year 8 maths

NSW syllabus
STRAND: NUMBER AND ALGEBRA
SUBSTRANDS: RATIOS AND RATES
FINANCIAL MATHEMATICS
Outcomes
A student operates with ratios and
rates, and explores their graphical
representation.
(MA4–7NA)
A student solves financial problems
involving purchasing goods.
(MA4–6NA)
© NESA, 2012
Bicycle gear ratios
The bicycle is renowned as the most energy-efficient means of human transport. A bicycle
with a range of gears is an extremely versatile and enjoyable machine. The ‘gear ratio’ of
a bicycle is the ratio of pedal rotations compared to the rate at which the wheels rotate.
Manufacturers apply the mathematics of gear ratios to provide cyclists with the range of
gears that is most useful for the style of bike.
Have you ever tried to ride up a steep hill in too high a gear or reached the bottom of a hill
while still in a very low gear? A bicycle rider has a comfortable range of pressures and rotation
rates that they can apply to the pedals. Gears make it easier to stay in this comfortable range
over a wide variety of riding conditions, such as BMX, downhill racing, a fast time trial for
racing bikes on flat ground, or climbing steep, rough trails on a mountain bike.
Unicycles have only one wheel and so have a ratio of 1 : 1 for pedal turns to wheel turns.
Unicycles can’t reach high speeds because it is very difficult to rotate pedals more than
about 100 rpm; however, riding a unicycle is fun and it requires strength and agility to remain
stable, especially when playing unicycle hockey!
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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