Yearly Plan – Mathematics Form 5 (2011)
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/Values 
Points to Note 

Learning Area : NUMBER BASES — 2 weeks First Term 

1
3/17/1/11 
1. Understand and use the concept of number in 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) 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
in the number system with a particular number base.
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
10/114/1/11 
(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.
(vi) Perform computations involving : a) addition b) subtration of two numbers in base two 
2
3
1

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.
Skill : Interpretation, converting numbers to base of two, eight, five and then.
Use of daily life examples Values : systematic, careful, patient 
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.
The usage of scientific calculator in performing the computitations.


Topic 2 : Graphs of Functions II — 3 weeks 

3 17/121/1/11

2.1 Understand and use the concept of graphs of functions 
(i) Draw the graph of a: a) linear function :
b) quadratic function
where a, b and c are constans, c) cubic function :
where a, b, c and d are constants,
d) reciprocal function
(ii) Find from the graph a) the value of y, given a value of x
given a value of y
(iii) Identify: a) the shape of graph given a type of function b) the type of function given a graph c) the graph given a function and vice versa
(iv) Sketch the graph of a given linear, quadratic, cubic or reciprocal function.

2
1
2
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
Play a game or quiz

Questions for 1..2(b) are given in the form of ; a and b are numerical values.
Limit cubic functions. Refer to CS.
For certain functions and some values of y, there could be no corresponding values of x.
Limit the cubic and quadratic functions. Refer to CS.
Limit cubic functions. Refer to CS.


4
24/128/1/11
5 31.106.2.2011 (CNY) 
2.2 Understand and use the concept of the solution of an equation by graphical method. 
(i) Find the point(s) of intersection of two graphs
(ii) Obtain the solution of an equation by finding the point(s) of intersection of two graphs
(iii) Solve problems involving solution of an equation by graphical method.

1
1
2

Explore using graphing calculator of GST to relate the xcoordinate of a point of intersection of two appropriate graphs to the solution of a given equation. Make generalisation about the point(s) of intersection of the two graphs.
Use everyday problems.
Skills : Mental process

Use the traditional graph plotting exercise if the graphing calculator or the GSP is unavailable.
Involve everyday problems. 

6
7/211/2/11

2.3 Understand and use the concept of the region representing inequalities in two variables.

(i) Determine whether a given point satisfies a) or or
(ii) Determine the position of a given point relative to the equation
(iii) Identify the region satisfying or
(iv) Shade the regions representing the inequalities a) or b) or
(v) Determine the region which satisfy two or more simultaneous linear inequalities.

2
2
2 
Include situations involving , , , or .
Values: Making conclusion, connection and comparison, careful

Emphasise on the use of dashed and solid line as well as the concept of region. 
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/Values 
Points to Note 
Topic/Learning Area : transformations iii ( 3 weeks ) 

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1





2 




2 


7
14/218/2/11 

3 



2 


8
21/225/2/11 

5 

– limit to translation, reflation & rotation. 

Topic/Learning Area : Matrices ( 4 weeks ) 

9
28/36/3/11 


1 

* m represents row * n represents column 
10



2 



CUTI PERTENGAHAN PENGGAL 1 [36/320/3/10] (WEEK 11) 
2 



12
21/325/3/11



2 




3 



13
28/33/4/11



2 

Unit matrix is denoted by I.
Limit to 3 rows and 3 columns. 

(i) Determine whether a 2 X 2 matrix is the inverse matrix of another 2 X 2 matrix.

3 

AA = I 

14
4/410/4/11 


5 

* limit to 2 unknowns. 
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/Values 
Points to Note 
Topic/Learning Area : 5. VARIATIONS (1 ½ Weeks) 

15
11/415/4/11 
5.1 Understand and use the concept of direct variation 

1
1
1

Discuss the characteristics of the graph of y agains x when y x.
Relate mathematical variation to Charles’s Law or the mation of the simple pendulum.
Discuss the characteristics of the graphs of y against x^{n}.
Communicative skills
Coorperation an d systematic

Y varies directly as x , yx. yx^{ n} , limit n to 2, 3 and ½
Y = kx where k is the constant of variation.


5.2 Understand and use the concept of inverse variation 
y 1/x; y 1/x^{2 } ^{
}y 1/x^{3}

1
1

Discuss the the form of the graph and relates it to science, eg. Boyle’s Law.
For cases y 1/x^{n} , n = 2,3 and ½, discuss the characteristics of the graph of y against 1/x^{n}
Graph drawing skill
Be straight and honest. 
Y varies inversely as x if and only if xy is a constant.
y 1/x
For the cases y 1/x^{n}, limit n to 2,3 and ½
If y 1/x, then y = k/x, where k is the constan t of variation.
Use: Y = k/x or x_{1}y_{1}=x_{2} y_{2 } to get the solution. 
16 18/422/4/11

5.3 Understand and use the concept of joint variation 
(i) Represent a joint variation by using the symbol for the following cases:
a) two direct variations b) two inverse variations c) a direct variation and an inverse variation.

1
1
1
1
1 
Discuss joint variation for the three cases in everyday life situations.
Relate to science, eg. Ohm’s Law.

For the cases y x^{n} z^{n}, Y 1/ x^{n} z^{n} and y x^{n} / z^{n}, Limit n to 2,3 and ½. 
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/Values 
Points to Note 

Topic/Learning Area 6: Gradient & area under a graph — 3½ weeks 

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25/439/4/11
18 2/56/5/11
19 20 21
22 23

6.1 Understand and use the concept of quantity represented by the gradient of a graph

(i) State the quantity represented by the gradient of a graph
(ii) Draw the distancetime graph, given:
(iii) Find and interpret the gradient of a distancetime graph
(iv) Find the speed for a period of time from a distancetime graph
(v) Draw a graph to show the relationship between two variables representing certain measurements and state the meaning of its gradient
PEPERIKSAAN PENGGAL 1
CUTI GAWAI/CUTI PENGGAL 1 
1
2
2
2
2

Use examples in various areas such as technology and social science
Use of daily life examples like speed of a car, Formula One Grand Prix, a sprinter
Compare and differentiate between distancetime graph and speedtime graph
Use real life situations such as traveling from one 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 distancetime graph.
Emphasise that: Gradient = change of distance Time = speed
Include graphs which consists of a combination of a few straight lines. For example,


2425
13/624/6/11

6.2 Understand the concept of quantity represented 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 finding the area under the following of speedtime graphs: a. v=k (uniform speed) b. v=kt c. 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 area under a graph may not represent any meaningful quantity. For example: The area under the distancetime graph. Discuss the formula for finding the area under a graph involving:
A combination of the above.

Include speedtime and accelerationtime 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:


Topic/Learning Area : PROBABALITY II Second Term — 2 weeks 

26
27/631/6/11

7.1 Understand and use the concept of probability of an event. 
(i) Determine the sample space of an experiment with equally likely outcomes.
(ii) Determine the probability of an event with equiprobable sample space.
(iii)Solve problems involving probability 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 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) =
Use tree diagram where appropriate.
Include everyday problems and making predictions. 

27
4/78/7/11 
7.2 Understand and used the concept of probability of the complement 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. 

28 
7.3 Understand use the concept of probability of combined event. 
(i) List the outcomes for events: (a) A or B as elements of set A È B (b) A and B as elements of set A Ç 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 the relationship between
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 twoway 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 twoway classification table :
Discuss :

Emphasise that :


Topic/Learning Area : BEARING — 1 week 

29
18/722/7/11

8.1. Understand and use the concept of bearing. 
(i) Draw and label the eight main compass directions: a) north, south, east, west b) north – east, north – west, south – east, south – west ii) State the compass angle of any compass direction.
(iii) Draw a diagram of a point which shows the direction of B relative to another point A given the bearing of B from A.
(iv) State the bearing point A from point B based on given information.

1
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 000^{0} to 360^{0}. They are measured in a clockwise direction from north. Due north is considered as bearing 000^{0}. For cases involving degrees up to one decimal point.

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/Values 
Points to Note 
Topic 9 Learning Area: EARTH AS SPHERE ( 3 weeks ) 

30
25/729/7/11

9.1 Understand and use 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 meridian with the longitude given. (iv) Find the difference between two longitudes 
1
1

Model such as globes should be used.
Introduce the meridian through Greenwich in England as the Greenwich Meridian with longitude 0° Discuss that:

Emphasise that longitude 180°E and longitue 180°W refer to the same meridian.
Express the difference between two longitudes with an angle in the range of 0° ≤ x ≤ 180° 
30

9.2 Understand and use the concept 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
Involve actual places on the earth.
Express the diffrence between two latitudes with an angle in the range of 0° ≤ 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 

A place on the surface of the earth is represented by a point.
The, location of a place A at latitude x°N and longitude y°E is written ,as A(x°N, y°E). 
31
1/85/8/11 
9.4 Understand and use the concept of distance on the surface on the earth to solve problems. 
(i) Find the length of an arc of a great 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 the distance between the two points along the same meridian. (iv) Find the distance between two points measured along the equator, given the longitude of both points. (v) Find the longitude of a point given the longitude of another point and 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.
(vii) State the relation between the length of an arc on the equatoq between two meridian and the lengthe of the corresponding arc on a parallel of latitude.
(viii) Find the distance between two points measured along a parallel of latitude.
(ix) Find the longitude of a point given the longitude of another point and the distance between the two points 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 the earth. 
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 value of this angle.
Use models such as the globe to find relationship between the radius of the earth and radii parallel of latitudes.
Find the distance between two cities or 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 the shortest distance between two points on the surface of the earth. 
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.
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. 

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/Values 
Points to Note 
Topic 10 Learning Area: PLANS AND ELEVATIONS 2 weeks


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8/812/8/11

10.1 Understand and use the concept of orthogonal projection. 

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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15/819/8/11
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3638
3941
4245 
10.2 Understand and use the concept of plan and elevation. 
of a solid object
solid object.
iv. Draw
of a solid object
CUTI PERTENGAHAN PENGGAL 2
[29.804/9/2011]
ULANGKAJI
PEPERIKSAAN PERCUBAAN SPM
ULANGKAJI
SPM 
1
2
1
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 structures, for example students’ or teacher’s 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.

Limit to fullscale drawings only.
Include drawing plan and elevation in one diagram showing projection lines. 