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GCSE · Ratio, Proportion and Rates of Change - Compound Measures

5.5 Speed and Density

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Which of these is the correct formula for calculating average speed?

A) speed = distance x time
B) speed = distance / time
C) speed = time / distance
D) speed = distance / time²

(Total for Question 1 is 1 mark)

A jogger runs 18 km in 1.5 hours at a constant speed. Work out her average speed, in km/h.

(Total for Question 2 is 2 marks)

A block of cheese has a mass of 480 g and a volume of 320 cm^3. Work out the density of the cheese, in g/cm^3.

(Total for Question 3 is 2 marks)

A cyclist travels at a constant speed of 20 m/s. Work out this speed in km/h.

(Total for Question 4 is 2 marks)

A coach travels at an average speed of 56 km/h for 2 hours 30 minutes. Work out the distance travelled.

(Total for Question 5 is 3 marks)

A car travels 195 miles at an average speed of 60 mph. Work out how long the journey takes. Give your answer in hours and minutes.

(Total for Question 6 is 3 marks)

The density of aluminium is 2.7 g/cm^3. A block of aluminium has a mass of 189 g. Work out the volume of the block.

(Total for Question 7 is 2 marks)

A liquid has a density of 1.25 g/cm^3. Work out the mass of 400 cm³ of the liquid. Give your answer in kilograms.

(Total for Question 8 is 3 marks)

The density of ice is 0.92 g/cm^3. Work out this density in kg/m^3.

(Total for Question 9 is 2 marks)

Priya drives 90 km in 1 hour 12 minutes. She then drives a further 60 km in 48 minutes. Work out her average speed for the whole journey. Give your answer in km/h.

(Total for Question 10 is 4 marks)

The distance-time graph shows Amir's cycle ride from home to the library and back.

(a)Work out Amir's speed on the journey to the library. Give your answer in km/h.

(Total for Question 11a is 2 marks)(2)

(b)Write down what is happening to Amir's distance from home between 15 and 25 minutes.

(Total for Question 11b is 1 mark)(1)

(c)Work out Amir's speed on the journey back home. Give your answer in km/h.

(Total for Question 11c is 2 marks)(2)

(Total for Question 11 is 5 marks)

A cheetah runs at a constant speed of 28 m/s. Show that this speed is equivalent to 100.8 km/h.

(Total for Question 12 is 3 marks)

A rock has a mass of 350 g and a volume of 140 cm^3. The density of water is 1 g/cm^3. Determine, showing your working, whether the rock will float or sink in water.

(Total for Question 13 is 3 marks)

A container holds 300 cm³ of oil, density 0.92 g/cm³, floating on top of 500 cm³ of water, density 1 g/cm^3. Work out the total mass of liquid in the container. Give your answer in kilograms.

(Total for Question 14 is 3 marks)

A shipping container holds gravel with a mass of 3.6 tonnes and a volume of 2.4 m^3. Work out the density of the gravel in kg/m^3.

(Total for Question 15 is 3 marks)

A ferry crosses a channel of length 32 km at an average speed of 24 km/h. It departs at 09:15. At what time does it arrive? Give your answer using the 24-hour clock.

(Total for Question 16 is 4 marks)

A snail moves at a constant speed of 0.048 km/h. Work out this speed in centimetres per minute.

(Total for Question 17 is 3 marks)

An alloy is made by combining 60 cm³ of copper, density 8.9 g/cm³, with 40 cm³ of tin, density 7.3 g/cm^3. Work out the density of the alloy. Give your answer correct to 3 significant figures.

(Total for Question 18 is 4 marks)

The speed limit on a stretch of road is 70 mph. A car travels 21 km in 10 minutes at a constant speed. Given that 5 miles is approximately equal to 8 km, determine whether the car is exceeding the speed limit. You must show your working.

(Total for Question 19 is 5 marks)

A stone is lowered into a cylindrical measuring cylinder of radius 3 cm. The water level rises by 4.5 cm. The stone has a mass of 315 g. Work out the density of the stone. Give your answer correct to 3 significant figures. (Volume of a cylinder = π r² h)

Diagram NOT accurately drawn

(Total for Question 20 is 4 marks)

Two cars start at the same time and travel towards each other from two towns 210 km apart. Car A travels at a constant speed of x km/h. Car B travels at a constant speed of (x + 15) km/h. The cars meet after 1 hour 24 minutes. Form and solve an equation to find the value of x.

(Total for Question 21 is 5 marks)

A brick exerts a pressure of 15 000 Pa on the ground. The brick has a mass of 6 kg. Take the gravitational field strength as g = 10 N/kg. Given that force = mass x g and pressure = force / area, work out the area of the brick in contact with the ground. Give your answer in cm^2.

(Total for Question 22 is 4 marks)

Mark scheme · 5.5 Speed and Density

Question 1

B1 B
Answer: B

Question 2

M1 18 / 1.5 oe
A1 12 (km/h) cao
Answer: 12 km/h

Question 3

M1 480 / 320 oe
A1 1.5 (g/cm³) cao
Answer: 1.5 g/cm³

Question 4

M1 20 x 3.6 oe, e.g. 20 x 3600 / 1000
A1 72 (km/h) cao
Answer: 72 km/h

Question 5

M1 2 hours 30 minutes = 2.5 hours oe
M1 56 x 2.5 (dep)
A1 140 (km) cao
Answer: 140 km

Question 6

M1 195 / 60 oe
A1 3.25 (hours) oe, e.g. 3 1/4
B1 3 hours 15 minutes ft from a correct time in hours
Answer: 3 hours 15 minutes

Question 7

M1 189 / 2.7 oe
A1 70 (cm³) cao
Answer: 70 cm³

Question 8

M1 1.25 x 400 oe
A1 500 (g)
B1 0.5 (kg) ft from a correct mass in grams
Answer: 0.5 kg

Question 9

M1 0.92 x 1000 oe
A1 920 (kg/m³) cao
Answer: 920 kg/m³

Question 10

M1 total distance = 90 + 60 = 150 (km)
M1 total time = 72 + 48 = 120 minutes = 2 hours oe
dM1 150 / 2 (dep on both previous method marks)
A1 75 (km/h) cao
Answer: 75 km/h

Question 11

(a) M1 15 minutes = 0.25 hours oe
(a) A1 40 (km/h) cao
(a) Answer: 40 km/h
(b) B1 Amir is stationary / at the library (not moving) oe
(b) Answer: Amir is stationary at the library.
(c) M1 25 minutes = 5/12 hour oe, e.g. 25/60
(c) A1 24 (km/h) cao
(c) Answer: 24 km/h

Question 12

M1 28 x 60 x 60 (= 100800) oe, or 28 x 3.6
M1 100800 / 1000 (dep), or equivalent single-step method giving km/h
A1 100.8 (km/h) cso
Answer: 100.8 km/h (given, shown)

Question 13

M1 350 / 140 oe
A1 2.5 (g/cm³) oe
C1 correct conclusion with reason, e.g. 'sinks, since 2.5 > 1' ft from their density
Answer: Sinks, since its density (2.5 g/cm³) is greater than the density of water (1 g/cm³).

Question 14

M1 300 x 0.92 (= 276) oe
M1 500 x 1 (= 500) oe
A1 0.776 (kg) cao, allow 776 (g)
Answer: 0.776 kg

Question 15

M1 3.6 tonnes = 3600 kg oe
M1 3600 / 2.4 (dep)
A1 1500 (kg/m³) cao
Answer: 1500 kg/m³

Question 16

M1 32 / 24 (= 4/3 or 1.333...) oe
M1 1.333... hours converted to 1 hour 20 minutes (dep) oe
dM1 09:15 + 1 hour 20 minutes (dep on previous method mark)
A1 10:35 cao
Answer: 10:35

Question 17

M1 0.048 x 1000 x 100 (= 4800) oe, converting km/h to cm/h
M1 4800 / 60 (dep)
A1 80 (cm/min) cao
Answer: 80 cm/min

Question 18

M1 mass of copper = 60 x 8.9 (= 534) oe
M1 mass of tin = 40 x 7.3 (= 292) oe
dM1 (534 + 292) / (60 + 40) (dep on both previous method marks)
A1 8.26 (g/cm³) cao
Answer: 8.26 g/cm³

Question 19

M1 10 minutes = 1/6 hour oe
dM1 21 / (1/6) (= 126) km/h (dep)
M1 126 x 5/8 oe, converting km/h to mph
A1 78.75 (mph), allow awrt 78.8
C1 correct conclusion ft, e.g. 'Yes, exceeding the limit since 78.75 > 70'
Answer: 78.75 mph; yes, the car is exceeding the speed limit.

Question 20

M1 π x 3² x 4.5 oe
A1 awrt 127 (cm³), e.g. 127.2 to 127.3
dM1 315 / their volume (dep)
A1 awrt 2.48 (g/cm³)
Answer: 2.48 g/cm³ (3 s.f.)

Question 21

M1 1 hour 24 minutes = 1.4 hours oe
M1 1.4x + 1.4(x + 15) = 210 oe, forming a correct equation
M1 2.8x + 21 = 210 oe, correct expansion/simplification
dM1 2.8x = 189 (dep)
A1 x = 67.5 cao
Answer: x = 67.5 (Car A's speed is 67.5 km/h)

Question 22

M1 6 x 10 (= 60) oe, finding the force
dM1 60 / 15000 (= 0.004) (dep), finding the area in m²
M1 0.004 x 10000 oe, converting m² to cm²
A1 40 (cm²) cao
Answer: 40 cm²

Speed and Density - Worksheets, Questions and Revision