LIU PO SHAN MEMORIAL COLLEGE

SCHEME OF WORK (2017-2018)

MATHEMATICS PANEL

Secondary : Five (Mathematics Module 2) Coordinator : Siu Kai Yiu

Textbook : Effective Learning Mathematics Module 2: Algebra and Calculus Volume1 - 2 (Chung Tai Educational Press) Periods per week : 1.5

Date/Week / Contents / Objectives / Assignments / Assessment / Remarks
SUMMER
LESSONS
4 - 9 - 2017
TO
29 - 9 - 2017
(W1 - W4) / Chapter 7 Differentiation
7.2Differentiation Rules / - Find derivatives by differentiation rules. / Ex. 7B
4,5,8,10,12,15,16,20,22,26,28,30,32,35,
36,39
Section Test / R - Ask students to derive the rules of differentiation from first principles.
7.3Differentiation of Composite Functions / - Find derivatives of composite functions by chain rule. / Ex.7C
1,2,5,6,8,9,12,13,16,18,20,23,28,30,31,
34,37,39
Section Test
7.4Implicit Differentiation / - Find derivatives by implicit differentiation. / Ex. 7D
1,3,4,6,8,10,13,18,20,24,27,28,29
Section Test
Chapter Test 1
7.5Differentiation of Trigonometric Functions / - Find derivatives of trigonometric functions. / Ex. 7E
3,6,9,10,14,18,19,22,24,26,28,31,35,36,
41,42,46,47,49,52,54
Section Test / R - Ask students to derive derivatives of trigonometric functions from first principles.
7.6Differentiation of Exponential Functions and
Logarithmic Functions
A.Differentiation of exponential functions
B.Differentiation of logarithmic functions
C.Logarithmic differentiation / - Find derivatives of exponential functions and
logarithmic functions.
- Find derivatives by logarithmic differentiation. / Ex. 7F
6,11,14,16,17,20,24,25,27,28,30,32,36,
37,40,45,48,49,51,53,55
Section Test
7.7Second Derivatives / - Find second derivatives of explicit functions. / Ex.7G
8,11,14,18,21,23,25,27,28,31,34,36,38
Section Test
Past Papers Questions
Chapter Test
Date/Week / Contents / Objectives / Assignments / Assessment / Remarks
3 - 10 - 2017
TO
20 - 12 - 2017
(W5 - W16) / Chapter 8 Application of Differentiation
8.1 Tangents and Normals / - Find the equations of the tangent and the normal to a curve at a point by differentiation. / Ex. 8A
1,4,5,7,10,15,16,17,19,23,24,26,27,28,31
Section Test
8.2 Local Extrema
A. Increasing and decreasing functions
B.Definitions of local extrema
C.Tests for local extrema / - Find the local extrema.
- Recognize the tests for local extrema, including the first derivative test and second derivative test. / Ex. 8B
3,5,6,9,11,13,20,22,24,25,28,31,34,40,42,43,44
Section Test
8.3 Concavity and Points of Inflexion
A. Concavity of a curve
B.Points of inflexion / - Recognize the concavity and points of inflexion of the graph of a function.
- Find the points of inflexion of the graph of a function through second derivatives. / Ex. 8C
4,7,10,12,13,15,16,20
Section Test
8.4 Asymptotes
A.Vertical asymptotes
B.Horizontal asymptotes
C.Oblique asymptotes / Find asymptotes of the graphs of functions. / Ex. 8D
3,4,7,9,11,14,16,18
8.5 Curve Sketching / Sketch the graphs of functions. / Ex. 8D
20,22,23,25,27
Section Test
Chapter Test 1 / E – Using GeoGebra to draw the graphs of polynomial functions and rational functions
8.6 Global Extrema / Find the global extrema of functions. / Ex. 8E
3,5,7,10,11,13 / S - Help students to understand daily examples of optimization
8.7 Applications of Global Extrema / Solve problems involving global extrema. / Ex. 8F
5,8,11,13,15,16,19,21,22
8.8 Rates of Change / Solve problems involving rates of change. / Ex. 8G
4,5,7,10,11,13,16,19,21,22
Section Test
Past Papers Questions
Chapter Test 2 / V, S - Help students to apply the concept of rates of change to understand real life problems in Physics and Engineering
First Term Exmaination
Date/Week / Contents / Objectives / Assignments / Assessment / Remarks
17 - 1 - 2018
TO
27 - 3 - 2018
(W20 - W30) / Chapter 9 Indefinite Integration and its Applications
9.1 Indefinite Integration / - Learn that indefinite integration is the reverse process of
differentiation.
- Understand the definition of indefinite integral.
9.2 Integration Formulae / - Find indefinite integrals using the integration formulae.
- Understand the properties of indefinite integrals. / Ex. 9A11,14,16,21,22,26,27,31,33,35,36,37,39
Section Test
9.3Integration by Substitution / - Use integration by substitution to find indefinite integrals. / Ex. 9B
10,12,13,16,18,19,22,25,27,28,33,35,38,39,41,42
Section Test
9.4Integration by Parts / Use integration by parts to find indefinite integrals. / Ex. 9C
2,5,7,9,12,13,15,17
Section Test
9.5Indefinite Integration of Trigonometric
Functions / - Find the indefinite integrals of trigonometric functions,,and.
- Use double angle formulae and product-to-sum formulae to find indefinite integrals.
- Find indefinite integrals in the forms, and. / Ex. 9D
4,10,12,14,16,18,20,22,24,27,29,31,32,34,35
Section Test
9.6Finding Indefinite Integrals by Trigonometric Substitutions / - Use trigonometric substitutions to find indefinite integrals. / Ex. 9E
6,7,11,12,13,17,20,21,22,24
Section Test
9.7Applications of Indefinite Integrals
A.Geometrical applications
B.Physical and real-life applications / - Apply indefinite integrals to geometry, physics and real life. / Ex. 9F
6,10,11,14,16,19,20,21,23
Section Test
Past Papers Questions
Chapter Test
Date/Week / Contents / Objectives / Assignments / Assessment / Remarks
9 - 4 - 2018
TO
4 - 5 - 2018
(W32 - W35) / Chapter 10Definite Integrals
10.1 Definite Integrals
A.Area under a curve
B. Definition of definite integral
C.Properties of definite integrals / - Recognize the concept of definite integration and understand the definition of the definite integral as the limit of a sum.
- Recognize the properties of definite integrals.
10.2 Fundamental Theorem of Calculus / - Understand the Fundamental Theorem of Calculus.
- Evaluate definite integrals by using the Fundamental Theorem of Calculus. / Ex. 10A
7,9,11,13,15,22,23,24,29,30
Section Test
10.3 Integration by Substitution / - Use integration by substitution to evaluate definite
integrals. / Ex. 10B
4,11,12,14,15,19,23,25,27,29,36,37,38
Section Test
10.4 Integration by Parts / Use integration by parts to evaluate definite integrals. / Ex. 10C
3,5,9,11,13,14,15,19, 20
Section Test
10.5 Definite Integration of Even, Odd and Periodic Functions / - Recognize the definitions of even, odd and periodic functions.
- Understand the properties of the definite integrals of
even, odd and periodic functions. / Ex. 10D
2,4,6,7,9,12,14,16,17,19
Section Test
Past Papers Questions
Chapter Test
Date/Week / Contents / Objectives / Assignments / Assessment / Remarks
7 - 5 - 2018
TO
5 - 6 - 2018
(W36 - W40) / Chapter 11Applications of Definite Integration
11.1 Area of Plane Figures
A.Area between a curve and the x-axis
B.Area between a curve and the y-axis
C.Area between two curves / Understand the application of definite integrals in finding the area of a plane figure. / Ex. 11A
6,8,10,12,14,16,17,19,22,24,27,29,33,35
Section Test / E – Using GeoGebra to show the area in a plane figure.
11.2 Volume of Solids of Revolution
A.Volume of a solid of revolution about a
coordinate axis
B.Volume of a hollow solid of revolution
about a coordinate axis
C.Volume of a solid of revolution about a
line parallel to a coordinate axis
D.Volume of a hollow solid of revolution
about a line parallel to a coordinate axis / Understand the application of definite integrals in finding the volume of a solid or a hollow solid of revolution about a coordinate axis or a line parallel to a coordinate axis by the disc method. / Ex. 11B
6,9,11,13,17,21,26,28,31,32,33
Section Test
Past Papers Questions
Chapter Test / E – Using GeoGebra to show the solid or hollow solid of revolution in the sense of 3-dimensional space.
V, S - Help students to apply the concept of rates of change to understand real life problems in Physics and Engineering
Final Examination