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8/8/2019 Yearlyplan mathF.5,2011
1/25
1
Yearly Plan Mathematics Form 5 (2011)
WeekNo
Learning ObjectivesPupils will be taught
to.....
Learning Outcomes
Pupils will be able to
No of
Periods
Suggested Teaching & Learning
activities/Learning Skills/ValuesPoints to Note
Learning Area : NUMBER BASES -- 2 weeks
First Term
1
3/1-7/1/11
1. Understand and use
the concept of numberin base two, eight and
five.
(i) State zero, one, two, three, ,as a number in base:
a) two
b) eight
c) five
(ii) State the value of a digit of a
number in base:
a) twob) eight
c) five
(iii) Write a number in base:
a) two
b) eight
c) five
in expanded notation
1
1
2
Use models such as a clock face or a
counter which uses a particular
number base.
Discuss
- Dicuss digits used- Place valuesin the number system with a
particular number base.
Skill : Interpretation, observe
connection between base two, eightand five.
Use of daily life examples
Values : systematic, careful, patient
Emphasis the ways to read numbers in
variours bases.
Give examples:
Numbers in base two are also know as
binary numbers.
Expanded notation
Give examples
2
10/1-
14/1/11
(iv) Convert a number in base:
a) two
b) eight
c) five
to a number in base ten and
vice versa.
2 Use number base blocks of twos,
eights and fives.
Perform repeated division to convert a
number in base ten to a number in other
bases.
Give examples.
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activities/Learning Skills/ValuesPoints to Note
(v) Convert a number in a certain
base to a number in another
base.
(vi) Perform computations
involving :
a) addition
b) subtrationof two numbers in base two
3
1
Discuss the special case of
converting a number in base two
directly to a number in base eight
and vice versa.
Skill : Interpretation, convertingnumbers to base of two, eight, fiveand then.
Use of daily life examples
Values : systematic, careful, patient
Limit conversion of numbers to base two,
eight and five only.
The usage of scientific calculator in
performing the computitations.
Topic 2 : Graphs of Functions II --- 3 weeks
317/1-
21/1/1
1
2.1 Understand
and use theconcept ofgraphs of
functions
(i) Draw the graph of a:
a) linear function :y = ax + b, where aand b are constant;
b) quadratic function
cbxaxy !2
,
where a, b and c are
constans, 0{a c) cubic function :
dcxbxaxy !23
,
where a, b, c and d are
constants, 0{a
d) reciprocal function
x
ay ! , where a is a
constants, 0{a
2 Explore graphs of functions using
graphing calculator or the GSP
Compare the characteristic of
graphs of functions with different
values of constants.
Values : Logical thinking
Skills : seeing connection, using
the GSP
Questions for 1..2(b) are given in the
form of 0
!
bxax; a and b are
numerical values.
Limit cubic functions.Refer to CS.
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(ii) Find from the graph
a) the value ofy, given a
value ofxb) the value(s) ofx,
given a value ofy
(iii) Identify:a) the shape of graph
given a type offunction
b) the type of functiongiven a graph
c) the graph given a
function and viceversa
(iv) Sketch the graph of a
given linear, quadratic,cubic or reciprocal
function.
1
2
2
Play a game or quiz
For certain functions and some valuesofy, there could be no corresponding
values ofx.
Limit the cubic and quadratic
functions.Refer to CS.
Limit cubic functions.
Refer to CS.
4
24/1-28/1/1
1
2.2 Understand
and use theconcept of thesolution of an
equation by
graphicalmethod.
(i) Find the point(s) of
intersection of two graphs
(ii) Obtain the solution of an
equation by finding the
point(s) of intersection oftwo graphs
(iii) Solve problems involvingsolution of an equation by
1
1
2
Explore using graphing calculator
of GST to relate thex-coordinate ofa point of intersection of twoappropriate graphs to the solution
of a given equation. Make
generalisation about the point(s) ofintersection of the two graphs.
Use everyday problems.
Use the traditional graph plotting
exercise if the graphing calculator orthe GSP is unavailable.
Involve everyday problems.
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Week
No
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to.....
Learning Outcomes
Pupils will be able to
No of
Periods
Suggested Teaching & Learning
activities/Learning Skills/ValuesPoints to Note
531.1-
06.2.2011
(CNY)
graphical method. Skills : Mental process
6
7/2-11/2/11
2.3 Understand anduse the concept of the
region representing
inequalities in two
variables.
(i) Determine whether a given
point satisfies
a) baxy ! or baxy " or baxy
(ii) Determine the position of a
given point relative to the
equation baxy !
(iii) Identify the regionsatisfying baxy " orbaxy
(iv) Shade the regions
representing the inequalities
a) baxy " or baxy b) baxy u or baxy e
(v) Determine the region whichsatisfy two or more
simultaneous linear
inequalities.
2
2
2
Include situations involving ax ! ,ax u , ax " , ax e or ax .
Values: Making conclusion,
connection and comparison, careful
Emphasise on the use of dashed and solid
line as well as the concept of region.
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activities/Learning Skills/ValuesPoints to Note
Week
No
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Points to Note
Topic/Learning Area :TRANSFORMATIONS III ( 3 weeks )
6
3.1 Understandingand use of theconcept ofcombination of
twotransformations.
(i) determine the image of anobject under combination oftwo isometrictransformations.
1 y using CD-Rom interactiveactivities.
y Everyday life example:around the school.
y Recall the types oftransformations:- translation- rotation- reflection- enlargement- isometric
transformation
(ii) determine the image of anobject under combination of:
a. two enlargementsb. an enlargement and and an
isometric transformation.
2 y using Geometers Sketchpad.y CD-Romy Give variety of examples to
show an enlargement and
isometric transformation.
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activities/Learning Skills/Values
Points to Note
(iii) Draw the image of an objectunder combination of two
transformations.
(iv) State the coordinates of theimage of a point undercombined transformations.
2 y Give examples on theblackboard and students are
asked to draw the image
under 2 transformations
y Tr. will state the coordinatesof the image of a point under
combined transformations.
7
14/2-
18/2/11
(v) Determine whethercombined transformation AB
is equivalent to combined
transformation BA.
3 y Using Maths exercise books(grids)
y Do exercises from thetextbooks
(vi) specify two successivetransformations in a
combined transformation
given the object and theimage.
2 y Outdoor activity studentsare brought to specific site ofthe school compound and ask
to identify the two successive
transformations : pictures
should consist of an object
and an image.
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WeekNo
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8
21/2-
25/2/11
(vii) Specify a transformationwhich is equivalent to the
combination of two
isometric transformations.
(viii) Solve problems involvingtransformations.
5 y Classroom activities useGSP and CD-ROM
(Multimedia Gallery)
y To specify isometrictransformation
y Different examples to begiven
y Various problem solvingquestions to be given
- limit to translation, reflation & rotation.
Topic/Learning Area :
MATRICES ( 4 weeks )
9
28/3-
6/3/11
4.1 Understand anduse the concept
of matrix.
(i) Form a matrix from giveninformation.
(ii) Determine:a. the number of rowsb. the number of columnsc. the order of a matrix(iii) Identify a specific element in
a matrix
1 y Understanding the concept ofmatrices through daily
examples:
- price of food on a menu- a contingent of altelitic- seating of students in
class
- mark sheet of studentsy Introduce the order (mxn) of
a matrix
y Class activity students arerequested to identify the
students seating position in
class
y Other examples give
* m represents row
* n represents column
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Points to Note
10 4.2 Understand anduse the concept
of equal matrices.
(i) Determine whether twomatrices are equal.
(ii) Solve problems involvingequal matrices.
2 y Teacher gives examples oftwo equal matrices and
discusses equal matrices in
terms of the corresponding
elements.
y Different problems given tosolve equal matrices.
4.3 Perform additionand subtraction
on matrices.
(i) Relate to real life situationssuch as keeping score of
medal tally or points insports.
(ii) Find the sum or thedifference of two matrices.
(iii) Perform addition andsubtraction on a few
matrices.
(iv) Solve matrix equationsinvolving addition and
subtraction.
CUTI PERTENGAHAN
PENGGAL 1 [36/3-20/3/10]
(WEEK 11)
2 y Teacher shows the examplesfrom the textbook to
determine how addition orsubtraction can be performed
on 2 given matrices.
y Examples given to find theaddition and subtraction of
two matrices.
y Examples given to solvematrix equations involving
additions and subtractions
y To include finding values ofunknown elements
y limit to not more than 3 rowsand 3 columns.
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12
21/3-
25/3/11
4.4 PerformMultiplication of
a matrix by a
number.
(i) Multiply a matrix by anumber.
(ii) Express a given matrix as amultiplication of another
matrix by a number.
(iii) Perform calculation onmatrices involving addition,subtraction and scalar
multiplication.(iv) Solve matrix equations
involving addition,
subtraction and scalar
multiplication.
2 y Teacher shows examples onscalar multiplication of
matrix:
- give examples of real lifesituations such as in
industrial productions.
y examples given on thecalculation of matrices
involving addition,
subtraction, and scalar
multiplication.
y Examples given on problemsolving questions.
y To include finding values ofunknown elements.
4.5 Performmultiplication oftwo matrices.
(i) determine whether twomatrices can be multipliedand state the order of the
product when the two
matrices can be multiplied.
(ii) Find the product of twomatrices.
(iii) Solve matrix equationsinvolving multiplication of
two matrices.
3 y Teacher gives real lifesituations. Examples:-
- to find the cost ofmeals in the
restaurant
- teacher shows how 2matrices can be
multiplied.
y Examples given for theproduct of two matrices.
y Examples given on problemsolving involvingmultiplication of 2 matrices.
y Limit to not more than 3 rowsand 3 columns
y Limit to 2 unknown elements
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13
28/3-3/4/11
4.6 Understand anduse the concept
of identify
matrix.
(i) determine whether a givenmatrix is an identity matrix
by multiplying it to another
matrix.
(ii) Write identity matrix of anyorder.
(iii) Perform calculationinvolving identity matrices.
2 y Teacher discusses theproperty of the number as an
identity for multiplication of a
number.
y Teacher introduces identitymatrix or unit matrix.
y Teacher gives examples ofidentity matrix of any order.
y Teacher discusses theproperties:
- AI = A- IA = A
Unit matrix is denoted by I.
Limit to 3 rows and 3 columns.
4.7 Understand anduse the conceptof inverse matrix.
(i) Determine whether a
2 X 2 matrix is the
inverse matrix of
another 2 X 2
matrix.(iii) Find the inverse matrix of a
2 X 2 matrix using:
a. the method of solvingsimultaneous linear
equations
b. a formula
3 y teacher introduces theconcept of inverse matrix and
its denotion.
y Examples given on problemsolving questions involving
matrix:- using simultaneous
linear equations
- using a formula
-1
AA = I
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14
4/4-10/4/11
4.8 Solvesimultaneous
linear equations
by usingmatrices.
(i) Write simultaneous linearequations in matrix form.
(ii) Find the matrix pq
in
a b p h
c d q k
!
using
the inverse matrix.
(iii) solve simultaneous linearequations by the matrixmethod.
(iv) Solve problems involvingmatrices.
5 y Teacher shows examples howto write simultaneous linear
equations in matrix form
y To solve simultaneous linearequations by using inverse
matrix
y Project involving matricesusing electronic spreadsheet
to be given to students.
* limit to 2 unknowns.
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Topic/Learning Area : 5. VARIATIONS
(1 Weeks)
15
11/4-
15/4/11
5.1 Understand and
use the concept ofdirect variation
(i) State the changes in aquantity with respect to the
changes in another quantity,in everyday life situations
involving direct variation.(ii) Determine from given
information whether aquantity.
(iii) Express a direct variation inthe form of equationinvolving two variables.
(iv) Find the value of a variablein a direct variation when
sufficient information isgiven.
(v) Solve problems involvingdirect variation for thefollowing cases:
y E x ; yE x2 ; y E x3 ;
y E x1/2 .
1
1
1
Discuss the characteristics of the graph
of y agains x when y E x.
Relate mathematical variation to
Charless Law or the mation of thesimple pendulum.
Discuss the characteristics of the graphs
of y against xn.
Communicative skills
Coorperation an d systematic
Y varies directly as x , yE x.
yE x n , limit E n to 2, 3 and
Y = kx where k is the constant of
variation.
5.2 Understand and
8/8/2019 Yearlyplan mathF.5,2011
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use the concept ofinverse variation
i) State the changes in aquantity with respect to
changes in another
quantity, in everyday
life situations involving
inverse variation.
ii) Determine form giveninformation whether a
quantity vaqries
inversely as another
quantity.
iii) Express an inversevariation in the form of
equation involving two
variables.
iv) Find the value of avariable in an inverse
variation whensufficient information
is given.
v) Solve problemsinvolving inverse
variation for the
following cases:
y w 1/x; y w 1/x2
y w 1/x3
;
y w 1/x1/2
1
1
Discuss the the form of the graph and
relates it to science, eg. Boyles Law.
For cases y w 1/xn
, n = 2,3 and ,
discuss the characteristics of the graph of
y against 1/xn
Graph drawing skill
Be straight and honest.
Y varies inversely as x if and only if xyis a constant.
y w 1/x
For the cases y w 1/xn, limit n to 2,3 and
If y w 1/x, then y = k/x, where k is the
constan t of variation.
Use:Y = k/x or
x1y1=x2 y2to get the solution.
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16
18/4-22/4/11
5.3 Understand and
use the concept of
joint variation
(i) Represent a joint
variation by using the
symbol w for the
following cases:
a) two direct variations
b) two inverse
variations
c) a direct variation
and an inverse
variation.
(ii) Express a jointvariation in the form of
equation.
(iii)
Find the value of avariable in a joint
variation when
sufficient information
is given.
(iv) Solve problemsinvolving joint
variation.
1
1
1
1
1
Discuss joint variation for the three cases
in everyday life situations.
Relate to science, eg. Ohms Law.
For the cases y w xn zn,
Y w 1/ xn
zn
and y w xn
/ zn,
Limit n to 2,3 and .
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Week
No
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Topic/Learning Area 6: GRADIENT & AREAUNDER A GRAPH --- 3 weeks
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17
25/4-
39/4/11
182/5-6/5/11
1920
21
22
23
6.1 Understand anduse the concept of
quantity represented
by the gradient of agraph
(i) State the quantity representedby the gradient of a graph
(ii) Draw the distance-timegraph, given:
a) a table of distance-timevalues
b) a relationship betweendistance and time
(iii) Find and interpret the
gradient of a distance-time graph
(iv) Find the speed for a period
of time from a distance-timegraph
(v) Draw a graph to show therelationship between two
variables representing certain
measurements and state themeaning of its gradient
PEPERIKSAAN
PENGGAL 1
CUTI GAWAI/CUTI
PENGGAL 1
1
2
2
2
2
Use examples in various areas suchas technology and social science
Use of daily life examples like
speed of a car, Formula One Grand
Prix, a sprinter
Compare and differentiate between
distance-time graph and speed-timegraph
Use real life situations such as
traveling from one place to anotherby train or by bus.
Use examples in social science and
economy, for example, the
increase in population in certain
years
Limit to graph of a straight line.
The gradient of a graph represents the
rate of change of a quantity on the
vertical axis with respect to the change
of another quantity on the horizontal
axis. The rate of change may have a
specific name for example speed for a
distance-time graph.
Emphasise that:
Gradient = change of distance
Time
= speed
Include graphs which consists of a
combination of a few straight lines.
For example,
Time, t
Distance, s
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24-25
13/6-24/6/11
6.2 Understand theconcept of quantity
represented by the area
under a graph
(i) State the quantity representedby the area under a graph
(ii) Find the area under a graph
(iii) Determine the distance by
finding the area under the
following of speed-time graphs:a. v=k (uniform speed)
b. v=ktc. v=kt + h
d. a combination of the above
(iv) Solve problems involving
gradient and area under a graph.
1
2
4
2
Discuss that in certain cases, the areaunder a graph may not represent any
meaningful quantity.
For example:
The area under the distance-time
graph.
Discuss the formula for finding the
area under a graph involving:
y A straight line which is parallel tothe x-axis
y A straight lien in the form ofy=kx+ h
A combination of the above.
Include speed-time and acceleration-time graphs.
Limit to graph of a straight line or a
combination of a few straight lines.
V represents speed, t represents time, h
and k are constants.
For example:
Speed, v
time, t
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Topic/Learning Area : PROBABALITY II
Second Term --- 2 weeks
26
27/6-
31/6/11
7.1 Understand anduse the concept of
probability of an
event.
(i) Determine the sample space
of an experiment withequally likely outcomes.
(ii) Determine the probability of
an event with equiprobablesample space.
(iii)Solve problems involvingprobability of an event.
1
1
1
Discuss equiprobable sample space
through concrete activities and begin
with simple cases such as tossing a
fair coin.
Use tree diagrams to obtain sample
space for tossing a fair coin or
tossing or tossing a fair dice
activities. The Graphing calculator
may also be used to simulate theseactivities.
Discuss events that produce
P(A) = 1 and P(A) = 0
Limit to sample space with equally
likely outcomes.
A sample space in which each outcomesis equally likely is called equiprobable
sample space.
The probability of an outcome A, with
equiprobable sample space
S, is P(A) = n ( A )n ( S )
( )n S
Use tree diagram where appropriate.
Include everyday problems and making
predictions.
27
4/7-8/7/11
7.2 Understand andused the concept of
probability of thecomplement of an
event.
(i) State the complement of an
event in :
(a) words
(b) set notations(ii) Find the probability of the
complement of an event.
1
1
Include events in real life
situations such as winning or
losing a game and passing or
failing an exam.
The complement of an event A is the set
of all outcomes in the sample space that
are not included in the outcomes of
event A.
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28 7.3 Understand usethe concept of
probability of
combined event.
(i) List the outcomes for events:(a) A or B as elements of set
A B
(b) A and B as elements of
set A B
(ii) Find the probability by
listing the outcomes of the
combined events :
(a) A or B(b) A and B
(iii) Solve problems involving
probability of combined
events.
2
2
1
Use real life situations to show therelationship between
y A or B and A By A and B and A B.
An example of a situation is being
chosen to be a member of an
exclusive club with restricted
conditions.
Use tree diagram and coordinateplanes to find all the outcomes of
combined events.
Use two-way classification tables of
events from newspaper articles or
statistical data to find probability of
combined events. Ask students to
create tree diagrams from these
tables. Example of a two-way
classification table :
Means of going to work
Officers Car Bus Others
Men 56 25 83
Women 50 42 37
Discuss :
y situations where decisionshave to be made onprobability, for example in
business, such as determining
the value for aspecific
insurance policy and time the
slot for TV advertisements
y the statement probability isthe underlying language of
statistics
Emphasise that :
y knowledge about probability isuseful in making decisions.
y prediction based on probabilityis not definite or absolute.
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Topic/Learning Area : BEARING --- 1 week
29
18/7-22/7/11
8.1. Understand anduse the concept of
bearing.
(i) Draw and label the eight maincompass directions:
a) north, south, east, west
b) north east, north west,
south east, south west
ii) State the compass angle ofany compass direction.
(iii) Draw a diagram of a point
which shows the direction ofB relative to another point A
given the bearing of B from
A.
(iv) State the bearing point A
from point B based on giveninformation.
(v) Solve problemsinvolving bearing.
1
1
1
2
Carry out the activities or gamesinvolving finding directions using a
compass such as treasure hunt or
scravenger hubt. It can also be about
locating several points on a map,
finding the position of students in
class.
Discuss the use of bearing in real life
situations. For example, a mapreading and navigation.
Compass angle and bearing are writtenin three digit form, from 000
0to 360
0.
They are measured in a clockwise
direction from north. Due north is
considered as bearing 0000. For cases
involving degrees up to one decimal
point.
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Week
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Topic 9
Learning Area: EARTH AS SPHERE ( 3 weeks )
30
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9.1 Understand anduse the concept of
longitude
(i) Sketch a great circle through the
north and south poles.
(ii) State the longitude of a given
point.
(iii) Sketch and label a meridianwith the longitude given.
(iv) Find the difference betweentwo longitudes
1
1
Model such as globes should be used.
Introduce the meridian through
Greenwich in England as the
Greenwich Meridian with longitude0
Discuss that:
y All points on a meridian have thesame longitude
y There are two meridians on agreat circle through both poles.
y Meridians with longitude xE(orW) and (180- x)W(or E) forma great circle through both poles.
Emphasise that longitude 180E and
longitue 180W refer to the same
meridian.
Express the difference between twolongitudes with an angle in the range
of 0 x 180
309.2 Understand and
use the concept oflatitude
(i) Sketch a circle parallel to the
equator.
(ii) State the latitude of a given
point.
(iii) Sketch and label a parallel of
latitude.
(iv) Find the difference between
two latitudes.
1
1
Discuss that all the points on a
paralell of latitude have the same
latitude.
Emphasise that
o the latitude of the equator is 0o latitude ranges from 0 to 90N
( or S )
Involve actual places on the earth.
Express the diffrence between two
latitudes with an angle in the range
of 0 x 180.
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30 9.3 Understand theconcept oflocations of a
place.
Use a globe or a map to find
locations of cities around the world.
Use a globe or map to name a placegiven its location.
1
1
i. State the latitude and longitudeof a given place
ii. Mark the location of a placeiii. Sketch and label the latitude and
longitude of a given place.
iv.
A place on the surface of the earth is
represented by a point.
The, location of a place A at latitudexN and longitude yE is written ,as
A(xN, yE).
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9.4 Understand anduse the concept of
distance on the surface
on the earth to solveproblems.
(i) Find the length of an arc of agreat circle in nautical mile, given
the subtended angle at the centre of
the earth and vice versa.
(ii) Find the distance between two
points measured along a meridian,
given the latitudes of both points.
(iii)Find a latitude of a point given
the latitude of another point and thedistance between the two points
along the same meridian.
(iv) Find the distance between twopoints measured along the equator,
given the longitude of both points.
(v) Find the longitude of a pointgiven the longitude of another pointand the distance between the two
points along the equator.
(vi) State the relation betwen the
radius of the earth and the radius of
a parallel of latitude.
Use the globe to find the distance
between two cities or town on the
same meridian.
Sketch the angle at the centre of the
earth that is subtentded by the arc
between two given points along the
equator. Discuss how to find the valueof this angle.
Use models such as the globe to find
Limit to nautical mile as the unit for
distance.
Explain one nautical mile as the
length of the arc of a great circle
subtending a one minute angle at the
centre of the earth.
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Topic 10
Learning Area: PLANS AND ELEVATIONS
2 weeks
(vii) State the relation between thelength of an arc on the equatoqbetween two meridian and the
lengthe of the corresponding arc ona parallel of latitude.
(viii) Find the distance between twopoints measured along a parallel oflatitude.
(ix) Find the longitude of a pointgiven the longitude of another point
and the distance between the twopoints along a parallel of latitude.
(x) Find the shortest distance
between two points on the surface
of the earth.
(xi) Solve problems involving :(a) distance between two points.
(b) travelling on the surface of theearth.
relationship between the radius of theearth and radii parallel of latitudes.
Find the distance between two citiesor town on the same parallel of
latitude as a group project.
Use the globe and a few pieces of
string to show how to determine theshortest distance between two points
on the surface of the earth.
Limit to two points on the equator or
the great a cirle through the polas.
Use knot as the unit for speed
navigation and aviation.
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10.1 Understand and
use the concept oforthogonal projection.
i. Identify orthogonalprojections.
ii. Draw orthogonalprojections, given an
object and a plane.
iii. Determine the differencebetween an object andits orthogonal
projections with respectto edges and angles.
1
2
2
Use models, blocks or plan and
elevation kit.Emphasise the different uses of dashed
lines and solid lines.
Begin wth the simple solid object such as
cube, cuboid, cylinder, cone, prism and
right pyramid.
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10.2 Understand anduse the concept of plan
and elevation.
i. Draw the plan of a solidobject.ii. Draw
- the front elevation- side elevation
of a solid object
iii. Draw the plan of asolid object.
iv. Draw
1
2
1
1
Carry out activities in groups wherestudents combine two or more
different shapes of simple solid
objects into interesting models and
draw plans and elevation for thes
models.
Use models to show that it isimportant to have a plan and at least
two side elevation to construct a solid
object.
Carry out group project:
Draw plan and elevations of buildings
Limit to full-scale drawings only.
Include drawing plan and elevation in onediagram showing projection lines.
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35
36-38
39-41
42-45
- the front elevation- side elevationof a solid object
CUTI PERTENGAHAN
PENGGAL 2
[29.8-04/9/2011]
ULANGKAJI
PEPERIKSAAN
PERCUBAAN SPM
ULANGKAJI
SPM
or structures, for example students orteachers dream home and construct a
scale model based on the drawings.
Involve real life situations such as in
building prototypes and using actual
home plans.