Compound measures.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Compound measures

Multiplicative reasoning

Lesson 2 of 4

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up

Multiplicative reasoning

Lesson 2 of 4

Answer each one, then check.

1

How many metres in a kilometre?

2

How many seconds in an hour?

3

Work out 240 ÷ 3.

4

How many cm³ in a litre?

5

What is the area of a rectangle 20 cm by 10 cm?

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up - Answers

Multiplicative reasoning

Lesson 2 of 4

1

How many metres in a kilometre?

1000

2

How many seconds in an hour?

3600

3

Work out 240 ÷ 3.

80

4

How many cm³ in a litre?

1000

5

What is the area of a rectangle 20 cm by 10 cm?

200 cm²

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Multiplicative reasoning

Lesson 2 of 4

1

Use speed = distance/time.

2

Use density = mass/volume.

3

Use pressure = force/area.

4

Convert between units for compound measures.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Formula Triangles

Multiplicative reasoning

Lesson 2 of 4

Cover what you want to find; what is left tells you what to do.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

The Three Formulae

Multiplicative reasoning

Lesson 2 of 4

Know these and their units.

Measure

Formula

Typical units

Speed

distance/time

km/h, m/s

Density

mass/volume

g/cm³, kg/m³

Pressure

force/area

N/m², Pa

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Speed

Multiplicative reasoning

Lesson 2 of 4

A train travels 240 km in 3 hours. Find its average speed.

1

Speed = distance/time

240/3

2

Work it out

80

ANSWER

80 km/h

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Density

Multiplicative reasoning

Lesson 2 of 4

A block of metal has mass 450 g and volume 60 cm³. Find its density.

1

Density = mass/volume

450/60

2

Work it out

7.5

ANSWER

7.5 g/cm³

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Pressure

Multiplicative reasoning

Lesson 2 of 4

A force of 600 N acts on an area of 0.5 m². Find the pressure.

1

Pressure = force/area

600/0.5

2

Work it out

1200

ANSWER

1200 N/m² (1200 Pa)

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Changing Units

Multiplicative reasoning

Lesson 2 of 4

Change 90 km/h into metres per second.

1

90 km is 90 000 m

90 × 1000

2

1 hour is 3600 s

90 000 ÷ 3600

3

Work it out

25

ANSWER

25 m/s

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Rearranging a Formula

Multiplicative reasoning

Lesson 2 of 4

Aluminium has density 2.7 g/cm³. Find the mass of a piece with volume 40 cm³.

1

Mass = density × volume

2.7 × 40

2

Work it out

108

ANSWER

108 g

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Watch the Units

Multiplicative reasoning

Lesson 2 of 4

Units must match before you divide.

Time

Change minutes to hours before dividing by km per hour: 30 minutes is 0.5 hours.

Area

1 m² is 10 000 cm², so pressure in N/m² needs area in m².

Density

1 g/cm³ is 1000 kg/m³.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Multiplicative reasoning

Lesson 2 of 4

Compound measure

A measure made from two other measures, such as speed.

Speed

Distance travelled per unit of time.

Density

Mass per unit of volume.

Pressure

Force per unit of area.

Newton (N)

The unit of force.

Pascal (Pa)

One newton per square metre.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Multiplicative reasoning

Lesson 2 of 4

YOUR TASK

Which Metal?

12 minutes

A mystery block has mass 540 g and volume 200 cm³. Work out its density and use the table to decide which metal it is: aluminium 2.7 g/cm³, iron 7.9 g/cm³, copper 8.9 g/cm³.

1

Divide mass by volume.

2

Compare with the table.

WHAT A GOOD ANSWER SHOWS

Density = 540 ÷ 200 = 2.7 g/cm³, so the block is aluminium.

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Can I...?

Multiplicative reasoning

Lesson 2 of 4

Use S = D ÷ T in all three forms.

Use D = M ÷ V in all three forms.

Use P = F ÷ A in all three forms.

Convert km/h to m/s.

Convert minutes to hours.

Use the correct units in an answer.

Choose the right formula.

Rearrange a formula.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Speed = distance ÷ time.

Density = mass ÷ volume.

Pressure = force ÷ area.

Convert units before calculating.

EXAM FOCUS

A block of metal has weight 40 N. Its largest face has area 0.02 m². Work out the pressure on the ground when it rests on this face. (2 marks)

Pressure is force divided by area, so the smaller the area, the greater the pressure. Make sure the area is in m² if the answer is in N/m².

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