Measures, bearings, speed, density & pressure – IGCSE Maths exam questions with mark scheme

1Grade 4–5Calculator3 marks

A car travels 162 km in 1 hour 48 minutes.

Work out the average speed of the car in kilometres per hour. [3]

for converting the time to hours, $1.8$ oe, or $108$ minutesM1
for $162 \div 1.8$ or $\dfrac{162}{108} \times 60$ oeM1
$90$ (km/h)A1
Answer: 90 km/h
Examiner tip: 1 hour 48 minutes is 1.8 hours, not 1.48 hours — divide the minutes by 60.

2Grade 6–7HigherCalculator4 marks

Metal $\mathbf{A}$ has a density of 8.4 g/cm$^3$. Metal $\mathbf{B}$ has a density of 4.5 g/cm$^3$.

240 cm$^3$ of metal $\mathbf{A}$ is mixed with 360 g of metal $\mathbf{B}$ to make an alloy.

Work out the density of the alloy. [4]

for mass of $\mathbf{A}$ $= 240 \times 8.4$ $(= 2016)$M1
for volume of $\mathbf{B}$ $= 360 \div 4.5$ $(= 80)$M1
(dep on at least one previous M1) for $\dfrac{2016 + 360}{240 + 80}$M1
$7.425$ (g/cm$^3$) (accept $7.43$ or $7.42$)A1
Answer: 7.425 g/cm³
Examiner tip: Densities cannot simply be averaged — find the total mass and total volume first, then divide.

3Grade 8–9HigherCalculator4 marks

Water flows through a cylindrical pipe into an empty cylindrical tank.

The pipe has an internal radius of 1.5 cm. The water flows through the pipe at a speed of 20 cm/s.

The tank has a radius of 40 cm and stands on horizontal ground.

Work out how long it takes for the depth of water in the tank to reach 30 cm.

Give your answer in minutes, correct to 1 decimal place. [4]

for volume of water needed $= \pi \times 40^2 \times 30$ $(= 48\,000\pi$ or $150\,796\ldots)$M1
for volume flowing per second $= \pi \times 1.5^2 \times 20$ $(= 45\pi$ or $141.37\ldots)$M1
for $\dfrac{48\,000\pi}{45\pi}$ $(= 1066.6\ldots$ seconds$)$ oeM1
$17.8$ (minutes)A1
Answer: 17.8 minutes
Examiner tip: In one second the water fills a cylinder of the pipe's cross-section that is 20 cm long — the speed is a length per second, not a volume.

Book a free introductory session and we'll find exactly which step is costing you.