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YUEN LONG MERCHANTS ASSOCIATION SECONDARY SCHOOL
Teaching Programme for S.1 Mathematics
Syllabus:
1.
2.
3.
4.
5.
6.
7.
8.
Basic Mathematics.
Directed numbers.
Using Algebra to Solve Problems (I).
Percentages (I).
Using Algebra to Solve Problems (II).
Estimation in Numbers and Measurement.
Introduction to Geometry.
Area and Volume (I).
9.
10.
11.
12.
13.
Introduction to Coordinates.
Symmetry and Transformation.
Angles in Intersecting and Parallel Lines.
Congruence and Similarity.
Introduction to Statistics.
Cycle
1
Topics/Learning Targets/Contents
Basic Mathematics.
Learning Targets
The students should be able to
1.
2.
3.
4.
revise the basic arithmetic skills learnt in primary levels,
revise the various types of numbers, including whole numbers and
fractions,
choose an appropriate measuring tool for a particular purpose,
choose an appropriate unit for a measurement.
Content
1. Types of Numbers.
2. The Four Fundamental Arithmetic Operations ( ,,, ).
2
3.
Multiples and Factors.
4.
Fractions.
Directed Numbers.
Content
1. The Concept and Applications of Directed Numbers.
2. Addition and Subtraction of Directed Numbers.
3. Multiplication and Division of Directed Numbers.
p. 1
Cycle
2–3
Topics/Learning Targets/Contents
Using Algebra to Solve Problems (I).
Learning Targets
The students should be able to
1. 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.
Contents
1. Introduction to Algebra.
2. Algebraic Equations (in One Unknown).
3.
4–5
Formulating Equations to Solve Problems.
Percentage (I)
Learning targets
The students should be able to
1.
2.
3.
4.
5.
understand and solve problems involving percentages,
apply percentage changes to solve simple selling problems,
solve simple profit and loss problems using percentage,
understand the meaning of discount and calculate everyday discount
problems,
apply percentages to solve problems involving simple interests.
Contents
1. Simple problems Involving Percentages.
2. Percentage change.
3.
4.
5.
Profit and loss.
Discount.
Simple Interest.
p. 2
Cycle
6–7
Topics/Learning Targets/Contents
Using Algebra to Solve Problems (II).
Learning Targets
The students should be able to
1. 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.
Contents
1. Formulae.
2. Formulating Inequalities.
3. Sequences.
4. Introduction to Functions.
8–9
Estimation in Measurement.
Learning targets
The students should be able to
1. be aware of the need to use estimation in real-life situations and to
judge the reasonableness of the results,
2.
3.
4.
5.
learn key methods in estimating numbers,
select and use different strategies of estimation to estimate the values of
given numerical expressions,
choose appropriate means of estimation and calculation,
understand the need to estimate in making measurements and the
estimation strategies we can use to obtain reasonable estimations.
Contents
1. Estimation in Numbers.
2. Estimation in Measurement.
Measuring Tools and Units.)
p. 3
(Including:
Choosing
Appropriate
Cycle
10 – 12
Topics/Learning Targets/Contents
Introduction to Geometry.
Learning targets
The students should be able to
1. 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.
5.
6.
recognize simple solids,
sketch the two-dimensional representation and cross-sections of simple
solids,
recognize simple polyhedra and some of their properties.
Contents
1. Basic geometric concepts.
2. Plane Figures.
3. Solid Figures. (Including: Polyhedra.)
First Term Examination
15 – 17
Area and Volume (I).
Learning targets
The students should be able to
1. 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.
Contents
1. Areas of Simple Polygons.
2. Total Surface Areas and Volumes of Prisms.
p. 4
Cycle
18 – 20
Topics/Learning Targets/Contents
Introduction to Coordinates.
Learning targets
The students should be able to
1. 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
5.
6.
system,
understand and use the polar coordinate system to describe positions of
points in a plane,
compare the rectangular with the polar coordinate system.
Contents
1. 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 targets
The 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.
Contents
1. Symmetry.
2. Transformation.
3. Transformations in a Rectangular Coordinate Plane.
p. 5
Cycle
23 – 24
Topics/Learning Targets/Contents
Angles in Intersecting and Parallel Lines.
Learning targets
The 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.
Contents
1. Angles Relating to Intersecting Lines.
2. Angles Relating to Parallel lines.
3. Conditions for Parallel Lines.
25 – 26
Congruence and Similarity.
Learning targets
The students should be able to
1. recognize congruent figures and relate the ideas of transformations and
symmetry to congruent triangles,
2.
3.
4.
5.
6.
recognize the properties of congruent triangles,
recognize the conditions for two triangles to be congruent and identify
whether two triangles are congruent or not,
recognize similar figures and relate the ideas of transformations and
symmetry to similar figures,
recognize the properties of similar triangles,
recognize the conditions for two triangles to be similar and identify
whether two triangles are similar or not.
Contents
1. The Meaning of Congruence.
2. Conditions for Triangles to be Congruent.
3. The Meaning of Similarity.
4. Conditions for Triangles to be Similar.
p. 6
Cycle
27 – 28
Topics/Learning Targets/Contents
Introduction to Statistics.
Learning targets
The students should be able to
1. 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
8.
data, and understand the influence that these graphs have on people,
identify source of deception in statistical graphs that tend to be
misleading and recognize the dangers of misinterpreting statistical data.
Contents
1. Different Stages of Statistics.
2.
3.
4.
5.
Collection of Data and their Classifications.
Organization of (Discrete) Data.
Presentation and Analysis of (Discrete) Data.
Uses and Misuses of Statistical Diagrams.
Second Term Examination
p. 7
YUEN LONG MERCHANTS ASSOCIATION SECONDARY SCHOOL
Teaching Programme of S.2 Mathematics
Syllabus:
1.
2.
3.
4.
5.
6.
7.
8.
Approximation and Errors.
Manipulation and Factorization of Polynomials.
Identities.
Formulae.
Linear Equations in Two Unknowns.
Rate and Ratio.
More about Data Handling.
Angles in Triangles and Polygons.
9.
10.
11.
12.
Introduction to Deductive Geometry.
Pythagoras’ Theorem.
Trigonometric Ratios.
Area and Volume (II).
Cycle
1–2
Topics/Learning targets/Contents
Approximation and Errors
Learning targets
The students should be able to
1. learn the basic concepts of significant figures,
2.
3.
4.
5.
acquire skills of rounding off numbers to a required number of
significant figures,
use significant figures in estimation,
recognize the approximate nature of measurement and understand the
concept of errors in measurement,
understand and calculate the maximum error, relative error, percentage
error and the range of actual value of a measurement.
Contents
1. Significant figures.
2.
3–4
Approximation and Errors in Measurement.
Manipulations and Factorization of Polynomials.
Learning targets
The 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,
p. 8
Cycle
3–4
Topics/Learning targets/Contents
Manipulations and Factorization of Polynomials.
Learning targets
The 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.
Contents
1. Index Notation.
2. Laws of Positive Integral Indices.
3. Polynomials.
4. Addition and Subtraction of Polynomials.
5. Multiplication of Polynomials.
6.
5–6
Factorization of Polynomials.
Identities
Learning targets
The students should be able to
1.
2.
3.
4.
explore the meaning of identities,
distinguish between equations and identities,
find the value of the unknown coefficients of constant in an identity.
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
Formulae
Learning targets
The students should be able to
1. 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.
p. 9
Cycle
7–8
Topics/Learning targets/Contents
Formulae
Contents
1. Algebraic Fractions.
2. Formulae and Substitution.
3. Change of Subject of a Formula.
9 – 10
Linear Equations in Two Unknowns.
Learning targets
The students should be able to
1. recognize and understand linear equations in two unknowns,
2.
3.
4.
5.
explore and plot the graphs of linear graphs in two unknowns,
explore the meaning of simultaneous equations,
solve simultaneous equations by graphical method and be aware of its
approximate nature,
solve simultaneous equations by algebraic method,
6.
learn to use algebraic language to formulate simultaneous equations.
Contents
1. Basic Knowledge of Linear Equations in Two Unknowns.
2. Solving Simultaneous Linear Equations in Two Unknowns by Graphical
Method.
3.
4.
11 – 12
Solving Simultaneous Linear Equations in Two Unknowns by Algebraic
methods.
Applications of Simultaneous Linear Equations in Two Unknowns.
Rate and Ratio.
Learning targets
The students should be able to
1. understand the meanings of rate and ratio,
2. recognize the notation of a : b , a : b : c ,
3.
4.
5.
know how to divide a given quantity under a given ratio,
understand the meaning of scale factor,
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
p. 10
Cycle
15 – 16
Topics/Learning targets/Contents
More about Data Handling.
Learning targets
The students should be able to
1. 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.
17 – 18
6.
understand the abuse of histograms, frequency curves and cumulative
frequency curves,
recognize the dangers of misinterpreting statistical data.
1.
Contents
Organization of (Continuous) Data.
2.
3.
4.
Presentation of (Continuous) Data.
Cumulative Frequency.
Misuses of Statistical Diagrams.
Angles in Triangles and Polygons.
Learning targets
The students should be able to
1. 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
5.
6.
and special angles using compasses and straight-edges,
appreciate the construction of geometrical figures using minimal tools,
construct some regular polygons using straight-edges and compasses.
1.
2.
3.
Contents
Angles and Sides of a Triangle.
Angles of a Polygon.
Basic Constructions.
p. 11
Cycle
19 – 20
Topics/Learning targets/Contents
Introduction to Deductive Geometry.
Learning targets
The students should be able to
1. 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.
Contents
1. in Studying Geometry Using Deductive Reasoning.
2.
21 – 22
Deductive Approach to Properties of Geometric Figures.
Pythagoras’ Theorem.
Learning targets
The students should be able to
1.
2.
3.
4.
5.
understand the meaning of square root,
use calculators to obtain square roots of a number,
learn Pythagoras’ Theorem and appreciate different proofs of it,
use Pythagoras’ Theorem to solve problems,
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 a .
13. appreciate the fact that surds can be expressed in more concise form.
Contents
1. 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.
p. 12
Cycle
23 – 26
Topics/Learning targets/Contents
Trigonometric ratios
Learning targets
The students should be able to
1. 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
300 , 450 and 600 ,
4.
5.
6.
find any trigonometric ratio between 00 and 900 by means of
Pythagoras Theorem,
explore the relations of trigonometric ratios,
prove simple trigonometric identities.
Contents
1. Concepts of Trigonometric Ratios.
27 – 28
2.
3.
4.
5.
6.
The Sine Ratio.
The Cosine Ratio.
The Tangent Ratio.
Applications of Trigonometric Ratios.
Trigonometric Ratios of Some Special Angles.
7.
8.
Using Pythagoras' Theorem to Find Trigonometric Ratios.
Basic Knowledge of Trigonometric Identities.
Area and volume (II).
Learning targets
The students should be able to
1. calculate circumference of circles,
2. explore the formula for the area of a circle and use the formula to
calculate areas of circles,
3.
4.
calculate arc lengths and areas of sectors,
understand and use the formulas for surface area and volume of
cylinders.
Contents
1. Circles.
2. Arcs and Sectors.
3. Cylinders.
Second Term Examination
p. 13
YUEN LONG MERCHANTS ASSOCIATION SECONDARY SCHOOL
Teaching Programme for S.3 Mathematics
Syllabus:
Cycle
1–2
1.
2.
3.
4.
5.
6.
7.
8.
More about Factorization of Polynomials.
Laws of Indices.
Percentage (II).
Linear Inequalities in One Unknown.
Introduction to Probability.
Measures of Central Tendency and Other Statistical Values.
More on Deductive Geometry.
Quadrilaterals.
9.
10.
11.
12.
More about Three Dimensional Figures.
Area and Volume (III)
Application in Trigonometry.
Coordinate Geometry of Straight Lines.
Topics/Objectives/Contents
More about Factorization of Polynomials.
Learning targets
The students should be able to
1. factorize polynomials by using identities including difference of two
2.
3.
squares and perfect square expression,
factorize polynomials by cross method,
factorize polynomials by using identities of the difference and sum of
two cubes.
Contents
1. 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 objectives
The students should be able to
1. 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,
p. 14
Cycle
Topics/Objectives/Contents
3–4
Laws of Indices.
Learning objectives
5. 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.
Contents
1. Zero and Negative Integral Indices.
2. Scientific notation.
3. Notation for Different Numeral Systems.
4.
5–6
Inter-conversions of Numbers of Different Numeral Systems.
Percentage (II)
Learning objectives
The students should be able to
1.
2.
3.
4.
5.
apply percentages to solve problems of compound interest,
apply percentages to solve problems involving increasing and
decreasing at constant rates,
apply percentages to solve practical problems involving successive and
component changes,
apply percentages to solve problems on rates payable of a property,
Apply percentages to solve problems on salaries tax payable.
Contents
1. 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 objectives
The students should be able to
1. 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.
Contents
1. Basic Knowledge of Inequalities.
2. Linear inequalities in One Unknown.
p. 15
9 – 10
Introduction to Probability.
Learning objectives
The students should be able to
1. 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.
Contents
1. The Meaning of Probability.
2. More about Probability.
3. Experimental Probability.
4.
11 – 12
Expected Values.
Measures of Central Tendency and Other Statistical Values.
Learning objectives
The students should be able to
1.
2.
3.
4.
5.
6.
understand the meanings of the three kinds of measures of central
tendency: mean, mode and median,
construct the data set from a given mean, median and mode,
compare 2 sets of data with given mean, median and mode,
find the mean, the median and the mode from a given set of ungrouped
or grouped data,
read the median, quartiles and percentiles from a cumulative frequency
polygon/curve,
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.
Contents
1. Introduction to Measures of Central Tendency.
p. 16
2.
Calculating the Averages and Other Statistical Values for Large Sets of
Data.
3.
4.
Effects of Changing Data on Averages.
Further Investigations on the Applications of the Mean – Weighted
Mean.
Misuses of Averages.
5.
First Term Examination
15 – 16
More on Deductive Geometry.
Learning objectives
The students should be able to
1. use the properties and conditions of equilateral triangles, congruent
triangles, similar triangles and isosceles triangles to perform some
simple deductive proofs.
2.
3.
3.
4.
identify some special lines inside a triangle including angle bisectors,
perpendicular bisectors, medians and altitudes,
recognize the triangle inequality,
explore and recognize the concurrence of intersecting lines inside a
triangle, and recognize the in-centre, circum-centre, orthocentre and
centroid of a triangle,
use a pair of compasses and straight edge to construct the various
centres of a triangle.
Contents
1. 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 objectives
The students should be able to
1. 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.
p. 17
Contents
1. Basic knowledge of Special Quadrilaterals.
2.
3.
4.
5.
19 – 20
Parallelograms.
Rhombuses, Rectangles and Squares.
Proofs Related to Parallelograms.
Midpoint Theorem and Intercept Theorem.
More about Three Dimensional Figures.
Learning objectives
The students should be able to
1. extend the idea of symmetry in 2-D figures to recognize and appreciate
2.
3.
4.
the reflectional and rotational symmetries in cubes and regular
tetrahedrons,
explore and identify the net of a given solid,
imagine and sketch the 3-D objects from given 2-D representations
from various views and recognize the limitation of 2-D.
explore the properties of simple 3-D objects, such as identifying
a. the distance between a point and a line
b. the angle between two planes
c. the projection of a straight line on a particular plane
d. the angle between a line and a plane
5. study Euler’s formula and regular polyhedra.
Contents
1. 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 objectives
The 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
5.
considering dimensions,
understand and use the relationships between sides, surface areas and
p. 18
volumes of similar figures.
Contents
1. 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 objectives
The students should be able to
1.
2.
3.
apply trigonometric ratios to solve practical problems involving
gradients,
apply trigonometric ratios to solve practical problems involving angles
of elevation and angles of depression,
apply trigonometric ratios to solve practical problems involving
bearings.
Contents
1. Gradients.
2. Angles of Elevation and Depression.
3. Bearings.
26 – 28
Coordinate Geometry of Straight Lines.
Learning objectives
The students should be able to
1. 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
6.
figures besides the deductive approach,
choose and use appropriate methods to prove results relating to
rectilinear figures.
Contents
1. 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.
p. 19
Second Term Examination
p. 20