CAIE IGCSE Mathematics Core C1.12 Rates Questions

Practise unit rates, rate conversions, density, population density and speed–distance–time calculations across numerical and contextual questions.

Exam points

convert compound units by applying the distance, mass or time conversion to the correct part of the rate
rearrange supplied rate formulas to calculate density, mass, volume or population density
use total distance divided by total time for average speed and convert all units before calculating

Covered syllabus points

C1.12.1 Use common measures of rate.C1.12.2 Apply other measures of rate.C1.12.3 Solve problems involving average speed

[Maximum number: 3]

A family go on a skiing holiday to America.

A ski lift, when full, takes 4000 passengers per hour.

This lift works for 10 hours a day.
One day, this lift is 90% full for 3 hours and 75% full for 7 hours.
Work out the number of passengers who take the lift that day.

31800\n\nM2 for $3\times\frac{90}{100}\times4000$ oe or $7\times\frac{75}{100}\times4000$ oe\nor M1 for $\frac{90}{100}\times4000$ oe or $\frac{75}{100}\times4000$ oe

[Maximum number: 3]

A bar of gold in the shape of a cuboid has dimensions 2 cm by 4 cm by 6.5 cm .
The density of gold is $19.32 \mathrm{~g} / \mathrm{cm}^{3}$ .
Calculate the mass of this bar of gold.
$\left[\right.$ Density $\left.=\frac{\text { mass }}{\text { volume }}\right]$

1004.64

M1 for $2 \times 4 \times 6.5$ oe implied by 52
M1 for $19.32=\frac{[\text { mass }]}{\text { their } 52}$ or better

[Maximum number: 2]

Miguel works in an office.

It takes Miguel 40 minutes to drive to work.

Miguel drives to work at an average speed of $57 \mathrm{~km} / \mathrm{h}$ .

Show that he drives 38 km .

$57\times\frac{40}{60}=38$
M1 for $\frac{40}{60}$ or $57\times40$

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Covered syllabus points

Question 1

Question 2

Question 3