MATHS 360 - GoGurucdn.goguru.com.sg/media/mce_sample/9789814684965.pdf · MATHS 360 NORMAL TECHNICAL (M)M360NTTB1_TP.indd 1 7/24/12 3:14 PM • ... CHAPTER 10 Volume and Surface Area

Dr Toh Tin LamReviewer: Stephen Chew

MATHS 360NORMAL TECHNICAL

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PrefaceMaths 360 Normal (Technical) is a new series of mathematics learning materials, designed primarily for students preparing for the Singapore GCE ‘N’ level examination. The series adopts the latest Mathematics Syllabus for Normal (Technical) from the Ministry of Education, Singapore.

The series consists of a textbook and a workbook for each level. The textbook examines mathematics from a real-world perspective, adopting a real-world approach that will help students appreciate the various applications of Mathematics. National Education (NE), financial literacy concepts and 21st century competencies are infused in the series, where appropriate.

There are a variety of learning experiences that include hands-on activities and the use of ICT. Cartoons and comics have been infused in the textbook and workbook where appropriate. They help students acquire new knowledge, as they depict what goes on in our daily lives and the decisions we make to achieve optimal results.

Students going through this series will find the learning of Mathematics an interesting and rewarding experience. At the same time, they will be prepared for the GCE ‘N’ level examination.

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PREFACE

CHAPTER 1 Numbers 1 1.1 Integers 2 1.2 The Four Operations 14 1.3 Squares and Square Roots 23 1.4 Cubes and Cube Roots 26 Chapter 1 Key Ideas 29 Chapter 1 Revision 30

CHAPTER 2 Fractions 33 2.1 Fractions 34 2.2 Comparing Fractions 41 2.3 Conversion between Improper Fractions and Mixed Numbers 44 2.4 Addition and Subtraction of Fractions 49 2.5 Multiplication of Fractions 55 2.6 Division of Fractions 59 2.7 Combined Operations on Fractions 63 Chapter 2 Key Ideas 67 Chapter 2 Revision 68

CHAPTER 3 Decimals 71 3.1 Fractions and Decimals 72 3.2 Compare Fractions and Decimals 76 3.3 Rounding Off 80 3.4 Estimation 86 3.5 The Four Operations of Decimals 92 Chapter 3 Key Ideas 103 Chapter 3 Revision 104

CHAPTER 4 Ratio 107 4.1 Introduction to Ratio 108 4.2 Equivalent Ratios 112 4.3 Problems involving Ratio 120 Chapter 4 Key Ideas 125 Chapter 4 Revision 126

Contents

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CHAPTER 5 Percentage 127 5.1 Expressing a Percentage as a Fraction or a Decimal 128 5.2 Converting a Fraction and a Decimal to a Percentage 134 5.3 Expressing a Quantity as a Percentage of Another 137 5.4 Finding a Quantity Given the Percentage 142 5.5 Finding the Whole Given a Percentage 145 5.6 Percentage Change 147 Chapter 5 Key Ideas 155 Chapter 5 Revision 156

CHAPTER 6 Angles 157 6.1 Angle Measurement 158 6.2 Types of Angles 162 6.3 Properties of Angles 167 6.4 Parallel Lines and Related Angles 174 Chapter 6 Key Ideas 179 Chapter 6 Revision 180

CHAPTER 7 Statistics 183 7.1 Collecting and Tabulating Data 184 7.2 Presenting and Interpreting Data 189 7.3 Analysing Statistical Diagrams 211 Chapter 7 Key Ideas 219 Chapter 7 Revision 220

CHAPTER 8 Symmetry 227 8.1 Line of Symmetry 228 8.2 Rotational Symmetry 238 Chapter 8 Key Ideas 244 Chapter 8 Revision 245 CHAPTER 9 Area and Perimeter 247 9.1 Conversion of Square Units 248 9.2 Parallelograms 250 9.3 Triangles 257 9.4 Trapeziums 262

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9.5 Area and Circumference of a Circle 267 9.6 Area and Perimeter of a Composite Plane Figure 274 Chapter 9 Key Ideas 278 Chapter 9 Revision 279 CHAPTER 10 Volume and Surface Area of Cubes and Cuboids 283 10.1 Conversion of Volume Units 284 10.2 Volume of Cubes and Cuboids 287 10.3 Surface Area of Cubes and Cuboids 293 10.4 Volume and Surface Area of Composite Solids 297 Chapter 10 Key Ideas 302 Chapter 10 Revision 303

CHAPTER 11 Algebra 305 11.1 Understanding Algebraic Expressions 307 11.2 Evaluating Algebraic Expressions and Formulae 318 11.3 Number Sequences 324 Chapter 11 Key Ideas 330 Chapter 11 Revision 331

CHAPTER 12 Mathematics in Practical Situations 333 12.1 Profi t and Loss 334 12.2 Hire Purchase 338 12.3 Household Finances 340 12.4 Time and Time Zones 343 Chapter 12 Key Ideas 349 Chapter 12 Revision 350

ANSWERS 353

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Numbers In Singapore, the temperature normally ranges between 25°C and 31°C. But doyou know that there are many places where the temperature drops to below 0°C?The lowest temperature ever recorded on Earth was −89.2°C, on 21 July 1983, at Vostok Station in Antarctica.

1CHAPTER

In this chapter, you will learn to:• use negative numbers• represent and arrange numbers on the number line• compare numbers using <, >, ≤, ≥• identify prime numbers• add, subtract, multiply and divide numbers using a calculator• � nd squares, cubes, square roots and cube roots of numbers using a calculator

1CHAPTER

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1-1Lesson Integers

The number system we use today is called the Hindi-Arabic system. We use ten basic symbols (known as digits) to form all the numbers in the system.

The position of the digit gives the value of the digit.

364

The value of each digit in 3 864 975 is shown below.3 864 975

In words, the number 3 864 975 is ‘three million, eight hundred and sixty-four thousand, nine hundred and seventy-fi ve’.

Zero serves an important function as a place holder.It keeps the other digits in the correct place value position.

E.g. seven hundred and fi ve = 705 ‘0’ in the tens place two thousand and three = 2003 ‘0’ in the hundreds place and tens place

Recall

Quick Check

460300

Discuss

Form the largest three-digit number with these digits: 3, 4 and 6 without repeating any digits.

5

70

900

4000

60 000

800 000

3 000 000

Give the value of the digit in bold for each of the following numbers.(a) 123 (b) 5247 (c) 680 174

(a) 100 (b) 40 (c) 80 000

2 Chapter 1

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Activity 1A Guess the Number

Negative NumbersLook at the sequence of numbers on the right. Can you fi ll in the boxes?

The number in the green box denotes ‘−1’, which is a negative number. It is read as ‘negative one’ not ‘minus one’.

In our daily life, many situations make use of negative numbers. The following are some examples.

(This game can be played as a class or in small groups.)

1 Randomly choose one student (call him or her X) to think of a number from a range of numbers. The rest of the class/group then tries to guess the number, by asking X Yes/No questions. Here is a sample conversation.

Student X : I am thinking of a number between 1 and 100. Student B : Is it more than 50? Student X : No. Student C : Is it an even number? Student X : No. Student D : Is it more than 20 but less than 40? Student X : Yes. Student E : Can you reach it by starting at zero and counting by fi ves? Student X : Yes. (At this stage, the class should be thinking of 25, 30 or 35.)

2 The winner is the one who can guess the correct number fi rst.

6 –1 5 –1 4 –1 3 –1 2 –1 1 –1 –1

–1 –1 –1 –1 –1 –1 –1 –1 –1 –1 –1 –1

‘G’ refers to the ground fl oor and –1 refers to one fl oor below the ground fl oor.

I am thinking of a number between 1 and 100.

Is it more than 50?

3Numbers

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When temperature falls below 0°C, it is recorded using negative numbers.

Some companies use negative numbers to refl ect their losses.E.g. Profi t = –$2 million

This means the company has incurred a loss of 2 million dollars.

–2 is read as ‘negative two’, not ‘minus two’.

The Number LineA number line can be used to show negative and positive numbers as shown below. The numbers to the left of zero are negative, and the numbers to the right of zero are positive.

Negative Positive

Negative numbers are always written with a negative (–) sign, but positive numbers are generally written without a positive (+) sign.

Activity 1B Negative Numbers

Look through some books or newspapers to search for two examples of negative numbers. How are negative numbers used in the two examples?

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

Profi t in millions ($) Company Growth

10

5

–5

1995 200520000 Year

Caution!!Numbers are arranged in ascending order on the number line. This means they are arranged from the smallest to the greatest, from left to right.The numbers to the left of 0 are smaller in value than the numbers to the right of 0.

4 Chapter 1

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