CAIE IGCSE Mathematics Extended E1.12.2 Apply Other Measures of Rate Questions

Practise applying density, fuel-consumption, flow and planting rates after converting geometric measurements and compound units consistently.

Exam points

calculate volume or area first and convert its units before applying the stated rate
use density = mass ÷ volume and rearrange it to find mass, density or volume
combine total fuel, distance or flow before expressing consumption or capacity in required units

[Maximum number: 4]

NOT TO SCALE

The diagram shows a field, ABCD with B north of A.
BD is a path across the field.
$A B=85 \mathrm{~m}, A D=72 \mathrm{~m}, B D=129 \mathrm{~m}$ , angle $B D C=39^{\circ}$ and angle $B C D=60^{\circ}$ .

Trees are planted in the field.

The number of trees planted is 1100 per hectare.
Calculate the total number of trees planted in the field. [ 1 hectare $=10000 \mathrm{~m}^{2}$ ]
The length of the rectangle is 80 cm , correct to the nearest 10 cm .

Calculate the upper bound of the width of the rectangle. cm

972 or 973
M1 for $[\triangle ABD]\frac{1}{2}\times85\times129\sin31.6^\circ$ oe
or $\frac{1}{2}\times129\times\text{their }44.5$ oe
M1 for $[\triangle BCD]\frac{1}{2}\times129\times\text{their }147\times\sin39^\circ$ oe
M1 for $\frac{\text{their total area}}{10000}\times1100$

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CAIE IGCSE Mathematics Extended E1.12.2 Apply Other Measures of Rate Questions question 1