1.1 Number Patterns and Sequences 21.2 Integers 51.3 Addition and Subtraction of Integers 121.4 Multiplication and Division of Integers 181.5 Combined Operations of Integers 22Mastery Practice 28

2.1 Comparing Fraction 322.2 Addition and Subtraction of Fractions 342.3 Multiplication and Division of Fractions 432.4 Combined Operations of Fractions 50Mastery Practice 55

3.1 Comparing Fraction 603.2 Addition and Subtraction of Fractions 603.3 Multiplication and Division of Fractions 633.4 Combined Operations of Fractions 70Mastery Practice 74

4.1 Indices 774.2 Multiplication of Numbers in Index Notation 794.3 Division of Numbers in Index Notations 814.4 Raising Numbers and Algebraic Terms in Index Notation to a Power 824.5 Negative Integral Indices 854.6 Fractional Indices 884.7 Computation Involving Laws of Indices 92Mastery Practice 96

Chapter 1 - Number Sequences and Integers 1

Chapter 2 - Fractions 31

Chapter 3 - Decimals 59

Chapter 4 - Indices 76

5.1 Exponential Notation 985.2 Addition and Substraction in Exponential Notation 1005.3 Multiplication and Division in Exponential Notation 1035.4 Combined Operations Using Exponential Notation 106Mastery Practice 109

6.1 Constructions 112Mastery Practice 130

7.1 Cubes and Cuboids 1357.2 Plan, Front Elevation and Side Elevation of 3-D Geometrical Shapes 138Mastery Practice 151

8.1 Equality 1568.2 Linear Equations in One Unknown 1588.3 Solutions of Linear Equations in One Unknown 162Mastery Practice 171

9.1 Relations 1759.2 Coordinates 1819.3 Scales of the Coordinate Axes 1869.4 Line Graphs 194Mastery Practice 199

10.1 Probability 204Mastery Practice 208

Chapter 5 - Exponential Notation 97

Chapter 6 - Geometrical Constructions 111

Chapter 7 - Solid Geometry 134

Chapter 8 - Linear Equations 155

Chapter 9 - Relations, Coordinates and Lines Graphs 174

Chapter 10 - Probability 203

Chapter 1 Number Sequences and Integers 1

1

Number Sequences and Integers

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 problem-solving; 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.

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

Answers:1. (a) 24 (b) 68 (c) 208 (d) 502. (a) 237, 273, 327, 372

(b) 865, 668, 658, 5683. (a) 1081 (b) 43

(c) 58 (d) 181444. (a) 13 (b) 402 (c) 67 (d) 9

Math Online

Visit these websites to know more about this chapter:http://www.mathsisfun.com/numberpatterns.html

2 Mathematics Mathayom 1

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 6 8 +2 +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 by adding 2 every time.

1 3 5 7 +2 +2 +2 +2

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

The cube numbers are13, 23, 33, 43, … = 1, 8, 27, 64, …

The triangular numbers are

1 3 6 10 +2 +3 +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

Chapter 1 Number Sequences and Integers 3

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, …

(a) 113, 115, 117, 119, 121, 123 +2 +2 +2 +2 +2 Even numbers. The 6th term is 123.

(b) 27, 64, 125, 216, 343, 512 ↓ ↓ ↓ ↓ ↓ ↓ 33 43 53 63 73 83

Cube numbers. The 6th term is 512.

(c) 25, 36, 49, 64, 81, 100 ↓ ↓ ↓ ↓ ↓ ↓ 52 62 72 82 92 102

Square numbers. The 6th term is 100

Try Question 1 in Test Yourself 1.1

B Recognising number pattern

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

1st term, T1 = 22nd term, T2 = T1 + 3 = 2 + 33rd term, T3 = T2 + 3 = 2 + 3 + 3 = 2 + (2 × 3)4th term, T4 = T3 + 3 = 2 + (3 × 3)nth term, Tn = 2 + [(n – 1) × 3]

The number pattern for this number sequence is Tn = 2 + [(n – 1) × 3]

Chapter 1 Number Sequences and Integers 15

15

Simplify each of the following.(a) 4 – (–3) (b) – 6 – 2

(a) 4 – (–3) = 7

0–3 –1–2 1 32 4

+7

Move 7 steps to the right.

(b) – 6 – 2 = –8

–4 0 21–2–3–5–6 –1

–8

Move 8 steps to the left.

16

–17 + (– 4) =

–17 + (– 4) = –17 – 4 + (– 4) = – 4

= –21

Try Question 7 in Test Yourself 1.3

To perform a subtraction involving three integers, always work out from left to right.

17

Simplify 8 – (– 4) – 3.

8 – (– 4) – 3 = 8 + 4 – 3 Work out from left to right.

= 12 – 3 = 9

Try Question 8 in Test Yourself 1.3

Simplifying addition and subtraction of integers:• a + (+b) = a + b• a + (–b) = a – b• a – (+b) = a – b• a – (–b) = a + b

16 Mathematics Mathayom 1

13

In the morning, the temperature of a city was –3°C. Its temperature then dropped by 5°C in the afternoon. At night, its temperature dropped by another 4°C. Find the temperature of the city at night.

–3 – 5 – 4 = –8 – 4 = –12

–1 31–3 5

–8

–4 40–8

–12

Therefore, the temperature of the city at night was –12°C.

Try Questions 9 – 11 in Test Yourself 1.3

1.3

1. Calculate each of the following.(a) –4 + 7 (b) –9 + 3(c) 5 + (–13) (d) –7 + (–2)(e) 6 + (–6) (f) –4 + (–8)

2. Simplify each of the following.(a) 5 + (–7) + 4 (b) 3 + 6 + (–10)(c) –7 + 1 + 2 (d) –4 + 9 + (–5)(e) –6 + (–4) + (–3) (f) –8 + (–7) + 10

3. A submarine was 40 m below sea level. Three hours later, it rose by 15 m. What was the new position of the submarine?

4. The temperature of a town was –3°C in the morning. Its temperature rose by 7°C at noon. What was the temperature of the town at noon?

26 Mathematics Mathayom 1

Example 1

Arrange –5, 4, –2, 3 and 1 in increasing order.

Increasing order: 1, –2, 3, 4, –5

• Didnotconsiderthenegativesign.• Positiveintegersarealwaysgreater

than negative integers.

–5 –3–4 10 2 3 4–1–2

Increasing order: –5, –2, 1, 3, 4

Example 2

Simplify 3 + (– 4).

–3 10 32–1–2–4

–7

Therefore, 3 + (– 4) = –7.

Finding the difference between the two integers.

Start from 3, move 4 steps to the left.

10 32–1

–4

Therefore, 3 + (– 4) = –1.

additionarrangingcombined operationdecreasing orderdivisiongreater thanhorizontalincreasing orderintegerlargest

less thanlike signmissing termsmultiplicationnegative directionnegative integernegative numbernegative signnumber linepositive direction

positive integerpositive numberpositive signproductquotientsequencesmallestsubtractionunlike signvertical

Chapter 1 Number Sequences and Integers 27

1. A sequence is a set of numbers written in an order that follows certain rule or pattern.

2. A number pattern is the method of obtaining numbers in a number sequence.

3. An integer is a whole number that has a positive sign (+) or a negative sign (–), including zero.

4. A positive integer is a whole number with a positive sign or without any sign.For examples, +3, +5, 9, 24.

5. A negative integer is a whole number with a negative sign.For examples, –2, – 4, –50.

6. Integers can be represented using a number line.For examples,

–3 10 32–1–2–4 4

Decreasing Increasing

7. Positive and negative numbers are frequently used in real life situations involving(a) an increase in value or a decrease in

value,(b) values greater than zero or less than

zero,(c) opposite direction.

8. Addition of integers is a process of finding the sum of two or more integers.For example, 2 + (–5) = –3

Start from 2, move 5 steps to the left.–3 10 2–1–2

–5

9. Subtraction of integers is a process of finding the difference between two integers.For example, 3 – (– 4) = 7

–3 10 32–1–2

+7

–4

10. Simplifying addition and subtraction of integers:•a + (+b) = a + b•a + (–b) = a – b•a – (+b) = a – b•a – (–b) = a + b

11. The product/quotient of two integers with the same sign is a positive integer.The product/quotient of two integers with different signs is a negative integer.• (+)×(+)=(+) • (+)÷(+)=(+)• (–)×(–) =(+) • (–)÷(–) =(+)• (+)×(–)=(–) • (+)÷(–) =(–)• (–)×(+)=(–) • (–)÷(+) =(–)

12. To perform computations involving combined operations,• calculatewithinthebracketsfirst.• f o l l o w e d b y d i v i s i o n o r

multiplication.• then addition or subtraction, from

left to right.

Move 7 steps to the right.

28 Mathematics Mathayom 1

Objective Questions

1. For the number sequence 4, 5, 7, 10, 14, , …, the missing number in the box is

A 19 C 16B 17 D 15

2. Given the number sequence 3, 5, 9, 15, 23, x, …, the value of x isA 28 C 35 B 33 D 41

3. If a number sequence follows the pattern of Tn = 2n + 1, what is the 21st term?A 43 C 20 B 40 D 21

2, 6, 10, 14, 18, …

4. What is the pattern of the above number sequence?A Tn = 2n + 2 B Tn = 4n – 2 C Tn = 2n – 2D Tn = 4n + 2

5. –34 – (–16) – (–7) =A –57 B –43 C –25D –11

6. How many negative integers are there between –5 and 2?A 6 C 4B 5 D 3

–12 –6 0x y

7. The above diagram shows a number line. The value of x + y isA –21 C –15B –18 D –9

8. 21 + (–7) + (–12) =A –40 C 2B –16 D 8

9. Which of the following is an integer?A 0 C 0.5

B 12

D 1 23

10. The integers between –3 and 1 areA –2, –1, 0 B –2, –1, 0, 1 C –3, –2, –1, 0D –3, –2, –1, 0, 1

11. If –7 m represents 7 m to the north, 5 m representsA 5 m to the north B 5 m to the south C 5 m to the eastD 5 m to the west

12. –13 – (–8) =A 21 B 5 C –5D –21

13. –20 – (–7) – 3 =A –10 B –16 C –24D –30

–17 –15 p q

14. The above diagram shows a number line. The value of p – q isA –24 C 2B –2 D 24

–3–4 10 2 3–1–2

15. The above number line showsA 3 – 4 – 1B 3 + (– 4) + (–1)C 3 + (– 4) + 3D 3 + (–7) + 3