RPT Math Form 5

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

4/1-8/1/10

 

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

  

  

Use models such as a clock face or a counter which uses a particular number base. 

Discuss 

-          Dicuss digits used 

-          Place values 

in the number system with a particular number base. 

  Skill  : Interpretation, observe connection between base two, eight and 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

 

11/1-16/1/10

    

(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 

  

  

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

       18/1-22/1/10

 

 

2.1  Understand and use the concept of graphs of functions

 

(i)   Draw the graph of a:

      a)  linear function :

           y = ax + b, where a 

          and b are constant;

      b) quadratic function

          ,  

          where a, b and c are

          constans,

      c)  cubic function :

       ,   

          where a, b, c and d are  

          constants,

     d)   reciprocal function

            , where a is a constants,

(ii)  Find from the graph

       a)  the value of y, given a 

            value of x

       b)  the value(s) 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

25/1-29/1/10

 

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 x-coordinate 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.

  

5 

1/2-5/2/10 

  

 

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

 

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 ) 

  

        
 

6

 

8/2-12/2/10

3.1     Understanding and use of the concept of combination of two transformations. (i)              determine the image of an object under combination of two isometric transformations. ·         using CD-Rom – interactive activities. 

·         Everyday life example: around the school. 

·         Recall the types of transformations: 

-          translation 

-          rotation 

-          reflection 

-          enlargement 

-          isometric transformation 

  
    (ii)            determine the image of an object under combination of:

  1. two enlargements 

    b.    an enlargement and and an isometric transformation.

 

·         using Geometer’s Sketchpad. 

·         CD-Rom 

·         Give variety of examples to show an enlargement and isometric transformation. 

  
 

7

13/2-21/2/10

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

(iv)          State the coordinates of the image of a point under combined transformations.

CUTI TAHUN BARU CINA

·         Give examples on the blackboard and students are asked to draw the image under 2 transformations 

·         Tr. will state the coordinates of the image of a point under combined transformations. 

  
8

22/2-26/2/10

  (v)         Determine whether combined transformation AB is equivalent to combined transformation BA. ·         Using Maths exercise books (grids) 

·         Do exercises from the textbooks 

  
(vi)       specify two successive transformations in a combined transformation given the object and the image. ·         Outdoor activity – students are brought to specific site of the school compound and ask to identify the two successive transformations :  pictures should consist of an object and an image.    
9

1/3-5/3/10

  (i)           Specify a transformation which is equivalent to the combination of two isometric transformations.

(ii)         Solve problems involving transformations.

·         Classroom activities – use GSP and CD-ROM (Multimedia Gallery) 

·         To specify isometric transformation 

·         Different examples to be given 

·         Various problem solving questions to be given 

  

- limit to translation, reflation & rotation. 

Topic/Learning Area :   

Matrices ( 4 weeks ) 

        
10

8//3-12/3/10

4.1     Understand and use the concept of matrix. (i)           Form a matrix from given information.

(ii)         Determine:

  1. the number of rows 

    b.          the number of columns

    c.          the order of a matrix

    (iii)       Identify a specific element in a matrix

 

·         Understanding the concept of matrices through daily examples: 

-          price of food on a menu 

-          a contingent of altelitic 

-          seating of students in class 

-          mark sheet of students 

·         Introduce the order (mxn) of a matrix 

·         Class activity – students are requested to identify the students’ seating position in class 

·         Other examples give 

*  m  represents  row 

*  n   represents column 

11

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.2     Understand and use the concept of equal matrices. (i)           Determine whether two matrices are equal.

(ii)         Solve problems involving equal matrices.

·         Teacher gives examples of two equal matrices and discusses equal matrices in terms  of the corresponding elements. 

·         Different problems given to  solve equal matrices. 

  
4.3     Perform addition and subtraction on matrices. (i)           Relate to real life situations such as keeping score of medal tally or points in sports.

(ii)         Find the sum or the difference of two matrices.

(iii)       Perform addition and subtraction on a few matrices.

(iv)       Solve matrix equations involving addition and subtraction.

CUTI PERTENGAHAN PENGGAL 1  [36/3-20/3/10]

(WEEK 11)

·         Teacher shows the examples from the textbook to determine how addition or subtraction can be performed on 2 given matrices. 

·         Examples given to find the addition and subtraction of two matrices. 

·         Examples given to solve matrix equations involving additions and subtractions 

·         To include finding values of unknown elements 

·         limit to not more than 3 rows and 3 columns. 
12

22/3-26/3/10

 

4.4     Perform Multiplication of a matrix by a number. (i)           Multiply a matrix by a number.

(ii)         Express a given  matrix as a multiplication of another matrix by a number.

(iii)       Perform calculation on matrices involving addition, subtraction and scalar multiplication.

(iv)       Solve matrix equations involving addition, subtraction and scalar multiplication.

·         Teacher shows examples on scalar multiplication of matrix: 

-       give examples of real life situations such as in industrial productions. 

·         examples given on the calculation of matrices involving addition, subtraction, and scalar multiplication. 

·         Examples given on problem solving questions. 

·         To include finding values of unknown elements. 

  
4.5     Perform multiplication of two matrices. (i)           determine whether two matrices can be multiplied and state the order of the product when the two matrices can be multiplied.

(ii)         Find the product of two matrices.

(iii)       Solve matrix equations involving multiplication  of two matrices.

·         Teacher gives real life situations.   Examples:- 

-          to find the cost of meals in the restaurant 

-          teacher shows how 2 matrices can be multiplied. 

·         Examples given for the product of two matrices. 

·         Examples given on problem solving involving multiplication of 2 matrices. 

  

·         Limit to not more than 3 rows and 3 columns 

·         Limit to 2 unknown elements 

 

13

29/3-2/4/10

 

4.6     Understand and use the concept of identify matrix. (i)           determine whether a given matrix is an identity matrix by multiplying it to another matrix.

(ii)         Write identity matrix of any order.

(iii)       Perform calculation involving identity matrices.

·         Teacher discusses the property of the number as an identity for multiplication of a number. 

·         Teacher introduces identity matrix or unit matrix. 

·         Teacher gives examples of identity matrix of any order. 

·         Teacher discusses the properties: 

-          AI  =  A 

-          IA  =  A 

  

Unit matrix is denoted by I. 

Limit to 3 rows and 3 columns. 

4.7     Understand and use the concept of 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:

  1. the method of solving simultaneous linear equations 

    b.            a formula

 

·         teacher introduces the concept of inverse matrix and its denotion. 

·         Examples given on problem solving questions involving matrix: 

-          using simultaneous linear equations 

-          using a formula 

  

      -1  

AA      =  I 

 

14

5/4-9/4/10

4.8     Solve simultaneous linear equations by using matrices. (i)           Write simultaneous linear equations in matrix form.

(ii)         Find the matrix  in   using the inverse matrix.

(iii)       solve simultaneous linear equations by the matrix method.

(iv)       Solve problems involving matrices.

·         Teacher shows examples how to write simultaneous linear equations  in matrix form 

·         To solve simultaneous linear equations by using inverse matrix 

·         Project involving matrices using electronic spreadsheet to be given to students. 

*  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

12/4-16/4/10

 

 5.1 Understand and use the concept of direct variation

 

(i)           State the changes in a quantity with respect to the changes in another quantity, in everyday life situations involving direct variation.

(ii)         Determine from given information whether a quantity.

(iii)       Express a direct variation in the form of equation involving two variables.

(iv)       Find the value of a variable in a direct variation when sufficient information is given.

(v)         Solve problems involving direct variation for the following cases:

    y   x ;   y  x2 ;  y  x3 ;

    y   x1/2 .

  

  

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 xn

Communicative skills 

Coorperation an d systematic 

  

Y varies directly as x , y x. 

y x 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   

i)                    State the changes in a quantity with respect to changes in another quantity, in everyday life situations involving inverse variation. 

ii)                  Determine form given information whether a quantity vaqries inversely as another quantity. 

iii)                Express an inverse variation in the form of equation involving two variables. 

iv)                Find the value of a variable in an inverse variation when sufficient information is given. 

v)                  Solve problems involving inverse variation for the following cases: 

y  1/x; y 1/x2 

      y 1/x3 ; y 1/x1/2 

  

  

Discuss the the form of the graph and relates it to science, eg. Boyle’s Law. 

For cases y 1/xn , n = 2,3 and ½, 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 xy is a constant. 

y 1/x 

For the cases y 1/xn, 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 

x1y1=x2 y2 

to get the solution. 

  

 

16

19/4-23/4/10

 

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. 

(ii)               Express a joint variation in the form of equation. 

(iii)             Find the value of a variable in a joint variation when sufficient information is given. 

(iv)             Solve problems involving joint variation. 

  

Discuss joint variation for the three cases in everyday life situations. 

Relate to science, eg. Ohm’s Law. 

For the cases y xn zn

Y  1/ xn zn and y xn / zn

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          
17

26/4-30/4/10

18

3/5-7/5/10

19

20

21

 

 

22

23

24

 

 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 distance-time graph, given:

a)      a table of distance-time values

b)      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 time from a distance-time 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

  

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 distance-time graph and speed-time 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 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, 

Distance, s

 

Time, t

 

 

25-26

21/6-2/7/10

 

 

 

 

 

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 speed-time 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.

 

  

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: 

·          A straight line which is parallel to the x-axis 

·          A straight lien in the form of y=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

 

Topic/Learning Area  :  PROBABALITY II 

Second Term                                  —  2 weeks    

        
 

 

27

5/7-9/7/10

 

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.

  

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. 

28

12/7-16/7/10

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. 

  

  

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. 

Use real life situations to show the relationship between 

·         A or B and A È B 

·         A and B and A Ç 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 : 

·         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 

·         the statement “probability is the underlying language of statistics” 

  

Emphasise that : 

·         knowledge about probability is useful in making decisions. 

·         prediction based on probability is not definite or absolute. 

  

  

  

  

Topic/Learning Area :  BEARING — 1 week          
 

29

19/7-23/7/10

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.

(ii)               Solve problems involving bearing.

  

  

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. 

 

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

26/7-30/7/10

 

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

  

  

Model such as globes should be used.

Introduce the meridian through Greenwich in England as the Greenwich Meridian with longitude 0°

Discuss that:

  • All points on a meridian have the same longitude 

    ·         There are two meridians on a great circle through both poles.

    ·         Meridians with longitude x°E(or W) and (180°- x°)W(or E) form a great circle through both poles.

 

  

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° 

31

2/8-6/8/10

 

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. 

  

  

Discuss that all the points on a paralell of latitude have the same latitude. 

  

Emphasise that 

o   the latitude of the equator is 0° 

o   latitude ranges from 0° to 90°N ( or S ) 

Involve actual places on the earth. 

Express the diffrence between two latitudes with an angle in the range of 0° ≤ x ≤ 180°. 

32

9/8-13/8/10

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. 

  

  i.         State the latitude and longitude of a given place 

ii.         Mark the location of a place 

iii.         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 latitude x°N and longitude y°E is written ,as A(x°N, y°E). 

 

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 
Topic 10  

Learning Area:  PLANS AND ELEVATIONS   

2  weeks 

     
 

33

16/8-20/8/10

 

 

10.1 Understand and use the concept of orthogonal projection.

 

        i.            Identify orthogonal projections.

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

    iii.            Determine the difference between an object and its orthogonal projections with respect to edges and angles.

 

  

  

Use models, blocks or plan and elevation kit.

 

34

 

23/8-27/8/10

 

10.2 Understand and use the concept of plan and elevation.

  

        i.            Draw the plan of a solid object. 

      ii.            Draw 

-          the front elevation 

-          side elevation 

of a solid object 

    iii.            Draw the plan of a  

      solid object. 

  iv.         Draw 

-          the front elevation 

-          side elevation 

                of a solid object 

CUTI PERTENGAHAN PENGGAL 2

 

[4/9-12/9/2010]

 

 

ULANGKAJI

[                  ]

 

 

 

PEPERIKSAAN PERCUBAAN SPM

[                           ]

 

 

 

SPM

  

  

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. 

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