LIU PO SHAN MEMORIAL COLLEGE SCHEME OF WORK (2014-2015) MATHEMATICS PANEL Secondary : Coordinator : Periods per week : Textbook : Date/Week SUMMER HOLIDAY Five (Mathematics Module 2) SIU Kai Yiu 3 New Progress in Senior Mathematics Module 2 Book 1 and 2 (Hong Kong Educational Publishing Co.) No. of Lessons Contents (15 hours) Chapter 4 Limits and Derivatives 4.1 Limits of functions Objectives Assignments - To understand the concepts of limits, discontinuous functions and continuous functions. Ex. 4.1 : Q.5,6 4.2 Find the Limit of a Function - To find the limits of functions with Ex. 4.2 : the use of rationalization Q.7,8,9,12,15,16,17,18,20,22 4.3 - To learn the concept of limits at infinity Limits at Infinity Ex. 4.3 : Q.2,4,6,8,10,12,15,16,19,20,21 Remarks I - Use GeoGebra to demonstrate the shape of curves of functions - To find the limits at infinity 4.4 Limits of Trigonometric Functions 4.5 Derivatives - To evaluate the limits of trigonometric functions Ex. 4.4 : Q.2,4,6,8,10,12,14,16,18,19 - To understand the definition of a Ex. 4.5 : tangent to a curve and learn the Q.2,3,6,8,9,10,14,16,17,18,21 method of finding the slopes of the tangents to a curve Supplementary Exercise - To define the derivative of a function - To evaluate the derivatives of functions from first principles Past Paper Questions I - Use GeoGebra to explain the concept of first principles of derivative Date/Week WEEK 1 to 4 No. of Lessons Contents (12 hours) Chapter 5 Differentiation (1) 5.1 Rules of Differentiation Objectives Assignments Remarks - To understand the concept of derivative of a function Ex. 5.1 : Q.6,7,9,12,13,15,17,19,21,23,25, 27,28 R - Ask students to derive the rules of differentiation from first principles. - To use the power rule, addition rule, product rule and quotient rule to find derivatives of functions. 5.2 Differentiation of composite functions - To use the chain rule to find the derivatives of functions with or without given substitutions of ‘intermediate’ functions Ex. 5.2 : Q.6,8,12,14,15,17,19,21,23,26,28, 30,31,33 5.3 Differentiation of Implicit Functions - To find the derivatives of implicit functions with the application of finding the slopes of tangents at given points Ex. 5.3 : Q.4,6,8,10,12,14,15,18,20,22 Supplementary Exercise Past Paper Questions WEEK 5 to 9 (15 hours) Chapter 6 Differentiation(2) 6.1 Differentiation of Exponential and Logarithmic Functions - To find the derivatives of functions Ex. 6.1 : involving exponential and Q.3,6,7,8,12,15,16,18,20,22,24,25, logarithmic functions 27,29,32,33,35,37,40,41 6.2 Differentiation of Trigonometric - To find the derivatives of functions Ex. 6.2 : Functions involving trigonometric functions Q.8,9,11,13,15,19,20,21,23,28,29, 32,33,35,37,41,43,45,48,49 - To find the second derivatives of an 6.3 Second Derivatives explicit function Ex.6.3 : Q.4,6,7,10,11,14,16,18,19,22,23,25,27 Supplementary Exercise Past Paper Questions Date/Week No. of Lessons Contents WEEK 10 to 17 (24 hours) Chapter 7 Applications of Differentiation 7.1 Tangents and Normals Objectives Assignments To find the equations of tangents and normals to a curve Ex. 7.1: Q.3,6,7,12,14,16,17,20,22, 24, 26 To find maxima and minima Ex. 7.2: Q.4,6,9,10,12,13,15,18 7.3 Curve Sketching To sketch curves of polynomial functions and rational functions Ex. 7.3: Q.4,5,8,9,10,12,14,16,17,19,20 7.4 Optimization Problems To solve the problems relating to maximum and minimum Ex. 7.4: Q.3,5,8,9,10,14,17,19,22,24 7.5 To solve the problems relating to rate Ex. 7.5: of change Q.3,6,7,10,12,14,16,18 7.2 Local Extrema and Derivative Tests Rates of Change Supplementary Exercise Past Paper Questions WEEK 19 to 20 FIRST TERM EXAMINATION WEEK 21 to 24 (27 hours) WEEK 26 to 30 Chapter 8 Indefinite Integrals 8.1 Concepts of Indefinite Integrals - To emphasize that d F(x) = f(x) dx f(x) dx = F(x) + c . - To introduce the terms primitive function, integral sign, integrand and constant of integration. Ex. 8.1 : Q.4,8,10,14,18,20,22,24,26, 28,32,34,36,38,40,42,44 Remarks I – Using GeoGebra to draw the graphs of polynomial functions and rational functions CLP - Help students to understand daily examples of optimization CLP - Help students to apply the concept of rates of change to understand real life problems in Physics and Engineering Date/Week No. of Lessons Contents 8.2 Indefinite Integration of Functions Objectives - To introduce the concept of indefinite integrals and some integration formulae. Assignments Ex. 8.2 : Q. 6, 8, 10, 12, 14, 16, 20, 22, 24, 26, 28, 32, 34, 36, 37, 39, 42, 43 - To introduce the simple properties : f(x) g(x) dx = f(x) dx g(x) dx and k f(x) dx = k f(x) dx - To derive the integration formulas for more complicated functions from the formulas of differentiation. - To find indefinite integrals of more complicated functions involving the expression (ax + b) or trigonometric functions 8.3 Integration by Substitution - To find indefinite integrals using integration by substitution. - To find indefinite integrals involving powers of trigonometric functions. Ex. 8.3 : Q. 6, 8, 10, 12, 14, 16, 19, 23, 25, 26, 27, 30, 32, 36, 38, 41, 44, 45, 46, 50, 52, 54, 56, 58 - To find indefinite integrals involving a 2 x 2 , x 2 a 2 or a 2 x 2 using trigonometric substitution 8.4 Integration by Parts - To illustrate the technique of integration by parts include x xe dx , x sin xdx and ln xdx . - To find indefinite integrals by using substitution and integration by parts. Ex. 8.4 : Q. 3, 6, 8, 9, 11, 14, 16, 20, 21, 23, 25, 27, 29, 31, 33 Remarks Date/Week No. of Lessons Contents 8.5 Applications of Indefinite Integrals WEEK 33 to 39 (21 hours) Chapter 9 Definite Integrals 9.1 Concepts of Definite Integrals Objectives - To solve geometrical application problems of indefinite integrals, application problems of indefinite integrals in physics, and other application problems of indefinite integrals. Assignments Ex. 8.5 : Q. 3, 6, 9, 11, 14, 16, 18, 20, 22 Supplementary Exercise Past Paper Questions - To recognize the concept of definite Ex. 9.1 : Q.2,5,6,8,12,14,15 integration. - To understand the properties of definite integrals. 9.2 Finding Definite Integrals of Functions - To find definite integrals from geometrical interpretation, from definition, and by using the basic properties. 9.3 Further Techniques of Definite Integration - To find definite integrals of Ex. 9.3 : algebraic functions, trigonometric Q.5,7,9,10,11,14,17,19,26,29, functions and exponential functions 31,33,35,37,39,42,43 9.4 Definite Integrals of Special Functions - To understand that the method of Ex. 9.4 : integration by parts for definite Q.3,6,9,11,13,14,15,17 integrals is very similar to the case of indefinite integrals, except lower Supplementary Exercise and upper limits are now required. Past Paper Questions - To understand the properties of the definite integrals of even, odd and periodic functions. - To find definite integrals of even functions, odd functions and periodic functions. Ex. 9.2 : Q.6,8,12,13,15,18,19,23,20, 25,26,30,32,33,35,37,39 Remarks Date/Week WEEK 40 WEEK 41 No. of Lessons Contents REVISION FINAL EXAMINATION Objectives Assignments Remarks