The G1, G2, and G3 subject syllabuses in Singapore secondary schools started for the Secondary 1 cohort in 2024, with G3 covering the most, followed by G2, and then G1.
In the G3 Mathematics is similar to the previous Math syllabus covered in the Express stream. The purpose of G3 Math is to build a strong foundation in mathematical concepts and skills for lifelong learning and real-world application. It focuses on developing problem-solving, reasoning, communication, and thinking skills while building confidence and interest in mathematics. Learning is organized into three main parts, with must emphasis on real-world problem solving. Through this, students apply mathematics to everyday situations such as travel, personal finance, sports, and data interpretation.
In this post, let’s look at what is covered in the G3 Mathematics Syllabus in detail in each year.
** Note that some schools may choose to cover different topics.
Here are the topics covered in G3 Mathematics.
Secondary 1 G3 Math Syllabus
Numbers and Algebra
1. Numbers and their operations
1.1. Primes and prime factorisation
1.2. Finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation
1.3. Negative numbers, integers, rational numbers, real numbers and their four operations
1.4. Calculations with calculator
1.5. Representation and ordering of numbers on the number line
1.6. Use of <, >, ≤, ≥
1.7. Approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, and estimating the results of computation)
2. Ratio and proportion
2.1. Ratios involving rational numbers and writing a ratio in its simplest form
2.2. Problems involving ratio
2.3. Proportion
2.4. Proportion questions involving 3 variables
3. Percentage
3.1. Expressing one quantity as a percentage of another
3.2. Comparing two quantities by percentage
3.3. Percentages greater than 100%
3.4. Increasing/decreasing a quantity by a given percentage
3.5 Concept of percentage point
3.6. Reverse percentages
3.7. Problems involving percentages
4. Rate and Speed
4.1. Rate
4.2. Speed, constant speed and average speed
4.3. Conversion of units for speed
4.4. Problems involving rate and speed
5. Algebraic expressions and formulae
5.1. Using letters to represent numbers
5.2. Interpreting notations
5.3. Evaluation of algebraic expressions and formulae
5.4. Translation of simple real-world situations into algebraic expressions
5.5. Recognising and representing patterns/relationships by finding an algebraic expression for the nth term
5.6. Addition and subtraction of linear expressions
5.7. Simplification of linear expressions such as −2(3x − 5) + 4x; (2x/3) − [3(x − 5)/2]
5.8. Use brackets and extract common factors
6. Functions and graphs
6.1. Cartesian coordinates in two dimensions
6.2. Graph of a set of ordered pairs as a representation of a relationship between two variables
6.3. Linear functions y = ax + b
6.4. Graphs of linear functions
6.5. The gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
7. Equations and inequalities
7.1. Concept of equation
7.2. Solving linear equations in one variable
7.3. Solving simple fractional equations that can be reduced to linear equations such as (2/3)x − (3/4)x + 4 = 0 or (3/6)x = 2 − x
7.4. Formulating a linear equation in one variable to solve problems
Geometry and Measurement
1. Angles, triangles and polygons
1.1. Right, acute, obtuse and reflex angles
1.2. Vertically opposite angles, angles on a straight line, angles at a point
1.3. Angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
1.4. Properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties
1.5. Classifying special quadrilaterals on the basis of their properties
1.6. Angle sum of interior and exterior angles of any convex polygon
1.7. Construction of simple geometrical figures from given data using compasses, ruler, set squares and protractors, where appropriate
2. Mensuration
2.1. Area of parallelogram and trapezium
2.2. Problems involving perimeter and area of composite plane figures
2.3. Volume and surface area of prism and cylinder
2.4. Conversion between cm² and m², and between cm³ and m³
2.5. Problems involving volume and surface area of composite solids
Probability and Statistics
1. Data handling and analysis
1.1. Simple concepts in collecting, classifying and tabulating data
1.2. Analysis and interpretation of:
• Tables
• Bar graphs
• Pictograms
• Line graphs
• Pie charts
1.3. Purposes and uses, advantages and disadvantages of the different forms of statistical representations
1.4. Explaining why a given statistical diagram leads to misinterpretation of data
Secondary 2 G3 Math Syllabus
Numbers and Algebra
1. Ratio and proportion
1.1. Map scales (distance and area)
1.2. Direct and inverse proportion
2. Algebraic expressions and formulae
2.1. Expansion of the product of algebraic expressions
2.2. Changing the subject of a formula
2.3. Finding the value of an unknown quantity in a given formula
2.4. Use of:
• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• a² − b² = (a + b)(a − b)
2.5. Factorisation of linear expressions of the form ax + bx + kay + kby
2.6. Factorisation of quadratic expressions ax² + bx + c
2.7. Multiplication and division of simple algebraic fractions such as (3a / 4b²)(5ab / 3), (3a / 4) ÷ (9a² / 10)
2.8. Addition and subtraction of algebraic fractions with linear or quadratic denominators such as:
• 1/(x − 2) + 2/(x − 3)
• 1/(x² − 9) + 2/(x − 3)
• 1/(x − 3) + 2/((x − 3)²)
3. Functions and graphs
3.1. Quadratic functions y = ax² + bx + c
3.2. Graphs of quadratic functions and their properties:
• Positive or negative coefficient of x²
• Maximum and minimum points
• Symmetry
4. Equations and inequalities
4.1. Concept of equation and inequality
4.2. Solving simple inequalities in the form ax + b ≤ c and ax + b < c, and representing the solutions on the number line
4.3. Graphs of linear equations in two variables (ax + by = c)
4.4. Solving simultaneous linear equations in two variables by:
• Substitution and elimination methods
• Graphical method
4.5. Solving quadratic equations in one variable by factorisation
4.6. Formulating a pair of linear equations in two variables to solve problems
Geometry and Measurement
1. Congruence and similarity
1.1. Congruent figures
1.2. Similar figures
1.3. Properties of similar triangles and polygons:
• Corresponding angles are equal
• Corresponding sides are proportional
1.4. Enlargement and reduction of a plane figure
1.5. Solving simple problems involving congruence and similarity
2. Pythagoras’ theorem and trigonometry
2.1. Use of Pythagoras’ theorem
2.2. Determining whether a triangle is right-angled given the lengths of three sides
2.3. Use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles
3. Mensuration
3.1. Volume and surface area of pyramid, cone and sphere
Probability and Statistics
1. Data handling and analysis
1.1. Analysis and interpretation of:
• Dot diagrams
• Histograms
• Stem-and-leaf diagrams
1.2. Purposes and uses, advantages and disadvantages of the different forms of statistical representations
1.3. Explaining why a given statistical diagram leads to misinterpretation of data
1.4. Mean, mode and median as measures of central tendency for a set of data
1.5. Purposes and use of mean, mode and median
1.6. Calculation of the mean for grouped data
2. Probability
2.1. Probability as a measure of chance
2.2. Probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability)
Secondary 3 and 4 G3 Math Syllabus
Numbers and Algebra
1. Numbers and their operations
1.1. Use of standard form
1.2. Positive, negative, zero and fractional indices
1.3. Laws of indices
2. Functions and graphs
2.1. Sketching the graphs of quadratic functions.
2.2. Graphs of power functions
2.3. Graphs of exponential functions
2.4. Estimation of the gradient of a curve by drawing a tangent
3. Equations and inequalities
3.1. Solving quadratic equations in one variable by:
• Formula
• Completing the square
• Graphical method
3.2. Solving fractional equations reducible to quadratic equations
3.3. Solving linear inequalities in one variable (including simultaneous inequalities) and representing solutions on the number line
3.4. Formulating a quadratic equation in one variable to solve problems
4. Set language and notation
4.1. Use of set language and notation:
• 4.2. Union and intersection of two sets
4.3. Venn diagrams
5. Matrices
5.1. Display of information in the form of a matrix of any order
5.2. Interpreting data in a given matrix
5.3. Product of a scalar and a matrix
5.4. Problems involving addition, subtraction and multiplication of matrices
Geometry and Measurement
1. Congruence and similarity
1.1. Scale drawings
1.2. Properties and construction of perpendicular bisectors of line segments and angle bisectors
1.3. Determining whether two triangles are congruent or similar
1.4. Ratio of areas of similar plane figures
1.5. Ratio of volumes of similar solids
2. Properties of circles
2.1. Symmetry properties of circles:
• Equal chords are equidistant from the centre
• The perpendicular bisector of a chord passes through the centre
• Tangents from an external point are equal in length
• The line joining an external point to the centre of the circle bisects the angle between the tangents
2.2. Angle properties of circles:
• Angle in a semicircle is a right angle
• Angle between tangent and radius of a circle is a right angle
• Angle at the centre is twice the angle at the circumference
• Angles in the same segment are equal
• Angles in opposite segments are supplementary
3. Pythagoras’ theorem and trigonometry
3.1. Extending sine and cosine to obtuse angles
3.2. Use of the formula 12absinC\frac{1}{2}ab \sin C21absinC for the area of a triangle
3.3. Use of sine rule and cosine rule for any triangle
3.4. Problems in two and three dimensions, including angles of elevation and depression and bearings
4. Mensuration
4.1. Arc length, sector area and area of a segment of a circle
4.2. Use of radian measure of angle (including conversion between radians and degrees)
5. Coordinate geometry
5.1. Finding the gradient of a straight line given the coordinates of two points
5.2. Finding the length of a line segment given the coordinates of its endpoints
5.3. Interpreting and finding the equation of a straight line in the form y=mx+cy = mx + cy=mx+c
5.4. Geometric problems involving the use of coordinates
6. Vectors in two dimensions
6.1. Use of vector notations
6.2. Representing a vector as a directed line segment
6.3. Translation by a vector
6.4. Position vectors
6.5. Magnitude of a vectors
6.6. Use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors
6.7. Multiplication of a vector by a scalar
6.8. Geometric problems involving the use of vectors
Probability and Statistics
1. Data handling and analysis
1.1. Quartiles and percentiles
1.2. Range, interquartile range and standard deviation as measures of spread for a set of data
1.3. Analysis and interpretation of:
• Cumulative frequency diagrams
• Box-and-whisker plots
1.4. Purposes and uses, advantages and disadvantages of the different forms of statistical representations
1.5. Calculation of the standard deviation for a set of data (grouped and ungrouped)
1.6. Using the mean and standard deviation to compare two sets of data
2. Probability
2.1. Probability of simple combined events (including use of possibility diagrams and tree diagrams where appropriate)
2.2. Addition and multiplication of probabilities (mutually exclusive events and independent events)