SECONDARY MATHEMATICS SYLLABUS · SINGAPORE
Useful whether you are checking what is coming next term, working out which level your child is actually sitting, or finding where a gap first opened.
The transition year — negative numbers, primes and factorisation, and letters used as unknowns for the first time.
Consolidation, and the year that sets Upper Secondary subject levels — heavier algebra, congruence and similarity, Pythagoras.
The content jump — coordinate geometry, indices and standard form, further trigonometry, circle properties. A-Math starts here.
The exam year — sets, matrices, vectors and combined probability on top of a full four-year revision programme.
Syllabus
Four years, and — since Full Subject-Based Banding replaced streaming — three levels of the same subject rather than three separate streams.
From 2027 the Singapore-Cambridge Secondary Education Certificate (SEC) replaces the O-Level, N(A)-Level and N(T)-Level as the single national leaving exam, with Mathematics taken at the student’s own G1, G2 or G3 level. IP students sit no national leaving exam.
Each card lists the chapter spine that level covers that year, and opens the full topic list on its own page. The chapter numbering that schools use is dropped here — four levels sit side by side and the numbering belongs to four different books.
Secondary 1 is where arithmetic becomes algebra. Students meet negative numbers, primes and factorisation, letters used as unknowns, and their first geometry that has to be argued rather than measured. All three levels cover the same strands — number, algebra, geometry and measurement, statistics — at different depth and pace.
Secondary 1 overviewThe most foundational of the three Full Subject-Based Banding levels — the syllabus formerly taught as Normal (Technical).
Numbers
Four Operations
Ratio
Percentage
Algebra
Angles
Statistics
Symmetry
Area and Perimeter
Surface Area and Volume
34 sub-topics — see the full list
The middle level under Full Subject-Based Banding — the syllabus formerly taught as Normal (Academic).
Primes, Highest Common Factor and Lowest Common Multiple
Integers, Rational Numbers and Real Numbers
Approximation and Estimation
Basic Algebra and Algebraic Manipulation
Linear Equations
Number Patterns
Percentage
Ratio and Rate
Angles and Triangles
Perimeter and Area of Plane Figures
Volume and Surface Area of Prisms and Cylinders
Statistical Data Handling
41 sub-topics — see the full list
The most demanding of the three levels — the syllabus formerly taught as Express, and the one Additional Mathematics builds on.
Primes, Highest Common Factor and Lowest Common Multiple
Integers, Rational Numbers and Real Numbers
Approximation and Estimation
Basic Algebra and Algebraic Manipulation
Linear Equations
Linear Functions and Graphs
Number Patterns
Percentage
Ratio and Rate
Basic Geometry
Polygons and Geometrical Constructions
Perimeter and Area of Plane Figures
Volume and Surface Area of Prisms and Cylinders
Statistical Data Handling
56 sub-topics — see the full list
The Integrated Programme six-year through-train. IP students do not sit the national leaving exam at the end of Sec 4.
Arithmetic I
Algebra I
Coordinate Geometry I
Statistics I
Geometry I
Trigonometry I
Sets
18 sub-topics — see the full list
Secondary 2 is the consolidation year, and the one that decides the most. Algebraic manipulation gets heavier (special identities, algebraic fractions), congruence and similarity arrive, and Pythagoras and trigonometric ratios open up right-angled triangles. The end of Sec 2 is when Upper Secondary subject levels and combinations are set, so a gap left open here is expensive.
Secondary 2 overviewThe most foundational of the three Full Subject-Based Banding levels — the syllabus formerly taught as Normal (Technical).
Triangles and Quadrilaterals
Linear Algebraic Expressions
Linear Equations in One Variable
Functions and Graphs
Proportion
Rate and Speed
Mathematics in Practical Situations
Congruence and Similarity
Pythagoras' Theorem
Data Analysis
Probability
Prisms and Cylinders
23 sub-topics — see the full list
The middle level under Full Subject-Based Banding — the syllabus formerly taught as Normal (Academic).
Linear Expressions, Linear Equations and Simple Inequalities
Linear Functions and Graphs
Simultaneous Linear Equations
Expansion and Factorisation of Algebraic Expressions
Expansion and Factorisation using Special Algebraic Identities
Algebraic Fractions
Direct and Inverse Proportions
Polygons and Geometrical Constructions
Congruence and Similarity
Pythagoras' Theorem
Volume and Surface Area of Pyramids, Cones and Spheres
Probability of Single Events
Statistical Diagrams
Averages of Statistical Data
50 sub-topics — see the full list
The most demanding of the three levels — the syllabus formerly taught as Express, and the one Additional Mathematics builds on.
Linear Graphs and Simultaneous Linear Equations
Linear Inequalities
Expansion and Factorisation of Algebraic Expressions
Expansion and Factorisation Using Special Algebraic Identities
Quadratic Equations and Graphs
Algebraic Fractions and Formulae
Direct and Inverse Proportions
Congruence and Similarity
Pythagoras' Theorem
Trigonometric Ratios
Volume and Surface Area of Pyramids, Cones and Spheres
Probability of Single Events
Statistical Diagrams
Averages of Statistical Data
54 sub-topics — see the full list
The Integrated Programme six-year through-train. IP students do not sit the national leaving exam at the end of Sec 4.
Algebra II
Algebra III
Arithmetic II
Trigonometry II
Geometry II
Statistics II
18 sub-topics — see the full list
Secondary 3 is the content jump. The Upper Secondary syllabus adds coordinate geometry, indices and standard form, further trigonometry, and the geometrical properties of circles. G3 students taking Additional Mathematics start it this year, alongside Elementary Mathematics — two syllabuses running in parallel.
Secondary 3 overviewThe most foundational of the three Full Subject-Based Banding levels — the syllabus formerly taught as Normal (Technical).
Indices and Standard Form
Map Scales
Algebraic Expansion, Fractions, and Expression for the nth Term of a Number Sequence
Factorisation and Formulas
Arc Lengths and Sector Areas
Pyramids, Cones and Spheres
Cumulative Frequency
Graphs of Linear Equations
Simultaneous Linear Equations
21 sub-topics — see the full list
The middle level under Full Subject-Based Banding — the syllabus formerly taught as Normal (Academic).
Algebraic Expressions and Formulae
Quadratic Equations and Graphs
Indices and Standard Form
Coordinate Geometry
Graphs of Functions and Graphical Solution
Trigonometry
Further Trigonometry
Congruence and Similarity
36 sub-topics — see the full list
The most demanding of the three levels — the syllabus formerly taught as Express, and the one Additional Mathematics builds on.
Quadratic and Fractional Equations
Simultaneous Linear Inequalities
Indices and Standard Form
Coordinate Geometry
Graphs of Functions and Graphical Solution
Further Trigonometry
Applications of Trigonometry
Arc Length, Sector Area and Radian Measure
Congruence and Similarity Tests
Area and Volume of Similar Figures and Solids
Geometrical Properties of Circles
42 sub-topics — see the full list
The Integrated Programme six-year through-train. IP students do not sit the national leaving exam at the end of Sec 4.
Algebra II
Relations and Functions I
Coordinate Geometry II
Trigonometry III
Matrices
16 sub-topics — see the full list
Secondary 4 is the exam year: a small amount of new content (sets, matrices, vectors, combined probability) on top of a full-syllabus revision programme. Current Sec 4 students sit the O-Level or N-Level; from 2027 that becomes the Singapore-Cambridge SEC. IP students sit no national exam and continue straight into JC.
Secondary 4 overviewThe most foundational of the three Full Subject-Based Banding levels — the syllabus formerly taught as Normal (Technical).
Fractional Equations
Graphs of Quadratic Functions
Quadratic Equations
Trigonometry
Revision of Sec 1–3 G1 content
Exam Application & Revision
14 sub-topics — see the full list
The middle level under Full Subject-Based Banding — the syllabus formerly taught as Normal (Academic).
Applications of Trigonometry
Arc Length, Area of Sector and Radian Measure
Probability of Combined Events
Cumulative Frequency
Mean and Standard Deviation
Geometrical Properties of Circles
Revision – Numbers and Algebra
Revision – Geometry and Measurement
Revision – Probability and Statistics
32 sub-topics — see the full list
The most demanding of the three levels — the syllabus formerly taught as Express, and the one Additional Mathematics builds on.
Sets
Probability of Combined Events
Statistical Data Analysis
Matrices
Vectors
Revision – Numbers and Algebra
Revision – Geometry and Measurement
Revision – Probability and Statistics
41 sub-topics — see the full list
The Integrated Programme six-year through-train. IP students do not sit the national leaving exam at the end of Sec 4.
Trigonometry IV
Calculus I
Probability
Vectors I
15 sub-topics — see the full list
The topic list is public. What it does not show is which junctions the marks are actually lost at.
Primary maths is arithmetic with a bar model. Secondary maths asks students to hold an unknown quantity as a letter and manipulate it. Students who never quite make that switch keep solving Sec 2 and Sec 3 problems with primary methods, which works until the numbers stop being friendly.
Expansion, factorisation and algebraic fractions are Sec 2 tools that Sec 3 quadratic equations, coordinate geometry and graph work assume completely. A student who was "fine" in Sec 2 can fall off sharply in Sec 3 without meeting a single genuinely new difficulty.
A G3 student taking Additional Mathematics is sitting two mathematics syllabuses in parallel from Sec 3, each with its own paper. The workload arrives in the same year as the Upper Secondary content jump, and time management usually breaks before understanding does.
Right-angled trigonometry in Sec 2 is memorisable. Further trigonometry, bearings and three-dimensional problems in Sec 3 are not — they need a student who can draw the triangle out of the situation first. Students who learned the Sec 2 version as three ratios to recall have nothing to fall back on.
Sec 4 adds relatively little content and asks students to hold four years of it at once. Without a revision plan that tracks coverage, the topics that get practised are the comfortable ones and the gaps stay exactly where they were.
Weekly live classes that follow the school year, with practice between lessons that targets what each student is actually getting wrong.
Classes run for G1, G2, G3 and IP separately, because the same topic is examined differently at each level. Students are grouped by learning pace as well as level.
When a Sec 3 student stalls on coordinate geometry, the practice engine works back through the Sec 2 algebra it depends on and rebuilds that first. Diagnosing across years is the point.
Every question is marked instantly with a worked solution, and wrong answers get feedback written for that specific error rather than a generic explanation.
Topics from earlier years resurface on a schedule before they would otherwise be forgotten — which is what makes Sec 4 revision a consolidation rather than a re-teach.
The aim is that by the exam year, revision is confirming what is secure rather than discovering what is not.
Program facts
The details parents usually want before booking a trial.
G1, G2, G3 and Integrated Programme, plus the IB-track Year 1 to Year 4 pages for ACS(I) and SJI.
Students are grouped by learning pace, not just by level — if no existing session matches your child’s pace, we open a new one.
Live and teacher-led, with targeted practice between lessons that carries instant marking and worked solutions.
The same fee at every level, with no exam-year surcharge.
See the teaching pace and the level fit before deciding anything.
Using this page
A topic list is only useful if it tells you where to look next.
Under Full Subject-Based Banding, Mathematics is taken at a level of its own — not fixed by the class a student is in. The chapter spines below differ enough between G1, G2 and G3 that a school worksheet usually identifies the level in one glance.
Most Upper Secondary difficulties are Lower Secondary gaps wearing a new name. Reading the years in order shows which earlier chapter the current one is standing on.
Each card links to the full topic list for that level and year, so you can see the chapters ahead rather than finding out from a test result.
Frequently asked questions
They are three levels of the same subject under Full Subject-Based Banding, replacing the old Normal (Technical), Normal (Academic) and Express streams. G3 is the most demanding and moves fastest; G2 covers most of the same ground at a steadier pace with fewer of the harder applications; G1 is the most foundational and keeps the work more concrete for longer. A student takes each subject at the level that fits them, so a child can sit Mathematics at G3 and another subject at G2.
Secondary 3 is where the Upper Secondary syllabus opens up. Across G2 and G3 the new ground is indices and standard form, coordinate geometry, graphs of functions and graphical solution, further trigonometry and its applications (including bearings and three-dimensional problems), arc length and sector area, and the geometrical properties of circles. G3 also adds similarity and congruence tests and the area and volume relationships between similar figures. G1 covers indices and standard form, map scales, algebraic expansion and factorisation, arc lengths and sector areas, and simultaneous linear equations.
Additional Mathematics starts in Secondary 3, taken alongside Elementary Mathematics rather than instead of it, and is offered to students taking Mathematics at G3 — each school sets its own performance bar for who may take it. It is a separate syllabus with its own exam paper, covering algebra at greater depth, trigonometric identities and equations, coordinate geometry of circles, and an introduction to differentiation and integration.
IP schools design their own scheme of work rather than teaching to a national leaving exam, so the sequence is theirs. The common shape is that content arrives earlier and is grouped in strands that spiral back each year — Algebra I, II and III across Sec 1 to Sec 3, Trigonometry I to IV across all four years — with calculus and vectors introduced in Sec 4 to bridge directly into JC H2 Mathematics. IP students do not sit the O-Level or the SEC.
From 2027 the Singapore-Cambridge Secondary Education Certificate (SEC) becomes the single national leaving exam, replacing the O-Level, N(A)-Level and N(T)-Level. Mathematics is taken at the student’s own G1, G2 or G3 level. Students sitting their leaving exam before then continue on the O-Level and N-Level papers.
Four, at most. Students are grouped by learning pace, not just by year level, so each lesson moves at the speed of the students actually in it. When no session matches a child’s pace, we open a new one. In a class that size, every child answers questions, gets their working checked, and gets help the moment they need it.
Yes — Secondary 1 to Secondary 4 across G1, G2, G3 and the Integrated Programme, plus the IB-track Year 1 to Year 4 pages for ACS(I) and SJI. Classes are grouped by learning pace as well as level, so students work with others actually moving at their speed.
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