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N13

Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate

Standard units

Worked answers, methods and verified real exam appearances for N13 on Edexcel GCSE Maths 1MA1.

Explanation

  • Standard units cover mass, length, time, money and other measures; compound measures combine units, such as kilometres per hour or grams per cubic centimetre. Choose units appropriate to the context, then convert all quantities to compatible units before calculating.
  • Length factors are squared for area and cubed for volume: because 1 m=100 cm1\text{ m}=100\text{ cm}, 1 m2=10000 cm21\text{ m}^2=10\,000\text{ cm}^2.
  • Time is base 6060, not base 100100, so 1.51.5 hours is 11 hour 3030 minutes.
  • Give money to the nearest penny when appropriate.
  • Examiners expect a numerical value and a correctly converted unit.

Worked example

A car travels 5454 km using 7.57.5 litres per 100100 km. Fuel costs £1.68\pounds1.68 per litre. Find the journey’s fuel cost.

  1. 1.Fuel used =54×7.5100=4.05=54\times\dfrac{7.5}{100}=4.05 litres.
  2. 2.Cost =4.05×1.68=6.804=4.05\times1.68=6.804 pounds.
  3. 3.Round money to the nearest penny.

Answer: £6.80\pounds6.80.

Common mistakes

  • Don't treat 1.51.5 hours as 11 hour 5050 minutes.
  • Don't use the factor 100100 rather than 1002100^2 when converting square metres to square centimetres.
  • Don't omit the compound unit from the final answer.

Exam tip

Write the target unit before starting; every conversion should move the data towards that unit.

Worked practice

Q1
Tier 1 · Easy

1

Change 2.752.75 kg to grams.

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
QuestionAnswerMarkMark scheme
1
  • 27502750 g
1There are 10001000 grams in a kilogram, so 2.75×1000=27502.75\times1000=2750 g.
Q2
Tier 2 · Standard

2

A workshop starts at 09:3809{:}38 and lasts for 11 hour 4747 minutes. Work out the finishing time.

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
QuestionAnswerMarkMark scheme
2
  • 11:2511{:}25
2Adding 11 hour gives 10:3810{:}38. Adding 4747 minutes gives 11:2511{:}25 because 2222 minutes reach 11:0011{:}00 and 2525 minutes remain.
Q3
Tier 3 · Hard

3

A car travels 5454 km and uses fuel at a rate of 7.57.5 litres per 100100 km. Fuel costs £1.68\pounds1.68 per litre. Work out the fuel cost for the journey, giving your answer to the nearest penny.

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
QuestionAnswerMarkMark scheme
3
  • £6.80\pounds6.80
4The fuel used is 54×7.5100=4.0554\times\dfrac{7.5}{100}=4.05 litres. The cost is 4.05×1.68=6.8044.05\times1.68=6.804, which rounds to £6.80\pounds6.80 to the nearest penny.
Q4
Tier 1 · Easy

4

Change 45004500 millilitres to litres.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
QuestionAnswerMarkMark scheme
4
  • 4.54.5 litres
1There are 10001000 millilitres in a litre, so 4500÷1000=4.54500\div1000=4.5 litres.
Q5
Tier 2 · Standard

5

A rectangular sheet is 0.270.27 m long and 4646 cm wide. Work out its area in square centimetres.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
QuestionAnswerMarkMark scheme
5
  • 12421242 cm2^2
20.270.27 m is 2727 cm. The area is therefore 27×46=124227\times46=1242 cm2^2.
Q6
Tier 3 · Hard

6

A tap delivers 1818 litres of water in 22 minutes 2424 seconds. Work out the average rate in millilitres per second.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
QuestionAnswerMarkMark scheme
6
  • 125125 ml/s
31818 litres is 1800018\,000 ml and 22 minutes 2424 seconds is 2×60+24=1442\times60+24=144 seconds. The average rate is 18000÷144=12518\,000\div144=125 ml/s.
Q7
Tier 2 · Standard

7

A delivery contains 88 cartons with mass 750750 g each and 33 cartons with mass 1.21.2 kg each. Work out the total mass of the cartons in kilograms.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
QuestionAnswerMarkMark scheme
7
  • 9.69.6 kg
3The eight smaller cartons have mass 8×750=60008\times750=6000 g, which is 66 kg. The other cartons have mass 3×1.2=3.63\times1.2=3.6 kg. The total is 6+3.6=9.66+3.6=9.6 kg.
Q8
Tier 3 · Hard

8

A printer produces 825825 labels in 22 minutes 3030 seconds. It continues at the same average rate for 77 minutes. Work out the number of labels produced in the 77 minutes.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
QuestionAnswerMarkMark scheme
8
  • 23102310 labels
422 minutes 3030 seconds is 150150 seconds, so the rate is 825÷150=5.5825\div150=5.5 labels per second. Seven minutes is 420420 seconds. The number produced is 5.5×420=23105.5\times420=2310 labels.
Q9
Tier 3 · Hard

9

A roll holds 2.352.35 km of cable. A technician cuts 4848 pieces, each 37.537.5 m long, from the roll. Work out the length of cable left. Give your answer in metres.

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
QuestionAnswerMarkMark scheme
9
  • 550550 m
3Convert the original length: 2.352.35 km =2350=2350 m. The pieces use 48×37.5=180048\times37.5=1800 m, so the length left is 23501800=5502350-1800=550 m.
Q10
Tier 3 · Hard

10

A runner covers 7.57.5 km at an average speed of 1212 km/h and then rests for 88 minutes. Work out the total time for the run and the rest. Give your answer in minutes.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
QuestionAnswerMarkMark scheme
10
  • 45.545.5 minutes (or 4545 minutes 3030 seconds)
4The running time is 7.5÷12=0.6257.5\div12=0.625 hours. This is 0.625×60=37.50.625\times60=37.5 minutes. Including the rest gives 37.5+8=45.537.5+8=45.5 minutes.

Verified exam appearances

SeriesPaperQuestionMarksCalculatorTierLinks
2019-061FQ64Non-calculatorFoundationQPMS
2019-061FQ11Non-calculatorFoundationQPMS
2019-112FQ103AllowedFoundationQPMS
2019-063FQ213AllowedFoundationQPMS
2022-111FQ64Non-calculatorFoundationQPMS
2019-061FQ184Non-calculatorFoundationQPMS
2023-062FQ144AllowedFoundationQPMS
2019-111FQ72Non-calculatorFoundationQPMS
2023-063FQ41AllowedFoundationQPMS
2019-112FQ63AllowedFoundationQPMS
2019-112FQ153AllowedFoundationQPMS
2019-061FQ94Non-calculatorFoundationQPMS
2021-111FQ93Non-calculatorFoundationQPMS
2022-061FQ73Non-calculatorFoundationQPMS
2019-062FQ123AllowedFoundationQPMS
2024-063FQ21AllowedFoundationQPMS
2023-062FQ31AllowedFoundationQPMS
2019-061FQ131Non-calculatorFoundationQPMS
2021-113FQ31AllowedFoundationQPMS
2022-061FQ114Non-calculatorFoundationQPMS
2024-113FQ86AllowedFoundationQPMS
2023-113FQ95AllowedFoundationQPMS
2023-063FQ104AllowedFoundationQPMS
2024-063FQ112AllowedFoundationQPMS
2022-112FQ74AllowedFoundationQPMS
2022-111FQ125Non-calculatorFoundationQPMS
2019-062FQ63AllowedFoundationQPMS
2019-111FQ83Non-calculatorFoundationQPMS
2024-113FQ105AllowedFoundationQPMS
2023-113HQ73AllowedHigherQPMS
2021-113FQ113AllowedFoundationQPMS
2023-113FQ122AllowedFoundationQPMS
2019-113FQ274AllowedFoundationQPMS
2021-113FQ83AllowedFoundationQPMS
2024-112FQ21AllowedFoundationQPMS
2022-112FQ105AllowedFoundationQPMS
2022-061FQ164Non-calculatorFoundationQPMS
2023-113FQ263AllowedFoundationQPMS
2021-113FQ103AllowedFoundationQPMS
2023-111FQ63Non-calculatorFoundationQPMS

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