Focus Smart Plus Maths Textbook M1 samplebook

BCB031038

Focus Smart Plus Mathematics Textbook

covers the entire range of topics included in the Basic Education Curriculum B.E. 2551 (Revised Edition B.E. 2560). Notes and plenty of exercises are given to help students understand and apply the concepts in daily life.

BCB031038 978-616-541-306-0

,!7IG1G5-ebdaga!

Cover Textbook Mathematic M1.indd 1

Based on the Basic Education Curriculum B.E. 2551 (Revised Edition B.E. 2560)

3/26/18 4:41 PM

© Pelangi Publishing (Thailand) Co., Ltd. 2018 All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means without permission of Pelangi Publishing (Thailand) Co., Ltd. 2018

TPage Textbook Mathematic M1.indd 1

ISBN 978-616-541-306-0 First Published 2561

3/26/18 4:37 PM

Contents Chapter

Chapter

Chapter

Chapter

Chapter

1

2

3 4

5

Number Sequences and Integers

1

1.1 Number Patterns and Sequences 1.2 Integers 1.3 Addition and Subtraction of Integers 1.4 Multiplication and Division of Integers 1.5 Combined Operations of Integers Mastery Practice

2 5 12 18 23 28

Fractions

29

Decimals

57

Indices

73

2.1 Rational Numbers 2.2 Comparing Fractions 2.3 Addition and Subtraction of Fractions 2.4 Multiplication and Division of Fractions 2.5 Combined Operations of Fractions Mastery Practice

3.1 Comparing Decimals 3.2 Addition and Subtraction of Decimals 3.3 Multiplication and Division of Decimals 3.4 Combined Operations of Decimals Mastery Practice

4.1 4.2 4.3 4.4

Indices Multiplication of Numbers in Index Notation Division of Numbers in Index Notation Raising Numbers and Algebraic Terms in Index Notation to a Power 4.5 Negative Integral Indices 4.6 Fractional Indices 4.7 Computation Involving Laws of Indices Mastery Practice

Exponential Notation

5.1 Exponential Notation 5.2 Addition and Subtraction in Exponential Notation 5.3 Multiplication and Division in Exponential Notation 5.4 Combined Operations Using Exponential Notation Mastery Practice

30 32 34 43 50 56

58 58 61 68 72

74 76 78

79 82 85 89 93

94

95 97 100 103 107

Chapter

Chapter

Chapter

Chapter

Chapter

Chapter

6

7 8 9

10

11

Ratios, Proportions and Percentages

6.1 6.2 6.3 6.4

Ratio of Two Quantities Proportion Ratio of Three Quantities Relationships between Percentages, Fractions and Decimals 6.5 Computations and Problems Involving Percentages Mastery Practice

108

109 112 118

126 129 139

Linear Equations

141

Linear Equations in Two Variables

159

Geometrical Constructions

183

Solid Geometry

205

7.1 Equality 7.2 Linear Equations in One Unknown 7.3 Solutions of Linear Equations in One Unknown Mastery Practice

8.1 Linear Equations in Two Variables 8.2 Graphs of Linear Equations in Two Variables 8.3 Simultaneous Linear Equations in Two Variables Mastery Practice

9.1 Constructions Mastery Practice

10.1 Cross-sections of Solids 10.2 Cubes and Cuboids 10.3 Plan, Front Elevation and Side Elevation of 3-D Geometrical Shapes Mastery Practice

Statistics

11.1 Statistics 11.2 Pictograms, Bar Charts and Line Graphs 11.3 Constructing Pie Charts 11.4 Obtaining and Interpreting Information from Pie Charts 11.5 Solving Problems Involving Pie Charts Mastery Practice

142 144 148 157

160 165 172 181

184 203

206 208

211 224

226

227 229 241 243 245 250

Special Features

in This Book

Learning Outcomes States the learning objectives of each chapter.

Flashback

Test Yoursel f Evaluates the understanding of the students for every subtopic.

Lists the important mathematical terminologies of each chapter.

Helps students to recall the basic concepts for the chapter.

Math Online Provides direct access to useful websites by scanning the QR codes given.

Consists of brief and concise notes that summarise the concepts learnt in each chapter.

Mastery Practice Provides subjective questions covering the entire learning outcomes of each chapter.

Points out the important tips for students to take note.

Example

Points out the common mistakes that students make and the correct ways of answering questions.

Consists of sample questions with complete and comprehensive solutions.

Provides direct access to the interactive exercises by scanning the QR codes given.

1

Chapter

Number Sequences and Integers

Flashback 1. Find the next number in each number sequence. (a) 32, 30, 28, 26, … (b) 8, 23, 38, 53, … (c) 13, 26, 52, 104, … (d) 800, 400, 200, 100, …

2. Arrange these numbers. (a) 372, 327, 237, 273 (in ascending order) (b) 658, 568, 668, 865 (in descending order) 3. Calculate the following. (a) 434 + 635 + 12 = (b) 143 – 31 – 69 = (c) 812 ÷ 14 = (d) 567 × 32 = 4. Evaluate (a) 40 ÷ 10 × 2 + 5 = (b) 214 × 2 – (676 ÷ 26) = (c) 516 + 310 – 759 = (d) 608 ÷ 16 – 812 ÷ 28 =

By the end of this chapter, you should be able to • analyse and explain relations of a given pattern.

• specify or give examples and compare added integral numbers, subtracted integral numbers and 0.

• add, subtract, multiple and divide integral numbers for the purpose of problemsolving; be aware of validity of the answers.

• explain the results obtained from the addition, subtraction, multiplication and division, and explain the relationship between addition and subtraction and between multiplication and division of integral numbers.

• apply knowledge and properties of integral numbers for problem-solving.

• uses estimation appropriately in various situations, as well as for considering validity of answers reached through calculation.

(c) 67

Math Online Visit this website to know more about this chapter.

(d) 9

(b) 402

4. (a) 13

(d) 18,144

(c) 58

3. (a) 1,081

(b) 43

2. (a) 237, 273, 327, 372 (b) 865, 668, 658, 568 (c) 208

1. (a) 24

Answers: Mathematics Focus Smart + MATHAYOM

Chapter 1 Number Sequences and Integers

1

1

(d) 50

(b) 68

1.1 Number Patterns and Sequences A Recognising some simple number patterns A sequence is a set of numbers written in an order according to a certain pattern or rule. The pattern of a number sequence is the method of obtaining numbers in the number sequence. The numbers in a sequence are called terms.

The even numbers make a sequence.

2

4 +2

6

8

+2

+2

+2

The first term in the above sequence is 2. To get the next term, we add 2 to its previous term.

The odd numbers make a sequence

1

by adding 2 every time.

3 +2

5

7

+2

+2

+2

The square numbers are 12, 22, 32, 42, … = 1, 4, 9, 16 …

The cube numbers are 13, 23, 33, 43, … = 1, 8, 27, 64, …

The triangular numbers are 1

3 +2

6 +3

10 +4

+5

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, …. To get the next term, we add the last two terms.

1+1=2 1+2=3 2+3=5 3+5=8 5 + 8 = 13

Mathematics

2

Focus Smart + MATHAYOM

1

Example 1 Describe each of the following number sequences. List the 6th term of each sequence. (a) 113, 115, 117, 119, … (b) 27, 64, 125, 216, … (c) 25, 36, 49, 64, …

Solution (a) 113,

115,

+2

117, +2

119, +2

121,

123

+2

+2

Even numbers. The 6th term is 123. (b) 27, ↓ 33

64, 125, 216, 343, 512 ↓ ↓ ↓ ↓ ↓

43 53 63 73 83 Cube numbers. The 6th term is 512.

(c) 25, 36, 49, 64, 81, 100 ↓ ↓ ↓ ↓ ↓ ↓ 2 2 2 2 2 5 6 7 8 9 102 Square numbers. The 6th term is 100.

Try Question 1 in Test Yourself 1.1

B Recognising number patterns Consider the number sequence below.

2, 5, 8, 11, 14, …

We can get the next term by adding 3 to its previous term.

2, 5, 8, 11, 14, … +3 +3 +3

+3

1 st term, T1 = 2 2 nd term, T2 = T1 + 3 = 2 + 3 3 rd term, T3 = T2 + 3 = 2 + 3 + 3 = 2 + (2 × 3) 4 th term, T4 = T3 + 3 = 2 + (3 × 3) n th term, Tn = 2 + [(n – 1) × 3] The number pattern for this number sequence is

Tn = 2 + [(n – 1) × 3] Mathematics Focus Smart + MATHAYOM

Chapter 1 Number Sequences and Integers

1

3

Example 2 For each number sequence, find the number pattern and state the 10th term. (a) 2, 8, 14, 20, 26, … (b) 110, 90, 70, 50, 30, … (c) 3, 6, 12, 24, 48, …

Solution (a) 2,

8,

+6

14,

+6

20,

+6

26, …

+6

T1 = 2 T2 = T1 + 6 = 2 + 6 T3 = T2 + 6 = 2 + 6 + 6 = 2 + (2 × 6) T4 = T3 + 6 = 2 + (2 × 6) + 6 = 2 + (3 × 6) Tn = 2 + [(n – 1) × 6] = 2 + (6n – 6) = 6n – 4 T10 = 6(10) – 4 = 56 (b) 110,

90,

70,

–20

–20

50,

–20

30, …

–20

T1 = 110 T2 =T1 – 20 = 110 – 20 T3 =T2 – 20 = 110 – 20 – 20 = 110 – (2 × 20) T4 =T3 – 20 = 110 – (2 × 20) – 20 = 110 – (3 × 20) Tn = 110 – [(n – 1) × 20] = 110 – 20n + 20 = 130 – 20n T10 = 130 – 20(10) = –70 (c) 3, ×2

6,

12,

×2

×2

24,

48, …

×2

T1 = 3 T2 = T1 × 2 = 3 × 2 T3 = T2 × 2 = 3 × 2 × 2 = 3 × 22 T 4 = T 3 × 2 = 3 × 22 × 2 = 3 × 23 Tn = 3 × 2(n – 1) T10 = 3 × 2(10 – 1) = 3 × 29 = 1,536 Try Question 2 in Test Yourself 1.1

Mathematics

4

Focus Smart + MATHAYOM

1

1.1

Test Yourself

1. Describe each of the number sequences.

List the 10th term of each number sequence. (a) 100, 102, 104, 106, 108, … (b) 144, 169, 196, 225, 256, … (c) 79, 81, 83, 85, 87, 89, … (d) 1, 8, 27, 64, 125, … (e) 3, 6, 10, 15, 21, … (f) 1, 1, 2, 3, 5, 8, …

2. Find the number pattern for each number sequence.

List the 25th term of each number sequence. (a) (b) (c) (d) (e)

10, 9.75, 9.5, 9.25, 9, …

7, 15, 23, 31, 39, …

3, 6, 9, 12, 15, …

7, 9, 11, 13, 15, 17, …

6, 18, 54, 162, 486, …

1.2 Integers A Understanding whole numbers An integer is a whole number that has a positive sign (+) or a negative sign (–), including zero. A positive integer is a whole number with a positive sign or without any sign. For examples, +2, +7, 8, 12. A negative integer is a whole number with a negative sign. For examples, –3, –10, –20.

Integers ..., –3, –2, –1, 0, 1, 2, 3,...

Negative integers

Positive integers Zero

Mathematics Focus Smart + MATHAYOM

Chapter 1 Number Sequences and Integers

1

5

Example 3 (a) Write +79 in words. (b) Write negative one hundred and fifty in figures.

Solution (a) Positive seventy-nine

(b)

–150

Try Questions 1 & 2 in Test Yourself 1.2

Example 4 State the integers from the list below.

2 1 , 6, –2.9, 0, 3 5 4

–2, +

Solution The integers are –2, 6 and 0.

Try Question 3 in Test Yourself 1.2

B Representing integers using a number line Integers can be represented using a horizontal or a vertical number line.

Negative integers –4

–3

–2

Zero

–1

0

Positive integers 1

2

Horizontal number line

4 3

Positive integers

2 1 0

Zero

–1 –2 –3

Negative integers

–4

Vertical number line Mathematics

6

Focus Smart + MATHAYOM

1

3

4

Example 5 (a) Use a number line to represent the integers from –5 to 3. (b) Mark 6, –3, –1 and 4 on a number line.

Solution (a) (b)

–5 –4

–3

–2

–1

0

1

2

3

–3

–1

0

1

2

3

4

5

–2

6

Try Question 4 in Test Yourself 1.2

C Comparing two integers On a horizontal number line, an integer is always greater than the integers to its left and less than the integers to its right.

For example, –2 is greater than – 4 but is less than 1.

–4

–3

–2

0

–1

1

2

3

Example 6 (a) Which integer is smaller, –5 or 3? (b) Which integer is greater, –2 or –8?

Solution (a)

–5

–4

–3

–2

–1

0

1

2

3

–4

–3

–2

–1

0

– 5 is smaller than 3. (b)

–8

–7

–6

–5

–2 is greater than –8.

Try Question 5 in Test Yourself 1.2

Mathematics Focus Smart + MATHAYOM

Chapter 1 Number Sequences and Integers

1

7

D Arranging integers in order We can arrange integers in increasing or decreasing order using a number line.

Example 7 (a) Arrange – 4, 6, –3, 5, 0 and 1 in increasing order. (b) Arrange 6, 0, 4, –2 and – 4 in decreasing order.

Solution (a)

–4 –3

–2 –1

0

1

2

3

4

5

6

4

5

6

Increasing order: – 4, –3, 0, 1, 5, 6 (b)

–4 –3

–2 –1

0

1

2

3

Decreasing order: 6, 4, 0, –2, – 4 Try Questions 6 & 7 in Test Yourself 1.2

We can identify the largest integer and the smallest integer by arranging the given integers in order.

Example 8 Determine the largest integer and the smallest integer from the following set of integers.

1, –2, 3, 0, –5

Solution –5

–4

–3

–2

–1

0

1

2

3

The largest integer is 3 and the smallest integer is –5.

Try Question 8 in Test Yourself 1.2

Mathematics

8

Focus Smart + MATHAYOM

1

If the pattern of a sequence of integers is determined, we can find the missing terms in the sequence.

Example 9 Copy and complete the following sequence of integers. , –5, 0, 5,

,

Solution –10 , –5, 0, 5, 10 , 15 +5

+5 +5

+5

+5

Try Question 9 in Test Yourself 1.2

E Uses of positive and negative numbers A positive number is a number with a positive sign (+) or without any sign.

For examples, +1, +

1 1 , +0.2, 7, 1.5, 1 .

3 4

A negative number is a number with a negative sign (–).

For examples, –2, –

1 , – 0.9.

2

Positive and negative numbers are frequently used in real life situations involving: (a) an increase in value or a decrease in value For example, the price of an egg increased by 20 Satang can be written as +20 Satang. The price of an egg decreased by 10 Satang can be written as –10 Satang. (b) values greater than zero or less than zero For example, 36 m above sea level is written as +36 m. 50 m below sea level is written as –50 m. (c) opposite direction For example, if 8 km to the north is represented by +8 km, 10 km to the south is represented by –10 km.

Mathematics Focus Smart + MATHAYOM

Chapter 1 Number Sequences and Integers

1

9

Example 10 Use a positive or a negative number to represent each of the following word descriptions. (a) A profit of 500 Baht (b) 3 hours before take-off (c) 5 m above sea level

Solution (a) +500 Baht or 500 Baht (b) –3 hours (c) +5 m or 5 m Try Questions 10 & 11 in Test Yourself 1.2

Test Yourself

1.2

1. Write each of the following integers in words. (a) –17

(b) +23

(c) +48

(d) –69

(e) –205

(f)

+416

2. Write each of the following integers in figures. (a) Negative forty-two (b) Positive nine (c) Positive sixty-eight (d) Negative two hundred and seventy 3. State the integers from the list below.

–9, +

1 4 , 6.2, 4, –78, – , – 9.6 3 5

4. Use a number line to represent the integers from (a) –3 to 4,

(b) –20 to –15.

5. Copy and complete each of the following with ‘is greater than’ or ‘is less than’. (a) – 4

+2

(b) +8

–9

(c) –3

–7

(d) –10

–6

(e) +9

–20

Mathematics

10

Focus Smart + MATHAYOM

1

6. Arrange each of the following sets of integers in increasing order. (a) –5, –3, 0, –1, 2, – 4 (b) 8, –7, –5, 6, –9, 3 7. Arrange each of the following sets of integers in decreasing order. (a) 9, –12, – 6, 3, 7, –10 (b) –11, – 4, 8, –3, 5, – 6 8. Determine the largest integer and the smallest integer from each of the following sets of integers. (a) –7, 5, –9, 3, 0, –2 (b) 8, –12, 13, –15, 7, 11 (c) –20, –15, –19, –7, –30 (d) 5, –15, –20, 15, 10, –5 9. Copy and complete each of the following sequences of integers. (a) 9, 5, 1, (b) –12, (c)

, , , ,

, , 3, 8,

,

(d) –32, (e)

,

, –10, – 4 , –23, –20,

, –13, – 4,

10. Use a positive or a negative number to represent each of the following word descriptions. (a) A loss of 800 Baht (b) 42 m below sea level (c) An increase of 5 m (d) 8°C below freezing point (e) 1 hour after take-off 11. Copy and complete each of the following. (a) If 2 km to the east is written as +2 km, 3 km to the west is written as . (b) If going up 4 steps is written as written as –5.

, going down 5 steps is

Mathematics Focus Smart + MATHAYOM

Chapter 1 Number Sequences and Integers

1

11

BCB031038

Focus Smart Plus Mathematics Textbook

covers the entire range of topics included in the Basic Education Curriculum B.E. 2551 (Revised Edition B.E. 2560). Notes and plenty of exercises are given to help students understand and apply the concepts in daily life.

BCB031038 978-616-541-306-0

,!7IG1G5-ebdaga!

Cover Textbook Mathematic M1.indd 1

Based on the Basic Education Curriculum B.E. 2551 (Revised Edition B.E. 2560)

3/26/18 4:41 PM