LIU PO SHAN MEMORIAL COLLEGE
SCHEME OF WORK (2011-2012)
MATHEMATICS PANEL
Secondary : Five (Mathematics Module 2)
Periods per week :
3
Date/Week
2 – 9 – 2011
to
23 – 9 – 2011
(1 – 4)
Coordinator : Chiu Kai Yuen
Textbook :
New Progress in Senior Mathematics Module 2 Book 1 & 2
(Hong Kong Educational Publishing Co.)
Contents
Objectives
Assignments
Chapter 6 Differentiation(2)
6.1 Differentiation of Exponential and
Logarithmic Functions
- To find the derivatives of functions involving exponential and
logarithmic functions
Ex. 6.1 : Q.3,6,7,8,12,15,16,18,20,22,24,25,
27,29,32,33,35,37,40,41
6.2
Differentiation of Trigonometric Functions
- To find the the derivatives of functions involving trigonometric functions
Ex. 6.2 : Q.8,9,11,13,15,19,20,21,23,28,29,
32,33,35,37,41,43,45,48,49
6.3
Second Derivatives
- To find the second derivatives of an explicit function
Ex.6.3 : Q.4,6,7,10,11,14,16,18,19,22,23,
25,27
Remarks
Supplementary Exercise
Chapter 7 Applications of Differentiation
7.1 Tangents and Normals
- 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
26 – 9 – 2011
to
25 – 11 – 2011
(5 – 13)
7.2
Local Extrema and Derivative Tests
- 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
7.4
Optimization Problems
- To solve the problems relating to maximum and minimum
Ex. 7.3: Q.4, 5, 8, 9, 10, 12, 14, 16, 17, 19, I – Using ‘Winplot’ to
draw the graphs of
20
polynomial functions
Ex. 7.4: Q.3, 5, 8, 9, 10, 14, 17, 19, 22, 24
and rational functions
7.5
Rates of Change
- To solve the problems relating to rate of change
Ex. 7.5: Q.3, 6, 7, 10, 12, 14, 16, 18
Supplementary Exercise
Date/Cycle
Contents
Chapter 8 Indefinite Integrals
8.1 Concepts of Indefinite Integrals
Objectives

d F(x)
= f(x)  f(x) dx = F(x) + c .
dx
- To introduce the terms primitive function, integral sign,
integrand and constant of integration.
- To introduce the concept of indefinite integrals and some
integration formulae.
- To introduce the simple properties :
- To emphasize that
 f(x)  g(x) dx =  f(x) dx   g(x) dx
 k f(x) dx = k  f(x) dx
28 – 11 – 2011
to
21 – 12 – 2011
Assignments
and
Indefinite Integration of Functions
- 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.
Ex. 8.2 : Q.6, 8, 10, 12, 14, 16, 20, 22,
24, 26, 28,32, 34, 36, 37, 39,
42, 43
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
a2  x2 ,
x 2  a 2 or
a 2  x 2 using trigonometric substitution
5 – 1 – 2012
to
19 – 1 – 2012
(19 – 21)
Ex. 8.1 : Q.4, 8, 10, 14, 18, 20, 22, 24, 26,
28, 32, 34, 36, 38, 40, 42, 44
8.2
(15 – 17)
Remarks
FIRST TERM EXAMINATION
I – Using ‘Winplot’ to
draw the graphs of
trigonometric
functions.
Date/Cycle
8.4
1 – 2 – 2012
to
17 – 2 – 2012
Contents
Integration by Parts
Objectives
- To illustrae the technique of integration by parts include
.
x
 xe dx  x sin xdx  ln xdx
Assignments
Ex. 8.4 : Q.3, 6, 8, 9, 11, 14, 16, 20, 21, 23,
25, 27, 29, 31, 33
Remarks
- To find indefinite integrals by using substitution and integration by parts.
8.5
Applications of Indefinite Integrals
(15 – 25)
- To solve geometrical application problems of indefinite integrals,
application problems of indefinite integrals in physics, and other
application problems of indefinite integrals.
Ex. 8.5 : Q.3, 6, 9, 11, 14, 16, 18, 20, 22
Supplementary Exercise
Chapter 9 Definite Integrals
9.1 Concepts of Definite Integrals
- To recognize the concept of definite integration.
Ex. 9.1 : Q.2, 5, 6, 8, 12, 14, 15
- To understand the properties of definite integrals.
- To find definite integrals from geometrical interpretation, from definition,
and by using the basic properties.
20 – 2 – 2012
to
30 – 3 – 2012
9.2
Finding Definite Integrals of Functions
- To find definite integrals of algebraic functions, trigonometric functions
and exponential functions
Ex. 9.2 : Q.6, 8, 12, 13, 15, 18, 19, 23, 20,
25, 26, 30, 32, 33, 35, 37, 39
(26 – 31)
9.3
Further Techniques of Definite Integration
- To understand that the method of integration by parts for definite
integrals is very similar to the case of indefinite integrals, except lower
and upper limits are now required.
Ex. 9.3 : Q.5, 7, 9, 10, 11, 14, 17, 19, 26,
29, 31, 33, 35, 37, 39, 42, 43
9.4
Definite Integrals of Special Functions
- To understand the properties of the definite integrals of even, odd and Ex. 9.4 : Q.3, 6, 9, 11, 13, 14, 15, 17
periodic functions.
- To find definite integrals of even functions, odd functions and periodic
functions.
Supplementary Exercise
Chapter 10 Applications of Definite Integrals
10.1 Finding Plane Areas by Integration
- To understand the application of definite integrals in finding the area of a
plane figure.
2 – 4 – 2012
to
7 – 6 – 2012
1. To help the students to
realize that the
constant of integration
determines the
position of the curve
relative to the
coordinate axes.
Ex. 10.1 : Q.2, 6, 8, 9, 12, 14, 16, 19, 22,
23, 27, 29
.
- To find the area of the region bounded by a curve and the x-axis, the yaxis and other lines.
- To find the area of the region bounded by two curves.
(32 – 41)
10.2
Volume of Solids of Revolution
- To find the volume of the solid of revolution about the x-axis, the y-axis Ex. 10.2 : Q.3, 6, 8, 11, 13, 16, 17, 20, 21,
23, 26, 27
or the lines parallel to the x-axis or y-axis.
- To apply both the disc method and the shell method.
Supplementary Exercise
I – Using ”Winplot” to
illustrate how the
given curve rotates
about the axis of
rotation.
8 – 6 – 2012
to
22 – 6 – 2012
Final Examination