Rancangan Pengajaran Tahunan MM YEARLY PLAN F4
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Transcript of Rancangan Pengajaran Tahunan MM YEARLY PLAN F4
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1LEARNING AREA:
STANDARD FORM Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 1 Students will be able to:
1 a) understand and use the
concept of significant
figure;
Discuss the significance of zero in
a number.
(ii) round off positive numbers to a given
number of significant figures when the
numbers are:
a) greater than 1;
b) less than 1;
Rounded numbers are
only approimates.
!imit to positive numbers
only.
Discuss the use of significant
figures in everyday life and other
areas.
(iii) perform operations of addition" subtraction"
multiplication and division" involving a few
numbers and state the answer in specificsignificant figures;
#enerally" rounding is
done on the final answer.
(iv) solve problems involving significantfigures;
$ a) understand and use theconcept of standard form to
solve problems.
%se everyday life situations suchas in health" technology" industry"
construction and business
involving numbers in standard
form.
%se the scientific calculator to
eplore numbers in standard form.
(v) state positive numbers in standard formwhen the numbers are:
a) greater than or e&ual to 1';
b) less than 1;
nother term for standardform is scientific
notation.
(vi) convert numbers in standard form to single
numbers;
(vii) perform operations of addition" subtraction"multiplication and division" involving anytwo numbers and state the answers in
standard form;
nclude two numbers instandard form.
(viii) solve problems involving numbers in
standard form.
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1LEARNING AREA:
STANDARD FORM Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: $ Students will be able to:* a) understand the concept
of &uadratic epression;
Discuss the characteristics of
&uadratic epressions of the form
cbxax ++$ " where a" band care
constants" a' andxis anun+nown.
(i) identify &uadratic epressions; nclude the case when b, '
and-or c, '.
(ii) form &uadratic epressions by
multiplying any two linear epressions;
mphasise that for the
termsx$andx" the
coefficients are understood
to be 1.
(iii) form &uadratic epressions based on
specific situations;
nclude everyday life
situations.
* a) factorise &uadratic
epression;
Discuss the various methods to
obtain the desired product.
(i) factorise &uadratic epressions of the
form cbxax ++$ " where b, ' or c, ';
(ii) factorise &uadratic epressions of the
formpx$q"pand qare perfect s&uares;1 is also a perfect s&uare.
/egin with the case a, 1.
plore the use of graphing
calculator to factorise &uadraticepressions.
(iii) factorise &uadratic epressions of the
form cbxax ++$ " where a" band cnot
e&ual to zero;
0actorisation methods that
can be used are:
cross method;
inspection.
(iv) factorise &uadratic epressionscontaining coefficients with common
factors;
a) understand the concept Discuss the characteristics of (v) identify &uadratic e&uations with one
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1LEARNING AREA:
STANDARD FORM Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: $ Students will be able to:of &uadratic e&uation; &uadratic e&uations. un+nown;
(vi) write &uadratic e&uations in general form
i.e.
'$
=++ cbxax ;
(vii) form &uadratic e&uations based onspecific situations;
nclude everyday lifesituations.
2 a) understand and use the
concept of roots of
&uadratic e&uations to solveproblems.
(i) determine whether a given value is a root
of a specific &uadratic e&uation;
Discuss the number of roots of a
&uadratic e&uation.
(ii) determine the solutions for &uadratic
e&uations by:
a) trial and error method;
b) factorization;
3here are &uadratic
e&uations that cannot besolved by factorization.
%se everyday life situations. (iii) solve problems involving &uadratice&uations.
(iv)
4hec+ the rationality of thesolution.
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1LEARNING AREA:
STANDARD FORM Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: $ Students will be able to:
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3LEARNING AREA:
SETS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: * Students will be able to:5 a) understand the concept of
set;
%se everyday life eamples to
introduce the concept of set.
(i) sort given ob6ects into groups; 3he word set refers to any
collection or group of
ob6ects.
(ii) define sets by:
a) descriptions;
b) using set notation;
3he notation used for sets isbraces" 7 8.
3he same elements in a set
need not be repeated.
9ets are usually denoted bycapital letters.
3he definition of sets has to
be clear and precise so that
the elements can beidentified.
(iii) identify whether a given ob6ect is an
element of a set and use the symbol or;
3he symbol (epsilon) isread is an element of or
is a member of.
3he symbol is read isnot an element of or is nota member of.
Discuss the difference
between the representation ofelements and the number ofelements in
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3LEARNING AREA:
SETS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: * Students will be able to:are not empty sets. set A.
(vi) determine whether a set is an empty set; 3he symbol (phi) or 7 8denotes an empty set.
(vii) determine whether two sets are e&ual; n empty set is also calleda null set.
= a) understand and use the
concept of subset" universal set
and the complement of a set;
/egin with everyday life
situations.
(i) determine whether a given set is a subset
of a specific set and use the symbol or;
n empty set is a subset of
any set.
very set is a subset ofitself.
(ii) represent subset using ? @ a) perform operations on
sets:
the intersection of sets;
the union of sets.
(i) determine the intersection of:
a) two sets;
b) three sets;
and use the symbol ;
nclude everyday life
situations.
Discuss cases when: (ii) represent the intersection of sets
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3LEARNING AREA:
SETS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: * Students will be able to: AB,
AB
using
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3LEARNING AREA:
SETS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: * Students will be able to: of sets;
() solve problems involving the union
of
sets;
nclude everyday life
situations.
(i) determine the outcome of combined
operations on sets;
(ii) solve problems involving combined
operations on sets.
nclude everyday life
situations.
1' 393 1
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4LEARNING AREA:
MATHEMATICA REASONING Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: Students will be able to:11 g) understand the concept of
statement;
ntroduce this topic using
everyday life situations.
(i) determine whether a given sentence is a
statement;
9tatements consisting of:
0ocus on mathematical
sentences.
(ii) determine whether a given statement is
true or false; words only" e.g. 0ive
is greater than two.;
numbers and words"e.g. 2 is greater than $.;
numbers and symbols"e.g. 2 A $.
Discuss sentences consisting
of: words only;
numbers and words;
numbers andmathematical symbols;
(iii) construct true or false statement using
given numbers and mathematicalsymbols;
3he following are not
statements: s the place value of
digit @ in 1@$>
hundredsB;
n2mC $s;
dd the twonumbers.;
xC $ , >.
1$ a) understand the concept of
&uantifiers all and some;
9tart with everyday life
situations.
(i) construct statements using the &uantifier:
a) all ;
b) some;
uantifiers such as every
and any can be introduced
based on contet.
(ii) determine whether a statement that
contains the &uantifier all is true orfalse;
Examples:
ll s&uares are foursided figures.
very s&uare is a four
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4LEARNING AREA:
MATHEMATICA REASONING Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: Students will be able to:sided figure.
ny s&uare is a foursided figure.
(iii) determine whether a statement can begeneralised to cover all cases by using
the &uantifier all;
Ether &uantifiers such asseveral" one of and
part of can be used based
on contet.
(iv) construct a true statement using the&uantifier all or some" given an
ob6ect and a property.
Example:
Object: 3rapezium.
Property: 3wo sides areparallel to each other.
Statement: ll trapeziums
have two parallel sides.
Object: ven numbers.
Property: Divisible by .
Statement: 9ome even
numbers are divisible by .
1$ a) perform operations
involving the words not orno" and and or on
statements;
/egin with everyday life
situations.
(i) change the truth value of a given
statement by placing the word not intothe original statement;
3he negation no can be
used where appropriate.
3he symbol F (tilde)
denotes negation.
Fp denotes negation ofp
which means notp or nop.
3he truth table forpand Fp
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4LEARNING AREA:
MATHEMATICA REASONING Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: Students will be able to:are as follows:
p Fp
3rue
0alse
0alse
3rue
(ii) identify two statements from a compoundstatement that contains the word and;
3he truth values for pandq are as follows:
p q
pand q
3rue 3rue 3rue
3rue 0alse 0alse
0alse 3rue 0alse
0alse 0alse 0alse
(iii) form a compound statement by
combining two given statements usingthe word and;
(iv) identify two statement from a compound
statement that contains the word or ;
3he truth values for por q
are as follows:
(v) form a compound statement bycombining two given statements using
the word or;
p q por
q
3rue 3rue 3rue
3rue 0alse 3rue
0alse 3rue 3rue
0alse 0alse 0alse
(vi) determine the truth value of a compound
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4LEARNING AREA:
MATHEMATICA REASONING Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: Students will be able to:statement which is the combination of
two statements with the word and;
(vii) determine the truth value of a compound
statement which is the combination oftwo statements with the word or.
1* a) understand the concept of
implication;
9tart with everyday life
situations.
(i) identify the antecedent and conse&uent of
an implication ifp" then q;
mplication ifp" then q
can be written aspq"and pif and only if q can
be written aspq" whichmeanspqand qp.
(ii) write two implications from a compound
statement containing if and only if;
(iii) construct mathematical statements in the
form of implication:
a) fp" then q;
b) pif and only if q;
(iv) determine the converse of a given
implication;
3he converse of an
implication is not
necessarily true.
(v) determine whether the converse of an
implication is true or false.
Example 1:
fxG *" then
xG 2 (true).
4onversely:
fxG 2" then
xG * (false).
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4LEARNING AREA:
MATHEMATICA REASONING Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: Students will be able to:Example 2:
fPQRis a triangle" then
the sum of the interior
angles ofPQRis 1>'.
(true)
4onversely:
f the sum of the interior
angles ofPQRis 1>'" thenPQRis a triangle.
(true)1 a) understand the concept of
argument;
9tart with everyday life
situations.
(i) identify the premise and conclusion of a
given simple argument;
!imit to arguments with
true premises.
(ii) ma+e a conclusion based on two given
premises for:
a) rgument 0orm ;
b) rgument 0orm ;
c) rgument 0orm ;
Hames for argument forms"
i.e. syllogism(0orm )"modusponens(0orm )
and modustollens(0orm
)" need not be introduced.
ncourage students toproduce arguments based on
previous +nowledge.
(iii) complete an argument given a premiseand the conclusion.
9pecify that these threeforms of arguments are
deductions based on two
premises only.
Argument Form
Premise 1: llAare!.
Premise 2: "isA.
Conclusion: "is!.
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4LEARNING AREA:
MATHEMATICA REASONING Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: Students will be able to:Argument Form :
Premise 1: fp" then q.
Premise 2:pis true.
Conclusion: qis true.
Argument Form :
Premise 1: fp" then q.
Premise 2: Hot qis true.
Conclusion: Hotpis true.
12 a) understand and use the
concept of deduction andinduction to solve problems.
%se specific
eamples-activities tointroduce the concept.
(i) determine whether a conclusion is made
through:
a) reasoning by deduction;
b) reasoning by induction;
(ii) ma+e a conclusion for a specific case
based on a given general statement" bydeduction;
(iii) ma+e a generalization based on the
pattern of a numerical se&uence" by
induction;
!imit to cases where
formulae can be induced.
(iv) use deduction and induction in problem
solving.
9pecify that:
ma+ing conclusionby deduction is definite;
ma+ing conclusionby induction is not
necessarily definite.
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4LEARNING AREA:
MATHEMATICA REASONING Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: Students will be able to:
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5LEARNING AREA:
THE STRAIGHT INE Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 2 Students will be able to:15 a) understand the concept of
gradient of a straight line;
%se technology such as the
#eometerIs 9+etchpad"
graphing calculators" graph
boards" magnetic boards" topomaps as teaching aids where
appropriate.
(i) determine the vertical and horizontal
distances between two given points on a
straight line.
/egin with concrete
eamples-daily situations tointroduce the concept of
gradient.
Discuss:
the relationship betweengradient and tan .
the steepness of thestraight line with different
values of gradient.
4arry out activities to find the
ratio of vertical distance to
horizontal distance for severalpairs of points on a straight
line to conclude that the ratio
(ii) determine the ratio of vertical distance to
horizontal distance.
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5LEARNING AREA:
THE STRAIGHT INE Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 2 Students will be able to:is constant.
15 a) understand the concept of
gradient of a straight line in4artesian coordinates;
Discuss the value of gradient if
Pis chosen as (x1"#1) andQis (x$"#$);
Pis chosen as (x$"#$) andQis (x1"#1).
(i) derive the formula for the gradient of a
straight line;
3he gradient of a straight
line passing through
P(x1"#1) and
Q(x$"#$) is:
1$
1$
xx
##m
=
(ii) calculate the gradient of a straight line
passing through two points;
(iii) determine the relationship between the
value of the gradient and the:
a) steepness"
b) direction of inclination"
of a straight line;
1= c) understand the concept ofintercept;
(i) determine thexKintercept and the#Kintercept of a straight line;
mphasise that thexKintercept and the#Kintercept
are not written in the form
of coordinates.
(ii) derive the formula for the gradient of astraight line in terms of thexKintercept
and the#Kintercept;
(iii) perform calculations involving gradient"
xKintercept and#Kintercept;
1= a) understand and use Discuss the change in the form (i) draw the graph given an e&uation of the mphasise that the graph
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5LEARNING AREA:
THE STRAIGHT INE Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 2 Students will be able to:e&uation of a straight line; of the straight line if the values
of mand care changed.
form
#, mxC c;
obtained is a straight line.
4arry out activities using the
graphing calculator"#eometerIs 9+etchpad or other
teaching aids.
(ii) determine whether a given point lies on a
specific straight line;
f a point lies on a straight
line" then the coordinates ofthe point satisfy the
e&uation of the straight line.
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5LEARNING AREA:
THE STRAIGHT INE Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 2 Students will be able to:point that satisfies both
e&uations.
%se the graphing calculator
and #eometerIs 9+etchpad orother teaching aids to find the
point of intersection.
a) drawing the two straight lines;
b) solving simultaneous e&uations.
1> c) understand and use the
concept of parallel lines.
plore properties of parallel
lines using the graphing
calculator and #eometerIs
9+etchpad or other teaching
aids.
(i) verify that two parallel lines have the
same gradient and vice versa;
(ii) determine from the given e&uationswhether two straight lines are parallel;
(iii) find the e&uation of the straight line
which passes through a given point and is
parallel to another straight line;
(iv) solve problems involving e&uations of
straight lines.
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LEARNING AREA:
STATISTICS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 5 Students will be able to:$1 a) understand the concept
of class interval;
%se data obtained from
activities and other sources
such as research studies to
introduce the concept of classinterval.
(i) complete the class interval for a set of
data given one of the class intervals;
(ii) determine:
a) the upper limit and lower limit;
b) the upper boundary and lowerboundary
of a class in a grouped data;
(iii) calculate the size of a class interval; 9ize of class interval
, Oupper boundary ?
lower boundaryP
(iv) determine the class interval" given a setof data and the number of classes;
(v) determine a suitable class interval for a
given set of data;
Discuss criteria for suitableclass intervals.
(vi) construct a fre&uency table for a givenset of data.
$$ a) understand and use the
concept of mode and mean ofgrouped data;
(i) determine the modal class from the
fre&uency table of grouped data;
(ii) calculate the midpoint of a class; Lidpoint of class
,$
1 (lower limit C upper
limit)
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LEARNING AREA:
STATISTICS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 5 Students will be able to:(iii) verify the formula for the mean of
grouped data;
(iv) calculate the mean from the fre&uency
table of grouped data;
(v) discuss the effect of the size of class
interval on the accuracy of the mean for a
specific set of grouped data..
$* a) represent and interpretdata in histograms with class
intervals of the same size to
solve problems;
Discuss the difference betweenhistogram and bar chart.
(i) draw a histogram based on the fre&uencytable of a grouped data;
%se graphing calculator toeplore the effect of different
class interval on histogram.
(ii) interpret information from a givenhistogram;
(iii) solve problems involving histograms. nclude everyday life
situations.
a) represent and interpret
data in fre&uency polygons tosolve problems.
(i) draw the fre&uency polygon based on:
a) a histogram;
b) a fre&uency table;
Qhen drawing a fre&uency
polygon add a class with 'fre&uency before the first
class and after the last class.
(ii) interpret information from a given
fre&uency polygon;
(iii) solve problems involving fre&uency
polygon.
nclude everyday life
situations.
$ a) understand the concept
of cumulative fre&uency;
(i) construct the cumulative fre&uency table
for:
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LEARNING AREA:
STATISTICS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 5 Students will be able to:a) ungrouped data;
b) grouped data;
(ii) draw the ogive for:
a) ungrouped data;
b) grouped data;
Qhen drawing ogive:
use the upperboundaries;
add a class with zerofre&uency before the first
class.
$2 c) understand and use the
concept of measures ofdispersion to solve problems.
Discuss the meaning of
dispersion by comparing a fewsets of data. #raphing
calculator can be used for thispurpose.
(i) determine the range of a set of data. 0or grouped data:
Range , Omidpoint of thelast class ? midpoint of the
first classP
(ii) determine:
a) the median;
b) the first &uartile;
c) the third &uartile;
d) the inter&uartile range;
from the ogive.
(iii) interpret information from an ogive;4arry out a pro6ect-research and
analyse as well as interpret the
data. resent the findings of the
pro6ect-research.
mphasise the importance of
honesty and accuracy in
(iv) solve problems involving data
representations and measures of
dispersion.
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LEARNING AREA:
STATISTICS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 5 Students will be able to:managing statistical research.
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!LEARNING AREA:
PROBABI IT" I Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: = Students will be able to:$5 a) understand the concept
of sample space;
%se concrete eamples such as
throwing a die and tossing a
coin.
(i) determine whether an outcome is a
possible outcome of an eperiment;
(ii) list all the possible outcomes of aneperiment:
a) from activities;
b) by reasoning;
(iii) determine the sample space of aneperiment;
(iv) write the sample space by using set
notations.
a) understand the conceptof events.
Discuss that an event is a subsetof the sample space.
Discuss also impossible events
for a sample space.
(i) identify the elements of a sample spacewhich satisfy given conditions;
n impossible event is anempty set.
(ii) list all the elements of a sample spacewhich satisfy certain conditions using set
notations;
Discuss that the sample space
itself is an event.
(iii) determine whether an event is possible
for a sample space.
$= a) understand and use theconcept of probability of an
event to solve problems.
4arry out activities to introducethe concept of probability. 3he
graphing calculator can be used
to simulate such activities.
(i) find the ratio of the number of times anevent occurs to the number of trials;
robability is obtained fromactivities and appropriate
data.
(ii) find the probability of an event from a
big enough number of trials;
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!LEARNING AREA:
PROBABI IT" I Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: = Students will be able to:
Discuss situation which results
in:
probability of event , 1.
probability of event , '.
(iii) calculate the epected number of times
an event will occur" given the probabilityof the event and number of trials;
mphasise that the value of
probability is between ' and 1.
(iv) solve problems involving probability;
redict possible events which
might occur in daily situations.
(v) predict the occurrence of an outcome and
ma+e a decision based on +nown
information.
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#LEARNING AREA:
CIRC ES III Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: > Students will be able to:$> a) understand and use the
concept of tangents to a
circle.
Develop concepts and abilities
through activities using
technology such as the
#eometerIs 9+etchpad andgraphing calculator.
(i) identify tangents to a circle;
(ii) ma+e inference that the tangent to a
circle is a straight line perpendicular to
the radius that passes through the contactpoint;
(iii) construct the tangent to a circle passing
through a point:a) on the circumference of the circle;
b) outside the circle;
(iv) determine the properties related to twotangents to a circle from a given point
outside the circle;
roperties of angle insemicircles can be used.
amples of properties of
two tangents to a circle:
A",!"
A"$, !"$
A$", !$"
A$"and !$"are
A
!
$ "
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#LEARNING AREA:
CIRC ES III Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: > Students will be able to:
congruent.
(v) solve problems involving tangents to a
circle.
Relate to ythagoras
theorem.
$@ a) understand and use the
properties of angle between
tangent and chord to solve
problems.
plore the property of angle in
alternate segment using
#eometerIs 9+etchpad or other
teaching aids.
(i) identify the angle in the alternate
segment which is subtended by the chord
through the contact point of the tangent;
(ii) verify the relationship between the angle
formed by the tangent and the chord with
the angle in the alternate segment which
is subtended by the chord;
A!E, !%E
"!%, !E%
(iii) perform calculations involving the angle
in alternate segment;
(iv) solve problems involving tangent to a
circle and angle in alternate segment.
*' a) understand and use the Discuss the maimum number (i) determine the number of common mphasise that the lengths
E
%
A ! "
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#LEARNING AREA:
CIRC ES III Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: > Students will be able to:
properties of common
tangents to solve problems.
of common tangents for the
three cases.
tangents which can be drawn to two
circles which:
a) intersect at two points;
b) intersect only at one point;
c) do not intersect;
of common tangents are
e&ual.
nclude daily situations. (ii) determine the properties related to thecommon tangent to two circles which:
a) intersect at two points;b) intersect only at one point;
c) do not intersect;
(iii) solve problems involving commontangents to two circles;
(iv) solve problems involving tangents and
common tangents.
nclude problems involving
ythagoras theorem.
*1 393 $
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$LEARNING AREA:
TRIGONOMETR" II Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: @ Students will be able to:
*$ ? * a) understand and use the
concept of the values of
sin " cos and tan ('*5') to solve problems.
plain the meaning of unit
circle.
(i) identify the &uadrants and angles in the
unit circle;
3he unit circle is the circle
of radius 1 with its centre at
the origin.
(ii) determine:
a) the value of#Kcoordinate;
b) the value ofxKcoordinate;
c) the ratio of#Kcoordinate toxK
coordinate;
of several points on the circumference ofthe unit circle;
/egin with definitions of sine"
cosine and tangent of an acute
angle.
##
$P
PQ===
1sin
xx
$P
$Q===
1cos
x
#
$Q
PQ==tan
(iii) verify that" for an angle in &uadrant of
the unit circle :
a) sin ,#Kcoordinate ;
b) cos,xKcoordinate;
c)coordinate
coordinatetan
=
x
# ;
(iv) determine the values of
a) sine;
b) cosine;
c) tangent;
of an angle in &uadrant of the unit
'
#
x
P &x'#(
#1
x Q
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$LEARNING AREA:
TRIGONOMETR" II Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: @ Students will be able to:
circle;
plain that the concept
sin ,#Kcoordinate ;
cos,xKcoordinate;
coordinate
coordinatetan
=
x
#
can be etended to angles in
&uadrant " and '" $='" *5'.
%se the above triangles to find
the values of sine" cosine and
tangent for *'" 2" 5'.
(vii) determine the values of sine" cosine and
tangent for special angles;
3eaching can be epandedthrough activities such as
reflection.
(viii) determine the values of the angles in&uadrant which correspond to the
values of the angles in other &uadrants;%se the #eometerIs 9+etchpad
to eplore the change in thevalues of sine" cosine and
tangent relative to the change in
angles.
(i) state the relationships between the values
of:
a) sine;
b) cosine; and
1 $
2o
1
5'o
*'o
1
$
*
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$LEARNING AREA:
TRIGONOMETR" II Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: @ Students will be able to:
c) tangent;
of angles in &uadrant " and < with
their respective values of the
corresponding angle in &uadrant ;
() find the values of sine" cosine and
tangent of the angles between @'and*5';
(i) find the angles between 'and *5'"given the values of sine" cosine or
tangent;
Relate to daily situations. (ii) solve problems involving sine" cosine
and tangent.
*2 a) draw and use the graphs
of sine" cosine and tangent.
%se the graphing calculator and
#eometerIs 9+etchpad toeplore the feature of the graphs
of
#, sin "#, cos "#, tan .
(i) draw the graphs of sine" cosine and
tangent for angles between 'and *5';
Discuss the feature of the graphs
of
#, sin "#, cos "#, tan .
(ii) compare the graphs of sine" cosine and
tangent for angles between 'and *5';
Discuss the eamples of these
graphs in other area.
(iii) solve problems involving graphs of sine"
cosine and tangent.
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1%LEARNING AREA:
ANG ES OF E EVATION AND DEPRESSION Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 1' Students will be able to:
*5 a) understand and use the
concept of angle of elevation
and angle of depression to
solve problems.
%se daily situations to
introduce the concept.
(i) identify:
a) the horizontal line;
b) the angle of elevation;
c) the angle of depression"
for a particular situation;
(ii) Represent a particular situation
involving:
a) the angle of elevation;
b) the angle of depression" usingdiagrams;
nclude two observations on
the same horizontal plane.
(iii) 9olve problems involving the angle of
elevation and the angle of depression.
nvolve activities outside
the classroom.
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11LEARNING AREA:
INES AND P ANES IN 3&DIMENSIONS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 11 Students will be able to:
*= ? *> a) understand and use the
concept of angle between
lines and planes to solve
problems.
4arry out activities using daily
situations and *Kdimensional
models.
(i) identify planes;
Differentiate between $K
dimensional and *Kdimensional
shapes. nvolve planes found in
natural surroundings.
(ii) identify horizontal planes" vertical planes
and inclined planes;
(iii) s+etch a three dimensional shape and
identify the specific planes;
(iv) identify:a) lines that lies on a plane;
b) lines that intersect with a plane;
(v) identify normals to a given plane;
/egin with *Kdimensional
models.
(vi) determine the orthogonal pro6ection of a
line on a plane;
(vii) draw and name the orthogonal pro6ectionof a line on a plane;
nclude lines in *Kdimensional shapes.
(viii) determine the angle between a line and a
plane;%se *Kdimensional models to
give clearer pictures.
(i) solve problems involving the angle
between a line and a plane.
a) understand and use theconcept of angle between
two planes to solve
(i) identify the line of intersection betweentwo planes;
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11LEARNING AREA:
INES AND P ANES IN 3&DIMENSIONS Form 4WEEK LEARNING OBJECTIVES
SUGGESTED TEACHING AND
LEARNING ACTIVITIESLEARNING OUTCOME POINTS TO NOTE
Students will be taught to: 11 Students will be able to:
problems.
(ii) draw a line on each plane which is
perpendicular to the line of intersectionof the two planes at a point on the line of
intersection;
%se *Kdimensional models togive clearer pictures.
(iii) determine the angle between two planeson a model and a given diagram;
(iv) solve problems involving lines and
planes in *Kdimensional shapes.
*@ K $ 0H! MR NLH3EH-R