Download SEKOLAH MENENGAH KEBANGSAAN RAJA PEREMPUAN, IPOH

SEKOLAH MENENGAH KEBANGSAAN RAJA PEREMPUAN, IPOH
SCHEME OF WORK MATHEMATICS S (PAPER 2)
PRA-U1 2010
WEEK/DATE
18
10.5.10-14.5.10
19 – 21
17.5.10-4.6.10
TOPIC/CONTENT
LEARNING OUTCOMES
ACTIVITIES &
VALUES
TEACHING AID
Induction set
Explaining relevant
examples.
White-board
Grid board
Soft wares
Calculator
CD and LCD
ORIENTATION WEEK
1. DATA
DESCRIPTION
1.1 Representation of data
i) Discrete and
continuous data
ii) Frequency
distribution
iii) Stemplots
iv) Frequency polygon
v) Histogram
vi) Ogive /cumulative
frequency curve.
5.6.10 – 20.6.10
22 – 24
21.6.10-9.7.10
LEARNING OBJECTIVES
1.2 Measures of central
tendency
i) mean
ii) mode
iii) median
iv) Boxplot
v) Relative frequency
distribution
Pupils should be able to
a) To distinguish between
discrete and continuous
data, grouped and
ungrouped data.
b) To construct and interpret
stemplots.
c) To construct and interpret frequency
polygon.
d)To construct and interpret histogram.
i) with equal class width
ii) with unequal class width
e) To construct and interpret
cumulative frequency
curve( ogive).
i) “less than “ ogive
ii) “more than” ogive
Pupils should be able to
a) identify the types of
data given.
b) apply the properties
of a stemplot.
c) apply the properties of
frequency polygon,
histogram and cumulative
frequency curve
FISRT SEMESTER BREAK
a) To calculate mean, mode &
a) use the correct formula to
median of ungrouped data.
determine the value of mean,
b) To calculate mean, mode & median
mode and median
of grouped data.
c) To determine the median & mode
from histogram.
d) To determine median & quartiles
from ogive.
e) To construct boxplots.
Show the correct
method of drawing
frequency polygon,
histogram and
ogive.
Moral Value:
Cooperation
Systematic
Concentrate
Discuss the
calculation of
mean, mode and
median for
ungrouped and
grouped data.
Graph paper
CD and LCD
Calculator
25 – 27
12.7.10- 30.7.10
1.3 Measures Of
Dispersion
i) Range
ii) Quartiles
iii) Interquartiles
range
iv) Semi-interquartiles
range
v) Variance
vi) Standard deviation
a) To calculate the range, first and third
quartile, interquartile and semiinterquartile range for ungrouped
data.
b)To calculate the variance and
standard deviation
c) To derive and use the formula
i  ( x  x) 2 =  x 2 - n(x) 2
a) apply the correct formula
a) differentiate the value of
interquartile and semiinterquartile range.
c) identify the properties of a
boxplot.
d) determine the upper and
lower outlier
e) answer STPM questions
Induction set.
Discuss the
calculation of the
measure of
dispersion.
Graph paper
CD & LCD
Calculator
d) To determine the shape of
distribution.
e) To construct a boxplot.
f) To identify the outliers.
28
2.8.10 – 6.8.10
29 - 30
9.8.10 – 20.8.10
USBF 2
Teacher explains
the rule of sets
2. PROBABILITY
2.1 Techniques of
counting
i) Sets
ii) Permutation
iii) Combination
Pupils should be able to
a) Counting rules for finite sets.
b) To apply the properties of sets.
c) To apply the formula of permutation
of
i) n different objects
ii) n objects taking r objects
iii) objects in a circular arrangement.
d) To apply the formula of
combination of n different objects
taking r objects each time
Pupils should be able to
a) the value of n factorial.
b) use the calculation of
n
Pr
c) use the calculation of
n
Cr
Discuss how to
solve problems
involving
permutations and
combinations
Moral Value:
Concern
Cooperation
Unity
Calculator
CD & LCD
31 - 32
23.8.10-3.9.10
4.9.10-12.9.10
2.2 Events and
Probabilities
i) Mutually exclusive
events.
ii) Independent events
iii) Conditional events
iv) Probability of
conditional events
v) Problems solving
a) To understand the concept of
sample space, event and
probabilities
b) To calculate the probability of an
event.
c) To distinguish between exclusive
and non-exclusive event.
d) To apply the formula
P(A  B)=P(A) +P(B)-P(A  B).
e) To apply the formula of
independent event
f) To apply the formula of conditional
event.
g) To calculate P(A/B) or P(B/A)
h) To apply the formula
P(A  B)= P(A) x P(B/A)
a) determine the probability of
a given event.
b) identify the relation between
independent and conditional
event.
SECOND MID TERM BREAK
HARI RAYA AIDILFITRI
Teacher explains
the rule of sets
Discuss how to
solve problems
involving
permutations and
combinations
Use of
P(A  B) = P(A) +
P(B) – P(A  B)
Teacher discuss the
meaning of
conditional and
independent events
and shows how to
use the formula
P(A  B) = P(A) x
P(B/A)
Calculator
CD & LCD
33 - 34
13.9.10-24.9.10
3. DISCRETE
PROBABILITY
DISTRIBUTIONS
3.1 Random Variables
i) Discrete Random
Variables (DRV)
ii) Continuous
Random
Variables
iii) Probability
distribution table
iv) Probability
distribution
3.2 Mathematical
Expectation
i) Mean, variance and
standard deviation
ii) Expected values and
Variance
Pupils should be able to
a) understand the concept of a DRV
b) construct a probability distribution
table for DRV
a) Understand the concept of
mathematical expectation
b) Calculate the expected value of X,
E(X)
c) Use the Expectation formula :
E(g(x)) = Σ g(x). P(X = x)
d) Show that E(a) = a,
E(aX  b) = aE(X)  b
e) Derive and use the formula
E(X - µ)2 = E(X2) - µ2
f) Calculate Var(X), Var( g(x) )
g) Use the formula to find the expected
and variance of linear combination
of two DRV, X , Y
Pupils should be able to
a) calculate the probability of
discrete random variable
b) solve problems on DRV
a) Calculate the mean and
variance of a discrete
random variable.
b) Use formulae :
E(aX
 b) = aE(X)  b
Var (aX
 b) = a 2 Var(X)
E(aX  bY) = aE(X)  bE(Y)
Var(aX  bY) = a Var(X) +
2
2
b Var(Y)
Explanation on
DRV and how to
construct the
probability
distribution table
for DRV
Teacher explains
the mathematical
expectation and
how to determine
E(X)
Students are asked
to prove all the
mathematical
expectations
Discuss the proof
of
E(X - µ)2 = E(X2) - µ2
Teacher shows
how to calculate
variance of X and
how to find the
expected and
variance of linear
combination of two
DRV, X , Y
Moral Value:
Gratitude
Systematic
Politeness
Calculator
CD & LCD
Reference book
35
27.9.10-1.10.10
3.3 The Binomial
Distribution
X ~ B(n, p)
a) Understand the concept of the
Binomial Distribution, X~ B(n, p)
b) Use the probability function of
X ~ B(n, p)
c) Find the mean and variance of X.
d) Determine the value of X that most
likely to occur.
a) Determine the probability of
an event that follows a
binomial distribution.
b) Determine the mean,
variance and standard
deviation of a binomial
distribution.
c) Solve problems involving
Binomial Distribution.
Teacher explains
the Binomial
Distribution and
how to solve the
problems involving
X ~ B(n, p)
Calculator
CD & LCD
36
4.10.10-8.10.10
3.4 Normal Distribution
a) Understand the concept of the
a) Find the probability of zscores for standard normal
distribution.
b) Convert a random variable of
a normal distribution , X, to
the standardised variable, Z.
c) Determine the probability of
an event that follows a
Normal Distribution.
d) Solve problems involving
Normal Distribution.
Teacher explains
the Normal
Distribution and
how to solve the
problems involving
Calculator
CD & LCD
X ~ N(  ,
 )
2
Normal Distribution, X ~ N(  ,  ).
b) Understand the use of the standard
normal distribution table.
c) Standardise a normal variable.
d) Use the normal distributions as
models for solving problems.
2
37
11.10.10 – 15.10.10
Revision
38 – 39
18.10.10 - 29.10.10
YEAR-END EXAMINATION
40
1.11.10 – 5.11.10
Post-Test Discussion
X ~ N(  ,
2)
41 – 42
8.11.10 – 19.11.10
Pupils should be able to
4. Network Planning
4.1 Network diagram
4.2 Critical path
4.2.1 Calculation of the
earliest event time
4.2.2 Calculation of the
latest event time
4.2.3 Calculation of project
completion time
4.3 Floats
a.) To understand the
concepts of activities,
events and networks
b.) To construct and interpret
networks
c.) To identify the critical
activities and critical
paths
d.) To calculate the
minimum completion
times
e.) To calculate and explain
total, free and
independent floats.
a.) Use the ruler for
constructing the activity
network
b.) To determine the
hanging activity
c.) To trace the critical path
d.) To calculate the earliest
event time
e.) To calculate the latest
event time
f.) To calculate the
completion time
g.) To determine the types
of floats
a.) Set induction
b.) Explaining
the use of
symbols
c.) Explaining
how to
construct an
activity
network
d.) Explaining
the contents
e.) Discussion
f.) Attempt past
year STPM
questions
g.) Ex 2.1 - 2.3
h.) Revision
exercises
Moral Value:
Cooperation
Systematic
Concentrate
Prepared by,
…………………………
(PN.FONG EE LIN)
Checked by,
…………………………
(PN. HJH. AZIAH BT SHAMSUDDIN)
Certified by,
…………………………
Verified by,
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