maths form 5 year plan

SCHEME OF WORK : FORM 5 MATHEMATICS (2011)

FIRST TERM

BIL LEARNING AREA /OUTCOMES JAN FEB MARCH APRIL MEI JUNE

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 41 NUMBER BASES R M M

S I I · Use models such as a clock face or a counter which uses

i. State zero, one, two, three……. T D D a particular number base.

as a number in base: · Discuss

a. two M S Y Y i. digits used;

b. eight F I E E E ii. Place values

c. five I D C A A in the number system ith a particular number base.

ii. State the value of adigit of a number in R T O R R · Emphasise the ways to read numbers in various bases.

base : S E N Examples :

a. two T R D E S

b. eight M X C

c. five T T A H

iii. Write anumber in base : E B E M O · Numbers in base two are also known as binary numbers.

a. two S R S I O Examples of numbers in expanded notation :

b. eight T E T N L

c. five A A

in expanded notation. K T B

iv. Convert a number in base : I R · Limit conversion of numbers to base two, eight and

a. two O E five only.

b. eight N A

c. five S K

to anumber in base ten and vice versa

v. Convert a number in a certain base to a number in

anoter base.

vi. Perform computations involving:

i. Addition

ii. Subtraction

of two numbers in base two

# Enrichment / Remedial Excercise #

SUGGESTED TEACHING AND LEARNING ACIVITIES

1.1 Number in base two, eight and five

i. 1012 is read as "one zero one base two".

ii. 72058 is read as "seven two zero five base eight".

iii. 43255 is read as "four three two five base five".

i. 101102 = 1 ´ 24 + 0 ´ 23 + 1 ´ 22 + 1 ´ 21 + 0 ´

ii. 3258 = 3 ´ 82 + 2 ´ 81 + 5 ´ 80

iii. 30415 = 3 ´ 53 + 0 ´ 52 + 4 ´ 51 + 1 ´ 50

FIRST TERM


1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

2 GRAPHS OF FUNCTIONS (II)

· Explore graphs of functions using graphing calcultor or

i. Draw the graph of a : the Geometer's Sketchpad.

F · Compare the characteristics of graphs of functions with

I different values of constants.

R M M · Limit cubic functions to the following forms :

S I I

T D D

M S Y Y

F I E E E

ii. Find from a graph : I D C A A

R T O R R

S E N

iii. Identify : T R D E S

a. the shape of graph given a type of function M X C

b. the tpe of function given a graph T T A H

c. the graph given a function and vice versa E B E M O

iv. Sketch the graph of a given linear, quadratic, cubic S R S I O · For graphs of cubic function, limit to

or reciprocal function. T E T N L

A A

K T B · Explore using graphing calcultor or Geometer's

i. Find the point(s) of intersection of two graphs. I R Sketchpad to relate the x-coordinate of a point of

ii. Obtain the solution of an equation by finding O E intersection of two appropriate graphs to the solution

the point(s) of intersection of two graphs. N A of a given equation.

iii. Solve problems involving solution of an equation S K · Use the traditional graph plotting exercise if the

by graphical method. graphing calulator or the Sketchpad is unavailable.

· Emphasise that :

i. Determine whether a given point satisfies : *For the region representing

ii. Determine the position of a given point relative

*For the region representing

iv. Shade the regions representing the inequalities :

drawn as a solid line to indicate that all points on the


2.1 Graphs of functions

a. Llinear function : y = ax + b

where a and b are constants

b. Quadratic function : y = ax2+ bx + c

where a, b and c are constants, a ≠ 0 y = ax3

c. Cubic function :y = ax3 + bx + cx + d y = ax3 + b

where a, b, c and d are constants, a ≠ 0 y = x3 + bx + c

d. Reciprocal function : y = a/x y = -x3 + bx + c

where a is a constants, a ≠ 0

a. the value of y, given the value of x

b. the value(s) of x, given a value of y

y = ax³ and y = ax3 + b

2.2 Solution of an equation by graphical method

2.3 Region representing inequalities in two variables

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

y > ax + b, the line

to the equation y = ax + b. y = ax + b is drawn as a dashed line to indicate that

iii. Identify the region satisfying y > ax + b or all points on the line y = ax + b are not in the region.

y < ax + b.

y > ax + b or y < ax + b, the line y = ax + b is

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

b. y > ax + b or y < ax + b line y = ax + b are in the region.

FIRST TERM


1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 v. Determine the region which satisfies two or more

simultaneous lnear inequalities.

# Enrichment / Remedial Excercise # F

I

3 TRANSFORMATIONS (III) R M M

*Revision on Transformations (I) & (II) S I I

- translation T D D

- reflection

- rotation M S Y Y

- enlargement F I E E E

I D C A A

R T O R R · Explore combined transformation using the graphing

i. Determine the image of an object under S E N calculator, the Geometer's Sketchpad, or the overhead

combination of two isometric transformations. T R D E S projector and transparencies.

ii. Determine the image of an object under M X C · Investigate the characteristics of an object and its

combination of : T T A H image under combined transfomation.

a. two enlargements E B E M O · Limits isometric transformations to translations,

b. an enlargement and an isometric S R S I O reflections and rotations.

transformation T E T N L

iii. Draw the image of an object under A A

combination of two transformations. K T B

iv. State the coordinates of the image of a point I R

under combined transformation. O E

v. Determine whether combined transformation AB N A

is equivalent to combined transformation BA. S K

vi. Specify two successive transformations in a

combined transformation given the object

and the image.

vii. Specify a transformation which is equivalent · Limits the equivalent transformations to translations,

to the combination of two isometric reflections and rotations.

transformations.

viii. Solve problems involving transformation.



3.1 Combination of two transformations

FIRST TERM


1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 2 34 MATRICES

· Emphasise that matrices are written in brackets.

i. Form a matrix from given information.

ii. Determine : F

a. the number of rows I

b. the number of columns R M M

c. the order of a matrix S I I

iii. Identify a specific element in a matrix. T D D

M S Y Y · Discuss equal matrices in terms of :

i. Determine whether two matrices are equal. F I E E E *the order

ii. Solve problems involving equal matrices. I D C A A *the coresponding elements

R T O R R

S E N · Limit to matrices with not more than three row and

i. Determine whether addition or subtrction can be T R D E S three columns.

performed on two given matrices. M X C

ii. Find the sum or the difference of two matrices. T T A H

iii. Perform addition and subtraction on a few matrices. E B E M O

iv. Solve matrix equations involving addition and S R S I O

subtraction. T E T N L

A A

K T B

i. Multiply a matrix by a number. I R

ii. Express a given matrix as a multiplication of O E

another matrix by a number. N A

iii. Perform calculation on matrices involving addition, S K

subtraction and scalar multiplication.

iv. Solve matrix equations involving addition,

subtraction and scalar multiplication.

· Limit to matrices with not more than three row and

i. Determine whether two matrices can be multiplied three columns.

and state the order of the product when the two · Limit to two unknown elements.

matrices can be multiplied.

ii. Find the product of two matrices.

iii. Solve matrix equations involving multiplication

of two matrices.


4.1 Matrix

· Emphasise that a matrix of order m x n is read as "an m

by n matrix".

4.2 Equal matrices

4.3 Addition and subtraction on matrices

4.4 Multiplication of a matrix by a number

4.5 Multiplication of two matrices

FIRST TERM


1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4· Discuss :

i. Determine whether a given matrix is an identity *an identity matrix is a square matrix

matrix by multiplying it to another matrix. *there is only one identity matrix for each order

ii. Write identity matrix of any order. F · Discuss :

iii. Perform calculation involving identity matrices. I

R M M

S I I

i. Determine whether a 2 x 2 matrix is the inverse T D D · Emphasise that :

matrix of another 2 x 2 matrix.

ii. Find the inverse matrix of a 2 x 2 matrix using : M S Y Y

a. the method of solving simultaneous linear F I E E E *inverse matrices can only exist for square matrices,

equations. I D C A A but not all square matrices have inverse matrices

b. a formula. R T O R R

S E N

T R D E S · Discuss why :

i. Write simultaneous linear equations in matrix form. M X C *the use of inverse matrix is necessary. Relate to

ii. Find the matrix p in a b p = h T T A H

q c d q k E B E M O *it is important to place the inverse matrix at the right

using the inverse matrix. S R S I O place on both sides of the equation

iii. Solve simultaneous linear equations by the matrix T E T N L · Limits to to unknowns.

method. A A · Simultaneous linear equations

iv. Solve problems involving matrices. K T B

I R in matrix form is

# Enrichment / Remedial Excercise # O E =

N A

S K

unknowns.

· The matrix method uses inverse matrix to solve

simultaneous linear equations.


4.6 Identity matrix

*AI = A

*IA = A

4.7 Inverse matrix · The inverse of matrix A is denoted A-1.

*if matrix B is the inverse of matrix A, then matrix A is

also the inverse of matix B, AB = BA = I

4.8 Simultaneous linear equations by using matrices

solving linear equations of type ax = b

ap + bq = h and cp + dq = k

where a, b, c, d, h and k are constants, p and q are

a bc d

pq

hk

a bc d

pq

hkA−1 =A−1

FIRST TERM


1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 45 VARIATIONS

· Discuss the characteristics of the graph using the

i. State the changes in a quantity with respect to the

changes in another quantity involving direct variation. F · If y varies directly as x, the relation is written as

ii. Determine from given information whether a I

quantity varies directly as another quantity. R M M

iii. Express a direct variation in the form of equation S I I

involving two variables. T D D variation.

iv. Find the value of a variable in a direct variation · Using :

when sufficient information is given. M S Y Y

v. Solve problems involving direct variation for the F I E E E ii.

following cases : I D C A A

R T O R R to get the solution.

S E N

T R D E S

i. State the changes in a quantity with respect to M X C

changes in another quantity involving inverse variation. T T A H

ii. Determine from given information whether E B E M O x x

a quantity varies inversely as another quantity. S R S I O

iii. Express an inverse variation in the form of T E T N L .

equation involving two variables. A A

iv. Find the value of a variable in an inverse variation K T B · For the cases ,

when sufficient information is given. I R

v. Solve problems involving inverse variation for the O E

following cases : N A

S K

· For the cases , ,

i. Represen 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.

sufficient information is given.


5.1 Direct variation

graph of y against x when y µ x.

y µ x.

· For the cases y µ xⁿ.limit n to 2, 3 and ½.

· If y µ x, then y = kx where k is the constant of

i. y = kx , or

y ∞ x ; y µ x2 ; y µ x3 ; y µ x1/2

5.2 Inverse variation · For the cases y µ xⁿ.n = 2, 3 and ½, discuss the

characteristics of the graphs of y against xⁿ.

· Discuss the form of the graph of y against 1 when y µ 1

· If y varies inversely as x, the relation is written as

limit n to 2, 3 and ½.

y µ 1 , y µ 1 , y µ 1

x2 x3 x1/2

5.3 Joint variation


y1

x1

=y2

x2

1yx

1n

yx

1n n

yx z

n ny x zn

n

xyz

iv. Solve problems involving joint variation.


SECOND TERM

BIL LEARNING AREA /OUTCOMES JUNE JULY AUGUST SEPT OCT NOV

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 46 GRADIENT AND AREA UNDER GRAPH

· Use examples in various areas

i. State the quantity represented by gradient such as technology and social science.

of a graph. · Compare and differentiate between

ii. Draw the distance-time graph, given : distance-time graph and speed-time graph.

a. a table of distance-time values E · Emphasise that :

b. a relationship between distance and time. S N gradient = change of distance = speed

iii. Find and interpret the gradient S P D change of time

of a distance-time graph. M E M

iv. Find the speed for a period of time I C S Y · Use real life situations such as travelling from

from a distance-time graph. D O T P E one place to another by train or by bus.

v. Draw a graph to show relationship between T N R M A · Use examples in social science and economy.

two variables representing certain measurement Y H D I R

and state the meaning of its gradient. E I A E

A R M L X S

R D I A C · Discuss that in certain cases, that area under a graph

i. State the quantity represented by the D E M H may not represent any meaningful quantity.

area under a graph. S T T X I O For examples :

ii. Find the area under a graph. C E E A N O The area under the distance-time graph.

iii. Determine the distance by finding the area H S R M A L Discuss the formula for finding area under a graph

under the following types of speed-time graph : O T M I T involving :

O N I H

L B A O O ii. a straight line in the form of y = kx + h

R T N L iii. a combination of the above.

d. a combination of the above. B E I S I

iv. Solve problems involving gradient and area R A O D NOTES:

under a graph. E K N A v represents speed,

A S Y t represent time,

# ENRICHMENT/REMEDIAL EXERCISE # K S h and k represent constants.


6.1 Quantity represented by the gradient of a graph

6.2 Quantity represented by the area under a graph.

a. v = k (uniform speed) i. a straight line which is parallel to the x-axis.

b. v = kt

c. v = kt + h

SECOND TERM


1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 47 PROBABILITY II

· Discuss equiprobable sample space through concrete

i. Determine the sample space of an activities and begin with simple cases such as

experiment with equally likely outcomes. tossing a fair coin.

ii. Determine the probability of an event · Use tree diagrams to obtain sample space for tossing

with equiprobable sample space. E a fair coin or tossing a fair die activities.

iii. Solve problems involving probablity of an event. S N The graphing calculator may also be used

S P D to simulate these activities.

7.2 Probability of the Complement of an Event M E M

i. State the complement of an event in : I C S Y

a. words D O T P E · Include events in real life situations such as

b. Set notation T N R M A winning or losing a game and passing or failing an exam.

ii. Find the probability of the complement of an eve Y H D I R

E I A E

A R M L X S · Use real life situations to show the relationship between

i. List the outcomes for event : R D I A C i. A or B and A U B

D E M H

S T T X I O

ii. Find the probability by listing the outcomes C E E A N O · An example of a situation is being chosen to be a

of the combined event : H S R M A L member of an exclusive club with restricted conditions.

a. A or B O T M I T · Use tree diagrams and coordinate planes to find all the

b. A and B O N I H outcomes of combined events.

iii. Solve problems involving probability L B A O O · Use two-way classification tables of events from

of combined event. R T N L newspaper articles or statistical data to find probability

B E I S I of combined events. Ask students to create tree

# ENRICHMENT/REMEDIAL EXERCISE # R A O D i. pengetahuan tentang kebarangkalian berguna untuk

E K N A diagrams from these tables.

A S Y

K S


7.1 Probability of an event

· Discuss events that produce P(A) = 1 and

p(A) = 0.

7.3 Probability of combined event

a. A or B as elements of set A È B ii. A and B and A Ç B.

b. A and B as elements of set A Ç B.

SECOND TERM


1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 48 BEARING

· Carry out activities or games involving finding

i. Draw and label the eight main compass directions : directions using a compass, such as treasure hunt or

a. north, south, east, west scavenger hunt. It can also be about locating several

b. North-east, north-west, south-east, south-west. points on a map.

ii. State the compass angle of any E

compass direction. S N NOTES:

iii. Draw a diagram of a point which shows the S P D Compass angle and bearing are written in

direction of B relative to another point A M E M three-digit form, from 000° to 360°. They are

given the bearing of B from A. I C S Y measured in a clockwise direction from north.

iv. State the bearing of point A from point B D O T P E Due north is considered as bearing 000° .

based on given information. T N R M A For cases involving degrees and minutes, state

v. Solve problems involving bearing. Y H D I R in degrees up to one decimal point.

E I A E

# ENRICHMENT/REMEDIAL EXERCISE # A R M L X S · Discuss the use of bearing in real life situations.

R D I A C For example, in map reading and navigation.

D E M H

S T T X I O NOTES:

C E E A N O Begin with the case where bearing of point B

H S R M A L from point A is given.

O T M I T

O N I H

L B A O O

R T N L

B E I S I

R A O D

E K N A

A S Y

K S


8.1 Bearing

SECOND TERMBIL LEARNING AREA /OUTCOMES JUNE JULY AUGUST SEPT OCT NOV

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 49 EARTH AS A SPHERE

· Model such as globes should be used.

i. Sketch a great circle through the north · Introduce the meridian through Greenwich in England

and south poles. as the Greenwich Meridian with longitude 0°.

ii. State the longitude of a given point. · Discuss that :

iii. Sketch and label a meridian with the longitude E i. all points on a meridian have the same longitude

given. S N ii. there are two meridians on a great circle through

iv. Find the difference between two longitude. S P D both poles

M E M iii. Meridians with longitudes x°E (or W) and

I C S Y (180°- x°) W (or E) form a great circle

i. Sketch a circle parallel to the equator. D O T P E through both poles.

ii. State the latitude of a given points. T N R M A · Discuss that all points on a parallel of latitude

iii. Sketch and label a parallel of latitude. Y H D I R have the same latitude.

iv. Find the difference between two latitudes. E I A E

A R M L X S

R D I A C · Use a globe or map to find locations of cities

i. State the latitude and longitude D E M H around the world.

of a given place. S T T X I O · Use a globe or a map to name a place

ii. Mark the location of a place. C E E A N O given its location.

iii. Sketch and label the latitude and longitude H S R M A L

of a given place. O T M I T

O N I H

L B A O O · Use the globe to find the distance between two

i. Find the length of an arc of a great circle in R T N L cities or towns on the same meridian.

nautical mile, given the subtended angle at the B E I S I

centre of the earth and vice versa. R A O D

ii. Find the distance between two points measured E K N A · Sketch the angle at the centre of the earth that

along a meridian, given the latitudes of both poin A S Y is subtended by the arc between two given points

iii. Find the latitude of a point given the latitude K S along the equator.

of another point and the distance between the

two points along the same meridian.

iv. Find the distance between two points


9.1 Longitude

9.2 Latitude

9.3 Location of a place

9.4 Distance on the surface of the earth

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. · Use models such as the globe to find relationships

vi. State the relation between the radius of the earth between the radius of the earth and radii

and the radius of a parallel of latitude. parallel of latitudes.


1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 vii. State the relation between the length of an arc on

the equator between two meridians and the length

of the corresponding arc on a parallel of latitude.

viii. Find the distance between two points measured · Find the distance between two cities or towns

along a parallel of latitude. on the same parallel of latitude as a group project.

ix. Find the longitude of a point given the longitude E

of another point and the distance between the S N

two points along a parallel of latitude. S P D

x. Find the shortest distance between two points M E M · Use the globe and afew pieces of string to show

on the surface of the earth. I C S Y how to determine the shortest distance between

xi. Solve problems involving : D O T P E two points on he surface of the earth.

a. distance between two points. T N R M A

b. travelling on the surface of the earth. Y H D I R

E I A E

# ENRICHMENT/REMEDIAL EXERCISE # A R M L X S

R D I A C

D E M H

S T T X I O

C E E A N O

H S R M A L

O T M I T

O N I H

L B A O O

R T N L

B E I S I

R A O D

E K N A

A S Y

K S



1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 410 PLANS AND ELEVATIONS

· Use models, blocks or plan and elevation kit.

i. Identify ortogonal projection.

ii. Draw ortogonal projection, given an object

and a plane.

iii. Determine the difference between an object and E

its ortogonal projection with respect to edges S N

and angles. S P D

M E M

I C S Y · Carry out activities in groups where students combine

i. Draw the plan of a solid object. D O T P E two or more different shapes of simple solid

ii. Draw : T N R M A objects into interesting models into interesting models

a. the front elevation Y H D I R and draw plans and elevations for these models.

b. side elevation E I A E · Use models to show that it is important to have a plan

of a solid object . A R M L X S at least two side elevations to construct a solid object.

iii. Draw : R D I A C · Carry out group project :

a. the plan D E M H Draw plan and elevations of buildings or structures, for

b. the front elevation S T T X I O examples students' or teacher's dream home and

c. the side elevation C E E A N O construct a scale model based on the drawings.

of a solid object to scale. H S R M A L

iv. Solve problems involving plan and elevation. O T M I T Involve real life situations such as in building prototypes

O N I H and using actual home plans.

# ENRICHMENT/REMEDIAL EXERCISE # L B A O O

R T N L

B E I S I

R A O D

E K N A

A S Y


10.1 Ortogonal projection

10.2 Plans and elevation

· Use models such as a clock face or a counter which uses

· Emphasise the ways to read numbers in various bases.

· Numbers in base two are also known as binary numbers.

i. 101102 = 1 ´ 24 + 0 ´ 23 + 1 ´ 22 + 1 ´ 21 + 0 ´ 20

· Explore graphs of functions using graphing calcultor or

· Compare the characteristics of graphs of functions with

intersection of two appropriate graphs to the solution

drawn as a solid line to indicate that all points on the

y = ax + b is drawn as a dashed line to indicate that

all points on the line y = ax + b are not in the region.

calculator, the Geometer's Sketchpad, or the overhead

· Emphasise that a matrix of order m x n is read as "an m

*it is important to place the inverse matrix at the right


· Discuss the form of the graph of y against 1 when y µ 1.

winning or losing a game and passing or failing an exam.

· Use real life situations to show the relationship between

member of an exclusive club with restricted conditions.

· Use tree diagrams and coordinate planes to find all the

newspaper articles or statistical data to find probability

i. pengetahuan tentang kebarangkalian berguna untuk

· Carry out activities in groups where students combine

objects into interesting models into interesting models

· Use models to show that it is important to have a plan

at least two side elevations to construct a solid object.

Draw plan and elevations of buildings or structures, for

Involve real life situations such as in building prototypes

PANITIA MATEMATIK SMK JUNJONG, 09000 KULIM, KEDAH

RANCANGAN PENGAJARAN TAHUNAN MATEMATIK TINGKATAN 5 (2003)

PENGGAL SATU

Bil ARAS BIDANG & HASIL PEMBELAJARAN JAN FEB MAC APRIL MEI JUN

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

*Pengajaran & Pembelajaran Matematik Menengah Atas

- Amalan / Cara Belajar Matematik yang Baik C

- Kurikulum Semakan 2000 U P

- Format Matematik SPM (Kod :1449) mulai 2003 T E

I P

1 ASAS NOMBOR E C

P R U

1 a. Menyatakan sifar, satu, dua, tiga ….. sebagai nombor E I T

dalam asas : R K I

i. dua T S

ii. lapan E U U A

iii. lima N J J A P

b. Menyatakan nilai sesuatu digit bagi suatu nombor G I I N E

dalam asas : A A A N

H N N P G

A E G

N N A

S G L

P A D G

E T U A

N U A L S

G A

G S T

A A U

L T

U

I

1.1 Nombor dalam Asas Dua, Asas Lapan & Asas Lima

PENGGAL SATU

Bil ARAS BIDANG & HASIL PEMBELAJARAN JAN FEB MAC APRIL MEI JUN

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

C

U P

T E

I P

E C

P R U

E I T

R K I

T S

E U U A

N J J A P

G I I N E

A A A N

H N N P G

A E G

N N A

S G L

P A D G

E T U A

N U A L S

G A

G S T

A A U

L T

U

I

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2012)

FIRST TERM

BIL LEARNING AREA /OUTCOMES JAN FEB MARCH APRIL MEI JUNE KONTRAK LATIHAN

######################################################################## OBJ SUB TOPICALTARIKH CATATAN1 NUMBER BASES C C C C

x U U U U

By using the number in base two, five and eight to : x T T T T

i. State zero, one, two, three in each base x I I I I

ii. State the value of a digit of each base x

iii. Write a number in expanded notation for base 2, 5, 8 and 10. x T S S S

iv. Convert a number in base 2 to 5, 2 to 8, 2 to 10, 5 to 8, 5 to 10, 8 to 10 and vice versa. x A E E E

vi. Perform computations involving addition and substraction of two numbers in base 2 x H K K K

# Enrichment / Remedial Excercise # U O O O

N L L L

2 GRAPH OF FUNCTIONS (II) x A A A

x B H H H

i. Draw the graph of a : x A

x R

x U

ii. Find from a graph : x

x C

iii. Identify : x I

a. the shape of graph using function b. the type of function, using a graph and vice versa x N

iv. Sketch the graph of a given linear, quadratic , cubic or reciprocal functions. x A

x

i. Find the point(s) of intersection of two graphs , ii. Solve problems by solution of 2 equat x

iii. Find solutions using graphical method x

x

i. Determine whether a given point satisfies y = ax + b or y > ax + b or y < ax + b. x

x

iii. Determine the region which satisfies two or more simultaneous lnear inequalities. x

# Enrichment / Remedial Excercise # x

3 TRANSFORMATIONS (III) U X

*Revision on Transformations (I) & (II) - translations, reflections, rotations and enlargements J X

I X

i. Determine, draw and state the image of a point under combined transformation A X

iv. Determine whether combined transformation AB is equivalent to BA. N X

v. Specify a transformation which is equivalent to the combination and problem solving. X


2.1 Graphs of functions

a. Llinear function : y = ax + b , b. Quadratic function : y = ax2+ bx + c,

c. Cubic function :y = ax3 + bx + cx + d and d. Reciprocal function : y = a/x.

a. the value of y, given the value of x, b. the value(s) of x, given a value of y


2.3 Region representing inequalities

ii. Identify and shade the region satisfying y > ax + b or y < ax + b.


# Enrichment / Remedial Excercise # ###X


FIRST TERM


######################################################################## OBJ SUB TOPICALTARIKH CATATAN4 MATRICES C X C C C

U X U U U

i. Form a matrix from given information, Identify a specific element in a matrix and T X T T T

ii. Determine the number of rows, columns and order of a matrix I X I I I

X

ii. Solve problems involving equal matrices. T X S S S

A X E E E

i. Determine whether addition or subtraction can be performed on two given matrices. H X K K K

ii. Find and perform the sum or the difference of two matrices and problem solving. U X O O O

N X L L L

i. Multiply a matrix by a number and problem solving. X A A A

B X H H H

i. Determine whether two matrices can be multiplied and state the order of the product A X

when the two matrices can be multiplied. R X

iii. Solve matrix equations involving multiplication of two matrices. U X

X

i. Determine whether a given matrix is an identity matrix by multiplying it to another matrix. C X

I X

i. Determine whether a 2 x 2 matrix is the inverse matrix of another 2 x 2 matrix. N X

A X U

i. Write simultaneous linear equations in matrix form. X J

ii. Find the matrix p in a b p = h using the inverse matrix. X I

q c d q k X A

iii. Solve simultaneous linear equations by the matrix method. X N

iv. Solve problems involving matrices. X

# Enrichment / Remedial Excercise # X###

5 VARIATIONS X

X

i. State the changes in a quantity with respect to changes in another quantity. X

ii. Determine from given information whether X

a quantity varies directly/ inversely or combined as another quantity. X

iii. Express the direct/ inverse or joint variation in the form of equation involving two variables. X

iv. Find the value of a variable in the direct/inverse/joint variation when sufficient information is given. X

4.1 Matrix

4.2 Equal matrices - i. Determine whether two matrices are equal.


4.4 Multiplication of a matrix

4.5 Multiplication of two matrices

4.6 Identity matrix

4.7 Inverse matrix


5.1 Direct variation - y ∞ x, 5.2 Inverse variation - y ∞ 1/ x and 5.3 Joint variation

v. Solve problems involving inverse variation for the following cases : X

# Enrichment / Remedial Excercise # X

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2012) FIRST TERM


######################################################################## OBJ SUB TOPICALTARIKH CATATAN6 GRADIENT AND AREA UNDER GRAPH C C X C C

U U X U U

i. State the quantity represented by gradient of a graph. T T X T T

ii. Draw the distance-time graph, given : I I X I I

a. a table of distance-time values X

b. a relationship between distance and time. T S X S S

iii. Find and interpret the gradient of a distance-time graph. A E X E E

iv. Find the speed for a period of time from a distance-time graph. H K X K K

v. Draw a graph to show relationship between two variables representing certain U O X O O

measurements and state the meaning of its gradient. N L X L L

A X A A

i. State the quantity represented by the area under a graph and find the area under a graph. B H X H H

iii. Determine the distance by finding the area under the following types of speed-time graph : A X

R X

iv. Solve problems involving gradient and area under a graph. U X

X

# ENRICHMENT/REMEDIAL EXERCISE # X

7 PROBABILITY II C U X X

I J X X

i. Determine the sample space, the probability of an event and problem solving. N I X X

7.2 Probability of the Complement of an Event A A X X

i. State the complement of an event in words or standard notation N X X

ii. Find the probability of the complement of an event. X X

### X X

i. List the outcomes for event : X X

X X

X X

ii. Find the probability by listing the outcomes of the combined event : X X

a. A or B and b. A and B X X

iii. Solve problems involving probability of combined event. X X

X X



a. v = k (uniform speed), b. v = kt and c. v = kt + h or a combination of the above.


7.3 Probability of combined event

a. A or B as elements of set A È B

b. A and B as elements of set A Ç B.

# ENRICHMENT/REMEDIAL EXERCISE # X X

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2012) FIRST TERM


######################################################################## OBJ SUB TOPICALTARIKH CATATAN8 BEARING C C X C C

U U X U U

i. Draw and label the eight main compass directions : T T X T T

a. north, south, east, west I I X I I

b. North-east, north-west, south-east, south-west. X

ii. State the compass angle of any compass direction. T S X S S

iii. Draw a diagram of a point which shows the direction of B relative to another point A A E X E E

given the bearing of B from A. H K X K K

iv. State the bearing of point A from point B based on given information. U O X O O

v. Solve problems involving bearing. N L X L L

A X A A

# ENRICHMENT/REMEDIAL EXERCISE # H X H H

U

EARTH AS A SPHERE B J X

A I X

i. Sketch/ labell a meridian with the longitude given R A X

ii. Find the difference between two longitude. U N X

### X

i. Sketch / state a circle parallel to the equator. X

ii. Find the difference between two latitudes. X

C X

i. State the latitude and longitude of a given place, mark the location and sketch the longitud I X

X

i. Find the length of an arc of a great circle in nautical mile, given the subtended angle at the X

centre of the earth and vice versa. X

ii. Find the distance between two points measured along a meridian, given the latitudes of both points. X

iii. Find the latitude/ longitude of a point given the latitude / longitude of another point and X

the distance between the two points along the same meridian/ latitude. X

iv. State the relation between the radius of the earth and the radius of a parallel of latitude. X

v. Find the shortest distance between two points X

vi. Problems solving. X

8.1 Bearing

9.1 Longitude

9.2 Latitude



X

# ENRICHMENT/REMEDIAL EXERCISE # X

S E C O N D T E R M - R E V I S I O N ( J U L Y - A U G) T R I A L ( A U G U S T ) G E M P U R S P M ( S E P T - O K T ) S P M ( N O V)

RANCANGAN PENGAJARAN DAN KONTRAKN PEMBELAJARAN TAHUNAN - MATEMATIK TING 4 2012

SEMESTER PERTAMA

BIL BIDANG DAN HASIL PEMBELAJARAN JAN FEB MARCHAPRIL MEI JUNE KONTRAK LATIHAN

######################################################################## OBJ SUB TOPIKAL TARIKH CATATAN1 BENTUK PIAWAI X C C C C

x U U U U

x T T T T

X I I I I

2 UNGKAPAN DAN PERSAMAAN KUADRATIK X T S S S

x A E E E

x H K K K

X X U O O O

X N L L L

U A A A

B J X H H H

3 SET / HIMPUNAN A I X

R A X

U N X

### X X

C X

I

4 PENAAKULAN MATEMATIK N X U

A X J

X I

X A

X N

X

X ###

X

5 GARIS LURUS X

X

I. ANGKA BEERTIII. BENTUK PIAWAI

i. UNGKAPAN KUADRATIKii. PEMFAKTORAN UNGKAPAN KUADRATIKiii. PERSAMAAN KUADRATIKiv. PUNCA-PUNCA BAGI PERSAMAAN KUADRATIK

I. SETII. Subset, SET SEMESTA DAN PELENGKAP BAGI SET III. OPERASI KE ATAS SET

i. PERNYATAANii. PENGKUANTITI 'SEMUA' DAN 'SEBILANGAN'iii. OPERASI MELIBATKAN 'BUKAN' , 'DAN' DAN 'ATAU'.iv. IMPLIKASI.v. HUJAHvi. ARUHAN DAN DEDUKSI

X

X

X

X

RANCANGAN PENGAJARAN DAN KONTRAK PEMBELAJARAN TAHUNAN - MATEMATIK TING 4 2012

SEMESTER PERTAMA

BIL BIDANG DAN HASIL PEMBELAJARAN JAN FEB MARCH APRIL MEI JUNE KONTRAK LATIHAN

######################################################################## OBJ SUB TOPIKAL TARIKH CATATAN6 STATISTIK C C X U U C C

U U X J J U U

T T X I I T T

I I X A A I I

X N N

T S S S

A E ###### E E

7 KEBARANGKALIAN I H K K K P X

U O O O E X

N L L L R X

A A A B X

B H H H I X

A N

8 BULATAN 111 R C X

U A X

N X

C G X

JULY AUG SEPT OKT NOV DIS

########################################################################

9 TRIGONOMETRI II U X X C C C C C C C C

J X X U U U P P P P U U U U U U U

I X X T L L E E E E T T T T T T T

A X X I A A P P P P I I I I I I I

N X X N N E E E E

10 SUDUT DONGAKAN DAN SUDUT TUNDUK X X S G G R R R R S S S S S S S

### X X E K K I I I I E E E E E E E

I. SUDUT DONGAKAN DAN SUDUT TUNDUK X X K A A K K K K K K K K K K K

O J J S S S S O O O O O O O

i. KECERUNAN BAGI GARIS LURUSii. PINTASANiii. PERSAMAAN GARIS LURUSiv. GARIS-GARIS SELARI

i. SELANG KELAS, MOD & MIN BAGI DATA TERKUMPULii. HISTOGRAMiii. POLIGON KEKERAPANiv. KEKERAPAN LONGGOKANv. SUKATAN SERAKAN

i. RUANG SAMPELii. PERISTIWAiii. KEBARANGKALIAN SUATU PERISTIWA

I. TANGEN KEPADA BULATANII. SUDUT ANTARA TANGEN DAN PERENTASIII. TANGEN SEPUNYA.

I. NILAI BAGI sin θ, Kos θ & tan θ (0° ≤ θ < 360°)II. GRAF BAGI sin, Kos Dan tan.

11 GARIS DAN SATAH DALAM TIGA MATRA L X X X I I A A A A L L L L L L L

A X X X A A A A A A A A A A A

H X X X N N N N H H H H H H H

X X X

i. SUDUT ANTARA GARIS DAN SATAHii. SUDUT ANTARA DUA SATAH

TARIKH : 10 JAN 20 KELAS : 5 AL FARABY (1200-110), 5 AR RAZI (145-220), 5 AKY (1050 - 1125)TOPIK : NUMBER BASESlearning area / outcomes : To identify the concept of :

a. Convert a number in certain bases to a certain bases : - base 2 to base 5 and vice versa - base 2 to base 8 and vice versa - base 5 to base 8 and vice versa

b. perform calculation using base 2 only - addition - substraction

Reflections :

5 AFB :

5 ARZ :

5 AKY :

TARIKH : 10 JAN 20 KELAS : 4 AL FARABY (8.20 -9.00)TOPIK : standard formsSubtopic : Standard Fprmlearning area / outcomes : To identify the concept of :

A X 10 index n, where n is integers

. Discuss the uses of standard form in everyday life and other area.

. Use the scientific calculator to explore standard form.

Reflections :


MASA & 1 2 3 4 5 6 7 8HARI 730-830 830-910 910-950 950-10301030-11001100-11351135-12101210-1245AHAD P 5KHW 5AK R

740-820 820-900 900-940 940-10201020-10501050-11251125-12001200-1235ISNIN 4AF E 5AK 5AF

SELASA 5KHW 5AF H 5 AKRABU 5AR A 5 KHW

KHAMIS 5AF T 5 AR 4 AF

v. Convert a number to a certain base

vi. Perform computations involving:

i. Addition

ii. Subtraction

of two numbers in base two


GRAPH OF FUNCTIONS (II)

· Explore graphs of functions using graphing calcultor or2.1 Graphs of functions

i. Draw the gr the Geometer's Sketchpad.

· Compare the characteristics of graphs of functions with

different values of constants.

· Limit cubic functions to the following forms :

ii. Find from

2

iii. Identify : · Emphasise that :

a. the sh *For the region representing

b. the typ

and vi is drawn as a dashed line .

iv. Sketch the *For the region representing

quadratic the line y = ax + b is

drawn as a solid line to indicate that

i. Find the all points on the

ii. Solve p

LEARNING AREA /OUTCOMES

iii. Find solutions using graphical method

i. Determine whether a given point satisfies :


ii. Determine the position of a given point relative

BIL

iv. Shade the regions representing the inequalities :

v. Determine the region which satisfies two or more

simultaneous lnear inequalities.


TRANSFORMATIONS (III)

*Revision on Transformations (I) & (II)

- translation

- reflection

- rotation

- enlargem · Explore combined transformation using the graphing

calculator, the Geometer's Sketchpad, or the overhead

i. Determin projector and transparencies.

3 ii. Draw the · Investigate the characteristics of an object and its

iii. State th image under combined transfomation.

of a poi · Limits isometric transformations to translations,

iv. Determi reflections and rotations.

a. Llinear function :

b. Quadratic function :

c. Cubic function :

d. Reciprocal function : y = ax3

y = ax3 + b

a. the value of y = x3 + bx + c

b. the value(s) of y = -x3 + bx + c

y < ax + b or y > ax + b,


line y = ax + b are in the region.

TEACHING AND

LEARNING

2.3 Region representing inequalities

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

to the equation y = ax + b.

iii. Identify the region satisfying y > ax + b or

y < ax + b.

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

ii. y > ax + b atau y < ax + b

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


is equivalent to combined transformation BA.

v. Specify a transformation which is equivalent

to the combination of two isometric

vi. Solve problems involving transformation.



MATRICES · Emphasise that matrices :

- are written in brackets.

i. Form a m - the order of matrix - m x n

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2011) ii. Determ is read as "an m by n matrix.

order of a · Discuss equal matrices in terms of :

iii. Identify *the order

BIL *the coresponding elements

i. Determine whether two matrices are equal.

ii. Solve p · Limit to matrices with not more than

three row and three columns.

i. Determine whether addition or subtraction can be

performed on two given matrices.

ii. Find and · Discuss :

of two mat *an identity matrix = square matrix

ii. Problems s *there is only one identity matrix for each order

· Discuss :

i. Multiply

ii. Problems

i. Determi · Emphasise that :

and stat

matrices

ii. Find the *inverse matrices can only exist for square matrices,

iii. Solve ma but not all square matrices have inverse matrices

of two mat · Discuss why :

*the use of inverse matrix is necessary. Relate to

i. Determin

matrix by *it is important to place the inverse matrix at the right

place on both sides of the equation

i. Determin · Limits to to unknowns.

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.

TEACHING AND

LEARNING

4.1 Matrix

4.2 Equal matrices


4.4 Multiplication of a matrix

*AI = A

*IA = A

4.5 Multiplication of two matrices· The inverse of matrix A is denoted A-1.


also the inverse of matix B, AB = BA = I

4.6 Identity matrix

solving linear equations of type ax = b

4.7 Inverse matrix


· Simultaneous linear equations

i. Write si

ii. Find the ma in matrix form is

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2011) =

using the inverse matrix.

iii. Solve

BIL method. unknowns.

iv. Solve problems involving matrices.

# Enrichment / Remedial Excercise #· The matrix method uses inverse matrix to solve

simultaneous linear equations.

VARIATIONS

· Discuss the characteristics of the graph using the

i. State th · If y varies directly as x, the relation is written as

changes in an

ii. Determi

a quanti

iii. Expresst variation.

form of · Using :

iv. Find the

joint var ii.

v. Solve pro to get the solution.

following

.

# Enrichment / Remedial Excercise #· For the cases ,


GRADIENT AND· Use examples in various areas

such as technology and social science.

i. State t · Compare and differentiate between

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2011) of a graph distance-time graph and speed-time graph.

ii. Draw th · Emphasise that :

a. a tab gradient = change of distance = speed

BIL b. a re change of time

iii. Find and interpret the gradient

TEACHING AND

LEARNING


ap + bq = h and cp + dq = k

where a, b, c, d, h and k are constants, p and q are

5.1 Direct variation - y ∞ x

5.2 Inverse variation - y ∞ 1/ x

5.3 Joint variation graph of y against x when y µ x.

y µ x.

· For the cases y µ xⁿ.limit n to 2, 3 and ½.

· If y µ x, then y = kx where k is the constant of

i. y = kx , or

· For the cases y µ xⁿ.n = 2, 3 and ½, discuss the

- y µ 1 , y characteristics of the graphs of y against xⁿ.

x· Discuss the form of the graph of y against 1 when y µ 1.

- y ∞ x ; · If y varies inversely as x, the relation is written as


TEACHING AND

LEARNING


a bc d

pq

hk

a bc d

pq

hkA−1

y1

x1

=y2

x2

1yx

of a dis · Use real life situations such as travelling from

iv. Find the one place to another by train or by bus.

from a d · Use examples in social science and economy.

v. Draw a g · Discuss that in certain cases, that area under a graph

two var may not represent any meaningful quantity.

and state For examples :

The area under the distance-time graph.

i. State t Discuss the formula for finding area under a graph

area und involving :

ii. Find the

iii. Determin ii. a straight line in the form of y = kx + h

under th iii. a combination of the above.

NOTES:

v represents speed,

d. a c t represent time,

iv. Solve pr h and k represent constants.

under a graph.

# ENRICHMENT/REMEDIAL EXERCISE #

PROBABILITY II

i. Determine the sample space of an

ii. Determine the probability of an event

iii. Solve problems involving probablity of an event.

7


7.2 Probability · Discuss equiprobable sample space through concrete

i. State th activities and begin with simple cases such as

a. words tossing a fair coin.

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2011) b. Set no · Use tree diagrams to obtain sample space for tossing

ii. Find th a fair coin or tossing a fair die activities.

BIL

i. List the · 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

ii. Find th i. A or B and A U B

of the

a. A or B · An example of a situation is being chosen to be a

b. A and member of an exclusive club with restricted conditions.

iii. Solve · Use tree diagrams and coordinate planes to find all the

of comb outcomes of combined events.

· Use two-way classification tables of events from

# ENRICHMENT/REMEDIAL EXERCISE # newspaper articles or statistical data to find probability

of combined events. Ask students to create tree


i. a straight line which is parallel to the x-axis.

a. v = k (uniform speed)

b. v = kt

c. v = kt + h


TEACHING AND

LEARNING

· Discuss events that produce P(A) = 1 and

7.3 Probability of combined event p(A) = 0.

a. A or B as elements of set A

b. A and B as elements of set A

ii. A and B and A Ç B.

BEARING diagrams from these tables.

NOTES:

i. Draw an Compass angle and bearing are written in

a. north three-digit form, from 000° to 360°. They are

b. Nort measured in a clockwise direction from north.

ii. State t Due north is considered as bearing 000° .

compass For cases involving degrees and minutes, state

iii. Draw a in degrees up to one decimal point.

8 directio · Discuss the use of bearing in real life situations.

given th For example, in map reading and navigation.

iv. State th NOTES:

based on Begin with the case where bearing of point B

v. Solve pro from point A is given.



EARTH AS A S · Model such as globes should be used.

· Introduce the meridian through Greenwich in England

i. Sketch a as the Greenwich Meridian with longitude 0°.

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2011) ii. State the · Discuss that :

iii. Sketch/ i. all points on a meridian have the same longitude

iv. Find the d ii. there are two meridians on a great circle through

BIL given. both poles

iii. Meridians with longitudes x°E (or W) and

i. Sketch a (180°- x°) W (or E) form a great circle

ii. State the through both poles.

iii. Sketch an · Discuss that all points on a parallel of latitude

iv. Find the have the same latitude.

· Use a globe or map to find locations of cities

i. State the around the world.

of a given · Use a globe or a map to name a place

ii. Mark the given its location.

iii. Sketch / · Use the globe to find the distance between two

cities or towns on the same meridian.

i. Find the · Sketch the angle at the centre of the earth that

nautical is subtended by the arc between two given points

centre of along the equator.

ii. Find th · Use models such as the globe to find relationships

along a m between the radius of the earth and radius

iii. Find the parallel of latitudes.

/ longitude of another point and the distance between the

two points along the same meridian/ latitude.

iv. State the relation between the radius of the earth

and the radius of a parallel of latitude.

v. Find the shortest distance between two points

vi. Solve problems involving :

a. distance between two points.

8.1 Bearing

TEACHING AND

LEARNING

9.1 Longitude

9.2 Latitude



b. travelling on the surface of the earth.



REVISION FOR SPM / GEMPUR SPM

. Discuss the significant of zero in a number.

. Discuss the uses of significant figures in everyday life

and other areas.

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 4 MATHEMATICS (2011). Use the scientific calculator to explore standard form.

. Discuss the characteristics of quadratic expression or

BIL

1 . Discuss the various methods to obtained the

desired products. Begin with a = 1.

. Discuss the number of roots of quadratic equations.

TEACHING AND

LEARNING

STANDARD FORM

I. Significant Figure

II. Standard Form

QUADRATIC EXPRESSIONS AND EQUATIONS

equations of the form ax®+bx +c=0 where a, b and c

i. Quadratic Expressions

are constants, a ≠ 0 and x is an unknown.

ii. Factorisation of Quadratic Expressions

iii. Quadratic Equations

iv. Roots of Quadratic Equations

SETS . Discuss the relationship between sets and universal sets.

2

. Discuss cases with :

. A ᶜ B .

. Focus on mathematical sentences.

. Identify the statement by finding the truth of the sentences.

3 .

. Discuss why {0} and {Ø} are not empty sets.

I. Set

II. Subset, Universal set & Complement of a set

. A ∩ B = Ø,

III. Operations on Sets

MATHEMATICAL REASONING

i. Statements

ii. Quantifiers ‘All’ and ‘ Some’

iii. Operation involving ‘Not’ or ‘No’, ‘And’ and ‘Or’ in Statements.

iv. Implication

v. Argument

4

. Discuss the relationship between gradient and tan θ;

. The steepness of the straight line with different value of gradient

. Find the ratio of vertical distance to horizontal distance

. Verify that m is gradient, c is y-intercept of a straight

line with equation y = mx + c

5

vi. Deduction and Induction

THE STRAIGHT LINE

i. Gradient of a Straight Line

ii. Intercept . Identify the concept of m, c and x-intercept.

iii. Equation of a straight line

iv. Parallel lines

9 10 11 12 131245-120 120-155 155-230 KLINTEN

1235-110 110-145 145-2205AF 5AR5 AK

4 AF4 AF

maths form 5 year plan

Documents

kontrak latihan obj

real life situations

simultaneous lnear inequalities

main compass directions

combined transformation ba

vice versa iv

perform computations involving

learning area outcomes