Ratio and proportion

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.
problem
Tyre wear

Age

11 to 14

Challenge level

A car with 5 tyres (four road tyres and a spare) travelled 30,000 km. All 5 tyres were used equally. How many kilometres' wear did each tyre receive?
problem
Striking gold

Age

16 to 18

Challenge level

Investigate some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold.
problem
Reductant ratios

Age

16 to 18

Challenge level

What does the empirical formula of this mixture of iron oxides tell you about its consituents?
problem
Gassy information

Age

16 to 18

Challenge level

Do each of these scenarios allow you fully to deduce the required facts about the reactants?
problem
Shepherd's flock

Age

14 to 16

Challenge level

Does Joseph have too many sheep in his flock...
problem
At a glance

Age

14 to 16

Challenge level

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
problem
Square pegs

Age

11 to 14

Challenge level

Which is a better fit, a square peg in a round hole or a round peg in a square hole?