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SMK St. Mark, Butterworth
Scheme of Work
Form 4 Mathematics ( 2013 )
First Term ( 20 weeks )
Weeks Topics Learning Objectives Learning Outcomes Teaching And Learning
Activities
Vocabulary
1 - 2 1. Standard
Form
1.1 Understand and use the
concept of significantfigure.
1.2 Understand and use the
concept of standard form tosolve problems
i. round off positive numbers to a given
number of significant figures when thenumber are :
a) greater than 1.
b) less than 1ii .perform operations of addition ,
subtraction , multiplication and division
involving a few numbers and state theanswer in specific significant figures .
iii. solve problems involving significant
figures .
i. state positive numbers in standard form
when the numbers are :a) greater than or equal to 10.
b) less than 1.ii. convert numbers in standard form to
single numbers.
iii. perform operations of addition,
subtraction , multiplication anddivision , involving any two numbersand state the answer in standard form
iv. solve problems involving numbers in
standard form.
Discuss the significance
of zero in a number.
- Working out mentally.
- Identifying relations.
Discuss the use of
significant figures ineveryday life and other
areas.
Use everyday life
situations such as inhealth,technology
,industry ,constructionand business involving
numbers in standard
form.
Use the scientificcalculator to explore
numbers in standard
form.
significance
significantfigure
relevant
round offaccuracy
single number
approximate
standard form
single numberscientific
notation
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Week Topics Learning Objectives Learning Outcomes Teaching And Learning
Activities
Vocabulary
34 2. Quadratic
Expressions
And
Equations
2.1 Understand the concept of
quadratic expression.
2.2 Factorise quadratic
expression.
2.3 Understand the concept of
quadratic equation
2.4 Understand and use the
concept of roots ofquadratic equations to
solve problems.
i. identify quadratic expressions .
angles of a polygons.
ii. form quadratic expressions by
multiplying any two linear expressions.iii. form quadratic expressions based on
specific situations.
polygon given the number of sides.
i. factorise quadratic expressions of the
form ax2 + bx + c , where b = 0 or c = 0.
ii. factorise quadratic expressions of the
form px2q ,p and q are perfect squares.
iii. factorise quadratic expressions of the
form ax2
+ bx + c, where a,b and c arenot equal to zero.
iv. factorise quadratic expressionscontaining coefficients with
common factors.
i. identify quadratic equations with one
unknown.ii. write quadratic equations in general form
i.e ax2 + bx + c = 0
iii. form quadratic equations based on
specific situations.
i. determine whether a given value is a root
of a specific quadratic equation.ii. determine the solution for quadratic
equations by ;a) trial and error method / b) factorizationiii.solve problems involving quadratic
equations
Discuss the
characteristics of
quadratic expressions of
the form ax2 + bx + c =0, where a , b and c are
constants , a 0 and x is
an unknown.
Discuss the various
methods to obtain the
desired product.
Begin with the case a =1
Explore the use ofgraphing calculator to
factorise quadraticexpressions.
Discuss the
characteristics ofquadratic equations.
Discuss the number of
roots of a quadraticequation.
Use everyday lifesituations.
quadratic
expression
constant
constant factorunknown
highest power
coefficient
expandterm
factorise
common factor
perfect squarecross method
inspectioncomplete
factorisation
quadratic
equationsgeneral form
substitute
roottrial and error
methodsolution.
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Week Topics Learning Objectives Learning Outcomes Teaching And Learning
Activities
Vocabulary
5 3. Sets 3.1Understand the concept of
set.
3.2 Understand and use the
concept o f subset ,universal set and the
complement of a set.
i. sort given objects into groups.
ii. define sets by ;
a) descriptions.
b) using set notation.iii. identify whether a given object is an
element of a set and use the symbol or
iv.represent sets by using Venn diagrams.v. list the elements and state the number of
elements of a set.
vi. determine whether a set is an empty set.
vii. determine whether two sets are equal.
i. determine whether a given set is a subset
of a specific set and use the symbol or
ii. represent subset using Venn diagram.
iii.list the subjects for a specific set.
iv. illustrate the relationship between setand universal set using Venn diagram.
v. determine the complement of a given set.
vi. determine the relationship between set ,subset ,universal set and the complement
of a set.
Use everyday life
examples to introduce the
concept of set.
Discuss why { o }and
{ } are not empty
sets.
Comparing and
contrasting
Drawing diagrams
Discuss the relationship
between sets anduniversal sets.
Identifying relations
set
element
description
labelset notation
denote
equal set
subset
universal set
complement of a
set
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Weeks Topics Learning Objectives Learning Outcomes Teaching And Learning
Activities
Vocabulary
6 3.3 Perform operations on sets
The intersectionof sets
The union of sets
i. determine the intersection of ;
a) two sets
b) three sets
and use the symbol .ii. represent the intersection of sets using
Venn diagram
iii. state the relationship between
a) A B and Ab) A B and B
iv. Determine the complement of the
intersection of sets.
v. solve problems involving the
intersection of sets.vi. determine the union of
a) two setsb) three sets
and use the symbol
vii. represent the union of sets using
Venn diagram.
viii.state the relationship between
a) A B and A
b) A B and B
ix. determine the complement of the union
of sets.x. solve problems involving the union of
sets.xi. determine the outcome of combined
operations on sets .
xii. solve problems involving combinedoperations on sets.
Discuss cases when;
A B = A B
Include everyday life
situations.
intersection
common
elements
7 Chinese New Year Holidays (11th
February17th
February)
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Weeks Topics Learning Objectives Learning Outcomes Teaching And Learning
Activities
Vocabulary
8 4.Mathematical
Reasoning
4.1 Understand the concept of
statement .
4.2 Understand the concept ofquantifiers all and
some
4.3 Perform operations
involving the words not
for no , and and oron statement.
i) determine whether a given sentence is a
statement
ii) determine whether a given statement is
true or false.iii) construct true or false statement using
given numbers and mathematical
symbols.
i) construct statements using the quantifier :a) all
b) someii) determine whether a statement that
contains the quantifier allis true or
falseiii) determine whether a statement can be
generalized to cover all cases by usingthe quantifier all
iv) construct a true statement using the
quantifier all or some given an
object and a property.
i) change the truth value of a given
statement by placing the word not into
the orginal statement.
Introduce this topic
using everyday life
situations.
Focus on mathematical
sentences.
Discuss sentencesconsisting of :1.words only
2. numbers and words
3. numbers and
mathematical symbols.
Quantifiers such asevery and any can be
introduced based oncontext.
Other quantifiers such as several ,one of and
part of can be usedbased on context.
The symbol ~ ( tilde )
denotes negation.
~p denotes negationof p which meansnot p or no p .
statement
true
false
mathematicalsentence
mathematical
statement
mathematicalsymbols
quantifierall
everyany
some
severalone of
part of
negatecontrary
object
negation
not pno ptruth table
truth value
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Weeks Topics Learning Objectives Learning Outcomes Teaching And Learning
Activities
Vocabulary
9
4.4 Understand the concept ofimplication
ii) identify two statements from a
compound statement that contains the
word and.
iii) form a compound statement bycombining two givens statements using
the word and
iv) identify two statements from a
compound statement that contains theword or
v) form a compound statements by
combining two given statements using
the word or
vi) determine the truth value of acompound statement which is the
combination of two statements with theword and
vii) determine the truth value of acompound statement which is the
combination of two statements with the
word or
i) identify the antecedent and consequentof an implication if p, then q .
ii) write two implication from a compound
statement.
iii) construct mathematical statementin the form of implicationa) if p , then q
b) p if and only if q
iv) determine the converse of a given
implication.v) determine whether the converse of an
implication is true or false.
and
compound
statement
or
implicationantecedent
consequent
converse
10 Assessment 1 (4th
March8th
March)
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Weeks Topics Learning Objectives Learning Outcomes Teaching And Learning
Activities
Vocabulary
11 - 12 4.5 Understand the concept of
argument.
4.6 Understand and use the
concept of deduction andinduction to solve
problems.
i) identify the premise and conclusion of a
given simple argument
ii) make conclusion based on two given
premises for :a) Argument Form I
b) Argument Form II
c) Argument Form III
iii) complete an argument given a premiseand the conclusion.
i) determine whether a conclusion is made
througha) reasoning by deduction
b) reasoning by induction.ii) make a conclusion for a specific case
based on a given general statement ,bydeduction .
iii) make generalization based on
the pattern of a numerical sequence ,byinduction.
iv) use deduction and induction in problemsolving .
Limit to arguments with
true premises.
Encourage students toproduce arguments based
on previous knowledge .
Limit to cases where
formulae can be induced.
Specify that:* making conclusion by
deduction is definite.
* making conclusion by
induction is notnecessarily
definite.
argument
premise
conclusion
reasoning
deductioninduction
pattern
specialconclusion
generalstatement
general
conclusion
specific case
numericalsequence.
Mid-term School Holidays (23rd
March31st
March)
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Weeks Topics Learning Objectives Learning Outcomes Teaching And Learning
Activities
Vocabulary
13 5. The Straight
Line
5.1 Understand the concept of
gradient of a straight line.
5.2 Understand the concept ofgradient of a straight line
in Cartesian coordinates.
5.3 Understand the concept of
intercept.
5.4 Understand and useequation of a straight line
i) determine the vertical and horizontal
distances between two given points on a
straight line.
ii) determine the ratio of vertical distanceto horizontal distance.
i) derive the formula for the gradient ofa straight line.
ii) calculate the gradient of a straight linepassing through two points.
iii) determine the relationship between thevalue of the gradient and the
a) steepness
b) direction of inclination of a straightline.
i). determine the xintercept and the y-
intercept of a straight line.
ii) derive the formula for the gradient of a
straight line in terms of the x- interceptand the y- intercept
iii) Perform calculations involving gradient
, xintercept and y- intercept
i) draw the graph given an equation of theform , y = mx +c
ii) determine whether a given point lies on
a specific straight line.
Use technology such as
the Geometers
Sketchpad , graphing ,
calculators , graph boards, magnetic boards , topo
maps as teaching aids
where appropriate.
Discuss :* the relationship
between gradient and
tan .
Discuss the value ofgradient if
* P is chosen as( x1 , y1 ) and Q is
( x2 , y2 )* P is chosen as
( x2 , y2 ) and Q is
( x1 , y1 ).
Discuss the change in theform of the straight lineif the values of m and c
are changed.
straight line
steepness
horizontal
distancevertical distance
gradient
ratio
acute angleobtuse angle
inclined upwards to the
rightinclined
downwards to
the rightundefined
x-intercept
y-intercept
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Weeks Topics Learning Objectives Learning Outcomes Teaching And LearningActivities
Vocabulary
14
5.5 Understand and use
the concept of parallellines.
iii) write the equation of the straight line
given the gradient and yintercept.
iv) determine the gradient and y- intercept
of the straight line which equation isthe form :
a). y = mx + c
b). ax + by = c
v) find the equation of the straight linewhich :a) is parallel to the x- axis
b) is parallel to the y- axis
c) passes through a given point and
has a specific gradient.d) passes through two given points.
vi) find the point of intersection of twostraight lines by :
a) drawing the two straight lines.b) solving simultaneous equations.
i) verify that two parallel lines have thesame gradient and vice versa.
ii) determine from the given equationwhether two straight lines are parallel.
iii) find the quation of the straight line
which passes through a given point and
is parallel to another straight l ine.iv) solve problems involving straight lines
Carry out activities using
the graphing calculator ,
Geometers Sketchpad or
other teaching aids.
Verify that m is the
gradient and c is the y
intercept of a straight linewith equation y = mx + c
Discuss and conclude that
the point of intersection is
the only point thatsatisfies both equation.
Explore properties ofparallel lines .
linear equation
graph
table of valuescoefficient
constant
satisfy
parallel
point of
intersection
simultaneousequation.
parallel lines .
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Weeks Topics Learning Objectives Learning Outcomes Teaching and Learning
Activities
Vocabulary
15 6. Statistics 6.1Understand the concept
of class interval
6.2 Understand and use theconcept of mode and
mean of grouped data
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 lower
boundary of a class in a groupeddata.
iii) calculate the size of a class interval.
iv) determine the class interval given a setof data and the number of classes
v) determine a suitable class interval forgiven set of data.
vi) construct a frequency table for a given
set of data.
i) determine the modal class from thefrequency table of grouped data.
ii) calculate the midpoint of a classiii) verify the formula for the mean of
grouped data .
iv) calculate the mean from the frequencytable of grouped data .
v) discuss the effect of the size of class
interval on the accuracy of the meanfor a specific set of grouped data.
Use data obtained from
activities and othersources such as research
studies to introduce theconcept of class interval
Size of class interval =
[ upper boundarylowerboundary ]
Discuss criteria for
suitable class intervals
Midpoint of class = ( lower limit + upper
limit )
statistics
class intervaldata
grouped dataupper limit
lower limitupper boundary
lower boundary
size of classinterval
frequency table
modemode class
meanmidpoint of a
class
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Weeks Topics Learning Objectives Learning Outcomes Teaching and Learning
Activities
Vocabulary
16
17
6.3Represent and interpret
data in histograms with
class intervala of the samesize to solve problems.
6.4 Represent and interpret
data in frequency
polygons to solveproblems.
6.5 Understand the concept ofcumulative frequency
i) draw a histogram based on the frequency
table of a grouped data.
ii) interpret information from a givenhistogram.
iii) solve problems involving histograms.
i) draw the frequency polygon based on
a) a histogram
b) a frequency table
ii) interpret information from a givenfrequency polygon.
iii) solve problems involving frequencypolygon
i) construct the cumulative frequency tablefor :
a) ungrouped datab) grouped data
ii) draw the ogive for :
a) ungrouped datab) grouped data
Discuss the difference
between histogram and
bar chart .
Use graphing calculator to
explore the effect of
different class interval onhistogram
When drawing a
frequency polygon add a
class with 0 frequencybefore the first class and
after the last class .
Include everyday lifesituations.
When drawing ogive :
use the upperboundaries
add a class withzero frequencybefore the first
class.
uniform class
interval
histogram
vertical axis
horizontal axis
frequency polygon
cumulativefrequency
ungrouped dataogive
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Weeks Topics Learning Objectives Learning Outcomes Teaching and Learning
Activities
Vocabulary
6.6 Understand and use the
concept of measures of
dispersion to solve
problems.
i) determine the range of a set of data
ii) determine :
a) the medium
b) the first quartilec) the third quartile
d) the interquartile range;from the ogive
iii) interpret information from an ogive .
iv) solve problems involving datarepresentations and measures ofdispersion.
For grouped data :
Range = [ midpoint of the
last classmidpoint ofthe first class ]
Emphasise the importance
of honesty and accuracyin managing statisticalresearch
range
measures of
dispersion
medianfirst quartile
third quartile
interquartile range
1819 Mid-year Examination (6th May17
th May)
20 Discussion of the mid-year examination paper
Mid-year School Holidays (25th
May9th
June)
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Second Term (22 weeks)
Weeks Topics Learning Objectives Learning Outcomes Teaching and Learning
Activities
Vocabulary
21 7. Probability 1 7.1 Understand the concept ofsample space.
7.2 Understand the concept
of events .
i) determine whether an outcome is apossible outcome of an experiment.
ii) list all the possible outcomes of an
experiment :
a) from activitiesb) by reasoning
iii) determine the sample space of an
experiment
iv) write the sample space by using set
notations.
i) identify the elements of a sample space
which satisfy given conditions .
ii) list all the elements of a sample spacewhich satisfy certain conditions using
set notation .iii) determine whether an event is possible
for a sample space.
Use concrete examplessuch as throwing a die
and tossing a coin .
Classifying Identifying
relations
Drawingdiagrams
An impossible event is an
empty set .
Discuss that an event is a
subset of the samplespace.
Discuss also impossible
events for a sample space.
Discuss that the sample
space itself is an event.
sample spaceoutcome
experiment
possible outcome
event
elementsubset
empty setimpossible event
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Weeks Topics Learning Objectives Learning Outcomes
Teaching And Learning
Activities
Vocabulary
22 - 23 7.3 Understand and use the
concept of probability ofan event to solve
problems
i) find the ratio of the number of times an
event occurs to the number of trials .ii) find the probability of an event from a
big enough number of trials.
iii) calculate the expected number of times
an event will occur ,given theprobability of the event and number oftrials.
iv) solve problems involving probability.
v) predict the occurrence of an outcome
and make a decision based on knowninformation.
Carry out activities to
introduce the concept ofprobability . The graphing
calculator can be used to
simulate such activities.
Probability is obtainedfrom activities and
appropriate data.
Discuss situation whichresults in :
probability ofevent =1
probability ofevent =0
Emphasise that the valueof probability is between0 and 1.
Predict possible events
which might occur indaily situations.
probability
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Weeks Topics Learning Objectives Learning Outcomes Teaching and Learning
Activities
Vocabulary
24 - 25 8. Circles II 8.1 Understand and use theconcept of tangents to a
circle .
8.2 Understand and use the
properties of angle
between tangent andchord to solve problems.
i) identify tangents to a circle .ii) make inference that the tangent to a
circle is a straight line perpendicular tothe radius that passes through the
contact point.iii) construct the tangent to a circle passing
through a point :
a) on the circumference of the circleb) outside the circle .
iv) determine the properties related to twotangents to a circle from a given point
outside the circle.
v) solve problems involving tangents to a
circle .
i) identify the angle in the alternate
segment which is subtended by the chord
through the contact point of the targent.ii) verify the relationship between the angle
formed by the tangent and the chordwith the angle in the alternate segment
which is subtended by the chord.
iii) perform calculations involving theangle in alternate segment .
iv) solve problems involving tangent to a
circle and angle in alternate segment.
Develop concepts andabilities through activities
using technology such asthe Geometers Sketchpad
and graphing calculator .
Relate to Pythagorastheorem.
Explore the property of
angle in alternate segment
using GeometersSketchpad or other
teaching aids
tangent to a circlecircle
perpendicular
radiuscircumference
semicircle
congruent
chords
alternate segment
major sectorsubtended
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Co
Weeks Topics Learning Objectives Learning Outcomes Teaching and LearningActivities
Vocabulary
28 - 30 9. Trigonometry
( II )
9.1Understand and use the
concept of values of sin ,
cos , tan ( 00
3600 ) to solve problems
i) identify the quadrants and angles in the
unit circle .
ii) determine :a) the value of y-coordinate ;
b) the value of x- coordinate ;c) the ratio of ycoordinate to x
coordinate ;of several points on the circumference
of the unit circle ;
iii) verify that , for an angle in quadrant 1of the unit circle;
a) sin = y- coordinateb) cos = x coordinate
c) tan = ycoordinate
xcoordinate
iv) determine the values ofa) sine b) cosine c) tangent
of an angle in quadrant 1 of the unit circle
v) determine the values of:
a) sine b) cosine
c) tangent for 900 3600
vi) determine whether the values of :
a) sine b) cosine c) tangentof an angle in a specific quadrant is
positive or negative;
vii) determine the values of sine ,cosine
and tangent for special anglesviii) determine the values of the angles in
quadrant 1 which correspond to the
values of the angles in other quadrant
Explain the meaning of
unit circle.
The unit circle is the
circle of radius 1 with itscentre at the origin .
Begin with definitions of
sine ,cosine and tangent
of an acute angle.
Explain that the concept
sin = y- coordinatecos = x coordinate
tan = ycoordinate
xcoordinate
can be extended to anglesin quadrant II , III and IV.
quadrant
sine
cosine
tangent
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31
v
alu
es
o
f
s
in
,
cos
,
t
a
n
(
val
ues
of
:
a
)s
in
e
b
)
cos
i
n
e
,a
n
d
00
,
450
,
6
00
,
900
,
18
00
,
2
7
0
0
,
3
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32
00
3
6
00
)t
o
sol
v
e
pr
o
b
l
ems
c)
tan
g
en
t
o
f
an
gl
es
i
n
qu
a
d
r
ant
I
6
00
.
Te
a
ch
i
ng
ca
nb
e
exp
a
n
d
ed
t
h
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33
9.
2
Dr
aw
an
d
use
t
h
eg
r
a
I
,
III
an
d
I
V
w
i
th
t
hei
r
res
p
e
c
tiv
e
r
o
ugh
ac
t
iv
i
ti
e
ss
uc
ha
s
ref
l
e
c
tio
n
.
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34
p
h
s
of
s
in
e
,
cos
in
ea
n
d
t
a
n
g
ent
v
a
lue
so
f
t
h
e
cor
re
spo
n
d
ing
a
n
gle
i
U
s
et
he
G
eo
m
et
e
rs
S
ket
c
h
pad
t
o
ex
p
l
7/29/2019 Math F4(2013)
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35
n
qua
dra
n
t
I
.
x
)f
in
dt
h
e
va
l
u
e
so
f
o
r
et
he
c
ha
n
ge
in
th
ev
a
l
ues
o
f
si
n
e
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37
l
e
sb
etw
e
en
900
an
d
36
00
xi
)
f
ind
t
e
cha
nge
in
an
g
les
.
Rel
a
t
et
o
d
ail
y
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38
h
e
an
gle
s
b
e
tw
e
en
00
an
d
3600
giv
e
n
s
i
tua
tio
n
U
se
the
g
rap
h
i
ng
c
a
l
cul
a
t
7/29/2019 Math F4(2013)
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39
t
he
val
u
es
of
sin
e,
cos
i
n
eo
r
tan
g
e
o
r
an
dG
e
om
e
te
r
s
Sk
etc
h
p
ad
t
o
exp
l
o
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40
n
t
xii
)s
o
lv
e
p
r
obl
em
si
n
v
olv
i
n
g
si
n
e
r
e
th
ef
e
at
u
re
of
th
eg
r
a
phs
o
f
y=
s
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41
,
cos
ine
a
n
d
t
ang
en
t
i
)
.dr
a
w
the
g
i
n
,y
=
c
os
,
y
=
t
a
n
D
i
scu
s
s
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42
r
a
phs
of
si
n
e
,
cos
in
ea
n
d
t
a
n
g
ent
f
t
he
fea
t
ur
e
o
f
th
e
gra
p
h
so
f
y
=
s
i
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43
o
r
an
gle
s
b
e
tw
e
en
00
an
d
3600
ii)
.
c
n
,
y
=
c
o
s
,
y
=t
a
n
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44
o
m
par
e
t
h
e
g
ra
p
hs
of
si
n
e
,c
o
s
i
ne
a
n
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45
d
ta
n
ge
n
t
f
or
ang
le
sb
e
t
wee
n
00
a
n
d
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46
3
600
ii
i
).
s
ol
v
ep
ro
ble
m
s
in
v
o
l
vin
g
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47
g
r
aph
s
o
f
s
in
e
,co
si
ne
a
n
dt
a
n
g
ent
3 Assessment
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48
2 2 (2nd
September
6th
September)
Weeks Topics Learning Objectives Learning Outcomes Teaching and LearningActivities Vocabulary
33 10. Angles Of
Elevation
And
Depression
10.1Understand and use the
concept of angle ofelevation and angle of
depression to solve
problems .
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 elevationb) the angle of depression using
diagrams .
iii) solve problems involving the angle of
elevation and the angleof depression.
Use daily situations to
introduce the concept
Include two observations
on the same horizontalplane.
Involve activities outsidethe classroom
angle of elevation
angle ofdepression
horizontal line
34 11. Lines and
Planes In 3
Dimensions
11.1 Understand and use the
concept of anglebetween lines and planes
to solve problems .
i) identify planes .
ii) identify horizontal planes ,vertical planesand inclined planes .
iii) sketch a three dimensional shape and
identify the specific planes .iv) identify ;
a) lines that lies on a planeb) lines that intersect with a plane.
v). identify normals to agiven plane .
vi) determine the orthogonal projection ofa line on a plane .
vii) draw and name the orthogonalprojection of a line on a plane.
viii) determine the angle between a line and
a plane.ix) solve problems involving the angle
Carry out activities using
daily situations and 3dimensional models .
Differentiate between 2dimensional and 3
dimensional shapes.Involve planes found in
natural surroundings.
Begin with 3dimensional
models
Include lines in 3
dimensional shapesUse 3dimensional
horizontal
plane
vertical plane
3- dimensionalnormal to a plane
orthogonalprojection
space diagonal
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49
between a line and a plane . models togive clearer
pictures .
Weeks Topics Learning Objectives Learning Outcomes Teaching and Learning
Activities
Vocabulary
3536 11. Lines and
Planes In 3
Dimensions
11.2 Understand and use theconcept of angle
between two planes
to solve problems.
i) identify the line of intersection betweentwo planes .
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 .iii) determine the angle between two planes
on a model and a given diagram .
iv) solve problems involving lines and
planes in 3dimensional shapes .
Angle betweentwo planes
3740 Final Year Examination (7th
October29th
October)
41 - 42 Discussion of the final year examination paper
Revision
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