MODUL NOTA RINGKAS & LATIHAN MATHEMATICS FORM 1

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(BERASASKAN

MATHEMAT

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N BUKU TEKS)

TICS FORM 1

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CONTENTS

CHAPTERS PAGES

CONTENTS i
CHAPTER 1: Rational Numbers 1–9
CHAPTER 2: Factors and Multiples 10 – 16
CHAPTER 3: Squares, Square Roots, Cubes and Cube Roots 17 – 22
CHAPTER 4: Ratios, Rates and Proportions 23 – 30
CHAPTER 5: Algebraic Expressions 31 – 35
CHAPTER 6: Linear Equations 36 – 43
CHAPTER 7: Linear Inequalities 44 –49
CHAPTER 8: Lines and Angles 50 – 57
CHAPTER 9: Basic Polygons 58 – 64
CHAPTER 10: Perimeter and Area 65 – 69
CHAPTER 11: Introduction of Set 70 – 74
CHAPTER 12: Data Handling 75 – 84
CHAPTER 13: The Pythagoras’ Theorem 85 – 89

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MODUL MATHS F1
CHAPTER 1 : RATIONAL NUMBERS

A) INTEGERS

1. Numbers written with the _______ sign or without any sign is known as positive numbers.
The examples are:
i) ___________
ii) __________
iii) __________

2. Numbers written with the ‘-’ sign are known as __________________________.
The examples are:
i) ___________
ii) __________
iii) __________

3. Groups of members consisting positive and negative whole numbers including zero are
called _______________.

4. Match and determine the following numbers as an integer or non-integer.

a) 28 ∎

b) 0 ∎ Integer

c) -1.5 ∎

d) 4 ∎
7

e) -12 ∎ Non – integer

f) 9 3 ∎
16

5. A positive integer is an integer ______ than zero while negative integer is integer that
________ than zero.

Negative Integer Positive Integer
The more the number is _______ than 0, The more the number is greater than 0, the
the further its position to the left on the further its position to the ________ on the
number line and the ________ will be its number line and the _________will be its
value. value.

2
6. Examples to arrange integers in order.

7. Extra exercises for subtopic A.

1. Determine the positive integer and the negative integer.
1
-8, 4, 5.1, -12.8, 7.06, -3, 7

2. Determine the largest integer and the smallest integer
a) -8, 6, -10, 4, 1, -3
b) 9, -13, 14, -16, 8, 12

3. Arrange each of the following sets of integers in ascending order.
a) -3, 0, 11, -14, -16, 18
b) -13, -3, 4, -19, 19, -4

4. Arrange each of the following sets of integers in descending order.
a) -1, -6, 5, 0, 3, -4
b) 5, -2, 7, -1, 3, -6

B) BASIC ARITHMETIC OPERATIONS INVOLVING INTEGERS

1. On a number line:

Addition of Subtraction of
i) positive integers are represented by i) positive integers are represented by
moving towards the _________ moving towards the __________

ii) negative integers are represented by ii) negative integers are represented by
moving towards the __________ moving towards the _________

3

2. Examples of addition & subtraction of integers.

a) 8 + (+3)
=8+3
= 11

b) 5 + (–2)
=5–2
=3

c) 2 – (+4)
=2–4
=–2

d) –1 – (–4)
= –1 + 4
=3

3. The _________ or quotient of two integers with the __________ sign is a positive integer
while the product or _________ of two integers with ____________ sign is a negative
integer.

4. The rules of multiplication and division of integers can be summarized as below.

5. The order of operations to perform computations involving combining operations of integers
are:

BRACKET ()
ORDER (power)
DIVISION (÷)
MULTIPLICATION (×)
ADDITION (+)
SUBTRACTION (–)

4
6. Examples to solve combined basic arithmetic operations of integer.

7. Rules / laws of arithmetic operations: b) Associative Law
Operations involve:
a) Commutative Law i)
Operations involve:
i) ii)
ii)

c) Distributive Law d) Identity Law
Operations involve:
i)

ii)

8. Extra exercises for subtopic B. 3. Calculate.
a) 35 ÷ (−5)
1. Calculate. b) −12 ÷ 2
a) −1 + 4
b) 2 + (−4) −24
c) 3 − 5
d) −6 − (−3) c) −8
4. Calculate each of the following.
2. Calculate.
a) −4 × 2 a) 3 + (−5) × 2 − 7
b) 3 × (−4) b) −6 + (7 − 10) ÷ (−3)
c) −7 × (−6)
−7+(−5)

c) 1−(−2)

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C) POSITIVE AND NEGATIVE FRACTIONS
1. Positive fractions are fractions _______ than zero whereas negative fractions are fractions

______ than zero.

____________________ ___________________
2. Example to arrange fraction in ascending order.

3. Exercises on arranging fractions.

a) Arrange − 1 , 1 , − 1 , 1 and − 3 in ascending order.
5 10 2 5 10

b) Arrange 1 , − 1 , − 1 , 3 and − 1 in descending order.
4 8 4 8 2

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4. Examples to solve combined basic arithmetic operations of positive & negative integers.

5. Exercises on solving combined basic arithmetic operations of positive & negative integers.

Solve each of the following.
1 1 3
a) −1 8 + 2 × 4

b) 1 1 ÷ �−1 1 − 34�
8 2

c) −1 1 ÷ 4 + 1 × 2 1
3 9 4 2

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D) POSITIVE AND NEGATIVE DECIMALS
1. Positive decimals are decimals _______ than zero whereas negative decimals are decimals

_______ than zero.

___________________ __________________

2. Example to arrange decimals in descending order.

3. Exercises on arranging fractions.
a) Arrange -1.6, 1.4, -3.8, -2.5 and 2.35 in ascending order.

b) Arrange 3.28, -4.1, -1.03, 2.2 and -2.3 in descending order.

4. Examples to solve combined basic arithmetic operations of positive & negative decimals.

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5. Exercise on solving combined basic arithmetic operations of positive & negative decimals.

Solve each of the following.
a) 4.2 + (−1.25) × 8.2

b) 8.91 ÷ (−0.02 − 1.6)

c) (−5.2 + 1.48) − 3.12 × 2.5

E) RATIONAL NUMBERS

1. Rational numbers are the numbers that can be written in _____________________, that is

, such that p and q are integers, q ≠ 0.

2. Examples of rational numbers.

a) 1 4 3 c) −9 d) 3.5
5
b) 4

YES YES YES YES

3. Examples to solve combined basic arithmetic operations of rational numbers.

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4. Some exercises problem solving for enrichment.

a) b)

Ishak, Jia Kang and Suresh went mountain- When doing charity work, Ali gives rice,

climbing together. At a certain instance, sugar and biscuits to 80 fire victims. If each
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Ishak was at a level 1.45 m higher than Jia victim gets 2 kg of rice, 2 kg of sugar and 0.4
1
Kang while Suresh was at a level 2 3 m lower kg of biscuits and these alms are equally

than Jia Kang. Ishak, Jia Kang and Suresh transported using three vans, explain how
had climbed 1.25 m, 0.5 m and 334 m
you would find the mass of alms transported

respectively. Find the positions of Jia Kang by a van. Give your answer correct to two

and Suresh now with reference to the decimal places.

position of Ishak.

Answer: Answer:

10

MODUL MATHS F1
CHAPTER 2 : FACTORS AND MULTIPLES

A) FACTORS, PRIME FACTORS AND HIGHEST COMMON FACTOR (HCF)
1. Factors of a number are __________________ that can be divide number _____________.
2. Examples:

a) Determine whether 12 is a factor of 36
36 ÷ 12 = 3
Thus, 12 is a factor of 36.

b) Determine whether 9 is a factor of 30
30 cannot be divided completely by 9
Thus, 9 is not a factor of 30.

3. Example to list all the factors of 18.

4. List all the prime factors of 36.

5. Prime factors are factors of a number that are, themselves, prime numbers. For example, the
factors of 18 are 1, 2, 3, 6, 9 and 18. Among these number, only 2 and 3 are __________.
Thus, 2 and 3 are prime factors of 18.

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6. Prime factorization or integer factorization of a number is breaking a number down into the

set of prime numbers which multiply together to result in the original number. It can be done
by:
a) _______________________________
b) _______________________________
7. Example to express 60 in the form of prime factorisation
a) Method of repeated division

b) Method of drawing a factor tree

7. A common factor is a number that can be divided into two different numbers, without leaving
a ______________.

8. Determine whether
a) 8 is a common factor of 32 and 48.
_______________________________
b) 9 is a common factor of 18, 36 and 56.
_______________________________

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8. The highest common factor (HCF) is found by finding all ___________________of two

numbers and selecting the largest one. For example, 8 and 12 have common factors of 1, 2
and 4. The HCF is _____.
9. HCF can be determined by using methods of
a) Listing the common factors
b) _________________
c) _________________
10. Examples to determine the HCF using 3 methods.

a) 18 and 24 [ Method of listing the common factors ]

b) 36, 60 and 72 [ Method of repeated division ]

c) 48, 64 and 80 [ Method of prime factorisation ]

B) MULTIPLES, COMMON MULTIPLES AND LOWEST COMMON MULTIPLE (LCM)

1. Multiples are numbers that result when we _________ one whole number by another whole
number while a common multiple is a number that is a multiple of two or more numbers.

Multiples Common multiples

The _________ are
known as multiples of 9

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2. The lowest common multiple (LCM) of two numbers is the _________ whole number which
is a multiple of both. For example, the common multiples of 6 and 8 are 24, 48, 72, 96, …. .
Among these common multiples, the first common multiple, 24 is the least number. Therefore,
the LCM of 6 and 8 is ______.

3. LCM can be determined by using methods of
a) _________________
b) _________________
c) Prime factorisation

4. Examples to determine the LCM using 3 methods.
a) 2 and 3 [ Method of listing the common multiples ]

b) 3, 6 and 9 [ Method of repeated division ]

c) 3, 8 and 12 [ Method of prime factorisation ]

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C) PROBLEM SOLVING INVOLVING HCF & LCM
1. There are four steps that can be followed in solving the problems involving HCF & LCM,

namely
1. U_____________the problem
2. D_____________ a plan/ strategy
3. I_____________ the strategy
4. D____________ reflection/ making a conclusion

2. HCF (keyword : maximum)
Example:
The Boy Scouts of a school held a charity activity. A total of 252 shirts, 180 pairs of trousers
and 108 pairs of socks were donated by members to an orphanage. All the items were divided
equally in each pack. What would be the maximum number of packs that were prepared?

Practice:
A piece of cardboard has length of 260 cm and width of 80 cm. Dania wants to cut the
cardboard into several pieces of squares. What is the largest measurement of side of the
square such that no cardboard is left?

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3. LCM (keyword : minimum)

Example:
Canned coffee is sold in 6 cans per box and canned tea is sold in 9 cans per box. Ainun wishes
to buy the same number of canned coffee and canned tea for her sister’s birthday party. What
is the minimum number of boxes of each type of canned drinks she needs to buy?

Practice:
A canteen serves curry noodles for every 4 days and ‘mi jawa’ for every 6 days. If the
canteen serves both curry noodles and ‘mi jawa’ noodles on a particular day, after how
many days later would both types of noodles be served again on the same day?

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3. Exercises for enrichment.

a)
Nurul, Hui Ling and Gopal were each Answer:
given a piece of ribbon of the same
length. They cut their own ribbons into
several pieces of the same length. The
pieces of ribbon cut by Nurul, Hui Ling
and Gopal measured 15 cm, 25 cm and
30 cm long respectively. All the
ribbons were cut and there were no
remainders left. What was the shortest
possible length of the ribbon given to
them?

b)
Three pieces of string have a length of Answer:
192 cm, 242 cm and 328 cm
respectively. Aishah wishes to cut the
strings so that every piece is cut into the
same number of segments with no extra
string left. What would be the
maximum number of segments that
each pieces of string can be cut into?

c) Answer:
The HCF of m and 54 is 6. Find the
largest value of m such that the value of
m is less than 54.

d)
The LCM of 36, 56 and n is 1512. What Answer:
is the smallest value of n?

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MODUL MATHS F1
CHAPTER 3 : SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS

A) SQUARES AND SQUARE ROOTS
1. The square of 4 can be written as ______. Thus, 42 = 16.
2. A number made by squaring a whole number is called _____________________. The

examples are 1, 4, 9, 16, 25 ……
3. Method of ____________________________ can be used to determine whether a number is

a perfect square or not.
For example, to determine whether 36 and 54 is a perfect square or not.

4. A _______________ of a number is a value that, when multiplied by itself, gives the number.
Its symbol is ________.

5. Finding the square and the square root are ______________ operations.

6. Examples for square and square roots.

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7. Generalisation about multiplication involving:

i) Square roots of the same numbers
- The product of two __________ square root number is the ___________________.
- For example, √ × √ =

ii) __________________________
- The product of two ________________ square root numbers is the
_________________ of the product of the two numbers.
- For example, √ × √ = √

B) CUBES AND CUBE ROOTS
1. The cube of 2 can be written as ______. Thus 23 = 8.
2. A number which is equal to the number, multiplied by itself, three times is called

__________________. The examples are 1, 8, 27, ……
3. Method of ____________________________ can be used to determine whether a number is a

perfect cube or not.
For example, to determine whether 64 and 240 is a perfect cube or not.

4. The ____________ of a number is a special value that, when used in a multiplication three
times, gives that number.

5. Finding the cube and the cube root are ______________ operations.

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6. Examples for cube and cube roots.

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7. Examples to perform computations involving different operations on squares, square roots,

cubes and cube roots.

8. Summary for this chapter

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9. Some exercises for enrichment.

a) Find the value of each of the following without using a calculator

i) �35�2=
ii) �− 32�3==

iii) �2654 =

iv) �1 7 =
9

v) 3√−0.064 =

b) Find the value of each of the following: iv) 42 × 3√−125

i) 3√8 + (−0.3)2

ii) √36 ÷ �2 21�2 v) 532 × 3√27 ÷ (−1)3

iii) 52 × 3√−216 ÷ �49 vi) 3�− 1 × �23 − �2 79�
343

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MODUL MATHS F1
CHAPTER 4 : RATIOS, RATES AND PROPORTIONS

A) RATIOS

1. Ratio is used to _______________________________ of the same kind that are measured in
the same unit. For example, the ratio of 2000 g to 7 kg can be represented as

2000 g : 7 kg
2 kg : 7 kg
2: 7

2. The ratio of a to b is written as ____________.

3. Represent each of the following in the form of : : .
1
a) 1 2 kg to 500 g to 1 kg

b) 0.2 m to 5 cm to 7.8 cm

4. Two ratios that have the same value are called ____________________.

5. Two ways to express a ratio in its simplest form are:
a) ___________ the quantities by the HCF
b) ___________ the quantities by the LCM

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6. Express each of the following ratios in its simplest form.

a) 3 : 3
4 5

b) 1 2 : 1 1 : 1 1
3 4 2

B) RATES

1. Rate is a special ____________________________________________________________.
It also shows how two quantity with _________________ units are related to each other.

2. Examples to do conversion of units of rates.

a) b)

Rajan is riding his bicycle at a speed of 5 The density of a type of metal is 2700 kg per m3.

m/s. Convert 5 m/s to km/h. State the density of this metal in g per cm3.

Answer: Answer:

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3. Try to solve this problem.
The density of gold is 19 300 kg per m3. Express the density of gold in g/cm3.

C) PROPORTIONS

1. Proportion is a relationship that states that the two ratios or two rates are ____________. It
can be expressed in the form of ________________.

For example:
If 10 beans have a mass of 17 g, then 30 beans have a mass of 51 g. Write a proportion for the
following situation.

Answer:

2. There are three methods in determining the unknown value in a proportion. They are:
a. Unitary method
b. ____________________
c. ___________________________

3. Example to use these three methods in determining the unknown value in a proportion is:

Electricity costs 43.6 sen for 2 kilowatt-hour (kWh). How many much does 30 kWh cost?

a) Unitary Method b) Proportion Method c) Cross Multiplication Method

Let the cost of electricity for Let the cost of electricity for 30

30 kWh be x sen. kWh be x sen.

Then, Then,

Thus, the cost of electricity consumption for 30kWh is RM6.54

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4. In cross multiplication method,

5. Lets practice.
a) Given p : q = 3 : 8, find the value of q if p = 18.

b) In a study carried out by a group of students, it was found that the ratio of the number of
students watched television to those played computer games during their free time is 5 : 3.
How many students watched television if 36 students played computer games?

D) RATIOS, RATES AND PROPORTIONS
1. By using examples, we can determine the ratio of three quantities when two or more ratios of

two quantities are given.
Example 1

Example 2
Nurin’s mother tries a bread
recipe by mixing flour with
water. The ratio of the flour
to the water is 5 : 3. If
Nurin’s mother has 480 g of
flour, what is the mass of
water, in g, that is needed?

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Example 3

Example 4

In funding a bicycle

shelter project, the ratio

of the donations

contributed by the

school canteen

operator, Jaya

Bookstore and PIBG is

2:6:5. If the PIBG had

donated RM900, find

the amounts donated by

the school canteen

operator and Jaya

Bookstore respectively.

Example 5

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2. Lets try to solve this problem.

a) Given the total cost for three T-shirts is RM112. The ratio of the costs for the three T-shirts
is 5 : 7 : 4. Determine the cost for each of the T-shirts.
[Let p, q, and r represent the costs of the three T-shirts.]

b) The ratio of Susan’s marks to Wei’s marks to Reza’s marks in a test was 6 : 7 : 2. Reza’s
marks was 48 marks less than Susan’s marks. Determine the total marks of three of them.
[Let s, w and r represent the marks of Susan, Wei and Reza respectively.]

3. Other example to determine the value related to a rate is:

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E) RELATIONSHIP BETWEEN RATIOS, RATES AND PROPORTIONS WITH

PERCENTAGE, FRACTIONS AND DECIMALS
1. Percentage is a ratio that describes a part of ____________.
2. Example of determining percentage of a quantity by applying the concept of proportion is:

3. Summary for this chapter is:

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4. Exercises for this topic:
a) At a sale carnival, Encik Rosli chooses a shirt from a rack which displays ‘45% price
reduction’. The original price of the shirt is RM85.00. when Encik Rosli scans the price tag
of the shirt, the scanner shows that the price is RM57.80. by applying the concept of
proportions, determine whether this percentage corresponds to the percentage reduction
displayed. Give a reason for your answer.

b) Rafi sold his bicycle for RM180 and made a loss of 10%. Calculate the original price of
the bicycle.

c) Nadia bought 90 pieces of biscuits. She gave 3 of the biscuits to her friends. Then, she gave
5

18 pieces of the biscuits to her brother. Find the percentage of the biscuits remained with

Nadia.

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MODUL MATHS F1
CHAPTER 5 : ALGEBRAIC EXPRESSIONS

A) VARIABLES AND ALGEBRAIC EXPRESSION

1. Variable is a _____________________________ value. We can use ___________ to
represent variables.

2. A variable has a fixed value if the represented quantity is always _____________ at any time
while a variable also has a varied value if the represented quantity ___________ over time.

3. Examples on how to derive an algebraic expression from a situation.

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4. An _______________________ is a mathematical expression that consists of variables,

numbers and operations. For examples, , + 3, + + 5, 7 ……..

5. The value of an algebraic expression can be determined by _________________ the variables
with given values.
Example:

6. An ______________________ is either a single number or variable, or numbers and variables
multiplied together. Terms are separated by + or − signs, or sometimes by divide. It consists
of ______________ and ______________.

7. When a term is made up of a constant multiplied by a variable or variables, that constant is
called a ________________.

8. An algebraic term can be written as the product of the ______________ and its __________.

9. Given 0.7 2ℎ, state the coefficient of algebraic term

a) kh = ________________

b) 0.7h = ________________

c) 0.7k2 = ________________

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10. Each pair of terms has the same variable with the same power is known as
____________________ while each pair of terms which does not have the same variable with
the same power is known as ______________________.

11. Examples of like and unlike terms:

Like Terms Unlike Terms
12 and 12
4 and −7ℎ and 6ℎ2
2
3 and 0.5

12. Circle whether each of the following pairs of algebraic terms is like terms or unlike terms.

a) and −8 Like terms Unlike terms
Like terms Unlike terms
b) 6 and Like terms Unlike terms

c) 0.6 2and 2 Like terms Unlike terms

d) and −
3

B) ALGEBRAIC EXPRESSIONS INVOLVING BASIC ARITHMETIC OPERATIONS

1. When adding and subtracting two or more algebraic expressions, gather the
_______________ first. Then, add or subtract the like terms.

34
2. Examples of product of the repeated multiplication of algebraic expressions are:

3. Write each of the following in the form of repeated multiplication.
a) ( − 6 )2 =
b) (3 + 2 )4 =
c) � ℎ �5=

4. To find the product of algebraic expressions with one term, gather all the
__________________ and then multiply the number with _____________ and the variable
with ______________.

35

5. Find the product/ quotient for the following questions.

a) 15 × �− 2 3 �
3

−21 5

b) 28 4
6. Simplify 5( + ) − �6 32 − 8 2 2 2�

7. Summary for this topic:

36

MODUL MATHS F1
CHAPTER 6 : LINEAR EQUATIONS

A) LINEAR EQUATIONS IN ONE VARIABLE

1. The mathematical sentence that involves equality is known as _______________. The symbol
_______ is used to show the relationship between two quantities that have the same value.

7ℎ + 2 3 + 1 = 6
5 3 − 4
+ 8 VS + 5 = 8

Expressions − 10 = 1
2

Equations

2. The equations that have the power of the variables is one is called ____________________.

3. The characteristics of a linear equation in one variable are:
• Has only _______ variable
• The power of the variable is ________
• It also has only one solution.

4. The solution of linear equation is the numerical value that _________________ the equation.
It is also known as the __________ of the equation.

5. The linear equation in one variable can be solved by using three methods as follows:
a. Trial and ___________________ method
b. Application of ______________________
c. _____________________ method

6. In a linear equation, the value on the left hand side is always _________ to the value on the
right hand side. Thus, the operations used in both sides must be the same in order to obey the
_____________________.

7. The backtracking method uses working __________________________ and usually is used
to solve problems that have known final value but the initial value is unknown.

37

38
8. Examples to solve equations in one variable.

9. The steps to solve problems involving linear equations in one variable:

Identify the
variable in the
problem and
represent the
variable with a
letter.

10. Solve each of the following linear equations.

a) + 8 = 16 c) −7 = 14

b) − 4 = −9 d) = −2
5

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B) LINEAR EQUATIONS IN TWO VARIABLES

1. Linear equations in two variables are equations that have
i. __________ variables
ii. The __________ of each variable is one.

2. It can be written in the general form of ax + by = c where a and b are non-zero. The examples:

i. 6 + 4 = 9

ii. 6 + 4 = −2

3. Examples to form linear equations in two variables.

=

=

4. A linear equation in two variables has _________ possible pairs of values of ____________.
Each pair of solutions also can be written in the __________________ (x, y).

Example:
Osman has bought a total of five jerseys for Harimau Team and Kancil Team.
What are the possible numbers of jerseys that can be bought for each team?

5. The steps to solve problems involving linear equations in one variable:

Solve the equation to find
the value of the other
variable.

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6. When the pairs of solutions are written in ordered pairs, these pairs can be plotted and
connected in a straight line ____________. All the points on the straight line are the
______________ of the linear equation.

Example of graph linear equations: ii. Negative gradient (negative linear eq)
i. Positive gradient (positive linear eq)

7. Lets practice.

Given 4 + 3 = 14.
a) Find the value of y when x = −1.

b) Find the value of x when y = 2.

8. Determine whether each of the following is the possible pairs of solutions for 3 + 2 = −7.
a) = −3, = 1

b) = 2, = −2

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C) SIMULTANEOUS LINEAR EQUATIONS IN TWO VARIABLES

1. Consider two linear equations in two variables, x and y, such as: 2x - 3y = 4, 3x + y = 1. So
here, we have here _____ equations and ______ unknowns. In order to find a solution for this
pair of equations, the unknown numbers x and y must satisfy both equations. Hence, we call
this system ________________________________.

2. The solution of simultaneous linear equations that has one point of intersection is known as a
_______________________.

3. There are three cases involving solution of simultaneous linear equations as in table below:

Condition of both straight lines Type of solution

4. The simultaneous linear equations in two variables can be solved by using:
i. ___________________ method
ii. ___________________ method

iii. ___________________ method

i)
Solve simultaneous linear
equations by using Graphical
Method

+ = 6 and 2 + = 8

From the graph drawn, the point of intersection is
(2, 4). Thus, the solution is x = 2 and y = 4.

ii)
Solve simultaneous linear
equations by using Substitution
Method

− 3 = 7 and 5 + 2 = 1

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iii)
Solve simultaneous linear
equations by using Elimination
Method

5. The steps for solving simultaneous linear equations in two variables using substitution
method:

Substitute the Substitute the
expression into value obtained
the other linear into the
equation. original
equation to
find the value
of the other
variable.

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6. The steps for solving simultaneous linear equations in two variables using elimination
method:

Multiply one or Substitute the
both equations value obtained
with a number so into the
that the original
coefficient of equation to
one of the find the value
variables is of the other
equal. variable.

7. Summary for this chapter:

8. Some exercises to solve equations by using simultaneous linear equations:

a) Solve these equations by using b) Solve these equations by using

substitution method. elimination method.

= − 3 and 3 + 2 = 11 3 − 2 = 7 and 4 − 3 = 5

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MODUL MATHS F1
CHAPTER 7 : LINEAR INEQUALITIES

A) LINEAR EQUATIONS IN ONE VARIABLE

1. The relationship between two quantities that do not have the same value is known as an
_________________. We write the comparison of the values of numbers by using
____________________________ .

2. For example, −2 < 3 and −2 > −7, these comparisons we called as __________________.

3. The symbols and their meaning we usually used in this chapter are:

Symbol Meaning Other meanings

i) < Less than Fewer than

ii) > Greater than More than

iii) ≤ Less than or equal to At most/ not more than/ maximum

iv) ≥ Greater than or equal to At least/ not less than/ minimum

4. The inequality also can be represented in the form of
a) _______________________
b) Algebraic _______________ for the relationship

5. The properties of inequalities are:

 If a is less than b, then b is greater than a.
If a < b, then b > a : ________________________________

 If a is less than b and b is less than c, then a is less than c.
If a < b < c, then a < c : _____________________________________________

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6. Some conclusion and examples can be shown are:

 The inequality symbol remains unchanged when adding or
subtracting a positive or negative number to or form both Examples:
sides of the inequality.

 i) The inequality symbol remains unchanged when
multiplying or dividing both sides of the inequality by a
positive number.

ii) The direction of the inequality symbol is reversed when
multiplying or dividing both sides of the inequality by a
negative number.

 When both sides of the inequality are multiplied by -1, the
direction of the inequality symbol is reversed.

 It is known as ________________________

 When performing reciprocal of both numbers on both sides
of the inequality, the direction of the inequality symbol is
reversed.

 It is known as _________________________

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7. Fill in the boxes with the symbol ‘<’ or ‘>’.

a) 4<5

4+1 5+1

8 > −1
b) 8 – (−9) −1 – (−9)

c) −7 < 1

−7 × 2 1×2

9>1
d) 9 ÷ (−2) 1 ÷ (−2)

B) LINEAR INEQUALITIES IN ONE VARIABLE

1. Linear inequalities in one variable is defined when the power of variable in a linear inequality
is _________. For examples,

 3 < 7, where the power of the variable x is 1 and
 − 4 > 5 + 2 , where the power of the variable y is 1

2. Determine whether each of the following relationships is a linear inequality in one variable.

State YES or NO for the answers.

a) − 4 ≥ 3 ____________________

b) < + 4 ____________________

c) 2 < − 7 ____________________

3. Solving a linear inequality in x is to find the _________________ that satisfy the inequality.
The process of solving linear inequalities is ________________ to the process of solving
linear equations. But then, we need to consider the ______________ of the inequality symbol
when solving linear inequalities.

4. To solve linear inequalities that involve multiplication or division, we need to ____________
or ______________ both sides of the inequality with an appropriate number so that the
____________________ of the variable becomes 1.

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Examples:

5. Solve each of the following inequalities.
a) + 4 > 2

b) 3 < 27

c) 1 + 3 ≤ − 7

d) 1−2 ≤ 7
3

e) 3 − 1 ≥ 2 + 1
2