Yearlyplan mathF.5,2012

8/3/2019 Yearlyplan mathF.5,2012

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Yearly Plan Mathematics Form 5 (2012)

Week

No

Learning Objectives

Pupils 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

4/1-6/1/12

1. Understand and use theconcept of number in basetwo, eight and five.

(i) State zero, one, two, three, , as anumber in base:

a) two

b) eight

c) five

(ii) State the value of a digit of a numberin base:

a) two

b) 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 connectionbetween base two, eight and five.

Use of daily life examplesValues : 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

09/1-13/1/12

(iv) Convert a number in base:

a) two

b) eight

c) five

to a number in base ten and vice versa.

(v) Convert a number in a certain base to

a number in another base.

2

3

Use number base blocks of twos, eights and

fives.

Discuss the special case of converting a

number in base two directly to a number in

base eight and vice versa.

Perform repeated division to convert a number in

base ten to a number in other bases.

Give examples.

Limit conversion of numbers to base two, eight and

five only.


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2

Week

No

Learning Objectives


Learning Outcomes


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(vi) Perform computations involving :

a) addition

b) subtration

of two numbers in base two

1

Skill : Interpretation, converting numbers tobase of two, eight, five and then.

Use of daily life examples

Values : systematic, careful, patient

The usage of scientific calculator in performing the

computitations.

Topic 2 : Graphs of Functions II --- 3 weeks

316/1-

20/1/12

2.1 Understand and usethe concept 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

(ii) Find from the grapha) the value ofy, given a

value ofx

b) the value(s) ofx,given a value ofy

(iii) Identify:a) the shape of graph

given a type of

2

2

Explore graphs of functions using graphingcalculator or the GSP

Compare the characteristic of graphs offunctions with different values of constants.

Values : Logical thinking

Skills : seeing connection, using the GSP

Play a game or quiz

Questions for 1..2(b) are given in the form of

0! bxax ; a and b are numericalvalues.

Limit cubic functions.

Refer to CS.

For certain functions and some values ofy,there could be no corresponding values ofx.

Limit the cubic and quadratic functions.

Refer to CS.


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Week

No

Learning Objectives


Learning Outcomes


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421/1-28/1/12

(CNY)

function

b) the type of functiongiven a graph

c) the graph given afunction and vice

versa

(iv) Sketch the graph of a given

linear, quadratic, cubic orreciprocal function.

1Limit cubic functions.Refer to CS.

5

30/1-

03/2/12

2.2 Understand and usethe concept of thesolution of an

equation bygraphical method.

(i) Find the point(s) of intersectionof two graphs

(ii) Obtain the solution of anequation by finding the point(s)

of intersection of two graphs

(iii) Solve problems involving

solution of an equation bygraphical method.

1

1

2

1

Explore using graphing calculator of GSTto relate thex-coordinate of a point ofintersection of two appropriate graphs to

the solution of a given equation. Makegeneralisation about the point(s) of

intersection of the two graphs.

Use everyday problems.

Skills : Mental process

Use the traditional graph plotting exercise if thegraphing calculator or the GSP is unavailable.

Involve everyday problems.

2.3 Understand and use 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 region

satisfying baxy " or

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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Week

No

Learning Objectives


Learning Outcomes


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Periods



baxy

(iv) Shade the regions

representing the inequalities

a) baxy " or baxy b) baxy u or baxy e

(v) Determine the region which

satisfy two or more

simultaneous linearinequalities.

Week

No

Learning Objectives

Pupils will be taught to.....Learning Outcomes


No of

Periods


activities/Learning Skills/Values

Points to Note

Topic/Learning Area :

TRANSFORMATIONS III ( 3 weeks )

7

13/1-17/1/12

3.1 Understanding anduse of the conceptof combination oftwo transformations.

(i) determine the image of an objectunder combination of two isometrictransformations.

1 y using CD-Rom interactiveactivities.

y Everyday life example: around theschool.

y Recall the types of transformations:- translation- rotation- reflection- enlargement- isometric transformation


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WeekNo

Learning ObjectivesPupils will be taught to.....

Learning Outcomes


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Points to Note

(ii) determine the image of an objectunder 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.

(iii) Draw the image of an object undercombination of two transformations.

(iv) State the coordinates of the image ofa point under combinedtransformations.

2 y Give examples on the blackboardand students are asked to draw the

image under 2 transformations

y Tr. will state the coordinates of theimage of a point under combined

transformations.

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20/2-24/2/12

(v) Determine whether combinedtransformation AB is equivalent tocombined transformation BA.

3 y Using Maths exercise books (grids)y Do exercises from the textbooks

(vi) specify two successivetransformations in a combinedtransformation given the object andthe image.

2 y Outdoor activity students arebrought to specific site of the 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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No of

Periods



Points to Note

9

27/2-

02/3/12

(vii) Specify a transformation which isequivalent to the combination of twoisometric transformations.

(viii) Solve problems involvingtransformations.

5 y Classroom activities use GSP andCD-ROM (Multimedia Gallery)

y To specify isometric transformationy Different examples to be giveny Various problem solving questions

to be given

- limit to translation, reflation & rotation.

UJIAN PERTENGAHAN PENGGAL 1 [ 27/2-----8/3/2012]

Topic/Learning Area :

MATRICES ( 4 weeks )

10

05/3-9/3/12

4.1Understand and use theconcept of matrix.

(i) Form a matrix from giveninformation.

(ii) Determine:a. the number of rows

b. 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 students

yIntroduce the order (mxn) of amatrix

y Class activity students arerequested to identify the students

seating position in class

y Other examples give

* m represents row

* n represents column

10 4.2Understand and use theconcept of equalmatrices.

(i) Determine whether two matricesare equal.

(ii)

Solve problems involving equalmatrices.

2 y Teacher gives examples of twoequal matrices and discusses equal

matrices in terms of thecorresponding elements.

y Different problems given to solveequal matrices.


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WeekNo


Learning Outcomes


No of

Periods



Points to Note

4.3Perform addition andsubtraction onmatrices.

(i) Relate to real life situations such askeeping score of medal tally or

points in sports.

(ii) Find the sum or the difference oftwo matrices.

(iii) Perform addition and subtractionon a few matrices.

(iv) Solve matrix equations involvingaddition and subtraction.

CUTI PERTENGAHAN PENGGAL 1 [10/3 - 18/3/2012]

(WEEK 11)

2 y Teacher shows the examples fromthe textbook to determine how

addition or subtraction can be

performed on 2 given matrices.

y Examples given to find the additionand subtraction of two matrices.

y Examples given to solve matrixequations involving additions and

subtractions

y To include finding values ofunknown elements

y limit to not more than 3 rows and 3columns.

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19/3-23/3/12

4.4Perform Multiplicationof a matrix by a

number.

(i) Multiply a matrix by a number.(ii) Express a given matrix as a

multiplication of another matrix bya number.

(iii) Perform calculation on matricesinvolving addition, subtraction and

scalar multiplication.(iv) Solve matrix equations involving

addition, subtraction and scalarmultiplication.

2 y Teacher shows examples on scalarmultiplication of matrix:

- give examples of real lifesituations such as in industrial

productions.

y examples given on the calculation ofmatrices involving addition,

subtraction, and scalar

multiplication.

y Examples given on problem solvingquestions.

y To include finding values ofunknown elements.


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8

WeekNo


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Points to Note

4.5Perform multiplicationof two matrices.

(i) determine whether two matricescan be multiplied and state theorder of the product when the twomatrices can be multiplied.

(ii) Find the product of two matrices.(iii) Solve matrix equations involving

multiplication of two matrices.

3 y Teacher gives real life situations.Examples:-

- to find the cost of meals inthe restaurant

- teacher shows how 2matrices can be

multiplied.

y Examples given for the product oftwo matrices.

y Examples given on problem solvinginvolving multiplication of 2

matrices.

y Limit to not more than 3 rows and 3columns

y Limit to 2 unknown elements

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26/3-

30/3/12

4.6Understand and use theconcept of identify

matrix.

(i) determine whether a given matrixis an identity matrix by multiplyingit to another matrix.

(ii) Write identity matrix of any order.(iii) Perform calculation involving

identity matrices.

2 y Teacher discusses the property ofthe number as an identity for

multiplication of a number.

y Teacher introduces identity matrixor unit matrix.

y Teacher gives examples of identitymatrix of any order.

y Teacher discusses the properties:- AI = A- IA = A

Unit matrix is denoted by I.

Limit to 3 rows and 3 columns.


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9

WeekNo


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Points to Note

4.7Understand and use theconcept of inversematrix.

(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 2matrix using:

a. the method of solving simultaneouslinear equations

b. a formula

3 y teacher introduces the concept ofinverse matrix and its denotion.

y Examples given on problem solvingquestions involving matrix:

- using simultaneous linearequations

- using a formula

-1

AA = I

14

2/4-05/4/12

4.8Solve simultaneouslinear equations by

using matrices.

(i) Write simultaneous linearequations in matrix form.

(ii) Find the matrix pq

in

a bp h

c d q k !

using the

inverse matrix.

(iii) solve simultaneous linear equationsby the matrix method.

(iv) Solve problems involving matrices.

5 y Teacher shows examples how towrite simultaneous linear equations

in matrix form

y To solve simultaneous linearequations by using inverse matrix

y Project involving matrices usingelectronic spreadsheet to be given to

students.

* limit to 2 unknowns.


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WeekNo


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Points to Note

Topic/Learning Area : 5. VARIATIONS

(1 Weeks)

15

10/4-13/4/12

5.1 Understand and use theconcept of direct variation

(i) State the changes in a quantity withrespect to the changes in another

quantity, in everyday life situationsinvolving direct variation.

(ii) Determine from given informationwhether a quantity.

(iii) Express a direct variation in theform of equation involving twovariables.

(iv) Find the value of a variable in adirect variation when sufficientinformation is given.

(v) Solve problems involving directvariation for the following cases:

yE

x ; yE

x

2

; yE

x

3

;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 the simple 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 use theconcept of inverse variation

i) State the changes in aquantity with respect tochanges 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 inverse variationDiscuss the the form of the graph and relates it

to science, eg. Boyles Law.

Y varies inversely as x if and only if xy is a

constant.

y w 1/x

For the cases y w 1/xn, limit n to 2,3 and


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Points to Note

in the form of equation

involving two variables.

iv) Find the value of a variablein an inverse variation when

sufficient information is

given.

v) Solve problems involvinginverse variation for the

following cases:

y w 1/x; y w 1/x2

y w 1/x3; y w 1/x

1/2

1

1

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.

If y w 1/x, then y = k/x, where k is the constan t

of variation.

Use:

Y = k/x or

x1y1=x2 y2

to get the solution.

1616/4-

20/4/12

5.3 Understand and use theconcept of jointvariation

(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 variationand an inverse

variation.

(ii) Express a joint variation inthe form of equation.

(iii) Find the value of a variablein a joint variation when

sufficient information is

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 x

n / zn,

Limit n to 2,3 and .


12/21

12

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Points to Note

given.

(iv) Solve problems involvingjoint variation


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Points to Note

Topic/Learning Area 6: GRADIENT & AREA UNDER A GRAPH --- 3 weeks17

23/4-27/4/12

18

30/4-6/5/11

1920

21

22

23

6.1 Understand and use theconcept of quantityrepresented by the gradient

of a graph

(i) State the quantity represented by thegradient of a graph

(ii) Draw the distance-time graph,given:

a) a table of distance-time valuesb) a relationship between

distance and time

(iii) Find and interpret the gradient of a

distance-time graph

(iv) Find the speed for a period of timefrom a distance-time graph

(v) Draw a graph to show therelationship between two variables

representing certain measurements andstate the meaning of its gradient

PEPERIKSAAN PENGGAL 1

[9/5----25/5/2012]

CUTI PENGGAL PERTAMA

[26/5------10/6/2012]

1

2

2

2

1

2

Use examples in various areas such as

technology and social science

Use of daily life examples like speed of acar, Formula One Grand Prix, a sprinter

Compare and differentiate between distance-time graph and speed-time graph

Use real life situations such as traveling fromone place to another by 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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Points to Note

24-25

11/6-22/6/12

6.2 Understand the concept

of quantityrepresented by the area

under a graph

(i) State the quantity represented by the

area under a graph

(ii) Find the area under a graph

(iii) Determine the distance by findingthe area under the following of speed-time graphs:

a. v=k (uniform speed)b. v=kt

c. v=kt + hd. a combination of the above

(iv) Solve problems involving gradientand area under a graph.

1

2

4

2

Discuss that in certain cases, the area under 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 to the x-axis

y A straight lien in the form of y=kx+ hA 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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Points to Note

Topic/Learning Area : PROBABALITY II

Second Term --- 2 weeks

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25/6-29/6/12


concept of probability of anevent.

(i) Determine the sample space of anexperiment with equally likely

outcomes.

(ii) Determine the probability of an

event with equiprobable samplespace.

(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 alsobe used to simulate these activities.

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 outcomes is

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 and usedthe concept of probabilityof the complement of anevent.

(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 orfailing 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.

28

10//7-13/7/12

7.3 Understand use the

concept of probabilityof combined event.

(i) List the outcomes for events:

(a) A or B as elements of set

A B

2 Use real life situations to show the

relationship between

y A or B and A B


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Points to Note

(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

1

y 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 coordinate planes 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 decisions have to

be made on probability, for example

in business, such as determining the

value for aspecific insurance policy

and time the slot for TV

advertisements

y the statement probability is theunderlying language of statistics

Emphasise that :

y knowledge about probability is usefulin making decisions.

y prediction based on probability is notdefinite or absolute.

Topic/Learning Area : BEARING --- 1 week

29

16/7-02/7/12

8.1. Understand and use theconcept 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 of any

1


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Points to Note

compass direction.

(iii) Draw a diagram of a point which

shows the direction of B relative toanother point A given the bearingof B from A.

(iv) State the bearing point A from pointB based on given information.

(v) Solve problemsinvolving bearing.

1

1

2

Carry out the activities or games involving

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 map reading and

navigation.

Compass angle and bearing are written in three

digit form, from 0000 to 3600. 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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Topic 9

Learning Area: EARTH AS SPHERE ( 3 weeks )

30

23/7-27/7/12


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 meridian with thelongitude given.

(iv) Find the difference between twolongitudes

1

Model such as globes should be used.

Introduce the meridian through Greenwich in

England as the Greenwich Meridian withlongitude 0

Discuss that:

y All points on a meridian have the samelongitude

y There are two meridians on a greatcircle through both poles.

Emphasise that longitude 180

E and longitue180W refer to the same meridian.

Express the difference between two

longitudes with an angle in the range of0

x 180


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18

1 y Meridians with longitude xE(or W) and(180- x)W(or E) form a great circle

through both poles.

309.2 Understand and use theconcept of latitude

(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 of0 x 180.

30 9.3 Understand the concept

of locations 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 place given

its location.

1

1

i. State the latitude and longitude of agiven place

ii. Mark the location of a place

iii. Sketch and label the latitude andlongitude 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 latitude xN and

longitude yE is written ,as A(xN, yE).

31

31/7-3/8/12


concept of distance on thesurface on the earth to solve

problems.

(i) Find the length of an arc of a great circle

in nautical mile, given the subtended angleat the centre of the earth and vice versa.

(ii) Find the distance between two pointsmeasured along a meridian, given the

latitudes of both points.

(iii)Find a latitude of a point given the

latitude of another point and the distancebetween the two points along the samemeridian.(iv) Find the distance between two pointsmeasured along the equator, given the

longitude of both points.(v) Find the longitude of a point given thelongitude of another point and the distance

1

2

Use the globe to find the distance between twocities or town on the same meridian.

Sketch the angle at the centre of the earth thatis subtentded by the arc between two given

points along the equator. Discuss how 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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19

between the two points along the equator.

(vi) State the relation betwen the radius ofthe earth and the radius of a parallel of

latitude.

(vii) State the relation between the length ofan arc on the equatoq between two meridian

and the lengthe of the corresponding arc ona parallel of latitude.

(viii) Find the distance between two pointsmeasured along a parallel of latitude.

(ix) Find the longitude of a point given the

longitude of another point and the distancebetween the two points along a parallel oflatitude.

(x) Find the shortest distance between two2points on the surface of the earth.

(xi) Solve problems involving :(a) distance between two points.(b) travelling on the surface of the earth.

2

the value of this angle.

Use models such as the globe to find

relationship between the radius of the earthand radii parallel of latitudes.

Find the distance between two cities or townon the same parallel of latitude as a group

project.

Use the globe and a few pieces of string toshow how to determine the shortest 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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No

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Points to Note

Topic 10

Learning Area: PLANS AND ELEVATIONS

2 weeks

32

7/8-

10/8/11

10.1 Understand and usethe concept of orthogonal

projection.

i. Identify orthogonalprojections.

ii. Draw orthogonal projections,given an object and a plane.

iii. Determine the differencebetween an object and its

orthogonal projections withrespect to 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.

33

13/8-17/8/12

10.2 Understand and usethe 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.

1

2

1

Carry out activities in groups where students

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 is important 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 or

Limit to full-scale drawings only.

Include drawing plan and elevation in one diagram

showing projection lines.


21/21

21

WeekNo


Learning Outcomes


No of

Periods



Points to Note

35

36-38

39-41

42-45

iv. Draw

- the front elevation- side elevation

of a solid object

CUTI PERTENGAHAN PENGGAL 2

[18.8---26//2012]

ULANGKAJI

PEPERIKSAAN PERCUBAAN SPM

[28/8------14/9/2012

ULANGKAJI

SPM

1

structures, for example students or teachers

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.

Yearlyplan mathF.5,2012

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