PARTICULARES

A brass block has a mass of 187 g and a volume of 22 cm³. a Calculate the density of brass in g/cm³.

A brass cylinder has a mass of 53 g.

b Calculate the volume of the cylinder.

Solution

a Density = mass ÷ volume = 187 ÷ 22

= 8.5 g/cm³ b Density = mass

volume 8.5 = 53

v

8.5

v

^{= 53}

v

^{= 53}_8.5 ^{= 6.2}

So the volume is 6.2 cm³.

Multiply both sides by

v

^.

Divide both sides by 8.5.

Practising skills

1 Which is better value?

a 1.5 litres of lemonade for 65p or 1 litre for 44p?

b 15 pencils for 99p or 12 for 75p?

c 3 kg of grass seed for £4.20 or 85 g for 96p?

d 650 g of dog food for £2.15, 1.5 kg for £4.65 or 5 kg for £18?

2 Lucy swims 500 m in 2 minutes and 20 seconds.

Calculate her speed in a metres per second b kilometres per hour.

3 A block of metal has a mass of 475 g and a volume of 225 cm³. Calculate the density in

a g/cm³ b kg/m³. 4 A cube has sides of 16.4 cm.

Its mass is 1.2 kg.

Calculate its density in g/cm³.

5 Dave runs

n

metres in

t

seconds. Write his speed in

a m/s b km/h.

Unit 11 Working with compound units Band g

6 The mass of this block of silver is 1260 g.

a Calculate the density of silver in g/cm³.

b Find the mass of a 20 centimetre cube of silver in kilograms.

7 This graph shows the way that the speed of one car changes in a certain 10 second period.

a What is happening to the car between 5 and 7 seconds into its journey?

b What is the rate of change of speed during the fi rst 5 seconds?

c What term describes the rate of change of speed?

Developing fl uency

1 Jean is driving from the south of France to Paris.

She sees a road sign.

She knows that it takes her 1 hour to travel 60 miles.

The time now is 10 pm.

Jean wants to get to Paris by 2.30 am.

Will she be able to get to Paris by 2.30 am?

2 Alex buys a 150 g bar of chocolate for £1.75 in the UK.

He knows that a 1

2 pound bar will cost the equivalent of £2.75 in the USA.

Where is it better value, in the UK or in the USA?

3 Salima knows that the fuel tank on her car has a capacity of 9 gallons.

When she was in France she fi lled up the tank from half full at a cost of €30.

£1 = €1.25

Work out the cost in pounds of a litre of fuel in France.

4 Match the following descriptions with the graphs.

a An object travels at a constant speed of 15 metres per second for fi ve seconds.

b An object travels 15 metres in fi ve seconds without accelerating.

c An object accelerates at a constant rate and reaches a speed of 15 metres per second in fi ve seconds.

5 Andy says that these two graphs are for the same car at the same time.

Is Andy correct?

Explain how you know.

0 2 4 6 8 10

10 0 20 30

Distance travelled (m)

Time (s)

0 2 4 6 8 10

10 0 20 30

Speed (m/s)

Time (s) 6 A £1 coin has a mass of 9.5 g.

Its diameter is 22.5 mm and its thickness is 3.15 mm.

Calculate the density of a £1 coin in g/cm³.

7 a A block of metal A weighs 486 g and has a volume of 180 cm³. A block of metal B weighs 26 700 kg and has a volume of 3 m³. Use the formula density = mass

volume to calculate the density of each block.

b Ben has a block of metal A and a block of metal B.

Both blocks are identical sizes.

Which block is heavier?

8 The pressure exerted by an elephant’s foot is

f

^N/m2 (newtons per square metre).

Write this in newtons per square centimetre.

9 A concrete block has a volume of

v

^cm3 and a mass of

m

^g.

Write the density in kg/m³.

10 Show that V metres per second is about the same speed as 2.25V miles per hour.

Problem solving

1 A car is travelling at 50 kilometres per hour.

a Work out how long it will take the car to travel 24 metres.

A bridge is 24 metres long.

b When you calculate the time a car takes to cross the bridge that is 24 metres long, why could your answer be different from your answer to part a?

ReasoningExam-styleReasoningExam-style

Unit 11 Working with compound units Band g

2 Bob is following a fi tness programme. He wears a device that monitors his calorie burn.

The graph shows some information about his calorie burn during a period of 15 minutes.

0 0 1 2 3 4 5 6 7 8

5 10

Minutes

Calories per minute

15 20 25

a Work out the number of calories Bob burned over the fi rst 5 minutes of the 15-minute period.

b Work out the average rate at which he burned calories over the 15 minutes.

Bob found that his average rate of calorie burn was 2.5 calories per minute when he was awake and 1.5 calories per minute when he was asleep.

c Work out the total number of calories Bob burned during a 24-hour period when he spent 8 hours asleep.

3 The diagram shows two bottles of the same make of shampoo.

1.8 litres

£4 2.5 litres

£5.80

Which bottle gives the better value for money?

You must show your working to support your choice.

4 The density of wood is 0.9 g/cm.

a Work out the density of the wood in kg/m³.

x

litres of oil have a mass of

y

^grams.

b Work out an expression for the density of the oil in kg/m³. 5 Jim uses a water meter in his house.

The cost of the water he uses during one year is the sum of the meter charge + the charge for the water used.

The meter charge is £41.

The charge for the water used is £2.10 per 1000 litres.

On average Jim uses 170 litres of water per day.

Work out the cost of the water Jim uses in one year.

Exam-styleExam-styleExam-styleExam-style

6 The BMI of a person is calculated using the rule BMI = mass in kg ÷ (height in m)²

Ideal BMIs lie between 18 and 25.

Bill weighs 154 pounds and has a height of 183 cm.

Does Bill have an ideal BMI? Give a reason for your answer.

7 Brass alloy is made by melting together copper and zinc in the ratio 3 : 2 by mass.

The density of copper is 8.94 g/cm³. The density of zinc is 6.57 g/cm³

a Find the mass of copper and the mass of zinc in 100 grams of the alloy.

b Work out the density of brass alloy.

8 A company sells gold bars in the shape of cuboids.

The measurements of a bar are 80 mm by 40 mm by 16 mm.

The density of gold is 19.32 g/cm³.

Midas thinks that the mass of the block is over 1 kilogram.

Is he correct? Explain your answer.

9 Here is a graph that shows the costs of hiring a cement mixer and a concrete leveller.

0 0 5 10 15 20 25 30

2 4

Days

Cost (£)

6 8 10 12

cement mixer

concrete leveller

a Find the difference in the daily rate of hiring each item of equipment.

b Find the equations of the two graphs.

Exam-styleExam-style Higher Tier only

Exam-style Higher Tier only

Exam-style

Unit 11 Working with compound units Band g

Reviewing skills

1 Peter is driving in France.

At 10 am he sees a road sign which says Calais 308 km.

Peter knows that he can drive at a maximum speed of 55 miles per hour.

Work out the earliest time Peter can get to Calais.

2 A 275 cm³ block of expanded polystyrene has a mass of 15 g.

What is the density of expanded polystyrene in kg/m³?

3 Peter’s water is unmetered. His water company provides the graph below so residents can work out how much they will be charged. The chargeable value of Peter’s house is £140.

20000 19000 18000 17000 16000 15000 14000 13000 12000 11000 10000 9000 8000 7000 6000 5000 4000 3000 2000

200 180

160 140

120

Total cost (p)

Chargeable value (£) 100 80

60 40

20 1000

0

a How much will Peter be charged? Give your answer in £.

b How much does the water company charge per £ of chargeable value?

Strand 2 Properties of shapes

Unit 1 Band b

Common shapes

Unit 5 Band e

Angles in triangles and quadrilaterals

Unit 4 Band d

Rotational symmetry

Unit 8 Band g

Angles in a polygon

Foundation 1

Unit 9 Band h

Congruent triangles and proof Page 193

Unit 10 Band h

Proof using similar and congruent triangles

Page 204 Unit 11 Band j

Circle theorems

Higher 2

Unit 2 Band c

Line symmetry

Unit 6 Band e

Types of quadrilateral

Foundation 1

Unit 3 Band d

Angle facts

Unit 7 Band f

Angles and parallel lines

Foundation 1

Units 1–8 are assumed knowledge for this book. They are reviewed and extended in the Moving on section on page 189.

In document UNIVERSIDAD COMPLUTENSE DE MADRID (página 140-148)