GCSE Standard and compound units Practice Questions

Free GCSE Standard and compound units practice questions with full step-by-step worked solutions. Covers converting length, metric units, converting mass, converting capacity. Practise exam-style problems and check your method.

converting lengthmetric unitsconverting massconverting capacityconverting timeconverting money
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Convert 55 km into metres.
Show worked solution

Worked solution

  1. Recall the conversion

    1 km=1000 m1\,\mathrm{km} = 1000\,\mathrm{m}

    There are 10001000 metres in every kilometre.

  2. Multiply

    5×1000=50005 \times 1000 = 5000

    Kilometres are larger than metres, so multiply by 10001000.

  3. State the answer

    5000 m5000\,\mathrm{m}

    So 5 km is 5000 m.

Answer
5000 m5000\,\mathrm{m}
Question 2
2 markseasy
A runner runs 6060 m in 1212 s. Work out the runner's speed.
Show worked solution

Worked solution

  1. Write the formula

    speed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}

    Speed is distance divided by time.

  2. Substitute the values

    speed=6012\text{speed} = \frac{60}{12}

    The distance is 60 m and the time is 12 s.

  3. Work out and add units

    =5 m/s= 5\,\mathrm{m/s}

    6060 divided by 1212 is 55, measured in metres per second.

Answer
5 m/s5\,\mathrm{m/s}
Question 3
2 marksintermediate
A car travels at a speed of 2020 m/s. How far does it travel in 1515 seconds?
Show worked solution

Worked solution

  1. Write the formula

    speed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}

    Start from the speed formula.

  2. Rearrange for distance

    distance=speed×time\text{distance} = \text{speed} \times \text{time}

    Multiply both sides by the time.

  3. Note the values

    speed=20, time=15\text{speed} = 20,\ \text{time} = 15

    The speed is 20 m/s and the time is 15 s.

  4. Substitute

    distance=20×15\text{distance} = 20 \times 15

    Put the numbers into the rearranged formula.

  5. Work it out

    20×15=30020 \times 15 = 300

    2020 times 1515 is 300300.

  6. State the answer with units

    300 m300\,\mathrm{m}

    The car travels 300300 metres.

Answer
300 m300\,\mathrm{m}
Question 4
4 markshard
A driver goes 300300 km in 44 hours, then returns the same 300300 km in 66 hours. Work out the average speed for the whole trip.
Show worked solution

Worked solution

  1. Recall the rule

    average speed=total distancetotal time\text{average speed} = \frac{\text{total distance}}{\text{total time}}

    Average speed uses the totals, not the average of the two speeds.

  2. Find the total distance

    300+300=600 km300 + 300 = 600\,\mathrm{km}

    The trip is 300300 km each way, so 600600 km altogether.

  3. Find the total time

    4+6=10 h4 + 6 = 10\,\mathrm{h}

    44 hours out and 66 hours back is 1010 hours.

  4. Substitute

    average=60010\text{average} = \frac{600}{10}

    Divide the total distance by the total time.

  5. Work it out

    600÷10=60600 \div 10 = 60

    600600 divided by 1010 is 6060.

  6. Attach the units

    60 km/h60\,\mathrm{km/h}

    The average speed is 6060 km/h.

  7. Check the outward speed

    300÷4=75 km/h300 \div 4 = 75\,\mathrm{km/h}

    The speed going was 7575 km/h.

  8. Check the return speed

    300÷6=50 km/h300 \div 6 = 50\,\mathrm{km/h}

    The speed coming back was 5050 km/h.

  9. Note the common error

    75+502=62.5≠60\frac{75 + 50}{2} = 62.5 \ne 60

    Averaging the two speeds gives the wrong answer of 62.562.5.

  10. State the final answer

    60 km/h60\,\mathrm{km/h}

    The correct average speed for the whole trip is 6060 km/h.

Answer
60 km/h60\,\mathrm{km/h}
Question 5
6 markschallenging
A driver travels 9090 km to a meeting at an average speed of 6060 km/h. For the 9090 km return trip, the driver wants the average speed for the whole round trip to be 7272 km/h. Work out the required speed on the return trip.
Show worked solution

Worked solution

  1. Understand the goal

    whole trip average=72 km/h\text{whole trip average} = 72\,\mathrm{km/h}

    The 7272 km/h applies to the entire there-and-back journey.

  2. Find the total distance

    90+90=180 km90 + 90 = 180\,\mathrm{km}

    The round trip is 9090 km each way, so 180180 km.

  3. Recall the rule

    average=total distancetotal time\text{average} = \frac{\text{total distance}}{\text{total time}}

    Average speed is total distance over total time.

  4. Rearrange for total time

    total time=total distanceaverage\text{total time} = \frac{\text{total distance}}{\text{average}}

    Divide the total distance by the target average speed.

  5. Substitute

    18072\frac{180}{72}

    Use 180180 km and 7272 km/h.

  6. Work out the total time

    180÷72=2.5180 \div 72 = 2.5

    The whole trip must take 2.52.5 hours.

  7. Attach units

    2.5 h2.5\,\mathrm{h}

    The total allowed time is 2.52.5 hours.

  8. Find the outward time

    9060\frac{90}{60}

    The way there is 9090 km at 6060 km/h.

  9. Work it out

    90÷60=1.590 \div 60 = 1.5

    The outward trip takes 1.51.5 hours.

  10. Find the return time

    2.5−1.52.5 - 1.5

    Subtract the outward time from the total time.

  11. Work it out

    2.5−1.5=12.5 - 1.5 = 1

    The return trip must take 11 hour.

  12. Find the return speed

    901\frac{90}{1}

    Return speed is 9090 km in 11 hour.

  13. Work it out

    90÷1=9090 \div 1 = 90

    The required return speed is 9090 km/h.

  14. Check the average

    1801.5+1=72\frac{180}{1.5 + 1} = 72

    180180 km in 2.52.5 hours is 7272 km/h, as required.

  15. State the final answer

    90 km/h90\,\mathrm{km/h}

    The driver must return at 9090 km/h.

Answer
90 km/h90\,\mathrm{km/h}

Unlock 65 more Standard and compound units questions

Create a free account to work through every GCSE Standard and compound units question with instant step-by-step worked solutions, progress tracking and interactive lessons.

  • Full worked solutions for every question
  • Interactive lessons and instant feedback
  • Track your mastery across every topic
Create a Free Account

No card required · Free forever

More Standard and compound units practice

Hard QuestionsWorked Solutions

Related Number topics

Upper and lower boundsError intervalsEstimating powers and rootsEstimation and checkingExact calculationFactors, multiples and primes