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HIGHER

3.10H Conversions and Units: Higher Tier Practice

EDEXCEL 1MA1 · Calculator allowed · about 65 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Convert 3.2 kilometres into metres.

(Total for Question 1 is 1 mark)

A recipe uses 450 millilitres of milk. Kit wants to make 0.6 of the recipe. Work out the volume of milk Kit needs in litres.

(Total for Question 2 is 2 marks)

Write 0.00042 kilograms in grams and then in milligrams.

(Total for Question 3 is 2 marks)

A rectangular metal plate measures 120 mm by 85 mm by 5 mm (thickness). Convert each dimension into centimetres and then work out the volume of the plate in cubic centimetres.

(Total for Question 4 is 3 marks)

A small bottle contains 250 cm³ of liquid with density 1.32 g/cm³. Calculate the mass of the liquid in grams and give the mass in kilograms to 3 significant figures.

(Total for Question 5 is 4 marks)

A cyclist travels 18 metres in 2 seconds. Work out the speed in metres per second and convert this speed into kilometres per hour, correct to the nearest whole number.

(Total for Question 6 is 5 marks)

An engineer is designing a cylindrical water tank with radius r metres and height h metres. Give an expression for the volume in cubic metres. The engineer needs the volume in litres. Show the algebraic steps to convert the expression for volume in m³ into litres and state the final expression in terms of r and h.

(Total for Question 7 is 6 marks)

A lorry carries fuel at a rate of 24 litres per minute to fill a generator. The generator requires fuel at a rate of 0.6 litres per second. Determine whether the lorry's supply rate is sufficient. Show your working and give a conclusion with appropriate units.

(Total for Question 8 is 8 marks)

Show that converting a speed of x metres per second into kilometres per hour gives 3.6x km/h. Then a car travels at 25 m/s. Without using a calculator, use your result to find its speed in km/h and determine whether it exceeds 90 km/h.

(a)Show that converting x m/s into km/h gives 3.6x km/h.(3)

(b)Use the result to find the speed of the car in km/h and state whether it exceeds 90 km/h.(4)

(Total for Question 9 is 7 marks)

Mark scheme · 3.10H Conversions and Units: Higher Tier Practice

Question 1

B1 3200 m cao
Answer: 3200 m

Question 2

M1 450 * 0.6 = 270 ml method or 450/1000 * 0.6
A1 0.27 L cao
Answer: 0.27 L

Question 3

M1 convert to grams: 0.00042 * 1000 = 0.42 g shown
A1 420 mg cao (0.42 g = 420 mg)
Answer: 0.42 g and 420 mg

Question 4

M1 correct conversion to cm: 12.0 cm, 8.5 cm, 0.5 cm
M1 method for volume: 12.0 * 8.5 * 0.5
A1 51 cm³ cao
Answer: 51 cm³

Question 5

M1 use mass = density * volume: 1.32 * 250
A1 330 g cao
M1 convert to kg: 330 / 1000
A1 0.330 kg awrt to 3 s.f. cao
Answer: 330 g and 0.330 kg

Question 6

M1 compute speed in m/s: 18 / 2 = 9 m/s
A1 9 m/s cao
M1 convert to km/h: 9 * 3.6 or 9 * 3600 / 1000
M1 method to nearest whole number shown
A1 32 km/h cao
Answer: 9 m/s, 32 km/h

Question 7

M1 write volume in m³: π * r² * h
M1 state conversion 1 m³ = 1000 L
M1 multiply expression by 1000 to convert to litres
A1 1000 * π * r² * h litres cao
M1 show any algebraic rearrangement if needed, e.g. V_L = 1000 π r² h oe
A1 final expression V_L = 1000 π r² h cao
Answer: Volume in m³ = π * r² * h. In litres: V = 1000 * π * r² * h L

Question 8

M1 convert lorry rate to litres per second: 24 / 60 = 0.4 L/s
A1 0.4 L/s cao
M1 compare 0.4 L/s with generator need 0.6 L/s
M1 state deficit: 0.6 - 0.4 = 0.2 L/s
A1 0.2 L/s shortfall cao
M1 convert shortfall to litres per minute if required: 0.2 * 60 = 12 L/min
A1 12 L/min cao
C1 conclusion: lorry rate is insufficient by 0.2 L/s or 12 L/min, so it cannot meet the generator demand
Answer: Lorry supplies 24 L/min = 0.4 L/s. Generator needs 0.6 L/s. Shortfall 0.2 L/s = 12 L/min. Conclusion: supply is insufficient.

Question 9

(a) M1 state or use 1 km = 1000 m and 1 h = 3600 s
(a) M1 correct method: convert x m/s to km/h as (x / 1000) * 3600 km/h
(a) A1 simplify 3600/1000 = 3.6 and conclude 3.6x km/h cao
(a) Answer: 3.6x km/h
(b) M1 substitute x = 25 into 3.6x: 3.6 * 25
(b) A1 90 km/h cao
(b) M1 compare 90 km/h with 90 km/h
(b) A1 correct conclusion: it does not exceed 90 km/h, it equals 90 km/h cao
(b) Answer: 90 km/h; it does not exceed 90 km/h, it equals 90 km/h

Conversions and Units: Higher Tier Practice - Worksheets, Questions and Revision