Liu Po Shan Memorial College
S4 Mathematics Teaching Scheme (2013-14)
Subject Teachers: Chan YT, Chau YY, *Lam YC, Siu KY, Wong CY
Lessons per week: 8 / 7
Textbook: New Century Mathematics 4A / 4B (Oxford)
Week / Date
Chapter
week 1 - 2 (3/9 – 13/9)
Chapter 1
Number Systems
week 3 – 5 (16/9 – 4/10)
Chapter 3
Quadratic Equations in One Unknown
week 6 – 7 (7/10 – 18/10)
Chapter 4
Basic Knowledge of Functions
week 8 – 9 (21/10 – 1/11)
Chapter 5
Quadratic Functions
week 10 – 12 (4/11 – 22/11)
Chapter 2
Equations of Straight Lines
week 13 – 15 (25/11 –13/12)
Chapter 6
More About Polynomials
week 16 (16/12 – 19/12)
Revision
week 17 – 18 (23/12 – 1/1)
Christmas and New Year Holiday
week 19 – 20 (2/1 – 16/1)
S4 First Term Exam
week 21 - 22 (20/1 – 27/1)
Chapter 8
Exponential Functions
week 22 – 23 (28/1 – 9/2)
Lunar New Year Holiday
week 24 (10/2 – 14/2)
Chapter 8
Exponential Functions
week 25 – 27 (17/2 – 7/3)
Chapter 9
Logarithmic Functions
week 28 - 29 (10/3 – 21/3)
Chapter 10
Rational Functions
week 30 - 32 (25/3 – 11/4)
Chapter 11
Basic Properties of Circles
week 33 – 34 ( 14/4 – 21/4)
Easter Holiday
week 35 – 38 (22/4 – 22/5)
Chapter 12
week 39 - 40 (26/5 – 5/6)
Revision
More About Basic Properties of Circles
week 41 – 42 (6/6 – 20/6)
S4 Final Exam
Page 1
Week / Date
Week 1
Week 1 - 2
Section
Learning Objective
Exercises
Remark
Revision
Chapter 1 Number Systems
1.1 The Real Number Systems
• Recognize the development of integers.
• Recognize the development of rational numbers.
• Review the method of converting recurring decimals into
fractions.
• Recognize the development of irrational numbers.
• Recognize the relationships between real numbers and
points on the number line.
1.2 Complex Numbers
• Understand the needs to extend the real numbers.
• Recognize imaginary numbers and imaginary units.
• Recognize complex numbers.
• Understand the classification in the complex number
system.
1A (1-5, 13, __, __)
1.3 Manipulation of Complex Numbers • Recognize the properties of the arithmetic operations of 1B (4-7, 17, 18, __, __)
imaginary numbers.
• Recognize the arithmetic operations of complex
numbers.
• Using the property of equality of complex numbers to
solve related problems.
* Section 1.1D Parts I, II and III: not to be covered in 4B and 4C
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Chapter 3 Quadratic Equations in One
Unknown
3.1 Solving Quadratic Equations by the •Learn to use different methods to factorize the
Factor Method
polynomials in quadratic equations so as to solve the
equations.
Week 3 – 5
3A (3, 7, 9, 13, 15, 23, __, __)
3.2 Solving Quadratic Equations by the
Graphical Method
• Recognize the use of the x-intercepts of the graph of a
quadratic equation in two unknowns to solve the
corresponding quadratic equation in one unknown.
3B (1, 3, 5, 7, __, __)
3.3 Solving Quadratic Equations by the
Quadratic Formula
• Recognize the quadratic formula and understand its
usage in solving quadratic equations.
3C (3, 7, 9, 13, 17, 21, __, __)
3.4 Relations between the Discriminant
and the Nature of Roots
• Recognize the discriminant from the quadratic formula
and its relation between the nature of roots of quadratic
equations.
3D (7, 9, 11, 13, 15, 19, __, __)
3.5 Practical Problems Leading to
Quadratic Equations
•Learn to solve practical problems using quadratic
equations systematically.
3E (3, 5, 7, 15, 21, __, __)
3.6 Forming Quadratic Equations
• Learn to form a quadratic equation from two given roots. 3F (3, 5, 7, 11, 15, __, __)
3.7 Relations between Roots and
Coefficients
•Understand the relations between the roots and
3G (3, 5, 9, 17, 19, __, __)
coefficients of a quadratic equation.
• Master the applications of the relations between the roots
and coefficients.
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Chapter 4Basic Knowledge of Functions
4.1 Basic Concept of Functions
• Recognize the independent and dependent variables of
functions.
• Recognize the definition of a function.
• Learn to use the definition of a function to determine
whether there is a function relation in a given equation.
4A (3, 5, 7, 11, __, __)
4.2 Representations of Functions
• Recognize the tabular method to represent a function
relation.
• Recognize the algebraic method to represent a function
relation.
• Recognize the graphical method to represent a function
relation.
Week 6 - 7
4B (5, 7, 9, 11, 15, 23, __, __)
4.3 Notation of a Function: f(x)
• Learn the different notations for a function.
• Perform calculations to find the value of a function.
• Understand the concept of domain and co-domain of a
function.
• Learn to find the methods of finding the domain of a
function and unknowns in a function.
• Perform four arithmetic of functions.
• Solve practical problems involving functions.
* Section 4.3C: not to be covered in 4B and 4C
Chapter 5 Basic Knowledge of Functions
5.1 Features of the Graphs of Quadratic • Recognize the graph of y=ax2and its features.
Functions
•Further recognize the graph of y = ax2 + bx + c and its
features.
Week 8 – 9
5.2 Finding the Maximum or Minimum •Learn to make a quadratic polynomial a perfect square
Values of Quadratic Functions by the
by the method of completing the square.
Algebraic Method
• Study the properties of quadratic functions using the
method of completing the squares.
• Learn to use the method of completing the square to
find the extreme values of quadratic functions and solve
problems related to the features of the graph.
• Use the method of completing the square to solve
application problems related to quadratic functions.
Page 4
5A (3, 5, 9, 12, 15, __, __)
5B (3, 5, 9, 13, 17, __, __)
I﹕Use drawing software and
its magnification function to
investigate the limitations of
graphical method and find the
way to obtain a more accurate
solution.
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Chapter 2 Equations of Straight Lines
2.1 Equations of Straight Lines
Week 10 – 12
• Learn to find the equation of a straight line from two
given points.
2A (5, 7, 12, 13, __, __)
• Learn to find the equation of a straight line from the
coordinates of a given point and the slope of the line.
2B (3, 5, 8, 9, 13, __, __)
•Learn to find the equation of a given straight line from its
slope and y-intercept.
•Learn to find the slope and y-intercept of a given straight
line from its equation.
•Learn to find the equation of a straight line from its
x-intercept and y-intercept.
•Recognize the equations of vertical lines, horizontal lines
and straight lines passing through the origin.
2.2 Number of Points of Intersection of •Understand and determine the number of points of
Two Straight Lines
intersection of two straight lines.
Chapter 6 More About Polynomials
6.1 Division of Polynomials
6.2 Remainder Theorem
Week 13 – 15
• Learn to perform divisions of polynomials by long
division.
6A (5, 9, 11, 13, 19, __, __)
• Recognize polynomials in one variable and their
function notations.
• Understand the Remainder Theorem.
• Know how to use the Remainder Theorem to find the
remainders or unknowns.
6B (3, 7, 9, 13, 21, __, __)
6.3 Factor Theorem
• Understand the Factor Theorem.
• Know how to use Factor Theorem and the known factor 6C (5, 7, 9, 13, 21, __, __)
to factorize polynomials.
• Know to factorize polynomials with leading coefficient
equal to 1.
• Know how to factorize polynomials with integral
coefficients.
Week 16
Revision
week 17 – 18
Christmas and New Year Holiday
Week 19 – 20
S4 First Term Examination
Page 5
Chapter 8 Exponential Functions I
8.1 Rational Indices
Week 21 – 22, 24
8.2 Exponential Functions
• Understand the meaning of the nth root of a number and
know how to express it with radical sign.
8A (3, 7, 9, 23, 29, __, __)
• Understand the meaning of rational indices and know
8A (15, 19, 25, 31, 33, 35, __, __)
how to use a calculator to find the values of expressions
involving rational indices or surds.
• Know how to simplify algebraic expressions involving
rational indices or surds by applying laws of rational
indices.
• Recognize the meaning of exponential functions.
• Know to plot the graphs of exponential and recognize
the properties of this kind of graph.
• Be able to apply the exponential functions to solve
various real-life problems.
* Sections 8.1C and 8.2B: not to be covered in 4B and 4C
Week 22 – 23
Lunar New Year Holiday
Page 6
8B (1,3, 5, 7, 11, __, __)
Chapter 9 Logarithmic Functions
9.1 Meaning of Logarithms
Week 25 – 27
• Recognize the meanings of logarithms and logarithmic
functions, and understand the relationship between
indices and logarithms and know how to find the value
of a logarithm or the unknown in a logarithm from its
definition.
• Understand and know how to apply the properties of
logarithms and the formula for change of base.
• Learn to find the values of logarithms (including
common logarithms) using a calculator.
9A (3, 5, 7, 13, 17, 19, 21, __)
9.2 Logarithmic Functions and Their • Explore and study the graphs of logarithmic functions,
Graphs
recognize their properties and the relationship between
them and the graphs of exponential functions.
9B (3, 5, 7, __, __)
9.3 Exponential Equations and
Logarithmic Equations
• Learn to use algebraic method, the definition and
properties of logarithms to solve exponential equations.
• Learn the techniques for solving logarithmic equations.
9C (3, 5, 11, 13, 19, 27, __, __)
9.4 Applications of Logarithms
• Appreciate the concept of logarithms being able to be
applied to represent the magnitudes of earthquakes, and
learn to make use of logarithmic functions to solve
application problems involving the magnitudes of
earthquakes.
• Appreciate the concept of logarithms being able to be
applied to represent the intensity level of sound, and
learn to make use of logarithmic functions to solve
application problems involving the intensity level of
sound.
• Understand the history of logarithmic tables and slide
rules and learn the applications of logarithmic table and
antilogarithmic table in calculations.
9D (5, 7, 9, 11, __, __)
* Sections 9.2 and 9.4: not to be covered in 4B and 4C
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Chapter 10 Rational Functions
10.1 Highest Common Factor and Least • Learn to make use of factorization to find the Highest
Common Multiple
Common Factor (H.C.F.) of polynomials in one or two
variables.
• Learn to make use of factorization to find the Least
Common Multiple (L.C.M.) of polynomials in one or
two variables.
Week 28 - 29
10.2 Addition and
Rational Functions
Subtraction
of • Recognize the rational function and its definition.
• Be able to perform addition and subtraction of rational
functions in one or two variables.
• Be able to find the unknowns in an identity of rational
functions.
10A (7, 9, 11, 17, 22, __, __)
10B (3, 5, 9, 13, 17, __, __)
10.3 Multiplication and Division of • Be able to perform multiplication and division of rational 10C (7, 11, 15, 19, 27, __, __)
Rational Functions
functions in one or two variables.
• Be able to perform mixed arithmetic operations of
rational functions in one or two variables.
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Chapter 11 Basic Properties of Circles
11.1 Basic Knowledge about Circles
11.2 Properties of Chords of a Circle
11.3 Angle Properties of a Circle
Week 30 - 32
• Recognize the names of various parts relating to a circle. 11A (3, 5, 15, 23, __, __)
• Recognize the names and the meanings of some special 11A (7, 9, 13, 17, __, __)
circles.
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• Understand various properties of perpendiculars from
centre of a circle to chords, and know how to make use of
those properties to solve problems involving circles.
• Understand the meanings and the properties of equal
chords and distance of chord from centre and know how
to make use of those properties to solve problems
involving circles.
• Understand the fact that when any three non-collinear
points are given, there can be one and only one circle
passing through these three points.
• Recognize the definitions of angles at the centre and
angles at the circumference, and understand the
relationship between them.
• Recognize the definition of angle in a semi-circle and
understand the properties of angle in a semi-circle
I﹕Use Geometer Sketchpad
to investigate the relationship
between tangent and radius.
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11B (3, 5, 13, 15, 19, __, __)
11B (7, 9, 11, 17, 21, __, __)
• Know how to make use of the properties of angles at the
centre, angles at the circumference and angle in a
semi-circle to solve problems involving circles.
• Recognize the meaning of angles in the same segment
and understand the property of angles in the same
segment.
• Know how to make use of the property of angles in the
same segment to solve problems involving circles.
11.4 Relationships among Angles, Arcs • Comprehend the equal relationships among angles, arcs 11C (5, 7, 11, 17, __, __)
and Chords
and chords.
11C (9, 13, 15, 21, __, __)
• Understand the proportion relations between arcs and
angles at the centre and between arcs and angles at the
circumference.
week 33 – 34
Easter Holiday
Page 9
I﹕Use Geometer Sketchpad
to investigate the relationship
between tangents and radius.
I﹕Use Geometer Sketchpad
to investigate the relationship
between tangents and radius.
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I﹕Use Geometer Sketchpad
to investigate the relationship
between tangent and radius.
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Chapter 12 More About Basic Properties
of Circles
12.1 Properties of Cyclic Quadrilaterals • Recognize the definition of cyclic quadrilaterals and
12A (3, 7, 8, 9, 15, 19, __, __)
understand the properties of opposite angles in cyclic
quadrilaterals.
• Know how to make use of the property of opposite
angles of a cyclic quadrilateral to solve problems
involving circles.
• Recognize the definition of exterior angles of a cyclic
12B (3, 5, 7, 11, 13, __, __)
quadrilateral and their relationship with interior opposite
angles.
12.2 Tests for Cyclic Quadrilaterals
12.3 Tangents to Circles
Week 35 – 38
12.4 Angles in the Alternate Segments
• Know how to test whether a set of given points (four
points) are concyclic (or form a cyclic quadrilateral)
according to the properties of cyclic quadrilaterals.
the alternate segment and know how to perform related
calculations using their properties.
12.5 Geometric Proofs on Circles
• Understand the working principles of induction and
deduction, and recognize their differences.
• Using the basic properties of circles learnt in Chapter 11
and in this chapter, prove more geometric properties
related to circles by deduction.
* Section 12.5: not to be covered in 4B and 4C
Week 39 – 40
Week 41 – 43
12C (7, 9, 11, 13, 17, __, __)
12D (3, 5, 11, 17, 21, __, __)
• Recognize the tangents to circles and the theorems of
testing for tangent lines.
• Know to use the basic properties of tangents to find
unknowns in circles.
12E (1, 5, 7, 11, 13, __, __)
• Understand the properties of tangents drawn from an
external point to a circle and know how to do calculation
according to the related theorems.
• Understand the concepts of common tangent and two
12F (3, 7, 11, 13, __, __)
circles touching each other and know how to solve
problems involving circles by applying the properties of
common tangent and two circles touching each other.
• Recognize the definition and properties of an angle in
Revision
S4 Final Examination
Page 10
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