GCSE Compound measures Practice Questions

Free GCSE Compound measures practice questions with full step-by-step worked solutions. Covers speed, distance divided by time, metres per second, distance = speed x time. Practise exam-style problems and check your method.

speeddistance divided by timemetres per seconddistance = speed x timetime = distance / speeddensity
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
A car travels 120120 km in 22 hours. Work out its average speed in km/h.
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Worked solution

  1. Write down the formula

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

    Speed is the distance divided by the time.

  2. Substitute the values and divide

    speed=1202=60\text{speed} = \frac{120}{2} = 60

    Dividing 120 by 2 gives 60.

  3. State the answer with its units

    60 km/h60\text{ km/h}

    The speed is 60 km/h.

Answer
60 km/h60\text{ km/h}
Question 2
2 markseasy
Which of these formulas correctly gives pressure?
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Worked solution

  1. Recall what pressure measures

    pressure=forcearea\text{pressure} = \frac{\text{force}}{\text{area}}

    Pressure measures how much force is pressing on each unit of area.

  2. Think about the units

    N/m2=Nm2\text{N/m}^2 = \frac{\text{N}}{\text{m}^2}

    The unit newtons per square metre is a force divided by an area, and the unit tells you the formula.

  3. Select the correct formula

    pressure=force÷area\text{pressure} = \text{force} \div \text{area}

    So pressure = force divided by area. For example, 180 N on 9 square metres gives 20 N per square metre.

Answer
pressure=forcearea\text{pressure} = \frac{\text{force}}{\text{area}}
Question 3
2 marksintermediate
Density is given by density = mass ÷ volume. Which rearrangement correctly gives the volume?
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Worked solution

  1. Write down the formula

    density=massvolume\text{density} = \frac{\text{mass}}{\text{volume}}

    Density is mass divided by volume.

  2. Multiply both sides by the volume

    density×volume=mass\text{density} \times \text{volume} = \text{mass}

    This clears the fraction and gives the mass.

  3. Divide both sides by the density

    volume=massdensity\text{volume} = \frac{\text{mass}}{\text{density}}

    So the volume is the mass divided by the density.

  4. Test the rearrangement with numbers

    847=12 cm3\frac{84}{7} = 12\text{ cm}^3

    A mass of 84 g and a density of 7 g per cubic centimetre give a volume of 12 cubic centimetres, and 7 times 12 is indeed 84.

  5. Check the answer by working backwards

    7×12=84 g7 \times 12 = 84\text{ g}

    Density times volume returns the mass, so the rearrangement is consistent.

  6. State the final answer

    volume=massdensity\text{volume} = \frac{\text{mass}}{\text{density}}

    The final answer is volume = mass divided by density.

Answer
volume=massdensity\text{volume} = \frac{\text{mass}}{\text{density}}
Question 4
4 markshard
A cyclist rides 2424 km at an average speed of 1616 km/h, rests for 1515 minutes, then rides a further 1818 km at an average speed of 2424 km/h. Work out the average speed for the whole journey, including the rest.
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Worked solution

  1. Write down the rule for average speed

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

    The rest counts as part of the total time, even though no distance is covered during it.

  2. Work out the time for the first ride

    2416=1.5 h\frac{24}{16} = 1.5\text{ h}

    Twenty-four km at 16 km/h takes one and a half hours.

  3. Convert the rest into hours

    15 min=1560=0.25 h15\text{ min} = \frac{15}{60} = 0.25\text{ h}

    Fifteen minutes is a quarter of an hour.

  4. Work out the time for the second ride

    1824=0.75 h\frac{18}{24} = 0.75\text{ h}

    Eighteen km at 24 km/h takes three quarters of an hour.

  5. Add the distances and the times

    total distance=42 km,total time=1.5+0.25+0.75=2.5 h\text{total distance} = 42\text{ km}, \quad \text{total time} = 1.5 + 0.25 + 0.75 = 2.5\text{ h}

    The cyclist covers 42 km in a total of 2.5 hours from start to finish.

  6. Divide the total distance by the total time

    422.5=16.8\frac{42}{2.5} = 16.8

    The average speed for the whole journey is 16.8 km/h.

  7. Check the answer by working backwards

    16.8×2.5=42 km16.8 \times 2.5 = 42\text{ km}

    Riding at 16.8 km/h for 2.5 hours covers 42 km, which matches the real total distance.

  8. Avoid the common error

    16+242=20≠16.8\frac{16 + 24}{2} = 20 \ne 16.8

    The mean of the two riding speeds is 20 km/h. That ignores the rest and ignores the different times spent riding, so it is wrong.

  9. Check the units

    kmhours=km/h\frac{\text{km}}{\text{hours}} = \text{km/h}

    Kilometres divided by hours gives km/h.

  10. State the final answer

    16.8 km/h16.8\text{ km/h}

    The final answer is 16.8 km/h.

Answer
16.8 km/h16.8\text{ km/h}
Question 5
5 markschallenging
Which of these is the greatest speed?
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Worked solution

  1. Decide on a common unit

    convert every speed into km/h\text{convert every speed into km/h}

    Speeds can only be compared once they are all written in the same unit.

  2. Convert 20 m/s

    20×3.6=72 km/h20 \times 3.6 = 72\text{ km/h}

    Multiplying metres per second by 3.6 gives kilometres per hour, because there are 3600 seconds in an hour and 1000 metres in a kilometre.

  3. Leave 70 km/h as it is

    70 km/h70\text{ km/h}

    This speed is already in the chosen unit.

  4. Convert 1.1 km per minute

    1.1×60=66 km/h1.1 \times 60 = 66\text{ km/h}

    There are 60 minutes in an hour, so multiply by 60.

  5. Convert 19 m/s

    19×3.6=68.4 km/h19 \times 3.6 = 68.4\text{ km/h}

    Nineteen metres per second is 68.4 kilometres per hour.

  6. Convert 1150 metres per minute

    1150×601000=69 km/h\frac{1150 \times 60}{1000} = 69\text{ km/h}

    In an hour this covers 69 000 metres, which is 69 km.

  7. Put the five speeds in order

    72>70>69>68.4>6672 > 70 > 69 > 68.4 > 66

    Once every speed is in km/h the comparison is straightforward.

  8. Identify the greatest

    20 m/s=72 km/h20\text{ m/s} = 72\text{ km/h}

    The greatest speed is 20 m/s, which is 72 km/h.

  9. Check the answer by working backwards

    72÷3.6=20 m/s72 \div 3.6 = 20\text{ m/s}

    Converting back gives 20 m/s, so the conversion was right.

  10. Avoid the common error

    20<7020 < 70

    Comparing the bare numbers 20 and 70 without converting would wrongly pick 70 km/h. The units must match first.

  11. Check the units

    m/s×3.6=km/h\text{m/s} \times 3.6 = \text{km/h}

    The factor 3.6 comes from multiplying by 3600 seconds and dividing by 1000 metres.

  12. Sanity-check the size of the answer

    20 m/s is about 45 mph20\text{ m/s is about }45\text{ mph}

    Seventy-two km/h is roughly 45 mph, a fast road speed, which is a sensible answer for the greatest of the five.

  13. Note how the formula rearranges

    speed=distancetime,distance=speed×time,time=distancespeed\text{speed} = \frac{\text{distance}}{\text{time}}, \quad \text{distance} = \text{speed} \times \text{time}, \quad \text{time} = \frac{\text{distance}}{\text{speed}}

    No rearrangement is needed here; the work is entirely in the units.

  14. Reflect on the method

    always convert before comparing\text{always convert before comparing}

    Comparing compound measures always starts by writing them all in one unit.

  15. State the final answer

    20 m/s20\text{ m/s}

    The final answer is 20 m/s, which is 72 km/h.

Answer
20 m/s=72 km/h20\text{ m/s} = 72\text{ km/h}

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