**MATHEMATICS CURRICULUM**

## EXPRESS (Four-Year Course)

## NORMAL ACADEMIC (Five-Year Course)

Sec 1 | Sec 2 | Sec 3/4 | Sec 5

** See Collections**

## EXPRESS (Four-Year Course)

### **Secondary One**

Number and Algebra

- Numbers and operations

*Primes and Prime factorisation, LCM**(Lowest Common Multiple)*,*HCF (Highest Common Factor), squares, cubes, square roots and cube roots by prime factorisation, negative numbers, integers, rational numbers, real numbers and their four operations, calculations with calculator, representation and ordering of numbers on the number line, use of <, >, ≤, ≥ and approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, and estimating the results of computation)* - Ratio and Proportion
- Percentage
- Rate and Speed

*Conversion of units and average and constant and rates and speeds* - Algebraic expression and formulae

*Simple algebraic expressions and formulae, translation of real-world situations into algebraic expressions, number patterns, simplification of linear expressions, common factors* - Functions and Graphs

*Relationship between two variables, linear functions, gradient concept* - Equations and Inequalities

*Solving linear equations, simple fractional equations*

Geometry and Measurement

- Angles, triangles and polygons

*Right, acute, obtuse and reflex angles, properties of triangles, special quadrilaterals and regular polygons, construction of simple geometrical figures from given data using compass, rule, set squares and protractors, where appropriate* - Mensuration
*Area of parallelogram and trapezium, volume and surface area of prism and cylinder, conversion between cm2 and m2 , and between cm3 and m3*

Statistics and Probability

- Data handling and analysis
*Tables, bar graphs, pictograms, line graphs, pie charts, purposes, advantages and disadvantages of different forms of representation, misinterpretations*

**Secondary Two**

Number and Algebra

- Ratio and proportion
*Maps and scales, direct and inverse proportion* - Algebraic expressions and formulae
*Expansion of product of algebraic expressions, subject of formula, expansion formulae, factorisation of linear and quadratic expressions, addition, subtraction, multiplication and division of simple algebraic fractions* - Functions and graphs
*Quadratic functions and their gradients, turning points and symmetry* - Equations and inequalities
*Graphs of linear equations of two variables, solving quadratic equations with one variable using factorisation, solving simultaneous equations with two variables using substitution, elimination and graphical methods,*

Geometry and Measurement

- Congruency and Similarity
*Congruent and similar figures, properties of similar triangles and polygons, enlargement and reduction of plane figures, scale drawing, solving simple congruency and similarity problems* - Pythagoras’ theorem and trigonometry
*Use of Pythagoras’ theorem, use of trigonometric ratios (sine, cosine, tangent) of acute angles in right-angled triangles* - Mensuration
*Volume and surface area of pyramid, cone and sphere*

Statistics and Probability

- Data handling and analysis
*Dot diagrams, histograms, stem-and-leaf diagrams, purposes, advantages and disadvantages of different forms of representation, misinterpretations, purposes and use of mean, median and mode, calculating mean for grouped data* - Probability
*Probability of single events*

### **Secondary Three/ Four**

Number and Algebra

- Numbers and Operations
*Use of standard forms, laws of indices* - Functions and graphs
*Sketching of quadratic graphs, power functions, exponential functions, estimation of gradient of curves with tangents* - Equations and inequalities
*Solving quadratic equations with one variable with formulae, completing square and graphical methods, solving fractional and linear equations with one variable* - Set Language and notation
*Use of set language, union and intersection of sets and venn diagrams* - Matrices
*Display, interpretation, addition, subtraction, multiplication of matrices*

Geometry and Measurement

- Congruency and Similarity
*Justifying congruency and similarity, ratio of areas and volumes of similar figures and solids* - Properties of circles
*Symmetry and angle properties of circles* - Pythagoras’ theorem and trigonometry
*Sine and cosine of obtuse angles, sine rule for area, sine and cosine rules for any triangle, problems in two and three dimensions, angles of elevation and depression, bearings* - Mensuration
*Arc length, sector area and area of segments, use and conversion of degree and radian measure of angle* - Coordinate Geometry
*Gradient of straight line, length of line segment, interpret and find equation of straight line, geometric problems using coordinates* - Vectors in two dimensions
*Translation by vector, position vectors, magnitude, scalar multiplication of vectors*

Statistics and Probability

- Data handling and analysis
*Quartiles, percentiles, range, interquartile range, standard deviation, cumulative frequency diagrams, box-and-whisker plots, purposes, advantages and disadvantages of different forms of representation, misinterpretations, purposes and use of mean, median and mode, calculating mean for grouped and ungrouped data, comparison of data* - Probability
*Probability of simple combined events, possibility and tree diagrams, mutually exclusive and independent events*

## NORMAL ACADEMIC (Five-Year Course)

**Secondary One**

Number and Algebra

- Numbers and operations
*Prime, LCM, squares, cubes, roots, rational and real numbers, symbols, number lines, approximation, rounding off, use of calculators* - Ratio and Proportion
*Comparison, relationship, division of ratios and fractions* - Percentage
- Rate and Speed
*Conversion of units and average and constant and rates and speeds*

*Simple algebraic expressions and formulae, translation of real-world situations into algebraic expressions, number patterns, simplification of linear expressions*- Equations and Inequalities
*Forming and solving linear equations*

Geometry and Measurement

- Angles, triangles and polygons
*Types of angles, angles in parallel lines, properties of triangles* - Mensuration
*Areas of parallelogram, trapezium, area and perimeter of plane figures, volume and surface area of prism and cylinder, conversions of units, area and volume of composite solids*

Statistics and Probability

- Data handling and analysis
*Tables, bar graphs, pictograms, line graphs, pie charts, purposes, advantages and disadvantages of different forms of representation, misinterpretations*

**Secondary Two**

Number and Algebra

- Ratio and proportion
*Maps and scales, direct and inverse proportion* - Algebraic expressions and formulae
*Expansion of product of two linear expressions, use of brackets, common terms, expansion formulae, factorisation of linear and quadratic expressions, multiplication and division of simple algebraic functions* - Functions and graphs
*Coordinates in two dimension plane, linear functions, gradient of linear graph* - Equations and inequalities
*Solving linear equation of one variable, concepts of inequalities, solving simple fractional equations, graphs of linear equations of two variables, solving quadratic equations with one variable using factorisation, solving simultaneous equations with two variables using substitution, elimination and graphical methods,*

Geometry and Measurement

- Angles, Triangles and Polygons
*Properties of special quadrilaterals and regular polygons, interior and exterior angles of polygon, perpendicular and angle bisectors, construction of simple geometric figures* - Congruency and Similarity
*Congruent and similar figures, properties of similar triangles and polygons, enlargement and reduction of plane figures, scale drawing, solving simple congruency and similarity problems* - Pythagoras’ theorem and trigonometry
*Use of Pythagoras’ theorem* - Mensuration
*Volume and surface area of pyramid, cone and sphere*

Statistics and Probability

- Data handling and analysis
*Dot diagrams, histograms, stem-and-leaf diagrams, purposes, advantages and disadvantages of different forms of representation, misinterpretations, purposes and use of mean, median and mode, calculating mean for grouped data* - Probability
*Probability of single events*

**Secondary Three/Four**

Number and Algebra

- Numbers and Operations
*Use of standard forms, laws of indices* - Algebraic expression and formulae
*Factorisation of linear expressions, changing subject of formula, solving for unknown value in a formula, addition and subtraction of algebraic fractions* - Functions and graphs
*Sketching of quadratic graphs and their properties, power functions, exponential functions, estimation of gradient of curves with tangents* - Equations and inequalities
*Solving quadratic equations with one variable with formulae, completing square and graphical methods, solving fractional and linear equations with one variable*

Geometry and Measurement

- Congruency and Similarity
*Enlargement and reduction of plane figures* - Properties of circles
*Symmetry and angle properties of circles* - Pythagoras’ theorem and trigonometry
*Sine, cosine and tangent of acute angles, sine and cosine of obtuse angles, sine rule for area, sine and cosine rules for any triangle, problems in two and three dimensions, angles of elevation and depression, bearings* - Mensuration
*Arc length, sector area and area of segments, use and conversion of degree and radian measure of angle* - Coordinate Geometry
*Gradient of straight line, length of line segment, interpret and find equation of straight line, geometric problems using coordinates*

Statistics and Probability

- Data handling and analysis
*Quartiles, percentiles, range, interquartile range, mean, standard deviation, cumulative frequency diagrams, box-and-whisker plots, purposes, advantages and disadvantages of different forms of representation, misinterpretations* - Probability
*Probability of simple combined events, possibility and tree diagrams, mutually exclusive and independent events*

**Secondary Five**

Number and Algebra

- Functions and graphs
*Sketching of quadratic graphs and their properties, power functions, exponential functions, estimation of gradient of curves with tangents* - Equations and inequalities
*Solving linear inequalities in one variable (including simultaneous inequalities) and representing the solution on the number line* - Set Language and notation
*Use of set language, union and intersection of sets and venn diagrams* - Matrices
*Display, interpretation, addition, subtraction, multiplication of matrices*

* *Geometry and Measurement

*Congruency and Similarity*

Ratio of areas of similar plane figures, ratio of volumes of similar solids- Vectors in two dimensions
*Translation by vector, position vectors, magnitude, scalar multiplication of vectors*