MATHEMATICS CURRICULUM
EXPRESS (Four-Year Course)
NORMAL ACADEMIC (Five-Year Course)
Sec 1 | Sec 2 | Sec 3/4 | Sec 5
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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 - Algebraic expression and formulae
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