LiuPoShanMemorialCollege

S4 Mathematics Teaching Scheme (2012-13)

Subject Teachers: Mr. Chiu K.Y., Ms.Fung P.L., Mr. Lam Y. C., Mr. Lo C.S., Ms.Sze S. Y.

Lessons per week: 8 / 7 Textbook: New Century Mathematics 4A / 4B (Oxford)

Week / Date / Chapter
week 1 (3/9 – 4/9) / Revision
week 1 - 2 (5/9 – 14/9) / Chapter 1 Number Systems
week 3 – 5 (17/9 – 5/10) / Chapter 3 Quadratic Equations in One Unknown
week 6 – 7 (8/10 – 19/10) / Chapter 4 Basic Knowledge of Functions
week 8 – 9 (22/10 – 2/11) / Chapter 5Quadratic Functions
week 10 – 12 (7/11 – 23/11) / Chapter 2 Equations of Straight Lines
week 13 – 15 (26/11 –14/12) / Chapter 6 More About Polynomials
week 16 (17/11 – 20/11) / Revision Factorization
week 17 – 18 (24/12 – 2/1) / Christmas and New Year Holiday
week 19 – 20 (3/1 – 18/1) / S4 First Term Exam
week 21(21/1 – 25 /1) / Chapter 7 Further Applications of Mathematics
week 22 - 23 (28/1 –6 /2) / Chapter 8 Exponential Functions
week 23 – 24 (7/2 – 18/2) / Lunar New Year Holiday
week 25 – 27 (19/2 – 8/3) / Chapter 9 Logarithmic Functions
week 28 - 29 (11/3 – 20/3) / Chapter 10Rational Functions
week 30 (25/3 – 28/3) / Chapter 11Basic Properties of Circles
week 31 – 32 ( 29/3 – 9/4) / Easter Holiday
week 32 – 33 (10/4 – 19/4) / Chapter 11Basic Properties of Circles
week 34 – 37 (22/4 – 16/5) / Chapter 12More About Basic Properties of Circles
week 38 (20/5 – 23/5) / Chapter 14Further Applications of Mathematics
week 39 - 40 (27/5 – 4/6) / Revision Formulas , Identities and Equations / Percentage
week 41 – 42 (5/6 – 20/6) / S4 Final Exam
Week / Date / Section / Learning Objective / Exercises / Remark
Week 1
(3/9 – 4/9) / Revision
Week 1 - 2
(5/9 – 14/9) / Chapter 1 Number Systems
1.1The Real Number Systems
1.2Complex Numbers
1.3Manipulation of Complex Numbers / • 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.
•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.
• Recognize the properties of the arithmetic operations of imaginary numbers.
•Recognize the arithmetic operations of complex numbers.
• Using the property of equality of complex numbers to solve related problems. / 1A (1-5, 13, __, __)
1B (4-7, 17, 18, __, __) / LD
Week 3 – 5
(17/9 – 5/10) / Chapter 3 Quadratic Equations in One Unknown
3.1 Solving Quadratic Equations by the Factor Method
3.2 Solving Quadratic Equations by the Graphical Method
3.3 Solving Quadratic Equations by the Quadratic Formula
3.4 Relations between the Discriminant and the Nature of Roots
3.5 Practical Problems Leading to Quadratic Equations
3.6 Forming Quadratic Equations
3.7Relations between Roots and Coefficients / •Learn to use different methods to factorize the polynomials in quadratic equations so as to solve the equations.
• 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.
• Recognize the quadratic formula and understand its usage in solving quadratic equations.
• Recognize the discriminant from the quadratic formula and its relation between the nature of roots of quadratic equations.
•Learn to solve practical problems using quadratic equations systematically.
• Learn to form a quadratic equation from two given roots.
•Understand the relations between the roots and coefficients of a quadratic equation.
• Master the applications of the relations between the roots and coefficients. / 3A (3, 7, 9, 13, 15, 23, __, __)
3B (1, 3, 5, 7, __, __)
3C (3, 7, 9, 13, 17, 21, __, __)
3D (7, 9, 11, 13, 15, 19, __, __)
3E (3, 5, 7, 15, 21, __, __)
3F (3, 5, 7, 11, 15, __, __)
3G (3, 5, 9, 17, 19, __, __) / LD
LD
Week 6 - 7 (8/10–19/10) / Chapter 4Basic Knowledge of Functions
4.1 Basic Concept of Functions
4.2 Representations of Functions
4.3 Notation of a Function: f(x) / • 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.
• 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.
• 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. / 4A (3, 5, 7, 11, __, __)
4B (5, 7, 9, 11, 15, 23, __, __)
Week 8 – 9 (22/10 – 2/11) / Chapter 5 Basic Knowledge of Functions
5.1 Features of the Graphs of Quadratic Functions
5.2 Finding the Maximum or Minimum Values of Quadratic Functions by the Algebraic Method / • Recognize the graph of y=ax2and its features.
•Further recognize the graph of y = ax2 + bx + c and its features.
•Learn to make a quadratic polynomial a perfect square by the method of completing the square.
• 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. / 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.
LD
Week 10 – 12 (7/11 – 23/11) / Chapter 2 Equations of Straight Lines
2.1 Equations of Straight Lines
2.2 Number of Points of Intersection of Two Straight Lines / • Learn to find the equation of a straight line from two given points.
• Learn to find the equation of a straight line from the coordinates of a given point and the slope of the line.
•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.
•Understand and determine the number of points of intersection of two straight lines. / 2A (5, 7, 12, 13, __, __)
2B (3, 5, 8, 9, 13, __, __)
Week 13 – 15 (26/11 –14/12) / Chapter 6 More About Polynomials
6.1 Division of Polynomials
6.2 Remainder Theorem
6.3 Factor Theorem / • Learn to perform divisions of polynomials by long division.
• 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.
• Understand the Factor Theorem.
• Know how to use Factor Theorem and the known factor to factorize polynomials.
• Know to factorize polynomials with leading coefficient equal to 1.
• Know how to factorize polynomials with integral coefficients. / 6A (5, 9, 11, 13, 19, __, __)
6B (3, 7, 9, 13, 21, __, __)
6C (5, 7, 9, 13, 21, __, __)
Week 16
(17/11 – 20/11) / Revision Factorization
week 17 – 18 (24/12 – 2/1) / Christmas and New Year Holiday
Week 19 – 20 (3/1 – 18/1) / S4 First Term Examination
Week 21
(21/1 –25/1) / Chapter 7FurtherApplications of Mathematics
7.1 Calculation of Profit and Selling Price / • Understand more sophisticated real-life problems related to profit and selling price and their functional relation.
• Appreciate the connections between the following areas:
—Setting up a functional relation between 2 variables from the conditions given in a question
—A function and its domain
—Finding the maximum/minimum value of a quadratic function
—Maximum/Minimum value of a function and its boundary conditions
Week 22 - 23 (28/1 –6/2) / Chapter 8 Exponential Functions I
8.1 Rational Indices
8.2 Exponential Functions / •Understand the meaning of the nth root of a number and know how to express it with radical sign.
•Understand the meaning of rational indices and know 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. / 8A (3, 7, 9, 23, 29, __, __)
8A (15, 19, 25, 31, 33, 35, __, __)
•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. / 8B (1,3, 5, 7, 11, __, __)
Week 23 – 24 (7/2 – 18/2) / Lunar New Year Holiday
Week 25 – 27 (19/2 – 8/3) / Chapter 9 Logarithmic Functions
9.1 Meaning of Logarithms
9.2Logarithmic Functions and Their Graphs
9.3 Exponential Equations and Logarithmic Equations

9.4 Applications of Logarithms

/ •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.
•Explore and study the graphs of logarithmic functions, recognize their properties and the relationship between them and the graphs of exponential functions.
• Learn to use algebraic method, the definition and properties of logarithms to solve exponential equations.
• Learn the techniques for solving logarithmic equations.
•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. / 9A (3, 5, 7, 13, 17, 19, 21, __)
9B (3, 5, 7, __, __)
9C (3, 5, 11, 13, 19, 27, __, __)
9D (5, 7, 9, 11, __, __) / LD
Week 28 - 29
(11/3 – 20/3) / Chapter 10 Rational Functions
10.1 Highest Common Factor and Least Common Multiple
10.2 Addition and Subtraction of Rational Functions
10.3 Multiplication and Division of Rational Functions / • Learn to make use of factorization to find the Highest 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.
• 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.
• Be able to perform multiplication and division of rational functions in one or two variables.
• Be able to perform mixed arithmetic operations of rational functions in one or two variables. / 10A (7, 9, 11, 17, 22, __, __)
10B (3, 5, 9, 13, 17, __, __)
10C (7, 11, 15, 19, 27, __, __) / LD
Week 30 (25/3 – 28/3) / Chapter 11 Basic Properties of Circles
11.1 Basic Knowledge about Circles
11.2 Properties of Chords of a Circle / •Recognize the names of various parts relating to a circle.
• Recognize the names and the meanings of some special circles.
• 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. / 11A (3, 5, 15, 23, __, __)
11A (7, 9, 13, 17, __, __) / I﹕Use Geometer Sketchpad to investigate the relationship between tangents and radius.
LD
I﹕UseGeometer Sketchpad to investigate the relationship between tangent and radius.
LD
week 31 – 32 ( 29/3 – 9/4) / Easter Holiday
Week 32-33 (10/4 – 19/4) / Chapter 11 Basic Properties of Circles
11.3 Angle Properties of a Circle
11.4 Relationships among Angles, Arcs and Chords / • 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
• 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.
•Comprehend the equal relationships among angles, arcs and chords.
• Understand the proportion relations between arcs and angles at the centre and between arcs and angles at the circumference. / 11B (3, 5, 13, 15, 19, __, __)
11B (7, 9, 11, 17, 21, __, __)
11C (5, 7, 11, 17, __, __)
11C (9, 13, 15, 21, __, __) / I﹕Use Geometer Sketchpad to investigate the relationship between tangents and radius.
LD
I﹕UseGeometer Sketchpad to investigate the relationship between tangent and radius.
LD
Week 34 – 37
(22/4 – 16/5) / Chapter 12 More About Basic Properties of Circles
12.1 Properties of Cyclic Quadrilaterals
12.2 Tests for Cyclic Quadrilaterals
12.3 Tangents to Circles
12.4 Angles in the Alternate Segments
12.5 Geometric Proofs on Circles / • Recognize the definition of cyclic quadrilaterals and 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 quadrilateral and their relationship with interior opposite angles.
• 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.
•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.
• 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 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 the alternate segment and know how to perform related calculations using their properties.
• 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. / 12A (3, 7, 8, 9, 15, 19, __, __)
12B (3, 5, 7, 11, 13, __, __)
12C (7, 9, 11, 13, 17, __, __)
12D (3, 5, 11, 17, 21, __, __)
12E (1, 5, 7, 11, 13, __, __)
12F (3, 7, 11, 13, __, __) / LD
LD
Week 38
(20/5 – 23/5) / Chapter 14 Further Application of Mathematics
14.1Ptolemy’s Theorem and Its Applications / • Recognize and understand the Ptolemy’s Theorem.
• Explore and investigate the applications of Ptolemy’s Theorem.
• Appreciate the connections between the following areas:
— properties of a cyclic quadrilateral
— angle properties of a circle
— Pythagoras’ Theorem
— properties of a regular pentagon
— solving quadratic equations in one unknown
Week 39 – 40
(27/5 – 4/6) / Revision Formulas, Identities and Equation / Percentage
Week 41 – 43 (5/6 – 20/6) / S4 Final Examination

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