Stewards Pooi Kei College Secondary 1 Mathematics Teaching Schedule ( )

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1 Stewards Pooi Kei College Secondary Mathematics Teaching Schedule (07-08) Subject Teachers: Ms. Connie Chow (Coordinator), Ms. Sabrina Cheung, Ms. Candy Wong No. of Periods/0-day Cycle: Cycle No. of Periods Teaching Topics/Content Teaching Concepts Chapter 0: Basic Mathematics 0. Types of Numbers 0. The Four Basic Arithmetic Operations 5 0. Multiples and Factors 0. Fractions Chapter : Directed Numbers. Directed Numbers and Number Line. Addition and Subtraction of Directed Numbers. Multiplication and Division of Directed Numbers - Chapter : Using Algebra to. Introduction to 8 solve problem (I) Algebra 5. Algebraic Equations. Formulating Equations to Solve Problems -5 Chapter : Using Algebra to. Formulae Solve Problems (II). Algebraic Inequalities. Sequences. Simple Idea of Functions 5-6 Chapter : Introduction to. Basic Geometric 6 Geometry Concepts. Plane Figures. Solid Figures 6-7 Chapter 5: Percentages (I) 5. Simple Problems Involving Percentages 5. Percentage Change 5. Profit and Loss 5. Discount 8 Chapter 6: Estimation in 6.Estimation in Numbers Numbers and Measurement 6. Estimation in

2 Chapter 7: Area and Volume (I) Chapter 8: Introduction to coordinates Chapter 9: Symmetry and Transformation Chapter 0: Angles in Intersecting and Parallel Lines Chapter : Congruence and Similarity Chapter : Introduction to Statistics Measurement 7. Review on Areas of Simple Polygons 7. Total Surface Areas and Volumes of Prisms 8. Rectangular Coordinate System 8. Lengths of the Line Segments in the Rectangular Coordinate System 8. Areas of Plane Figures in the Rectangular Coordinate System 8. Polar Coordinates 9. Symmetry 9. Transformation 9. Transformations in a Rectangular Coordinate Plane ** Transformations in a Polar Coordinate Plane 0. Angles Relating to Intersecting Lines 0. Angles Relating to Parallel Lines 0. Conditions for Parallel Lines. The Meaning of Congruence. Conditions for Triangles to be Congruent. The Meaning of Similarity. Conditions for Triangles to be Similar. Different Stages of Statistics. Collection of Data and their Classifications

3 5. Organization of Data. Presentation and Analysis of Data.5 Uses and Misuses of Statistical Diagrams

4 Stewards Pooi Kei College Secondary Mathematics Teaching Schedule (07-08) Subject Teachers: Mr. Daniel Luk(Coordinator), Mr. Patrick Cheung, Ms. Katsy Wu No. of Periods/0-day Cycle: No. of No. of Cycles Periods Z Teaching Topics/Content Chapter Manipulations and Factorization of Polynomials Chapter Identities Chapter Approximation and Errors Chapter Formulae Chapter 5 Linear Equations in Two Unknowns Chapter 6 More About Data Handling Teaching Concepts Index Notation Laws of Positive Integral Indices Polynomials Addition and Subtraction of Polynomials Multiplication of Polynomials Factorization of Polynomials Meaning of Identities The Difference of Two Squares Identity The Perfect Square Identities Significant Figures Approximation and Errors in Measurement Algebraic Fractions Formulae and Substitution Change of Subject of a Formula Basic Knowledge of Linear Equations in Two Unknowns Solving Simultaneous Linear Equations in Two Unknowns by Graphical Method Solving Simultaneous Linear Equations in Two Unknowns by Algebraic Method Applications of Simultaneous Linear Equations in Two Unknowns Organization of Data Presentation of Data Cumulative Frequency

5 Misuse of Statistical Diagrams 8-9 Chapter 7 Rate Rate and Ratio Ratio Application of Ratio 9-0 Chapter 8 Angles and sides of a Triangle Angles in Triangles and Angles of a Polygon Polygons Basic Constructions 0- Book B Studying Geometry Using Deductive Chapter 9 Reasoning 6 Introduction to Deductive Deductive Approach to Properties of Geometry Geometric Figures - Chapter 0 Square Roots Pythagoras Theorem Pythagoras Theorem and Its Application Converse of Pythagoras Theorem and Its Application Rational Numbers and Irrational Numbers Operations of Surds - Chapter Concepts of Trigonometric Ratios Trigonometric Ratios The Sine Ratio The Cosine Ratio The Tangent Ratio Applications of Trigonometric Ratios Trigonometric Ratios of Some Special Angels Using Pythagoras Theorem to find Trigonometric Ratios Basic Knowledge of Trigonometric Identities 5 Chapter Circles Area and Volume (II) Arcs and Sectors Cylinders

6 Stewards Pooi Kei College Secondary Mathematics Teaching Schedule (07-08) Subject Teachers: Mr. Dennis Wong (S Coordinator), Ms. Shirley Tsang, Ms. Jovi Ma, Ms. Katsy Wu No. of Periods/0-day Cycle: No. of No. of Cycles Periods - - Teaching Topics/Content Chapter : Percentage Chapter : More about Factorization of Polynomials Teaching Concepts.0 Revision about percentage change. Simple Interest. Compound Interest. Increasing or Decreasing at a Constant Rate. More about Percentage Changes Successive Percentage Changes Percentage Changes of Different Components.5 Taxation Rates Salaries Tax. Factorization Using Identities Using the Difference of Two Squares Identity Using the Perfect Square Identities. Factorization using the cross-method. Factorization using the difference and sum of two cubes identities -.5 Chapter : Laws of Indices Chapter 6: Measures of central tendency and other statistical values. Zero Index and Negative Integral Indices. Scientific Notation. Notation for Different Numeral Systems. Inter-conversion of Numbers of Different Numeral Systems 6. Introduction to measures of central tendency mean, median, mode Constructing a Data Set from Known Averages Comparing Two Sets of Data with Known Averages

7 .5 6. Calculating the averages Calculate the averages for a set of discrete data Calculate the averages into intervals 6. Effects of changing data on averages 6. Further investigations on the applications of the mean weighted mean 6.5 Misuses of averages NSS Material: Measures of Dispersion Chapter : Coordinate Geometry of Straight Lines Chapter : Linear Inequalities in One Unknown Range and Inter-quartile Range Box-and-whisker Diagrams Comparing the Dispersions of Different Sets of Data Effects on the Dispersion with Change in Data. Distance between Two Points. Slope of a Straight Line Slope Formula Inclination. Parallel Lines and Perpendicular Lines Parallel Lines Perpendicular Lines. Point of Division Mid-point Formula Section Formula. Basic Knowledge of inequalities Solutions of in equalities and their representations Basic Properties of inequalities. Linear inequalities in One Unknown Solving linear inequalities in one unknown Applications of linear inequalities in one unknown 7-8 Chapter 7: More on Deductive Geometry 7. Solve geometric problems on triangles Congruent triangles Similar triangles

8 Chapter 8: Quadrilaterals Chapter 5: Introduction to Probability Chapter 0: Area and Volume (III) Isosceles triangles 7. Special lines in triangles 7. Relations between lines in a triangle Triangle inequality Relations between special lines in a triangle 8. Basic Knowledge of Special Quadrilaterals Basic Knowledge of Quadrilaterals Definitions of Special Quadrilaterals 8. Parallelograms Properties of Parallelograms Tests for Parallelograms 8. Rhombuses, Rectangles and Squares Properties of Rhombuses Properties of Rectangles Properties of Squares 8. Proofs Related to Parallelograms 8.5 Mid-point Theorem and Intercept Theorem Mid-point Theorem Intercept Theorem 5. The Meaning of Probability 5. More about Probability Methods for Listing Possible Outcomes Geometric Probability 5. Experimental Probability 5. Expected Values Expected Number of Occurrence Expected Value of a Variable 0. Pyramids Volume of a Pyramid Volume of a Frustum Surface Area of a Pyramid 0. Circular Cones Volume of a Right Circular Cone Volume of a Frustum Surface Area of a Right Circular Cone

9 Spheres Volume of a Sphere Surface Area of a Sphere 0. The Dimensions of Length, Area and Volume 0.5 Similar Plane Figures and Similar Solids Similar Plane Figures Similar Solids Chapter 9: More about -D Figures 9. Symmetry of -D Figures Reflectional Symmetry Rotational Symmetry 9. Nets of -D Figures 9. Further Knowledge on -D Representations of -D Objects Front, Side and Top Views of -D Objects Identifying -D Objects from Given -D Representations 9. Points, Straight Lines and Planes of -D Figures Distance between a Point and a Straight Line Distance between a Point and a Plane Relationship between Two Straight Lines Relationship between a Straight Line and a Plane Relationship between Two Planes 9.5 Knowledge on Regular Polyhedra 8 NSS Material: More about -D Figures Numerical Calculation of Angles between points, lines and planes 5 Chapter. Gradients

10 Applications in Gradient of an Inclined Plane Trigonometry Gradient and Inclination Gradient on Map. Angles of Elevation and Depression. Bearings 6 Revision

11 Stewards Pooi Kei College Secondary Mathematics Module Teaching Schedule (07-08) Subject Teachers: Mr. Jimmy Tse No. of Periods/0-day Cycle: 6 No. of Cycles No. of Periods Teaching Topics/Content Ch 0 Bridge Chapter Ch Surds, Mathematical Induction and Binomial Theorem Teaching Concepts To review the meaning of rational indices and the laws of rational indices. To review the meaning of logarithms and the properties of logarithms. To review the meaning of the notation n! To rationalize the denominators of expressions k of the form. a ± b To understand the principle of mathematical induction. To apple the principle of mathematical induction to prove propositions related to the summation of a finite sequence To understand the Binomial Theorem and use the theorem to expand binomials with positive integral indices. To prove the Binomial Theorem Ch. 0 Systems of Linear Equation To recognize the concept of systems of linear equations of order and order. To solve systems of linear equations of order and order by inverse matrix method, Cramer s rule To determine the number of solutions of a system of linear equations of order or order. 5 7 Ch. 0 To solve systems of linear equations of order

12 Systems of Linear Equation Ch. 9 Matrices and Determinants Chapter Limits and the Number e and order by inverse matrix method, Cramer s rule and Gaussian elimination. To determine the number of solutions of a system of linear equations of order or order. To find the general solution of a system of linear equations of order or order. To recognize the concept and features of systems of homogeneous linear equations. To understand the necessary and sufficient condition hat determines whether a system of homogeneous linear equations has non-trivial solutions. To understand the concept addition and scalar multiplication of matrices. To understand the properties of basic operations of matrices. To understand the multiplication of matrices To understand the properties of multiplication of matrices. To recognize the concept and properties of determinants of order and order. To understand the concept, operations and properties of inverses of square matrices of order and order. To understand the concept of the limit of a sequence. To recognize the number e as the limit of a special sequence, and know that e x can be expressed as an infinite series. To understand the concept of continuous and discontinuous functions and learn how to distinguish them from their graphs. To recognize the continuity of some special functions from their graphs, including the absolute value functions, signum function, ceiling function and floor function. To learn various theorems on limits of a function at a certain value, including those on the limits

13 0.5 of sum, difference, product, quotient, scalar multiple, composite functions, etc. and use them to find the limit. To learn various theorems on limits of a function at infinity and use them to find the limit. - Chapter Differentiation To understand the concept and definition of the derivative of a function and its notations. To learn the process of finding the derivatives of some basic functions from first principles. To understand some basic rules of differentiation: the constant rule, power rule constant factor rule, sum rule, difference rule, product rule, quotient rule and chain rule. -5 Chapter 5 Applications of Differentiation To find the equations of tangents and normals to a curve. To understand the concept of increasing and decreasing functions and the concavity of a function. To find maximum and minimum points and points of inflexion of functions and identify the global extrema. To sketch graphs of polynomial functions.

14 Stewards Pooi Kei College Secondary Mathematics Teaching Schedule (07-08) Subject Teachers: Ms. Candy Wong (S Coordinator), Ms. Connie Chow, Mr. Patrick Cheung, Mr. Daniel Luk No. of Periods/0-day Cycle: 0 No. of Cycles No. of Periods Teaching Topics/Content Teaching Concepts 0 Revision on Section A Review the junior topics on Section A - Book A Revise the concept of slope and coordinate Chapter geometry of straight lines. Equations of Straight Lines Identify the slope and y-intercept of given straight lines (with given coordinates). Sketch the straight lines by some given conditions. Learn to find the equation of a given straight line from its slope 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. Extended Mathematics: Apply rate of change to distance-time and Distance-time graphs speed-time graphs Book A Revise the techniques of solving linear Chapter.0 Review equations in one unknown and factorization of quadratic polynomials in one unknown. Chapter. Solving Quadratic Equations by the Factor Method Introduce to students the quadratic equations in one unknown and the principle of factor method: if mn = 0, then m = 0 or n = 0, and let students recognize the factor methods through examples. Through examples, let students learn to write a quadratic equation in one unknown in the

15 general form. Then, factorize the quadratic polynomial in one variable on one of the sides of the equation. Subsequently, find the roots of the equation. Point out to students that when the equation has two equal real roots (double roots, or known as repeated roots), this should be specified after the root. Remind students to pay attention to the cases of missing root(s). Chapter. Solving Quadratic Equations by the Quadratic Formula Point out the limitations on the factor method and explain to students the deduction process of the quadratic formula. Demonstrate to students how to solve quadratic equations in one unknown using the quadratic formula. Point out to students that a quadratic equation in one unknown can have two distinct real roots, two equal real roots (double roots) or no real roots. By making use of the web pages of computer programs on the internet, obtain approximated values of the required roots of a quadratic equations quickly. Chapter.5 Practical Problems Leading to Quadratic Equations Guide students to follow the steps involved when using quadratic equations in one unknown to solve practical problems. Remind students that meaningless answers or those not satisfying the given conditions must be rejected. Through examples, guide students to learn the required techniques involved in solving practical problems leading to quadratic equations. Chapter. Solving Quadratic Equations Through examples, guide students to draw the graph of the quadratic equation in two

16 by the Graphical Method 5 Book 5A Chapter More about Equations Chapter. Solving Simultaneous Equations by Graphical Method 5 Chapter. Solving Simultaneous Equations by Algebraic Method 5 Chapter. Relations between the Discriminant and the Nature of Roots unknowns within a specified range and let students recognize that the x-intercepts of the graph are the roots of the corresponding quadratic equations. Introduce the term parabola. Through examples, guide students to read the roots of the equation ax + bx + c = 0 off the x-intercepts of the graph of y = ax + bx + c. Hence realize that a quadratic equation may have two roots, two equal real roots (double roots) or no real roots. By making use of graphing software, obtain the graph of a quadratic equation in two unknowns and the approximated values of the real roots of the corresponding quadratic equation in one unknown. Through examples, guide students to draw the graph of y = ax + bx + c and to make use of it to solve the equation ax + bx + c = 0. Discuss with students the limitations on the graphical method and how to improve these limitations. Use the graphical method to solve simultaneous equations in two unknowns (one linear and one quadratic in the form y = ax + bx + c). Use the algebraic method to solve simultaneous equations in two unknowns (one linear and one quadratic). Guide students to determine the nature of roots of the quadratic equation ax + bx + c = 0 from the value of expression b ac instead of solving the equation and introduce the term discriminant, its symbol and pronunciation. Explain to students the relation between the

17 value of the discriminant and the number of real roots, and the relation between the value of discriminant and the number of x-intercepts in the corresponding graph of the quadratic equation in two unknowns. Discuss and investigate with students that the equation ax + bx + c = 0 must have two distinct real roots when a and c are opposite in signs. Through examples, consolidate students understanding about the discriminant. 5 Book.6 Forming Quadratic Equations 5-6 Chapter.7 Relations between Roots and Coefficients A. Sum and Product of Two Roots 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. Learn to use the relations between the roots and coefficients to form a quadratic equation. 6-7 BookB Chapter 0 Basic Properties of Circles Revise angles in lines and rectilinear figures, congruence and similarity and Pythagoras Theorem. 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

18 8 Chapter More about Basic Properties of Circles 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 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. 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

19 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 and in this chapter, prove more geometric properties related to circles by deduction. 9 Book A Chapter Number Systems Chapter.0 Review Review the concept of equations 9 Chapter. The Real Number System 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.

20 Recognize the relationships between real numbers and points on the number line. 9 Chapter. Complex Numbers 9 Chapter. Simple Arithmetic of 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. 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. 9 Chapter Basic Knowledge 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. 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

21 function. Perform four arithmetic of functions. Solve practical problems involving functions. 0 Chapter 5 Quadratic Functions Revise the perfect square identities. Recognize the graph of y=ax and its features. Further recognize the graph of y = ax 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. + bx + c 0- Chapter 6 More about Polynomials Revise the concept of polynomial. 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. Know how to factorize polynomials with

22 integral coefficients. - Chapter Basic Trigonometry Revise the knowledge about trigonometric ratios and the effects of transformation on the points in the coordinate plane. Understand angles of rotation and the quadrants in which they lie. Understand the definitions of the trigonometric ratios of any angle. Explore the change in the signs of the trigonometric ratios in different quadrants. Explore the patterns of the values of trigonometric ratios. Know how to use a calculator to find the values of trigonometric ratios of any angle. Learn the basic trigonometric identities. Know to use the identities to simplify trigonometric ratios of n 90 ±θ to those of θ. Recognize the graph of y = sin x. Recognize the graph of y = cos x. Recognize the graph of y = tan x. Learn to find the corresponding angle from the value of a given trigonometric ratio. Learn the method for solving equations involving one kind of trigonometric ratio. Learn the method for solving equations involving two kinds of trigonometric ratios. Book 5B Understand the basic concept of solving

23 - Chapter 9 Solving Triangles Book 5A Chapter 5 More about Probabilities triangles Understand the sine formula. Solve triangles or find the unknowns of the triangles by using the sine formula. Understand the cosine formula. Solve triangles or find the unknowns of the triangles by using the cosine formula. Understand the formula absin C for areas of triangles and use this formula to find the areas and unknowns of triangles. Understand Heron s formula and use this formula to find the areas or unknowns of triangles. Recognize the notation of set. Recognize the union, intersection and complement of set. Understand the concept of mutually exclusive events and the addition law of probability. Understand the concept of complementary events Understand the concept of independent events and the multiplication law of probability Recognize the concept and notation of conditional probability.

24 Stewards Pooi Kei College Secondary 5 Mathematics Module Teaching Schedule (07-08) Subject Teachers: Mr. Genthew Leung No. of Periods/0-day Cycle: 6 No. of No. of Cycles Periods 5 6 Teaching Topics/Content Chapter. Scalar Products and Vector Products Chapter Limits and the Number e Teaching Concepts To understand the definition and properties of the scalar product (dot product) of vectors. To understand the applications of the scalar product including finding angles between two vectors, determining orthogonally and finding the projection of a vector onto another vector. To understand the definition and properties of the vector product (cross product) of vectors in R. To understand the applications of the vector product including finding vectors orthogonal to two given vectors and the areas of parallelograms and triangles. To understand the properties of scalar triple products. To find the volume of a parallelepiped using scalar triple products. To find of a matrix for a given transformation of the plane, using the unit base vectors. To understand the concept of the limit of a sequence. To recognize the number e as the limit of a special sequence, and know that e x can be expressed as an infinite series. To recognize the definition and notation of the natural logarithm. To understand the concept of continuous and discontinuous functions and learn how to

25 distinguish them from their graphs. To recognize the continuity of some special functions from their graphs, including the absolute value functions, signum function, ceiling function and floor function. To learn various theorems on limits of a function at a certain value, including those on the limits of sum, difference, product, quotient, scalar multiple, composite functions, etc. and use them to find the limit. To learn finding the limit of a function by two special limits: 6 7 Z Chapter Differentiation x sinθ e lim and lim θ 0 θ x 0 x To learn various theorems on limits of a function at infinity and use them to find the limit. To understand the concept and definition of the derivative of a function and its notations. To learn the process of finding the derivatives of some basic functions from first principles. To understand some basic rules of differentiation: the constant rule, power rule constant factor rule, sum rule, difference rule, product rule, quotient rule and chain rule. To learn differentiation for different types of functions: trigonometric functions, exponential functions and logarithmic functions. 8 9 Chapter Differentiation To learn how to find derivatives by implicit differentiation. To understand the technique of logarithmic differentiation. To understand the meaning of second derivative and its notation. To learn how to find the second derivative of an

26 explicit function. 0 Chapter 5 Applications of Differentiation To find the equations of tangents and normals to a curve. To understand the concept of increasing and decreasing functions and the concavity of a function. To find maximum and minimum points and points of inflexion of functions and identify the global extrema. To sketch graphs of polynomial functions. To understand the concept of even and odd functions and to identify symmetry of a curve Chapter 5 Applications of Differentiation To identify the limitations on the values of x and y in rational function. To understand the concept of vertical, horizontal and oblique asymptotes of the graphs of rational functions. To sketch graphs of rational functions. To apply differentiation to solve the problems relating to rate of change, maximum and minimum. To draw and interpret graphs form given equation y = Ax + Bx + Cx + D + E x + F in which x the constants are numerical and at least three of them are zero.

27 Stewards Pooi Kei College Secondary 5 Mathematics Teaching Schedule (07-08) Subject Teachers: Mr. Sabrina Cheung (S5 Coordinator), Ms. Connie Chow, Ms. Joanna Leung, Mr. Daniel Luk and Mr. Dennis Wong No. of Periods/0-day Cycle: 9-0 No. of No. of Teaching Topics/Content Teaching Concepts Cycles Periods 6 Summer Homework Follow-up of summer homework - Book 5A Chapter 7 Review the knowledge of rate, ratio, percentages and linear equations in two unknowns. Variations Understand direct variations and their graphs. Know how to solve problems involving direct variation. Understand inverse variations and their graphs. Know how to solve problems involving inverse variation. Understand joint variations. Know how to solve problems involving joint variation. Understand partial variations. Know how to solve problems involving partial variation. Apply direct, inverse, joint and partial variations in solving real-life problems. - 6 Book 5B Chapter Applications in Trigonometry Apply knowledge in trigonometry in solving problems in -D. Apply knowledge in trigonometry in finding the angles and lengths in -D figures. Identify clearly the angles between two intersecting lines, the angles between a line and a plane and angles between two intersecting planes in a -D figure, and find related triangles to find the unknowns. Apply knowledge in trigonometry in solving

28 problems in -D (including problems involving height, the inclination, bearing, etc.) 5-6 Chapter 0 Rational Functions Revise the concepts of H.C.F. and L.C.M., the operations of polynomials and factor theorem. 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. 6-7 Book B Chapter 8 Exponential Functions Revise the concepts and laws of integral indices. 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. 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.

29 7-8 Book B Chapter 9 Logarithmic Functions 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. 9 Book5A Chapter 6 Explore and solve real-life problems related to probability.

30 0- Further Application of Mathematics Book5A Chapter 8 Equations of Circles Appreciate the connections between the following areas: Calculation of probability Calculation of expected value Estimation Explore and solve real-life problems related to profit, selling price and maximum value. Appreciate the connections between the following areas: Applications of percentages Using a polynomial to express a value Using a function to represent a value Finding the maximum value of a function Review equations of straight lines, the nature of roots of quadratic equations and the basic properties of circles. Recognize the standard form of the equations of circles. Learn to find the equations of circles in the standard form. Recognize the general form of the equations of circles. Learn to convert the equation of a circle into the general form. Learn to find the coordinates of the centre, the radius or other information from the equations of circles. Learn to determine if a given point lies inside, outside or on the circle. Determine the nature of circles from the equations. Learn to find the equations of circles from different given conditions. Understand the possible points of intersection of a straight line and a circle. Learn to find the number of points of intersection of a straight line and a circle. Learn to find the coordinates of points of intersection of a straight line and a circle.

31 Book5A Chapter 9 Locus Book5A Chapter Measures of Dispersion Book5A Chapter More about Dispersion Learn to find the equations of tangents to a circle. Review the distance between a point and a line, the distance between two parallel lines, and the distance formula. Understand the concept of locus. Learn to describe and sketch the locus of points satisfying given conditions. Understand that the same type of locus can be formed under different conditions. Learn to describe the locus of points with algebraic equations including equations of straight lines, circles and parabolas. Review continuous data, cumulative frequency and measures of central tendency. Understand the basic concepts of dispersion. Find the range for ungrouped data and grouped data. Use range to compare the dispersions of two sets of data. Find the inter-quartile range for ungrouped data and grouped data. Use inter-quartile range to compare the dispersions of two sets of data. Learn how to draw a box-and-whisker diagram. Interpret a box-and-whisker diagram. Learn to compare the distributions of different sets of data by box-and-whisker diagrams. Find the standard deviation for ungrouped data and grouped data. Use standard deviation to compare the dispersions of two sets of data. Able to choose a suitable measure of dispersion to compare the dispersions of different sets of data. Compare precision and consistency by standard deviation. Understand the application of standard deviation in real-life problems involving standard score.

32 Understand the application of standard deviation in real-life problems involving normal distribution. Explore the effect on dispersion when a common constant is added to or subtracted from each datum. Explore the effect on dispersion when each datum is multiplied by a positive constant. Explore the effect on dispersion when a datum is deleted from a set of data. Explore the effect on dispersion when a datum is added to a set of data. 5 Book 5B Chapter Linear Inequalities in One Unknowns Compound Linear Inequalities in One Unknown Solving Quadratic Inequalities in One Unknown by the Graphical Method Solving Quadratic Inequalities in One Unknown by the Algebraic Method 5-6 Book 6 Chapter Linear Inequalities in Two Unknowns and Linear Programming Review compound inequalities involving AND Solve linear inequalities in two unknowns graphically. Solve systems of linear inequalities in two unknowns graphically. 7 Book5A Chapter Further Applications of Mathematics 7 Revision Recognize a surveying activity. Explore and solve more sophisticated real-life problems related to trigonometry. Appreciate the connections between the following areas: trigonometry of right-angled triangles sine formula and cosine formula equation of circles use of rate quadratic equations in one unknown

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34 Stewards Pooi Kei College Secondary 6 Mathematics Module Teaching Schedule (07-08) Subject Teachers: Mr. Genthew Leung No. of Periods/0-day Cycle: 6 No. of No. of Teaching Topics/Content Teaching Concepts Cycles Periods - Ch 6 To understand the concept of indefinite X Indefinite Integration integration as a reverse process of differentiation. To understand the primitive function of a function is not unique and the meaning of the notation of indefinite integration. To master the basic rules and properties of indefinite integration and use them to find simple indefinite integrals of algebraic functions. To use the basic rules and properties of indefinite integration to find indefinite integrals of other function. To apple indefinite integration in find the equations of curves and other physical applications. To understand the concept of integration by substitution and to use this method to find indefinite integrals. To learn some other techniques of integration involving trigonometric functions. To understand the concept of integration by parts and to use this method to find indefinite integrals. Ch 7 To recognize the concept of definite Definite Integration integration as the limit of a sum and find definite integrals from definition. To understand the properties of definite

35 Chapter 8 Applications of Definite Integration Areas of Plane Figures integrals. To understand the Fundamental Theorem of Calculus. To find definite integrals of algebraic functions, trigonometric functions and exponential functions. To use integration by substitution to find definite integrals. To use integration by parts to find definite integrals. To understand the properties of the definite integrals of even, odd and periodic functions. Review graphs of quadratic functions, point(s) of intersection of two graphs and the volume of a cylinder. Understand the concept to apply the definite integrals in finding the area of a plane figure. Know how to find the area between a curve and the x-axis. Know how to find the area between a curve and the y-axis. Know how to find the area between two given curves. -5 Volumes of Solids of Revolution 6 Ch More about Trigonometric Functions (half of the chapter has been taught in S.5) Understand solids of revolution. Use the disc method to find the volume of a solid (or hollow solid) of revolution about a coordinate axis. Use either the disc method or the shell method to find the volume of a solid (or hollow solid) of revolution about a line parallel to a coordinate axis. To understand the concept of radian measure. To find arc lengths and areas of sectors through radian measure. To recognize trigonometric functions like cosecant, secant and cotangent and their graphs.

36 To learn various trigonometric identities. To simplify expressions using trigonometric identities. To understand compound angle formulae and double angle formulae for the functions sine, cosine and tangent. To understand product-to-sum and sum-to-product formulae for the functions sine and cosine. 7 Revision by Sections Paper Practice 8,9 Revision

37 Stewards Pooi Kei College Secondary 6 Mathematics Teaching Schedule (07-08) Subject Teachers: Mr. Jimmy Tse (S6 Coordinator), Mr. Genthew Leung, Ms. Joanna Leung, Mr. Dennis Wong, Ms Candy Wong No. of Periods/0-day Cycle: - No. of No. of Teaching Topics/Content Teaching Concepts Cycles Periods Summer Homework Review of Summer Homework - Book5A Recognize the definitions of mutually exclusive Chapter events and non-mutually exclusive events, and Permutation and Combination understand the addition rule in the counting principle. Understand the multiplication rule in the counting principle. Understand the concept and notation of permutation. Recognize the definition and notation of factorial. Know how to solve problems on the permutation of distinct objects without repetition. Understand the concept of combination and the difference between combinations and permutations. Solve problems on the combination of distinct objects without repetition. Solve related problems in daily life application and past exam papers.

38 Book 6 Chapter Arithmetic Sequences Review the basic knowledge of sequence. Understand the relationship between two adjacent terms of an arithmetic sequence and the meaning of common difference. Be able to determine whether a given sequence is an arithmetic sequence. Understand the general term of an arithmetic sequence. Make use of the general term formula of an arithmetic sequence to find the first term, number of terms or common difference. Understand some important properties of arithmetic sequences. Understand the summation formula of arithmetic sequences and use the formula to solve problems. Apply arithmetic sequences and their summation to solve related problems including geometrical problems and daily-life application problems Book 6 Chapter Geometric Sequences Understand the relationship between two adjacent terms in a geometric sequence and the meaning of common ratio. Determine whether a given sequence is a geometric sequence. Understand the general term of a geometric sequence. Find the first term, the number of terms and the common ratio of a geometric sequence by using the formula of the general term. Understand some important properties of geometric sequences. Understand the formula of the sum of a geometric sequence and use the formula to solve related problems.

39 Book 5A Chapter More about Graphs of Functions Understand the meaning of infinity. Explore the formula of the sum to infinity of a geometric sequence and use the formula to solve related problems. Apply geometric sequences and their summation to solve related problems, including geometrical problems and real-life problems. Revise the knowledge of functions, symmetry and transformation. Revise the graphs of some common functions. Revise the properties of graphs of functions. Learn how to solve an equation by using the intersection points of the corresponding graph and the x-axis. Learn how to solve an equation by using the intersection points of the corresponding graph and a horizontal line. Understand the meaning of different regions on the graph of a function, and hence find the solutions of inequalities involving functions. Comprehend the meanings of translating upward, downward, to the left and to the right, and the effects of these transformations on function relations. Grasp the meanings of enlargement and reduction along the x-axis or the y-axis, and the effects of these transformations on function relations. Understand the meanings of reflection in the x-axis or the y-axis, and the effects of these transformations on function relations Book 6 Chapter Uses and Abuses of Statistics Recognize the concepts of populations and samples and understand their relations. Understand the necessity of sample survey in statistical activities. Recognize some methods of probability sampling.

40 Recognize some methods of non-probability sampling. Understand the differences between probability sampling and non-probability sampling. Learn the use of wording in designing questionnaires. Learn the setting of appropriate answer options in designing questionnaires. Learn to know that questions in designing questionnaires should be arranged logically. Discuss the uses of statistical surveys. Discuss the abuses of statistical surveys. Assess the credibility of different statistical survey reports.