Singapore maths syllabus

1
LOWER SECONDARY
MATHEMATICS SYLLABUS
SPECIAL/EXPRESS
NORMAL ACADEMIC
NORMAL TECHNICAL
CURRICULUM PLANNING AND DEVELOPMENT DIVISION
MINISTRY OF EDUCATION
SINGAPORE
© MINISTRY OF EDUCATION
ALL RIGHTS RESERVED
YEAR OF IMPLEMENTATION FROM 2001

2
CONTENTS
1 INTRODUCTION ……………………………………………………..………….. 3
2 AIMS OF MATHEMATICS EDUCATION .……………………………………... 4
3 FRAMEWORK OF THE MATHEMATICS PROGRAMME ..….……………... 5
4 GENERAL ASSESSMENT GUIDELINES ...…………………………………... 8
5 OBJECTIVES OF THE LOWER SECONDARY MATHEMATICS
PROGRAMME ..………………………………………………………………….. 10
6 CONTENT CHART
• Secondary One & Two (Special/Express Course) …………..……………. 11
7 SYLLABUS
• Secondary One (Special/Express Course) ..…………………..…………..
• Secondary Two (Special/Express Course) ………………………………...
13
21
8 CONTENT CHART
• Secondary One & Two (Normal Academic Course) ..……..…………..…. 27
9 SYLLABUS
• Secondary One (Normal Academic Course)... .……………..…………….
• Secondary Two (Normal Academic Course) ...…………………………….
29
36
10 CONTENT CHART
• Secondary One & Two (Normal Technical Course) ..……..…………..…. 41
11 SYLLABUS
• Secondary One (Normal Technical Course)... .……………..…………….
• Secondary Two (Normal Technical Course) ...…………………………….
43
50
12 APPENDIX: DEFINITION OF SUGGESTED THINKING SKILLS …………. 55

3
INTRODUCTION
The Ministry of Education’s vision of “Thinking School, Learning Nation” gives impetus for
the infusion of three initiatives: Thinking Skills, Information Technology (IT) and National
Education into the curriculum. As we move towards a knowledge-based society that is
powered by IT, the need to prepare our people for the challenges and opportunities of the
future becomes obvious. Besides being proficient in the use of IT, pupils will need to be able
to think creatively, learn independently and work successfully in teams. Above all, as
Singapore’s economy moves towards globalisation, they need to have a strong feeling for
home and remain Singaporean in heart, mind and being. Against this background and with
the Desired Outcomes of Education as the overarching aim, the mathematics syllabus was
revised.
This revised mathematics syllabus better reflects the recent developments in mathematics
education. The focus of the syllabus is mathematical problem solving. The emphasis is on
the development of concepts, skills and its underlying processes. This, together with the
explication of thinking skills and the integration of IT in mathematics teaching and learning,
will give leverage to the development of mathematical problem solving.
This syllabus consists of two parts.
Part A explains the philosophy of the syllabus and the spirit in which it should be
implemented. It also spells out the objectives of the mathematics programme.
The framework of the mathematics programme summarises the essence of mathematics
teaching and learning in schools. The learning of mathematics at all levels involves more
than the basic acquisition of concepts and skills. It also involves an understanding of the
mathematical thinking and general problem-solving strategies, having positive attitudes to
and an appreciation of mathematics as an important and powerful tool in everyday life. This
framework forms the basis for mathematics teaching and learning in schools.
Part B gives the syllabus content for each level. Care has been taken to ensure that there is
continuity from the primary to the secondary level. In the syllabus, the spiral approach is
adopted to ensure that each topic is covered at appropriate levels in increasing depth to
enable pupils to consolidate the concepts and skills learnt and to further develop them. All
topics come with ‘Learning Outcomes’ to enable teachers to monitor pupils' progress. The
‘Remarks’ column provides teachers with guidance in interpreting the syllabus.
This syllabus is a guide for teachers to plan their mathematics programmes. Teachers need
not be bound by the sequence of topics presented here but should ensure that the hierarchy
and linkages are maintained. Teachers should exercise flexibility and creativity when using
the syllabus.

PART A
4
AIMS OF MATHEMATICS EDUCATION IN SCHOOLS
Mathematics education aims to enable pupils to:
• acquire and apply the skills and knowledge relating to number, measure and space in
mathematical situations that they will meet in life.
• acquire mathematical concepts and skills necessary for a further study in mathematics
or other disciplines.
• develop the ability to make logical deduction and induction as well as to explicate their
thinking and reasoning skills through the solving of mathematical problems.
• use mathematical language to communicate mathematical ideas and arguments
precisely, concisely and logically.
• develop positive attitudes towards mathematics including confidence, enjoyment and
perseverance.
• appreciate the power and structure of mathematics, including patterns and relationships,
and to enhance their intellectual curiosity.

PART A
5
FRAMEWORK OF THE MATHEMATICS PROGRAMME
The conceptualisation of the mathematics syllabus is based on the following framework:
Appreciation
Interest Monitoring one’s
Confidence own thinking
Perseverance
Estimation and
Approximation
Mental calculation Thinking skills
Communication Heuristics
Use of mathematical tools
Arithmetic manipulation
Algebraic manipulation
Handling data Numerical
Geometrical
Algebraic
Statistical
The primary aim of the mathematics programme is to enable pupils to develop their ability in
mathematical problem solving. Mathematical problem solving includes using and applying
mathematics in practical tasks, in real life problems and within mathematics itself. In this
context, a problem covers a wide range of situations from routine mathematical problems to
problems in unfamiliar context and open-ended investigations that make use of the relevant
mathematics and thinking processes.
The attainment of this mathematical problem solving ability is dependent on five inter-related
components - Concepts, Skills, Processes, Attitudes and Metacognition
1 Concepts
Concepts refer to the basic mathematical knowledge needed for solving mathematical
problems. They cover the following:
•••• Numerical concepts
• Geometrical concepts
• Algebraic concepts
• Statistical concepts

PART A
6
2 Skills
Skills refer to the topic-related manipulative skills that pupils are expected to use when
solving problems. They include:
• Estimation and approximation
• Mental calculation
• Communication
• Use of mathematical tools
• Arithmetic manipulation
• Algebraic manipulation
• Handling data
3 Processes
Processes refer to the thinking and heuristics involved in mathematical problem solving.
Some thinking skills and heuristics, which are applicable to problem solving at the
secondary level, are listed below.
Thinking skills:
• Classifying
• Comparing
• Identifying Attributes & Components
• Sequencing
• Induction
• Deduction
• Generalising
• Justifying
• Verifying
• Spatial visualisation
Heuristics for problem solving:
• Act it out
• Use a diagram/model
• Use guess-and-check
• Make a systematic list

PART A
7
• Look for pattern(s)
• Work backwards
• Use before-after concept
• Make suppositions
• Restate the problem in another way
• Simplify the problem
• Solve part of the problem
• Think of a related problem
• Use equations
(Refer to Appendix A for the definitions of the suggested thinking skills.)
4 Attitudes
Attitudes refer to the affective aspects of mathematics learning such as:
• enjoying mathematics
• appreciating the beauty and power of mathematics
• showing confidence in using mathematics
• persevering in solving a problem
5 Metacognition
Metacognition refers to the ability to monitor one's own thinking processes in problem
solving. This includes:
•••• constant and conscious monitoring of the strategies and thinking processes used
in carrying out a task
•••• seeking alternative ways of performing a task
•••• checking the appropriateness and reasonableness of answers
This framework encompasses the whole mathematics programme for primary and
secondary schools. The secondary curriculum is a continuation of the primary
curriculum.

PART A
8
GENERAL ASSESSMENT GUIDELINES
Assessment is an integral part of the teaching-learning process. The main purpose of
mathematical assessment should be to improve the teaching and learning of mathematics.
Therefore we need assessment that:
• is continual and provides accurate and useful information about pupils’ learning
• supports the programme in its aim to enable pupils to develop their problem solving
ability and in its emphasis on developing mathematical concepts, skills and thinking, as
well as positive attitudes towards mathematics
Teachers should assess different aspects of thinking, learning and behaviour. They should
try to incorporate, where appropriate, the following aspects in the assessment tasks set as
these are the key features of the syllabus:
• mental calculation
• mathematical communication
• practical uses of mathematics
• investigative work
• problem solving
• critical thinking
• creative work
• use of information technology
Continual Assessment
It is important to carry out assessment on a continual basis. Teachers should use continual
assessment to:
• obtain information about pupils’ learning, suitability of teaching methods and materials
and effectiveness of the teaching programme
• identify any learning difficulties that pupils may encounter or misconceptions that they
may have so as to plan effective remedial help
• provide prompt feedback to pupils on their progress and attainment
• promote pupils’ confidence in doing mathematics by focusing on what they can achieve
rather than what they cannot
In continual assessment, teachers should use a variety of assessment modes as different
modes provide different kinds of feedback about pupils. The modes used should yield the
feedback required, and collectively, they give teachers a more comprehensive profile of the
pupils.
Assessment can be carried out through:
• classroom observations;
• oral communication
• written assignments and tests
• practical and investigative tasks

PART A
9
From observations of pupils engaged in a task and through their responses in oral
communication, immediate feedback can be obtained on their understanding of concepts,
thinking processes, mastery of skills and even their attitudes towards mathematics. Written
assignments and tests help teachers to track the progress of pupils and are useful in the
assessment of content and procedures, mathematical thinking and problem solving.
Through practical and investigative tasks, teachers can assess pupils’ problem solving skills,
creative and critical thinking as well as their attitudes. If the tasks are done in groups,
teamwork can also be assessed.
Semestral Assessment
Semestral assessment comprises the mid-year and end-of-year examinations, which are
common school-based examinations administered under formal conditions. The purpose of
semestral assessment is to determine how far pupils have achieved the overall programme
objectives for the semester or year. As such, it should be broad in coverage, test a
representative sample of the syllabus taught and reflect its emphasis.

PART A
10
OBJECTIVES OF THE LOWER SECONDARY MATHEMATICS PROGRAMME
The objectives of the lower secondary mathematics programme are to enable pupils to:
• develop an understanding of mathematical concepts - numerical, geometrical, algebraic,
statistical;
• perform calculations by using suitable methods, including mental calculation, with and
without a calculating aid;
• develop the ability to estimate and to make approximations and also to be alert to the
reasonableness of results and measurements;
• apply systems of measurement in everyday use and in the solutions of problems;
• use geometrical instruments;
• collect and analyse data;
• interpret, use and present information in written, graphical, diagrammatic and
tabular forms;
• understand and use mathematical language, symbols and diagrams to represent and
communicate mathematical ideas effectively;
• recognise and apply spatial relationships in two and three dimensions;
• recognise the appropriate mathematical procedures for a given situation;
• recognise patterns and structures in a variety of situations and form, and/or justify
generalisations;
• apply and interpret mathematical concepts learnt in familiar and unfamiliar contexts,
including daily life;
• think logically and derive conclusions deductively and apply these processes in
mathematical situations;
• analyse problems; formulate them into mathematical terms and use the appropriate
strategies to solve them; verify and interpret the solutions; and present their
mathematical arguments and solutions in a logical and clear fashion;
• recognise the relationships between topics in the syllabus;
• become aware of the application of mathematics in other subjects;
• develop an inquiring mind through investigative activities;
• enjoy learning mathematics through a variety of activities.

SPECIAL/EXPRESS PART B
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Content Chart - Secondary One & Two (Special/Express Course)
Secondary One Secondary Two
1 Whole numbers
• the four operations
• ordering
• factors and multiples
2 Fractions and decimals
• concept and notation
• ordering
3 Approximation and estimation
• rounding off
• estimation
4 Use of a scientific calculator
5 Squares, square roots, cubes and
cube roots
6 Number sequences
7 Measures and money
8 Ratio, proportion and rate
9 Percentage
10 Simple financial transactions
11 Real numbers
• integers
• rational and irrational numbers
1 Arithmetic problems
2 Standard form
3 Number sequences
1 Perimeter and area
• square, rectangle, triangle,
parallelogram, trapezium, circle
2 Volume and surface area
• cube, cuboid, prism, cylinder
• sphere, pyramid and cone
2 Arc length and sector area
1 Algebraic expressions and
formulae
2 Simple algebraic manipulation
3 Simple linear equations
1 Algebraic manipulation and
formulae
2 Solutions of equations
• simultaneous linear equations
• simple fractional equations
• quadratic equations

SPECIAL/EXPRESS PART B
12
Content Chart - Secondary One & Two (Special/Express Course)
1 Graphs of linear and quadratic
functions
2 Graphs in practical situations
1 Simple plane figures
2 Simple solid figures
3 AngIe properties
• angles formed with a common
vertex
• angles formed with parallel
lines
• angle properties of triangles
• angle properties of squares,
rectangles, parallelograms and
rhombuses
4 Geometrical construction
of simple geometrical
figures
1 Motion geometry
• reflection
• rotation
• translation
• enlargement
2 Similar and congruent figures
3 Angle properties of polygons
4 Scale drawing
5 Symmetry
• line symmetry
• rotational symmetry
1 Handling data
• table and chart
• pictogram
• dot diagram
• bar graph
• line graph
• pie chart
• stem and leaf diagram
• histogram
1 Averages
• mean
• mode
• median
1 Pythagoras’ theorem
2 Trigonometrical ratios:
• sine
• cosine
• tangent
1 Problem solving heuristics
2 Practical uses of Mathematics

LEVEL : SEC 1 (SPECIAL/EXPRESS) PART B
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TOPICS/OUTCOMES REMARKS
ARITHMETIC
Pupils should be able to
1 Whole numbers
The four operations
• use the four operations for calculations
with whole numbers
• Include combined operations, i.e. correct
ordering of operations and the use of
brackets
• Include mental calculation and estimation
• Include awareness of the following
(i) commutative law
(ii) associative law
(iii) distributive law
• Exclude tedious calculations when the use
of a calculator is not allowed
Ordering
• order numbers
• use the following symbols correctly:
=, ≠, >, <, ≥, ≤
• Include the use of the number line
Factors and multiples
• use prime numbers, common factors
and common multiples
• Include the use of index notation and the
terms “prime factorization”, “ HCF” and
“LCM”
• Include odd and even numbers
Concept and notation
• use fractions and decimals
• convert fractions to decimals, and vice
versa
• Include the use of facts such as
0.25 =
1
4
, 0.75 =
3
4
, 0.125 =
1
8
0.333 ≈
1
3
, 0.667 ≈
2
3
• Exclude conversion of recurring decimals
to fractions
Ordering
• compare and order fractions and
decimals
• Include comparison of fractions with
decimals

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The four operations
with fractions and decimals
• Include
i) combined operations
ii) rounding off decimals to a specific
degree of accuracy
iii) mental calculation and estimation
Rounding off
• round off numbers and measures to a
specified degree of accuracy
• Include
i) decimal places and significant figures
ii) the use of the approximation sign “≈”
Estimation
• make estimates of numbers and
measures
• Include use of estimation to check the
reasonableness of answers
• Include mental estimation
• use the relevant keys of a scientific
calculator
• Include appropriate checks of accuracy by
estimation, e.g. in evaluating 47 600 ÷ 85
as 560, pupils should recognize that
47 600 ÷ 85 ≈ 600 (not 6 or 6 000)
• Pupils should be able to round off the
answer in the context of a given problem,
e.g. pupils should realize the absurdity of
giving the speed of a car to 5 decimal
places
5 Squares, square roots, cubes and cube
roots
• find squares, square roots, cubes and
cube roots of numbers
• Include the use of the square root sign
" " and cube root sign " 3 "
• Include estimation
• Include the use of the following keys of a
calculator:
2
x , x ,
y
x ,
y
x /1

15
6 Number sequences
• continue a given number sequence • Recognize simple number patterns and
state the rules for the patterns
Mass, length, time and money
• solve problems involving the use of units
of mass, length, time, money
• Include
i) use of the term: “capacity”
ii) practical activities to reinforce concept
of units of measures
iii) conversion of measures and currency
iv) calculation of time in terms of the 24-
hour and 12-hour clocks
• reading of clocks, dials and timetables
Ratio and proportion
• find the ratio of two or more quantities • Include expressing a ratio in its lowest
terms
• state the relationship between ratio and
fraction
• Include rewriting x : y = a : b
as x = (
a
b
) y
• use direct and inverse proportion • Include the concept of reciprocals
• solve problems involving ratio and
proportion
• Include scales
Rate
• recognize and use common measures of
rate
• Include conversion such as km/h to m/s
and vice versa
• solve problems involving rate • Include calculation of average speed
9 Percentage
• convert between
− percentage and fraction
− percentage and decimal
i) 25% = 0.25 =
1
4
ii) 50% = 0.5 =
1
2
iii) 75% = 0.75 =
3
4
iv) 20% = 0.2 =
1
5
v) 80% = 0.8 =
4
5

16
• calculate a given percentage of a
quantity
• Include reverse problems
Example:
40% of a class are boys. If there are 16
boys, find the number of pupils in the class.
• express one quantity as a percentage of
another
• calculate percentage increase/decrease • Include reverse problems such as finding
the original salary given the new salary and
the percentage increase
• solve problems involving percentage
• solve problems on personal and
household finance, and simple financial
transactions
• Include
i) earnings, simple interest, compound
interest (without use of formulae), hire-
purchase, discount, commission, profit
and loss, money exchange and
taxation
ii) reverse problems such as finding the
cost price given the selling price and
the percentage profit
• extract data from tables and charts to
solve problems
11 Real numbers
Integers
• manipulate integers (positive, negative
and zero)
• Include ordering on the number line
Rational and irrational numbers
• recognize rational and irrational numbers • Include understanding of the following
terms and their relationships:
Real numbers
irrational numbers
rational numbers
fractions integers
(+ve, -ve) (+ve, 0, -ve)

17
• manipulate rational numbers
• find an approximate value of an irrational
number with a calculator
• Exclude tedious computations
MENSURATION
• find the perimeters and areas of squares,
rectangles, triangles, parallelograms,
trapeziums and circles
• Include figures related to these shapes
• solve problems involving the perimeters and
areas of squares, rectangles, triangles,
parallelograms, trapeziums and circles
• find the volumes and surface areas of
cubes, cuboids, prisms and cylinders
• Include nets of these solids
• Include finding the volumes of
composite solids
• Exclude oblique prisms and oblique
cylinders
• solve problems involving the volumes and
surface areas of cubes, cuboids, prisms
and cylinders
• Include problems involving density
ALGEBRA
1 Algebraic expressions and formulae
• use letters to represent numbers
• express basic arithmetic processes
algebraically
• substitute numbers for words and letters in
formulae and expressions
• manipulate simple algebraic expressions • Include collecting like terms and
removing brackets

18
3 Simple linear equations
• solve simple linear equations • Include simple cases involving fractional
and decimal coefficients
Examples:
i)
1
2
x + 5 = x -
1
3
ii) 2 + 0.6x = 2x
• solve problems involving linear
equations
GEOMETRY
• identify the following plane figures:
− triangles: isosceles triangles,
equilateral triangles, right-angled
triangles, acute-angled triangles,
obtuse-angled triangles and
scalene triangles
− special quadrilaterals: squares,
rectangles, parallelograms,
rhombuses, trapeziums and kites
− polygons: pentagons, hexagons,
octagons and decagons
• Include the use of the following geometrical
terms:
point, line, plane, parallel,
perpendicular, right angles, acute,
obtuse and reflex angles,
complementary and
supplementary angles, base
angles, interior and exterior
angles, regular and irregular
polygons, diagonal and vertex
• Include tiles and tessellations
• identify the following simple solid figures:
cubes, cuboids, prisms, cylinders,
pyramids, cones and spheres
• Include sketching of these solids
3 Angle properties
Angles formed with a common vertex
• calculate unknown angles involving:
− adjacent angles on a straight line
− vertically opposite angles
− angles at a point
Angles formed with parallel lines
− corresponding angles
− alternate angles
− interior angles between parallel lines

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Angle properties of a triangle
− angle sum of a triangle
− base angles of an isosceles triangle
− angles of an equilateral triangle
− exterior angle of a triangle
Angle properties of squares, rectangles,
parallelograms and rhombuses
• calculate unknown angles using the
angle properties of
− squares
− rectangles
− parallelograms
− rhombuses
• Include angle properties related to their
diagonals
4 Geometrical construction of simple
geometrical figures
• measure line segments and angles • Use rulers, set-squares, protractors and
compasses
• draw line segments, angles, parallel
lines and perpendicular lines
• Include cases where the following are
given:
i) the distance from a point to a line
ii) the distance between two parallel
lines
• construct angle bisectors and
perpendicular bisectors
• Use protractors, set squares, compasses
and straight edges/rulers
• construct simple geometrical figures
from given data
• Include drawing the nets of cubes, cuboids,
prisms and pyramids
STATISTICS
1 Handling data
• collect, classify and tabulate data • Include the use of tally marks
• read and interpret tables and statistical
diagrams
• construct a bar graph, pie chart,
pictogram, dot diagram, line graph, stem
and leaf diagram, and histogram with
equal intervals

20
PROBLEM SOLVING
• use appropriate heuristics to solve
problems
2 Practical uses of mathematics
• solve mathematical problems in
everyday life

21
ARITHMETIC
• solve problems involving measures, money,
ratio, proportion, rate and speed,
percentage, personal and household finance
and simple financial transactions
2 Standard form
• read and write numbers in standard form A x
10
n
where n is a positive or negative integer,
and 1 ≤ A < 10
• Include significant figures of numbers
written in a standard form
• Include estimation and approximation
3 Number sequences
• formulate the algebraic expression for the
general term of a number sequence
• Exclude direct application of arithmetic
progression and geometric progression
formulae
MENSURATION
spheres, pyramids and cones
• Include the use of the term
“hemisphere”
• Include nets where applicable
• Exclude oblique pyramids and cones
• solve problems involving the volumes and
surface areas of spheres, pyramids and
cones
• express arc length as a fraction of
circumference and sector area as a fraction
of the area of a circle
• find arc length and sector area • Include finding the area of a segment of
a circle
• solve problems involving arc length and
sector area

22
ALGEBRA
1 Algebraic manipulation and formulae
• expand products of simple algebraic
expressions
• Examples:
i) (ax + b) (cx + d)
ii) (ax + by) (cx + dy)
(a, b, c and d are integers)
• factorize algebraic expressions of the
form:
ax + ay
ax + bx + kay + kby
a
2
x
2
− b
2
y
2
a
2
± 2ab + b
2
ax
2
+ bx + c
• manipulate simple algebraic fractions • Include only simple expressions such as
the following:
i)
x
3
+
x − 4
2
ii)
2
3
x
-
3 5
2
( )x −
iii) (
3
4
a
) (
5
3
ab
)
iv)
3
4
a
÷
9
10
a
v)
1
2x −
+
3
2
−x
• Expressions such as
4
1
2
−x
+
2
5
−x
and
44
4
2
2
++
−
xx
x
will be introduced at the upper
secondary level
• transform simple formulae • Exclude formulae involving square roots
Simultaneous linear equations
• solve simultaneous linear equations in
two unknowns
• Include both the elimination and
substitution methods
• solve problems involving simultaneous
linear equations

23
Simple fractional equations
• solve fractional equations involving
numerical and linear algebraic
denominators
• Examples:
i)
x
3
+
x − 2
4
= 3
ii)
3
x
= 6
iii)
3
2x −
= 6
• Exclude fractional equations such as
1
2x −
+
2
3x −
= 2
1
2
• solve problems involving simple
fractional equations
Quadratic equations
• solve quadratic equations by
factorization
• solve problems involving quadratic
equations
GRAPHS
1 Graphs of linear and quadratic functions
• use cartesian coordinates in two
dimensions
• draw graphs of linear and quadratic
functions
• Include finding the value of y from the
graph given the value of x, and vice versa
• use graphical methods to solve
simultaneous linear equations
• interpret and use graphs in practical
situations
• Include travel graphs (distance-time
graphs) and conversion graphs
• draw graphs using data from practical
situations
• Include the choice of appropriate scales

24
GEOMETRY
1 Motion Geometry
Reflection, rotation, translation,
enlargement
• draw the reflection of a simple plane
figure in horizontal or vertical lines
• Include “line of reflection” (mirror line)
• draw the rotation of a simple plane
figure, about the origin of the x-y plane,
or a vertex or a mid-point of an edge of
the figure, through multiples of 90°
• Include ”centre of rotation” and “angle of
rotation”
• draw the translation of a simple plane
figure in the x-y plane
• Include only movements parallel to the x
and y axes
• draw an enlargement of a given plane
figure
• Include “centre of enlargement” and “scale
factor” (scaling up or down)
• Exclude negative scale factors
• identify reflection, rotation, translation
and enlargement of a given plane figure
• Exclude problems involving finding “line of
reflection”, “centre of rotation”, “angle of
rotation”, "centre of enlargement” and
“scale factor”
• draw the image of a figure involving
combined movements
• Exclude more than 2 movements
• recognise similar and congruent figures
• find unknown sides/angles of
similar/congruent figures
• Exclude tests for similarity and congruency
between two triangles
3 Angle properties of polygon
• calculate
− the sum of interior angles of a
polygon
− the sum of exterior angles of a
polygon
• Include regular polygons
• calculate unknown angles of a polygon • Include finding the number of sides of a
polygon

25
4 Scale drawing
• read and make scale drawings
5 Symmetry
Line symmetry and rotational symmetry
• identify line and rotational symmetry of
plane figures
• Include ‘line of symmetry’ and ‘centre and
order of rotational symmetry’
• Exclude the use of the term ‘point
symmetry’
• use symmetrical properties of triangles,
quadrilaterals and regular polygons
• Include properties of these figures directly
related to their symmetries
• use symmetrical properties of prisms,
cylinders, pyramids and cones
• Include ‘plane of symmetry’ and ‘axis of
rotational symmetry’
STATISTICS
1 Averages
• find mean, median and mode • Distinguish between the purposes for which
mean, median and mode are used
• Exclude grouped data
TRIGONOMETRY
1 Pythagoras' theorem
• state Pythagoras’ theorem • Include the converse of the theorem
• Proving of the theorem is not required
• apply Pythagoras’ theorem to find a side
of a right-angled triangle
• solve problems applying Pythagoras’
theorem
2 Trigonometrical ratios: sine, cosine and
tangent
• state the sine, cosine and tangent ratios
for an acute angle of a right-angled
triangle

26
• find the values of the trigonometrical
ratios with a calculator
• Include the use of inverse trigonometrical
function keys of the calculator
• apply the sine, cosine or tangent ratio for
an acute angle to find
− a side of a right-angled triangle
− an angle of a right-angled triangle
• Exclude expressing angles in degrees and
minutes
• solve trigonometrical problems in two
dimensions
• Include angles of elevation and depression
PROBLEM SOLVING
problems
everyday life

NORMAL ACADEMIC PART B
27
Content Chart - Secondary One & Two (Normal [Academic] Course)
1 Whole numbers
• ordering
• ordering
• rounding off
• estimation
cube roots
6 Number sequences
9 Percentage
10 Real numbers
• integers
• rational and irrational numbers
3 Standard form
4 Number sequences
• square, rectangle, triangle,
parallelogram, trapezium, circle
• cube, cuboid, prism, cylinder
• sphere, pyramid and cone
formulae
1 Algebraic manipulation and
formulae
• simple linear equations
• simultaneous linear equations
• simple fractional equations

NORMAL ACADEMIC PART B
28
Content Chart - Secondary One & Two (Normal [Academic] Course)
1 Graphs of linear and quadratic
functions
3 AngIe properties
vertex
• angles formed with parallel lines
rhombuses
4 Geometrical construction of
simple geometrical figures
3 Scale drawing
4 Symmetry
• line symmetry
1 Handling data
• table and chart
• pictogram
• dot diagram
• bar graph
• line graph
• pie chart
• stem and leaf diagram
• histogram
1 Averages
• mean
• mode
• median

LEVEL : SEC 1 (NORMAL ACADEMIC) PART B
29
ARITHMETIC
1 Whole numbers
The four operations
with whole numbers
• Include combined operations, i.e. the
correct ordering of operations and the use
of brackets
(i) commutative law
Ordering
• order numbers
=, ≠, >, <, ≥, ≤
“LCM”
versa
0.25 =
1
4
, 0.75 =
3
4
, 0.125 =
1
8
0.333 ≈
1
3
, 0.667 ≈
2
3
to fractions
Ordering
decimals
decimals

30
The four operations
• Include
ii) rounding-off decimals to a specific
degree of accuracy
Rounding off
• Include
Estimation
measures
• Use the relevant keys of a scientific
calculator
47 600 ÷ 85 ≈ 600 (not 6 or 6 000)
places
roots
• Include the use of the square root sign
‘ ‘, and cube root sign ‘ 3 ‘
calculator:
2
x , x ,
y
x ,
y
x /1
6 Number sequences
• continue a given number sequence • Recognise simple number patterns and

31
of mass, length, time, money
• Include
i) use of the term “capacity”
ii) practical activities to reinforce concept
of units of measures
iii) conversion of measures and currency
iv) calculation of time in terms of the 24-
hour and 12-hour clocks
v) reading of clocks, dials and timetables
terms
fraction
as x = (
a
b
) y
• use direct and inverse proportion • Include the concept of reciprocals
• solve problems involving ratio and
proportion
• Include scales
Rate
• recognize and use common measures of
rate
• Include conversion such as km/h to m/s
and vice versa
• solve problems involving rate • Include calculation of average speed
9 Percentage
• convert between
i) 25% = 0.25 =
1
4
ii) 50% = 0.5 =
1
2
iii) 75% = 0.75 =
3
4
iv) 20% = 0.2 =
1
5
v) 80% = 0.8 =
4
5

32
quantity
Example:
boys, find the number of pupils in the class
another
• solve problems involving percentage
10 Real numbers
Integers
• manipulate integers (positive, negative
and zero)
• Include ordering the number line
Rational and irrational numbers
• recognize rational and irrational numbers • Include understanding the following terms
and their relationships:
Real numbers
irrational numbers
rational numbers
fractions integers
(+ve, -ve) (+ve, 0, -ve)
• manipulate rational numbers
• find an approximate value of an irrational
number with a calculator
• Exclude tedious computations
MENSURATION
• find the perimeters and areas of
squares, rectangles, triangles,
• solve problems involving the perimeters
and areas of squares, rectangles,
triangles, parallelograms, trapeziums
and circles

33
• Include finding the volumes of composite
solids
cylinders
• solve problems involving the volumes
and surface areas of cubes, cuboids,
prisms and cylinders
ALGEBRA
1 Algebra expression and formulae
algebraically
• substitute numbers for letters in
formulae and expressions
2. Simple Algebraic Manipulation
• manipulate simple algebraic expressions • Include collecting like terms and removing
brackets
GEOMETRY
1 Simple Plane Figures
scalene triangles
terms:
perpendicular, right angles, acute,
complementary and
angles, interior and exterior
angles, regular and irregular
polygons, diagonal and vertex
• include tiles and tessellations

34
• Include sketching these solid figures
3 Angle properties
− angle sum of a triangle
− base angles of an isosceles triangle
− angles of an equilateral triangle
− exterior angle of a triangle
angle properties of
− squares
− rectangles
− parallelograms
− rhombuses
diagonals
4. Geometrical construction of simple
geometrical figures
compasses

35
given:
i) the distance from a point to a line
ii) the distance between two parallel lines
• construct simple geometrical figures
from given data
• Include the drawing of nets of cubes,
cuboids, prisms and pyramids
STATISTICS
1 Handling data
diagrams
pictogram, dot diagram, line graph, stem
and leaf diagram, and histogram with
equal intervals
PROBLEM SOLVING
problems
everyday life

36
ARITHMETIC
transactions
• Include
interest (without use of formulae), hire-
purchase, discount, commission, profit
and loss, money exchange and
taxation
ii) reverse problems such as finding the
solve problems
• solve problems involving measures,
money, ratio, proportion, scale, rate,
speed and percentage
3 Standard form
• read and write numbers in standard form
A x 10
n
where n is a positive or negative
integer, and 1 ≤ A < 10
• Include significant figures of numbers
written in standard form
• Include estimation and approximation
4 Number sequences
• formulate the algebraic expression for
the general term of a number sequence
• Exclude direct application of arithmetic
progression and geometric progression
formulae
MENSURATION
spheres, pyramids and cones
• Include the use of the term “hemisphere”
• Include nets where applicable
• Exclude oblique pyramids and cones
and surface areas of spheres, pyramids
and cones

37
• express arc length as a fraction of
circumference and sector area as a
fraction of the area of a circle
• find arc length and sector area • Include finding the area of a segment of a
circle
• solve problems involving arc length and
sector area
ALGEBRA
1 Algebraic manipulation and formulae
expressions
• Examples:
i) (ax + b) (cx + d)
ii) (ax + by) (cx + dy)
form:
ax + ay
ax + bx + kay + kby
a
2
x
2
− b
2
y
2
a
2
± 2ab + b
2
ax
2
+ bx + c
• manipulate simple algebraic fractions • Include only simple expressions such as
the following:
i)
x
3
+
x − 4
2
ii)
2
3
x
-
3 5
2
( )x −
iii) (
3
4
a
) (
5
3
ab
)
iv)
3
4
a
÷
9
10
a
v)
1
2x −
+
2
3x −

38
Simple linear equations
• solve simple linear equations • Include simple cases involving fractional
and decimal coefficients
Examples:
i)
1
2
x + 5 = x -
1
3
ii) 2 + 0.6x = 2x
equations
Simultaneous linear equations
• solve simultaneous linear equations in
two unknowns
• Include both the elimination and
substitution methods
• solve problems involving simultaneous
linear equations
Simple fractional equations
• solve fractional equations involving
numerical and linear algebraic
denominators
• Examples:
i)
x
3
+
x − 2
4
= 3
ii)
3
x
= 6
iii)
3
2x −
= 6
• Exclude fractional equations such as
1
2x −
+
2
3x −
= 2
1
2
• solve problems involving simple
fractional equations
GRAPHS
1 Graphs of linear and quadratic functions
dimensions
• draw graphs of linear and quadratic
functions
• Include finding the value of y from the
graph given the value of x, and vice versa

39
situations
• Include travel graphs (distance-time
graphs) and conversion graphs
situations
• Include choice of appropriate scales
GEOMETRY
• recognise similar and congruent figures
• find unknown sides/angles of
similar/congruent figures
• Exclude tests for similarity/congruency
between two triangles
2 Angle properties of a polygon
• calculate
- the sum of interior angles of a
polygon
- the sum of exterior angles of a
polygon
• calculate unknown angles of a polygon • Include finding the number of sides of a
polygon
3 Scale Drawing
4 Symmetry
plane figures
symmetry’
rotational symmetry’

40
STATISTICS
1 Averages
• find mean, median and mode • Distinguish between the purposes for which
PROBLEM SOLVING
problems
everyday life

NORMAL TECHNICAL PART B
41
Content Chart - Secondary One & Two (Normal [Technical] Course)
1 Whole numbers
• ordering
• ordering
• rounding off
• estimation
cube roots
7 Ratio, proportion, scale, rate and
speed
8 Percentage
3 Directed numbers
• ordering
4 Number sequences
• square
• rectangle
• triangle
• parallelogram
• trapezium
• circle
• cube
• cuboid
• prism
• cylinder
formulae
• substitution
• simplification
formulae
• substitution
• manipulation
2 Solutions of simple linear
equations

NORMAL TECHNICAL PART B
42
Content Chart - Secondary One & Two (Normal [Technical] Course)
1 Linear graphs
3 AngIe properties
vertex
• angles formed with parallel
lines
rhombuses
4 Construction of triangles
1 Symmetry
• line symmetry
3 Geometrical construction
• simple four-sided figures
• scale drawing
1 Handling data
• table and chart
• pictogram
• dot diagram
• bar graph
• line graph
• pie chart
• histogram
1 Averages
• mean
• mode
• median
3 Mathematics for leisure and
recreation*
3 Mathematics for leisure and
recreation*
*Non-examination topic

LEVEL : SEC 1 (NORMAL TECHNICAL) PART B
43
ARITHMETIC
1 Whole numbers
The four operations
with whole numbers
• Include combined operations, i.e. correct
ordering of operations and the use of
brackets
(i) commutative law
Ordering
• order numbers
=, ≠, >, <, ≥, ≤
“LCM”
versa
0.25 =
1
4
, 0.75 =
3
4
, 0.125 =
1
8
0.333 ≈
1
3
, 0.667 ≈
2
3
to fractions
Ordering
decimals
decimals

44
The four operations
• Include
ii) rounding off decimals to a specific
degree of accuracy
Rounding off
• Include
Estimation
measures
• use the relevant keys of a scientific
calculator
47 600 ÷ 85 ≈ 600 (not 6 or 6 000)
places
roots
• Include the use of the square root sign ‘ ‘
and the cube root sign ‘ 3 '
calculator:
2
x , x ,
y
x ,
y
x /1
• use common instruments to measure
quantity
• Include measuring capacity/volume of a
liquid
• Common instruments refer to rulers,
measuring cylinders, weighing scales and
stop-watches

45
of mass, length, time and money
• Include
(i) conversion of measures and currency
(ii) calculation of time in terms of 24-hour
and 12-hour clocks
(iii) reading of clocks, dials, timetables and
charts
terms
fraction
as x = (
a
b
) y
• use ratio, proportion and scale • Include direct proportion and inverse
proportion
• Include map reading and estimating
distance from the map
• Include the concept of reciprocals
• solve problems involving ratio, proportion
and scale
Rate and speed
• use common measures of rate and
speed
• Include conversion such as km/h to m/s and
vice versa
• solve problems involving rate and speed • Include calculation of average speed
8 PERCENTAGE
• convert between
i) 25% = 0.25 =
1
4
ii) 50% = 0.5 =
1
2
iii) 75% = 0.75 =
3
4
iv) 20% = 0.2 =
1
5
v) 80% = 0.8 =
4
5
quantity
Example:
boys, find the number of pupils in the class.

46
another
MENSURATION
• find the perimeters and areas of
squares, rectangles, triangles,
• solve problems involving the perimeters
and areas of squares, rectangles,
triangles, parallelograms, trapeziums
and circles
ALGEBRA
algebraically
Substitution
expressions and formulae
• Exclude expressions with brackets
• Exclude expressions involving squares and
higher powers
Simplification
• simplify simple algebraic expressions • Include collecting like terms
• Exclude removing of brackets at this level
• Exclude expressions involving squares and
higher powers

47
GEOMETRY
scalene triangles
terms:
perpendicular, right angle, acute,
complementary and
angle, interior and exterior angles,
regular and irregular polygons,
diagonal and vertex
• Include tiles and tessellations
• Include sketching these solid figures
3 Angle properties
− the angle sum of a triangle
− the base angles of an isosceles
triangle
− the angles of an equilateral triangle
− the exterior angle of a triangle

48
angle properties of a
− square
− rectangle
− parallelogram
− rhombus
diagonals
4 Construction of triangles
compasses
given:
(i) the distance from a point to a line
(ii) the distance between two parallel lines
• construct triangles from given data
STATISTICS
1 Handling data
diagrams
pictogram, dot diagram, line graph, and
histogram with equal intervals

49
PROBLEM SOLVING
problems
everyday life
3 Mathematics for leisure and recreation*
• appreciate solving non-routine problems • Non-routine problems in this topic refer to
simple puzzles and simple problems for
leisure and recreation
* Non-examination topic

50
ARITHMETIC
transactions
• Include
interest (without the use of formulae),
hire-purchase, discount, commission,
profit and loss, money exchange and
taxation
II) reverse problems such as finding the
solve problems
• solve problems involving measures,
money, ratio, proportion, scale, rate,
speed and percentage
3 Directed numbers
• use directed numbers • Include the use of the term "integers"
(positive, negative, zero)
Ordering
• compare and order directed numbers • Include ordering on the number line
The four operations
• use the four operations for calculation
with directed numbers
• Include combined operations and the use of
brackets
4 Number sequences
• continue a given number sequence • Recognise simple number patterns and

51
MENSURATION
• Include finding the volumes of composite
solids
cylinders
and surface areas of cubes, cuboids,
prisms and cylinders
ALGEBRA
Substitution
expressions and formulae
Manipulation
• simplify simple algebraic expressions • Include collecting like terms and removing
brackets
expressions
• Examples:
(i) (ax + b) (cx + d)
(ii) (ax + by) (cx + dy)
form:
ax + ay
ax + bx + kay + kby
a
2
x
2
- b
2
y
2
x
2 ± 2xy + y
2
ax
2
+ bx + c

52
Solution of simple linear equations
• solve simple linear equations • Include cases involving fractional and
decimal coefficients
Examples:
(i)
1
2
x + 5 = x -
1
3
(ii) 2 + 0.6x = 2x
equations
GRAPHS
1 Graphs
Linear graphs
dimensions
• draw linear graphs • Include finding the value of y from the graph
given the value of x, and vice versa
situations
• Include travel graphs (distance-time graphs)
and conversion graphs
situations
• Include choice of appropriate scales
GEOMETRY
1 Symmetry
plane figures
symmetry’

53
rotational symmetry'
2 Construction
Simple four-sided figures
• Construct simple four-sided figures
Scale drawing
3 Angle properties of polygon
• calculate
- the sum of interior angles of a
polygon
- the sum of exterior angles of a
polygon
• calculate the unknown angles of a
polygon
• Include finding the number of sides of a
polygon
STATISTICS
1 Averages
• find the mean, median and mode • Distinguish between the purposes for which

54
PROBLEM SOLVING
problems
everyday life
3 Mathematics for leisure and recreation*
• appreciate solving non-routine problems • Non-routine problems in this topic refer to
simple puzzles and simple problems for
leisure and recreation
* Non-examination topic

APPENDIX
55
DEFINITION OF SUGGESTED THINKING SKILLS
• Classifying - using relevant attributes to sort, organise and group information
• Comparing - using common attributes to identify commonalities and
discrepancies across numerous sets of information
• Identifying Attributes & Components - recognising and articulating the parts
that together constitute a whole
• Sequencing - placing items in a hierarchical order according to a quantifiable
value
• Induction - drawing a general conclusion from clues gathered (from specific to
general)
• Deduction - inferring various specific situations or examples from given
generalisations (from general to specific)
• Generalising - using repeated, controlled and accurate observations to develop
a rule, principle or formula that explains a number of related situations
• Verifying - checking or confirming the truth of an idea, using specific standards
or criteria of evaluation
• Spatial Visualisation - visualising a situation or an object and mentally
manipulating various alternatives for solving a problem related to a situation or
object without the benefit of concrete manipulatives

Singapore maths syllabus

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