star Gazing

Age

14 to 16

Challenge level

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
problem

A Shade Crossed

Age

14 to 16

Challenge level

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?
problem

ArRh!

Age

14 to 16

Challenge level

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?
problem

Six Notes All Nice Ratios

Age

14 to 16

Challenge level

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.
problem

A Scale for the Solar System

Age

14 to 16

Challenge level

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?
problem

Mixed Up Mixture

Age

14 to 16

Challenge level

Can you fill in the mixed up numbers in this dilution calculation?
problem

Contact

Age

14 to 16

Challenge level

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
problem

Gift of Gems

Age

14 to 16

Challenge level

Four jewellers share their stock. Can you work out the relative values of their gems?