YUEN LONG MERCHANTS ASSOCIATION SECONDARY SCHOOL Teaching Programme for S .1 Mathematics

Syllabus: 1. Basic Mathematics.

2. Directed numbers.3. Using Algebra to Solve Problems (I).4. Percentages (I).5. Using Algebra to Solve Problems (II).6. Estimation in Numbers and Measurement.7. Introduction to Geometry.8. Area and Volume (I).9. Introduction to Coordinates.10. Symmetry and Transformation.11. Angles in Intersecting and Parallel Lines.12. Congruence and Similarity.13. Introduction to Statistics.

Cycle Topics/Learning Targets/Contents 1 Basic Mathematics.

Learning TargetsThe students should be able to1. revise the basic arithmetic skills learnt in primary levels,2. revise the various types of numbers, including whole numbers and

fractions,3. choose an appropriate measuring tool for a particular purpose,4. choose an appropriate unit for a measurement.Content1. Types of Numbers.2. The Four Fundamental Arithmetic Operations ( ).3. Multiples and Factors.4. Fractions.

2 Directed Numbers.

Content1. The Concept and Applications of Directed Numbers.2. Addition and Subtraction of Directed Numbers.3. Multiplication and Division of Directed Numbers.

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Cycle Topics/Learning Targets/Contents 2 – 3 Using Algebra to Solve Problems (I).

Learning TargetsThe students should be able to1. recognize and appreciate the use of letters to represent numbers,2. understand the uses of algebraic language,3. translate word phrases into algebraic expressions and vice versa.4. note the differences between the language of arithmetic and the

language of algebra,5. formulate algebraic expressions,6. use different skills to solve algebraic equations in one unknown,7. formulate and solve algebraic equations in one unknown step by step

from given situations.Contents1. Introduction to Algebra.2. Algebraic Equations (in One Unknown).3. Formulating Equations to Solve Problems.

4 – 5 Percentage (I)

Learning targetsThe students should be able to1. understand and solve problems involving percentages,2. apply percentage changes to solve simple selling problems,3. solve simple profit and loss problems using percentage,4. understand the meaning of discount and calculate everyday discount

problems,5. apply percentages to solve problems involving simple interests.Contents1. Simple problems Involving Percentages.2. Percentage change.3. Profit and loss.4. Discount.5. Simple Interest.

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Cycle Topics/Learning Targets/Contents 6 – 7 Using Algebra to Solve Problems (II).

Learning TargetsThe students should be able to1. formulate simple algebraic inequalities to solve problems,2. recognize some common formulae that can be expressed in algebraic

form,3. investigate patterns of various number sequences, and use algebraic

expressions to describe those patterns,4. obtain a preliminary idea of functions.Contents1. Formulae.2. Formulating Inequalities.3. Sequences.4. Introduction to Functions.

8 – 9 Estimation in Measurement.

Learning targetsThe students should be able to1. be aware of the need to use estimation in real-life situations and to

judge the reasonableness of the results,2. learn key methods in estimating numbers,3. select and use different strategies of estimation to estimate the values of

given numerical expressions,4. choose appropriate means of estimation and calculation,5. understand the need to estimate in making measurements and the

estimation strategies we can use to obtain reasonable estimations.Contents1. Estimation in Numbers.2. Estimation in Measurement. (Including: Choosing Appropriate

Measuring Tools and Units.)

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Cycle Topics/Learning Targets/Contents 10 – 12 Introduction to Geometry.

Learning targetsThe students should be able to1. recognize the common terms and notations in geometry such as points,

lines, planes, angles, parallel and perpendicular lines, and know how to identify different types of angles,

2. recognize plane figures, including circles, triangles, polygons, and know how to identify different types of polygons,

3. explore ways of using some common tools of geometry to construct polygons, circles, parallel and perpendicular lines,

4. recognize simple solids,5. sketch the two-dimensional representation and cross-sections of simple

solids,6. recognize simple polyhedra and some of their properties.Contents1. Basic geometric concepts.2. Plane Figures.3. Solid Figures. (Including: Polyhedra.)

First Term Examination

15 – 17 Area and Volume (I). Learning targetsThe students should be able to1. use different methods to calculate the areas of simple polygons,2. understand different types of prisms, including cubes and cuboids,3. understand and calculate the surface areas and volumes of prisms.Contents1. Areas of Simple Polygons.2. Total Surface Areas and Volumes of Prisms.

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Cycle Topics/Learning Targets/Contents 18 – 20 Introduction to Coordinates.

Learning targetsThe students should be able to1. understand and use the rectangular coordinate system to describe

positions of points in a plane,2. locate a point in a plane be means of an ordered pair in rectangular

coordinate system,3. calculate the distance between two points on a horizontal or vertical line

in the rectangular coordinate system,4. calculate the areas of simple figures in the rectangular coordinate

system,5. understand and use the polar coordinate system to describe positions of

points in a plane,6. compare the rectangular with the polar coordinate system.Contents1. Rectangular Coordinate System.2. Lengths of Line Segments in the Rectangular Coordinate System.3. Areas of Plane Figures in the Rectangular Coordinate System.4. Polar coordinates.

21 – 22 Symmetry and Transformation.

Learning targetsThe students should be able to 1. recognize reflectional and rotational symmetries in 2-D plane figures,2. recognize the effect on 2-D plane figures after the transformation,

including reflection, rotation, translation and enlargement/reduction,3. appreciate the presence of symmetrical figures around us and use of

transformation s on figures in daily life,4. describe intuitively the effects of transformation on coordinates of

points.Contents1. Symmetry.2. Transformation.3. Transformations in a Rectangular Coordinate Plane.

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Cycle Topics/Learning Targets/Contents 23 – 24 Angles in Intersecting and Parallel Lines.

Learning targetsThe students should be able to 1. recognize angles associated with intersecting lines; angles at a point,

adjacent angles on a straight line, vertically opposite angles,2. explore and use the properties of the angles in (1),3. recognize angles associated with parallel lines; corresponding angles,

alternate angles, interior angles on the same side of the transversal,4. explore and use the properties of the angles in (2),5. explore and use the conditions for parallel lines.Contents1. Angles Relating to Intersecting Lines.2. Angles Relating to Parallel lines.3. Conditions for Parallel Lines.

25 – 26 Congruence and Similarity.

Learning targetsThe students should be able to1. recognize congruent figures and relate the ideas of transformations and

symmetry to congruent triangles,2. recognize the properties of congruent triangles,3. recognize the conditions for two triangles to be congruent and identify

whether two triangles are congruent or not,4. recognize similar figures and relate the ideas of transformations and

symmetry to similar figures,5. recognize the properties of similar triangles,6. recognize the conditions for two triangles to be similar and identify

whether two triangles are similar or not.Contents1. The Meaning of Congruence.2. Conditions for Triangles to be Congruent.3. The Meaning of Similarity.4. Conditions for Triangles to be Similar.

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Cycle Topics/Learning Targets/Contents 27 – 28 Introduction to Statistics.

Learning targetsThe students should be able to1. recognize various stages involved in statistics,2. learn different methods of collecting data,3. understand the existence of different type of data,4. understand the criteria and the method of organizing discrete data,5. learn to construct and interpret simple statistical graphs,6. analyze and predict a trend from the broken-line graph,7. choose appropriate diagrams/graphs to present a given set of discrete

data, and understand the influence that these graphs have on people,8. identify source of deception in statistical graphs that tend to be

misleading and recognize the dangers of misinterpreting statistical data.Contents1. Different Stages of Statistics.2. Collection of Data and their Classifications.3. Organization of (Discrete) Data.4. Presentation and Analysis of (Discrete) Data.5. Uses and Misuses of Statistical Diagrams.

Second Term Examination

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YUEN LONG MERCHANTS ASSOCIATION SECONDARY SCHOOL Teaching Programme of S .2 Mathematics

Syllabus: 1. Approximation and Errors.

2. Manipulation and Factorization of Polynomials.3. Identities.4. Formulae.5. Linear Equations in Two Unknowns.6. Rate and Ratio.7. More about Data Handling.8. Angles in Triangles and Polygons.9. Introduction to Deductive Geometry.10. Pythagoras’ Theorem.11. Trigonometric Ratios.12. Area and Volume (II).

Cycle Topics/Learning targets/Contents 1 – 2 Approximation and Error s

Learning targetsThe students should be able to 1. learn the basic concepts of significant figures,2. acquire skills of rounding off numbers to a required number of

significant figures,3. use significant figures in estimation,4. recognize the approximate nature of measurement and understand

the concept of errors in measurement,5. understand and calculate the maximum error, relative error,

percentage error and the range of actual value of a measurement. Contents1. Significant figures.2. Approximation and Errors in Measurement.

3 – 4 Manipulations and Factorization of Polynomials .

Learning targetsThe students should be able to 1. learn the index notation of numbers with positive integral indices,2. explore the laws of positive integral indices,3. use the laws of positive integral indices to simplify simple algebraic

expressions,4. recognize polynomial as an example of algebraic expressions,

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Cycle Topics/Learning targets/Contents 3 – 4 Manipulations and Factorization of Polynomials .

Learning targetsThe students should be able to 5. recognize polynomial and the meaning of the terminology involved.6. add and subtract polynomials,7. learn the multiplication of polynomials,8. understand factorization as a reverse process of expansion,9. learn simple methods of factorization, including taking out common

factors and grouping terms.Contents1. Index Notation.2. Laws of Positive Integral Indices.3. Polynomials.4. Addition and Subtraction of Polynomials.5. Multiplication of Polynomials.6. Factorization of Polynomials.

5 – 6 Identities

Learning targetsThe students should be able to 1. explore the meaning of identities,2. distinguish between equations and identities,3. find the value of the unknown coefficients of constant in an identity.4. discover and use the identities: difference of two squares and perfect

square expressions.Contents

1. Meaning of identities.2. The Difference of Two Squares Identities.3. The Perfect Square Identities.

7 – 8 Formula e

Learning targets The students should be able to1. recognize simple algebraic fractions,2. learn the operations on simple algebraic fractions,3. further study the meaning of formulas and the use of substitution in

formulas,4. identify the subject of a formula and learn how to change subject.

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Cycle Topics/Learning targets/Contents 7 – 8 Formula e

Contents1. Algebraic Fractions.2. Formulae and Substitution.3. Change of Subject of a Formula.

9 – 10 Linear Equations in Two Unknowns .

Learning targetsThe students should be able to1. recognize and understand linear equations in two unknowns,2. explore and plot the graphs of linear graphs in two unknowns,3. explore the meaning of simultaneous equations,4. solve simultaneous equations by graphical method and be aware of its

approximate nature,5. solve simultaneous equations by algebraic method,6. learn to use algebraic language to formulate simultaneous equations.Contents1. Basic Knowledge of Linear Equations in Two Unknowns.2. Solving Simultaneous Linear Equations in Two Unknowns by

Graphical Method.3. Solving Simultaneous Linear Equations in Two Unknowns by

Algebraic methods.4. Applications of Simultaneous Linear Equations in Two Unknowns.

11 – 12 Rate and Ratio.

Learning targetsThe students should be able to1. understand the meanings of rate and ratio,2. recognize the notation of , ,3. know how to divide a given quantity under a given ratio,4. understand the meaning of scale factor,5. apply rate and ratio to solve real-life problems including areas, maps

and plans.Contents

1. Rate.2. Ratio.3. Applications of Ratio.

First Term Examination

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Cycle Topics/Learning targets/Contents 15 – 16 More about Data H andling.

Learning targetsThe students should be able to1. understand the method of grouping continuous data into frequency

distribution table and learn the various terminology of lass interval,2. understand and construct histograms, frequency polygons and frequency

curves,3. read data and frequency from the graphs and hence interpret the results,4. understand, construct and interpret simple cumulative frequency

polygons and cumulative frequency curves,5. understand the abuse of histograms, frequency curves and cumulative

frequency curves,6. recognize the dangers of misinterpreting statistical data.

Contents1. Organization of (Continuous) Data.2. Presentation of (Continuous) Data.3. Cumulative Frequency.4. Misuses of Statistical Diagrams.

17 – 18 Angles in Triangles and Polygons.

Learning targetsThe students should be able to1. use the properties of lines and angles of triangles, including sum of

exterior angles of a triangle, properties of isosceles and equilateral triangles,

2. use the formulae fir the angle sum of the interior angles and exterior angles of polygons,

3. explore regular polygons and tessellate,4. explore methods to construct angle bisectors, perpendicular bisectors

and special angles using compasses and straight-edges,5. appreciate the construction of geometrical figures using minimal tools,6. construct some regular polygons using straight-edges and compasses.

Contents1. Angles and Sides of a Triangle.2. Angles of a Polygon.3. Basic Constructions.

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Cycle Topics/Learning targets/Contents 19 – 20 Introduction to Deductive Geometry.

Learning targetsThe students should be able to1. recognize the limitations of the intuitive approach in learning geometry,2. learn the basic concepts of statements and deductive reasoning,3. understand deductive approach to studying geometric properties,4. develop an intuitive idea of deductive reasoning by presenting proofs of

geometric relating to angles and parallel lines.Contents1. in Studying Geometry Using Deductive Reasoning.2. Deductive Approach to Properties of Geometric Figures.

21 – 22 Pythagoras’ Theorem.

Learning targetsThe students should be able to1. understand the meaning of square root,2. use calculators to obtain square roots of a number,3. learn Pythagoras’ Theorem and appreciate different proofs of it,4. use Pythagoras’ Theorem to solve problems,5. learn the converse of Pythagoras’ Theorem and use it to prove

problems,6. recognize the existence of irrational numbers and surds,7. appreciate the dynamic element of mathematical knowledge through

studying the story of the first crisis of mathematics.8. understand the meaning of rational and irrational numbers,9. explore how to represent rational and/or irrational numbers on the

number line,10. understand the inter-conversion between recurring decimals and

fractions, 11. understand the meaning of surds as irrational numbers,12. using the properties of radicals to manipulate commonly encountered

surds including the rationalization of denominators of the form .13. appreciate the fact that surds can be expressed in more concise form.Contents1. Square roots.2. Pythagoras’ Theorem and Its Applications.3. Converse of Pythagoras’ Theorem and Its Applications.4. Rational Numbers and Irrational Numbers.5. Operations of Surds as Irrational Numbers.

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Cycle Topics/Learning targets/Contents 23 – 26 Trigonometric ratios

Learning targetsThe students should be able to1. understand and use the sine, cosine and tangent ratios for angles

between 00 and 900,2. apply the trigonometric ratios in solving practical problems related to

two-dimensional figures and real life problems, 3. explore the exact values of trigonometric ratios of the special angles

, and ,4. find any trigonometric ratio between and by means of

Pythagoras Theorem,5. explore the relations of trigonometric ratios,6. prove simple trigonometric identities.

Contents1. Concepts of Trigonometric Ratios.2. The Sine Ratio.3. The Cosine Ratio.4. The Tangent Ratio.5. Applications of Trigonometric Ratios.6. Trigonometric Ratios of Some Special Angles.7. Using Pythagoras' Theorem to Find Trigonometric Ratios.8. Basic Knowledge of Trigonometric Identities.

27 – 28 Area and volume (II).

Learning targetsThe students should be able to1. calculate circumference of circles,2. explore the formula for the area of a circle and use the formula to

calculate areas of circles,3. calculate arc lengths and areas of sectors,4. understand and use the formulas for surface area and volume of

cylinders.Contents1. Circles.2. Arcs and Sectors.3. Cylinders.

Second Term Examination

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YUEN LONG MERCHANTS ASSOCIATION SECONDARY SCHOOL Teaching Programme for S .3 Mathematics

Syllabus: 1. More about Factorization of Polynomials.

2. Laws of Indices.3. Percentage (II).4. Linear Inequalities in One Unknown.5. Introduction to Probability.6. Measures of Central Tendency and Other Statistical Values.7. More on Deductive Geometry.8. Quadrilaterals.9. More about Three Dimensional Figures.10. Area and Volume (III)11. Application in Trigonometry.12. Coordinate Geometry of Straight Lines.

Cycle Topics/Objectives/Contents 1 – 2 More about Factorization of Polynomials.

Learning targetsThe students should be able to1. factorize polynomials by using identities including difference of two

squares and perfect square expression,2. factorize polynomials by cross method,3. factorize polynomials by using identities of the difference and sum of

two cubes.Contents1. Factorization Using Identities.2. Factorization Using the Cross-method.3. Factorization Using the Difference and Sum of Two Cubes Identities.

3 – 4 Laws of Indices.

Learning objectivesThe students should be able to1. extend and explore the meaning of the meaning of the index notation of

numbers with zero or negative exponents,2. explore, understand and use the laws of indices to simplify simple

algebraic expressions.,3. understand the meaning of scientific notation,4. apply scientific notation in real life situations,

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Cycle Topics/Objectives/Contents 3 – 4 Laws of Indices.

Learning objectives5. understand and compare various number notations in real-life situations,6. foster a sense of place values in different number notations,7. understand the inter-conversion between simple binary/hexadecimal

numbers and decimal numbers.Contents1. Zero and Negative Integral Indices.2. Scientific notation.3. Notation for Different Numeral Systems.4. Inter-conversions of Numbers of Different Numeral Systems.

5 – 6 Percentage (II)

Learning objectivesThe students should be able to1. apply percentages to solve problems of compound interest,2. apply percentages to solve problems involving increasing and

decreasing at constant rates,3. apply percentages to solve practical problems involving successive and

component changes,4. apply percentages to solve problems on rates payable of a property,5. Apply percentages to solve problems on salaries tax payable.Contents1. Compound Interest.2. Increasing at a Constant Rate.3. Decreasing at a Constant Rate.4. More about Percentage Changes.5. Taxation.

7 – 8 Linear Inequalities in One Unknown.

Learning objectivesThe students should be able to1. represent the solution of an inequality on a number line,2. explore the basic properties of inequalities,3. solve linear inequalities in one unknown and apply them to daily life.Contents1. Basic Knowledge of Inequalities.2. Linear inequalities in One Unknown.

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9 – 10 Introduction to Probability. Learning objectivesThe students should be able to1. explore the meaning of probability through various activities,2. get an intuitive idea about the relation between probability and relative

frequency as found in statistics or simulation activities,3. calculate the theoretical probability by listing the sample space and

counting,4. investigate probability in real life activities, including geometric

probability,5. compare the experimental and theoretical probabilities,6. recognize the meaning of expectation.Contents1. The Meaning of Probability.2. More about Probability.3. Experimental Probability.4. Expected Values.

11 – 12 Measures of Central Tendency and Other Statistical Values.

Learning objectivesThe students should be able to1. understand the meanings of the three kinds of measures of central

tendency: mean, mode and median,2. construct the data set from a given mean, median and mode,3. compare 2 sets of data with given mean, median and mode,4. find the mean, the median and the mode from a given set of ungrouped

or grouped data,5. read the median, quartiles and percentiles from a cumulative frequency

polygon/curve,6. be aware that the mean of grouped data is an estimation,7. discuss the relative merits of different measures of central tendency for

a given situation so as choose the most suitable central tendency to represent data,

8. explore and make conjectures on the effects of the central tendency in various situations,

9. understand weighted mean and be aware of its use in various real life situations,

10. discuss the misuse of averages in various real life situations and recognize the dangers of misusing averages.

Contents1. Introduction to Measures of Central Tendency.

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2. Calculating the Averages and Other Statistical Values for Large Sets of Data.

3. Effects of Changing Data on Averages.4. Further Investigations on the Applications of the Mean – Weighted

Mean.5. Misuses of Averages.

First Term Examination

15 – 16 More on Deductive Geometry. Learning objectivesThe students should be able to1. use the properties and conditions of equilateral triangles, congruent

triangles, similar triangles and isosceles triangles to perform some simple deductive proofs.

2. identify some special lines inside a triangle including angle bisectors, perpendicular bisectors, medians and altitudes,

3. recognize the triangle inequality,3. explore and recognize the concurrence of intersecting lines inside a

triangle, and recognize the in-centre, circum-centre, orthocentre and centroid of a triangle,

4. use a pair of compasses and straight edge to construct the various centres of a triangle.

Contents1. Use the Deductive Approach to Solve Geometric Problems on

Triangles.2. Special lines in Triangles.3. Relations between Lines in a Triangle.

17 – 18 Quadrilaterals.

Learning objectivesThe students should be able to1. understand further some special quadrilaterals and their definitions,2. explore the properties of parallelograms by deductive reasoning and

study the tests for parallelograms,3. explore the properties of some special quadrilaterals, such as

rhombuses, rectangles and squares by deductive reasoning,4. perform simple proofs related to parallelograms,5. understand and apply the midpoint theorem and the intercept theorem.

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Contents1. Basic knowledge of Special Quadrilaterals.2. Parallelograms.3. Rhombuses, Rectangles and Squares.4. Proofs Related to Parallelograms.5. Midpoint Theorem and Intercept Theorem.

19 – 20 More about Three Dimensional Figures.

Learning objectivesThe students should be able to1. extend the idea of symmetry in 2-D figures to recognize and appreciate

the reflectional and rotational symmetries in cubes and regular tetrahedrons,

2. explore and identify the net of a given solid,3. imagine and sketch the 3-D objects from given 2-D representations

from various views and recognize the limitation of 2-D.4. explore the properties of simple 3-D objects, such as identifying

a. the distance between a point and a lineb. the angle between two planesc. the projection of a straight line on a particular planed. the angle between a line and a plane

5. study Euler’s formula and regular polyhedra.Contents1. Symmetry of 3-D Figures.2. Nets of 3-D figures.3. Further Knowledge on 2-D Representations of 3-D Objects.4. Points, Straight Lines and Planes of 3-D Figures.5. Knowledge on Regular Polyhedra.

21 – 23 Area and Volume (III).

Learning objectivesThe students should be able to 1. understand and use the formulas for volumes and surface areas of

pyramids,2. understand and use the formulas for volumes and surface areas of right

circular cones,3. understand and use the formulas for volumes and surface areas of

spheres,4. distinguish between formulas for length, area, and volume by

considering dimensions,5. understand and use the relationships between sides, surface areas and

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volumes of similar figures.Contents1. Pyramids.2. Circular cones.3. Spheres.4. The Dimensions of Length, Area and Volume.5. Similar Plane Figures and Similar Solids.

24 – 25 Application of Trigonometry.

Learning objectivesThe students should be able to1. apply trigonometric ratios to solve practical problems involving

gradients,2. apply trigonometric ratios to solve practical problems involving angles

of elevation and angles of depression,3. apply trigonometric ratios to solve practical problems involving

bearings.Contents1. Gradients.2. Angles of Elevation and Depression.3. Bearings.

26 – 28 Coordinate Geometry of Straight Lines.

Learning objectivesThe students should be able to1. understand and use formula of distance and slope,2. understand the conditions for parallel lines and perpendicular lines,3. use ratio to find the coordinates of midpoint,4. use ratio to find the coordinates of an internal point of division,5. appreciate the analytic approach to prove results relating to rectilinear

figures besides the deductive approach,6. choose and use appropriate methods to prove results relating to

rectilinear figures.Contents1. Distance between Two Points.2. Slope of a Straight Line.3. Parallel Lines and Perpendicular Lines.4. Point of (Internal) Division.5. Applications of the Analytic Approach in Geometry.

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Second Term Examination

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