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