A car travels 150 km in 2 hours 30 minutes.
Work out the average speed of the car in km/h. [2]
- $150 \div 2.5$ (or $150 \div 150 \times 60$)M1
- 60 km/hA1
- Answer: 60 km/h
- Examiner tip: 2 hours 30 minutes is 2.5 hours, not 2.3 hours.
Mia cycles at an average speed of 12 km/h for 45 minutes.
How far does she cycle? [2]
- $12 \times 0.75$ or $12 \times \frac{45}{60}$ or $3 \times 3$M1
- 9 kmA1
- Answer: 9 km
- Examiner tip: Change minutes into hours before multiplying by a speed in km/h.
A solid metal block is a cuboid measuring 8 cm by 5 cm by 2 cm.
The mass of the block is 632 g.
Work out the density of the metal. [3]
- volume $= 8 \times 5 \times 2$ (= 80)M1
- $632 \div$ their volumeM1
- 7.9 g/cm³A1
- Answer: 7.9 g/cm³
- Examiner tip: Density = mass ÷ volume; always state the units (g/cm³).
A box exerts a force of 750 newtons on the floor.
The area of the box in contact with the floor is 0.25 m².
(a) Work out the pressure on the floor. Use pressure $= \dfrac{\text{force}}{\text{area}}$ [2]
(b) The box is replaced by one with the same force but half the contact area. Describe the effect on the pressure. [1]
- (a) $750 \div 0.25$ oeM1
- 3000 (units not required; if given, accept N/m² or Pa)A1
- (b) the pressure doubles oe, e.g. 'it is twice as big', or 6000 (N/m²) stated; 'increases' alone scores B0B1
- Answer: (a) 3000 N/m² (b) the pressure doubles
- Examiner tip: Dividing by a decimal less than 1 makes the answer bigger – 187.5 means you multiplied.
A train is 120 m long. It travels at a constant speed of 54 km/h.
(a) Convert 54 km/h into metres per second. [2]
(b) The train goes through a tunnel that is 240 m long. Work out the time, in seconds, from the front of the train entering the tunnel to the back of the train leaving it. [2]
- (a) $54 \times 1000 \div 3600$ (or $\div 60 \div 60$)M1
- 15 m/sA1
- (b) $(240 + 120) \div$ their 15M1
- 24 sA1
- Answer: (a) 15 m/s (b) 24 seconds
- Examiner tip: The train must travel the tunnel length PLUS its own length before the back leaves.
An alloy is made by mixing 120 cm³ of metal A with 60 cm³ of metal B.
Metal A has density 8.9 g/cm³. Metal B has density 2.7 g/cm³.
Assume the volume of the alloy is the sum of the two volumes.
Work out the density of the alloy. Give your answer correct to 3 significant figures. [4]
- mass of one metal: $120 \times 8.9 = 1068$ or $60 \times 2.7 = 162$M1
- total mass $1068 + 162 = 1230$M1
- total mass $\div (120 + 60)$M1
- 6.83 g/cm³A1
- Answer: 6.83 g/cm³
- Examiner tip: Do not average the two densities (5.8) – find the total mass and divide by the total volume.
Priya drives 45 km at an average speed of 60 km/h.
She then drives a further 30 km, which takes her 40 minutes.
Work out her average speed for the whole journey. Give your answer to 1 decimal place. [4]
- $45 \div 60$ (= 0.75 hours or 45 minutes)M1
- total time $0.75 + \frac{40}{60}$ $(=1.41\dot{6}$ hours$)$ or $45 + 40$ $(= 85$ minutes$)$M1
- $(45 + 30) \div$ their total time in hours, e.g. $75 \div 1.41\dot{6}$, or $75 \div 85 \times 60$M1
- 52.9 (units not required; accept 52.94… seen if then rounded incorrectly)A1
- Answer: 52.9 km/h
- Examiner tip: Average speed is total distance ÷ total time – never the mean of the two speeds.
A stone has a mass of 250 g, correct to the nearest 10 g.
Its volume is 32 cm³, correct to the nearest cm³.
(a) Work out the upper bound for the density of the stone. [3]
(b) By considering bounds, work out the density of the stone to a suitable degree of accuracy. You must give a reason for your answer. [2]
- (a) 255 or 31.5 seenB1
- upper bound of mass $\div$ lower bound of volume, i.e. $255 \div 31.5$M1
- 8.095… (accept 8.1 or better)A1
- (b) $245 \div 32.5$ (= 7.538…)M1
- 8 g/cm³, because both bounds round to 8 to 1 significant figureA1
- Answer: (a) 8.095… g/cm³ (b) 8 g/cm³ (both bounds round to 8 to 1 s.f.)
- Examiner tip: For the maximum density divide the BIGGEST mass by the SMALLEST volume.
A coach leaves a bus station at 10:50
It travels 168 km at an average speed of 80 km/h.
At what time does the coach arrive? [3]
- $168 \div 80$ (= 2.1 hours) oe, e.g. 80 km in 60 min so 8 km in 6 minM1
- converts 0.1 hours to 6 minutes, or 2.1 hours to 2 hours 6 minutes or 126 minutes (do not award for 2 hours 10 minutes)M1
- 12:56 (accept 12.56, 12 56, 12:56 pm). 13:00 from 10:50 + 2 h 10 min scores M1 M0 A0A1
- Answer: 12:56
- Examiner tip: 2.1 hours is 2 hours 6 minutes, not 2 hours 10 minutes: multiply the decimal part by 60.
Leah runs at an average speed of 5 metres per second.
Sam runs at an average speed of 20 kilometres per hour.
Who runs faster? You must show your working. [3]
- starts to convert to common units, e.g. $5 \times 60$ (= 300 m per minute) or $5 \times 3600$ (= 18 000 m/h) or $20 \times 1000$ (= 20 000 m/h) or $20 \div 60$M1
- complete conversion of one speed: 18 (km/h) or 5.5… / 5.6 (m/s) or two speeds in the same units, e.g. 18 000 and 20 000 m/hM1
- Sam, with correct comparable figures, e.g. 18 km/h < 20 km/h or 5 m/s < 5.55… m/s (accept 5.6)C1
- Answer: Sam (Leah's 5 m/s = 18 km/h, which is less than 20 km/h)
- Examiner tip: A bare 'Sam' with no supported comparison scores nothing: both speeds must end up in the same units.
A bottle contains 2.5 litres of olive oil.
The density of the olive oil is 0.91 g/cm³.
Work out the mass of the olive oil in the bottle. Give your answer in kilograms. [3]
(1 litre = 1000 cm³)
- 2500 (cm³) seen or used, or density written as 0.91 kg per litreB1
- their volume × 0.91 in consistent units, e.g. $2500 \times 0.91$ (= 2275 g) or $2.5 \times 0.91$ (kg)M1
- 2.275 kg (accept 2.27 or 2.28). 2275 with no conversion to kg scores B1 M1 A0A1
- Answer: 2.275 kg
- Examiner tip: Mass = density × volume, but the volume must be in cm³ to match g/cm³ — then divide grams by 1000 for kg.
Tom cycles from his home to a lake, stops for a rest, cycles further on to a café, then cycles straight back home.
The distance–time graph shows his journey.
(a) For how many minutes did Tom rest? [1]
(b) Work out Tom's average speed, in km/h, for the first 30 minutes of his journey. [2]
(c) On which part of the journey was Tom cycling fastest? Give a reason for your answer. [1]
- (a) 15 (minutes)B1
- (b) $10 \div 30$ (km per minute) or $10 \div 0.5$ or $10 \times 2$M1
- (b) 20 (km/h); answer of 0.33… with no conversion scores M1 A0A1
- (c) the journey back home (from 75 to 120 min) with a reason, e.g. 'the line is steepest' or speed 24 km/h compared with 20 km/h and 16 km/h; allow 'covers 18 km in 45 min' compared with another sectionC1
- Answer: (a) 15 minutes (b) 20 km/h (c) the return journey home — steepest line (24 km/h)
- Examiner tip: Speed on a distance–time graph is the gradient: the steepest section, up or down, is the fastest.
A solid block in the shape of a cuboid measures 20 cm by 40 cm by 50 cm.
The block exerts a force of 240 newtons on a floor.
The block can be placed on the floor on any one of its faces.
Work out the difference between the greatest possible pressure and the least possible pressure on the floor.
Give your answer in N/m². [4]
pressure $= \dfrac{\text{force}}{\text{area}}$
- identifies the smallest or largest face: $20 \times 40$ (= 800 cm²) or $40 \times 50$ (= 2000 cm²), or 0.08 m² or 0.2 m²M1
- correct conversion of area to m² (e.g. $800 \div 10\,000$) or lengths converted to metres before multiplying (0.2, 0.4, 0.5)M1
- $240 \div 0.08$ (= 3000) and $240 \div 0.2$ (= 1200), or both pressures in N/cm² (0.3 and 0.12) with intention to subtractM1
- 1800 (N/m²); 0.18 (N/cm²) scores M1 M0 M1 A0A1
- Answer: 1800 N/m²
- Examiner tip: Converting cm² to m² means dividing by 10 000, not 100 — convert the lengths to metres first to avoid this.
Town A and town B are 161 km apart along a straight road.
A car leaves town A at 10:00 and drives towards town B at a constant speed of 64 km/h.
A lorry leaves town B at 10:15 and drives towards town A along the same road at a constant speed of 52 km/h.
At what time do the car and the lorry pass each other? [4]
- distance travelled by car before 10:15: $64 \times 0.25$ (= 16 km), or $64 \times \frac{15}{60}$P1
- remaining distance $161 - 16$ (= 145 km) or combined (closing) speed $64 + 52$ (= 116 km/h); alternatively forms equation $64(t + 0.25) + 52t = 161$P1
- $145 \div 116$ (= 1.25 hours or 75 minutes), or solves to $t = 1.25$P1
- 11:30 (accept 11.30 am)A1
- Answer: 11:30
- Examiner tip: The car has a 15-minute head start: work out how far it has gone before the lorry sets off, then use the combined speed.
A crown is made only from gold and silver.
The density of gold is 19.3 g/cm³. The density of silver is 10.5 g/cm³.
The crown has a mass of 705 g and a volume of 42 cm³.
Assume the volume of the crown is equal to the volume of gold plus the volume of silver.
Work out the percentage of the mass of the crown that is gold. Give your answer correct to 1 decimal place. [5]
- sets up equations or a single equation in volumes, e.g. $g + s = 42$ and $19.3g + 10.5s = 705$, or $19.3x + 10.5(42 - x) = 705$ (allow equations in masses, e.g. $\frac{m}{19.3} + \frac{705 - m}{10.5} = 42$)M1
- correct method to eliminate a variable or clear fractions, e.g. $8.8x = 705 - 441$ (= 264), or $10.5m + 19.3(705 - m) = 42 \times 19.3 \times 10.5$M1
- volume of gold = 30 (cm³) (or volume of silver = 12 cm³); via the mass route, mass of gold = 579 (g) (or mass of silver = 126 g)A1
- $\frac{579}{705} \times 100$ with mass of gold from their volume, e.g. $30 \times 19.3$ (= 579 g); ft their volume of goldM1
- 82.1 (%)A1
- Answer: 82.1%
- Examiner tip: Mass and volume both add, but densities do not: set up one equation for volume and one for mass.
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