Applying number: metric units, money, currency & time – IGCSE Maths exam questions with mark scheme

1Grade 1–3FoundationCalculator3 marks

(a) Change $3.4$ km into metres. [1]

(b) Change $650$ g into kilograms. [1]

(a) $3400$ (m)B1
(b) $0.65$ (kg) (accept $0.650$)B1
(c) $2500$ (ml)B1
Answer: (a) 3400 m (b) 0.65 kg (c) 2500 ml
Examiner tip: Decide first whether the number should get bigger or smaller: changing to a smaller unit (km to m) means multiplying, so 3.4 km cannot be 0.0034 m.

2Grade 4–5Calculator3 marks

(a) A train leaves Leeds at 09:47 and arrives in London at 11:15. How long does the journey take? Give your answer in hours and minutes. [1]

(b) A plane leaves Dubai at 22:40 local time. The flight takes 7 hours 25 minutes. The local time in London is 3 hours behind the local time in Dubai.

Work out the local time in London when the plane lands. [2]

(a) 1 hour 28 minutes (accept 88 minutes)B1
(b) for 22:40 + 7 h 25 min $=$ 06:05 (next day) oe, or for 22:40 $-$ 3 h $=$ 19:40 (London time at take-off)M1
(b) 03:05 (accept 3:05 am, 0305; do not accept 3:05 pm)A1
Answer: (a) 1 h 28 min (b) 03:05
Examiner tip: Time is not decimal: 11:15 − 09:47 done on a calculator gives 1.68, which is not 1 h 68 min; count on to 10:00 (13 min) then to 11:15 (1 h 15 min).

3Grade 4–5FoundationCalculator4 marks

The exchange rate is £1 $=$ €1.16

(a) Amira changes £350 into euros. How many euros does she get? [2]

(b) A jacket costs €89 in Paris. The same jacket costs £79 in London. In which city is the jacket cheaper? You must show your working. [2]

(a) for $350\times1.16$M1
(a) €406A1
(b) for $89\div1.16\ (=76.72\ldots)$ or $79\times1.16\ (=91.64)$M1
(b) Paris, with correct comparable figures, e.g. £76.72 (or £76.70, £77) and £79, or €89 and €91.64A1
Answer: (a) €406 (b) Paris (£76.72 < £79, or €89 < €91.64)
Examiner tip: In (b) the answer 'Paris' alone scores nothing: you must convert one price so both are in the same currency and show the two values you compared.

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4Grade 4–5Calculator3 marks

Orange juice is sold in two sizes.

Small carton: 750 ml for \$2.85
Large carton: 1.2 litres for \$4.38

Which carton is the better value for money? You must show how you decide. [3]

for converting to the same units, e.g. $1.2$ litres $=1200$ ml or $750$ ml $=0.75$ litresM1
for a complete method to compare, e.g. $2.85\div0.75\ (=3.80)$ and $4.38\div1.2\ (=3.65)$ (dollars per litre), or $750\div2.85\ (=263.1\ldots)$ and $1200\div4.38\ (=273.9\ldots)$ (ml per dollar) oeM1
Large carton, with correct figures, e.g. \$3.65 < \$3.80 per litreA1
Answer: Large carton (\$3.65 per litre against \$3.80 per litre)
Examiner tip: Compare like with like: dividing \$4.38 by 1.2 but \$2.85 by 750 gives figures in different units that cannot be compared.

5Grade 4–5Calculator3 marks

(a) Change $3.2\ \text{m}^2$ into $\text{cm}^2$. [1]

The diagram shows a fish tank in the shape of a cuboid. It is 1.2 m long, 50 cm wide and 40 cm high.

(b) Work out how many litres of water the tank holds when it is full. ($1$ litre $=1000\ \text{cm}^3$) [2]

(a) $32\,000$ (cm²)B1
(b) for $120\times50\times40\ (=240\,000\ \text{cm}^3)$ oe, e.g. $1.2\times0.5\times0.4=0.24\ \text{m}^3$M1
(b) $240$ (litres)A1
Answer: (a) 32 000 cm² (b) 240 litres
Examiner tip: There are $100^2=10\,000$ cm² in 1 m², not 100; and in (b) the lengths must all be in the same unit before multiplying.

6Grade 4–5Calculator2 marks

Use your calculator to work out $$\frac{\sqrt{18.4+3.7^2}}{2.1\times0.65}$$

(a) Write down all the figures on your calculator display. [1]

(b) Give your answer to (a) correct to 3 significant figures. [1]

(a) $4.150039\ldots$ (at least the first 5 figures, $4.1500$)B1
(b) $4.15$ (ft their (a) if it has more than 3 sig figs)B1ft
Answer: (a) 4.150039279 (b) 4.15
Examiner tip: Use brackets: type the whole numerator as $\sqrt{(18.4+3.7^2)}$ and the denominator as $(2.1\times0.65)$, otherwise the calculator divides only part of the expression.

7Grade 6–7HigherCalculator5 marks

The table gives information about Kwame's electricity bill for one quarter of the year.

Meter reading at start	47 386 units
Meter reading at end	48 217 units
Cost per unit	28.6 cents
Daily standing charge	52 cents per day
Number of days	91

Tax of $5\%$ is added to the total of the unit cost and the standing charge.

Work out the total amount Kwame has to pay. Give your answer in dollars. (100 cents $=$ \$1) [5]

for $48\,217-47\,386\ (=831)$M1
for $831\times28.6\ (=23\,766.6$ cents$)$ or $831\times0.286\ (=237.66\ldots)$M1
for $91\times52\ (=4732$ cents$)$ or $91\times0.52\ (=47.32)$M1
for $(237.666+47.32)\times1.05$ oe, i.e. adding the two charges and increasing by $5\%$M1
\$299.24 (accept \$299.23 to \$299.24)A1
Answer: \$299.24
Examiner tip: Mixing cents and dollars is the commonest error: an answer of \$29 923 or \$2.99 should tell you the units have been mixed up.

8Grade 6–7HigherCalculator4 marks

Exchange rates:

\$1 (US) $=$ 3.67 dirhams (AED)
\$1 (US) $=$ 83.2 rupees (INR)

Ravi has 1500 dirhams. He changes them into rupees at these rates. The exchange office takes $2\%$ commission from the 1500 dirhams before changing his money.

How many rupees does Ravi receive? Give your answer to the nearest rupee. [4]

for $1500\times0.98\ (=1470)$ or $1500\times0.02\ (=30)$ seenM1
for dividing by $3.67$, e.g. $1470\div3.67\ (=400.54\ldots)$ or $1500\div3.67\ (=408.71\ldots)$M1
for a complete method, e.g. $1500\times0.98\div3.67\times83.2$ oeM1
$33\,325$ (rupees)A1
Answer: 33 325 rupees
Examiner tip: Go through the common currency: dirhams ÷ 3.67 gives dollars, then dollars × 83.2 gives rupees; multiplying 1470 by 3.67 is the wrong direction.

9Grade 6–7HigherCalculator4 marks

Mei works a basic week of 37.5 hours. Her basic rate of pay is £14.20 per hour.

Any overtime is paid at 1.5 times the basic rate.

One week Mei was paid £666.69 in total.

How much overtime did she work that week? Give your answer in hours and minutes. [4]

for $37.5\times14.20\ (=532.50)$M1
for $666.69-532.50\ (=134.19)$ and $14.20\times1.5\ (=21.30)$M1
for $134.19\div21.30\ (=6.3)$M1
6 hours 18 minutesA1
Answer: 6 hours 18 minutes
Examiner tip: 6.3 hours is not 6 hours 30 minutes: convert the decimal part by $0.3\times60=18$ minutes.

10Grade 8–9HigherCalculator5 marks

Leon is painting the four walls of a room. The room is a cuboid 4.8 m long and 3.6 m wide. The walls are 2.65 m high.

The door, which he will not paint, is a rectangle 0.9 m by 2.0 m. There are no windows.

Each wall needs two coats of paint. One litre of paint covers 12 m² for one coat.

Paint is sold in 2.5 litre tins costing €18.40 and 1 litre tins costing €8.95.

Work out the least it will cost Leon to buy enough paint. You must show your working. [5]

for wall area $2\times(4.8+3.6)\times2.65\ (=44.52)$ oeM1
for subtracting the door and doubling for two coats, e.g. $(44.52-1.8)\times2\ (=85.44)$M1
for $85.44\div12\ (=7.12$ litres$)$M1
for a valid combination of tins giving at least 7.12 litres, e.g. $3\times2.5$ litres, with its cost, or a comparison such as $2\times18.40+3\times8.95\ (=63.65)$M1
€55.20 (from three 2.5 litre tins)A1
Answer: €55.20 (three 2.5 litre tins)
Examiner tip: 7.12 litres must be rounded up, and 2 large + 2 small tins (7 litres) is not enough; a large tin is cheaper per litre (€7.36), so three large tins is cheapest.

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