RPT Math F5 2018 SMK Methodist

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LEARNING AREA/WEEKS

LEARNING OBJECTIVES

LEARNING OUTCOME TEACHING AND LEARNING

ACTIVITIES

STRATEGIES 1. Number Bases

(Week 1 – Week 3) 1.1 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 number.

(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) subtraction

of two numbers in base two.

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

Number base blocks of twos, eights and fives can be used to demonstrate the value of a number in the respective number bases.

For example: 2435 is

2 4 3 Discuss

 digits used

 place values

in the number system with a particular number bases.

Number base blocks of twos, eights and fives can also be used here. For example, to convert 1010 to a number in base two, use the concept of least number of blocks (23_{), tiles (2}2_), rectangles (21_{) and squares (2}0_{). In this} case, the least number of objects needed here are one block, zero tiles, one rectangle and zero squares. So, 1010 = 10102.

Thinking Skills

-working out mentally -identifying relationship

Teaching Strategies

-Contextual learning - Constructivism - Mastery

learning - Exploratory

Vocabulary

-expand notation

Teaching Aids

- model (clock face)

Moral Values

Cooperation, rational

Thinking Skills

-working out mentally -identifying relationship - problem solving

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LEARNING

AREA/WEEKS OBJECTIVES LEARNING LEARNING OUTCOME TEACHING AND LEARNINGACTIVITIES STRATEGIES

Discuss the special case of converting a number in base two directly to a number in base eight and vice versa. For example, convert a number in base two directly to a number in base eight through grouping of three consecutive digits.

Perform addition and subtraction in the conventional manner.

For example: 1 0 1 0 + 1 1 0 ____________ ____________

Vocabulary

-convert

Teaching Aids

- models - reference book

Moral Values

Cooperation, honesty, courage.

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2. Graph of functions II (Week 4 –6)

2.1 Understand and use the concept of graph of functions.

(i) Draw the graph of a : (a) linear function: y = ax + b, a,b are constants. (b) quadratic function : y = ax2_{+ bx + c,}

a, b, c are constants, a ≠ 0. (c) cubic function :

y = ax3_{+ bx}2_{+ cx + d,}

a, b, c, d are constant, a ≠ 0. (d) reciprocal function :

y = a/x,

a constant, a ≠ 0. (ii) Find from a graph :

(a) value of y given 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 of graph.

(c) the graph given a function and vice versa.

Explore graph of functions using graphing calculator or the Geometer’s Sketchpad.

Compare the characteristics of graph of functions with different values of constants.

For example :

Graph B is broader than graph A and intersects the vertical axis above the horizontal axis.

Thinking Skills

working out mentally identify relationship

-Contextual learning - Constructivism -Mastery learning - Exploratory

Vocabulary

- Linear function - Quadratic function - Cubic function - Reciprocal function \

Teaching Aids

Graph box

Scientific Calculator CDROM

ACTIVITIES

STRATEGIES

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2. Graph of functions II (Week 4 –6)

2.1 Understand and use the concept of graph of functions.

(iii) Identify :

(a) the shape of graph given a type of function.

(b) the type of function given of graph.

(c) the graph given a function and vice versa.

Explore graph of functions using graphing calculator or the Geometer’s Sketchpad.

Compare the characteristics of graph of functions with different values of constants.

For example :

Graph B is broader than graph A and intersects the vertical axis above the horizontal axis.

Thinking Skills

working out mentally identify relationship

- Linear function - Quadratic function - Cubic function - Reciprocal function \

Teaching Aids

Graph box

Scientific Calculator CDROM

2.2 Understand and use the concept of the solution of an equation by graphical method

1 2.3 Understand and use the concept of the region representing inequalities in two variables

(iv) Sketch the graph of a given linear, quadratic, cubic or reciprocal function.

(i) Find the point(s) of intersection of two graphs.

(ii) Obtain the solution of an equation by finding the

(iii) Point(s) of intersection of two graphs.

(iv) Solve problems involving (v) solution of an equation by

graphical method.

(i) Determine whether a given points satisfies:

y = ax + b or y > ax + b or y < ax + b.

As reinforcement, let students play a game; for example matching cards of graphs with their respective functions. When the students have their

matching partners, ask them to group themselves into four groups of types of functions. Finally, ask each group to name the type of function that is depicted on the cards.

Explore using graphing calculator or the Geometer’s Sketchpad to relate the x-coordinate of a point of intersection of two appropriate graphs to the solution of a given equation. Make generalization about the point(s) of intersection of the two graphs.

Moral Values

Teaching Strategies: -Constructivism -graphing

-cooperative learning - Mastery

learning - Exploratory - Problem solving

Vocabulary:

4

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LEARNING

AREA/WEEKS LEARNING OBJECTIVS LEARNING OUTCOMES

TEACHING AND LEARNING

ACTIVITIES STRATEGIES

LEARNING

AREA/WEEKS OBJECTIVES LEARNING LEARNING OUTCOMEStudent will be able to… TEACHING AND LEARNINGACTIVITIES STRATEGIES 4. Matrices

(Week 7 – 9) 4.1 Understand and use the concept of matrix.

4.2 Understand and use the concept of equal matrices.

4.3 Related to real life situations such as in industrial productions.

4.4 Perform multiplication of a matrix by a number.

4.5 Perform multiplication of two matrices

(i) Form a matrix from given information. (ii) Determine :

i. The number of rows ii. the number of columns iii. The order of a matrix

(iii) Identify a specify element in a matrix.

(i). Determine whether two matrices are equal. (ii). Solve problem involving equal matrices.

(i) Determine whether addition or subtraction can be performed on two given matrices.

(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.

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

(i) Determine whether two matrices can be multiplied and state the order of the product when two matrices can be multiplied

Represent data in real life situations, for example, the price of food on a menu, in table form and then in matrix form.

Use student seating positions in the classroom by rows and columns to identify a student who is sitting in a particular row and in particular column as a concrete example. Discuss equal matrices in term of :

 The order

 The corresponding elements.

Related to real life situations such s keeping score of medal tally or point in sports.

Related to real life situations such as in industrial productions.

Related to real life situations such as finding the cost of a meal in the restaurant

For matrices A and B, discuss the relationship between AB and BA Begin with discussing the property of the number 1 as an identity for multiplication of numbers.

Discuss:

 an identity matrix is a square

 there is only one identity matrix for each order

Discuss the properties:

 AI=A  IA=A

Relate to the property of multiplicative inverse of numbers. Example:

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LEARNING

4.6 Understand and use the concept of identity matrix.

4.7 Understand and use the concept of inverse matrix

4.8 solve simultaneous linear equations by using matrices

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

multiplication of two matrices

(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

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

(ii) Find the inverse matrix of a 2 x 2 matrix using:

(a) the method of solving simultaneous linear equations

(b) a formula

(i) Write simultaneous linear equations in matrix form

(ii) Find the matrix _

(iii) Solve simultaneous linear equations by the matrix method

2 x 2-1₌₂-1_{x 2= 1}

Use the method of solving simultaneous linear equations to show that not all square matrices have inverse matrices.

Using matrices and their respective inverse matrices in the previous method to relate to the formula. Express each inverse matrix as a multiplication of a matrix by a number. Compare the scalar multiplication to the original matrix and discuss how the determinant is obtained.

Discuss the condition for the existence of inverse matrix.

Related to equal matrices by writing down the simultaneous equations as equal matrices first.

Discuss why:

 The use of inverse matrix is necessary. Relate to solving linear equations of type ax = b

 It is important to place the inverse matrix at the right place on both sides of the equation.

Relate the use of matrices to other areas such as in business or economy, science etc.

Carry out projects(electronic spreadsheet) -inverse matrix

Vocabulary

-standard form -single number -scientific notation

- matrix method

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LEARNING

(iv) Solve problems involving matrices

LEARNING

5. Variations (Week 10 - 11)

5.1 Understand and use the concept of direct variations

5.2 Understand and use the concept of inverse 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 varies directly as another quantity.

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

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

(v) Solve problems involving direct variations for the followinf cases :

2 3

1 2

;

y

x y

x

y

x

y

x

�

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

(ii) Determine from given information whether a quantity varies inversely as

Discuss the characteristics of the graph of y against x when y

�

x.

Relate mathematical variation to other area such as science and technology. For example, the Charles Law or motion of the simple pendulum.

For the cases

y

�

x

n , n = 2,3,

1

2

,

discuss the characteristics of the graph of y against n

x

.

Discuss the form of the graph of y

against

1 x

when

1 y

x

�

.

Relate to other areas like science and technology. For example, Boyle’ Law.

Thinking Skills

-working out mentally -identifying Relationship - making inference

Vocabulary

- Direct variations - quantity

- constant of variations - variable

Teaching Aids

-flash card -scientific calculator

Moral Values

Rationality, courage

Thinking Skills

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LEARNING

5. Variations (Week 10 - 11)

5.3 Understand and use the concept of joint variation.

another quantity

(iii) Express as inverse variation in form of equation involving two variables.

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

(v) Solve problems involving inverse variations for the following cases :

2

1 3

2

1

1 ;

;

1

1 ;

y

x

y

x

�

(i) Represent a joint variation by using the symbol

�

for the following cases : a) two direct variations

b) two inverse variations

c) a direct variations and an inverse variation.

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

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

(iv) Solve problems involving joint variation

For the cases 1 , 2,3 1 2

n

y n and

x 

� ,

discuss characteristics of graph y against _x1n.

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

Relate to other areas like science and technology.

For example:

V

I

R

�

means the current I varies

directly as the voltage V and varies inversely as the resistance R.

-identifying Relationship - problem solving

Vocabulary

- inverse variation

Teaching Aids

-scientific calculator

Moral Values

Diligence, moderation

Thinking Skills

-working out mentally -identifying Relationship - problem solving - decision making

Vocabulary

- joint variation

Teaching Aids

-scientific calculator

Moral Values

Patience, diligence

8 (19.3.2018 – 25.3.2018)

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LEARNING

ACTIVITIES

STRATEGIES

6. Gradient and area under a graph.

( Week 12 - 13 )

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

6.2 Understand the concept of quantity represent any meaningful quantity.

(i) State the quantity represented by the gradient of 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 variable representing certain measurement and state the meaning of its gradient.

(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 types of speed-time graphs:

Use examples in various areas such as technology and social science.

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

Use real life situations such as travelling from one place to another by train or by bus.

Use examples in social science and economy.

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

CCTS

i)Thinking skills : - interpreting - generalization -drawing diagram.

ii) Teaching strategies: - discussion

Vocabulary: - gradient - distance-time -speed-time -acceleration -deceleration -constant speed -distance -average speed -uniform speed

Moral value: - Cooperation - rationality

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LEARNING

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.

parallel to the x-axis.

 a straight line in the form of y = kx + h.

 a combination of the above.

LEARNING

7. Probability

( Week 14-15 )

7.1 Understand and use the concept of probability of an event

7.2 Understand and use the concept of probability of combined event

7.3 Understand and use the concept of probability of combined 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

(i) State the complement of an event in :

a) words b) set notation

(ii) Find the probability of the complement of an event

(i) List the outcomes for events:

(ii) Find the probability by

Discuss equiprobable sample space through concrete activities, begin with simple cases ( tossing fair coin) Use tree diagrams to obtain sample space for tossing a fair coin or tossing a fair die activity.

Produce P(A) = 1 and P(A) = 0. Include events in real life situations such as winning or losing a game and passing or failing an exam.

Use real life situations to show the relationship between

 A or B and A  B

 A and B and A ∩ B.

An example of situation being chosen to be a member of an exclusive club with restricted conditions.

Use tree diagrams& coordinate planes to find 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 diagram from these tables. Example(two-wayclassification table) Means of going to work Officers car bus Others Men 56 25 83 -equiprobably sample space - Contextual Learning

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LEARNING

listing the outcomes of the combined event:

a) A or B b) A and B

(iii) Solve problems involving probability of combined event.

Discuss:

Situation where decisions to be made based on probability, example in business, as determining the value for a specific insurance policy and time the slot for TV advertisements. The statement “ probability is the underlying language of statistics”.

Vocabulary

- combined event

Teaching Aids

- CD-ROM - worksheets

LEARNING

8.Bearing (Week 16 - 17)

8.1 Understand and use the

concept of bearing (i) Draw and label the eight main compass direction: b. North,South,East,West c. North-East, North-West d. South –East, South-West. e.

(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 of point A from point B based on given information.

(v) Solve problems involving bearing.

Carry out activities or games involving finding direction using a compass, such as treasure hunt or scavenger hunt. It can also be about locating several points on a map.

Discuss the use of bearing in real life situation. For example, in map reading and navigation.

Thinking Skills

-describing -interpreting -drawing diagram -problem solving

-Contextual learning - Constructivism - Mastery learning

Vocabulary

-north-east -south-east -north-west -south-west -compass angle -bearing

Teaching Aids

-compass. Map, scientific calculator, geometry set, worksheets.

Moral Values

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9. Earth as a sphere (Week 18 – 19)

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 the a meridian with the longitude given.

Models such as globes should be used.

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

Thinking Skills

-working out Mentally -classifying -categorizing

- Constructivism - Exploratory

Teaching Aids

-globe or map

LEARNING

12 MID YEAR EXAMINATION

(Week 20 – 22)

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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 the a meridian with the longitude given.

Models such as globes should be used.

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

Thinking Skills

-working out Mentally -classifying -categorizing

Teaching Aids

-globe or map

2 3 4 5

9.2 Understand and use the concept of latitude.

9.3 Understand the concept of location of a place

iv) Find the difference between two longitudes.

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

i) State the latitude and longitude of a given place

ii) Mark the location of a place

Discus that:

 All points on a meridian have the same longitude

 There are two meridians on a great circle through both poles

 Meridians with longitudes x˚E (0r W) and 180˚ - x˚)W (or E) form a great circle through both poles.

Emphasize that

 The latitude of the equator is 0˚

 Latitude ranges from 0˚ to 90˚ ( or S )

Involve actual places on the earth.

Express the difference between two latitudes with an angle in the range of 0˚ < x < 180˚.

Use a globe or a map to find locations of cities around the world

Use a globe or a map to name a place given its location.

Moral Values

Thinking Skills

-compare and contrast -constructing

Teaching Aids

-globe or map

Moral Values

Thinking Skills

-working out Mentally -describing -giving opinion

- Constructivism

MID YEAR EXAMINATION

(Week 20 – 22)

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LEARNING

9.4 Understand and use the concept of distance on the surface of 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 latitude of point given latitude of another point and distance between two points along same meridian.

iv) Find the distance between two points measured along the equator, given the longitudes 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 relation between radius of earth and the radius of a parallel of latitude. vii) State the relation between the length of an arc on the equator between two meridians and length of corresponding arc on a parallel of latitude.

viii) Find 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) traveling on surface of earth

Use a globe to find the distance between two cities or towns on the same meridians.

Sketch the angle at the centre of the earth that is subtended 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 relationships between the radius of the earth and radii parallel of latitudes

Find the distance between two cities or towns 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.

Thinking Skills

-working out Mentally -giving opinion

Vocabulary

Nautical mile

Teaching Aids

-globe or map

Moral Values

Thinking Skills

-working out Mentally -constructing -problem solving

Teaching Aids

-globe or map

Moral Values

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LEARNING

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LEARNING

AREA/WEEKS LEARNING OBJECTIVES LEARNING OUTCOME TEACHING AND LEARNINGACTIVITIES STRATEGIES

10. Plans and elevations (Week 25 - 26)

10.1 Understand and use the concept of orthogonal projection

10.2 Understand and use the concept of plan and elevation

(i) Identify orthogonal projection.

(ii) Draw orthogonal projection, given an object and a plan.

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

(i) Draw the plan of a solid object.

(ii) Draw

a) the front elevation b) side elevation of a solid

object.

(iii) Draw a) the plan

b) the front elevation c) the side elevation of a solid object to scale.

(iv) Solve problems involving plan and elevation.

Use models, blocks or plan and elevation kit.

Carry out activities in groups where students combine two or more different shapes of simple solid objects into interesting models and draw plans and elevations for these models.

Use models to show that it is important to have a plan and at least two side elevations 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.

Thinking Skills

- identifying relationship - describing - problem solving - drawing diagrams

- Contextual learning

Cooperation, rational, justice, freedom, courage

3.

Transformation III (Week 27 – 28)

3.1 Understand and use the concept of combination of two transformations.

I. Determine the image of an object under combination of two isometric transformations.

II. Determine the image of an object under combination of:

a) two enlargements b) an enlargement and an

isometric transformation. III. Draw the image of an object under

Relate to transformations in real life situation such as tessellation patterns on walls, ceiling or floors.

Explore combined transformation using the graphing calculator, the Geometer’s Sketchpad, or the overhead projector and transparencies.

Thinking Skill

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LEARNING

(ii) Draw

object.

Thinking Skills

combination of two transformations. Mastery learning LEARNING

3.2 Understand and use the concept of combination of two transformations.

III. State the coordinates of the image of a point under combined transformation IV. Determine whether combined

transformation AB is equivalent to combined transformation BA. V. Specify two successive

Investigate the characteristics of an object and its image under

combined transformation.

Carry out projects to design patterns using combined transformations that

Conceptual Learning Constructivism Cooperative Learning Enquiry

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LEARNING

(ii) Draw

object.

Thinking Skills

transformations in a combined transformation given the object and the image.

VI. Specify a transformation which is equivalent to the combination of two isometric transformations.

Solve problems involving transformation

can be used as decorative purposes. These projects can then be presented in classroom with the students describing or specifying the transformations involved.

Use the Sketchpad to prove the single transformation which is equivalent to the combination of

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LEARNING

(ii) Draw

object.

Thinking Skills

- Contextual learning - Constructivism - Mastery

learning

Vocabulary

Orthogonal Projection Plan

Front elevation Side elevation

Teaching Aids

- models - blocks - plan and

elevation kit

Moral Values

two isometric transformations. Sketchpad

- graphing calculator -graph paper -a pair of compass -ruler

Moral Values

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LEARNING

(ii) Draw

object.

Thinking Skills

learning

Vocabulary

Teaching Aids

elevation kit

Moral Values

Physical Cleanliness

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LEARNING

(ii) Draw

object.

Thinking Skills

learning

Vocabulary

Teaching Aids

elevation kit

Moral Values

REVISION SPM TRIAL WEEK 29

SPM EXAMINATION 2018

5.11.2018 – 4.12.2018

REVISION FOR SPM 2018 UNTIL WEEK 40

SPM TRIAL EXAMINATION

13.8.2018 (WEEK 30)

31.8.2018 – NATIONAL DAY

(22)

RPT Math F5 2018 SMK Methodist

4

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(19.3.2018 – 25.3.2018)

12

MID YEAR EXAMINATION

(Week 20 – 22)

MID YEAR EXAMINATION

(Week 20 – 22)

SPM EXAMINATION 2018

5.11.2018 – 4.12.2018

SPM TRIAL EXAMINATION

13.8.2018 (WEEK 30)

31.8.2018 – NATIONAL DAY

SMK METHODIST ACS (M) JALAN LINTANG 70000 SEREMBAN NEGERI

SEMBILAN

RANCANGAN PENGAJARAN TAHUNAN

YEARLY LESSON PLAN

MATEMATIK

TINGKATAN 5

TAHUN 2018