ST. FRANCIS' CANOSSIAN COLLEGE
MATHEMATICS DEPARTMENT
CURRICULUM PLANNING (2009-2010)
SUBJECT
: Mathematics & Statistics
SUBJECT TEACHERS : Ms. Q. Kwok
Month
Sep
2009
(cycles
1-2)
Ch.
Ch.1
Sep
2009
(cycles
2-3)
Ch
10, 11
Sep
(cycles
3-4)
12
CLASSES
: F.6S
TEXT BOOK : New Way Maths. & Stat. for HK AS-Level VOL. 1 & 2 (second edition)
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
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 Cr
5. Applications of permutations & combinations
Basic statistical measures and their interpretation
1. Measures of central tendency: mean, mode,
1. To learn some ways of measuring central tendency and
modal class and median
dispersion of distributions
2. Measures of dispersion: range, interquartile
2. To be able to infer from these measures
range, percentiles, variance and standard
3. To be able to construct and interpret graphical
deviation
representations of distributions, including stem-and-leaf 3. Frequency distribution, cumulative frequency
diagrams
distribution and their graphical representations
including stem-and-leaf diagrams and their
interpretations
4. Box-and-whisker diagrams
Sample space, event and probability of an event
1. To understand the set notation for application in
1. Set notation
probability
2. Sample space, event and probability
2. To understand the meaning of sample space, event and 3. Mutually exclusive, exhaustive and
probability of an event
complementary events
3. To learn the concept of mutually exclusive, exhaustive 4. Further examples
and complementary events
4. To find the probability of an event
Resources / Remarks
Maths & daily life -Probability of MarkSix:
http://www.lottodna.co
m/chance.asp
I.T.: Statistics & you
Getting latest daily-life
statistics figures from
our government
homepage at
http://www.info.gov.hk
I.T.: Comparing
different data displaying
method by using excel
I.T.: Experimental
probability
Using computer
program to simulate
tossing a die for any no.
of time so as to let
students explore
Month
Oct
(cycles
5-6)
Ch.
13
Oct Nov
(cycles
7-10)
14, 15
5. To use simple permutations and combinations in
finding probabilities
Objectives
More about Probability
1. To learn and apply the law
P( A  B)  P( A)  P( B)  P( A  B)
2. To define conditional probability & independent events
3. To learn and apply the law P( A  B)  P( A) P( B / A)
4. To learn and apply the Bayes' theorem for simple cases
1.
2.
3.
4.
Bernoulli, binomial, geometric & Poisson distributions
and their applications
To understand the concept of a random variable and a
probability function
To learn the probability function for the 4 different
distributions
To recognize the mean and variance of the distributions
To apply the formulae to practical problems
Detailed Content
experimental
probability
Resources / Remarks
1. The additional rule
2. Conditional probabilities
3. Bayes' Theorem
Extensive Readings (eg
testing of AIDs) +
HKAL statistics at
www.hkeaa.edu.hk
1. Random variable, probability function, discrete
probability distribution and expectation
2. Bernoulli distribution
3. Binomial distribution
4. Geometric distribution
5. Poisson distribution
6. Means and variances
7. Applications of Bernoulli, binomial, geometric
and Poisson distributions
Internet Resources:
1. stat.net
http://www.hkedstat.net
1.
2.
3.
4.
Activity:
Investigation on the
distribution of our I.Q.
at
www.iqtest.com
Nov –
Dec
(cycles
11-12)
16
The normal distribution and its application
1. To learn the normal curve and standard normal curve
2. To understand the use of normal table
3. To solve practical problems
Dec
(cycles
13)
17
Population Parameters and Sample Statistics
1. To learn related terminology
1. Basic terminology
2. To acquire preliminary idea of sampling distribution
2. Sample mean distribution
3. To learn some simple population estimators
3. Parameters estimation
Christmas and New Year Holiday
Normal distribution
Normal curve and standard normal curve
Normal table
Application of normal distribution
2. Binomial
Distribution Utility
www.hofstra.edu
Month
Jan.
2010
(cycles
14-15)
Ch.
18
Feb
(cycles
16 17)
2
Objectives
Comparison of frequency distributions with fitted
probability distributions
1. To use statistical models to approximate observed
distributions
2. To compare frequency distributions with fitted
probability distributions
Detailed Content
Resources / Remarks
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
1. Ideas of goodness-of-fit of an assumed
probability distribution to a set of observed data
2. Comparison with fitted distribution
n
r 0
a 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 
CAL Program from:
www.ssc.edu.hk/sscho
me/super_tutor/ms/calc
ultaor%201.htm
Lunar New Year Holiday
3
Mar
(cycles
19-20)
April(c
ycles
21-22)
4
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
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
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
1.
2.
3.
4.
5.
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
Easter Holiday
Use of excel to show
pattern of exponential
graph
Game: Tower of Hanoi
Month
May
(cycles
23-24)
Ch.
5
MayJune
(cycles
23-24)
6
Objectives
Limit & Derivative
1. To understand and to accept intuitive concept of limit
2. To be able to evaluate limit of simple functions
3. To understand the idea of derivative
4. To be able to find the derivatives of simple functions
from
first principles
Differentiation
1. To acquire general techniques of differentiation
Detailed Content
Resources / Remarks
1. Limit of a function
2. Derivative of a function
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
June
Term Ends
June
Final Exam
Calculus CD-ROM fr.
Sch. Library