Units of measure - Edexcel GCSE Maths (Calculator) Exam Questions

Practise 19 exam-style questions on Units of measure for Edexcel GCSE Maths (Calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.

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1–5 marks each
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19 questions, marked as you go

Sample questions with model answers

Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.

Question 1

2 marks

Change 64 800 cm² into m².

Model answer

\(1 \text{ m}^2 = 100 \times 100 = 10\,000 \text{ cm}^2\)
\(64\,800 \div 10\,000 = 6.48\)
64 800 cm² = 6.48 m²

Explanation

A square of side 1 m is 100 cm by 100 cm, so 1 m² = 10 000 cm². To change cm² into m², divide by 10 000. Dividing by 100 (giving 648 m²) is the most common mistake.

Mark scheme

1 mark
M1 for dividing by 10 000 (or by \(100^2\) or \(100 \times 100\))
1 mark
A1 for 6.48 m²
cao; correct answer with no working scores full marks

Question 2

2 marks

On average, a person's heart beats 72 times each minute.

Work out the number of times it beats in one year of 365 days.
Give your answer in standard form, correct to 3 significant figures.

Model answer

Beats in one hour: \(72 \times 60 = 4320\)
Beats in one day: \(4320 \times 24 = 103\,680\)
Beats in one year: \(103\,680 \times 365 = 37\,843\,200\)
\(= 3.78 \times 10^7\) (3 s.f.)

Explanation

Change the time step by step: 60 minutes in an hour, 24 hours in a day, 365 days in a year. In standard form the first number must be between 1 and 10, and 37 843 200 = 3.78432 × 10⁷, which rounds to 3.78 × 10⁷.

Mark scheme

1 mark
M1 for \(72 \times 60 \times 24 \times 365\) oe
e.g. 37 843 200 seen
1 mark
A1 for \(3.78 \times 10^7\)
cao (the answer must be in standard form to 3 s.f.); correct answer with no working scores full marks

Question 3

3 marks

The fuel consumption of a car is 48 miles per gallon.

1 mile = 1.609 km
1 gallon = 4.546 litres

Show that the fuel consumption of the car is approximately 17 kilometres per litre.

Model answer

48 miles \(= 48 \times 1.609 = 77.232\) km
So the car travels 77.232 km on 1 gallon = 4.546 litres.
\(77.232 \div 4.546 = 16.989...\) km per litre
16.989... ≈ 17 kilometres per litre

Explanation

Change the distance (miles into km) and the amount of fuel (gallons into litres) separately, then divide distance by fuel to get km per litre. In a "show that" question you must show a more accurate value, such as 16.99, before saying it is approximately 17. Multiplying by 4.546 instead of dividing gives about 351, which is clearly not sensible.

Mark scheme

1 mark
M1 for \(48 \times 1.609\) (= 77.232 km per gallon)
or for 1.609 ÷ 4.546 (= 0.3539...)
1 mark
M1 for their 77.232 \(\div 4.546\) oe
oe, e.g. \(48 \times 1.609 \div 4.546\) as one calculation
1 mark
C1 for 16.98... or 16.99 seen, leading to approximately 17 km per litre
a value to at least 3 significant figures must be seen; answer only scores 0

Question 4

4 marks

Water flows along a pipe at a speed of 1.5 metres per second.
The cross-section of the pipe has an area of 6 cm².

The water from the pipe fills an empty tank.
The tank holds 2.5 m³ of water.

How long does it take to fill the tank?
Give your answer in minutes, correct to the nearest minute.

Model answer

Speed: 1.5 m/s = 150 cm/s
Each second, a length of 150 cm of water with cross-section 6 cm² flows out.
Volume each second \(= 6 \times 150 = 900\) cm³
2.5 m³ \(= 2.5 \times 1\,000\,000 = 2\,500\,000\) cm³
Time \(= 2\,500\,000 \div 900 = 2777.7...\) seconds
\(2777.7... \div 60 = 46.29...\) minutes
46 minutes (to the nearest minute)

Explanation

Each second the water moves 1.5 m along the pipe, so the volume that flows out each second is a prism: cross-section area × length. Work in one unit throughout (cm and cm³ here, using 1 m³ = 1 000 000 cm³), then divide the tank's volume by the volume per second. Mixing cm² with m/s without converting is the usual error.

Mark scheme

1 mark
P1 for 1.5 m/s = 150 cm/s, or 6 cm² = 0.0006 m²
1 mark
P1 for the volume flowing each second, e.g. \(6 \times 150 = 900\) cm³ or \(0.0006 \times 1.5 = 0.0009\) m³
1 mark
P1 for a complete method for the time, e.g. \(2\,500\,000 \div 900\) (= 2777.7... seconds) or \(2.5 \div 0.0009\)
1 mark
A1 for 46 minutes
cao; correct answer with no working scores full marks

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