DSKP KSSM Mathematics Form 4 and 5_Versi English

Matematik

Tingkatan 4 dan 5

(EDISI BAHASA INGGERIS)

vii



Matematik

Tingkatan 4 dan 5

(EDISI BAHASA INGGERIS)

Bahagian Pembangunan Kurikulum
MEI 2019

vii

Terbitan 2019

© Kementerian Pendidikan Malaysia

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Pentadbiran Kerajaan Persekutuan, 62604 Putrajaya.

CONTENT

Rukun Negara......................................................................................................................................................................................... vii
Falsafah Pendidikan Kebangsaan........................................................................................................................................................... iix
Definisi Kurikulum Kebangsaan.............................................................................................................................................................. ix
Kata Pengantar....................................................................................................................................................................................... xi
Introduction.............................................................................................................................................................................................. 1
Aims......................................................................................................................................................................................................... 2
Objectives................................................................................................................................................................................................ 2
The Framework of Secondary School Standard-based Curriculum........................................................................................................ 4
Focus....................................................................................................................................................................................................... 5
21st Century Skills.................................................................................................................................................................................... 13
Higher Order Thinking Skills.................................................................................................................................................................... 14
Teaching and Learning Strategies.......................................................................................................................................................... 15
Cross-Curricular Elements...................................................................................................................................................................... 19
Classroom Assessment........................................................................................................................................................................... 22

Content Organisation.............................................................................................................................................................................. 26
Content Standards, Learning Standards and Performance Standards Form 4..................................................................................... 29
31
Quadratic Functions and Equations in One Variable....................................................................................................................... 35
Number Bases................................................................................................................................................................................... 39
Logical Reasoning............................................................................................................................................................................. 45
Operations on Sets.......................................................................................................................................................................... 49
Network in Graph Theory................................................................................................................................................................. 53
Linear Inequalities in Two Variables ............................................................................................................................................... 57
Graphs of Motion.............................................................................................................................................................................. 61
Measures of Dispersion for Ungrouped Data................................................................................................................................... 65
Probability of Combined Events....................................................................................................................................................... 71
Consumer Mathematics: Financial Management............................................................................................................................. 75
Content Standards, Learning Standards and Performance Standards Form 5...................................................................................... 77
Variation........................................................................................................................................................................................... 81
Matrices............................................................................................................................................................................................ 87
Consumer Mathematics: Insurance.................................................................................................................................................. 91
Consumer Mathematics: Taxation.................................................................................................................................................... 95
Congruency, Enlargement and Combined Transformations............................................................................................................

Ratio and Graphs of Trigonometric Functions.................................................................................................................................. 101
Measures of Dispersion of Grouped Data........................................................................................................................................ 105
Mathematical Modeling ................................................................................................................................................................... 111
Panel of Writers ..................................................................................................................................................................................... 115
Panel of Translators............................................................................................................................................................................... 117
Acknowledgement.................................................................................................................................................................................. 120



RUKUN NEGARA

BAHAWASANYA Negara kita Malaysia mendukung cita-cita hendak:
Mencapai perpaduan yang lebih erat dalam kalangan seluruh masyarakatnya;

Memelihara satu cara hidup demokratik;
Mencipta satu masyarakat yang adil di mana kemakmuran negara

akan dapat dinikmati bersama secara adil dan saksama;
Menjamin satu cara yang liberal terhadap tradisi-tradisi

kebudayaannya yang kaya dan berbagai corak;
Membina satu masyarakat progresif yang akan menggunakan

sains dan teknologi moden;

MAKA KAMI, rakyat Malaysia, berikrar akan menumpukan seluruh tenaga dan usaha
kami untuk mencapai cita-cita tersebut berdasarkan atas prinsip-prinsip yang berikut:

KEPERCAYAAN KEPADA TUHAN
KESETIAAN KEPADA RAJA DAN NEGARA

KELUHURAN PERLEMBAGAAN
KEDAULATAN UNDANG-UNDANG
KESOPANAN DAN KESUSILAAN

vii

FALSAFAH PENDIDIKAN KEBANGSAAN

“Pendidikan di Malaysia adalah suatu usaha berterusan ke arah lebih
memperkembangkan potensi individu secara menyeluruh dan bersepadu untuk
melahirkan insan yang seimbang dan harmonis dari segi intelek, rohani, emosi
dan jasmani, berdasarkan kepercayaan dan kepatuhan kepada Tuhan. Usaha ini
adalah bertujuan untuk melahirkan warganegara Malaysia yang berilmu
pengetahuan, berketerampilan, berakhlak mulia, bertanggungjawab dan
berkeupayaan mencapai kesejahteraan diri serta memberikan sumbangan
terhadap keharmonian dan kemakmuran keluarga, masyarakat dan negara”

Sumber: Akta Pendidikan 1996 (Akta 550)

iix

DEFINISI KURIKULUM KEBANGSAAN

3. Kurikulum Kebangsaan
(1) Kurikulum Kebangsaan ialah suatu program pendidikan yang
termasuk kurikulum dan kegiatan kokurikulum yang merangkumi
semua pengetahuan, kemahiran, norma, nilai, unsur kebudayaan dan
kepercayaan untuk membantu perkembangan seseorang murid
dengan sepenuhnya dari segi jasmani, rohani, mental dan emosi
serta untuk menanam dan mempertingkatkan nilai moral yang diingini
dan untuk menyampaikan pengetahuan.

Sumber: Peraturan-Peraturan Pendidikan (Kurikulum Kebangsaan) 1997
[PU(A)531/97.]

ix



KATA PENGANTAR KSSM MATHEMATICS FORM 4 AND 5

Kurikulum Standard Sekolah Menengah (KSSM) yang dilaksanakan DSKP yang dihasilkan juga telah menyepadukan enam tunjang
secara berperingkat mulai tahun 2017 akan menggantikan Kurikulum Kerangka KSSM, mengintegrasikan pengetahuan, kemahiran dan
Bersepadu Sekolah Menengah (KBSM) yang mula dilaksanakan nilai, serta memasukkan secara eksplisit Kemahiran Abad Ke-21 dan
pada tahun 1989. KSSM digubal bagi memenuhi keperluan dasar Kemahiran Berfikir Aras Tinggi (KBAT). Penyepaduan tersebut
baharu di bawah Pelan Pembangunan Pendidikan Malaysia(PPPM) dilakukan untuk melahirkan insan seimbang dan harmonis dari segi
2013-2025 agar kualiti kurikulum yang dilaksanakan di sekolah intelek, rohani, emosi dan jasmani sebagaimana tuntutan Falsafah
menengah setanding dengan standard antarabangsa. Kurikulum Pendidikan Kebangsaan.
berasaskan standard yang menjadi amalan antarabangsa telah
dijelmakan dalam KSSM menerusi penggubalan Dokumen Standard Bagi menjayakan pelaksanaan KSSM, pengajaran dan
Kurikulum dan Pentaksiran (DSKP) untuk semua mata pelajaran pembelajaran guru perlu memberi penekanan kepada KBAT dengan
yang mengandungi Standard Kandungan, Standard Pembelajaran memberi fokus kepada pendekatan Pembelajaran Berasaskan
dan Standard Prestasi. Inkuiri dan Pembelajaran Berasaskan Projek, supaya murid dapat
menguasai kemahiran yang diperlukan dalam abad ke-21.
Usaha memasukkan standard pentaksiran dalam dokumen
kurikulum telah mengubah lanskap sejarah sejak Kurikulum Kementerian Pendidikan Malaysia merakamkan setinggi-tinggi
Kebangsaan dilaksanakan di bawah Sistem Pendidikan penghargaan dan ucapan terima kasih kepada semua pihak yang
Kebangsaan. Menerusinya murid dapat ditaksir secara berterusan terlibat dalam penggubalan KSSM. Semoga pelaksanaan KSSM
untuk mengenal pasti tahap penguasaannya dalam sesuatu mata akan mencapai hasrat dan matlamat Sistem Pendidikan
pelajaran, serta membolehkan guru membuat tindakan susulan bagi Kebangsaan.
mempertingkatkan pencapaian murid.
Dr. MOHAMED BIN ABU BAKAR
Timbalan Pengarah
Bahagian Pembangunan Kurikulum
Kementerian Pendidikan Malaysia

xi

KSSM MATHEMATICS FORM 4 AND 5

1

KSSM MATHEMATICS FORM 4 AND 5

INTRODUCTION

KSSM Mathematics is a core subject that is learned by all pupils under In order to develop individual’s potential, intellectual proficiency and
the National Education System. In Malaysia, each pupil gets the human capital, Mathematics is the best medium because of its nature
opportunity to go through at least six years of basic education in that encourages logical and systematic thinking. Thus, the
primary school and five years in secondary school. Mathematics development of the Mathematics curriculum takes into consideration
programme at secondary school level is divided into three the needs of developing the country, and factors that contribute to the
programmes: Mathematics at lower secondary, Mathematics at upper development of individuals who can think logically, critically,
secondary and Additional Mathematics at upper secondary. analytically, creatively and innovatively. This is consistent with the
need to provide adequate mathematical knowledge and skills to
The secondary school Mathematics content is essentially a ensure that this country is able to compete internationally and meet
continuation of knowledge and skills learnt at the primary school level. the challenges of the 21st century. The different backgrounds and
Secondary school Mathematics aims, among others, to develop the abilities of the pupils are given special attention in determining the
knowledge and skills of the people to enable them to solve problems knowledge and skills learned in the programme.
in their daily lives, further their studies to a higher level and thus
function as an effective workforce.

The restructring of KSSM Mathematics takes into consideration the
continuity from primary to secondary school and onto a higher level.
In addition, the benchmarking of Mathematics curriculum in Malaysia
has been carried out against high performing countries in the
international assessments. This measure is to ensure that
Mathematics curriculum in Malaysia is relevant and at par with other
countries.

1

AIMS KSSM MATHEMATICS FORM 4 AND 5

KSSM Mathematics aims to produce individuals who are  interpreting, applying and evaluating mathematical
mathematically fikrah, which means individuals who can think outcomes.
mathematically, creative and innovative as well as competent in
applying mathematical knowledge and skills effectively and 3. Apply the knowledge and skills of mathematics in making
responsibly to solve problems and make decisions, based on the reasonable judgments and decisions to solve problems in a
attitudes and values so that they are able to deal with challenges in variety of contexts.
their daily lives, in line with the development of science and
technology as well as the challenges of the 21st century. 4. Enhance mathematical skills related to Number and
Operations, Measurement and Geometry, Relationship and
OBJECTIVES Algebra, Statistics and Probability, and Discrete Mathematics
such as:
The Form 4 and 5 KSSM Mathematics enables pupils to achieve the  collecting and handling data.
following objectives:  representing and interpreting data.
 recognising relationship and representing them
1. Develop an understanding of the concepts, laws, principles and mathematically.
theorems related to Number and Operations, Measurement  using algorithms and relationship.
and Geometry, Relationship and Algebra, Statistics and  making estimation and approximation.
Probability, and Discrete Mathematics.  measuring and constructing.

2. Develop capacity in: 5. Practise consistently the mathematical process skills which are
 formulating situations into mathematical forms. problem solving, reasoning, mathematical communication,
 using concepts, facts, procedures and reasoning. making connection and representation.

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KSSM MATHEMATICS FORM 4 AND 5

6. Cultivate the use of mathematical knowledge and skills in
making reasonable judgments and decisions effectively and
responsibly in real-life situations.

7. Realise that mathematical ideas are inter-related,
comprehensive and integrated body of knowledge, and are able
to relate mathematics with other disciplines of knowledge.

8. Use technology in concept building, mastery of skills,
investigating and exploring mathematical ideas and solving
problems.

9. Foster and practise moral values, positive attitudes towards
mathematics and appreciate the importance and the beauty of
mathematics.

10. Develop higher-order, critical, creative and innovative thinking.
11. Practise and further develop generic skills to face challenges of

the 21st century.

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KSSM MATHEMATICS FORM 4 AND 5

THE FRAMEWORK OF SECONDARY SCHOOL STANDARD-BASED CURRICULUM

KSSM is built on the basis of six fundamental pillars: capital who appreciates values based on spiritual practices,
Communication; Spiritual, Attitude and Values; Humanities; knowledge, personal competence, critical and creative thinking as
Personal Competence; Physical Development and Aesthetics; and well as innovative thinking as shown in Figure 1. The Mathematics
Science and Technology. These six pillars are the main domain curriculum is developed based on the six pillars of the KSSM
that supports one another and are integrated with critical, creative Framework.
and innovative thinking. The integration aims to produce human

Figure 1: The Framework of Secondary School Standard-Based Curriculum
4

FOCUS KSSM MATHEMATICS FORM 4 AND 5

KSSM Mathematics focuses on developing individuals who Four key elements that contribute to the development of individuals
internalise and practise mathematical fikrah. The Mathematics possessing mathematical fikrah are:
Curriculum Framework as illustrated in Figure 2, is fundamental to  Learning areas
the implementation of the Mathematics curriculum in the  Values
classroom.  Skills
 Mathematical processes

 Number & Operations
 Measurement & Geometry
 Relationship & Algebra
 Statistics & Probability
 Discrete Mathematics

 Problem Solving  Mathematical Values
 Reasoning  Universal Values
 Communication
 Representation
 Connection

 Mathematical Skills
 21st Century Skills
 Higher-Order Thinking Skills

Figure 2: The Mathematics Curriculum Framework for Secondary Schools
5

Mathematical Fikrah KSSM MATHEMATICS FORM 4 AND 5

According to the Fourth Edition of Kamus Dewan (2005), fikrah  Statistics and Probability
means capability of thinking and thoughts. In the context of  Discrete Mathematics
mathematics education, mathematical fikrah refers to the qualityof
pupils to be developed through the national mathematics education Mathematical Processes
system. Pupils who acquire mathematical fikrah are capable of
doing mathematics, understanding mathematical ideas, and Mathematical processes that support effective and thoughtful
applying the knowledge and skills of mathematics responsibly in teaching and learning are:
daily life, guided by good attitudes and values.  Problem solving;
 Reasoning;
Mathematical fikrah also intends to produce individuals who are  Mathematical communication;
creative, innovative and well-equipped to the needs of the 21st  Representation; and
century, as the country is highly dependent on the ability of human  Making connections.
capital to think and generate new ideas. All the five mathematical processes are inter-related and need to
be implemented and integrated across the curriculum.
Learning Area
Problem solving is the heart of mathematics. Hence, problem-
The content of Mathematics covers five main learning areas that solving skills need to be developed comprehensively and integrated
are inter-related, namely: across the Mathematics curriculum. In accordance with the
importance of problem solving, mathematical processes are the
 Number and Operations backbone of the teaching and learning (T&L) of mathematics and
 Measurement and Geometry should be able to mould pupils who are capable of using a variety of
 Relationship and Algebra problem-solving strategies, higher order thinking skills, creative and
innovative. Teachers need to design T&L sessions which

6

focuses on problem solving. Activities carried out should engage KSSM MATHEMATICS FORM 4 AND 5
pupils actively by posing a diversity of questions and tasks that
contain both routine and non-routine questions. Solving problem The following are some of the processes that need to be
involving non-routine questions basically needs thinking and emphasised through problem solving, that is the development of
reasoning at a higher level. These skills should be consistently pupils’ capacity in:
cultivated by the teachers to produce pupils who are able to  Formulating mathematical situations involving various contexts
compete globally.
such as personal, community, scientific and occupation.
The following problem-solving steps should be emphasised so that  Using and applying concepts, facts, procedures and reasonings
pupils can solve problems systematically and effectively:
in solving problems.
 Understanding and interpreting problems  Interpreting, evaluating and reflecting on the solutions or
 Devising a strategy
 Implementing the strategy decisions made and determine whether they are reasonable.
 Doing reflection
Reflection is an important step in problem solving. Reflection allows
The application of various strategies in problem solving, including pupils to see, understand and appreciate perspectives of others
the steps involved, has to be used widely. Among the strategies from different angles as well as enables pupils to consolidate their
commonly used are drawing diagrams, identifying patterns, making understanding of the concepts learned.
tables/charts or systematic lists, using algebra, trying simpler
cases, reasoning out logically, using trial and improvement, making Reasoning is an important basis for understanding mathematics
simulation, working backwards as well as using analogies. more effectively and meaningfully. The development of
mathematical reasoning is closely related to pupils’ intellectual
development and communication. Reasoning not only develops the
capacity of logical thinking but also increases the capacity of critical
thinking that is fundamental in understanding mathematics deeply
and meaningfully. Therefore, teachers need to provide space and
opportunity by designing T&L activities that require pupils to

7

do mathematics and be actively involved in discussing KSSM MATHEMATICS FORM 4 AND 5
mathematical ideas.
graphs, diagrams, etc), help pupils to understand and apply
The element of reasoning in T&L prevents pupil from assuming mathematics more effectively.
mathematics as just a set of procedures or algorithms that should
be followed to obtain a solution without understanding the Teachers should be aware of the opportunities that exist during
mathematical concepts in depth. Reasoning not only changes pupil’s T&L sessions to encourage pupils to express and present their
paradigm from emphasising on the importance of procedural mathematical ideas by using appropriate questioning techniques.
knowledge but also gives mental and intellectual empowerment when Communication that involves a variety of perspectives and points
pupils are guided and trained to make and validate conjectures, of view helps pupils to better improve their mathematical
provide logical explanations, analyse, evaluate and justify the understanding whilst enhancing their self-confidence.
mathematical activities. Such training would build pupils’ confidence
and courage, in line with the aim of developing powerful mathematical The significant aspect of mathematical communication is the ability
thinkers. to provide effective explanation as well as to understand and apply
the correct mathematical notations. Pupils should use the
Communication in mathematics is the process of expressing mathematical language and symbols correctly to ensure that
ideas and understanding in verbal, visual or written form using mathematical ideas can be explained precisely.
numbers, notations, symbols, diagrams, graphs, pictures or words.
Communication is an important process in learning mathematics Effective communication requires an environment that is always
because mathematical communication helps pupils to clarify and sensitive to the needs of pupils so that they feel comfortable while
reinforce their understanding of mathematics. Through speaking, asking and answering questions, explaining and justifying
communication, mathematical ideas can be better expressed and their views and statements to their classmates and teachers. Pupils
understood. Communication in mathematics, whether verbal, should be given the opportunity to communicate actively in a variety
written form or using symbols and visual representations (charts, of settings, for example while doing activities in pairs, groups or
while giving explanation to the whole class.

8

Representation is an important component of mathematics and KSSM MATHEMATICS FORM 4 AND 5
often used to represent real-world phenomena. Therefore, there
must be a similarity between the aspects of the world that is being Making connections between areas in mathematics such as
represented and the world that it is representing. Representation counting, geometry, algebra, measurement and statistics is
can be defined as any notations, letters, images or concrete objects important for pupils to learn concepts and skills integratedly and
that symbolise or represent something else. meaningfully. By recognising how the concept or skills of different
areas are related to each other, mathematics will be viewed and
At secondary school level, representing ideas and mathematical studied as a discipline that is comprehensive and connected to
models generally make use of symbols, geometry, graphs, algebra, each other, thus allowing abstract concepts to be understood
diagrams, concrete representations and dynamic software. Pupils easily.
must be able to change from one form of representation to another
and recognise the relationship between them, and use various When mathematical ideas are connected to daily life experiences
representations, which are relevant and required to solve problems. within and outside the classroom, pupils will be more aware of the
use, the importance, the strength and the beauty of mathematics.
The use of various representations helps pupils to understand Besides, they are also able to use mathematics contextually in
mathematical concepts and relationships, communicate their other disciplines and in their daily lives. Mathematical models are
thinking, reasoning and understanding; recognise the relationship used to describe real-life situations mathematically. Pupils will
between mathematical concepts and use mathematics to model realise that this method can be used to solve problems or to
situations, physical and social phenomena. When pupils are able predict the possibility of a situation based on the mathematical
to represent concepts in different ways, they will be flexible in their models.
thinking and understand that there are variety of ways to represent
mathematical ideas that enable problems to be solved easily. In implementing the KSSM Mathematics, the opportunity to make
connection should be established so that pupils can relate
conceptual knowledge to procedural knowledge and be able to
relate topics in Mathematics in particular and relate mathematics to

9

other fields in general. This will increase pupils’ understanding of KSSM MATHEMATICS FORM 4 AND 5
mathematics, making it clear, more meaningful and interesting.
 Choose and use various types of reasoning and methods of
Mathematical Process Standards proving.

The following are the mathematical process standards to be  Make, investigate and verify mathematical conjectures.
achieved by pupils through the implementation of this curriculum.  Develop and evaluate mathematical arguments and proofs.
 Make decisions and justify the decisions made.
Table 1: Mathematical Process Standards
COMMUNICATION IN MATHEMATICS
PROBLEM SOLVING  Organise and incorporate mathematical thinking through
 Understand the problems.
 Extract relevant information in a given situation and communication to clarify and strengthen the understanding
of mathematics.
organise information systematically.  Communicate mathematical thoughts and ideas clearly and
 Plan various strategies to solve problems. confidently.
 Implement the strategies according to the plan.  Use the language of mathematics to express mathematical
 Generate solutions to meet the requirements of the ideas precisely.
 Analyse and evaluate the mathematical thinking and
problem. strategies of others.
 Interpret the solutions.
 Review and reflect upon the solutions and strategies used. REPRESENTATION
 Illustrate mathematical ideas using various types of
REASONING
 Recognise reasoning and proving as fundamentals to representations.
 Make interpretations from given representations.
mathematics.  Choose the appropriate types of representations.
 Recognise patterns, structures, and similarities within real-  Use various types of mathematical representations to:

life situations and symbolic representations. i) simplify complex mathematical ideas.
ii) assist in problem solving.
iii) develop models and interpret mathematical phenomena.
iv) make connections between various types of

representations.

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CONNECTION KSSM MATHEMATICS FORM 4 AND 5
 Identify and use the connection between mathematical
mathematical tools strategically, accurately and effectively is
ideas. strongly emphasised in the teaching and learning of mathematics.
 Understand how mathematical ideas are inter-related and The mathematical tools include papers and pencils, rulers,
protractors, compasses, calculators, electronic spreadsheets,
form a cohesive unity. dynamic software and others.
 Relate mathematical ideas to daily life and other fields.
The rapid progress of various technologies in todays’ life has
Skills in Mathematics Education resulted in the use of technologies as an essential element in the
T&L of mathematics. Effective teachers will maximise the potential
The skills that need to be developed and nurtured among pupils and technological capabilities so that pupils can build
through this subject include Mathematical Skills, 21st Century Skills understanding and increase their proficiency and interest in
and Higher-Order Thinking Skills (HOTS). mathematics. Due to the capacity and effectiveness of technology
in the T&L of mathematics content, teachers need to embrace the
The mathematical skills refer to among others the skills of use of technology, particularly scientific and graphing calculators,
measuring and constructing, estimating and rounding, collecting computer software like Geometer's Sketchpad, Geogebra,
and handling data, representing and interpreting data, recognising electronic spreadsheets, learning software (courseware), the
relationships and representing mathematically, translating real-life Internet and others.
situations into mathematical models, using precise language of
mathematics, applying logical reasoning, using algorithms and However, technology need to be used wisely. Scientific calculator
relationships, using mathematical tools, solving problems, making for example is not to be used to the extent that the importance of mental
decisions and others. In addition, the curriculum also demands the calculations and basic computations is neglected. Efficiency in
development of pupils’ mathematical skills in aspect related to carrying out the calculations is important especially in the lower
creativity, the needs for originality in their thinking and the ability to level and pupils should not totally rely on calculators. For example,
see things around them with new and different perspectives in although the graphing calculator helps pupils to visualise the nature
order to develop creative and innovative individuals. The use of

11

of a function and its graph, the use of papers and pencils is still the KSSM MATHEMATICS FORM 4 AND 5
learning outcome that has to be achieved by all pupils. Similarly, in
seeking the roots of the quadratic equations, the basic concept must Values in Mathematics Education
first be mastered by pupils. Technology should be used wisely to
help pupils form concepts, enhance understanding, visualise Values are affective qualities intended to be developed through the
concepts and others, while enriching pupils learning experiences. T&L of mathematics using appropriate contexts. Values are usually
taught and learned implicitly through the learning sessions. Moral
Specifically, the skills in using technology that need to be nurtured values being instilled will manifest good attitudes. The application
in pupils through Mathematics are the ability of pupils in: of values and attitudes in the T&L of mathematics are intended to
 Using technology to explore, carry out research, construct produce individuals who are competent in terms of knowledge and
skills as well as having good characters. Embracing moral values
mathematical models hence form deep understanding of the will produce virtuous young generation with noble personal
mathematical concepts. qualities and good attitudes.
 Using technology to help in calculations to solve problems
effectively. Values that need to be developed in pupils through the T&L of
 Using technology, especially electronic and digital technology mathematics are:
to find, manage, evaluate and communicate information.  Mathematical values – values within the knowledge of
 Using technology responsibly and ethically.
mathematics which include emphasis on the properties of the
The use of technology such as dynamic software, graphing mathematical knowledge; and
calculator, the Internet and others need to be integrated into the  Universal values - universal noble values that are applied
T&L of mathematics to help pupils form deep understanding of across all subjects.
concepts especially abstract concepts.
The development of values through T&L of mathematics should
also involve the elements of divinity, faith, interest, appreciation,
confidence, competence and tenacity. Belief in the power and
greatness of God can basically be nurtured through the content of

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KSSM MATHEMATICS FORM 4 AND 5

the curriculum. The relationship between the content learned and Table 2: Pupils’ Profile DESCRIPTION
the real world enables pupils to see and validate the greatness and
the power of the Creator of the universe. PUPILS’
PROFILE
The elements of history and patriotism should also be inculcated
through relevant topics to enable pupils to appreciate mathematics Resilient They are able to face and overcome
as well as to boost interest and confidence in mathematics. difficulties and challenges with wisdom,
Historical elements such as certain events involving confidence, tolerance, and empathy.
mathematicians or a brief history of a concept or symbol are also
emphasised in this curriculum. Competent They voice out and express their thoughts,
Communicator ideas and information confidently and
21st CENTURY SKILLS creatively, in verbal and in written form,
using various media and technology.
One of the aims of KSSM is to produce pupils who possess the 21st
century skills by focussing on thinking skills, living skills and career, Thinker They think critically, creatively and
guided by the practice of moral values. The 21st Century skills aim innovatively; able to solve complex
to produce pupils who have the characteristics specified in the problems and make ethical decisions. They
pupils’ profile as in Table 2, so that they are able to compete at a think about learning and themselves as
global level. The mastery of the Content Standards and the learners. They generate questions and be
Learning Standards in the Mathematics curriculum contributes to open towards other individual’s and
the acquisition of the 21st Century Skills among the pupils. communities’ perspectives, values, and
traditions. They are confident and creative
in handling new learning areas.

Team Work They can co-operate effectively and
harmoniously with others. They shoulder
responsibilities together as well as respect
and appreciate the contributions from each
member of the team. They acquire
interpersonal skills through collaborative
activities, and this makes them better
leaders and team members.

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KSSM MATHEMATICS FORM 4 AND 5

PUPILS’ HIGHER ORDER THINKING SKILLS
PROFILE
Inquisitive DESCRIPTION Higher-Order Thinking Skills (HOTS) are explicitly stated in the
curriculum so that teachers are able to translate it into their T&L to
Principled They develop natural inquisitiveness to promote a structured and focused thinking among pupils.
explore new strategies and ideas. They Explanation of HOTS focuses on four levels of thinking as shown
Informed learn skills that are necessary for inquiry- in Table 3.
learning and research, as well as display
Caring independent traits in learning. The pupils Table 3: Level of Thinking in HOTS
continuously enjoy life-long learning
Patriotic experiences. LEVEL OF EXPLANATION
THINKING
They have a sense of integrity and sincerity,
equality, fairness and respect the dignity of Applying Using knowledge, skills and values in different
individuals, groups and community. They situations to perform certain tasks.
are responsible for their actions,
consequences and decisions. Analysing Breaking down information into smaller parts in
order to understand and make connections
They obtain knowledge and develop a between these parts.
broad and balanced understanding across
various disciplines of knowledge. They Evaluating Making considerations and decisions using
explore knowledge efficiently and effectively knowledge, experience, skills, and values as
in terms of local and global contexts. They well as providing justification.
understand issues related to ethics or laws
regarding information acquired. Creating Producing creative and innovative ideas,
products or methods.
They show empathy, compassion and
respect towards the needs and feelings of HOTS is the ability to apply knowledge, skills and values to reason
others. They are committed to serve the out and make reflection to solve problems, make decisions,
society and ensure the sustainability of the
environment.

They demonstrate their love, support and
respect for the country.

14

innovative and able to create something. HOTS includes critical KSSM MATHEMATICS FORM 4 AND 5
and creative thinking, reasoning and thinking strategies.
TEACHING AND LEARNING STRATEGIES
Critical thinking skills is the ability to evaluate a certain idea
logically and rationally in order to make sound judgements using Good T&L of mathematics demands teachers to carefully plan
logical reasoning and evidences. activities and to integrate diversified strategies that enable pupils to
not only understand the content in depth, but to challenge them to
Creative thinking skills is the ability to produce or create think at a higher level.
something new and worthy using authentic imagination and
thinking out of the ordinary. The T&L of mathematics emphasises active pupil participation,
which among others, can be achieved through:
Reasoning skills is an individual’s ability to make logical and  Inquiry-based learning, which includes investigation and
rational considerations and evaluations.
exploration of mathematics;
Thinking strategies is a structured and focused way of thinking to  Problem-based learning; and
solve problems.  The use of technology in concept buidling.

HOTS can be applied in classrooms through reasoning, inquiry- Inquiry-based is an approach that emphasises learning through
based learning, problem solving and projects. Teachers and pupils experience. Inquiry generally means to seek information, to
need to use thinking tools such as thinking maps and mind maps question and to investigate real-life phenomena. Discovery is a
as well as high-level questioning techniques to encourage pupils to major characteristic of inquiry-based learning. Learning through
think. discovery occurs when the main concepts and principles are
investigated and discovered by pupils themselves. Through the
activities, pupils will investigate phenomena, analyse patterns thus
form their own conclusions. Teachers then guide pupils to discuss
and understand the concept of mathematics through the results of
the inquiry. KSSM Mathematics emphasises deep

15

conceptual understanding, efficiency in manipulation, the ability to KSSM MATHEMATICS FORM 4 AND 5
reason and communicate mathematically. Thus, the T&L that
involves inquiry, exploration and investigation of mathematics questioning techniques are needed to enable pupils to discover the
should be conducted wherever appropriate. Teachers need to rules, patterns or the properties of mathematical concepts.
design T&L activities that provide space and opportunities for pupils
to make conjectures, reason out, ask questions, make reflections The use of teaching aids and carrying out tasks in the form of
and thus form concepts and acquire knowledge on their own. presentations or project work need to be incorporated into the
learning experience in order to develop pupils who are competent
A variety of opportunities and learning experiences, integrating the in applying knowledge and skills of mathematics in solving
use of technology, and problem solving that involves a balance of problems involving everyday situations as well as to develop soft
both routine and non-routine questions, are also emphasised in the skills among them. Other diversified T&L approaches and
T&L of mathematics. Non-routine questions requiring higher-order strategies such as mastery learning, contextual learning,
thinking are emphasised in order to achieve the vision of producing constructivism, project-based learning, problem-based learning
human capital who can think mathematically, creatively and and others should be implemented in accordance to the needs and
innovatively, are able to compete in the era of globalisation and to appropriateness.
meet the challenges of the 21st century.
The learning of mathematics that embraces fikrah needs to be
Mathematics is a discipline of knowledge consisting of concepts, manifested in the T&L. Thus, T&L strategies should be pupil-
facts, characteristics, rules, patterns and processes. Thus, the centred to enable them to interact and acquire the learning skills
strategies used in the T&L of mathematics require diversity and through their own experiences. Approaches and strategies of
balance. The traditional strategy is sometimes still necessary when learning, such as inquiry-discovery, mathematical exploration and
teaching a procedural-based content. On the other hand, certain investigation and pupil-centred activities with the aid of
contents require teachers to provide learning activities that enable mathematical tools that are appropriate, comprehensive and
pupils to discover the concept on their own. Thus, structured effective can make the learning of mathematics useful and
challenging which in turn will form the basis for deep understanding
of concepts.

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Teachers need to diversify the methods and strategies of T&L to KSSM MATHEMATICS FORM 4 AND 5
meet the needs of pupils with various abilities, interests and
preferences. The active involvement of pupils in meaningful and classroom. Mathematics is the science of patterns and relations
challenging T&L activities should be designed specifically to cater which has aesthetic values that are closely related to the natural
their needs. Every pupil should have an equal opportunity to form phenomena. Hence, mathematics is the cornerstone and the
conceptual understanding and procedural competence. Therefore, catalyst for the development of creativity and innovative skills
teachers should be mindful in setting the ecosystem of learning and among pupils through suitable tasks and activities.
intellectual discussions that require pupils to collaborate in solving
meaningful and challenging tasks. Teachers need to design T&L activities that encourage and foster
creativity and innovation. Among the strategies that can be used is
Creativity and innovation are key elements in the development of to involve pupils in complex cognitive activities such as:
a knowledgeable society in the 21st century. Both of these elements  The implementation of tasks involving non-routine questions
will significantly contribute to the social and individual prosperity of
a country. Malaysia needs creative and innovative human capital requiring diversified problem-solving strategies and high level
in order to compete in todays’ world which is increasingly of thinking;
competitive and dynamic. Education is seen as a means in the  The use of technology to explore, build conceptual
formation of creativity and innovation skills among the people. understanding and solve problems;
 Fostering a culture in which pupils showcase creativity and
Creativity and innovation are interrelated. In general, creativity innovation in a variety of forms; and
refers to the ability to produce new ideas, approaches or actions.  Design T&L activities that provide space and opportunities for
Innovation is the process of generating creative ideas in a certain pupils to perform mathematics and build understanding through
context. Creativity and innovation capabilities are the skills that can inquiry-based exploration and investigation.
be developed and nurtured among pupils through T&L in the

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STEM APPROACH (Science, Technology, Engineering and KSSM MATHEMATICS FORM 4 AND 5
Mathematics)
STEM teaching and learning which is contextual and authentic is
STEM approach is the T&L method which applies integrated able to encourage in-depth learning among pupils. Pupils can work
knowledge, skills and values of STEM through inquiry, problem in groups or individually according to their ability to cultivate the
solving or project in the context of daily life, environment and local STEM practices, as follows:
as well as global community, as shown in Diagram 3. 1. Questioning and identifying problems.
2. Developing and using models.
3. Planning and carrying out investigations.
4. Analysing and interpreting data.
5. Using mathematical and computational thinking.
6. Developing explanation and designing solutions.
7. Engaging in argument and discussion based on evidence.
8. Acquiring information, evaluating and communicating about the

information.

Diagram 3: STEM as Teaching and Learning Approach
18

CROSS-CURRICULAR ELEMENTS KSSM MATHEMATICS FORM 4 AND 5

Cross-curricular Elements (EMK) is a value-added element applied 3. Moral Values
in the T&L process other than those specified in the Content  Moral values are emphasised in all subjects so that pupils
Standard. These elements are applied to strengthen the skills and are aware of its importance, hence practise good values.
competency of the intended human capital who will be capable of  Moral values include aspects of spirituality, humanity and
dealing with the current and future challenges. The elements in the citizenship that are being practised in daily life.
EMK are as follows:
4. Science and Technology
1. Language  Increasing the interest in science and technology can
 The use of proper language of instruction should be improve literacy in science and technology among pupils.
emphasised in all subjects.  The use of technology in teaching can support and
 During the T&L of every subject, aspect of pronunciation, contribute to a more efficient and effective learning.
sentence structure, grammar, vocabulary and grammar  Integration of science and technology in T&L encompasses
should be emphasised to help pupils organise ideas and four main factors:
communicate effectively. (i) Knowledge of science and technology (facts,
principles, concepts related to science and
2. Environmental Sustainability technology);
 Developing awareness and love for the environment needs (ii) Scientific skills (thinking processes and certain
to be nurtured through the T&L process in all subjects. manipulative skills);
 Knowledge and awareness on the importance of the (iii) Scientific attitude (such as accuracy, honesty, safety);
environment would shape pupils’ ethics in appreciating (iv) The use of technology in T&L activities.
nature.

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5. Patriotism KSSM MATHEMATICS FORM 4 AND 5
 The spirit of patriotism is to be fostered in all subjects, extra-
curricular activities and community services.  Features of entrepreneurship can be applied in T&L through
 Patriotism develops the spirit of love for the country and activities that could foster attitudes such as diligence,
instils a sense of pride of being Malaysians amongst pupils. honesty, trustworthy, responsibility and to develop creative
and innovative minds to market the idea.
6. Creativity and Innovation
 Creativity is the ability to use imagination to collect, 8. Information and Communication Technology (ICT)
assimilate and generate ideas or create something new or  Application of ICT element into the T&L is to ensure that
original by inspiration or combinations of existing ideas. pupils can apply and consolidate the knowledge and skills
 Innovation is the application of creativity through learned.
modification, correcting and practising the ideas.  The application of ICT not only encourages pupils to be
 Creativity and innovation go hand in hand and are needed creative but also makes T&L more interesting and fun as
in order to develop human capital that can face the well as improving the quality of learning.
challenges of the 21st century.  ICT should be integrated in the lesson based on appropriate
 Elements of creativity and innovation should be integrated topics to be taught to further enhance pupils’ understanding
into the T&L. of the content.
 One of the emphases in ICT is the computational thinking
7. Entrepreneurship that can be applied in all subjects. Computational thinking
 The inculcation of entrepreneurial elements aims to is a skill that applies the concepts of logical reasoning,
establish the characteristics and the practice of algorithm, resolution, pattern recognition, scaling and
entrepreneurship so that it becomes a culture among assessment in the process of solving computer assisted
pupils. problems.

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9. Global Sustainability KSSM MATHEMATICS FORM 4 AND 5
 Global Sustainability elements aim to produce pupils who
have sustainable thinking and are responsive to the Indirect application is integrated through other topics across the
environment in their daily lives by applying the knowledge, curriculum. Exposure to financial management in real life is
skills and values acquired through the elements of important to provide pupils with the knowledge, skills and
Sustainable Consumption and Production, Global values that can be applied effectively and meaningfully.
Citizenship and Unity.
 The Global Sustainability elements are significant in
preparing pupils to face the challenges and current issues
at different levels; local, national and global.
 These elements are taught directly and indirectly in the
relevant subjects.

10. Financial Education
 Application of financial education elements aims at shaping
the future generation that is capable of making right
financial decisions, ethical practice and financial
management skills to manage the financial affairs
responsibly.
 Elements of financial education can be applied in T&L
directly or indirectly. Direct application is done through the
topics that contain explicit financial elements such as the
calculation of simple interest and compound interest.

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CLASSROOM ASSESSMENT KSSM MATHEMATICS FORM 4 AND 5

Classroom assessment is a process to obtain information on pupils’  Assessing the level of pupils’ performance based on Learning
progress which is planned, carried out and reported by the teachers Standards and Performance Standards.
concerned. This process is ongoing to enable teachers to
determine the level of pupils’ performance.  Taking follow-up actions for improvement and consolidation
purposes.
Teachers can implement formative and summative assessments
as classroom assessments. Formative assessments are carried  Holistic, that is taking into account various levels of cognitive,
out during the teaching and learning processes, while summative affective and psychomotor.
assessments are carried out at the end of a learning unit, term,
semester or year. Teachers need to plan, construct items,  Fair to all pupils.
administer, mark, record and report pupils’ performance level in the
subjects taught based on the DSKP. General Performance Level

In order to ensure that assessment helps to improve the ability and Performance level is a form of achievement statement that shows
performance of the pupils, teachers should carry out the the progress of pupils’ learning. There are six levels of
assessment that has the following features: performance that indicate level of performance that are arranged
 Using various assessment methods such as observation, oral in hierarchy. This level of performance takes into account the
knowledge, skills and mathematical processes specified in the
and writing. curriculum. The Performance Standards (SPi) for each topic is
 Taking into account the knowledge, skills and values that are constructed based on the General Performance Level as in
Table 4. The purpose of SPi is to help teachers to make
intended in the curriculum. professional judgement in determining the level of performance
 Allowing pupils to exhibit various learning capabilities. that needs to be reported in a given duration or time frame.

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Table 4: Statements of General Performance Level of KSSM MATHEMATICS FORM 4 AND 5
KSSM Additional Mathematics
Teachers can record pupils progress in Teacher’s Record Books,
exercise books, note books, checklist, tables or others.

PERFORMANCE INTERPRETATION
LEVEL
Assessment of Values

Demonstrate basic knowledge such as Elements of attitudes and values that need to be displayed and
1 stating a certain mathematical idea either practised by pupils are assessed continuously through various
media such as observations, exercises, presentations, pupils’
verbally or non-verbally. verbal responses, collaborative activities and others. The
achievement report of these elements can be done during mid-year
Demonstrate understanding such as or whenever necessary to observe the progress of pupils and help
2 explaining a certain mathematical concept them improve the practice of good values, based on Table 5.

either verbally or non-verbally. Table 5: Level of Values Internalisation in Mathematics
Education
Apply understanding such as performing
3 calculations, constructing tables and drawing

graphs.

Apply suitable knowledge and skills such as

4 using algorithms, formulae, procedures or
basic methods in the context of solving

simple routine problems.

Apply suitable knowledge and skills in new

situations such as performing multi-step VALUE IN MATHEMATICS INTERNALISATION
EDUCATION LEVEL
5 procedures, using representations based on
different sources of information and reason

out directly in the context of solving complex Interested in learning
mathematics.
routine problems.
Appreciate the aesthetic
Apply suitable knowledge and skills such as values and the importance of Low:
mathematics. 1, 2 or 3 out of all the
using information based on investigation and standards listed are
observed
6 modelling in solving complex problems
situations; reason out at a higher level, form

new approaches and strategies in the context Confident and patient in
learning mathematics.
of solving non-routine problems creatively.

23

VALUE IN MATHEMATICS INTERNALISATION KSSM MATHEMATICS FORM 4 AND 5
EDUCATION LEVEL
Overall Performance Level
Willing to learn from Medium
mistakes. 4, 5 or 6 out of all the Overall Performance Level for each subject should be determined
standards listed are at the end of each year. This level comprises the aspects of content,
Work towards accuracy. observed skills and mathematical processes, which are emphasised in the
curriculum, including higher-order thinking skills. Thus, teachers
Practise self-access learning. need to evaluate pupils collectively, comprehensively and
holistically, taking into consideration pupils’ activities on a
Dare to try something new High continuous basis through various media such as achievement in
7, 8 or 9 out of all the examination, topical tests, observations, exercises, presentations,
Work systematically standards listed are pupils’ verbal responses, group work, projects and so on
observed Elements, which are emphasised in the Performance Level
Use mathematical tools According to Learning Areas and Overall Performance Level,
accurately and effectively. should be developed in an integrated manner among the pupils
through various tasks. Therefore, teachers have to use their
Level of value internalisation in mathematics education is wisdom in making professional judgement to determine pupils’
categorised into three levels, which are low, medium and high. overall performance level as in Table 6.

Teachers need to assess these elements holistically and
comprehensively through detailed observations as well as using
professional judgements to determine the level of internalisation of
values that should be given to each pupil.

24

KSSM MATHEMATICS FORM 4 AND 5

Table 6: Statements of Overall Performance Level PERFORMANCE CONTENTS, SKILLS AND
LEVEL MATHEMATICAL PROCESSES

PERFORMANCE CONTENTS, SKILLS AND  make direct reasoning;
LEVEL MATHEMATICAL PROCESSES communicate briefly when
giving interpretations, results
Pupils are able to: and reasoning.

 answer questions where all related Pupils are able to:
information are given and questions  use explicit models effectively in

1 are clearly defined concrete complex situations,
 identify information and carry out  choose and integrate different
routine procedures according to
clear instructions. representations and relate to real
4 world situations
Pupils are able to:
 use skills and reasonings flexibily
 recognise and interpret situations based on deep understanding and
directly communicate with explanations and
arguments based on interpretations,
2  use single representation discussions and actions.
 use algorithms, formulae,
procedures or basic methods Pupils are able to:
 make direct reasoning and interpret  develop and use models for complex
the results obtained.
Pupils are able to: situations
 perform procedures that are stated  identify constraints and make
clearly, including multi-steps
procedures specific assumptions
 apply suitable problem-solving
3  apply simple problem- solving 5 strategies
strategies  work strategically using in-depth

 interpret and use representations thinking skills and reasoning
based on different sources of  use various suitable representations
information
and display in-depth understanding
 reflect on results and actions

25

PERFORMANCE CONTENTS, SKILLS AND KSSM MATHEMATICS FORM 4 AND 5
LEVEL MATHEMATICAL PROCESSES
Based on Overall Performance Level, it is clear that teachers should
 conclude and communicate with use tasks with various levels of difficulty and complexity which are
explanations and arguments based able to access various elements and pupils’ performance level.
on interpretations, discussions and Holistic assessments are needed in developing pupils with global
actions skills. Content mastery has to be supported by pupils’ ability to
achieve and apply processes, hence display the ability in solving
Pupils are able to: complex problems especially those involving real-life situations. It
is important that teachers carry out comprehensive assessments
 conceptualise, make generalisations and provide fair and just report of each pupil’s performance level.
and use information based on
investigations and modelling of CONTENT ORGANISATION
complex situations
The implementation of KSSM Mathematics is in accordance with
 relate information sources and the Surat Pekeliling Ikhtisas which is being enforced now. The
flexibly change one form of minimum hours per year for the T&L of KSSM Mathematics Form
representations to another 4 and 5 is 112 hours.

6  possess high level of mathematical KSSM Mathematics consists of three components: Content
thinking and reasoning skills Standards (SK), Learning Standards (SP) and Performance
Standards (SPi). The interpretation of each part is as in Table 7.
 demonstrate in-depth understanding;
form new approaches and strategies
to handle new situations

 conclude and communicate with
explanations and arguments based
on interpretations, discussions,
reflections and actions accurately.

26

Table 7: Interpretation of Content Standard, Learning Standard KSSM MATHEMATICS FORM 4 AND 5
and Performance Standard
achieve the SP. Teachers can carry out additional activities other
Content Standard Learning Performance than those suggested according to their creativity and the needs to
Standard Standard achieve the SP.

Specific statement Criterion set or Set of general criteria The contents of KSSM Mathematics are organised and arranged
on what pupils indicators of the that shows the levels according to independent and complete subunits based on modular
should know and quality of learning of performance that approach. Modular approach in T&L enables teachers to arrange
be able to do in a and achievement pupils should display the topics and standards accordingly based on pupils’ ability. This
certain schooling that can be as an indicator that approach can be implemented in two ways as follow:
period which measured for they have mastered  Linear modular approach - SK or SP delivered sequentially
encompasses the each Content a certain matter.
aspects of Standard. according to the arrangement of the DSKP
knowledge, skills  Non-linear modular approach – SK or SP delivered
and values.
unsequentialy.
In the content organisation, there is a Note column. This column
contains the limitations and scope of SK and SP, suggested The scope of contents for Form 4 and 5 KSSM Mathematics are as
activities, information or notes that support teachers' understanding shown in Table 8.
and mathematical processes that need to be implemented to

27

KSSM MATHEMATICS FORM 4 AND 5

Table 8: Form 4 and 5 KSSM Mathematics Contents

LEARNING AREA TITLE FORM 4 TITLE FORM 5

Number and Operations  Number Bases  Consumer Mathematics: Insurance

 Consumer Mathematics: Financial Management  Consumer Mathematics: Taxation

Relationship and Algebra  Quadratic Functions and Equations in One  Variation
Variable  Matrices
 Mathematical Modeling
 Linear Inequalities in Two Variables
 Graphs of Motion

Statistic and Probability  Measures of Dispersion for Ungrouped Data  Measures of Dispersion for Grouped Data
 Probability of Combined Events

Measurement and Geometry  Congruency, Enlargement and Combined
Transformations

 Ratios and Graphs of Trigonometric
Functions

Discrete Mathematics  Logical Reasoning
 Operations on Sets
 Network in Graph Theory

28

KSSM MATHEMATICS FORM 4 AND 5

Content Standards,
Learning Standards
and Performance Standards

Form 4

29

KSSM MATHEMATICS FORM 4

30

KSSM MATHEMATICS FORM 4

LEARNING AREA

RELATIONSHIP AND ALGEBRA

TOPIC

1.0 QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

31

KSSM MATHEMATICS FORM 4

1.0 QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

CONTENT STANDARDS LEARNING STANDARDS NOTES

1.1 Quadratic Functions and Pupils are able to: Suggested Activities:
Equations The use of dynamic geometry software is
1.1.1 Identify and describe the characteristics of encouraged throughout this topic.
quadratic expressions in one variable. Notes:
Exploratory activities involving the following cases
1.1.2 Recognise quadratic function as many-to- need to be carried out:
one relation, hence, describe the (i) The power of the variables is not a whole
characteristics of quadratic functions.
number;
(ii) = 0 or = 0, or = = 0 in 2 + + .

Notes:
Exploratory activities involving graphs of quadratic
functions need to be carried out.
Characteristics of quadratic functions include:
(i) Curved shape of the graph
(ii) Maximum or minimum point
(iii) The axis of symmetry of the graph is parallel

to the y-axis.
Suggested Activities:
The vertical line test can be used to determine
many-to-one relation.

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KSSM MATHEMATICS FORM 4

CONTENT STANDARDS LEARNING STANDARDS NOTES

1.1.3 Investigate and make generalisation about
the effect of changing the values of , and
on graphs of quadratic functions,
( ) = 2 + + .

1.1.4 Form quadratic functions based on Notes:
situations, and hence relate to the quadratic Real-life situations need to be involved.
equations. Quadratic equation in the form of
2 + + = 0 needs to be involved.
1.1.5 Explain the meaning of roots of a quadratic
equation. Exploratory activities need to be carried out.
Limit to real roots.
The position of the roots on the graphs of
quadratic equations needs to be discussed.

1.1.6 Determine the roots of a quadratic equation Suggested Activities:
by factorisation method.
Graphical method using dynamic geometry
software is encouraged.

1.1.7 Sketch graphs of quadratic functions. Notes:

For the quadratic functions with no real roots, limit
to the cases where the maximum or minimum

point lies on the y -axis.

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CONTENT STANDARDS LEARNING STANDARDS KSSM MATHEMATICS FORM 4

1.1.8 Solve problems involving quadratic NOTES
equations.
Notes:
Creating situations based on quadratic equations
need to be involved.
Identifying quadratic graph, given its quadratic
function and vice versa, need to be involved.

PERFORMANCE LEVEL PERFORMANCE STANDARDS
1
2 DESCRIPTOR
3
4 Demonstrate the basic knowledge of quadratic expressions, functions and equations in one variable.

5 Demonstrate the understanding of quadratic expressions, functions and equations in one variable.

6 Apply the understanding of quadratic functions and equations in one variable to perform simple tasks.

Apply appropriate knowledge and skills of quadratic functions and equations in one variable in the context
of simple routine problems solving.

Apply appropriate knowledge and skills of quadratic functions and equations in one variable in the context
of complex routine problems solving.

Apply appropriate knowledge and skills of quadratic functions and equations in one variable in the context
of non-routine problems solving in a creative manner.

34

KSSM MATHEMATICS FORM 4

LEARNING AREA

NUMBER AND OPERATIONS

TOPIC

2.0 NUMBER BASES

35

KSSM MATHEMATICS FORM 4

2.0 NUMBER BASES LEARNING STANDARDS NOTES
CONTENT STANDARDS
Pupils are able to: Notes:
2.1 Number Bases

2.1.1 Represent and explain numbers in various Conversions and calculations involving number
bases in terms of numerals, place values, bases using calculators are not allowed except for
digit values and number values based on the conceptual exploration and checking of answers
collection process. throughout this topic.

Bases are limited to less than 10.

Concrete materials and diagrams need to be used
in forming the concepts of number bases.

Example: The number 128

In terms of place value:

81 80
12

In terms of digit value:
1 × 81 and 2 × 80
= 8 and 2
In terms of number values:
(1 × 81) + (2 × 80)
=8+2
= 1010

36