law ting pong secondary school s4 mathematics 2019 …

Mathematics (S4)/ Course Outline (2019-20)

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LAW TING PONG SECONDARY SCHOOL S4 MATHEMATICS 2019 – 2020

Course Outline 1. Introduction The Department of Mathematics at LTPSS strives to develop students’ mathematical knowledge, skills and concepts that can facilitate their future development in various aspects. Our curriculum aims to provide content knowledge which serves as a means to develop students’ thinking abilities and foster students’ generic skills and positive attitudes towards mathematics learning. 2. Objectives The objectives of the Mathematics Curriculum are to:

2.1. Knowledge Domain

To induce children to understand and grasp the knowledge of the following: the quadratic equations; the functions and graphs; the equation of straight lines; the more about polynomials the exponential functions the logarithmic functions;


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the variations;

2.2. Skill Domain

To develop the following skills and capabilities in: reasoning mathematically, i.e. they should conjecture, test and build arguments about the validity of a proposition; applying mathematical knowledge to solve a variety of problems; number sense and spatial sense; handling data and generating information; learning mathematics independently and collaboratively for the whole life.


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2.3. Attitude Domain

To foster the attitudes to: be confident in their abilities to do mathematics; willingly apply mathematical knowledge; be willing to persist in solving problems; be willing to work cooperatively with people and to value the contribution of others.

3. Textbook (Book 4A) Mathematics in Action 4A (2nd Edition) – Longman Hong Kong Education. (Book 4B) Mathematics in Action 4B (2nd Edition) – Longman Hong Kong Education 4. Role of Parents at home Parents are encouraged to talk to their child about their learning in class on a regular basis. They should also discuss the results obtained by their child to find out how well they are doing in their mathematics course.


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5. Curriculum

Week Period Chapter Learning Target Remarks Test

1 5/9-6/9

(2)

Administration work

Collecting Summer Holiday HW

Explore the rules of Maths

lesson

2 9/9-13/9

(6)

Ch1 Quadratic Equation in One Unknown

(I)

1.1 Real Number System

1.2 Factor Methods

To understand the real number system

To solve the quadratic equation using factor method

3 16/9-20/9

(6)

1.3 Quadratic Formula

1.4 Graphical Method To solve the quadratic equation by taking square

roots.

To solve quadratic equation using quadratic formula

To solve the equation by plotting and reading from

the graphs

4 23/9-27/9

(6)

1.5 Problems Leading to Quadratic

Equations

To solve real-life problems that involve quadratic

equations

CT1(26/9)


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5 2/10-4/10

(3)

Ch2 Quadratic Equation in One Unknown

(II)

2.1 Roots of a Quadratic Equation

To understand the relation between discriminant and

the nature of its roots

To recognize the nature of roots from the graph

6 8/10-11/10

(4)

2.2 Forming Quadratic Equations

To form a quadratic equation with given roots

To form a quadratic equation using sum and product

of its roots.

To understand the relations between the roots and

coefficient of a quadratic equation

7 14/10-18/10

(6)

2.3 Roots and Coefficients

2.4 Complex Number

To perform addition, subtraction, multiplication and

division of complex number

CT2(17/10)

8 21/10-25/10

(6)

Ch3 Function and Graph

3.1 Functions

3.2 Notation of Function

3.3 Functions and Graphs

To understand the concept of functions

To find the values of functions

To recognize the notation and find the value of

function

To understand the feature of the graph of functions

9 28/10-1/11

(7)

3.4 Optimum Values To understand the optimum value and the feature of

graph of the quadratic function

To understand the method of completing square

To solve practical problems relate to the optimum

value

CT3(31/10)


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10 4/10-8/10 TERM BREAK

11 11/11-15/11

(6)

Ch5 More about Polynomials

5.1 Revision of Polynomials

5.2 Division of Polynomials Ch5 More

about Polynomials

To review the basic operations

To manipulate long division of polynomials

12 18/11-22/11

(6)

5.3 Remainder Theorem

5.4 Factor Theorem

To understand and apply remainder theorem

To understand and apply the factor theorem

To factorize polynomials up to degree 3

13 25/11-29/11

(4)

5.4 Rational Functions

5.5 H.C.F and L.C.M of Polynomials To find the H.C.F. and L.C.M of a polynomial

To perform operations of rational functions.

CT5(28/11)

14 2/12-6/12

(6)

Ch9 Variations

9.1 Basic Concept of Variation

9.2 Direct Variation

To understand the basic concept of variation

through daily life example

To understand the concept of direct variation

To explore the algebraic and graphical

representation in direct variations

To solve real life problems involving direct

variation


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15 9/12-13/12

(6)

9. 3 Inverse Variation

9.4 Joint Variation

To understand the concept of inverse variation

To solve real life problems involving inverse

variation

To understand the concept of joint variation

To solve real life problems involving joint variation

16 16/12-19/12

(4)

9.5 Partial Variation

To understand the concept of partial variation

To solve real life problems involving partial

variation

CT9(19/12)

17 – 18 24/12-3/1 CHRISTMAS AND NEW YEAR HOLIDAY

19 6/1-10/1

(6)

Revision

20 – 21 13/1-23/1

Mid-term assessment

22 24/1-31/1 LUNAR NEW YEAR HOLIDAY

23 3/2-7/2

(6)

Ch4 Equation of Straight Lines

4.1 Equation of Straight Lines

Revision of Chapter 3

Understand and apply the point-slope, two-point,

slope-intercept form to find the equation of straight

lines


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24 10/2-14/2

(6)

4.1 Equation of Straight Lines

4.2 General Form of Equation of a

Straight Line

Understand and apply the slope-intercept form to

find the equation of straight lines

To explore the properties of a straight line from its

equation in general form

25 17/2-20/2

(4)

4.3 Intersection of Straight Lines

To determine the number of intersections CT4(20/2)

26 24/2-28/2

(6)

Ch 10

More about Trigonometry

10.1

Angles of Rotation

10.2 Trigonometry Ratios of Any Angle

To understand the definition of angle of rotation in

quadrant

To understand the definition of trigonometric

ratios of any angle

Understand the signs of trigonometry rations in

different quadrant and the ‘CAST’ diagram

27 3/3-6/3

(4)

10.3 Graphs of Trigonometric Functions

To understand the features of graph of

trigonometric function

28 9/3-13/3

(6)

10.4 Graphical Solutions

Solving Trigonometric Equations To solve trigonometric equations graphically

29 16/3-20/3

(6)

10.5 Trigonometry Identities

To learn to simplify trigonometric expression and

prove trigonometric identities

CT10(19/3)

30 23/3-27/3

(6)

Ch6 Exponential Function

6.1 Rational Indices

6.2 Exponential Equation

To understand and use the laws of rational indices

Learn to solve equation in the form of cx nm

=


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31 30/3-31/3

(2)

6.3 Exponential Functions

To Understand the exponential functions and their

properties

To recognize the feature of the graphs of

exponential functions

CT6(26/3)

31 SPORT DAYS

32 EXPERIENTIAL LEARNING WEEK (ELW)

33 EASTER HOLIDAY


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34 20/4-24/4

(6)

Ch7 Logarithmic Functions

7.1 Common Logarithms

7.2 Application of Common Logarithms

To understand the definition of common logarithms

To learn the properties of common logarithms

To solve logarithmic equation

To apply logarithms in real life situation

35 27/5-28/5

(2)

7.3 Logarithms to an Arbitrary Base

To understand the definition of logarithms to an

arbitrary base

36 4/5-8/5

(6)

7.4 Graph of Logarithm Function To learnt the properties of logarithms to an arbitrary

base

CT7(7/5)

37 11/5-15/5

(6)

Ch8 More about Equations

8.1 Solving Simultaneous Equation by the

Algebraic Method

8.2 Solving Simultaneous Equation by the

Graphical Method

To recognize the feature of the graphs of logarithm

Understand the relation between xay = and

xy alog=

To solve simultaneous equations by algebraic

method

To solve simultaneous equations by graphical

method

38 18/5-22/5

(6)

8.3 Equations reducible to Quadratic

Equations

8.4 Practical Problems

To use the discriminant to find the number of

intersections between a straight line and a quadratic

curve

CT8(21/5)

39 – 40 25/5-5/6

(12)

Revision


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41 – 42 EXAM

43 PAPER CHECKING


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6. Assessment 6.1 Formative Assessment

Classwork will be given every lesson. Students should complete assigned exercises after school which can consolidate their learning and elaboration skills.

Homework/Section Quizzes will be given at least once per topic. Corrections must be done. Chapter Tests will be conducted throughout the year.

Assessment Format Weighting Time

Homework/ Section Quizzes

MC, short questions 20% 5~10 mins

Chapter Test MC, short questions and conventional questions 80% 40mins

6.2 Summative Assessment

Examination will be conducted during the year to judge the extent of students' learning. The purpose is to grade or certify students, evaluate their progress or to find out the effectiveness of a curriculum.

Assessment Format Mark

Distribution

Time

Mid Year Assessment Section A Multiple Choice questions Section B Short questions Section C Conventional questions

100 1hr45mins

Final Exam

Paper 1 (65%)

Section A1 SQ Section A2 SQ Section B LQ

35 35 35

2hrs15mins

Paper 2 (35%)

Section A MC Section B MC

30 15 1hr15mins


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6.3 Weighting of Component Parts

Term Type of assessment Assessment item Weighting

I Sep to Dec

Formative Assessment Section Quizzes, Uniform Test 30%

Summative Assessment Mid-term Test 10%

II Jan to Jun

Formative Assessment Section Quizzes, Uniform Test 30%

Summative Assessment Final Exam 30%

Mathematics Compulsory Part (S.5)/Course Outline (2019-20)

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LAW TING PONG SECONDARY SCHOOL S.5 Mathematics Compulsory Part 2019 – 2020

Course Outline

1. Introduction

The Department of Mathematics at LTPSS strives to develop students’ mathematical knowledge, skills and concepts that can facilitate their future development in various aspects. Our curriculum aims to provide content knowledge which serves as a means to develop students’ thinking abilities and foster students’ generic skills and positive attitudes towards mathematics learning.

2. Objectives

The objectives of the Senior Secondary Mathematics Education are to: provide students with mathematical tools for their personal development and future career pathways. provide a foundation for students who may further their studies in Mathematics or related areas. develop in students the generic skills, and in particular, the capability to use mathematics to solve problems, reason and communicate. develop students’ competence and confidence in dealing with mathematics needed in life. help students to fulfill their potential in mathematics.

3. Textbook

NSS Mathematics in Action Second Edition 5A, 5B and 6A (Compulsory Part) Pearson Education Asia Limited CM Yeung, KH Yeung, YF Kwok, HW Lee, HY Cheung and PF Man


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4. Curriculum Week Period Chapter Learning Target Test

1 2/9 – 6/9 (2)

Ch3 Inequalities

3.1 Compound Linear

Inequalities in One Unknown

Learn the concept of compound linear inequalities in one unknown connected by logical

operators ‘and’ or ‘or’.

Learn how to solve compound linear inequalities in one unknown and represent the solutions

graphically.

Solve problems leading to compound linear inequalities.

2 9/9 – 13/9 (6)

3.1 Compound Linear


(Con’t)

3.2 Solving Quadratic


by the Graphical Method

Learn to solve quadratic inequalities in one unknown by the graphical method.

3 16/9 – 20/9 (6)

3.3 Solving Quadratic


by the Algebraic Method

3.4 Problems Leading to

Quadratic Inequalities in One

Unknown

Learn to solve quadratic inequalities in one unknown by the method of tabulation.

Learn to solve quadratic inequalities in one unknown algebraically when the corresponding

quadratic equation has a double real root or no real roots.

Learn to solve real-life application problems involving quadratic inequalities in one unknown.

Learn to solve real-life application problems involving quadratic inequalities in one unknown.

20/9

Ch.3

Test


3

4 23/9 – 27/9 (6) Ch4 Linear Programming

4.1 Linear Inequalities in Two

Unknowns

4.2 Solving Systems of Linear

Inequalities in Two

Unknowns Graphically

Learn the concept of linear inequalities in two unknowns and their graphical representations.

Learn to solve system of linear inequalities in two unknowns graphically

5

30/9 – 4/10 (3) 4.3 Linear Programming Understand the concept of linear programming and learn how to find the optimal solution

subject to given constraints.

6 7/10 – 11/10 (3) 4.4 Applications of Linear

Programming

Learn how to solve real-life problems on linear programming. 11/10

Ch.4

Test

7 14/10 – 18/10 (6) Ch7 Equations of Circles

7.1 Equations of Circles

7.2 More about equations of

Circles

Understand and apply the standard form to find equations of circles.

Understand and apply the general form to find equations of circles.

Find equations of circles based on other given information.


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8 21/10 – 25/10 (6) 7.3 Intersection between a

Straight Line and a Circle

Ch8 Locus

8.1 Concept of a Locus

Learn to find the coordinates of the intersection(s) of a straight line and a circle.

Determine the number of intersections of a straight line and a circle.

Find the equations of tangents to a circle

Understand the concept of a locus.

9 28/10 – 1/11 (6) 8.2 Sketch and Description of

a Locus

8.3 Algebraic Equation of a

Locus

Sketch and describe the locus of moving points on a plane satisfying given conditions.

Recognize that different conditions can give rise to the same locus.

Describe the locus of points with algebraic equations.

1/11

Ch.7 & 8

Test

10 Term Break

11 11/11 – 15/11 (6) Ch1 Basic Properties of

Circle

1.1 Basic terms of a Circle

1.2 Chords of a Circle

Understand the basic terminologies related to a circle.

Understand the basic properties of chords.

Learn to apply the basic properties of chords of circle to solve related geometric problems.


5

12 18/11 – 22/11 (5) 1.3 Angles in a Circle

1.4 Relationships among

Arcs, Chords and Angles

Understand the angle properties of a circle.

Learn to apply the angle properties of a circle to solve related geometric problems.

Understand the relationships among arcs, chord and angles.

Learn to apply the relationships among arcs, chords and angles to solve related geometric

problems.

13 25/11 – 29/11 (5) 1.5 Cyclic Quadrilaterals

1.6 Concyclic Points

Understand the basic properties of cyclic quadrilaterals.

Learn to apply the basic properties of cyclic quadrilaterals to solve related geometric problems.

Understand the definition of concyclic points.

Learn to test for concyclic points.

29/11

Ch.1

Test

14 2/12 – 6/12 (6) Ch2 Tangents to Circles

2.1 Tangents to a Circle and

their Properties

2.2 Tangents from an

External Point

Understand and apply the basic properties of tangents to a circle.

Understand and apply the properties of tangents from an external point to a circle


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15 9/12 – 13/12 (6) 2.2 Tangents from an

External Point (Con’t)

2.3 Angles in the Alternate

Segment

Understand and apply the properties of angles in the alternate segment of a circle 13/12

Ch.2

Test

16 16/12 – 20/12 (5) Ch5 Applications of

Trigonometry in

2-dimensional Problems

5.1 Area of a Triangle

5.2 The Sine Formula

Understand and use the formula to find the areas of triangle.

Understand and use the Heron’s formula to find the areas of triangles.

Understand and use the sine formula to solve triangles.

17-18 Christmas Holiday

19 6/1 – 10/1 (6) 5.3 The Cosine formula

5.4 Trigonometric Problems

in Two Dimensions

Understand and use the cosine formula to solve triangles.

Apply trigonometric knowledge in solving 2-dimensional problems relating to angle of

elevation/depression.

Apply trigonometric knowledge in solving 2-dimensional problems relating to bearings

9/1

Ch.5

Test

10/1

Return

paper for

revision

20-22 Mid Year assessment

Lunar New Year Holiday


7

23 3/2 – 7/2 (6) Ch6 Applications of

Trigonometry in


6.1 Basic Terminologies in


6.2 More Examples on


Understand the basic terminologies related to points, lines, angles and planes in three

dimensions.

Learn how to identify the angles between two lines, a line and a plane, and two intersecting

planes.

Understand the concept of the line of greatest slope.

Solve 3-dimensional problems of cuboids and inclined planes by applying trigonometric

knowledge.

Solve 3-dimensional problems of prisms and pyramids by applying trigonometric knowledge.

Determine whether an angle is the angle between two intersecting planes.

24 10/2 – 14/2 (6) 6.3 Practice 3-dimensional

Problems

Apply trigonometric knowledge in solving practical 3-dimensional problems involving angles of

elevation/depression and bearings.

Apply trigonometric knowledge in solving advanced 3-dimensional problems such as

paper-foldings.

14/2

Ch.6

Test

25 17/2 – 21/2 (5) Ch9 Measures of Dispersion

9.1 Introduction to Measures

of Dispersion

9.2 Range and Inter-quartile

Range

Understand the concept of dispersion.

Understand the concepts of range and inter-quartile range.

Find the range and inter-quartile range for both grouped and ungrouped data sets.


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26 24/2 – 28/2 (6) 9.3 Box-and-Whisker

Diagram

9.4 Standard Deviation

Construct box-whisker diagrams.

Understand the concept of standard deviation for both grouped and ungrouped data.

27 2/3 – 6/3 (4) 9.4 Standard Deviation

(con’t)

9.5 Comparing Dispersions

Using Appropriate Measures

Use appropriate measures to compare the dispersions of different sets of data.

28 9/3 – 13/3 (6) 9.6 Applications of Standard

Deviation

9.7 Effects of Data Change on

Measures of Dispersion

Understand the applications of standard deviation to real-life problems involving standard scores

and normal distribution.

Explore the effects on the measures of dispersion subject to the following conditions:

- Adding a common constant to each datum of the set of data

- Multiplying each datum of the set of data by a common constant

- Removing a datum from a set of data

- Adding a datum to a set of data

13/3

Ch.9

Test

29 16/3 – 20/3 (6) Ch10 Permutation and

Combination

10.1 Basic Principles of

Counting

10.2 Permutation

Understanding the addition rule and multiplication rule in the counting principle.

Solve problems by applying the addition rule and multiplication rule.


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30 23/3 – 27/3 (6) 10.2 Permutation

(Con’t)

10.3 Combination

Understand the factorial notation.

Understand the notation and concept of permutation.

Solve problems on the permutation of distinct objects without repetition.

31 30/3 – 3/4 (3) 10.3 Combination

(Con’t) Understand the notation and concept of combination.

Solve problems on the combination of distinct objects without repetition.

3/4

Ch.10

Test

32-33 ELW

Easter Holiday

34 20/4 – 24/4 (6) Ch11 More about Probability

11.1 Set Language

11.2 Using Set Language in

Probability

11.3 Addition Law of

Probability

Recognize the notations of sets.

Use Venn diagrams to represent sets and their elements.

Recognize the set notations including union, intersection and complement.

Understand the concepts of sample spaces and events.

Apply the concepts of sets to find probabilities.

Understand the concept of mutually exclusive events.

Understand the addition law of probability.

Understand the concept of complementary events.

Apply the addition law of probability to real-life problems.


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35 27/4 – 1/5 (3) 11.4 Multiplication Law of

Probability for Independent

Events

11.5 Conditional Probability

and Multiplication Law of

Probability for Dependent

Events

Understand the concept of independent events.

Understand the multiplication law of probability for independent events.

Apply the multiplication law of probability to real-life problems.

Understand the concept of dependent events.

Understand the concept of conditional probability and its notation.

Understand the multiplication law of probability for dependent events.

36 4/5 – 8/5 (6) 11.5 Conditional Probability

and Multiplication Law of

Probability for Dependent

Events (Con’t)

11.6 Using Permutation and

Combination to Solve

Probability Problems

Apply the multiplication law of probability to real-life problems.

Use permutation and combination to solve probability problems.

8/5

Ch.11

Test


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37 11/5 – 15/5 (6) S6 Ch1 Arithmetic and

Geometric Sequences

1.1 Review on Sequences

1.2 Arithmetic Sequences

Understand the concept of the general term of a sequence.

Understand the concept, the general term and the properties of an arithmetic sequence.

38 18/5 – 22/5 (6) 1.3 Geometric Sequences

1.4 Problems Involving

Arithmetic and

Geometric Sequences

Understand the concept, the general term and the properties of a geometric sequence.

Able to solve practical problems involving arithmetic or geometric sequences.

22/5

S6 Ch.1

Test

39 25/5 – 29/5 (6) S6 Ch2 Summation of

Arithmetic and Geometric

Sequences

2.1 Summation of a

Sequence

2.2 Summation of an

Arithmetic Sequence

Understand the concept of a series.

Understand the concept of an arithmetic series.


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40 1/6 – 5/6 (6) 2.3 Summation of a

Geometric Sequence

2.4 Applications of the

Summation of Arithmetic

and Geometric

Sequences

Understand the concept of a geometric series.

Able to solve real-life problems using summation formulas of arithmetic and geometric

sequences.

4/6

S6 Ch.2

Test

5/6

Return

paper for

revision

Final Examination

5. Assessment 5.1 Formative Assessment Classwork will be given every lesson. Students should complete assigned exercises after school which can consolidate their learning and

elaboration skills. Homework/Section Quizzes will be given in the end of each unit, to assess students’ learning outcome for the material. Chapter Tests will be conducted throughout the year.

Assessment Format Weighting Time

Homework/ Section Quizzes

MC, short questions 20% 5~10 mins

Chapter Test MC, short questions and conventional questions 80% 40mins


13

5.2 Summative Assessment

Mid Year Assessment and Final Examination will be conducted during this year to assess students’ learning outcome. The purpose is to grade and evaluate their progress or to find out the effectiveness of a curriculum.

Assessment Format Mark

Distribution

Time

Mid Year Assessment Section A Multiple Choice questions Section B Short questions Section C Conventional questions

100 1hr45mins

Final Exam

Paper 1 (65%)

Section A1 SQ Section A2 SQ Section B LQ

35 35 35

2hrs15mins

Paper 2 (35%)

Section A MC Section B MC

30 15 1hr15mins

5.3 Weighting of Component Parts Term Type of assessment Assessment item Weighting I Sep to Jan

Formative Assessment Homework/Section Quizzes, Chapter test 30% Summative Assessment Mid Year Assessment 10%

II Jan to Jun

Formative Assessment

Homework/Section Quizzes, Chapter Test 30%

Summative Assessment Final Exam 30%


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6. Role of Parents at home Parents are encouraged to talk to their child about their learning in class on a regular basis. They should also discuss the results obtained by their child to find out how well they are doing in their mathematics course.

law ting pong secondary school s4 mathematics 2019 …

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