Lower Secondary Mathematics Syllabus Guide
Sec 1 and Sec 2: every topic, three strands, and the A-Math choice before Sec 3
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Lower Secondary Mathematics (Sec 1 & 2) in brief
Lower Secondary Mathematics is the first two years of the MOE G2 and G3 Mathematics syllabuses, which run from Secondary One to Four and were implemented starting with the 2020 Secondary One cohort. The content is organised in three strands: Number and Algebra, Geometry and Measurement, and Statistics and Probability. Unlike lower secondary science, the maths syllabus sets out content by year, with separate lists for Secondary One, Secondary Two and Secondary Three/Four. G3 and G2 have their own lists.
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G2 covers most of the same topics but spreads them over more time, so some content that G3 meets in Sec 1 or Sec 2 arrives a year or two later at G2. There is no national exam in Sec 1 or Sec 2.
Which syllabus Sec 1 and Sec 2 students follow
MOE runs five secondary mathematics syllabuses: G3 Mathematics, G2 Mathematics, G1 Mathematics, G3 Additional Mathematics and G2 Additional Mathematics. In Sec 1 and Sec 2 every student takes Mathematics at one of the three levels. G3 and G2 share one document, the G2 and G3 Mathematics Syllabuses, Secondary One to Four (MOE, PDF). G1 has its own syllabus, listed on the MOE Full SBB syllabus page.
The G3 and G2 syllabuses keep the content of the 2020 Express and Normal (Academic) syllabuses. Under Full Subject-Based Banding, which began with the 2024 Secondary 1 cohort, the streams were removed and each subject is taken at G1, G2 or G3. Both syllabuses organise the content into the same three strands: Number and Algebra, Geometry and Measurement, and Statistics and Probability.
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Sec 1 Mathematics topics at G3 and G2
The table lists every Secondary One topic by its MOE code and name, grouped by strand. The G3 column summarises the G3 Secondary One content. The G2 column says where the G2 Secondary One list differs. A topic marked "not in Sec 1" is taught later at that level, not dropped.
See every Sec 1 topic by strand
| Strand | Topic (MOE name) | G3 in Sec 1 | G2 in Sec 1 |
|---|---|---|---|
| Number and Algebra | N1. Numbers and their operations | Primes and prime factorisation, HCF and LCM, squares, cubes, square roots and cube roots by prime factorisation, negative numbers, integers, rational and real numbers, calculator work, the number line, the symbols <, >, ≤ and ≥, rounding to decimal places or significant figures, and estimation | Same as G3 |
| Number and Algebra | N2. Ratio and proportion | Ratios involving rational numbers, writing a ratio in its simplest form, and ratio problems | Same, plus a recap of comparing quantities by ratio, ratio and fraction, dividing a quantity in a given ratio, and equivalent ratios |
| Number and Algebra | N3. Percentage | One quantity as a percentage of another, comparing by percentage, percentages over 100%, increasing or decreasing by a percentage (including percentage point), reverse percentages, and percentage problems | Same, plus expressing a percentage as a fraction or decimal and finding a percentage increase or decrease |
| Number and Algebra | N4. Rate and Speed | Average rate, speed, constant speed and average speed, converting units such as km/h to m/s, and rate and speed problems | Same, plus the link between distance, time and speed, speed in different units, and finding one of the three from the other two |
| Number and Algebra | N5. Algebraic expressions and formulae | Letters for numbers, algebraic notation, evaluating expressions and formulae, writing expressions for real-world situations, the nth term of a pattern, adding, subtracting and simplifying linear expressions, using brackets and extracting common factors | Same start, but simplifying only with integer coefficients. Extracting common factors waits for Sec 2 |
| Number and Algebra | N6. Functions and graphs | Cartesian coordinates, graphs of ordered pairs, linear functions y = ax + b and their graphs, and gradient as vertical change over horizontal change | Not in Sec 1 (taught in Sec 2) |
| Number and Algebra | N7. Equations and inequalities | The concept of an equation, solving linear equations in one variable, simple fractional equations that reduce to linear equations, and forming a linear equation to solve problems | Linear equations with integer coefficients and forming a linear equation. Fractional coefficients and fractional equations wait for Sec 2 |
| Geometry and Measurement | G1. Angles, triangles and polygons | Types of angle, angles at a point and on a straight line, vertically opposite angles, angles with parallel lines (corresponding, alternate, interior), properties of triangles, special quadrilaterals and regular polygons, symmetry, interior and exterior angle sums of polygons, and constructions with compasses, ruler, set squares and protractor | Angle facts, parallel lines and properties of triangles only. Quadrilaterals, polygons and constructions wait for Sec 2 |
| Geometry and Measurement | G5. Mensuration | Area of parallelogram and trapezium, perimeter and area of composite figures, volume and surface area of prisms and cylinders, converting cm² to m² and cm³ to m³, and composite solids | Same as G3 |
| Statistics and Probability | S1. Data handling and analysis | Collecting, classifying and tabulating data, reading tables, bar graphs, pictograms, line graphs and pie charts, choosing a representation, and explaining why a diagram misleads | Same as G3 |
Source: MOE, G2 and G3 Mathematics Syllabuses, Secondary One to Four, Content by Levels. Codes such as N5 and G1 are MOE topic numbers, not subject levels. They skip numbers that first appear in a later year, which is why the Sec 1 geometry list jumps from G1 to G5.
Sec 2 Mathematics topics at G3 and G2
Sec 2 is where the two levels move furthest apart. G3 goes on to quadratics, algebraic fractions and trigonometry. G2 completes the G3 Sec 1 content first, then adds the core Sec 2 topics. Probability appears for the first time at both levels.
See every Sec 2 topic by strand
| Strand | Topic (MOE name) | G3 in Sec 2 | G2 in Sec 2 |
|---|---|---|---|
| Number and Algebra | N2. Ratio and proportion | Map scales (distance and area), and direct and inverse proportion | Same as G3 |
| Number and Algebra | N5. Algebraic expressions and formulae | Expanding products of algebraic expressions, changing the subject of a formula, finding an unknown in a formula, the identities (a + b)², (a - b)² and a² - b², factorising ax + bx + kay + kby, factorising quadratics ax² + bx + c, multiplying and dividing simple algebraic fractions, and adding and subtracting algebraic fractions with linear or quadratic denominators | Simplifying with fractional coefficients, expanding the product of two linear expressions, brackets and common factors, the three identities, factorising quadratics, and multiplying and dividing simple algebraic fractions. Changing the subject, the four-term factorisation and adding algebraic fractions wait for Sec 3/4 |
| Number and Algebra | N6. Functions and graphs | Quadratic functions y = ax² + bx + c and their graphs: the sign of the x² coefficient, maximum and minimum points, and symmetry | Cartesian coordinates, linear functions and their graphs, and gradient (the G3 Sec 1 content). Quadratic graphs wait for Sec 3/4 |
| Number and Algebra | N7. Equations and inequalities | Equation and inequality, simple inequalities such as ax + b ≤ c on the number line, graphs of ax + by = c, simultaneous linear equations by substitution, elimination and graphs, quadratic equations by factorisation, and forming a pair of linear equations | Linear equations with fractional coefficients, properties of inequality, simple inequalities such as ax ≤ b, simple fractional equations, graphs of ax + by = c, simultaneous linear equations, and forming one or two linear equations. Quadratic equations wait for Sec 3/4 |
| Geometry and Measurement | G1. Angles, triangles and polygons | Completed in Sec 1 | Special quadrilaterals, regular polygons and symmetry, angle sums of polygons, and constructions |
| Geometry and Measurement | G2. Congruence and similarity | Congruent and similar figures, properties of similar triangles and polygons, enlargement and reduction of a plane figure, and simple congruence and similarity problems | Congruent and similar figures and properties of similar triangles and polygons. Enlargement and problem solving wait for Sec 3/4 |
| Geometry and Measurement | G4. Pythagoras' theorem and trigonometry | Pythagoras' theorem, testing whether a triangle is right-angled, and sine, cosine and tangent in right-angled triangles | Pythagoras' theorem and the right-angle test. Trigonometric ratios wait for Sec 3/4 |
| Geometry and Measurement | G5. Mensuration | Volume and surface area of pyramid, cone and sphere | Same as G3 |
| Statistics and Probability | S1. Data handling and analysis | Dot diagrams, histograms and stem-and-leaf diagrams, mean, mode and median and when to use each, and the mean of grouped data | Same as G3 |
| Statistics and Probability | S2. Probability | Probability as a measure of chance, and single events found by listing all possible outcomes | Same as G3 |
Schools set their own order within each year, so the term in which a topic is taught varies. The year a topic belongs to is fixed by the syllabus.
G2 vs G3 Lower Secondary Mathematics: what changes
In lower secondary science, MOE marks some learning outcomes as optional for G2. The maths syllabus works differently. It gives G3 and G2 their own year-by-year content lists. Every topic in the G3 Sec 1 and Sec 2 lists also appears in the G2 syllabus, but G2 often reaches it a year or two later. G2 also spends more time on number work carried over from primary school, such as ratio, percentage and speed.
The content that is truly G3 only comes at upper secondary: set language and notation, matrices, vectors, sketching quadratic graphs from their factorised and completed-square forms, simultaneous linear inequalities, tests for congruent and similar triangles, and area and volume ratios of similar figures. MOE lists these as G3 content for Sec 5 students taking G2 Mathematics.
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| Point | G2 | G3 |
|---|---|---|
| Syllabus | MOE G2 Mathematics, Secondary One to Four | MOE G3 Mathematics, Secondary One to Four |
| Strands | Number and Algebra, Geometry and Measurement, Statistics and Probability | The same three strands |
| Sec 1 algebra | Expressions and linear equations with integer coefficients | Adds common factors, fractional equations and linear graphs |
| Sec 2 algebra | Linear graphs, simultaneous equations, expansion and factorising quadratics | Adds quadratic graphs and equations, changing the subject and algebraic fractions |
| Trigonometry | From Sec 3 | Sine, cosine and tangent in Sec 2 |
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All G3 Sec 1 and Sec 2 content that G2 reaches later
- N5 Algebraic expressions and formulae: extracting common factors (G3 Sec 1, G2 Sec 2), and changing the subject of a formula, finding an unknown in a formula, factorising ax + bx + kay + kby and adding algebraic fractions (G3 Sec 2, G2 Sec 3/4).
- N6 Functions and graphs: coordinates, linear functions and gradient (G3 Sec 1, G2 Sec 2), and quadratic functions and their graphs (G3 Sec 2, G2 Sec 3/4).
- N7 Equations and inequalities: simple fractional equations (G3 Sec 1, G2 Sec 2), and solving quadratic equations by factorisation (G3 Sec 2, G2 Sec 3/4).
- G1 Angles, triangles and polygons: special quadrilaterals, regular polygons, polygon angle sums and constructions (G3 Sec 1, G2 Sec 2).
- G2 Congruence and similarity: enlargement and reduction, and simple congruence and similarity problems (G3 Sec 2, G2 Sec 3/4).
- G4 Pythagoras' theorem and trigonometry: sine, cosine and tangent in right-angled triangles (G3 Sec 2, G2 Sec 3/4).
G1 students follow a separate MOE G1 Mathematics syllabus. Students can move to a more demanding level after Sec 1 based on their performance in secondary school, so a strong G2 student may later take G3 Mathematics. That student will need the G3 content listed above.
From PSLE model drawing to algebra
Algebra is the largest change in Sec 1. Many PSLE word problems are solved with model drawing, where bars stand for the unknown amounts. The Sec 1 syllabus asks students to use letters to represent numbers, to write expressions for real-world situations, and to form and solve a linear equation to answer a problem. The MOE syllabus describes this shift in one line: "Through algebra, we generalise arithmetic."
Our reading, not an MOE rule: the model is still useful in Sec 1, as a way to see the relationships before writing the equation. The marks, though, go to the equation and its working, and by Sec 2 most problems (simultaneous equations, quadratics, inequalities) are too large for a bar model.
Which level a student starts at depends on PSLE results. Under Full SBB (MOE), a student with AL 5 or better in Standard Mathematics can take Sec 1 Mathematics at G3 even if most other subjects are at G2. AL 6 in Standard Mathematics or AL A in Foundation Mathematics allows G2. For the year ahead, see our guides to moving from PSLE 2026 to Secondary 1 in 2027 and the PSLE Mathematics syllabus.
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How Sec 1 and Sec 2 Mathematics is assessed
There is no national exam in Sec 1 or Sec 2. MOE says students take the national examination in their final year. Until then, tests and examinations are set by the school, and formats, weightings and topic order differ from school to school.
The syllabus gives three assessment objectives for G3 and G2 Mathematics. AO1 is using and applying standard techniques. AO2 is solving problems in a variety of contexts, including forming problems in mathematical terms and interpreting the answer. AO3 is reasoning and communicating mathematically, which means justifying statements and writing explanations and arguments. MOE also expects every student to meet problems in real-world contexts over the four years, such as transport schedules, floor plans, simple and compound interest, taxation and utilities bills.
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Looking for help in a particular year? See Secondary 1 Maths tuition or Secondary 2 Maths tuition.
The end-of-Sec-2 choice: E-Math only or E-Math with A-Math
Mathematics stays compulsory at upper secondary. Additional Mathematics (A-Math) is an elective that students can add in Sec 3, and MOE publishes G2 and G3 Additional Mathematics syllabuses (MOE, PDF). There is no G1 A-Math. MOE says schools guide subject and subject-level choices on a holistic view of each student's strengths, interests and ability to cope (MOE, Full SBB), so Sec 1 and Sec 2 maths results matter even without a national exam.
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| Point | E-Math only | E-Math with A-Math |
|---|---|---|
| What it is | Mathematics, the compulsory subject | Mathematics plus Additional Mathematics as an elective |
| Subject levels | G1, G2 or G3 | A-Math at G2 or G3, taken alongside Mathematics |
| When chosen | Before Sec 3, with school guidance | Before Sec 3, with school guidance |
Our view, not an MOE rule: the Sec 2 topics that matter most for A-Math are the algebra ones, namely expansion and factorisation, algebraic fractions, changing the subject, and quadratic functions and equations. A student who is secure on these is better placed for A-Math than one whose marks come mainly from geometry and statistics. Read more in E-Math vs A-Math: which to take at Sec 3, and the upper secondary Mathematics syllabus guide and Additional Mathematics syllabus guide.
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Sec 1 and Sec 2 students will sit the SEC, not the O-Level
From the 2027 graduating cohort, students sit the Singapore-Cambridge Secondary Education Certificate (SEC), with different papers for each subject level (MOE, Full SBB). Every current Sec 1 and Sec 2 student will graduate in 2028 or later and sit the SEC, with Mathematics taken at G1, G2 or G3. Our guide on how the SEC replaces the O-Level from 2027 explains what else changes.
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Official syllabus: MOE, G2 and G3 Mathematics syllabuses, Sec 1 to 4 (PDF) · MOE, G2 and G3 Additional Mathematics syllabuses (PDF) · MOE, Full SBB syllabuses
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Lower Secondary Mathematics (Sec 1 & 2): frequently asked questions
What topics are in the Sec 1 maths syllabus?
At G3, Sec 1 covers numbers and their operations, ratio, percentage, rate and speed, algebraic expressions, linear functions and graphs, linear equations including simple fractional equations, angles, triangles and polygons, mensuration of prisms and cylinders, and data handling. G2 covers the same number, mensuration and data topics but leaves linear graphs, fractional equations, quadrilaterals and polygons, and constructions to Sec 2.
What topics are in the Sec 2 maths syllabus?
At G3, Sec 2 covers map scales and proportion, expansion and factorisation, algebraic fractions, changing the subject of a formula, quadratic functions and equations, inequalities, simultaneous equations, congruence and similarity, Pythagoras' theorem and trigonometric ratios, pyramids, cones and spheres, averages and statistical diagrams, and probability of single events. G2 covers most of these but leaves quadratics, trigonometry, changing the subject and adding algebraic fractions to Sec 3/4.
What is the difference between G2 and G3 maths in lower secondary?
G2 and G3 have separate year-by-year content lists in the same MOE syllabus document. Everything G3 covers in Sec 1 and Sec 2 is also in G2, but G2 often reaches it a year or two later and spends more time on primary number work. Content that is only in G3, such as sets, matrices and vectors, comes at upper secondary.
Is there a national exam for Sec 1 or Sec 2 maths?
No. Lower secondary maths is assessed by the school through tests and examinations. Students take the national examination, the SEC from 2027, in their final year of secondary school.
Can my child take G3 maths in Sec 1?
A student with AL 5 or better in PSLE Standard Mathematics can take Mathematics at G3 from the start of Sec 1, whichever Posting Group they entered through. Students can also move to a more demanding level later based on their performance in secondary school.
When do students choose A-Math?
Before Sec 3, at the end of Sec 2. Mathematics is compulsory at upper secondary, and Additional Mathematics is an elective offered at G2 and G3. Schools consider each student's strengths, interests and ability to cope when guiding the choice.