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LIU PO SHAN MEMORIAL COLLEGE S2 MATHEMATICS TEACHING SCHEDULE (2011 – 2012) Week and Date 1 – 3 (2/9 – 14/9) 3 – 5 (15/9 – 30/9) 6–8 (29/9 – 26/10) 9 – 10 (28/10 – 2/11) 10 – 12 (3/11 – 16/11) 13 – 15 (17/11 – 6/12) 15 – 17 (7/12 – 21/12) 17 –19 (23/12 – 2/1) 19 (4/1 – 5/1) 19 – 21 (6/1 – 19/1) 21 – 23 (20/1 – 31/1) 23 – 25 (1/2 – 16/2) 25 – 27 (17/2 – 1/3) 27 – 28 (2/3 – 9/3) 29 - 30 (12/3 – 22/3) 31 (26/3 – 29/3) 31 – 34 (30/3 – 18/4) 34 – 35 35 – 39 38 – 41 41 – 44 (19/4 – 3/5) (4/5 – 21/5) (22/5 – 7/6) (8/6 – 21/6) Chapter Topic Ch 2 Introduction to Polynomials Ch 3 Identities Ch 4 Formulas 1st term test Ch 5 Linear Equations in Two Unknowns Ch 6 Rate and Ratio Ch 1 Approximation and Errors Christmas Holiday Revision 1st term examination Chinese New Year Holiday Ch 7 Handling Continuous Data Ch 8 Angles in Triangles and Polygons Ch 9 Introduction to Deductive Geometry Ch 10 Pythagoras’ Theorem 2nd term test Ch 11 Trigonometric Ratios Ching Ming Festival and Easter Holiday (4/4 – 15/4) Ch 11 Trigonometric Ratios Ch 12 Area and Volume (II) Ch 12 Area and Volume (II) 2nd term examination Setter: 1st term test : Sze Siu Yu 1st term examination : Kwok Wing Fai 2nd term test : Lo Yee Ting 2nd term examination : Fung Pui Ling Codes : I --- I. T C--- Civic Education P --- Project R --- Reading No. of School Days 8 12 16 (total : 36) 10 11 11 (total : 32) 2 (total : 2) 12 10 6 9 (total : 37) 6 10 10 12 (total : 38) LD---Learning Diversity T --- Tailor 1 TEXTBOOK : New Century Mathematics (2A, 2B) TEACHER : Lo Yee Ting, Fung Pui Ling, Sze Siu Yu, Kwok Wing Fai Ch 2 Introduction to Polynomials Week 1–3 Section LearningTargets Exercises 2.1 Index Notation •Learn the index notation. Ex. 2A : 3, 4, 5, 6, 7, 8, __, __ Ex. 2B 1, 2, 3, 4, 5, 6, 7, 8, 12-15,__, __ 2.2 Laws of Indices A. Multiplication of Powers B. Division of Powers C. Powers of Powers D. Powers of Products and Powers of Quotients 2.3 Polynomials A. Basic Knowledge about Polynomials B. The Degree of a Polynomial C. Arrangement of Terms of a Polynomial D. Value of a Polynomial • Explore the multiplication law of indices for positive integers. •Explore the division law of indices for positive integers. • Explore the power law of indices for positive integers. • Explore the powers of products and quotients for positive integral indices. • Recognize polynomial and the meaning of the terminology involved. • Understand the degree of polynomial. • Learn different ways to arrange the terms in polynomial. •Learn to find the value of polynomial. Ex. 2C 4, 5, 6, 7, 8, 9,10,__, __ 2.4 Addition and Subtraction of Polynomials • Learn the addition and subtraction of polynomials. Ex. 2D 1, 2, 3, 4, 5, 6, 7, 8, ,__, __ 2.5 Multiplication of Polynomials • Learn the multiplication of polynomials. Ex. 2E 1, 3, 5, 7, 9, 11, 13,__, __ 2.6 Simple Factorization of Polynomials A. Taking out Common Factors B. Grouping Terms • Understand factorization as a reverse process of expansion. • Learn the method of taking out common factors. Ex. 2F 1, 3, 5, 7, 9, 11, 13,__, __ Remarks I: E-book Supp. Ex. 2 Challenging Problems 2 Revision Test MC(LD) 2 Ch 3 Week 3-5 Identities Section 6-8 Exercises 3.1 Meaning of Identities A. Meaning of Identities and the Tests for Identities B. Finding Unknown Constants in and Identity • Explore the meaning of identities. • Distinguish between equations and identities. •Find unknown coefficients or constants in identities. Ex. 3A 1, 3, 5, 7, 9, 11, 13,__, __ 3.2 The Difference of Two Squares •Discover and use the difference of two squares identity. Ex. 3B 1, 4, 7, 10, 13, 16, __, __ 3.3 The Perfect Square Identities A. Square of Sum of Two Numbers B. Square of Difference of Two Numbers • Discover and use the identity related to (a + b)2. •Discover and use the identity related to (a − b)2. Ex.3C 1, 3, 5, 7, 9, 11, 13, 15, 17, __, __ Ch 4 Week LearningTargets Remarks I: E-book Workbook 2A Supp. Ex. 3 Test Bank (Chap. 3) Revision Test MC(LD) Formulas Section LearningTargets 4.1 Simple Algebraic Fractions A. Simplification of Algebraic Fractions B. Operations on Algebraic Fractions • Recognize and simplify simple algebraic fractions. •Learn the operations on simple algebraic fractions. 4.2 Formulas and Substitution • Study the meaning of formulas and the use of substitution in formulas. Exercises Ex.4A 1, 4, 7, 10, 13, 16, 19,__, __ Ex. 4B 1, 3, 5, 7, 9, 11, __, __ Remarks I: E-book Supp. Ex. 4 Challenging Problems 4 Revision Test MC MC(LD) 3 4.3 Change of Subject of a Formula Ch 5 Week 10-12 • Identify the subject of a formula and learn how to change the subject of a formula from one variable to another variable. Ex. 4C 1, 3, 5, 7, 9, 11, 13,__, __ Linear Equations in Two Unknowns Section LearningTargets Exercises 5.1 Basic Knowledge of Linear Equations in Two Unknowns A. Solutions of Linear Equations in Two Unknowns B. Graphs of Linear Equations in Two Unknowns 5.2 Solving Simultaneous Linear Equations in Two Unknowns by the Graphical Method • Recognize linear equations in one unknown/two unknowns. • Know how to find the solutions of linear equations in two unknowns. •Explore and plot the graphs of linear equations in two unknowns. Ex. 5A 2, 3, 4, 5, __, __ • Explore the meaning of simultaneous equations. • Learn to solve simultaneous equations by graphical method. . Ex. 5B 1, 2, 3, 4, 5, 6, __, __ 5.3 Solving Simultaneous Linear Equations in Two Unknowns by Algebraic Methods A. Method of Substitution B. Method of Elimination • Learn to solve simultaneous equations by method of substitution. • Learn to solve simultaneous equations by method of elimination. Ex.5C 1, 3, 5, 7, 9, __, __ 5.4 Applications of Simultaneous Linear Equations in Two Unknowns •Learn to use algebraic language to formulate simultaneous equations and solve problems. Ex. 5D 1, 3, 5, 7, 9, __, __ Remarks I: E-book Supp. Ex. 5 Challenging Problems 5 Revision Test MC (LD) Ex. 5E 1, 2, 3, 4, 5, __, __ 4 Ch 6 Week 13-15 Rate and Ratio Section LearningTargets 6.1 Rate •Understand the meaning of rate. Ex. 6A 1, 2, 3, 4, 6, 7,__, __ 6.2 Ratio A. The Meaning of Ratio B. Simplification of Ratio C. Three-term Ratio D. Dividing a Quantity in a Given Ratio • Understand the meaning of ratio. • Recognize the notation of two-term ratio a : b. • Learn the simplification of ratio. •Recognize the notation of three-term ratio •Know how to divide a quantity under a given ratio. Ex. 6B 3, 4, 5, 6, 7,__, __ 6.3 Applications of Ratio A. Similar Figures B. Scale Drawings Ch 1 Week 15-17 Exercises Remarks I: E-book a : b : c. • Understand the meaning of scale factor. • Apply scale factor to solve real-life problems involving similar figures. • Apply scale factor to solve real-life problems involving scale drawings such as maps and plans Ex. 6C 1, 2, 3, 4, 5, __, __ Supp. Ex. 6 Challenging Problems 6 Revision Test MC (LD) Approximation and Errors Section 1.1 Significant Figures A. Basic Concepts of Significant Figures B. Round-off to Required Number of Significant Figures C. Using Significant Figures in Estimation LearningTargets Exercises • Learn the basic concepts of significant figures. •Learn the skills of rounding off numbers to required number of significant figures. •Learn how to use significant figures in estimation. Ex. 1A 2, 3, 5, 6, 7, __, __ Remarks I: E-book Supp. Ex. 1 5 1.2 Approximation and Errors in Measurement A. The Appropriate Nature of Measurement B. Errors in Measurement C. Relative Error D. Percentage Error Ch 7 Week 23-25 • Recognize the approximate nature of measurement. • Learn the concept of error. • Learn how to estimate the maximum error of a measurement. • Understand and calculate relative error. • Understand and calculate percentage error. Ex. 2, 3, 4, 5, 6,__, __ Challenging Problems 1 Revision Test MC (LD) Handling Continuous Data Section 7.1 Organization of Continuous Data LearningTargets • Learn how to organize a given set of continuous data. . Exercises Ex. 7A 1, 2, 3, 4, __, __ Remarks I: E-book T: Class 2A 7.2 A. B. C. 7.3 A. B. C. Presentation of Continuous Data Histogram Frequency Polygon Frequency Curve Cumulative Frequency Cumulative Frequency Table Cumulative Frequency Polygon Cumulative Frequency Curve 7.4 Misuses of Statistical Diagrams A. Mislead People by Using an Improper Scale B. Mislead people by Covering up Parts of Data C. Using an Improper Statistical Diagram • Learn to construct and interpret histogram. • Learn to construct and interpret frequency polygon • Learn to construct and interpret frequency curve. Ex. 7B 1, 2, 3, 4, __, __ • Understand and know how to construct cumulative frequency table. • Understand, construct and interpret cumulative frequency polygon. • Understand, construct and interpret cumulative frequency curve. Ex. 7C 1, 2, 3, 4, __, __ and Class 2B will not teach Chapter 7.4 Misuses of Statistical Diagrams. Aware of the use of improper scales in statistical graphs that may cause misinterpretation. • Aware of statistical graphs that hide part of data to cause misinterpretation. •Aware of the use of improper statistical graphs that may cause misinterpretation. Ex. 7D 1, 2, 3, 4, __, __ Supp. Ex. 7 Challenging Problems 7 Revision Test MC (LD) 6 Ch 8 Week 25-27 Angles in Triangles and Polygons Section LearningTargets Exercises 8.1 Angles and Sides of a Triangle A. Exterior Angles of a Triangle B. Isosceles Triangles C. Equilateral Triangles • Explore and use the property of exterior angles of a triangle. • Explore and use the properties of isosceles triangles. • Explore the conditions for a triangle to be isosceles. • Explore and use the properties of equilateral triangles Ex. 8A 1, 3, 5, 7, 9, __, __ 8.2 A. B. C. • Explore and use the formula for the sum of the interior angles of polygons. • Explore and use the formula for the sum of the exterior angles of polygons. • Explore regular polygons that tessellate. Ex. 8B 1, 3, 5, 7, 9, __, __ Ex. 8C 1, 3, 5, 7, 9, __, __ Angles of a Polygon Sum of Interior Angles of a Polygon Sum of Exterior Angles of a Polygon Tessellation Ex. 8D 1, 3, 5, 7, 9, __, __ Ch 9 Week 27-28 Remarks I: E-book Supp. Ex. 8 Challenging Problems 8 Revision Test MC (LD) T: T: All students will not teach chapter 8.3 Introduction to Deductive Geometry Section 9.1 Studying Geometry Using Deductive Reasoning A. Limitations of the Intuitive Approach B. Deductive Approach 9.2 Deductive Approach to Properties of Geometric Figures A. Proving Geometric Properties Relating to Intersecting and Parallel Lines B. Proving Geometric Properties Relating to Triangles LearningTargets Exercises Remarks • Recognize the limitations of the intuitive approach in learning geometry. • Learn the basic concept of deductive approach. Ex. 9 1, 2, 3, 4, __, ___ T: Class 2A 2B will not teach this topic •• Prove geometric properties related to intersecting lines and parallel lines by the deductive approach. • Prove geometric properties related to triangles by the deductive approach. (T) Ex. 9 6, 7, 8, 9, __ , __ I: E-book Supp. Ex. 9 Challenging Problems 9 Revision Test MC (LD) 7 Ch 10 Week 29-30 Pythagoras’ Theorem Section 10.1 Square Roots A. Introduction to Square Roots B. Finding the Values of Square Roots Using a Calculator 10.2 Pythagoras’ Theorem and Its Applications A. Introduction to Pythagoras’ Theorem B. Applications of Pythagoras’ Theorem C. The Beauty of Mathematics: The Discovery and Proofs of Pythagoras’ Theorem LearningTargets Exercises • Learn the meaning of square root and the method to represent square root. • Learn to use a calculator to obtain square roots of a number. Ex.10A 4, 5, 6, 7, 8, 9, __, __ • Explore the relations between the three sides of a right-angled triangle. • Introduce Pythagoras’ theorem and its simple application. • Learn applications of Pythagoras’ theorem on simple geometric figures. Use Pythagoras’ theorem to solve real-life problems involving lengths of sides of right-angled triangles. • Appreciate different proofs of Pythagoras’ theorem including those from ancient China. Ex. 10B 3, 4, 5, 6, 7, 8, 9, __, __ 10.3 Converse of Pythagoras’ Theorem and Its Applications •Learn the converse of Pythagoras’ theorem and use it to solve problems. Ex. 10C 3, 4, 5, 6, 7, 8, 9, __, __ 10.4 Rational Numbers and Irrational Numbers A. Integers, Fractions and Decimals B. Irrational Numbers C. Representation of Rational and Irrational Numbers on a Number Line • Revise the concepts of integers, fractions and decimals. •Introduce the concept of rational numbers. •Recognize the existence of irrational numbers and surds. • Explore how to represent rational numbers and irrational numbers on the number line. Ex. 10D 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, __, __ 10.5 Operations of Surds A. Simplification of Surds B. Addition, Subtraction and Multiplication of Surds C. Division of Surds • • • • • • Understand the meaning of surds as irrational numbers. Learn the rules for multiplying surds. Understand how to express a given surd in its simplest form. Learn the addition and subtraction of surds. Learn the multiplication of surds. Learn the division of surds. Remarks I: E-book Supp. Ex. 10 T: All students will not teach chapter 10.4C Challenging Problems 10 Revision Test MC (LD) Ex. 10E 4, 5, 6, 7, 8, 9, __, __ • Learn how to rationalize the denominators of the form a . • Learn the mixed operations of surds involving multiplication and division. 8 Ch 11 Week 31-35 Trigonometric Ratios Section LearningTargets Exercises 11.1 Concepts of Trigonometric Ratios •Recognize trigonometry and some related basic terms. Ex.11A 4, 5, 6, 7, 8, 9, __, __ 11.2 The Sine Ratio A. Ratio of Opposite Side to Hypotenuse B. Using a Calculator to Find sin C. Finding Angle from sin D. Simple Applications of the Sine Ratio • Understand the sine ratio for angles between 0° and 90°. •Learn to find the sine ratio of an acute angle in a right-angled triangle. •Learn how to use a calculator to find sin • Learn how to find the angle from given sin . •Study some simple applications of the sine ratio. • Understand the cosine ratio for angles between 0° and 90°. • Learn to find the cosine ratio of an acute angle in a right-angled triangle. •Learn how to use a calculator to find cos or the corresponding angle . • Study some simple applications of the cosine ratio. Ex. 11B 1, 2, 3, 4, 5, 6, __, __ • Understand the tangent ratio for angles between 0° and 90°. •Learn to find the tangent ratio of an acute angle in a right-angled triangle •Learn how to use a calculator to find tan or the corresponding angle . •Study some simple applications of the tangent ratio. Ex. 11D 1, 2, 3, 4, 5, 6, __, __ 11.3 The Cosine Ratio A. Ratio of Adjacent Side to Hypotenuse B. Using a Calculator to Find cos or the Corresponding Angle C. Simple Applications of the Cosine Ratio 11.4 The Tangent Ratio A. Ratio of Opposite Side to Adjacent Side B. Using a Calculator to Find tan or the Corresponding Angle C. Simple Applications of the Tangent Ratio 11.5 Applications of Trigonometric Ratios A. Solving Problems Involving Plane Figures B. Solving Real-life Problems 11.6 Trigonometric Ratios of Some Special Angles 11.7 Using Pythagoras’ Theorem to Find Trigonometric Ratios Ex. 11C 1, 2, 3, 4, 5, 6, __, __ • Learn to apply the sine ratio, cosine ratio and tangent ratio to find unknowns in plane figures. • Learn to apply the trigonometric ratios to solve real-life problems Ex. 11E 1, 2, 3, 4, 5, 6, __, __ • Explore the exact values of trigonometric ratios of the special angles 30°, 45° and 60°. Ex. 11F 1, 2, 3, 4, 5, 6, __, __ • Find trigonometric ratios of any acute angle by means of Pythagoras’ theorem. Ex. 11H 1, 2, 3, 4, 5, 6, __, __ Remarks I: E-book Supp. Ex. 11 Challenging Problems 11 Revision Test MC (LD) T: Class 2A 2B students will not teach chapter 11.8D 9 11.8 Basic Knowledge of Trigonometric Identities A. Ratio of sin to cos B. Sum of Squares of sin and cos C. Trigonometric Ratios of Complementary Angles Ch 12 Week 35-41 • Learn and use the identity tan sin . cos Ex. 11I 1, 2, 3, 4, 5, 6, __, __ • Learn and use the identity sin 2 cos2 1. • Learn the relations between trigonometric ratios of complementary angles Area and Volume (II) Section 12.1 Circles A. Review on Circumference of a Circle B. Area of a Circle 12.2 Arcs and Sectors A. Length of an Arc B. Area of a Sector 12.3 Cylinders A. Surface Area of a Cylinder B. Volume of a Cylinder LearningTargets • Calculate the circumference of a circle. • Explore and use the formula for the area of a circle. Exercises Ex. 12A 1, 2, 3, 4, 5, 6, 7,__, __ •Find any trigonometric ratio between 0° and 90° by means of Pythagoras’ theorem.. Ex. 12B 1, 2, 3, 4, 5, 6, 7,__, __ • Understand and use the formula for the surface area of a cylinder. •Understand and use the formula for the volume of a cylinder. Ex.12C 1, 2, 3, 4, 5, 6, __, __ Remarks I: E-book Supp. Ex. 12 Challenging Problems 12 Revision Test MC (LD) 10