FOCUS KSSM Mathematics F1 (2023)

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CC031233
FORM
1 KSSM FOCUS





Mathematics








FOCUS KSSM Form 1 – a complete and precise series of reference books with Mathematics FORM
special features to enhance students’ learning as a whole. This series covers the 1 KSSM
latest Kurikulum Standard Sekolah Menengah (KSSM) and integrates Ujian Akhir
Dual Language Programme
Sesi Akademik (UASA) requirements. A great resource for every student indeed! Mathematics


• Ng Seng How (Textbook Writer)
REVISION REINFORCEMENT EXTRA • Ooi Soo Huat (Textbook Writer)
› Comprehensive Notes & ASSESSMENT FEATURES • Yong Kuan Yeoh (Textbook Writer)
› Example and Solution › Formative Practices › Maths Info • Moy Wah Goon
› Tips › Summative Practices › HOTS Challenge • Dr. Chiang K. W.
› Common Mistakes
› UPSA Model Paper › Daily Application
› UASA Model Paper › TIMSS Challenge
› Answers › Digital Resources QR Code





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UPSA & UASA Model Papers
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ISBN: 978-629-7557-15-1
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Format: 190mm X 260mm TP Focus 2023 Maths F1_pgi CRC














Mathematics FORM







Dual Language Programme 1 KSSM




• Ng Seng How (Textbook Writer)
• Ooi Soo Huat (Textbook Writer)
• Yong Kuan Yeoh (Textbook Writer)
• Moy Wah Goon
• Dr. Chiang K. W.

Format: 190mm X 260mm TP Focus 2023 Maths F1_pgii CRC



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Mathematics PT3 Mathematical Formulae
Exclusive Features of this Book



Learning Area: Number and Operations
Infographic
visually highlights Chapter 1 Rational Numbers 4 99° 9.2.3 Mathematics Form 1 Chapter 9 Basic Polygons
Solve problems involving
triangles
the key concepts Find the value of x in the diagram above. 6
x
41°
of each chapter to Solution: Common A D
x = 99° + 41°
= 140°
mistake 1 115°
enhance students’ KEYWORDS 5 INFO In the diagram above, ABC is a right-angled
x
B
C
learning. • Identity Law (a) diagrams. value of x. Example
• Distributive Law
triangle and ADC is a straight line. Find the
Find the value of x in each of the following
• Associative Law
Solution:
Access to
INFOGRAPHIC • Commutative Law (b) /ADB + 115° = 180° The sum of the interior
• Integer
• Rational number x angle and its adjacent provides
• Fraction x exterior angle is 180°.
• Decimal 26° Thus, /ADB = 180° – 115°
• Zero = 65° solution
(c) /BAD = /ADB = 65° ABD is an isosceles
Chapter Introduction 32° Given ABC is a right-angled triangle. for example of
triangle.
So, /ABC = 90°.
contains picture and Solution: x x + 90° + 65° = 180° questions in the

Therefore, x = 180° – 90° – 65°
question to stimulate (a) x = 60° Equilateral triangle 7 = 25° subtopics.
interest and thinking (b) x + 26° + 26° = 180° P x 94° S CHAPTER
x + 52° = 180°
x = 180° – 52°
= 128°
about the chapter’s Do you know, the temperature in some deserts is very high during the day and very low at (c) x + x + 32° = 180° Q R 22° T 9
2x + 32° = 180°
average temperature in most deserts reaches 38°C during the day. Whereas in some deserts,
content. night? The air in the desert is very dry and caused the heat to drop very fast at night. The 2x = 180° – 32° Solution:
the temperature decreases to –4°C at night. This temperature varies depending on the location
In the diagram above, PRT and QRS are straight
of the deserts. In your opinion, does the difference of both temperature is high?
lines. Find the value of x.
= 148°
In triangle SRT,
Therefore, x = 148° 2 /SRT = 180° – 94° – 22°
1
= 64°
= 74°
Therefore, /PRQ = 64°
/PQR = /PRQ = 64°
Mathematics Form 1 Chapter 8
Therefore, x = 180° – 64° – 64°
Try questions 3 and 4 in Formative Practice 9.2 Lines and Angles
= 52°
Mathematics Form 1 Chapter 5 Algebraic Expressions Summative Practice
(c) (h + 5) × (h + 5) × (h + 5) × (h + 5) Section A 8 131 Full
(d) (2a – 5b) × (2a – 5b)
solution
HOTS Challenge HOTS Challenge Daily Application 3. Write each of the following in the form of 1. Which of the following angles cannot be 5. In the diagram below, KL and MN are parallel
Praktis Formatif 1
a ruler?
repeated multiplication.
(c) (3ab + 2p) 2
lines. GH is a straight line.
constructed using only a pair of compasses and
(b) (2pq) 4
A 22.5°
(a) (7 – x) 3
B 75°
provide questions 4. Given (px – y) n = (5x + qy)(5x + qy) where n, D 160° K G p M q H
p and q are integers. Find the values of p, q
C 82.5°
and n.
that stimulate 13y m 11y m 5. Find the product for each of the following. 2. Name angle p and angle q. L N
(a) 2a × 5a 7
A Corresponding angles
6x m
20x m
student’s higher Diagram above shows a cuboid aquarium. The (b) –6x 3 y × (–8x 4 y) 3 5 A 75° A Section B Summative Practice
B Alternate angles
C Cojugate angles
(c) 1 ab 5 × 14bc 2
2
height of the water level in the aquarium is 11y m.
D Complementary angles
(d) 18p 2 q 6 × 1 – 1 p 2 × 2 pq 3
In the construction above, angle A constructed is
order thinking The empty space will be filled when 18x identical 6. Find the quotient for each of the following. CHAPTER D 105° 1. (a) Complete the table below by giving two provides ample
marbles are put into the aquarium and 30x 2 y m 3 of
B 80°
water will overflow at the same time. What is the
C 90°
(a) 24k 3 h 8 ÷ 6kh 3
volume, in m 3 , of a marble?

examples of each type of angle stated.
skills. Solution: (b) 28a 5 bc 2 ÷ (–12a 4 b) 5 3. T Type of angle Two examples of angle questions to test
[2 marks]
5pq 6
Volume of a marble
(c) 40pq 3
Volume of empty + Volume of overflowed
Obtuse angle
(d) –16x 3 y 4
water
20y 3 z
= space The number of marbles 7. Simplify each of the following. P 55° Q x R Reflex angle students’ mastery
= 20x × 6x × (13y – 11y) + 30x 2 y (a) mn 4 × 3mp ÷ (–12mn 3 ) CHAPTER In the diagram above, PQR and SQT are straight (b) Match the following diagrams with the given
S
estimated angles.
18x

[2 marks]

= 20x × 6x × 2y + 30x 2 y (b) –6ab 3 ÷ (–21a 2 bc) × 5ab 4 c 5 8 B 80° • of the chapter.
lines. Find the value of x.
A 105°
18x
= 240x 2 y + 30x 2 y 8. Simplify each of the following. 2 C 85° • 290°
(a) 6(r + st) – 1 7rs – 8s 2 t
18x
D 55°
3s
= 270x 2 y (b) 4y + 3xy + (2 – 5x) 4. P • • 140°
18x
y

= 15xy m 3 9. The volume of a cube is (x – 2y) 3 cm 3 . What is S
Try questions 9 – 10 in Formative Practice 5.2 the total surface area of the cube? Applying M 2. (a) Mark (✓) for the true statement and (✗) for
the false statement.
[2 marks]
Formative Practice 1. Simplify each of the following. 10. P Q R In the diagram above, line RS is the perpendicular point and b and c are supplementary
Formative Practice 5.2
R
80° and 110° are supplementary angles.
Q
If a, b and c are three angles at one
bisector of line PQ. Which of the following is not
provides questions (a) (7a + 10b) + (3a – 2b + 7) V W S 10xy cm true? (b) By using a pair of compasses and a ruler,
angles, then a = 180°.
(b) (xy – 8y + 11) – (7xy + 5y – 2)
A ∠SMQ = 90°
(c) (3p + q) + (9p – 5q + 4) – (p – 4q – 1)
B RM = MS
T
16xy cm
C PM = MQ
U
to test students’ (d) (–4m – 8n + 7mn) – (–3m + mn) 10 the midpoint of edge PR and the ratio of length compasses and a ruler. B, starting from the given line AB. [2 marks]
construct and mark an angle of 60° at point
(e) 1 5 pq – 1 pr 2 – 1 4 pq + pr – 8 2 + pq
3
Diagram above shows a rectangle PRTU. Q is D RS can be constructed using a pair of
2
of RS to ST is 3 : 2. If PQWV is a square,
2
A
(f) 1 3 kh + 6pq 2 + 1 6 kh – pq 2 + kh
1
2
understanding of 2. Simplify each of the following. find the area of the shaded region in terms of 124 B
Applying
x and y.
(b) xy × xy × xy × xy × xy × xy × xy
the subtopics and (a) k × k × k × k × k 75
reinforce learning. Mathematics Form 1 Chapter 9 Basic Polygons ANSWERS Answers
TIPS
3. The name of a polygon is given according • Hexagon ABCDEF in Example 2 can also be Chapter 1 Rational Numbers 6. (a) 491 (b) 530 help students
(c) 4 900
to the number of sides. labelled and named as follows. Formative Practice 1.1 (e) 2 804 (d) 27 (d) (i) –1 7 , –1 1 , – 5 , 1 1 , 3
8
2
(f) 120
8
Name of Number Example of B C F A 1. Positive numbers: 8. Water level decreases by 6 m. (ii) 3 , 1 1 , – 5 , –1 1 , –1 7 4 2 to check and
7. 15 m below sea level
shape
4
2
polygon of sides D E C B 2 , 7.3, 5, +3 9. (a) Leong will not receive a prize 4. (a) –1 3 8 (b) 3 2 8
8
5
because he answered 13 questions
Negative numbers:
Triangle 3 A F E D –10, –67, – 3 , –8.9 correctly, 2 questions incorrectly (c) –1 1 18 (d) – 3 4 evaluate their
and 1 question not answered; The
4
(e) – 6
B A a negative number) (b) John will likely receive a prize. If 7 (f) 1 7 9
total marks that he obtained is 34.
(Zero is not a positive number and not
he answered 13 questions correctly
Quadrilateral 4 F 2. (a) –7 levels (b) +500 m and 3 questions not answered, so (g) –1 1 3 (h) –4 1 8
(i) 4
(c) –RM450
C E 3. (a) –100 (d) +RM0.50 If he answered 13 questions 15 performance.
the total marks obtained is 36 marks.
(e) –150 m
(f) –3 cm
Tips Pentagon 5 Try question 3 in Formative Practice 9.1 4. Positive integer: 4; marks. correctly, 1 question incorrectly and 5. 2 250 m below sea level 10
D
2 questions not answered, maybe
(b) +38 or 38
the total marks obtained is 35
(c) –45
sugar.
6. Not enough. Still short of 7 kg of
Negative integer: –8, –3
5. (a)
points out Hexagon 6 7 Formative Practice 9.1 Mathematics Form 1 Chapter 4 1 2 Ratios, Rates and Proportions 1. (a) Formative Practice 1.4
Formative Practice 1.3
–3
–2
1. (a)
4
(b)
4
important tips for Heptagon 8 1. Find the number of vertices and number of A basket contains 3 oranges, 4 apples and – – 2 7 7 1 – 3 – 7 –0.4 (b) –0.2 –0.1 0.2 0.3
diagonals of a polygon with
– –
7
–9 1

–15
(b) 7 sides,
Ratios
4.1
–3
3
(b)
6
(a) 5 sides,
(d) 21 sides.
Octagon
6. (a) 8
(c) 11 sides,
(b) –15
7. (a) Largest integer: 6;
–5.2 –3.9
1

Smallest integer: –10
–1–
students to take Nonagon 9 2. Determine whether each of the following 6 guavas. Represent each of the following – – 2 3 0 1 – 3 2. (a) 2.9 –1.3 2.6 3.9
4.1.1
Represent the relation between
3
(b) Largest integer: 14;
relations in the form of ratio.
statements is true or false.

(a) A polygon with 8 sides has 8 vertices.
(c)
Smallest integer: –16
three quantities
(a) The number of oranges to the number of
(b) A polygon with 13 sides has 65 diagonals.
(b) –5.6
8. (a) –6, –5, –4, –2, 1, 3
apples.
(c) –1.11
1
– –
1
(b) –10, –8, –6, 3, 7, 9
– –
2
note of. Decagon 10 3. Draw each of the following polygons, then label (b) The number of guavas to the number of 8 1 – 1 – 6 1 – 3 1 – 3. (a) (i) –6.7, –3.31, –1.4, 3.87, 4.5
(c) –16, –14, –3, 0, 11, 18
3
(d) –19, –13, –4, –3, 4, 19
I used bricks and concrete of the best
oranges to the number of apples.
(ii) 4.5, 3.87, –1.4, –3.31, –6.7
(d)
quality to build
9. (a) 5, 3, 0, –1, –4, –6
and name the polygons. the wall. The concrete that
(b) (i) –5.2, –3.0, –0.4, 0.9, 1.4
(b) 7, 5, 3, –1, –2, –6
(c) The number of apples to the total number
(a) Polygon with 6 sides. of 1 part of cement, 2
I used are made up
(ii) 1.4, 0.9, –0.4, –3.0, –5.2
– –
1
(c) 4, 2, 1, –1, –3, –7
of fruits in the basket.
3
(b) Polygon with 9 sides. parts of gravel.
4
– –
parts of sand and 3
8
(c) (i) –4.11, –3.22, –1.44, 1.55, 2.33
(d) –1, –3, –5, –8, –10, –12
(ii) 2.33, 1.55, –1.44, –3.22, –4.11
2
(d) (i) –5.44, –5.42, –2.9, 0.03, 0.3
Sketch a polygon with 6 sides. Then, label and (c) Polygon with 10 sides. CHAPTER Solution: (b) 3 2. (a) 4 5 (b) –1 1 2 2 4. (a) –1.66 (ii) 0.3, 0.03, –2.9, –5.42, –5.44
Formative Practice 1.2
(a) The ratio of the number of oranges to the
(b) –1.2
1. (a) 5
(c) –9.35
number of apples = 3 : 4
(d) 8.985
(c) –2 3
(c) –1
(e) 2
5
name the polygon. Properties of Triangles and 9 (b) The ratio of the number of guavas to the (d) –2 1 9 (g) –19.35 (f) –6.665
(e) –3
(d) –14
(h) –5.647
(f) 11
(g) –10
(i) –3.072
Solution: 9.2 the Interior and Exterior 2. (a) –16 number of oranges to the number of apples 8 8 CHAPTER 2 8 5. –4°C
3. (a) (i) – 1 , – 3 , – 1 , 1 , 5
2
(h) –4
Mark the 6 points. (c) 42 (b) –20 Follow the correct order of the

8
2
8
C Angles of Triangles 3. (a) –15 = 6 : 3 : 4 (d) 36 (ii) 5 , 1 , – 1 , – 3 , – 1 6. Danny gained a profit of RM185.
D Join all the points to (c) 7 (b) –7 quantities. 8 4 2
B form a closed figure. Geometric properties of 4. (a) 0 (d) 12 (b) (i) – 7 , – 2 , 1 , 1 , 3 5 ‒; +; ‒ TIMSS Challenge
10
(b) 1
(c) 12
5 10 2
5
E A Label all the vertices. 9.2.1 triangles 5. (a) 10 Ratio (d) 27 (ii) 3 , 1 , 1 , – 2 , – 7 10 Digital Resources
(b) 0
2 10
5
(c) 40
VIDEO
(e) 15
F 1. The triangles are named based on their (g) –6 (d) 17 (c) (i) –1 1 , –1 1 , – 5 , 4 , 7 Formative Practice 1.5
(f) –28
3
Therefore, the polygon is a hexagon ABCDEF. geometric properties. (c) The ratio of the number of apples to the 6 6 6 6 9 9 3 1. All the numbers given are rational help learners
(h) –4
numbers.
(ii) 7 , 4 , – 5 , –1 1 , –1 1
9
9
–8 = –8 ; 3.15 = 63 ; 1 1 = 6
1
total number of fruits in the basket
triangles and their respective geometric
5
20
Maths Info MATHS INFO 2. The following table shows the types of be = 4 : (3 + 4 + 6) 2. (a) –7.2 (b) 2.58 5 better comprehend
(c) –0.3125
can
(d) –3.905
INFO
triangles
categorised according to their length of
These
= 4 : 13
properties.
TIPS
Do you know why the cement, sand
are properly arranged either clockwise or
and gravel must be mixed following
consists of The letters labelled on the vertices of a polygon sides and the size of angles. 129 • Case (a) and (b) are relations comparing 205 concepts and
certain ratio? If the concrete
contains too much of cement, it
anticlockwise.
part to part.
becomes brittle. If the concrete
• Case (c) is a relation comparing part to the
is not strong enough.
extra info and contains too much of sand, then it whole quantity. deepen learning.
Try questions 1 and 2 in Formative Practice 4.1
knowledge related 1. Ratio is used to represent a relation Represent each of the following in the form of *Video/Info
between two or three quantities in the
2
form of a : b or a : b : c.
to the chapter. 2. Ratio can be used to compare part to part a : b : c. 2
or part to whole of the quantities.
(a) 1 1 kg to 500 g to 1 kg
3. When comparing two quantities with
the same unit, the ratio formed has no (b) 0.2 m to 5 cm to 7.8 cm
unit. Solution:
(a) First convert the unit of g to kg.
4. Conversion of units is required if the units
1 000
involved in the comparison are different 500 g = 500
like kg and g, m and cm and so on.
= 1 kg
2
47
iii
F1 Exclusive Features.indd 3 02/03/2023 1:27 PM

Mathematical Formulae









NUMBER AND OPERATIONS MEASUREMENT AND GEOMETRY

Number of diagonals of = n(n – 3)
Commutative Law a polygon with n sides 2

a + b = b + a Area of a rectangle = Length × Width
1
a × b = b × a Area of a triangle = × Length of base × Height
2
Associative Law Area of a parallelogram = Length of base × Height
(a + b) + c = a + (b + c)
1
Area of a kite = × Product of two diagonals
(a × b) × c = a × (b × c) 2

Sum of two
1
Distributive Law Area of a trapezium = × parallel sides × Height
a × (b + c) = a × b + a × c 2
a × (b – c) = a × b – a × c
Pythagoras Theorem
Identity Law

a + 0 = a a c
a × 0 = 0 b
a × 1 = a c = a + b 2
2
2
a + (–a) = 0
1
a × = 1 STATISTICS AND PROBABILITY
a


RELATIONSHIP AND ALGEBRA a

a = a × a × ... × a
n

n times
• Angle of sector, a = Frequency of data × 360°
(a + b) = (a + b) × ... × (a + b) Total frequency
n
Angle of sector
n times • Percentage = 360° × 100%












iv





0a F1 Formulae Mathematics.indd 4 02/03/2023 1:29 PM

CONTENTS






Mathematical Formulae iv 4.5 Relationship between Ratios, Rates
and Proportions with Percentages,
Fractions and Decimals 59
LEARNING AREA Number and Operations
Summative Practice 4 63

Chapter
Chapter
1 Rational Numbers 1 5 Algebraic Expressions 65
1.1 Integers 2 5.1 Variables and Algebraic
1.2 Basic Arithmetic Operations Expressions 66
involving Integers 4 5.2 Algebraic Expressions involving
1.3 Positive and Negative Fractions 8 Basic Arithmetic Operations 71
1.4 Positive and Negative Decimals 12 Summative Practice 5 76
1.5 Rational Numbers 14
Summative Practice 1 16 Chapter
6 Linear Equations 78
Chapter
2 Factors and Multiples 18 6.1 Linear Equations in One Variable 79
6.2 Linear Equations in Two Variables 82
2.1 Factors, Prime Factors and Highest 6.3 Simultaneous Linear Equations
Common Factor (HCF) 19 in Two Variables 85
2.2 Multiples, Common Multiples and Summative Practice 6 88
Lowest Common Multiple (LCM) 23
Summative Practice 2 26 Chapter
7 Linear Inequalities 90
Chapter
3 Squares, Square Roots, Cubes 7.1 Inequalities 91
28
and Cube Roots
7.2 Linear Inequalities in One
3.1 Squares and Square Roots 29 Variable 94
3.2 Cubes and Cube Roots 36 Summative Practice 7 99
Summative Practice 3 44
Measurement and
LEARNING AREA Geometry
LEARNING AREA Relationship and Algebra
Chapter
8 Lines and Angles 100
Chapter
4 Ratios, Rates and 46 8.1 Lines and Angles 101
Proportions
8.2 Angles related to Intersecting
4.1 Ratios 47 Lines 116
4.2 Rates 51 8.3 Angles related to Parallel Lines
4.3 Proportions 53 and Transversals 118
4.4 Ratios, Rates and Proportions 54 Summative Practice 8 124



v





0b F1 Contents.indd 5 02/03/2023 1:28 PM

Chapter LEARNING AREA Statistics and Probability
9 Basic Polygons 127

9.1 Polygons 128 Chapter
9.2 Properties of Triangles and 12 Data Handling 175
the Interior and Exterior Angles
of Triangles 129 12.1 Data Collection, Organization
9.3 Properties of Quadrilaterals and Representation Process,
and the Interior and Exterior and Interpretation of Data
Angles of Quadrilaterals 133 Representation 176
Summative Practice 9 137 Summative Practice 12 192

Chapter
10 Perimeter and Area 140 Measurement and
LEARNING AREA
Geometry
10.1 Perimeter 141
10.2 Area of Triangles, Parallelograms, Chapter
Kites and Trapeziums 146 13 The Pythagoras Theorem 195
10.3 Relationship between Perimeter
and Area 154 13.1 The Pythagoras Theorem 196
Summative Practice 10 157 13.2 The Converse of Pythagoras
Theorem 199
Summative Practice 13 202
LEARNING AREA Discrete Mathematics

Chapter
11 Introduction to Set 161 Answers 204


11.1 Set 162
11.2 Venn Diagrams, Universal
Sets, Complement of a Set
and Subsets 166
Summative Practice 11 173




UPSA Model Paper UASA Model Paper
(Ujian Pertengahan Sesi Akademik) (Ujian Akhir Sesi Akademik)



https://qr.pelangibooks.com/?u=FocusMatF1UPSA https://qr.pelangibooks.com/?u=FocusMatF1UASA


Answers for UPSA and UASA Model Papers



https://qr.pelangibooks.com/?u=FocusMatF1AnsUjian



vi





0b F1 Contents.indd 6 02/03/2023 1:28 PM

Learning Area: Number and Operations

Chapter
1 Rational Numbers




















KEYWORDS


• Identity Law
Access to • Distributive Law
INFOGRAPHIC • Associative Law
• Commutative Law
• Integer
• Rational number
• Fraction
• Decimal
• Zero



























Do you know, the temperature in some deserts is very high during the day and very low at
night? The air in the desert is very dry and caused the heat to drop very fast at night. The
average temperature in most deserts reaches 38°C during the day. Whereas in some deserts,
the temperature decreases to –4°C at night. This temperature varies depending on the location
of the deserts. In your opinion, does the difference of both temperature is high?






1





F1 Chapter 1.indd 1 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers


1.1 Integers 1
Represent each of the following by using a
positive number or a negative number.
1.1.1 Recognise positive and negative (a) A loss of RM750.
numbers based on real-life
situations (b) The price of a packet of nasi lemak has
increased by 50 cents.
1. We usually use positive and negative (c) Price of share market of Company P has
CHAPTER
numbers in our daily life. increased by RM2.10 within 1 month.
1
(a) A positive number is a number that is Solution:
greater than 0.
A positive number is written with or (a) –RM750
without the (+) sign. (b) +50 cents or 50 cents
1 1
For example, +1, +3.5, + or 1, 3.5, (c) +RM2.10
2 2
are positive numbers. Try questions 1 – 2 in Formative Practice 1.1
(b) A negative number is a number that is
less than 0.
A negative number is written with (–) 2
sign.
1 Complete the following sentences.
For example, –1, –3.5, – 2 are negative
numbers. (a) 400 m to the right is written as +400. Thus,
250 m to the left is written as .

MATHS INFO (b) 56 km to the west is written as –56. Thus,
INFO
65 km to the east is written as .
• 1 is an integer. • 3.5 is a decimal. (c) 35 m above the sea level is written as 35 m.
1 Thus, 12 m below the sea level is written as
• is a fraction.
2 .
2. The situations that can be represented by Solution:
positive and negative numbers: (a) –250
(a) The movement to the north is (b) +65 or 65
represented by a positive number (c) –12
and the movement to the south is
represented by a negative number. Try question 3 in Formative Practice 1.1
(b) The upward movement is represented
by a positive number and the downward
movement is represented by a negative 1.1.2 Recognise and describe integers
number.
(c) The temperature that is higher than
0°C is represented by a positive number 1. In Section 1.1 & 1.2, only positive integers
and the temperature that is lower and negative integers are discussed.
than 0°C is represented by a negative (a) A positive integer is an integer that is
number. greater than 0.
(d) Profit is represented by a positive For example, +2, +5, +17 or 2, 5, 17 are
number and loss is represented by a positive integers.
negative number. (b) A negative integer is an integer that is
(e) The increase in the price is represented less than 0.
by a positive number and the decrease For example, –2, –5, –17 are negative
in the price is represented by a negative integers.
number.

2





F1 Chapter 1.indd 2 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

TIPS (b) Vertical number line

• Integers are …, –2, –1, 0, 1, 2, … 3
• The positive integers are 1, 2, 3, 4, …
• The negative integers are …, –4, –3, –2, –1 The value is 2 Positive
integers
increasing
3 1 CHAPTER
Determine the positive integer and the negative 1
integer. 0 Zero
1
–3, +4.5, 8, +16, –2.4, –4 –1
2
The value Negative
Solution: is decreasing –2 integers
Positive integer: 8, +16 –3
Negative integer: –3
Note that the positive integers are
Try question 4 in Formative Practice 1.1
located above zero whereas the negative
integers are located below zero.

1.1.3 Represent integers on number 4
lines and make connections
between the values and Represent the following integers on number
positions of the integers with line.
respect to other integers on the (a) –3, –2, 2, 3
number line (b) –20, –16, –8, 4, 8
Solution:
1. Integers can be represented using a (a)
horizontal number line or a vertical
number line. –3 –2 –1 0 1 2 3
(a) Horizontal number line (b)
–20 –16 –8 4 8
–12 –4 0
The value is decreasing The value is increasing
–4 –3 –2 –1 0 1 2 3 4 Try question 5 in Formative Practice 1.1
Negative integers Positive integers
Zero
1.1.4 Compare and arrange integers
Note that the positive integers are in order
located on the right hand side of zero
whereas the negative integers are 1. On a number line, the integers to the right
located on the left hand side of zero. are greater than the integers to the left or
the integers to the left are less than the
integers to the right.
MATHS INFO

INFO
2. Based on the position of integers on
Zero is neither a positive integer nor a negative a number line, the integers can either
integer. Zero is the separator for positive units and be arranged in ascending order or in
negative units on a number line. descending order.




3





F1 Chapter 1.indd 3 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

5 (e) 150 m below sea level.
(f) The decrease of water level by 3 cm.
Determine the greater integer.
(a) –2 or 4 (b) –1 or –7 3. Complete the following sentences.
(a) The movement of a car 85 km to the north
Solution: is written as +85. Thus, the movement of
(a) 4 is greater than –2. a van 100 km to the south is written as
A positive number is always greater than a .
negative number. (b) 8°C below the freezing point is written as
CHAPTER
–8. Thus, 38°C above freezing point is
1
(b) written as .
–7 –6 –5 –4 –3 –2 –1 0 (c) An eagle flies 80 m above sea level. The
position of the eagle is written as +80. A
turtle is located 45 m below sea level. The
–1 is located on the right hand side of –7. position of the turtle is written as .
Thus, –1 is greater than –7.
4. Determine the positive integer and the negative
Try questions 6 – 7 in Formative Practice 1.1 integer.
–8, 4, 5.1, –12.8, 7.06, –3, 1
7
6 5. Represent the following integers on number
lines.
(a) Arrange –3, –4, 0, –1 and 2 in ascending (a) –2, 1, –3, 2, 4 (b) –3, –9, 6, 3, –15
order.
(b) Arrange –4, –1, 3, 1 and –3 in descending 6. Determine the greater integer.
order. (a) 8 or –1 (b) –15 or –19
Solution: 7. Determine the largest integer and the smallest
integer.
(a)
(a) –8, 6, –10, 4, 1, –3
–4 –3 –2 –1 0 1 2 (b) 9, –13, 14, –16, 8, 12
8. Arrange each of the following sets of integers
Ascending order: –4, –3, –1, 0, 2 in ascending order.
(a) –6, –4, 1, –2, 3, –5
(b) (b) 9, –8, –6, 7, –10, 3
–4 –3 –2 –1 0 1 2 3 (c) –3, 0, 11, –14, –16, 18
(d) –13, –3, 4, –19, 19, –4
9. Arrange each of the following sets of integers
Descending order: 3, 1, –1, –3, –4 in descending order.
(a) –1, –6, 5, 0, 3, –4
Try questions 8 – 9 in Formative Practice 1.1
(b) 5, –2, 7, –1, 3, –6
(c) 4, 1, –3, –7, 2, –1
Formative Practice 1.1 (d) –12, –5, –8, –3, –1, –10


1. Determine the positive numbers and the
negative numbers.
–10, 2 , 7.3, 5, –67, – 3 , –8.9, 0, +3 1.2 Basic Arithmetic Operations
5 4 involving Integers
2. Represent each of the following by using a
positive number or a negative number. 1.2.1 Addition and Subtraction of
(a) An elevator goes down 7 levels. Integers
(b) 500 m above sea level.
(c) A loss of RM450. 1. Addition of two or more integers is the
(d) The price of share market of Maju Company
increased by RM0.50. process of finding the sum of the integers.



4





F1 Chapter 1.indd 4 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

2. Subtraction between two integers is the 2. The sign of the quotient for division of
process of finding the difference between integers is shown below.
the two integers.
• (+) ÷ (+) = (+)
3. Addition or subtraction of two integers • (+) ÷ (–) = (–)
can be represented by using a number line. • (–) ÷ (+) = (–)
• (–) ÷ (–) = (+) CHAPTER
7

Calculate. 8 1
(a) –1 + 4
(b) 2 + (–4) Calculate.
(c) 3 – 5 (a) –4 × 2 (b) 3 × (–4)
(c) –7 × (–6)
(d) –6 – (–3)
Solution:
Solution: (a) –4 × 2
(a) –1 + 4 4 units to the right = –(4 × 2) (–) × (+) = (–)
= 3 = –8
–1 0 1 2 3
(b) 3 × (–4)
= –(3 × 4) (+) × (–) = (–)
(b) 2 + (–4) 4 units to the left = –12
= 2 – 4
= –2 –2 –1 0 1 2 (c) –7 × (–6)
= +(7 × 6) (–) × (–) = (+)
= 42
(c) 3 – 5 5 units to the left
= –2
–2 –1 0 1 2 3 Try question 2 in Formative Practice 1.2



(d) –6 – (–3) 3 units to the right 9
= –6 + 3
= –3 –6 –5 –4 –3 Calculate.
(a) 35 ÷ (–5) (b) –12 ÷ 2
–24
(c)
Try question 1 in Formative Practice 1.2 –8
Solution:
(a) 35 ÷ (–5) = –(35 ÷ 5) (+) ÷ (–) = (–)
1.2.2 Multiplication and Division of = –7
Integers
(b) –12 ÷ 2 = –(12 ÷ 2) (–) ÷ (+) = (–)
1. The sign of the product for multiplication = –6
of integers is shown below.
–24 24
• (+) × (+) = (+) (c) –8 = 8 (–) ÷ (–) = (+)
• (+) × (–) = (–) = 3
• (–) × (+) = (–)
• (–) × (–) = (+) Try question 3 in Formative Practice 1.2






5





F1 Chapter 1.indd 5 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

1.2.3 Perform computations involving (b) –6 + (7 – 10) ÷ (–3) Brackets ( )
combined basic arithmetic
operations of integers = –6 + (–3) ÷ (–3) × / ÷ from
= –6 + [(–3) ÷ (–3)] left to right
1. The order of operations involving addition, = –6 + 1 + / – from
subtraction, multiplication, division and = –5 left to right
brackets is as shown below.
CHAPTER
Bracket Perform the basic
1
↓ –7 + (–5) –7 – 5 arithmetic operations
× or ÷ from left to right (c) 1 – (–2) = 1 + 2 for numerator and
↓ –12 denominator separately.
+ or – from left to right = 3
= – 4 Simplified
10

Solve each of the following. Try question 5 in Formative Practice 1.2
(a) –8 + (–3) – (–5)
(b) 2 × (–8) ÷ 4
Solution: 1.2.4 Describe the laws of arithmetic
(a) –8 + (–3) – (–5) = –8 – 3 + 5 operations
= –11 + 5 + / – from
= –6 left to right 1. The law of arithmetic operations:
(a) Commutative Law
(b) 2 × (–8) ÷ 4 = –(2 × 8) ÷ 4
= –16 ÷ 4 a + b = b + a
= –(16 ÷ 4) × / ÷ from a × b = b × a
left to right
= –4
(b) Associative Law
Try question 4 in Formative Practice 1.2
(a + b) + c = a + (b + c)
(a × b) × c = a × (b × c)

11
Calculate each of the following. (c) Distributive Law
(a) 3 + (–5) × 2 – 7
(b) –6 + (7 – 10) ÷ (–3) a × (b + c) = a × b + a × c
a × (b – c) = a × b – a × c
–7 + (–5)
(c)
1 – (–2)
Solution: (d) Identity Law
(a) 3 + (–5) × 2 – 7 a + 0 = a a + (–a) = 0
= 3 + –(5 × 2) – 7 × / ÷ from a × 0 = 0 a × 1 = a

left to right
= 3 + (–10) – 7 1
= –7 – 7 + / – from a × a = 1
= –14 left to right





6





F1 Chapter 1.indd 6 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

1.2.5 Perform efficient computations Solution:
by using the laws of basic Current temperature of ice cube
arithmetic operations = 0°C – 2°C + 35°C
= –2°C + 35°C
= 33°C
12
Calculate each of the following using efficient Try questions 7 – 8 in Formative Practice 1.2 CHAPTER
computation.
(a) (105 + 47) + 13 1
(b) (4 × 9) × 25 14 Daily Application
(c) 3 × 102 Company A & D has 3 branches, namely,
(d) 39 × 5 + 12 × 5 P, Q and R. In 2016, branch P had a loss of
Solution: RM14 230, branch Q gains a profit of RM32 000
(a) (105 + 47) + 13 and branch R had a loss of 2 times of branch
= 105 + (47 + 13) Associative Law P. Explain whether Company A & D gains profit
= 105 + 60 in 2016.
= 165 Solution:
Branch P has a loss of RM14 230.
(b) (4 × 9) × 25 ➞ –RM14 230
= (9 × 4) × 25 Commutative Law
= 9 × (4 × 25) Branch Q has a profit of RM32 000.
= 9 × 100 ➞ +RM32 000
= 900 Associative Law Branch R has 2 times the loss of branch P.
➞ 2 × (–RM14 230)
(c) 3 × 102
= 3 × (100 + 2) –RM14 230 + RM32 000 + 2 × (–RM14 230)
= 3 × 100 + 3 × 2 Distributive Law = –RM14 230 + RM32 000 + (–RM28 460)
= 300 + 6 = –RM14 230 + RM32 000 – RM28 460
= 306 = –RM10 690 - sign shows loss.

(d) 39 × 5 + 12 × 5 Thus, Company A & D does not gain profit.
= (39 + 12) × 5 Distributive Law Company A & D had a loss of RM10 690.
= 51 × 5
= 255 Try question 9 in Formative Practice 1.2

Try question 6 in Formative Practice 1.2 Common mistake 1

INFO
1.2.6 Solve problems involving Formative Practice 1.2
integers
1. Calculate each of the following.
13 (a) 3 + (+2) (b) –3 + 6
The initial temperature of an ice cube in a (c) 7 + (–8) (d) –5 + (–9)
(f) 2 – (–9)
(e) 4 – 7
beaker is 0°C. When a pinch of salt was added, (g) –6 – 4 (h) –7 – (–3)
the temperature of the ice cube dropped by
2°C. Then, the ice cube was heated until the 2. Evaluate each of the following.
temperature increased by 35°C. Find the current (a) 8 × (–2) (b) –4 × 5
temperature, in °C, of the melted ice cube. (c) (–6) × (–7) (d) (–3) × (–12)




7





F1 Chapter 1.indd 7 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers


3. Evaluate each of the following. 1.3 Positive and Negative
(a) 45 ÷ (–3) (b) –28 ÷ 4 Fractions
–36
(c) (–49) ÷ (–7) (d)
–3 1.3.1 Represent positive and negative
4. Calculate. fractions on number lines
(a) 5 – (–2) + (–7)
(b) –4 + 3 – (–2) 1. Representing the positive and the negative
CHAPTER
(c) –21 ÷ 7 × (–4) fractions on a number line is the same as
1
(d) 81 ÷ (–9) × (–3) integers.
The value is decreasing The value is increasing
5. Evaluate. 1 1 1 1 1 1 1 1
(a) –7 × (–2) + (–4) –– –– 3 –– –– + – + – + – + –
3
3
3
3
3
3
3
(b) 8 ÷ (–4) – (–2)
2
1
4
3
4
1
(c) 42 – (–16) ÷ (–8) –– –– 3 –– 2 –– 0 – – – –
3
3
3
3
3
3
3
3
(d) 7 + (–5) × (–2) Negative fractions Zero Positive fractions
(e) 10 – 20 ÷ (–2) + (–5)
(f) –6 × [12 + (–7)] – (–2) 2. Note that the positive fractions are located
16 – (–2) on the right hand side of zero whereas the
(g)
–5 + 2 negative fractions are located on the left
–23 + 7 hand side of zero.
(h)
1 – (–3)

INFO
6. Solve each of the following using efficient MATHS INFO
calculation.
(a) 401 + 82 + 8 The fractions can also be represented by using
(b) 500 + 47 – 17 vertical number line.
(c) 49 × 50 × 2
(d) 3 × 81 ÷ 9
(e) 701 × 4 15
(f) 15 × 3 + 25 × 3
Represent the following fractions on number
7. An eagle flew 20 m above sea level. A fish lines.
was 35 m vertically below the eagle. Find the 1 2 4 3
position of the fish. (a) 5 , – 5 , – 5 , 5

8. The water level in a reservoir decreases by (b) – 5 , 1 , – 2 , – 1
2 m every day. Find the total decrease of water 6 3 3 6
level, in m, after 3 days.
Solution:
9. In a Mathematics quiz, for each correct answer (a)
will be awarded 3 marks, for each wrong 4 2 1 3
5
5
answer will be deducted 2 marks and for each –– 3 –– 1 0 – 2 –
5
5
unanswered question will be deducted 1 mark. –– –– –
5
5
5
The quiz has 16 questions and the contestants
who scored 35 and above will be given a prize. (b) 4 2 2 1
(a) Leong gave 13 correct answers and 2 –– = – – – = –
3
3
6
6
wrong answers. Determine whether Leong
will be awarded a prize. Give your reason. 5 2 1 1
(b) John gave 13 correct answers. Is it possible –– –– –– –
6
3
6
3
3
2
for John to receive the prize? Give your –– –– 0 – 1
reason. Analysing Evaluating 6 6 6
Try question 1 in Formative Practice 1.3
8
F1 Chapter 1.indd 8 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

1.3.2 Compare and arrange fractions 17
in order
1
1
(a) Arrange – , 1 , – , 1 and – 3 in
5 10 2 5 10
1. On a number line, the fractions to the right ascending order.
is larger than the fractions to the left. 1 1 1 3 1
(b) Arrange , – , – , and – in CHAPTER
2. Based on the position of fractions on 4 8 4 8 2
a number line, the fractions can either descending order.
be arranged in ascending order or in Solution: 1
descending order.
1
1
1
3
(a) – , 10 , – , 1 , – 10
2
5
5
16 ↓ ↓ ↓ ↓ ↓ Equalize the
denominator
Determine the largest fraction. 2 1 5 2 3
,
1 1 – 10 , 10 , – 10 10 , – 10
(a) – or
2 3
7 3
(b) –3 or –1 Draw a number line to represent the given
8 4 fractions.
2 5
(c) –1 or –1
3 6
Solution: –– –– –– – –
1
2
3
2
5
1 1 10 10 10 10 10
(a) is larger than – . 1 3 1 1 1
3 2 –– –– –– – –
2 10 5 10 5
A positive fraction is always larger than a Original fractions
negative fraction.
Thus, the fractions arranged in ascending
7 3
1
1
1
(b) –3 or –1 order is – , – 3 , – , 1 , .
8 4 2 10 5 10 5
Compare the whole number of the two (List the fractions on a number line from
mixed numbers: left to right.)
–1 is larger than –3.
3 7
Thus, –1 is larger than –3 .
4 8
Alternative Method
2 5 4 5
(c) –1 or –1 ➞ –1 or –1
3 6 6 6 1 1 1 1 3
– , , – , , –
–10 –11 5 10 2 5 10 Equalize the
➞ or
6 6 ↓ ↓ ↓ ↓ ↓ denominator
2 1 5 2 3
,
Compare the values of numerators for – 10 , 10 , – 10 10 , – 10
the two negative fractions with the same
denominator: Compare the numerators with the same
–10 is larger than –11. denominators. Arrange the fractions based on
10 11 the values of numerators, from the smallest
Thus, – 6 is larger than – 6 . value to the largest value.

2 5 5 3 2 1 2
Thus, –1 is larger than –1 . – , – , – , ,
3 6 10 10 10 10 10
1 3 1 1 1
= – , – , – , ,
2 10 5 10 5
Try question 2 in Formative Practice 1.3
9

F1 Chapter 1.indd 9 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

1 1 1 3 1
(b) , – , – , , – Bracket
4 8 4 8 2 Equalize the ↓
↓ ↓ ↓ ↓ ↓ denominators × or ÷ from left to right
2 1 2 3 4
, – , – , , – ↓
8 8 8 8 8 + or – from left to right
Draw a number line to represent the given
fractions.
CHAPTER
18
1
4 2 1 2 3
–– –– –– – – Solve each of the following.
8 8 8 8 8
1 1 1 1 3 1 1 3
–– –– –– – – (a) –1 + ×
2 4 8 4 8 8 2 4
1
Original fractions 1 1 3
(b) 1 ÷ –1 – 2
8 2 4
Thus, the fractions arranged in descending (c) –1 ÷ 4 + 1 × 2 1 Change the
1
3 1 1 1 1 3 9 4 2
order are , , – , – , – . mixed number to
8 4 8 4 2 improper fraction.
(List the fractions on a number line from Solution:
1
9
right to left.) (a) –1 + 1 × 3 = – + 1 × 3
8 2 4 8 2 4
9 1 3
Alternative Method = – + 1 2 × 4 2
8
9 3
1
1
1 , – , – , 3 , – 1 = – + 8 × / ÷ from
8
left to right
4 8 4 8 2 Equalize the 6
↓ ↓ ↓ ↓ ↓ denominators = – 8
2 , – 1 , – 2 , 3 , – 4 3 The lowest
8 8 8 8 8 = – term
4
Compare the numerators that have the same
denominators. Arrange the fractions based 1 1 3 Change to
1
on the values of numerators, from the largest (b) 1 ÷ –1 – 4 2 improper fraction.
2
8
value to the smallest value.
3 , 2 , – 1 , – 2 , – 4 9 1 3 3 2 Equalize the
8 8 8 8 8 = 8 ÷ – – 4 denominators for the
2
calculation in the
3 1 1 1 1 bracket
= , , – , – , – 9 6 3
1
8 4 8 4 2 = ÷ – – 2
8 4 4
Do the operations inside
Try question 3 in Formative Practice 1.3 9 9 the brackets first
= ÷ –
8 1 2
4
1.3.3 Perform computations involving = 9 × – 4 Change ÷ into × and
9
combined basic arithmetic 8 1 2 inverse the fraction – .
9
1
operations of positive and = – 4
negative fractions 2
1. The order of operations involving addition, 1 4 1 1
subtraction, multiplication, division and (c) –1 ÷ 9 + 4 × 2 2
3
brackets for fractions is the same as the 4 4 1 5 Change to
order of operations involving integers. = – ÷ 9 + 4 × 2 improper fraction.
3
10



F1 Chapter 1.indd 10 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

3
1 4 4 2 1 1 5 × / ÷ from Thus, the company gained a profit of RM1
= – ÷ 9 + 4 × 2 2 left to right million in the period of three years. 4
3
1 4 9 2 1 1 5 2
= – × 4 + 4 × 2 Try questions 5 – 6 in Formative Practice 1.3
3
5
= –3 + Common CHAPTER
8 mistake 2
Praktis Formatif 1
3 HOTS Challenge
= –2
8 INFO Fill in the blanks with ‘+’, ‘‒’, ‘×’ and ‘÷’ without 1
repetition to get the largest value.
Try question 4 in Formative Practice 1.3
(‒8) (‒10) 8 (‒4) 1
1.3.4 Solve problems involving Solution:
fractions 4 (–) × (–) = (+)

(–8) × (–10) + 8 – (–4) ÷ 1
19 Daily Application 1442443 14243
2 Get the
1 Get the
larger value smaller value
The table below shows the profit / loss of a
company in three consecutive years. 3 (+) + (+) = (+)
Year Profit / Loss
1
2014 Profit of RM1 million Formative Practice 1.3
3
1. Represent each of the following on number
1
2015 Loss of RM2 million lines.
4
4
2
2
(a) 1 , – , 3 , – (b) 1 , – , 0, –1 1
2016 2 times of the profit in the year 2014 7 7 7 7 3 3 3
1 1 1 1 1 1 1 3
(c) , – , – , (d) – , , , –
Calculate the profit or loss, in million, of the 6 2 3 3 4 8 2 8
company in the period of three years. Give your 2. Determine the larger fraction.
answer in fraction form. 2 4 1 1
(a) – , (b) –5 , –1
Solution: 3 5 2 2
3
1
7
(c) –2 , –2 7 (d) –3 , –2 , –2 1
1
1 1 1 Negative sign 5 10 8 9 6
1 + –2 2 + 2 × 1 shows loss.
3 4 3 3. Arrange each of the following in
1
1 1 4 (i) ascending order,
= 1 – 2 + 2 × 2
3 4 3 (ii) descending order.
1
4 9 4 1 3 1 5 1
= – + 2 × 2 (a) , – , – , , –
3 4 3 2 8 2 8 8
4 9 8 2 1 1 3 7
= – + (b) – , , , , –
3 4 3 5 10 2 5 10
1
5
1
16 27 32 (c) –1 , – , 4 , –1 , 7
= – + 3 6 9 6 9
12 12 12 1 5 1 7 3
21 (d) 1 , – , –1 , –1 ,
= 4 8 2 8 2
12
7 4. Calculate each of the following.
=
4 (a) 1 + –2 1 2 1 2
3
1
– –
3 2 4 8
= 1
4
11
F1 Chapter 1.indd 11 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

2. Note that the positive decimals are located
1
1 2
(b) –2 × 4 ÷ – 2 on the right hand side of zero whereas the
2 5 3
negative decimals are located on the left
1 1 5
1 2
(c) 1 × – – hand side of zero.
9 5 6
7 3 5

INFO
(d) – + × MATHS INFO
8 10 12
3 1 5
1
CHAPTER
(e) – ÷ 1 – 2 Decimals can also be represented by using vertical
4 2 8 number line.
1
5
8
3
1
× –
(f) –3 + 12 2 1 15 2 20
4
1 4 2 1
(g) –1 – ÷ 2 × Represent the following decimals on number
4 9 3 2
lines.
1 5 3 1
1 2
(h) –2 ÷ + × – (a) 1.0, –1.5, –0.5, 1.5, –2.0
2 8 4 6
(b) –1.2, 1.2, –4.8, 3.6, –2.4
2 2 5 1
1 2
(i) – × 1 – – ÷ 1 Solution:
7 5 6 4
(a)
–2.0 –1.5 –0.5 1.0 1.5
3
5. A submarine was submerged as deep as of –1.0 0 0.5
5
250 m per minute. Find the new position, in m,
1 (b)
of the submarine after hour.
4 –4.8 –2.4 –1.2 1.2 3.6
Applying
–3.6 0 2.4
6. Normala buys 6 packets of sugar with mass of
1
3 kg each. She needs 2 kg of sugar to bake Try question 1 in Formative Practice 1.4
10 2
a cake. Is Normala’s sugar enough for her to
bake the cake? Give your reason. 1.4.2 Compare and arrange decimals
Applying Analysing in order
1. On a number line, the decimals to the right
is larger than the decimals to the left.
1.4 Positive and Negative 2. Based on the position of decimals on
Decimals the number line, the decimals can either
be arranged in ascending order or in
1.4.1 Represent positive and negative descending order.
decimals on number lines
21
1. Representing the decimals on a number
line is the same as integers. Determine the largest decimal.
(a) 1.8 or –4.5
(b) –5.35 or –8.6
The value is decreasing The value is increasing
(c) –3.62, –4.82 or –3.67
–0.1 –0.1 –0.1 –0.1 +0.1 +0.1 +0.1 +0.1
Solution:
–0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.4
(a) 1.8 is larger than –4.5.
Negative decimals Positive decimals A positive decimal is always larger than a
Zero
negative decimal.
12





F1 Chapter 1.indd 12 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

(b) –5.35 Thus, the decimals arranged in descending
–5 is larger than –8. order are 3.28, 2.2, –1.03, –2.3, –4.1.
–8.6
–5.35 is larger than –8.6. Try question 3 in Formative Practice 1.4
(c) –3.62, –4.82 or –3.67
Compare the value of first digit, –3 is larger 1.4.3 Perform computations involving CHAPTER
than –4. Thus, –4.82 is the smallest. combined basic arithmetic
operations of positive and
For –3.62 and –3.67, compare the value of negative decimals 1
the last digit because the values of the first
digit and the second digit are the same.
1. The order of operation involving addition,
Since, –0.02 is larger than –0.07, –3.62 is subtraction, multiplication, division and
larger than –3.67.
brackets for decimals is the same as
Therefore, –3.62 is the largest. integers.

Try question 2 in Formative Practice 1.4 Bracket
↓
× or ÷ from left to right
22 ↓
(a) Arrange –1.6, 1.4, –3.8, –2.5 and 2.35 in + or – from left to right
ascending order.
(b) Arrange 3.28, –4.1, –1.03, 2.2 and –2.3 in
descending order. 23
Solution:
(a) Positive numbers: 1.4 and 2.35 Solve each of the following.
Compare the value of the first digit, 1 and 2. (a) 4.2 + (–1.25) × 8.2
2 is larger than 1. Thus, 2.35 is larger than (b) 8.91 ÷ (–0.02 – 1.6)
1.4. (c) (–5.2 + 1.48) – 3.12 × 2.5
Arrange in ascending order: 1.4, 2.35
Negative numbers: –1.6, –3.8 and –2.5 Solution:
Compare the value of the first digit and (a) 4.2 + (–1.25) × 8.2 × / ÷ from left to right
arrange the decimals in ascending order = 4.2 + (–10.25)
based on the value of the first digit, that is = 4.2 – 10.25
–3.8, –2.5, –1.6. = –6.05
Thus, the decimals arranged in ascending
order are –3.8, –2.5, –1.6, 1.4, 2.35. (b) 8.91 ÷ (–0.02 – 1.6) Perform computation
in the bracket first.
= 8.91 ÷ (–1.62)
(b) Positive numbers: 3.28, 2.2
Compare the value of the first digit, 3 and = –(8.91 ÷ 1.62)
2. = –5.5
3 is larger than 2. Thus, 3.28 is larger than Perform
2.2. (c) (–5.2 + 1.48) – 3.12 × 2.5 computation in
Arrange in descending order: 3.28, 2.2 = –3.72 – 3.12 × 2.5 the bracket first.
Negative numbers: –4.1, –1.03 and –2.3 = –3.72 – 7.8
Compare the value of the first digit and = –11.52 × / ÷ from left to right
arrange the decimals in descending order
based on the value of the first digit, that is Try question 4 in Formative Practice 1.4
–1.03, –2.3, –4.1.



13





F1 Chapter 1.indd 13 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

1.4.4 Solve problems involving (g) –2.25 – 1.125 × 3.8 ÷ 0.25
decimals (h) –0.5 ÷ 0.8 + 1.55 × (–3.24)
(i) –4.8 × 1.4 – (–2.28) ÷ 0.625
24 Daily Application 5. In an experiment, the initial temperature of
a metal rod was 35.3°C. The temperature of
A turtle was 10.28 m below the sea level. The the metal rod dropped by 45.5°C and then
vertical distance between a fish and the turtle increased by 6.2°C. Find the final temperature,
is 3.85 m. State the possible positions, in m, of in °C, of the metal rod. Applying
CHAPTER
the fish.
1
Solution: 6. Danny bought 2 500 units and 3 000 units of
There are two possible positions. shares of a company at the price of RM1.76
per unit and RM1.68 per unit respectively. At
Either the fish is located above the turtle or the the end, he sold all the shares at the price
fish is located below the turtle. of RM1.75 per unit. Determine whether Danny
If the fish is located above the turtle, then the gained profit. Give your reason.
position of the fish = –10.28 + 3.85 Applying Analysing
= –6.43 m
If the fish is located below the turtle, then the
position of the fish = –10.28 – 3.85
= –14.13 m 1.5 Rational Numbers
Thus, the possible position of the fish is either
6.43 m below the sea level or 14.13 m below 1.5.1 Recognise and describe rational
the sea level.
numbers
Try questions 5 – 6 in Formative Practice 1.4
1. A rational number is a number that can
a
Formative Practice 1.4 be written in the form of b , where a and
b are integers and b ≠ 0.
1. Represent the following decimals on number
lines.
(a) 0.2, –0.1, 0.3, –0.4, –0.2 25
(b) –1.3, –3.9, 2.6, –5.2, 3.9
Determine whether the following numbers are
2. Determine the largest decimal. rational numbers. Explain your answer.
(a) –2.3 or 2.9
2
(b) –5.6 or –7.3 (a) 1 (b) –0.24 (c) 4
(c) –1.12, –3.52 or –1.11 3
3. Arrange each of the following in Solution:
(i) ascending order,
(ii) descending order. 2 5 Express the number in
(a) 1 = improper fraction.
(a) 3.87, –1.4, –6.7, 4.5, –3.31 3 3
(b) –0.4, 0.9, –5.2, 1.4, –3.0 2
(c) 2.33, –3.22, –4.11, 1.55, –1.44 Thus, 1 is a rational number.
3
(d) –5.42, –5.44, 0.3, –2.9, 0.03
4. Calculate each of the following. 24 Express in the fraction
(a) 0.7 + (–2.4) – (–0.04) (b) –0.24 = – 100 of hundredths.
(b) –1.5 × 3.2 ÷ 4
(c) (–1.4) × 3.25 – 4.8 = – 6 In the lowest term.
(d) 0.245 + (–2.3) × (–3.8) 25
(e) –5.6 ÷ (–1.5 – 1.3)
(f) (–1.75 + 4.85) × (–2.15) Thus, –0.24 is a rational number.



14





F1 Chapter 1.indd 14 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

TIPS 27 Daily Application

–0.24 can be expressed in the fraction form A submarine was located 650 m below the sea
by using a scientific calculator. level. The submarine rose 20.5 m per minute
2
Press (–) 0 . 2 4 = SHIFT /c for 20 minutes and then descended 135 m.
d
5
Find the final position, in m, of the submarine. CHAPTER
4 Solution:
(c) 4 = 1
1 Final position of the submarine
1
Thus, 4 is a rational number. 2
= –650 + 20 × 20.5 + –135 5 2
Try question 1 in Formative Practice 1.5 2
= –650 + 20 × 20.5 – 135
5
= –650 + 410 – 135.4
26 = –240 – 135.4
Calculate each of the following. = –375.4
1 5 2 1
(a) 4.7 – –1 8 × 5 , give the answer as a Thus, the final position of the submarine was
decimal. 375.4 m below the sea level.
1 1 1 2 Try questions 4 – 6 in Formative Practice 1.5
(b) –0.75 + 8 ÷ 2 × 0.8, give the answer as a

fraction.
Solution: TIMSS Challenge
Fill in the blanks with the symbol ‘+’ or ‘‒’ to get
1
(a) 4.7 – –1 5 2 × 1 the largest value.
8
5
1
5 1 10 1 2 2 (–7.5)
–
= 4.7 + 1 × 2
8 5
Change into
= 4.7 + 1.625 × 0.2 decimals.
= 4.7 + 0.325
= 5.025 Formative Practice 1.5
1 1 1 2
(b) –0.75 + 8 ÷ 2 × 0.8 1. Determine whether the numbers –8, 3.15,
1
1 75 1 1 2 8 Change into 1 and – 2 are rational numbers. Give your
= – 100 + 8 ÷ 2 × 10 fraction. 5 3
reason.
2
3
1
= – + 1 × 2 × 4 2. Calculate each of the following. Give your
4
8
5
answer in decimal form.
1 3 1 2 4
= – + × 1 4
(a) –5.2 + 2 × –
4
4
5
2 1 2
5
2 4
= – × (b) [6 + (–2.13)] × 2
4 5 3
1
2 (c) –2 ÷ [5.2 – (–2.8)]
= – 2
5
1
1
(d) –2.53 + – – 3 ÷ 0.6 2
Try questions 2 – 3 in Formative Practice 1.5 8 4
15
F1 Chapter 1.indd 15 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers


3. Calculate each of the following. Give your 6. In a Mathematics Quiz, each contestant is
answer in fraction form. given 10 questions. Each correct answer will
1
(a) 2.25 + –1 1 2 × 8 be awarded 3 marks, each wrong answer will
be deducted 1.5 marks and each unanswered
2
1 1 question will be deducted 1 marks. The table
1 2
(b) – ÷ 0.1 + – 2
8 4 shows the number of questions answered by 3
1
1
2
(c) 3.65 + –2 – 2 × 2 1 contestants.
4
5
CHAPTER
1
1
(d) –1.625 + 1 ÷ 1 1 2 × 0.4 Number of Number of
1
8
2
Contestant questions questions
4. Puan Hasnah had 4.5 kg of sugar. She used answered answered
1 of the sugar to bake a cake. Calculate the correctly wrongly
4
mass, in kg, of the remaining sugar. Give the
answer in fraction form. Applying Emilia 5 4
5. The initial depth of a pond was 2.52 m. When Ker Er 5 5
the surrounding temperature increased, the
1
water level of the pond descended of the
3 Tharishini 4 0
initial level. Then, water was pumped into the
pond until the levels increased by 12.5 cm. Among the three contestants, who scored the
Calculate the current height, in m, of the water highest marks? Explain your answer.
level of the pond. Give the answer in decimal Analysing Evaluating
form. Applying
Summative Practice 1 Full
solution



Section A 4. The diagram below shows a number line. P and
Q are decimal numbers.
1. Which of the following is an integer?
3
A C √5 –1.7 P Q –0.8 –0.5
4
B 6.7 D 0 Determine the value of P and Q.
A P = –1.4, Q = –1.3
2. Which of the following shows ascending order? B P = –1.1, Q = –1.4
7
A 2, , 0.5, –2, –1 C P = –1.3, Q = –1.4
2 D P = –1.4, Q = –1.1
B –12, –14, –16, –18, –20
1 3 14
C –0.25, , , 4.2, 5. Which of the following is the correct calculation
4 5 3 3
D 0.9, 0.6, 0.3, 0, – 0.3 for 6(–2 + 8) × 4.8 ÷ ?
5
A –36 × 8
3. 2 + 2 + 2 + 3 = × 2 + 5 5
7 7 7 7 7 7 B 36 × 4.8 ×
3
The missing value in is 3
C 36 × 4.8 ×
A 2 C 4 5
B 3 D 5 D 6(–6) × 8




16





F1 Chapter 1.indd 16 02/03/2023 1:35 PM

Mathematics Form 1 Chapter 1 Rational Numbers

Section B (b) (i) State the biggest and the smallest
fraction based on the fraction numbers
1. (a) Arrange the following numbers in descending below. [2 marks]
order. [1 mark]
4 1 1 1 1 1 1
7, – 6 , 3.8, 3 , – 4.8, –10 – , , , – ,
5 5 9 6 4 5 8

(b) Match. [3 marks] CHAPTER
(ii) The diagram below shows a number line.
(4 + 7) + 3 Associative
= 4 + (7 + 3) law 1
M –0.4 0.4 N 2.0
3(3 + 5) Distributive State the value of M and of N. [2 marks]
= 3 × 3 + 3 × 5 law
(c) The diagram below shows a number line.
Commutative
7 + 3 = 3 + 7 law
—
S –2 –1 1.5 T
4
2. (a) Fill in the blanks with ‘+’, ‘-’, ‘×’, ‘÷’. [2 marks] Determine the value of S – T. [3 marks]
Analysing
(i) −9 (−7) = −2 × [6 (−2)] 20
2. (a) (i) Sam wanted to simplify 9 .
(ii) 6 + (−8) 4 = −4 (−1)
The following are Sam’s steps of working.
(b) Fill in the blanks with ‘+’ or ‘−‘ to obtain the 20 = 20 Step 1
smallest value. [2 marks] 9 4 + 5
1 = 20 + 20 Step 2
(i) (−6) 5.3 4 5
4
7 = 5 + 4 Step 3
(ii) −3.5 (−8)
5 = 9 Step 4
3. (a) The diagram below shows 4 number cards. Sam’s friend, Daniel told him that his
working was incorrect. Which step of
–10 11 –13 5 Sam’s working is incorrect? What is the
actual answer? [2 marks]
Fill in the blanks with the suitable number Applying
from the diagram to form an arrangement of 2
integer in descending order. [2 marks] (ii) Given 7.5 ÷ 5 − 3.51 = x × 0.5.
Find the value x. [2 marks]
8 , , –8 , , –12
(b) Given that 3 of Alvin’s money is equal to
(b) Mark (3) against the rational number and (7) 2 4
against the irrational number. [2 marks] 3 of Daniel’s money. If Daniel has RM360,
calculate the total amount of their money.
(i) π (ii) −3.5 [3 marks]

(c) Mr. Foo bought 2 000 unit shares of Company
Section C A & B at the price of RM2.48 per unit. On the
next day, the shares decreased by 5 cents
1. (a) Cindy has 2 480 pieces of stamps. The
1 per unit and Mr. Foo bought another 3 000
number of Ahmad’s stamp is of Cindy’s unit shares. If Mr. Foo sold all his shares
8
stamp, while Muthu has 4 times the number at the price of RM2.46 per unit, determine
whether Mr. Foo gained profit. Hence, give
of stamps that Ahmad has. All the stamps your opinion on why Mr. Foo bought the
are collected and arrange into 10 albums.
Calculate the number of stamps in each shares when the price of shares decreased.
[3 marks]
album. [3 marks]
Analysing Evaluating


17





F1 Chapter 1.indd 17 02/03/2023 1:35 PM

Learning Area: Measurement and Geometry

Chapter
9 Basic Polygons




















































A cobweb is a structure used by a spider to trap its prey. The construction of cobwebs
consists of various basic polygons. What is the shape of the polygon that is in the cobwebs?




Access to
INFOGRAPHIC
KEYWORDS


• Vertex • Triangle • Exterior angle
• Kite • Side • Right angle
• Axis of symmetry • Quadrilateral • Acute angle
• Diagonal • Obtuse angle • Trapezium
• Rhombus • Interior angle





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Mathematics Form 1 Chapter 9 Basic Polygons


9.1 Polygons 1
Find the number of vertices and the number of
diagonals of a polygon with 11 sides.
9.1.1 Number of sides, vertices and
diagonals of polygons Solution:
Number of vertices = number of sides
= 11
Diagonals 11 – 3 = 8

VIDEO Therefore, the number of diagonals
1. A polygon is a closed two-dimensional = 2(8) + 7 + 6 + 5 + 4 + 3 + 2 + 1
= 44
shape where the sides are made up of
straight lines.
Alternative Method
2. A polygon has at least three sides.
3. In a polygon, By using the formula,
(a) vertices are points where two sides 11(11 – 3)
meet, number of vertices = 2
(b) diagonals are lines joining two non- 11(8)
adjacent vertices. = 2
= 44
Diagonal
Vertex
Side Try questions 1 and 2 in Formative Practice 9.1

4. In a polygon,
(a) number of vertices = number of sides 9.1.2 Draw, label and name the
(b) number of diagonals can be determined polygons
by following the steps below:
1. Capital letters can be used to label the
Identify the Subtract 3 from the vertices of a polygon.
number of sides number of sides.
of the polygon. Let the result be p. 2. A polygon can be drawn by following the
steps below.
CHAPTER
Identify the Mark the number of points
The value of 2p is
9
The value of p number of equal to the number of
is multiplied then added to all sides of the sides.
by 2. Thus, we the integers that polygon.
get 2p. is less than p until Make sure there is no three
the value 1. or more points in a line.

5. The number of diagonals of a polygon
can be determined by using the following Join all the points Label all the
formula: to form a closed vertices of the
n(n – 3) shape.
Number of diagonals = , polygon.
2
where n represents the number of sides of
the polygon.
Name the polygon according to the letters
at the vertices that have been labelled.
6. A triangle does not have any diagonal.



128





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Mathematics Form 1 Chapter 9 Basic Polygons

3. The name of a polygon is given according TIPS
to the number of sides.
• Hexagon ABCDEF in Example 2 can also be
Name of Number Example of
polygon of sides shape labelled and named as follows.
B C F A
Triangle 3 D B
A E
E C
F D
Quadrilateral 4
B A
F
Pentagon 5 C E
D

Hexagon 6
Try question 3 in Formative Practice 9.1

Heptagon 7
Formative Practice 9.1

1. Find the number of vertices and number of
Octagon 8
diagonals of a polygon with
(a) 5 sides, (b) 7 sides,
(c) 11 sides, (d) 21 sides.
Nonagon 9
2. Determine whether each of the following
statements is true or false.
Decagon 10 (a) A polygon with 8 sides has 8 vertices.
(b) A polygon with 13 sides has 65 diagonals.
3. Draw each of the following polygons, then label
and name the polygons.
2 (a) Polygon with 6 sides.
(b) Polygon with 9 sides.
Sketch a polygon with 6 sides. Then, label and (c) Polygon with 10 sides.
name the polygon. CHAPTER
Solution:

Mark the 6 points. 9.2 Properties of Triangles and 9
D C the Interior and Exterior
Join all the points to
B form a closed figure. Angles of Triangles
E
A Label all the vertices. 9.2.1 Geometric properties of
F
triangles
Therefore, the polygon is a hexagon ABCDEF.
1. The triangles are named based on their
geometric properties.
MATHS INFO 2. The following table shows the types of

INFO
triangles and their respective geometric
The letters labelled on the vertices of a polygon properties. These triangles can be
are properly arranged either clockwise or categorised according to their length of
anticlockwise. sides and the size of angles.




129





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Mathematics Form 1 Chapter 9 Basic Polygons

Types of triangles according to the length

INFO
of sides: MATHS INFO
Number
Types of Geometric There are triangles that can be categorised into
triangles of axes of properties two different types of triangles. For example,
symmetry
Equilateral All the sides
triangle have the
same length.
3 All the Isosceles triangle Isosceles triangle
interior or right-angled or obtuse-angled
triangle.
angles are triangle.
60°.

Isosceles Two of the Try question 1 and 2 in Formative Practice 9.2
triangle sides have
the same
1 length.
The two 9.2.2 Interior and exterior angles of
base angles triangles
are equal.
1. For a triangle,
Scalene All the (a) the sum of all the interior angles is
triangle sides have 180°,
None different (b) the sum of the interior and its adjacent
lengths.
exterior angle is 180°,
(c) the exterior angle is equal to the sum
of two opposite interior angles.
Types of triangles according to the size of
angles:
a + b + c = 180°
Number b
Types of Geometric c + d = 180°
of axes of
triangles symmetry properties a c d d = a + b
Acute-angled All the angles
triangle are acute
CHAPTER
None angles. 3
9

80°
Obtuse-angled One of the
triangle angles is an 41° x
None obtuse angle.
Find the value of x in the diagram above.
Solution:
Right-angled One of the 41° + 80° + x = 180° The sum of all interior
triangle angles in the angles of a triangle is
triangle is a x = 180° – 41° – 80° 180°.
None
right angle = 59°
(90°).




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Mathematics Form 1 Chapter 9 Basic Polygons

4 9.2.3 Solve problems involving
triangles
99°
x 6
41°
A
Find the value of x in the diagram above.
D
Solution:
x = 99° + 41° Common 115°
= 140° mistake 1 B x C
INFO
In the diagram above, ABC is a right-angled
5 triangle and ADC is a straight line. Find the
value of x.
Find the value of x in each of the following
diagrams. Solution: The sum of the interior
(a) (b) /ADB + 115° = 180° angle and its adjacent
exterior angle is 180°.
x
Thus, /ADB = 180° – 115°
= 65°
x 26°
ABD is an isosceles
/BAD = /ADB = 65° triangle.
(c)
32° Given ABC is a right-angled triangle.
So, /ABC = 90°.
x + 90° + 65° = 180°
x
Therefore, x = 180° – 90° – 65°
= 25°
Solution:

(a) x = 60° Equilateral triangle 7

S CHAPTER
(b) x + 26° + 26° = 180° P
x 94°
x + 52° = 180°
x = 180° – 52° R 9
= 128°
Q 22° T
(c) x + x + 32° = 180° In the diagram above, PRT and QRS are straight
2x + 32° = 180° lines. Find the value of x.
2x = 180° – 32° Solution:
= 148° In triangle SRT,

148° /SRT = 180° – 94° – 22°
Therefore, x = = 64°
2
= 74° Therefore, /PRQ = 64°

/PQR = /PRQ = 64°
Therefore, x = 180° – 64° – 64°
Try questions 3 and 4 in Formative Practice 9.2
= 52°



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Mathematics Form 1 Chapter 9 Basic Polygons

8 3. Find the value of x in each of the following
triangles.
P T (a) (b)
x
26° 88°
x
Q R x 46° 32°

S (c) (d)
In the diagram above, PRS is a straight line. 132°
Find the value of x. 101°
Solution: x x x
180° – 26° ∆PQR is an
/PRQ =
2 isosceles triangle. 4. Find the value of x in each of the following
= 77° diagrams.
(a) (b)
So, /TPR = 77° Alternate angles.
x
∆PRT is an x
Then, /PRT = 77° isosceles triangle. 152° 48°
34°
Therefore, x = 180° – 77° Angles on a (c) (d)
= 103° straight line. x
78°
x
Try questions 5 – 10 in Formative Practice 9.2 x
148°
Formative Practice 9.2 5. P

1. State the type of each of the following triangles. S
(a) (b) y 138° 21° x
R Q
134°
In the diagram above, PSR is a straight line.
32° Find the value of x and of y.
(c) (d) 6. P

T
CHAPTER
112°
9
70°
40°
y x
S R Q
2. For each of the following triangles, state the
number of axes of symmetry. In the diagram above, QRS is a straight line.
(a) (b) Find the value of x and of y.
7. T
x U
72°

(c) (d) P Q R
56°
48° 45°
S
66° In the diagram above, PQR and SQT are
straight lines. Calculate the value of x.




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Mathematics Form 1 Chapter 9 Basic Polygons

(ii) All the interior angles are 90°.
8.
(iii) The diagonals are of equal length
and bisectors of each other.

55° (b) Square
x

Number of axes of
Find the value of x in the diagram above. symmetry: 4
Analysing
9. S Geometric properties:
T (i) All the sides have equal length.
x x
68° (ii) The opposite sides are parallel.
(iii) All the interior angles are 90°.
130° (iv) The diagonals are of equal length
P Q R and perpendicular bisectors of
each other.
In the diagram above, PQR is a straight line.
Find the value of x. Analysing
(c) Parallelogram
10.
R
Number of axis of
Q y symmetry: None

Geometric properties:
(i) The opposite sides are parallel
54° S
P T and of equal length.
V x
(ii) The opposite angles are equal.
U
(iii) The diagonals are bisectors of
In the diagram above, RQV, PVST and QSU each other.
are straight lines. RQV is an axis of symmetry
of the triangle PQS. Find the value of x and (d) Rhombus
of y. Analysing

Number of axes of
symmetry: 2 CHAPTER
9.3 Properties of Quadrilaterals
and the Interior and Exterior Geometric properties: 9
Angles of Quadrilaterals (i) All the sides have equal length.
(ii) The opposite sides are parallel.
(iii) The opposite angles are equal.
9.3.1 Geometric properties of (iv) The diagonals are perpendicular
quadrilaterals
bisectors of each other.
1. The following are the types of quadrilaterals (e) Trapezium
and their respective geometric properties.
(a) Rectangle
Number of axis of
symmetry:
Number of axes of
symmetry: 2 In general: None.
Geometric properties:
Geometric properties: (i) Only one pair of opposite sides is
(i) The opposite sides are parallel parallel.
and of equal length.



133





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Mathematics Form 1 Chapter 9 Basic Polygons

(f) Kite b c a = c
b = d
a d
Number of axis of
symmetry : 1
9
Geometric properties: R
(i) Two pairs of adjacent sides are of S 115° 118°
equal length.
(ii) Has one pair of opposite angles 68° x
with the same size. P Q
(iii) One of the diagonals is the Find the value of x in the above diagram.
perpendicular bisector of the
other. Solution: The sum of
(iv) One of the diagonals is the angle x + 115° + 118° + 68° = 360° the interior
angles of a
bisector of the angles at the x + 301° = 360° quadrilateral
vertices. x = 360° – 301° is 360°.
= 59°
10

MATHS INFO
INFO
Q P
x
Some trapeziums may have one axis of symmetry
if the two sides which are not parallel are of equal R 52°
length. S T
In the diagram above, PQRS is a parallelogram
and RST is a straight line. Find the value of x.
Solution:
/PSR = 180° – 52° Adjacent angles on
a straight line.
= 128°
Try question 1 in Formative Practice 9.3 Opposite angles in
Therefore, x = 128° a parallelogram.

9.3.2 Interior and exterior angles of
quadrilaterals Try questions 2 – 4 in Formative Practice 9.3
CHAPTER
9
1. For a quadrilateral,
(a) the sum of all interior angles is 360°. 9.3.3 Solve problems involving
(b) the sum of interior angle and its quadrilaterals
adjacent exterior angle is 180°.


c 11
b
a + b + c + d = 360° A
a d e d + e = 180° 75° B
x C

2. In a parallelogram (or rhombus), the F 50° E 100° D
opposite angles are equal.
In the diagram above, ABC and FED are straight
lines. Find the value of x.




134





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Mathematics Form 1 Chapter 9 Basic Polygons

Solution: Solution:
/CEF + 100° = 180° The adjacent angles /QSR = 45° The base angle of an
isosceles triangle.
on a straight line.
/CEF = 180° – 100°
= 80°
So, /SQR = 180° – 45° – 45°
/CBF = 180° – 75° The sum of the interior angles = 90°
= 105° of a quadrilateral is 360°.
/PQT = 90° Vertically opposite angles
So, x + 105° + 50° + 80° = 360°
x + 235° = 360°
Therefore, x = 360° – 90° – 68° – 110°
Therefore, x = 360° – 235° = 92°
= 125°
14
Common mistake 2 P Q
x
INFO 40° S
T
136°
12 R
In the diagram above, PQST is a parallelogram.
P Q
46° Find the value of x.
R U Solution:
x
S T /QST = 180° – 40° Interior angles
= 140°
In the diagram above, QRS is a straight line.
Find the value of x. /QSR = 360° – 136° – 140°
Solution: = 84°
/QRU = 46° Alternate angles. 180° – 84°
Therefore, x = 2
/SRU = 180° – 46° Opposite angles in = 48°
= 134° a parallelogram.

Therefore, x = 134° 15 CHAPTER

Q 9
9.3.4 Solve problems involving the x
combinations of triangles and
quadrilaterals
R S
32°
13 U
P T
P U
x In the diagram above, PRST is a rhombus and
110°
QRUT is a straight line. Find the value of x.
S 68°
Q T Solution:
45° /RPS = 32° Alternate angles
R
In the diagram above, PQR and SQT are straight /PUR = 90° The diagonals of a rhombus
lines. Find the value of x. intersect at right angles.



135





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Mathematics Form 1 Chapter 9 Basic Polygons

/PRQ = 90° + 32°
Exterior angles (c) Quadrilateral P has equal opposite angles
= 122° of triangle PUR. and its opposite sides are parallel and of
180° – 122° equal length. State the type of quadrilateral
Therefore, x = P.
2
= 29° (d) Which quadrilateral has only one pair of
sides that is parallel?
Try questions 5 – 8 in Formative Practice 9.3
(e) State two common geometric properties of
a rectangle and a parallelogram.
TIMSS Challenge (f) Quadrilateral Q has two axes of symmetry.
Is a rhombus also a type of parallelogram? Determine the type of quadrilateral Q.
Explain. (g) Which quadrilateral has diagonals that
bisect each other at right angles?
(h) List all the quadrilaterals that have diagonals
HOTS Challenge which are of equal length and bisect each
Praktis Formatif 1
S other.
T
2. Find the value of x in each of the following
P x R diagrams.
Q (a) (b)
The diagram above shows the isosceles triangles 132°
PQT, QTR and TRS which are inscribed in a right- 124° 51° x
angled triangle PRS. Find the value of x. 93°
51°
Solution: x
/PTQ = x The base angle of
an isosceles triangle.
/TQR = /TPQ + /PTQ (c) (d)
= x + x 110°
= 2x x 152° 86°
/TRQ = 2x 40° x 88°
91°
/RTS = /TPR + /TRP
= x + 2x
= 3x
3. Find the value of x in each of the following
/TSR = 3x diagrams.
So, 3x + x + 90° = 180° (a) (b)
CHAPTER
4x + 90° = 180°
9
4x = 180° – 90° x 131°
= 90° 38°
90° x
x =
4
= 22.5°
4. In each of the following diagrams, PQRS is a
parallelogram and RST is a straight line. Find
the value of x.
(a) (b)
Formative Practice 9.3 Q R Q
x P 48°
1. (a) Name the quadrilaterals that have equal S
interior angles. R 135° x P
(b) Name the quadrilaterals that have four S T T
sides of equal length.




136





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Mathematics Form 1 Chapter 9 Basic Polygons


5. 7. U T
T S R 52° S
x 70° 148° y R
34°
120° 109°
x
P Q P Q
In the diagram above, RST is a straight line. In the diagram above, PQSU is a parallelogram.
Find the value of x. Find the value of x and of y.

6. 8.
R Q S y R
y 152°
x U P T 125° x
Q
T 38°
S
P
In the diagram above, RSTU is a trapezium,
PQRU is a parallelogram and PUT is an In the diagram above, PQST is a kite and PQR
equilateral triangle. Find the value of x and of y. is a straight line. Find the value of x and of y.






Summative Practice 9 Full
solution

Section A

1. 3. What is the number of diagonals of a polygon
• Two of its sides have the same length. with 10 sides?
• Two base angles are the same.
A 70 C 35
The statement above is the properties of a B 80 D 10
triangle. What is the name of the triangle?
A Equilateral triangle 4.
B Isosceles triangle CHAPTER
C Right-angled triangle P Q
D Scalene triangle 9
2. The diagram below shows an isosceles triangle S
PQR. R
P

69º The Diagram above shows four quadrilaterals
4 cm drawn on square grid. Which of the quadrilateral
42º y P, Q, R and S, is a trapezium?
Q R A P and Q
5.6 cm B Q and S
State the value of PQ and y. C S and R
A PQ = 4 cm, y = 69° D P and S
B PQ = 5.6 cm, y = 69° 5. Name a polygon that has 9 sides.
C PQ = 4 cm, y = 42° A Pentagon C Nonagon
D PQ = 5.6 cm, y = 42°
B Heptagon D Decagon




137





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Mathematics Form 1 Chapter 9 Basic Polygons

Section B
Polygon Number of Number of
1. (a) In the space provided, draw a labelled vertices diagonals
example of a heptagon. [2 marks]
Hexagon
Octagon

4. (a) Write ‘T’ for the true statement and ‘F’ for the
(b) Complete the following table for the type of false statement. [3 marks]
given triangles. [2 marks] (i) A rectangle has four sides of ( )

Triangle Type of triangle equal length.
(i) (ii) The diagonals of a rhombus ( )
intersect at right angles.
(iii) An equilateral triangle has ( )
interior angle of 60° each.

(ii) 2 cm (b) In the diagram below, PQS and QRT are
5 cm straight lines.
Q
6 cm S P
48º
125º
2. (a) Complete the following table for the type of
given quadrilaterals. [3 marks] x
R
Type of T
Quadrilateral
quadrilateral Mark (3) at the correct calculation to
(i) determine the value of x. [1 mark]
x = 90° − 48°
(ii) x = 180° − 125°
x = 48° + 55°


(iii) Section C
1. (a) (i) S U
78°
CHAPTER
x
(b) P Q R

9
Q
48°
R T
P
In the diagram above, PQR, SQT and
TRU are straight lines. Find the value of x.
[2 marks]
(ii)
The diagram above is drawn on square 80°
grid. On the grid, mark the point S to 4x
form a parallelogram PQRS.
[1 mark] x 2x
3. Complete the following table for the number of The diagram above shows a piece of
vertices and the number of diagonals for the paper cut by a student. Find the value
stated polygons. [4 marks] of x. [2 marks]



138





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Mathematics Form 1 Chapter 9 Basic Polygons

(b) P (c) P
Q Q
x x u S
v
R w
U 80° x
S 70°
102° V U T
y 18°
In the diagram above, QRU, VRS and VUT
R T are straight lines. Find the value of u + v +
In the diagram above, PQST is a straight line. w + x. Analysing [3 marks]
Find the value of x and of y. [3 marks]
(c) T 3. (a) The diagram below shows an incomplete
7-sided polygon.
122° S
P y x R (i) Complete the polygon [1 mark]
(ii) Name the polygon [1 mark]
(iii) State the number of diagonals of the
40°
polygon. [1 mark]
Q
In the diagram above, PQST is a kite and
PSR is a straight line. Find the value of x
and of y. Analysing [3 marks]
2. (a) (i) R

(b) (i) P Q
x
110° S P
y
142°
S R
Q
In the diagram above, PQR is an In the diagram above, PQRS is a
rectangle. PR and QS are the diagonals
equilateral triangle and SQR is an of the rectangle. Find the value of x.
isosceles triangle. Find the value of y. [2 marks]
[2 marks]
(ii) (ii)
P P Q S
T x
26° 160° R 65° CHAPTER
T
40° 9
Q R x
U
In the diagram above, URS and QRT are
straight lines. Find the value of x.
S [2 marks]
In the diagram above, PRS is a straight
line. Find the value of x. [2 marks] (c) S
T
(b)
P U
28° T U
x S
y P y R
54° Q
Q R
In the diagram above, PQRU is a parallelogram. The diagram above shows four isosceles
QST and PUT are straight lines. Find the triangles PQU, UQT, TQR and RTS that are
value of x and of y. Analysing inscribed in a right-angled triangle PRS. Find
[3 marks] the value of y. Analysing [3 marks]



139





F1 Chapter 9.indd 139 02/03/2023 1:47 PM

ANSWERS






6. (a) 491 (b) 530 7 1 5 1 3
Chapter (d) (i) –1 , –1 , – , 1 ,
1 Rational Numbers (c) 4 900 (d) 27 8 2 8 4 2
(e) 2 804 (f) 120 (ii) 3 , 1 1 , – , –1 1 , –1 7
5
7. 15 m below sea level 2 4 8 2 8
Formative Practice 1.1 8. Water level decreases by 6 m. 4. (a) –1 3 (b) 3
9. (a) Leong will not receive a prize 8
1. Positive numbers: because he answered 13 questions 1 3
2 , 7.3, 5, +3 correctly, 2 questions incorrectly (c) –1 18 (d) – 4
5 and 1 question not answered; The
6
Negative numbers: total marks that he obtained is 34. (e) – (f) 1 7 9
7
3
–10, –67, – , –8.9 (b) John will likely receive a prize. If 1 1
4 he answered 13 questions correctly (g) –1 3 (h) –4 8
(Zero is not a positive number and not and 3 questions not answered, so 4
a negative number) the total marks obtained is 36 marks. (i) 15
2. (a) –7 levels (b) +500 m If he answered 13 questions
(c) –RM450 (d) +RM0.50 correctly, 1 question incorrectly and 5. 2 250 m below sea level
(e) –150 m (f) –3 cm 2 questions not answered, maybe 6. Not enough. Still short of 7 kg of
3. (a) –100 the total marks obtained is 35 sugar. 10
marks.
(b) +38 or 38
(c) –45
4. Positive integer: 4; Formative Practice 1.4
Negative integer: –8, –3 Formative Practice 1.3
5. (a) 1. (a)
1. (a)
–3 –2 1 2 4 –0.4 –0.2 –0.1 0.2 0.3
4
– – – – 2 – 1 – 3
(b) 7 7 7 7 (b)
–15 –9 –3 3 6 (b)
–5.2 –3.9 –1.3 2.6 3.9
6. (a) 8 (b) –15 1 2 0 1
7. (a) Largest integer: 6; –1– 3 – – 3 – 3 2. (a) 2.9
Smallest integer: –10 (b) –5.6
(b) Largest integer: 14; (c) (c) –1.11
Smallest integer: –16 3. (a) (i) –6.7, –3.31, –1.4, 3.87, 4.5
8. (a) –6, –5, –4, –2, 1, 3 – – – – 1 1 – – 1 (ii) 4.5, 3.87, –1.4, –3.31, –6.7
1
(b) –10, –8, –6, 3, 7, 9 2 3 6 3 (b) (i) –5.2, –3.0, –0.4, 0.9, 1.4
(c) –16, –14, –3, 0, 11, 18 (ii) 1.4, 0.9, –0.4, –3.0, –5.2
(d) –19, –13, –4, –3, 4, 19 (d) (c) (i) –4.11, –3.22, –1.44, 1.55, 2.33
9. (a) 5, 3, 0, –1, –4, –6 (ii) 2.33, 1.55, –1.44, –3.22, –4.11
(b) 7, 5, 3, –1, –2, –6 – – – – 1 – 1 – 1 (d) (i) –5.44, –5.42, –2.9, 0.03, 0.3
3
(c) 4, 2, 1, –1, –3, –7 8 4 8 2 (ii) 0.3, 0.03, –2.9, –5.42, –5.44
(d) –1, –3, –5, –8, –10, –12 4. (a) –1.66 (b) –1.2
2. (a) 4 (b) –1 1 (c) –9.35 (d) 8.985
5 2 (e) 2 (f) –6.665
Formative Practice 1.2 3 1 (g) –19.35 (h) –5.647
(c) –2 (d) –2
1. (a) 5 (b) 3 5 9 (i) –3.072
(c) –1 (d) –14 1 3 1 1 5 5. –4°C
(e) –3 (f) 11 3. (a) (i) – , – , – , 2 , 8 6. Danny gained a profit of RM185.
2
8
8
(g) –10 (h) –4 5 1 1 3 1
2. (a) –16 (b) –20 (ii) 8 , 2 , – , – , – 2
8
8
(c) 42 (d) 36 TIMSS
2
3. (a) –15 (b) –7 (b) (i) – 7 , – , 1 , 1 , 3 ‒; +; ‒
(c) 7 (d) 12 10 5 10 2 5
2
4. (a) 0 (b) 1 (ii) 3 , 1 , 1 , – , – 7 Formative Practice 1.5
(c) 12 (d) 27 5 2 10 5 10
5. (a) 10 (b) 0 1 1 5 4 7 1. All the numbers given are rational
(c) 40 (d) 17 (c) (i) –1 3 , –1 6 , – , 9 , 9 numbers.
6
(e) 15 (f) –28 7 4 5 1 1 –8 = –8 ; 3.15 = 63 ; 1 1 = 6
(g) –6 (h) –4 (ii) 9 , 9 , – , –1 6 , –1 3 1 20 5 5
6
2. (a) –7.2 (b) 2.58
(c) –0.3125 (d) –3.905
204
F1 Answers.indd 204 02/03/2023 1:33 PM

Mathematics Form 1 Answers

3. (a) –9 3 Chapter 2
4 2 Factors and Multiples Summative Practice
(b) –1 1 Section A
2 1. C 2. C 3. D 4. C 5. B
(c) –5 4 TIMSS 6. D 7. B 8. C
5 96 people Section B
7
(d) – 20 Formative Practice 2.1 1.
1
4. 3 3 kg 1. (a) Yes (b) No
8 (c) Yes (d) Yes
5. 1.805 m (e) Yes (f) Yes 4
6. Tharishini scored the highest marks. 2. (a) 1, 2, 17, 34 28
Emilia: 5 questions answered correctly, (b) 1, 2, 3, 4, 6, 12
4 questions answered incorrectly and (c) 1, 2, 3, 6, 13, 26, 39, 78 2 28
1 question not answered. The marks (d) 1, 3, 5, 7, 15, 21, 35, 105
obtained is 8.5. (e) 1, 2, 7, 14, 49, 98
Ker Er: 5 questions answered correctly, (f) 1, 3, 37, 111
5 questions answered incorrectly and 3. (a) 5 × 19 2.
0 question not answered. The marks (b) 2 × 2 × 2 × 2 × 3
obtained is 7.5. (c) 2 × 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Tharishini: 4 questions answered (d) 2 × 2 × 2 × 2 × 2
(e) 5 × 13
correctly, 0 questions answered 12 3 3 3 3 3 3
incorrectly and 6 questions not (f) 2 × 2 × 31
answered. The marks obtained is 9. 4. (a) Yes (b) Yes 16 3 3 3 3
(c) Yes (d) No
(e) Yes (f) No 3. (a) 2 × 2 × 3 × 5 = 60
2 × 2 × 3 × 5 × 7 = 420
Summative Practice 1 5. (a) 1, 2, 4 (b) Thus, LCM for 2, 4 and 9
(b) 1, 2, 4
(c) 1, 2
Section A (d) 1, 5 = 2 × 2 × 3 × 3
1. D 2. C 3. A 4. D 5. B (e) 1, 2, 3, 4, 6, 12 = 36
(f) 1, 2, 3, 6 4. (a) 2, 3
Section B 6. (a) 12 (b) 18 (b) Thus, HCF for 36, 44 and 56
1. (a) 7, 3.8, 3 1 , –4.8, –6 4 , –10 (c) 6 (d) 10 = 2 × 2
5 5 (e) 6 (f) 6
(b) 7. 4 m × 4 m = 4
8. 9 gift packs Section C
9. (a) 32 cm 1. (a) 12, 24, 36, 48
(b) 22 strips of ribbon
(b) 4
2. (a) (i) +, – Formative Practice 2.2 (c) 5 + 37, 11 + 31, 13 + 29, 19 + 23
(ii) , × 2. (a) 38
(b) (i) +, – 1. (a) Yes (b) 180
(c) 17
(ii) –, + (b) Yes
(c) Yes 3. (a) 5
3. (a) 5, –10 (d) No (b) 40
(b) (i) 7 (e) Yes (c) (i) 18 pages
(ii) 2 photos and 3 paragraphs
(ii) 3 (f) Yes
2. (a) 15, 30, 45, 60, 75 4. (a) 23, 46, 69, 92
(b) 36, 72, 108, 144, 180 (b) 6
Section C (c) 112, 224, 336, 448, 560 (c) 1 260 cm
1. (a) 403 (d) 72, 144, 216, 288, 360 5. (a) 3 packs of souvenirs
(b) (i) Smallest fraction: – 1 (e) 30, 60, 90, 120, 150 (b) (i) 60 packs
5 (f) 60, 120, 180, 240, 300 (ii) 2 erasers, 3 pencils and 4 pens
Biggest fraction: 1 (g) 252, 504, 756, 1 008, 1 260 (c) 3 and 4
4
(h) 1 260, 2 520, 3 780, 5 040, 6 300
(ii) M = –1.2, N = 1.2 3. (a) 56
(c) –7 (b) 60 Chapter Squares, Square Roots,
3
2. (a) (i) Step 2; 2 2 (c) 15 Cubes and Cube Roots
(d) 90
9
(ii) 30.48 (e) 90 Formative Practice 3.1
(b) RM680 (f) 144
(c) Mr Foo gained a profit of RM50. (g) 98 1. (a) 4
2
(h) 30
Mr. Foo bought the shares when the (b) 7 2
price of shares decreased because 4. 4 packets of red balloon and 3 packets
the average cost of 1 unit of shares of purple balloon 2.
is lower. 5. 90 minutes
205





F1 Answers.indd 205 02/03/2023 1:33 PM

Mathematics Form 1 Answers

6 squares each of size 1 unit × 1 unit 5. (a) –729 (b) – 64 3. (a) 36
cannot be arranged to form a square. 343
Therefore, 6 is not a perfect square. 38
(c) 0.008 (d) 39 4 9
3. (a) No (b) Yes 125
(c) No (d) Yes 6. (a) 13 824 2 2 3 3
(b) –531.441 (b)
4. (a) 6 × 6 = 6 343 Length of side Total surface
(c)
1 000 of the small area of a small
2 cube (cm) cube (cm)
(b) 23 = 23 (d) –3 103
1 331 3 √1 000 6 × 10 2
(c) Area of square in the diagram 7. (a) 2 (b) –6
= 20 × 20 (c) 8 (d) –9 4. (a) 324 = 2 × 2 × 3 × 3 × 3 × 3
= 400 units 2 8. (a) – 1 (b) 3 √ 324 = 2 × 3 × 3
6 4
Length of the square (c) 2 1 (d) –0.3 = 18
2 (b) √2 744 = √2 × 7 = 14
3  3
3
3
= 400 (e) –0.7 (f) 0.11
9. (a) 2.41 (b) 4.97 Section C
= 20 × 20 (c) 0.90 (d) –1.16 1. (a) (i) 1.29
(ii) 27 + 64 + 125 = 216
= 20 units 10. (a) 27 (b) 1.2 m
(b) –1 331 (c) 64 000 cm 3
5. (a) 121 (b) 16 (c) –64 000 2. (a) (i) 64 (ii) –0.3
81
9
(c) 1.69 (d) 226 981 (b) 8 means the total number of
2
25
6. (a) 1 369 (b) 169 11. (a) 2.3 (b) –4.8 squares on the chessboard. 64
(d) 4.4
(c) –3.3
(c) 219.04 means the number of squares at
12. 6 cm each side of the chessboard.
7. (a) 7 (b) 12 (c) 1 600 tiles
(c) 15 (d) 20 13. RM1 080 3. (a) (i) P : 2 or 9 or 9 2
2
8. (a) 2 (b) 1 5 14. (a) 72 (b) 2.75 Q: 7
2
7 8 (c) –0.12 (d) 9 R: √27
3
(c) 5 (d) 0.11 11 (ii) 729
8 (e) 50.35 (f) –1.37 (b) (i) 50 mm (ii) 50 mm 3
3
9. (a) 7.28 (b) 6.87 (g) –0.015 (h) –2 1 (c) Length of side of the game board
(c) 0.64 (d) 3.81 4 = 246
10. (a) 2 500 (b) 900 (i) –3 (j) 30 1 = 15.7 cm
(c) 64 2 Thus, the game board can fit into
11. (a) 5.7 (b) 4.7 (k) 105 (l) 0.11 box B and C.
(c) 11.2 (m) 61 1 (n) 308
12. (a) 13 (b) 0.6 (o) 3 2 Chapter Ratios, Rates and
4
(c) 14 (d) 1 1 29 Proportions
5
13. (a) 400 tiles (b) RM2 200 Summative Practice 3 Formative Practice 4.1
14. (a) 7 m (b) 576 tiles
Section A 1. (a) 6 : 7 (b) 4 : 7
Formative Practice 3.2 1. C 2. B 3. D 4. C 5. A (c) 7 : 17
6. D 2. (a) 11 : 19 (b) 19 : 11
1. (a) 10 3 (c) 11 : 30
(b) 5 3 Section B 3. (a) 25 : 46 : 24
2. 9 units cubes cannot be arranged 1. (a) 25, 36 (b) 20 : 90 : 43
to form a cube. Therefore, 9 is not a (b) Volume of Legth of side (c) 36 : 66 : 25
perfect cube. cube of the cube (d) 5 : 12 : 18
3. (a) Yes (b) Yes (cm ) 3 (cm) (e) 40 : 120 : 27
(c) No (d) Yes (f) 17 : 15 : 20
10 3 3 √1 000 1 × 5
4. (a) 1 = = 5
4. (a) 3 7 × 7 × 7 = 7 3 3 × 5 15
2. 3 4 × 6 24
3
(b) 1 2 = 1 2 3 2 (b) 4 5 = 5 × 6 = 30
1
1
–
–
3
5
5
(c) Length of the side of a cube 4 × 2 8 3 512 (c) 16 = 16 ÷ 4 = 4
6
24
24 ÷ 4
= 3 512 (d) 54 = 54 ÷ 3 = 18
27 27 ÷ 3 9
= 3 8 × 8 × 8
64 5. (a) No (b) Yes
= 8 units (c) Yes (d) No
206
F1 Answers.indd 206 02/03/2023 1:33 PM

Mathematics Form 1 Answers

6. (a) 1 : 3 : 5 = 4 : 12 : 20 TIMSS Summative Practice 4
(b) 2 : 8 : 6 = 12 : 48 : 36
(c) 35 : 28 : 56 = 5 : 4 : 8 (a) 41 : 28 Section A
(b) Total marbles = 41 + 28
(d) 84 : 28 : 70 = 6 : 2 : 5 = 69 marbles 1. D 2. B 3. A 4. C 5. C
Total number of parts in the ratio 6. A 7. C
7. (a) 6 : 3 = 2 + 1 Section B
(b) Remove 4 bricks from stack I and = 3
2 bricks from stack II or, Remove 3 parts represent 69 marbles. 1. (a) Distance
2 bricks from stack 1 and 1 brick 1 part represents 23 marbles. travelled (km) 160 240 300
from stack II 2 parts represent 46 marbles.
8. (a) 1 : 1 (b) 3 : 2 Therefore, 5 marbles have to be Volume of petrol 8 12 15
(c) 1 : 2 : 4 (d) 1 : 3 : 5 transferred from box Y to box X. (l)
(e) 3 : 4 : 10 (f) 7 : 5 : 3 3
(g) 8 : 6 : 9 (h) 18 : 20 : 45 (b) 5 g/cm
Formative Practice 4.4 = 5 ÷ 1 000 kg
9. (a) 5 : 4 (b) 1 : 3 1÷ 1 000 000 m 3
(c) 10 : 1 : 3 (d) 5 : 7 : 3 1. (a) 2 : 3 : 7
(e) 3 : 10 : 4 (f) 10 : 5 : 6 (b) 8 : 2 : 5 = 5 × 10 3 kg/m
3
(g) 5 : 2 : 10 (h) 2 : 5 : 3 (c) 9 : 12 : 32
2. 7 : 9 : 6 2. (a) 75; 35
10. (a) 6 : 5 (b) 11 : 12 : 10 (b)
(c) 10 : 33 3. (a) 3 : 8 (b) 32 p q r
4. 147 workers
11. (a) 1 : 2 5 5 15 37.5
(b) 3 : 2 : 4 5. (a) k = 130, n = 39 8
(c) 4 : 9 (b) p = 70, q = 98
6. Green umbrella = 48, Red umbrella = 40 Section C
Formative Practice 4.2 7. (a) 1 : 2 1. (a) (i) 63 : 45 : 72 = 7 : 5 : 8
(b) p = 20, n = 12
1. (a) Rate = 15 people ; number of (ii) 300
3 cars 8. (a) 4 : 15 (b) 3 : 9 : 4
people and number of cars (b) Gani = 18 pens, Samad = 15 pens (c) (i) 3 : 2 : 1
9. p = 96, q = 24, r = 60 (ii) 1 500 kg
(b) Rate = 40 kg ; mass (kg) and 10. A = RM343, B = RM441, C = RM196 2. (a) 57
1 hour
time (hours) 11. k = 81, m = 45, n = 54 (b) RM14
(c) 3 : 5 : 10
(c) Rate = RM10 ; price (RM) and 12. Rosli = RM8 000, Zul = RM4 000
4 pens 13. Green paint = 7.8 l, Blue paint = 7.4 l,
number of pens Yellow paint = 8 l Chapter Algebraic Expressions
5
(d) Rate = 12 km ; distance (km) 14. 76
2 hours 15. 126 units
and time (hours) 1 Formative Practice 5.1
16. 4 hours
2. 0.5 m per hour 2 1. (a) m represents the number of beads
3. (a) RM0.75 per orange or RM0.75/ 17. 40 cm bought by Alen.
orange 18. 24 l (b) s represents the temperature in
(b) 80 metres per minute or 80 m/ 19. 150 seconds Cameron Highlands on a certain
minute 20. 1.4°C per hour day.
(c) RM3 per kg or RM3/kg 1 2. (a) s has a fixed value because the
(d) 45 words per minute or 45 words/ 21. 2 2 hours
minute boiling point of water is unchanged
over time.
4. (a) RM0.18/cm Formative Practice 4.5 (b) t has a varied value because the
(b) 20 m/s time taken by each participant is
(c) 4 000 kg/m 3 1. 36% different.
(d) 0.0012 N/cm 2 (c) x has a varied value because the
(e) 2 592 km/h 2 2. 1 : 8 number of students who obtained
5. B, A, C 3. 22% grade A depends on the students’
6. Best = Q, worst = R 4. 54% performance.
5. 28% 3. (a) x + 3 2 (b) hk – 5
(c) (2ab) cm
(d) 15 – p
Formative Practice 4.3 6. 25% 4. (a) 5x + 6y (b) 3n – 2m
7. RM11, RM1.50 5. (a) 101 (b) 33
1. (a) RM48 = RM72 8. 50 members
4 kg 6 kg (c) 22 1
(b) 40 km = 64 km 9. 20 questions 2
1 cm 1.6 cm 10. RM44 6. (a) 8x + 22y (b) RM84
(c) 10 km = 25 km 11. 25% 7. (a) 27 – 6h – 6k (b) RM39.60
40 minutes 100 minutes 5
12. RM1 800 2 2
2. (a) 117 (b) 487.5 13. 48.4 kg 8. (a) 9h, 4k, 3 1 (b) 3 x , x
2
(c) 6 (d) 16 (c) mn, 13p q, 6 t
3. 432 students 14. 36%, RM720 9. (a) 2hk (b) 2gk (c) 2gh
4. 63 years 3 3 3
207




F1 Answers.indd 207 02/03/2023 1:33 PM

Mathematics Form 1 Answers

(d) 2k (e) 2h (f) 2 Section C (c) Let the maximum and minimum
3 3 3 1. (a) (i) 1 (ii) 11 2 temperature in a town be p°C and
5
5
10. (a) – x y (b) – px (b) RM(200 – 5x – 2y) 5 q°C respectively.
2
6 6 x + 19 p ‒ q = 23
1
(c) – x 3 (c) 3 years (d) Let the price of a smart phone
6 and a tablet be RMa and RMb
2. (a) a = 17, b = –12, c = 11 respectively.
11. (a) Unlike terms because they have 5pr 2 a = 2b
the same variable, ab but different (b) – 16q s 3. (a) The difference between integers a
2 2
powers. (c) (i) 10(x + 5) cm and b is 50.
(b) Like terms because they have the (ii) 130 cm (b) The total age of Mr. Lee and his
same variable, f and the same 37 grandson is 82 years old.
power. 3. (a) (i) – 20 m + 8n – 10 (c) Hwa Seng bought x packets of
(c) Like terms because they have the (ii) 4ab – 11bc + 8 biscuits which costs RM3 per packet
same variable, pqr and the same (b) 4mn – 5 and y packets of sweets which costs
power. (c) (12xy + 19x – 4y – 4) m RM2 per packet at a total price of
(d) Unlike terms because they have RM48.
different variables.
(d) The total price of 3 oranges which
costs RMu each and 4 apples which
Chapter
TIMSS 6 Linear Equations costs RMv each is RM12.
(x + 6) cm 4. (a) m = 4
(b) n = ‒21
TIMSS
Formative Practice 5.2 32 cm 5. (a) x ‒2 0 1
1. (a) 10a + 8b + 7 y ‒4 2 5


(b) −6xy – 13y + 13 Formative Practice 6.1
(c) 11p + 5 1. (a) Yes (b) No (b) x –3 0 6
(d) 6mn − m – 8n (c) Yes (d) No
1
3
(e) – pq – pr + 8 2. (a) 3x = 12 y 9 5 –3
4 2 (b) 4p = 16
(f) 11 kh + 5pq (c) Let the number is n. 6. (a) 50 cents coins.
6 Then, n ÷ 7 = ‒2 (b) 32 pieces of coins.
2. (a) k 5 (b) (xy) 7 (d) Let the age of Akmal’s brother is x 7. (a) Yes
(c) (h + 5) 4 (d) (2a – 5b) 2 years old. (b) No
Then, x + x ‒ 7 = 45
3. (a) (7 – x)(7 – x)(7 – x) 3. (a) The sum of integers y and 5 is 6. 8. (a) p = 5, q = 0; p = 7, q = 1; p = 9,
(b) (2pq)(2pq)(2pq)(2pq) (b) Henry’s height last year was q = 2
(c) (3ab + 2p)(3ab + 2p) t cm. This year, Henry’s height has (b) s = 0, t = 2; s = 1, t = ‒2; s = 2,
t = ‒6
4. p = 5, q = −1, n = 2 increased by 3 cm and becomes 158 (c) x = ‒2, y = 6; x = 0, y = 3; x = 2,
5. (a) 10a (b) 48x y cm. y = 0
7 2
8
(c) 7ab c (d) – 12 p q (c) The area of a rectangle with length (d) u = ‒1, v = ‒3; u = 2, v = 2; u = 5,
6 2
4 9
p cm and width 6 cm is 48 cm .
2
5 (d) The sum of 7 and three times the v = 7
7
6. (a) 4k h (b) – ac 2 integer m is –8. 9. p = 1, q = 4; p = 2, q = 3; p = 3, q = 2;
2 5
3 p = 4, q = 1
1
3
(c) q 3 (d) – 4x y 4. x = 3
8 5z 5. (a) No 10. 8 years or 9 years
1 10 (b) Yes 11. Let x be the number of blue pens
6 4
7. (a) – mnp (b) b c
4 7 (c) No purchased and y be the number of
8. (a) 11r + 26st (b) 6 – 2x 6. (a) x = 2 (b) s = ‒2 black pens purchased.
3 (c) m = 10 (d) y = ‒7 x = 1, y = 4; x = 2, y = 3; x = 3, y = 2;
2
9. 6(x − 2y) cm 2 (e) r = 12 (f) t = ‒15 x = 4, y = 1
7. (a) w = 4 (b) w = 2
2 2
10. 64x y cm 2
(c) x = ‒3 (d) x = 22
(e) y = 6 (f) y = ‒2 Formative Practice 6.3
Summative Practice 5 (g) z = 9 (h) z = 7
2 1. (a) x = 3, y = 5
Section A 8. 2p + 10 = 28; p = 9 (b) x = 2, y = 5
1. B 2. D 3. A 4. B 5. C 9. 21 years (c) x = 4, y = 2
(d) x = 1, y = 7
Section B 10. n = 8 2. (a) p = 1, q = 2
1. (a) (i) 28 – y (ii) 3 2 x (b) m = 3, n = –2
(b) (i) –7p r (ii) –pqr Formative Practice 6.2 (c) u = 2, v = 1
2
(d) x = 7, y = 2
2.
1. (a) Yes (b) No 3. (a) a = 4, b = ‒1
(c) No (d) Yes (b) p = ‒2, q = 5
2. (a) x + y = 16 (c) h = ‒3, k = 2
(b) Let Rohaiza’s age is x and (d) x = 1, y = ‒3
Khairunisa’s age is y. 4. 14, 42
x + y = 85
208
F1 Answers.indd 208 02/03/2023 1:33 PM

Mathematics Form 1 Answers

5. 3 years 3. (a) (c) Yes
6. 21 cm (d) No
2 (e) Yes
(f) Yes
Summative Practice 6 (b) 4. (a) x . 3
(b) x < 9
Section A –1 (c) x , ‒4
1. C 2. D 3. A 4. C 5. B (d) x < ‒32.5
6. C (c) 5. (a) x > 3
(b) x , 4
Section B –4 (c) x , 5
1. (a) Yes (d) x < 3
(b) No (d) (e) x , 10
(c) No 6. 18 books
(d) Yes 7 7. (a) x > 2
(b) x , ‒8
2. (c) 6 < x , 8
4. (a) x . ‒11 (d) ‒4 < x < 4
(b) x < 1 8. (a) ‒2 , x < 2
7
(c) x > ‒6 (b) x < 4
(c) 5 , x , 20
(d) x , 0.3
9. (a) ‒3, ‒2, ‒1, 0, 1
5. (a) (i) h is greater than 48. (b) ‒5, ‒4, ‒3, ‒2, ‒1, 0
(c) 5, 6, 7, 8, 9
(ii)
Section C 48
1. (a) (i) p + 6 = 12 h . 48 Summative Practice 7
(ii) q – (– 6) = 25
(iii) –5w = 35 (b) (i) t is less than 8. Section A
(b) m = 1 , n = 1 (ii) 1. B 2. A 3. C 4. D 5. D
2
(c) RM50 8 Section B (b) 7
1. (a) 7
2. (a) (i) p – p – 5 = 10 t , 8 (c) 3 (d) 3
2
(ii) x = 4 and y = –2 is not (c) (i) v is less than or equal to 110. 2. 3(2 – x) . 2x + 4
the solution for equation (ii) 6 – 3x . 2x + 4
5x + 3y = 16.
(b) (i) q = 5 110 –5 x . –2
(ii) h = 4 v < 110 x , 2 5
(c) 375 g
6. (a) 1 , 8
(b) 0 . ‒5 Section C
(c) ‒10 , 7 1 1
Chapter (d) ‒12 , ‒9 1. (a) (i) ‒1.24 . –1 2 ; –1 2 , ‒1.24
7 Linear Inequalities
7. (a) 1 , 11 (ii) b < 4 000
(b) ‒3 , 7
Formative Practice 7.1 (c) ‒7 , 3 (b) ‒2 < x , 7
(d) ‒10 , ‒1 (c) Chong’s answer is incorrect because
1. (a) ,; 8. (a) , the width of the rectangle must be
4 is less than 7 (b) , less than 170 cm.
(b) .; (c) .
8 is greater than ‒3 (d) . 2. (a) (i)
(c) ,;
– 1 5 is less than 0.1 Formative Practice 7.2 1 2 3 4 5
(d) .; (ii)
‒0.25 is greater than – 1 1. (a) x . 7
(b) n < 50
2
(c) p > 60 –8 –7 –6 –5
2. (a) (i) x is less than 1;
(ii) x , 1 2. (a) The number of passengers in a bus (iii)
cannot exceed 60 passengers.
(b) (i) x is less than ‒3; (b) Asmidar brought more than 3 pencils
(ii) x , ‒3 to school. –7 –6 –5 –4 –3
(c) (i) x is greater than 0; (c) The height limit of vehicles in a car
(ii) x . 0 park cannot exceed 2 m. (iv)
(d) (i) x is greater than ‒2; 3. (a) Yes
(ii) x . ‒2 (b) No 5 6 7 8 9


209





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Mathematics Form 1 Answers

(b) ‒2, ‒1, 0, 1, 2, 3, 4, 5, 6 (b) 18. (a)
(c) 1 < x < 38, where x is integer


Chapter
8 Lines and Angles 69°
70°
79°
Formative Practice 8.1 32° P Q
1. (a) Yes
(b) No Angle on a straight line
(c) Yes
2. (a) Yes
(b) No
(c) Yes (b)
3. (a) 3.6 cm. Using thumb tacks of 69°
length 1 cm. 70°
(b) 5 cm. Using paper clips of length 79°
3 cm. 32°
(or other objects with known B
measurement) A
4. (a) 5.3 cm (b) 3.9 cm Reflex angle
5. (a) Appears more than 90° but less
than 120°. Therefore, the estimated
size is about 110°.
(b) Appears slightly less than 90°. (diagrams are not drawn to scale.)
Therefore, the estimated size is
about 80°. 69° 19. (a)
(c) Appears less than 180°. Therefore, 70° 79°
the estimated size is about 160°.
6. (a) 71° 32°
(b) 125°
(c) 174°
7. (a) One whole turn angle One whole turn angle P Q
(b) Reflex angle (or other possible answers.)
(c) Angle on a straight line 9. (a) 107° N
8. (a) (b) 67°
10. (a) True because 124° + 56° = 180°
(b) True because 80° + 10° = 90°
(c) False because 290° + 80° ≠ 360° (b)
145° (d) True because A + B = 360°
35° (e) False, for example 110° + 10° = 120°
85°
(f) True, for example 280° + 80° = 360°
11. (a) Complementary angles P N Q
(b) Conjugate angles
(c) Complementary angles
Angle on a straight line (d) Supplementary angles
12. p = 41°, q = 139°, r = 80°, s = 51° (diagrams are not drawn to scale.)
13. p = 74°, q = 16° or p = 16°, q = 74°
14. p = 113°, q = 67° or p = 67°, q = 113° 20. (a)
145°
35° 15. p = q = 90° P Q
85° 16. p = 90°, q = 270°
17. (a)
A 5 cm B N

Reflex angle (b)
(b)
5.8 cm
N
(c)
145°
35° 6.9 cm
85°
(d) P
7.4 cm Q
One whole turn angle
(or other possible answers.) (diagrams are not drawn to scale.) (diagrams are not drawn to scale.)



210





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Mathematics Form 1 Answers

21. (a) (b) (i) 138° (b)
(ii) 5.8 cm

Formative Practice 8.2 Q
P
1. (a) (i) p and q A B
(ii) p and r (or q and r)
(b) (i) k and n
(ii) k and m (or m and n)
(c) (i) x and z
(ii) y and z (or x and y) (or other possible answers.)
Construct two angles of 60°
adjacently. Construct an angle 2. (a) 3. (a) Corresponding angles
bisector of the second angle of 60°
to obtain the angle of 30°. n
(or other possible ways to m y
construct.)
(b) (b) r q
s p
n y
m

(b) Interior angles
45° (c)
m
Construct an angle of 90° as in n p
question (a). Construct an angle y r
bisector of the angle of 90°. q
(or other possible ways to s
construct.)
(d)
(c)

y
n
m (c) Alternate angles


105° 3. (a) x = 126°, y = 54° q
(b) x = 48°, y = 48° r
4. (a) x = 146°, y = 96° p s
Construct two angles of 60° (b) x = 26°, y = 146°
adjacently. Construct the angle 5. x = 29°, y = 78°
bisector of the second angle of 60° 6. x = 23°, y = 90°
twice to obtain the angles of 30°
and 15°.
(or other possible ways to TIMSS (d) Corresponding angles
construct.)
x = 57°
22. (a)
S
Formative Practice 8.3 r
6 cm p s
4 cm 15° 1. q
P
Q R

(b) (i) 89° 4. (a)
(ii) 4.47 cm
2. (a) p
23. (a) A B r
b c
S Q a
q
T
2 cm P
P Q R



211





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Mathematics Form 1 Answers

(b) 2. (a) Chapter
80° and 110° are 9 Basic Polygons
suplementary angle. 7
c
r If a, b and c are three Formative Practice 9.1
b p angles at one point and 3
q b and c are suplementary 1. (a) 5 vertices, 5 diagonals
angles, thus a = 180°.
a (b) 7 vertices, 14 diagonals
(b) (c) 11 vertices, 44 diagonals
5. (a) Parallel (d) 21 vertices, 189 diagonals
(b) Not parallel 2. (a) True
6. (a) x = 90°, y = 65° A (b) True
(b) x = 88°, y = 100° 60° 3. (a)
7. a = 78°, b = 65°, c = 65°, d = 65° C
8. a = 66°, b = 36° B B D
9. a = 35°, b = 63° 3. (a) (i) 3 Hexagon
ABCDEF
10. x = 40°, y = 94° (ii) 3 A E
11. x = 118°, y = 70° (b) F
12.
(or other possible answers)
(b)
a C
b B D
N
Redzuan P Nonagon
A E
Puan ABCDEFGHI
Syazwani M I F
H G
13. x = 53°, y = 78° 4. x = 35° (or other possible answers)
14. (a) 56° y = 65° (c)
(b) 56° z = 145° C D E
15. (a) x = 72°, y = 48° x + y + z = 245°
(b) 250° B F Decagon
(c) 72° Section C A G ABCDEFGHIJ
1. (a)
J I H
Summative Practice 8 (or other possible answers)
a
Section A n p
1. D 2. C 3. D 4. B 5. A m Formative Practice 9.2

Section B (b) x = 49°, y = 102°, x + y = 151° 1. (a) Equilateral triangle
(c) (i) (b) Scalene triangle / Obtuse-angled
1. (a) Type of Two examples triangle
angle of angle R (c) Right-angled triangle
Q (d) Isosceles triangle
Obtuse 100°, 120° 120° 2. (a) 1
angle (Angle that is (b) 3
more than 90° (c) 1
and less than (d) 1
180° accepted) S P 3. (a) 44°
(b) 60°
Reflex 190°, 220° (ii) 2.5 cm; 81° (c) 24°
angles (Angle that is 2. (a) (i) x = 60° (d) 39.5°
more than 180° (ii) a = 108°, b = 72° 4. (a) 62°
and less than (b) 82°
360° accepted) (b) x = 136°, y = 60°, x + y = 196° (c) 129°
(c) x = 30°, y = 60°, z = 90° (d) 74°
3. (a) y = 275°
(b) (b) x = 18°, y = 47° 5. x = 96°; y = 21°
(c) (i) 36° 6. x = 60°; y = 86°
(ii) 8° 7. 46°
4. (a) x = 42° 8. 95°
(b) x = 65°, y = 50° 9. 76°
(c) 75° or 285° ; 100° or 260° 10. x = 54°; y = 144°




212





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Mathematics Form 1 Answers

4. (a) (i) F 1
TIMSS (ii) T 3. (a) 2 xt
Yes. A rhombus has two pairs of parallel (iii) T (b) ab
sides. (b) x = 48° + 55° 1
(c) hk
2
Section C
Formative Practice 9.3 1. (a) (i) 99° (d) 1 2 (m + n)t
(ii) 40°
1. (a) square, rectangle 4. (a) 11.4 cm 2
(b) square, rhombus (b) x = 162°; y = 60° (b) 13.2 mm 2
(c) parallelogram (c) x = 35°; y = 99° (c) 13.6 cm
2
(d) trapezium 2. (a) (i) 25° (d) 41.87 m 2
(e) the opposite sides are of equal (ii) 103° 5. (a) 27.54 cm 2
length, the diagonals are bisectors (b) x = 82°; y = 98° (b) 530 cm 2
of each other. (c) 370°
(f) rectangle, rhombus 3. (a) (i) 6. 8 cm
(g) square, rhombus 7. RM85 200
(h) square, rectangle
2. (a) 92° TIMSS
(b) 87° 36 cm
(c) 119°
(d) 34° (ii) Heptagon
3. (a) 38° (iii) 14 Formative Practice 10.3
(b) 49° (b) (i) 19° 1. X has the smallest perimeter because
4. (a) 45° (ii) 110° the difference between its length and
(b) 132° (c) 18° width is the smallest.
5. 119° Z has the largest perimeter because the
6. x = 148°; y = 32° Chapter difference between its length and width
7. x = 34°; y = 50° 10 Perimeter and Area is the largest.
8. x = 55°; y = 142° 2. (a)
Formative Practice 10.1 5 cm
Summative Practice 9 1. (a) 40 cm (b) 50 cm
(c) 39 cm (d) 39 cm
Section A 2. (a) 19.4 cm (b) 16.2 cm 6 cm
1. B 2. B 3. C 4. D 5. C or other suitable answers such that
3. (a) Estimation = 11.5 cm, the difference between the length
Section B perimeter = 12.1 cm and width is less than 7 cm.
1. (a) B The difference between the (b)
value of the estimated perimeter
and the actual measurement is
A C small, therefore the estimation is 2 cm
accurate.
D (b) Estimation = 14 cm, 15 cm
G F perimeter = 16.6 cm or other suitable answers such that
The difference between the value the difference between the length
of the estimated perimeter and and width is more than 7 cm.
E the actual measurement is large,
therefore the estimation is less 3. 22 cm
(b) (i) Right-angled triangle accurate. 4. 225 m 2
(ii) Scalene triangle 4. 220 m 5. 52 cm 2
2. (a) (i) Trapezium 5. 56 cm 6. 4 937.5 m 2
(ii) Rhombus 6. 312.5 m
(iii) Rectangle
7. Same perimeter Summative Practice 10
(b)
Section A
Q 1. A 2. C 3. D 4. A
R
P Section B
S 1. (a) (i) 25.1 cm
(ii) 58 cm
(b) 37 cm

2. (a) 1 2 ab
3. Number of Number of
Polygon Formative Practice 10.2 (b) ab
verticles diagonals
Hexsagon 6 9 1. (a) 30 units 2 (b) 20 units 2 (c) 1 2 ab
Octagon 8 20 2. (a) 17 units 2 (b) 26.6 units 2 (d) 1 (a + b)t
2



213





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Mathematics Form 1 Answers

Section C 7. 0 (b) T
1. (a) The area of shape B is larger than 8. (a) n(E) = 8 S 3
the area of shape A. (b) n(F) = 6
(b) (i) Estimation = 14 cm, (c) n(G) = 11 6 1 2 0
perimeter = 14 cm 9. n(I) = 2, n(J) = 4 4
There is no difference between 7 5
the estimated perimeter with 10. (a) Equal sets –1
the actual perimeter, thus the (b) Not equal sets
estimation is accurate. (c) Equal sets
(ii) Estimation = 16.8 cm, (d) Equal sets
perimeter = 19.2 cm (e) Not equal sets (c) X
The difference between the (f) Not equal sets Y
estimated perimeter with the 11. h = 5
actual perimeter is huge, thus
the estimation is inaccurate.
(c) (i) 12 Formative Practice 11.2
(ii) 22
2. (a) 22 cm 1. (a) Universal set
(b) 88.2 cm 2 (b) Not a universal set
(c) 540 m 2 (c) Universal set 9. (a)
3. (a) 3 cm 2. (a) A9 = {–4, –3, 0, 1, 2, 3} L
(b) (i) Rectangle C (b) B9 = {–4, –3, –2, –1} P
(ii) Area in descending order: 3. (a) K
E, G, F, H ξ
The difference between the a F e
length and the width of square E b c
is the smallest, that is 0, followed
by G, F and H. Square H shows d f
the largest difference between
the length and width.
(c) 30 cm (b)
4. (a) 32 cm (b) H
(b) 79 m ξ N
(c) 140 cm 2 1 2 M
G 3
4 5
0
Chapter 8 6
11 Introduction to Set 7
10 9
Formative Practice 11.1 (c) 10.
1. Metal: Aluminium, Steel, Iron, Zinc, ξ H E ξ B A 5
Copper. A 3
Furniture: Table, Chair, Cupboard. J U 4 2
Colour: Orange, Blue, Yellow, Black, K M 9 6
Green, White, Red. N 8 7
2. (a) A is the set of the states in
Malaysia.
(b) K is the set of perfect squares that 4. (a) {3, 5, 10, 15} (b) {26, 33} 11. (a)
is not more than 100. 5. (a) A9 = {70, 80, 90}
(c) L is the set of the first five alphabets. (b) 4 ξ B
3. (a) {blue, yellow, red, white} (c) 6 A
(b) F = {K, E, R, J, A, Y} 6. (a) True
(c) G = {4, 8, 12, 16, 20, 24, 28, 32, 36} (b) False
4. (a) P = {x : x is the prime factors of (c) False
28} (d) True
(b) A = {x : x is the month which starts 7. (a) φ, {8}
with the letter J} (b) φ, {h}, {p}, {v}, {h, p}, {h, v}, {p, v},
(c) B = {x : x is the multiples of 3 and {h, p, v} (b)
x , 100} (c) φ, {57}, {75}, {57, 75} ξ
5. (a) Empty set 8. (a) E
(b) Empty set P C D
(c) Not an empty set Q a
(d) Not an empty set
e
6. (a) False (b) True u i
(c) True (d) True
(e) True (f) False o




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F1 Answers.indd 214 02/03/2023 1:33 PM

Mathematics Form 1 Answers

12. (a) (c) P = {Tioman Island, Perhentian 2. (a) Categorical data. For example,
Island, Langkawi Island} the favourite fruits of students are
ξ
L Numbers of option durians, bananas and oranges.
S R = Number of subset of P (b) Numerical data. For example,
= 2 3 the mass of students is 42.3 kg,
40.7 kg and 45.4 kg.
= 8 → Continuous data
2. (a) (i) {5, 7, 10, 20, 30} (c) Categorical data. For example,
(ii) S  Q  P the brands of smartphones are
(b) (i) S  L ‘Samsung’, ‘Apple’ and ‘Sony’.
(ii) R  L9 (b) (i) (d) Numerical data. For example, the
quantity of rainfall recorded in one
13. (a) ξ
P month is 2.5 cm, 3.1 cm and 4.0 cm.
ξ → Continuous data
A L S (e) Numerical data. For example, the
History marks of the students are
B C D 70, 85 and 64.
→ Discrete data
(f) Categorical data. For example, the
genre of songs is pop, jazz and rock.
(ii) Yes, because P’ is not female
students that is equal to set of 3. (a) Destination Tally Frequency
(b) (i) B  A male students.
(ii) C  D9 or D  C9 A IIII IIII 9
(c) E  A9 and E  D9. Set E is in the (c) (i) C IIII IIII II 12
universal set but lies outside set A A
and set D. Tom B J IIII IIII 9
C Lee
Daniel
Malar
Ravi Jacky Ying Total 30
Summative Practice 11 Mira
Ali Jeane (b) Japan and Australia
Anwar
Section A
1. C 2. B 3. D 4. A 5. A 4. (a) Number Tally Frequency
(ii) Set A is universal set; C  B, of pens
Section B B  A 2 IIII 5
1. (a) A ≠ φ
(b) B = φ 3 IIII III 8
(c) C = φ Chapter Data Handling
12
(d) D ≠ φ 4 IIII II 7
2. (a)  (b) 
(c)  (d)  TIMSS 5 IIII 4
3. Total 24
Number of Visitors to the Museum
(b) 4 students
(c) 2 students
Friday Monday 5. (a) 32
(b) 1 : 2
4. (a) 3 45° 45° 6. Construct a pie chart representation.
(b) 3 Thursday 135°
(c) 7 45° Tuesday Method of
(d) 3 ordering Percentage Angle of sector
pizza
Section C Wednesday Walk-in 30% 30 × 360° = 108°
1. (a) (i) U  T   100
(ii) S  U9 Phone 45
calls 45% × 360° = 162°
(b) 100
Formative Practice 12.1
ξ Online
Y 25% 25 × 360° = 90°
1. (a) Counting by observation or survey. booking 100
(b) Counting by observation or survey.
X Z
(c) Measuring by conducting Total 100% 360°
experiment.
(d) Measuring by conducting interview
or survey.


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F1 Answers.indd 215 02/03/2023 1:33 PM

Mathematics Form 1 Answers

Method of Ordering Pizza 10. (a) Convert to a bar chart representation. A bar chart representation is converted
to a line graph representation because
Favourite Snacks of Children the line graph can show changes in
Awang’s annual income over a period
Online Walk-in of five years.
booking 108° 13. (a) Fees
162° Number of students 6 4 (b) 22.5%
(c) RM2 000
Phone 14. (a) Wednesday
calls 2 (b) RM30
(c) RM400
0 (d) RM375
This pie chart is suitable to make
comparisons between each method of Potato chips Burger Cake Keropok 15. (a) RM7 000
ordering pizza compared to the total (b) RM180 000
number of orders more clearly. Type of snacks (c) 25%
7. (a) Construct a horizontal bar chart (or A dot plot representation is converted 16. (a) Highest score = 39, lowest score = 7
a vertical bar chart) representation. to a bar chart representation (b) 2
because the bar chart can compare 5
Favourite Types of Games the number of children who like (c) 32%
different types of snacks.
(b) A pie chart representation is not 17. (a) RM25 000
Pingpong
suitable because pie charts only (b) RM18 000
compare the percentage of children (c) 36%
Hockey who like each type of snack from the (d) RM120 million
total and could not show the number 18. (a) 20 teenagers
of each snack.
Games Football 11. Convert to a bar chart representation. (b) 1 5
(c) 4 times
Volleyball Brand Number of shoes
19. (a)
A 25 Height of Computer Club Members
Basketball B 20 12
C 30
0 4 8 12 16 20 24 28 32 10
Number of students D 15
E 10 8
This bar chart is suitable to Frequency
compare the number of students 6
who like different types of games. Sales of Branded Shoes
4
30
8. Construct a dot plot representation. 25 2
Number of shoes 15 0
Number of Books Borrowed 20
10
5 141 – 145 146 – 150 151 – 155 156 – 160 161 – 165 166 – 170 171 – 175
Height (cm)
0
0 1 2 3 4 A B C D E
Number of books Brand (b) No, because the height of students
A pie chart representation is converted is a continuous data. A bar chart is
This dot plot is suitable to show the to a bar chart representation because only suitable for discrete data which
has empty spaces between each bar
number of books borrowed by 10 the bar chart could show comparisons and the arrangement of data is not
students and the size of data is small. of the number of branded shoes that is important.
9. Construct a stem-and-leaf plot sold. 20. (a) The data is not displayed accurately
representation. 12. Convert to a line graph representation. because the scale on the vertical axis
Awang’s Annual Income does not start from zero. It is found
Scores of Students in a Quiz that the height of bar in year 2016
Stem Leaf 4.8 is 3 times the height of bar in year
0 6 8 9 9 4.4 2015, which gives a misconception
1 0 0 4 4 5 5 8 4.0 that the profit obtained in the year
2 0 2 2 6 7 Income (RM ten thousands) 3.6 2016 is 3 times the profit of the
3 3 7 3.2 year 2015. In contrast, the profit
only increases by RM100 000. The
Key : 0 | 6 means a score of 6. 2.8 vertical axis should start from zero
The stem-and-leaf plot is suitable to 2.4 to avoid confusion.
show the scores of each student in a
quiz. 0 2012 2013 2014 2015 2016
Year


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F1 Answers.indd 216 02/03/2023 1:33 PM