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MATHEMATICS CURRICULUM

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EXPRESS (Four-Year Course)

Secondary One

Number and Algebra
1. Numbers and operations
Prime, LCM, squares, cubes, roots, rational and real numbers, symbols, number lines, approximation, rounding off, use of calculators
2. Ratio and Proportion
3. Percentage
4. Rate and Speed
Conversion of units and average and constant and rates and speeds
5. 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
6. Functions and Graphs
Relationship between two variables, linear functions, gradient concept
7. Equations and Inequalities
Solving linear equations, simple fractional equations
8. Problems in real-world contexts
Simple interest, taxation, instalments, utilities bills, currency exchange, analysing data from tables and graphs

Geometry and Measurement

1. Angles, triangles and polygons
Types of angles, angles in parallel lines, properties of triangles, special quadrilaterals, regular polygons, interior and exterior angles in polygon, bisectors, construction of simple geometrical figures
2. 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

1. Data analysis
Tables, bar graphs, pictograms, line graphs, pie charts, purposes, advantages and disadvantages of different forms of representation, misinterpretations

Secondary Two

Number and Algebra

1. Ratio and proportion
Maps and scales, direct and inverse proportion
2. 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
3. Functions and graphs
4. 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,
5. Problems in real-world contexts
Simple interest, taxation, instalments, utilities bills, currency exchange, analysing data from tables and graphs

Geometry and Measurement

1. 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
2. Pythagoras’ theorem and trigonometry
Use of Pythagoras’ theorem, use of trigonometric ratios (sine, cosine, tangent) of acute angles in right-angled triangles
3. Mensuration
Volume and surface area of pyramid, cone and sphere

Statistics and Probability

1. Data 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
2. Probability
Probability of single events

Secondary Three/ Four

Number and Algebra

1. Numbers and Operations
Use of standard forms, laws of indices
2. Functions and graphs
Sketching of quadratic graphs, power functions, exponential functions, estimation of gradient of curves with tangents
3. Equations and inequalities
Solving quadratic equations with one variable with formulae, completing square and graphical methods, solving fractional and linear equations with one variable
4. Problems in real-world contexts
Simple interest, taxation, instalments, utilities bills, currency exchange, analysing data from tables and graphs, distance-time, speed-time graphs
5. Set Language and notation
Use of set language, union and intersection of sets and venn diagrams
6. Matrices
Display, interpretation, addition, subtraction, multiplication of matrices

Geometry and Measurement

1. Congruency and Similarity
Justifying congruency and similarity, ratio of areas and volumes of similar figures and solids
2. Properties of circles
Symmetry and angle properties of circles
3. 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
4. Mensuration
Arc length, sector area and area of segments, use and conversion of degree and radian measure of angle
5. Coordinate Geometry
Gradient of straight line, length of line segment,  interpret and find equation of straight line, geometric problems using coordinates
6. Vectors in two dimensions
Translation by vector, position vectors, magnitude, scalar multiplication of vectors

Statistics and Probability

1. Data 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
2. Probability
Probability of simple combined events, possibility and tree diagrams, mutually exclusive and independent events

Secondary One

Number and Algebra

1. Numbers and operations
Prime, LCM, squares, cubes, roots, rational and real numbers, symbols, number lines, approximation, rounding off, use of calculators
2. Ratio and Proportion
Comparison, relationship, division of ratios and fractions
3. Percentage
4. Rate and Speed
Conversion of units and average and constant and rates and speeds
5. Algebraic expression and formulae
Simple algebraic expressions and formulae, translation of real-world situations into algebraic expressions, number patterns, simplification of linear expressions
6. Equations and Inequalities
Forming and solving linear equations
7. Problems in real-world contexts
Simple interest, taxation, instalments, utilities bills, currency exchange, analysing data from tables and graphs

Geometry and Measurement

1. Angles, triangles and polygons
Types of angles, angles in parallel lines, properties of triangles
2. 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

1. Data analysis
Tables, bar graphs, pictograms, line graphs, pie charts, purposes, advantages and disadvantages of different forms of representation, misinterpretations

Secondary Two

Number and Algebra

1. Ratio and proportion
Maps and scales, direct and inverse proportion
2. 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
3. Functions and graphs
Coordinates in two dimension plane, linear functions, gradient of linear graph
4. 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,
5. Problems in real-world contexts
Simple interest, taxation, instalments, utilities bills, currency exchange, analysing data from tables and graphs

Geometry and Measurement

1. 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
2. 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
3. Pythagoras’ theorem and trigonometry
Use of Pythagoras’ theorem
4. Mensuration
Volume and surface area of pyramid, cone and sphere

Statistics and Probability

1. Data 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
2. Probability
Probability of single events

Secondary Three/Four

Number and Algebra

1. Numbers and Operations
Use of standard forms, laws of indices
2. 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
3. Functions and graphs
Sketching of quadratic graphs and their properties, power functions, exponential functions, estimation of gradient of curves with tangents
4. Equations and inequalities
Solving quadratic equations with one variable with formulae, completing square and graphical methods, solving fractional and linear equations with one variable
5. Problems in real-world contexts
Simple interest, taxation, instalments, utilities bills, currency exchange, analysing data from tables and graphs, distance-time, speed-time graphs

Geometry and Measurement

1. Congruency and Similarity
Enlargement and reduction of plane figures
2. Properties of circles
Symmetry and angle properties of circles
3. 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
4. Mensuration
Arc length, sector area and area of segments, use and conversion of degree and radian measure of angle
5. Coordinate Geometry
Gradient of straight line, length of line segment,  interpret and find equation of straight line, geometric problems using coordinates

Statistics and Probability

1. Data 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
2. Probability
Probability of simple combined events, possibility and tree diagrams, mutually exclusive and independent events

Secondary Five

Number and Algebra

1. Set Language and notation
Use of set language, union and intersection of sets and venn diagrams
2. Matrices
Display, interpretation, addition, subtraction, multiplication of matrices

Geometry and Measurement

1. Vectors in two dimensions
Translation by vector, position vectors, magnitude, scalar multiplication of vectors