F.6 MS curriculum (02/03)
page
ST. FRANCIS' CANOSSIAN COLLEGE
MATHEMATICS DEPARTMENT
CURRICULUM PLANNING (2002-2003)
SUBJECT
: Mathematics & Statistics
SUBJECT TEACHERS : Ms. K. Lee (F.6A), Ms. Q. Kwok (F.6S)
TEXT BOOK : New Way Maths. & Stat. for HK AS-Level (Vol. 1 & 2) 2nd Ed.
Month
Ch.
Sept. 2002 1
(cycles 1-2)
Objectives
Permutations & Combinations
1. To learn the Fundamental Principle of Multiplication
2. To learn the fundamental ideas of permutations and
combinations
3. To have simple applications to problems including
arrangements and selections
Detailed Content
Assignments/Resources
1. The Fundamental Principle of Multiplication
2. Definition of permutations & combinations
3. Distinction between permutations and
combinations
4. The symbols r!, n Pr and n C r
5. Applications of permutations & combinations
Maths & daily life -Probability of Mark-Six:
http://www.lottodna.com/ch
ance.asp
Sept. - Oct 2
(cycles 3-4)
The Binomial Expansion
1. To learn the binomial expansion of (1 + x)n when n is a
positive integer
2. To study the expansion as an infinite series when n is not a
positive integer and x< 1
1. The expansion of (1  x ) n   Crn x r when n is a
Oct.
3
(cycles 5-6)
The Exponential Function
1. To study the properties and graphs of the exponential
functions
2. To solve simple equations with unknown indices
3. To have some knowledge about exponential series
n
r 0
positive integer
2. The expansion of (1 + x)n when n is not a positive
integer and x< 1
3. Pascal Triangle
4. The summation notation 
1.
2.
3.
4.
5.
6.
Definition of an exp function
Properties of exp functions
Sketch of the graph of an exp function
Solving simple equations with unknown indices
The exponential series
Application of exp functions
CAL Program from:
www.ssc.edu.hk/sschome/su
per_tutor/ms/calcultaor%20
1.htm
Use of excel to show pattern
of exponential graph
Game: Tower of Hanoi
1
F.6 MS curriculum (02/03)
Month
Ch.
Oct - Nov
4
(cycles 7-9)
Nov
(cycle 10)
Dec
(cycles 11 12)
Feb.
Objectives
The Logarithmic Function
1. To study the properties and graphs of the log functions to
any base
2. To solve simple equations involving logarithms
3. To apply the reduction of the relation y = kxn to a linear
relation
Detailed Content
1.
2.
3.
4.
5.
Assignments/Resources
Definition of a log function
Properties of log functions
Sketch of the graph of a log function
Solving simple equations involving logarithms
Reduction of y = kxn to a linear relation
Common Test
5
1.
2.
3.
4.
Dec
Jan 2002
(cyc.13-14)
Jan – Feb
(cycles 1517)
page
Limit & Derivative
To understand and to accept intuitive concept of limit
To be able to evaluate limit of simple functions
To understand the idea of derivative
To be able to find the derivatives of simple functions from
first principles
1. Limit of a function
2. Derivative of a function
Christmas & New Year Holiday
First Term Exam
6
Differentiation
1. To acquire general techniques of differentiation
Lunar New Year Holiday
1. Basic differentiation rules
2. Differentiation of composite functions by chain
rule
3. Differentiation of inverse functions
4. Differentiation of exponential and log functions
5. Second derivatives of simple functions
Calculus CD-ROM fr. Sch.
Library
Holiday assignment: supp.ex. on techniques of differentiation
2
F.6 MS curriculum (02/03)
Month
Feb - Mar
(cycles 1821)
Ch.
7
Apr
(cycle 22)
Apr
(cycles 2223)
Objectives
Application of differentiation
1. To find the gradient of a curve
2. To solve problems involving rate of change
3. To solve problems on maximization and minimization
4. To do approximation
5. To sketch simple curves
Detailed Content
1.
2.
3.
4.
5.
Assignments/ Resources
Gradient
Rate of change
Maxima & Minima
Approximation
Simple curve-sketching
2nd Term Common Test
8
Apr
Apr - May
(cycles 2426)
page
9
Indefinite Integration
1. To perform indefinite integration as the reverse process of
differentiation
2. To learn standard formulae for indefinite integration
1. Indefinite integration
2. Some formulae for indefinite integration
3. Integration by substitution
Easter Holiday
Holiday assignment: supp.ex. on applications of differentiation
Definite Integration
1. To define definite integral intuitively as a limit of sum
2. To learn the properties of definite integral and its relation
with indefinite integrals
3. To evaluate definite integrals
4. To find plane areas
5. To evaluate definite integral using the trapezoidal rule
1.
2.
3.
4.
Definite integral
Properties of definite integral
Plane areas
Approximation of definite integrals using the
trapezoidal rule
3
F.6 MS curriculum (02/03)
Month
Ch.
May - June
(cycles 27 28)
Bk.2
Ch1,
2
June
page
Objectives
Detailed Content
Basic statistical measures and their interpretation
1. To learn some ways of measuring central tendency and
dispersion of distributions
2. To be able to infer from these measures
3. To be able to construct and interpret graphical
representations of distributions, including stem-and-leaf
diagrams
FINAL EXAMINATION
1. Measures of central tendency: mean, mode, modal
class and median
2. Measures of dispersion: range, interquartile range,
percentiles, variance and standard deviation
3. Frequency distribution, cumulative frequency
distribution and their graphical representations
including stem-and-leaf diagrams and their
interpretations
4. Box-and-whisker diagrams
Holiday assignment: supp.ex. on integration
Assignments/Resources
4