Collins Int. LS SB 9 - Look Inside

13.5mm spine

Collins

STAGE 9: STUDENT’S BOOK

Series editor: Alastair Duncombe Authors: Belle Cottingham, Alastair Duncombe, Rob Ellis, Amanda George, Claire Powis, Brian Speed This Student’s Book provides comprehensive coverage of Stage 9 of the Cambridge Lower Secondary Mathematics curriculum framework (0862) from 2020 through 26 clear and supportive chapters.

The course encourages students to make links between the topics, build on what they already know, and develop their confidence in Thinking and Working Mathematically.

Registered Cambridge International Schools benefit from high-quality programmes, assessments and a wide range of support so that teachers can effectively deliver Cambridge Lower Secondary.

Visit www.cambridgeinternational.org/lowersecondary to find out more.

This resource is endorsed by Cambridge Assessment International Education

✓ Provides support as part of a set of resources

for the Cambridge Lower Secondary Mathematics curriculum framework (0862) from 2020

✓ Has passed Cambridge International’s rigorous quality-assurance process

✓ Developed by subject experts ✓ For Cambridge schools worldwide

78554 Secondary Maths SB9 cvr.indd 1 Maths Maths Maths 99 Lower 9 Lower Lower Second Second Second Student Student Student Book Book Book 2nd 2nd 2nd Edition.indd Edition.indd Edition.indd 111

Find us at www.collins.co.uk/international facebook.com/collinsint @Collins_Int

Cambridge Lower Secondary Maths STAGE 9: STUDENT’S BOOK

Cambridge Lower Secondary Maths

Cambridge Lower Secondary

Maths

STAGE 9: STUDENT’S BOOK

ISBN 978-0-00-837855-4

9 780008 378554

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Angles

2

You will learn how to: • Derive and use the formula for the sum of the interior angles of any polygon.

• Know that the sum of the exterior angles of any polygon is 360°.

• Use properties of angles, parallel and intersecting lines, triangles and quadrilaterals to calculate missing angles.

Starting point Do you remember…

•

that corresponding, alternative and vertically opposite angles are equal?

For example, find the sizes of angles marked x and y. x y

54°

•

that angles in a triangle add up to 180° and that angles in a quadrilateral add up to 360°?

For example, find the sizes of the angles marked a and b.

310°

b

a

•

110°

how to use properties of the exterior angle of a triangle?

For example, calculate the size of angle u.

85°

45°

u

This will also be helpful when…

•

you learn to solve problems that involve bearings.

Chapter 2: Angles

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11

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Worked example 2 Martha wants to collect data on the wingspans of greenfinches (a type of bird). She expects the birds to have a wingspan of between 24 cm and 28 cm. Design a data collection sheet with four class intervals that would be suitable for collecting Martha’s data. All class intervals should have equal width.

Wingspan, x (cm)

Tally

The data collection sheet needs four rows, so split the interval between 24 cm and 28 cm into four classes:

Total

24 ≤ x < 25

4 cm

24 cm

25 ≤ x < 26

28 cm

24 x 25 25 x 26 26 x 27 27 x 28 25 26 27 28 24 1 cm 1 cm 1 cm 1 cm

26 ≤ x < 27

The data being collected are continuous so each class interval should be written with inequality symbols.

27 ≤ x < 28

Worked example 3 The table shows information about the number of cars for sale in a garage.

Cars less than 3 years old

Cars 3 or more years old

with air conditioning

without air conditioning

with air conditioning

without air conditioning

Petrol engine

11

5

4

6

Diesel engine

7

2

3

9

Show this information as a Venn diagram. less than 3 years old

with air conditioning

Begin by drawing the circles for the Venn diagram.

Three circles are needed as there are three categories: • type of engine (petrol or diesel) • age (less than 3 years or 3 or more years) • air conditioning (with or without) This Venn diagram has eight sections where numbers can be written. These match with the eight cells in the table.

petrol engine

30

Stage 9: Student’s Book

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3 Write as an ordinary number: a) 6 × 105

b) 3.8 × 104

c) 7 × 10–6

d) 8.03 × 10–3

e) 1 × 106

f) 9.09 × 10–4

g) 6.261 × 107

h) 5.077 × 10–5

i) 9.2 × 103

a) 20 000

b) 0.000082

c) 356 000

d) 0.03801

e) 1 500 000

f) 560

g) 0.000571

h) 17

i) 0.1

4 Write in standard form:

5 Benigno, Melinda and Sonto want to write the number 1 in standard form.

Benigno says it is 1 × 101 Melinda says it is 1 × 100 Sonto says it is just 1 Explain which answer is correct. Explain why the other two answers are incorrect.

6 Write each number in standard form.

Tip

3

a) 50 × 10

4

b) 0.8 × 10

c) 306 × 10

d) 44 × 10

e) 0.1 × 10

f) 10 × 106

–3

–4

5

7 Technology question Most scientific calculators have a standard form mode, or ‘Sci’ mode. In this mode, all calculated numbers are shown in standard form. Find out how to put your calculator into this mode.

Use your calculator to convert these numbers to standard form. a) 720 000

b) 0.0000081

c) 50 800 000

d) 0.00004105

e) 9 346 415

f) 0.0000004

You may find it easier to convert to ordinary numbers first.

Tip In standard form mode on many calculators, if you type an ordinary number and press ‘=’ or ‘enter’, the calculator displays the number in standard form.

8 Technology question To enter a number in standard form, such as 2.7 × 10–11, into a calculator, either: type 2.7 × 10, then the index key (which may be marked ^ or xy), and then −11, or type 2.7, then the key labelled ‘× 10x’, ‘EXP’ or ‘EE’ (which means ‘× 10 to the power’), and then −11.

Use a calculator to do these calculations. a) (3 × 106) × (2 × 107)

b) (6.8 × 107) ÷ (4 × 10–12)

c) (5 × 1014) + (7 × 1013)

d) (3.7 × 10–10) – (5.8 × 10–11)

Discuss In question 8, in which calculation(s) do the brackets affect the result? Explain your answers.

44

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Discuss In part a) of the Worked example, the direction of the 180° rotation was not stated. Should it have been?

Exercise 1 1 Shape X is transformed to shape Y. Copy and complete the description of this transformation.

10

A ………………… in the line …………….

9

y

8 7 6

X

Y

5 4 3 2 1 0

1

2

3

4

5

6

7

8

9

10

6

7

8

9

10

x

2 Shape X is transformed to shape Y. Copy and complete the description of the transformation.

10

A ………………… centre ………………..

9

through ……………….

8

y

X

7 6 5

Y

4 3 2 1 0

66

1

2

3

4

5

x

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