DSKP KSSM MATHEMATICS FORM 4(DLP)

Matematik

Tingkatan 4

(EDISI BAHASA INGGERIS)



Matematik

Tingkatan 4

(EDISI BAHASA INGGERIS)

Bahagian Pembangunan Kurikulum
APRIL 2018

Terbitan 2018

© Kementerian Pendidikan Malaysia

Hak Cipta Terpelihara. Tidak dibenarkan mengeluar ulang mana-mana bahagian artikel, ilustrasi dan isi kandungan buku ini dalam apa juga
bentuk dan dengan cara apa jua sama ada secara elektronik, fotokopi, mekanik, rakaman atau cara lain sebelum mendapat kebenaran
bertulis daripada Pengarah, Bahagian Pembangunan Kurikulum, Kementerian Pendidikan Malaysia, Aras 4-8, Blok E9, Parcel E, Kompleks
Pentadbiran Kerajaan Persekutuan, 62604 Putrajaya.

CONTENT

Rukun Negara...................................................................................................................................................................................... v
Falsafah Pendidikan Kebangsaan....................................................................................................................................................... vi
Definisi Kurikulum Kebangsaan........................................................................................................................................................... vii
Kata Pengantar.................................................................................................................................................................................... ix
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................................................................................................................................................................ 15
Teaching and Learning Strategies....................................................................................................................................................... 16
Cross-Curricular Elements................................................................................................................................................................... 20
Classroom Assessment....................................................................................................................................................................... 23

Content Organisation......................................................................................................................................................................... 27
Quadratic Functions and Equations in One Variable.................................................................................................................... 29
Number Bases................................................................................................................................................................................ 33
Logical Reasoning.......................................................................................................................................................................... 37
Operations on Sets........................................................................................................................................................................ 43
Network in Graph Theory............................................................................................................................................................... 47
Linear Inequalities in Two Variables.............................................................................................................................................. 51
Graphs of Motion........................................................................................................................................................................... 55
Measures of Dispersion for Ungrouped Data............................................................................................................................... 59
Probability of Combined Events..................................................................................................................................................... 63
Consumer Mathematics: Financial Management........................................................................................................................... 69
73
Panel of Writers.................................................................................................................................................................................... 75
Panel of Translators............................................................................................................................................................................. 77
Acknowledgement................................................................................................................................................................................

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 hidup 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

v

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)

vi

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.]

vii



KATA PENGANTAR

Kurikulum Standard Sekolah Menengah (KSSM) yang DSKP yang dihasilkan juga telah menyepadukan enam tunjang
dilaksanakan secara berperingkat mulai tahun 2017 akan Kerangka KSSM, mengintegrasikan pengetahuan, kemahiran dan
menggantikan Kurikulum Bersepadu Sekolah Menengah (KBSM) nilai, serta memasukkan secara eksplisit Kemahiran Abad Ke-21
yang mula dilaksanakan pada tahun 1989. KSSM digubal bagi dan Kemahiran Berfikir Aras Tinggi (KBAT). Penyepaduan tersebut
memenuhi keperluan dasar baharu di bawah Pelan Pembangunan dilakukan untuk melahirkan insan seimbang dan harmonis dari segi
Pendidikan Malaysia (PPPM) 2013-2025 agar kualiti kurikulum intelek, rohani, emosi dan jasmani sebagaimana tuntutan Falsafah
yang dilaksanakan di sekolah menengah setanding dengan Pendidikan Kebangsaan.
standard antarabangsa. Kurikulum berasaskan standard yang
menjadi amalan antarabangsa telah dijelmakan dalam KSSM Bagi menjayakan pelaksanaan KSSM, pengajaran dan
menerusi penggubalan Dokumen Standard Kurikulum dan pembelajaran guru perlu memberi penekanan kepada KBAT
Pentaksiran (DSKP) untuk semua mata pelajaran yang dengan memberi fokus kepada pendekatan Pembelajaran
mengandungi Standard Kandungan, Standard Pembelajaran dan Berasaskan Inkuiri dan Pembelajaran Berasaskan Projek, supaya
Standard Prestasi. murid dapat menguasai kemahiran yang diperlukan dalam abad
ke-21.
Usaha memasukkan standard pentaksiran di 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 Kebangsaan.
bagi mempertingkatkan pencapaian murid.
SHAZALI BIN AHMAD
Pengarah
Bahagian Pembangunan Kurikulum
Kementerian Pendidikan Malaysia

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KSSM MATHEMATICS FORM 4

INTRODUCTION

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

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

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AIMS KSSM MATHEMATICS FORM 4

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:
KSSM Mathematics Form 4 and 5 enable 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. Further develop capacity in: 5. Practise the mathematical process skills consistently that 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

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

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 support 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

KSSM Mathematics focuses on developing individuals who Four key elements that contribute to the development of indivuals
internalise and practise mathematical fikrah. The Mathematics who posses 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  Mathematical Skills
 Connection  21st Century Skills
 Higher-Order Thinking Skills

Figure 2: The Mathematics Curriculum Framework for Secondary Schools

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Mathematical Fikrah KSSM MATHEMATICS FORM 4

According to the Fourth Edition (2005) of Kamus Dewan, fikrah  Statistics and Probability
means capability of thinking and thoughts. In the context of  Discrete Mathematics
mathematics education, mathematical fikrah refers to the quality of
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  Making connection; and
century, as the country is highly dependent on the ability of human  Representation.
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 skill needs to be developed comprehensively and
are inter-related, namely: integrated across 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 creative, innovative and
 Relationship and Algebra capable of using a variety of problem-solving strategies and higher
order thinking skills. Teachers need to design T&L sessions which

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KSSM MATHEMATICS FORM 4

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

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do mathematics and be actively involved in discussing KSSM MATHEMATICS FORM 4
mathematical ideas.
graphs, diagrams, etc), help pupils to understand and apply
The elements of reasoning in the T&L prevent pupils from looking mathematics more effectively.
at 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 during T&L
mathematical concepts in depth. Reasoning does not only change sessions to encourage pupils to express and present their
pupils’ paradigm from emphasising on the importance of procedural mathematical ideas by using appropriate questioning techniques.
knowledge but also gives thinking and intellectual empowerment Communication that involves a variety of perspectives and points
when 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 develop pupils’
confidence and courage, in line with the aim of developing powerful The significant aspect of mathematical communication is the
mathematical thinkers. ability to provide effective explanation as well as to understand
and apply the correct mathematical notations. Pupils should use
Communication in mathematics is the process of expressing the 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 verbally, in 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.

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Representation is an important component of mathematics and KSSM MATHEMATICS FORM 4
often used to represent real-world phenomena. Therefore, there
must be a similarity between the aspects of the world that is being Making connections among the fields 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 so that pupils are able to learn concepts and skills in an
that symbolise or represent something else. integrated manner. By recognising how the concept or skills in
different fields are related to each other, mathematics will be viewed
At secondary school level, representing ideas and mathematical and studied as an integrated discipline, having links between one
models generally make use of symbols, geometry, graphs, algebra, another and allowing the abstract concepts to be more easily
diagrams, concrete representations and dynamic software. Pupils understood.
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
representations, which are relevant and required to solve problems. experiences within and outside the classroom, pupils will be
more aware of the use, the importance, the strength and the
The use of various representations helps pupils to understand beauty of mathematics. Besides, they are also able to use
mathematical concepts and relationships, communicate their mathematics contextually in other disciplines and in their daily
thinking, reasoning and understanding; recognise the relationship lives. Mathematical modellings are used to describe real-life
between mathematical concepts and use mathematics to model situations mathematically. Pupils will find that this method can
situations, physical and social phenomena. When pupils are able be used to find solutions to problems or to predict the possibility
to represent concepts in different ways, they will be flexible in their of a situation based on the mathematical modelling.
thinking and understand that there are varieties of ways to
represent mathematical ideas that enable problems to be easily In implementing the Mathematics curriculum, the opportunities to
solved. make connections 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 other fields in general. This will enhance pupils’ mathematical

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understanding, making mathematics clearer, meaningful and KSSM MATHEMATICS FORM 4
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
 Identify and use the connection between mathematical
develop creative and innovative individuals. The use of
ideas. mathematical tools strategically, accurately and effectively is
 Understand how mathematical ideas are inter-related and strongly emphasised in the teaching and learning of mathematics.
The mathematical tools include papers and pencils, rulers,
form a cohesive unity. protractors, compasses, calculators, electronic spreadsheets,
 Relate mathematical ideas to daily life and other fields. dynamic software and others.

Skills The rapid progress of various technologies in todays’ life has
resulted in the use of technologies as an essential element in the
The skills that need to be developed and nurtured among pupils T&L of mathematics. Effective teachers will maximise the potential
through this subject include Mathematical Skills, 21st Century and technological capabilities so that pupils can build
Skills and Higher Order Thinking Skills (HOTS). understanding and increase their proficiency and interest in
mathematics. Due to the capacity and effectiveness of technology
The mathematical skills refer to among others the skills of in the T&L of mathematics content, teachers need to embrace the
measuring and constructing, estimating and rounding, collecting use of technology, particularly scientific and graphing calculators,
and handling data, representing and interpreting data, recognising computer software like Geometer's Sketchpad, Geogebra,
relationships and representing mathematically, translating real-life electronic spreadsheets, learning software (courseware), the
situations into mathematical models, using precise language of Internet and others.
mathematics, applying logical reasoning, using algorithms and
relationships, using mathematical tools, solving problems, making However, technology must be used wisely. For example, scientific
decisions and so on. In addition, the curriculum also demands the calculator should not be used as to neglect the importance of mental
development of pupils’ mathematical skills related to creativity, the calculations and basic computations. Efficiency in carrying out the
needs for originality in their thinking and the ability to see things calculations is important especially in the lower level and pupils
around them with new and different perspectives in order to should not totally rely on calculators. For example, although the

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graphing calculator helps pupils to visualise the nature of a function KSSM MATHEMATICS FORM 4
and its graph, fundamentally the use of papers and pencils is still
the learning outcome to be achieved by all pupils. Similarly, in T&L of mathematics to help pupils form deep understanding of
seeking the roots of the quadratic equations, the basic concept must concepts especially abstract concepts.
first be mastered by pupils. Technology should be used wisely to
help pupils form concepts, enhance understanding, visualise Values in Mathematics Education
concepts and others, while enriching pupils learning experiences.
Values are affective qualities intended to be developed through the
Specifically, the skills of using the technology that need to be T&L of mathematics using appropriate contexts. Values are usually
nurtured in the pupils through Mathematics are the ability of pupils taught and learned implicitly through the learning sessions. Moral
in: values being instilled will manifest good attitudes. The application
 Using technology to explore, carry out research, construct of values and attitudes in the T&L of mathematics are intended to
produce individuals who are competent in terms of knowledge and
mathematical modelling and hence form deep understanding skills as well as having good characters. Embracing moral values
of the mathematical concepts. would produce a virtuous young generation with noble personal
 Using technology to help in calculations to solve problems qualities and good attitudes.
effectively.
 Using technology, especially electronic and digital technology Values that need to be developed in pupils through the T&L of
to find, manage, evaluate and communicate information. mathematics are:
 Using technology responsibly and ethically.  Mathematical values – values within the knowledge of

The use of technology such as dynamic software, graphing mathematics which include emphasis on the properties of the
calculator, the Internet and so on needs to be integrated into the mathematical knowledge; and
 Universal values - universal noble values that are applied
across all subjects.

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KSSM MATHEMATICS FORM 4

The development of values through T&L of mathematics should 21st CENTURY SKILLS
also involve the elements of divinity, faith, interest, appreciation,
confidence, competence and tenacity. Belief in the power and One of the aims of KSSM is to produce pupils who possess the 21st
greatness of God can basically be nurtured through the content of century skills by focussing on thinking skills, living skills and career,
the curriculum. The relationship between the content learned and guided by the practice of moral values. The 21st Century skills aim
the real world enables pupils to see and validate the greatness and to produce pupils who have the characteristics specified in the
the power of the Creator of the universe. pupils’ profile as in Table 2, so that they are able to compete at a
global level. The mastery of the Content Standards and the
The elements of history and patriotism should also be inculcated Learning Standards in the Mathematics curriculum contributes to
through relevant topics to enable pupils to appreciate mathematics the acquisition of the 21st Century Skills among the pupils.
as well as to boost interest and confidence in mathematics.
Historical elements such as certain events involving Table 2: Pupils’ Profile
mathematicians or a brief history of a concept or symbol are also
emphasised in this curriculum. PUPILS’ DESCRIPTION
PROFILE

Resilient They are able to face and overcome
difficulties and challenges with wisdom,
confidence, tolerance, and empathy.

Competent They voice out and express their thoughts,
Communicator ideas and information confidently and
creatively, in verbal and in written form,
using various media and technology.

Thinker They think critically, creatively and
innovatively; able to solve complex
problems and make ethical decisions. They
think about learning and themselves as

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KSSM MATHEMATICS FORM 4

PUPILS’ DESCRIPTION PUPILS’ DESCRIPTION
PROFILE PROFILE
Team Work learners. They generate questions and be Informed They obtain knowledge and develop a
open towards other individual’s and broad and balanced understanding across
Inquisitive communities’ perspectives, values, and Caring various disciplines of knowledge. They
traditions. They are confident and creative explore knowledge efficiently and effectively
Principled in handling new learning areas. Patriotic in terms of local and global contexts. They
understand issues related to ethics or laws
They can co-operate effectively and regarding information acquired.
harmoniously with others. They shoulder
responsibilities together as well as respect They show empathy, compassion and
and appreciate the contributions from each respect towards the needs and feelings of
member of the team. They acquire others. They are committed to serve the
interpersonal skills through collaborative society and ensure the sustainability of the
activities, and this makes them better environment.
leaders and team members.
They demonstrate their love, support and
They develop natural inquisitiveness to respect for the country.
explore new strategies and ideas. They
learn skills that are necessary for inquiry-
learning and research, as well as display
independent traits in learning. The pupils
continuously enjoy life-long learning
experiences.

They have a sense of integrity and sincerity,
equality, fairness and respect the dignity of
individuals, groups and community. They
are responsible for their actions,
consequences and decisions.

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HIGHER ORDER THINKING SKILLS KSSM MATHEMATICS FORM 4

Higher Order Thinking Skills (HOTS) are explicitly stated in the innovate and able to create something. HOTS includes critical and
curriculum so that teachers are able to translate it into their T&L to creative thinking, reasoning and thinking strategies.
promote a structured and focused thinking among pupils.
Explanation of HOTS focuses on four levels of thinking as shown Critical thinking skills is the ability to evaluate a certain idea
in Table 3. logically and rationally in order to make sound judgments using
logical reasoning and evidences.
Table 3: Level of Thinking in HOTS
Creative thinking skills is the ability to produce or create
LEVEL OF EXPLANATION something new and worthy using authentic imagination and
THINKING thinking out of the ordinary.

Applying Using knowledge, skills and values in different Reasoning skills is an individual’s ability to make logical and
situations to perform certain tasks. rational considerations and evaluations.

Analysing Breaking down information into smaller parts in Thinking strategies is a structured and focused way of thinking to
order to understand and make connections solve problems.
between these parts.
HOTS can be applied in classrooms through reasoning, inquiry-
Evaluating Making considerations and decisions using based learning, problem solving and projects. Teachers and pupils
knowledge, experience, skills, and values as need to use thinking tools such as thinking maps and mind maps
well as providing justification. as well as high-level questioning techniques to encourage pupils to
think.
Creating Producing creative and innovative ideas,
products or methods.

HOTS is the ability to apply knowledge, skills and values to reason
out and make reflection to solve problems, make decisions,

15

KSSM MATHEMATICS FORM 4

TEACHING AND LEARNING STRATEGIES

Good T&L of mathematics demands teachers to carefully plan conceptual understanding, efficiency in manipulation, the ability to
activities and to integrate diversified strategies that enable pupils reason and communicate mathematically. Thus, the T&L that
to not only understand the content in depth, but to challenge them involves inquiry, exploration and investigation of mathematics
to think at a higher level. should be conducted wherever appropriate. Teachers need to
design T&L activities that provide space and opportunities for
The T&L of mathematics emphasises active pupil participation, pupils to make conjectures, reason out, ask questions, make
which among others, can be achieved through: reflections and thus form concepts and acquire knowledge on their
 Inquiry-based learning, which includes investigation and own.

exploration of mathematics; A variety of opportunities and learning experiences, integrating the
 Problem-based learning; and use of technology, and problem solving that involves a balance of
 The use of technology in concept buidling. both routine and non-routine questions, are also emphasised in the
T&L of mathematics. Non-routine questions requiring higher-order
Inquiry-based is an approach that emphasises learning through thinking are emphasised in order to achieve the vision of producing
experience. Inquiry generally means to seek information, to human capital who can think mathematically, creatively and
question and to investigate real-life phenomena. The discovery is innovatively, are able to compete in the era of globalisation and to
a major characteristic of inquiry-based learning. Learning through meet the challenges of the 21st century.
discovery occurs when the main concepts and principles are
investigated and discovered by pupils themselves. Through the Mathematics is a discipline of knowledge consisting of concepts,
activities, pupils will investigate phenomena, analyse patterns and facts, characteristics, rules, patterns and processes. Thus, the
thus form their own conclusions. Teachers then guide pupils to strategies used in the T&L of mathematics require diversity and
discuss and understand the concept of mathematics through the balance. The traditional strategy is sometimes still necessary when
results of the inquiry. KSSM Mathematics emphasises deep

16

teaching a procedural-based content. On the other hand, certain KSSM MATHEMATICS FORM 4
contents require teachers to provide learning activities that enable
pupils to discover the concept on their own. Thus, structured challenging which in turn will form the basis for deep understanding
questioning techniques are needed to enable pupils to discover the of concepts.
rules, patterns or the properties of mathematical concepts. Teachers need to diversify the methods and strategies of T&L to
meet the needs of pupils with various abilities, interests and
The use of teaching aids and carrying out tasks in the form of preferences. The active involvement of pupils in meaningful and
presentations or project work need to be incorporated into the challenging T&L activities should be designed specifically to cater
learning experience in order to develop pupils who are competent to their needs. Every pupil should have an equal opportunity to form
in applying knowledge and skills of mathematics in solving conceptual understanding and procedural competence. Therefore,
problems involving everyday situations as well as to develop soft teachers should be mindful in providing the ecosystem of learning
skills among them. In addition, teachers need to use diversified and intellectual discussions that require pupils to collaborate in
approaches and strategies in T&L such as cooperative learning, solving meaningful and challenging tasks.
mastery learning, contextual learning, constructivism, project-
based learning and so on. Creativity and innovation are key elements in the development
of a knowledgeable society in the 21st century. Both of these
The learning of mathematics that embraces fikrah needs to be elements will significantly contribute to the social and individual
manifested in the T&L. Thus, T&L strategies should be pupil- prosperity of a country. Malaysia needs creative and innovative
centred to enable them to interact and acquire the learning skills human capital in order to compete in todays’ world which is
through their own experiences. Approaches and strategies of increasingly competitive and dynamic. Education is seen as a
learning, such as inquiry-discovery, mathematical exploration and means in the formation of creativity and innovation skills among the
investigation and pupil-centred activities with the aid of people.
mathematical tools that are appropriate, comprehensive and
effective can make the learning of mathematics useful and Creativity and innovation are interrelated. In general, creativity
refers to the ability to produce new ideas, approaches or actions.
Innovation is the process of generating creative ideas in a certain

17

context. Creativity and innovation capabilities are the skills that can KSSM MATHEMATICS FORM 4
be developed and nurtured among pupils through the T&L in the
classroom. Mathematics is the science of patterns and relations Other diversified T&L approaches and strategies such as mastery
which has aesthetic values that are closely related to the natural learning, contextual learning, constructivism, project-based
phenomena. Hence, mathematics is the cornerstone and the learning, problem-based learning and others should be
catalyst for the development of creativity and innovative skills implemented in accordance to the needs and appropriateness.
among pupils through suitable tasks and activities.

Teachers need to design T&L activities that encourage and foster
creativity and innovation. Among the strategies that can be used is
to involve pupils in complex cognitive activities such as:
 The implementation of tasks involving non-routine questions

requiring diversified problem-solving strategies and high level
of thinking;
 The use of technology to explore, build conceptual
understanding and solve problems;
 Fostering a culture in which pupils showcase creativity and
innovation in a variety of forms; and
 Design T&L activities that provide space and opportunities for
pupils to perform mathematics and build understanding through
inquiry-based exploration and investigation.

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STEM APPROACH (Science, Technology, Engineering and KSSM MATHEMATICS FORM 4
Mathematics)
STEM T&L which is contextual and authentic is able to encourage
STEM approach is the T&L method which applies integrated in-depth learning among pupils. Pupils can work in groups or
knowledge, skills and values of STEM through inquiry, problem individually according to their ability to cultivate the STEM
solving or project in the context of daily life, environment and local 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

19

CROSS-CURRICULAR ELEMENTS KSSM MATHEMATICS FORM 4

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 help and contribute
 During the T&L of every subject, aspect of pronunciation, 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 and
nature. (iv) The use of technology in T&L activities.

20

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

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9. Global Sustainability KSSM MATHEMATICS FORM 4
 Global Sustainability elements aim to produce pupils who
have sustainable thinking and are responsive to the Indirect application is integrated through other topics across
environment in their daily lives by applying the knowledge, the curriculum. Exposure to financial management in real
skills and values acquired through the elements of life is important to provide pupils with the knowledge, skills
Sustainable Consumption and Production, Global and 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.

22

CLASSROOM ASSESSMENT KSSM MATHEMATICS FORM 4

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 with 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, the teacher should carry out the the progress of pupils’ learning. There are six levels of performance
assessment that has the following features: that indicate level of performance that are arranged in hierarchy.
 Using various assessment methods such as observation, oral This level of performance takes into account the knowledge, skills
and mathematical processes specified in the curriculum. The
and writing. Performance Standards (SPi) for each topic is constructed based
 Taking into account the knowledge, skills and values that are on the General Performance Level as in Table 4.

intended in the curriculum.
 Allowing pupils to exhibit various learning capabilities.

23

Table 4: General Performance Level KSSM MATHEMATICS FORM 4

PERFORMANCE INTERPRETATION Teachers can record pupils’ progress in teaching record books,
LEVEL exercise books, notebooks, checklists, tables or other suitable
documents. The performance level can be recorded into the
Demonstrate basic knowledge such as reporting template after the T&L for each topic is completed.
1 stating a certain mathematical idea either
Assessment of Values
verbally or non-verbally.

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

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 Table 5: Value Assessment in Mathematics

5 procedures, using representations based on VALUE IN MATHEMATICS
different sources of information and reason EDUCATION
INTERNALISATION
out directly in the context of solving complex LEVEL

routine problems.

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

new approaches and strategies in the context

of solving non-routine problems creatively.

24

KSSM MATHEMATICS FORM 4

VALUE IN MATHEMATICS Overall Performance Level
EDUCATION
INTERNALISATION
LEVEL

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

Level of value internalisation in mathematics education is
categorised into three levels, which is low, medium and high.

Teachers need to assess these elements holistically and Table 6: Overall Performance Level
comprehensively through detailed observations as well as using
professional judgments to determine the level of internalisation of PERFORMANCE CONTENTS, SKILLS AND
values that should be given to each pupil. LEVEL MATHEMATICAL PROCESSES

Pupils are able to:

1  answer questions where all related
information are given and questions
are clearly defined

25

KSSM MATHEMATICS FORM 4

PERFORMANCE CONTENTS, SKILLS AND PERFORMANCE CONTENTS, SKILLS AND
LEVEL MATHEMATICAL PROCESSES LEVEL MATHEMATICAL PROCESSES

 identify information and carry out  use skills and reasonings flexibily
routine procedures according to based on deep understanding and
clear instructions. communicate with explanations and
arguments based on interpretations,
Pupils are able to: discussions and actions.

 recognise and interpret situations Pupils are able to:
directly
 develop and use models for complex
2  use single representation, use situations
algorithms, formulae, procedures or
basic methods  identify constraints and make
specific assumptions
 make direct reasoning and interpret
the results obtained.  apply suitable problem-solving
strategies
Pupils are able to:
5  work strategically using in-depth
 perform procedures that are stated thinking skills and reasoning
clearly, including multi-steps
procedures  use various suitable representations
and display in-depth understanding
 apply simple problem- solving
3 strategies, interpret and use  reflect on results and actions
 conclude and communicate with
representations based on different
sources of information explanations and arguments based
 make direct reasoning; on interpretations, discussions and
communicatebriefly when giving actions
interpretations, results and
reasoning.

Pupils are able to:

 use explicit models effectively in Pupils are able to:
4 concrete complex situations,
6  conceptualise, make generalisations
 choose and integrate different and use information based on
representations and relate to real investigations and modelling of
world situations complex situations

26

KSSM MATHEMATICS FORM 4

PERFORMANCE CONTENTS, SKILLS AND CONTENT ORGANISATION
LEVEL MATHEMATICAL PROCESSES

 relate information sources and The implementation of KSSM Mathematics is in accordance with
flexibly change one form of the Surat Pekeliling Ikhtisas which is being enforced now. The
representations to another minimum hours per year for T&L KSSM Mathematics Form 4 and
5 is 112 hours.
 possess high level of mathematical
thinking and reasoning skills KSSM Mathematics consists of three components: Content
Standards (SK), Learning Standards (SP) and Performance
 demonstrate in-depth understanding; Standards (SPi). The interpretation of each part is as in Table 7.
form new approaches and strategies
to handle new situations

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

Based on the Overall Performance Level, it is clear that teachers Table 7: Interpretation of Content Standard, Learning Standard
should use tasks with various levels of difficulty and complexity and Performance Standard
which are able to access various elements and pupils’ mastery
level. Holistic assessment is needed in developing pupils with Content Standard Learning Performance
global skills. Content mastery has to be supported by pupils’ ability Standard Standard
to achieve and apply processes, hence display the ability in solving
complex problems especially those involving real-life situations. It Specific statement Criterion set or Set of general criteria
is important that teachers carry out comprehensive assessments on what pupils indicators of the that shows the levels
and provide fair and just report of each pupil’s Performance Level. should know and quality of learning of performance that
be able to do in a and achievement pupils should display
certain schooling that can be as an indicator that
period which measured for they have mastered
encompasses the each Content a certain matter.
aspects of Standard.
knowledge, skills
and values.

27

KSSM MATHEMATICS FORM 4

In the content organisation, there is a Note column. This column Table 8: KSSM Mathematics Form 4 Contents
contains the limitations and scope of SK and SP, suggested
activities, information or notes that support teachers' understanding LEARNING AREA TITLE
and mathematical processes that need to be implemented to Number and Operations
achieve the SP. Teachers can carry out additional activities other Relationship and Algebra  Number Bases
than those suggested according to creativity and the needs to  Consumer Mathematics:
achieve the SP. Statistic and Probability
Discrete Mathematics Financial Management
The contents of KSSM Mathematics are organised and arranged
according to independent and complete subunits based on modular  Quadratic Functions and
approach. Modular approach in T&L enables teachers to arrange Equations in One Variable
the topics and standards accordingly based on pupils’ ability. This
approach can be implemented in two ways as follow:  Linear Inequalities in Two
 Linear modular approach - SK or SP delivered sequentially Variables

according to the arrangement of the DSKP  Graphs of Motion
 Non-linear modular approach – SK or SP delivered
 Measures of Dispersion for
unsequentialy. Ungroup Data

The scope of contents of Mathematics Form 4 is as shown in  Probability of Combined
Table 8. Events

 Logical Reasoning
 Operations on Sets
 Network in Graph Theory

28

KSSM MATHEMATICS FORM 4

LEARNING AREA

RELATIONSHIP AND ALGEBRA

TOPIC

1.0 QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

29

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
1.1.1 Identify and describe the characteristics of The usage of dynamic geometry software is
quadratic expressions in one variable. encouraged throughout this topic.

Notes:

Exploratory activities involving the following cases
need to be carried out:

(i) The power of the variables is not a whole
number;

(ii) = 0 or = 0, or = = 0 in 2 + + .

1.1.2 Recognise quadratic function as many-to- Notes:
one relation, hence, describe the
characteristics of quadratic functions. 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.

30

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
equations. Real-life situations need to be involved.

Quadratic equation in the form of
2 + + = 0 needs to be involved.

1.1.5 Explain the meaning of roots of a quadratic Notes:
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.

31

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 the 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.

32

KSSM MATHEMATICS FORM 4

LEARNING AREA

NUMBER AND OPERATIONS

TOPIC

2.0 NUMBER BASES

33

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

34

KSSM MATHEMATICS FORM 4

CONTENT STANDARDS LEARNING STANDARDS NOTES

2.1.2 Convert numbers from one base to another Notes:
using various methods.
Various methods include the use of place values
and divisions.

Suggested Activities:

Bases of more than 10 can be explored as
enrichment.

2.1.3 Perform computations involving addition and
subtraction of numbers in various bases.

2.1.4 Solve problems involving number bases.

35

KSSM MATHEMATICS FORM 4

PERFOMANCE LEVEL PERFOMANCE STANDARDS
1
2 DESCRIPTOR
3
4 Demonstrate the basic knowledge of number bases.
5
Demonstrate the understanding of number bases.
6
Apply the understanding of number bases to perform simple tasks.

Apply appropriate knowledge and skills of number bases in the context of simple routine problem solving.

Apply appropriate knowledge and skills of number bases in the context of complex routine problem
solving.

Apply appropriate knowledge and skills of number bases in the context of non-routine problem solving in
a creative manner.

36

KSSM MATHEMATICS FORM 4

LEARNING AREA

DISCRETE MATHEMATICS

TOPIC

3.0 LOGICAL REASONING

37

KSSM MATHEMATICS FORM 4

3.0 LOGICAL REASONING LEARNING STANDARDS NOTES
CONTENT STANDARDS Pupils are able to:
3.1.1 Explain the meaning of a statement and Notes:
3.1 Statements The meaning of statements is explained in the
hence determine the truth value of a context of logical reasoning.
statement. Statements include using numerals and
mathematical symbols.
3.1.2 Negate a statement. Statements involving quantifiers which means “all”
and “some” need to be involved.
3.1.3 Determine the truth value of a compound
statement. Notes:
Change the truth value of the statement by using
3.1.4 Construct statement in the form of “not” or “no”.
implication
(i) If p then q Notes:
(ii) p if and only if q A compound statement is a combination of two
statements using “and” or “or”.
3.1.5 Construct and compare the truth value of
converse, inverse and contrapositive of an Notes:
implication. “If p then q” is an implication which is formed from
antecedent, p and consequent, q.

Notes:
Mathematical statements need to be emphasised.

38