Rancangan Tahunan Matematik 2012

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BIL LEARNING AREA /OUTCOMES

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 21 NUMBER BASES R

1.1 Number in base two, eight and five S

i. State zero, one, two, three……. T

as a number in base:

a. two M S

b. eight F I E

c. five I D C

ii. State the value of adigit of a number in R T O

base : S E N

a. two T R D

b. eight M

c. five T T iii. Write anumber in base : E B E

a. two S R S

b. eight T E T

c. five A

in expanded notation. K

iv. Convert a number in base :

a. two

b. eight

c. five

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 #

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2 GRAPHS OF FUNCTIONS (II)

2.1 Graphs of functions

i. Draw the graph of a :

a. Llinear function : y = ax + b F

where a and b are constants I

b. Quadratic function : y = ax 2 + bx + c R

where a , b and c are constants, a ≠ 0 S

c. Cubic function :y = ax 3

+ bx + cx + d T

where a , b , c and d are constants, a ≠ 0

d. Reciprocal function : y = a/x M S

where a is a constants, a ≠ 0 F I E

ii. Find from a graph : I D C

a. the value of y , given the value of x R T O

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

iii. Identify : T R D

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

b. the tpe of function given a graph T T

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

iv. Sketch the graph of a given linear, quadratic, cubic S R S

or reciprocal function. T E T

A

2.2 Solution of an equation by graphical method K

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.

2.3 Region representing inequalities in two variables

i. Determine whether a given point satisfies :

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

ii. Determine the position of a given point relative

to the equation y = ax + b.

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

y < ax + b .

iv. Shade the regions representing the inequalities :

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

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

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

v. Determine the region which satisfies two or more

simultaneous lnear inequalities.

# Enrichment / Remedial Excercise # F

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3 TRANSFORMATIONS (III) R

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

- translation T

- reflection

- rotation M S

- enlargement F I E

I D C

3.1 Combination of two transformations R T O

i. Determine the image of an object under S E N

combination of two isometric transformations. T R D

ii. Determine the image of an object under M

combination of : T T a. two enlargements E B E

b. an enlargement and an isometric S R S

transformation T E T

iii. Draw the image of an object under A

combination of two transformations. K

iv. State the coordinates of the image of a point

under combined transformation.

v. Determine whether combined transformation AB

is equivalent to combined transformation BA.

vi. Specify two successive transformations in a

combined transformation given the object

and the image.vii. Specify a transformation which is equivalent

to the combination of two isometric

transformations.

viii. Solve problems involving transformation.


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4 MATRICES

4.1 Matrix

i. Form a matrix from given information.

ii. Determine : F

a. the number of rows I

b. the number of columns R

c. the order of a matrix S

iii. Identify a specific element in a matrix. T

4.2 Equal matrices M S

i. Determine whether two matrices are equal. F I E

ii. Solve problems involving equal matrices. I D C

R T O

4.3 Addition and subtraction on matrices S E N

i. Determine whether addition or subtrction can be T R D

performed on two given matrices. M

ii. Find the sum or the difference of two matrices. T Tiii. Perform addition and subtraction on a few matrices. E B E

iv. Solve matrix equations involving addition and S R S

subtraction. T E T

A

4.4 Multiplication of a matrix by a number K

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.

4.5 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.

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4.6 Identity matrix

i. Determine whether a given matrix is an identity

matrix by multiplying it to another matrix.

ii. Write identity matrix of any order. F

iii. Perform calculation involving identity matrices. I

R

4.7 Inverse matrix S

i. Determine whether a 2 x 2 matrix is the inverse T

matrix of another 2 x 2 matrix.

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

a. the method of solving simultaneous linear F I E

equations. I D C

b. a formula. R T O

S E N

4.8 Simultaneous linear equations by using matrices T R D

i. Write simultaneous linear equations in matrix form. M

ii. Find the matrix p in a b p = h T Tq c d q k E B E

using the inverse matrix. S R S

iii. Solve simultaneous linear equations by the matrix T E T

method. A

iv. Solve problems involving matrices. K


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5 VARIATIONS

5.1 Direct variation

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

changes in another quantity involving direct variation. F

ii. Determine from given information whether a I

quantity varies directly as another quantity. R

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

involving two variables. T

iv. Find the value of a variable in a direct variation

when sufficient information is given. M S

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

following cases : I D C

y ∞ x ; y x 2 ; y x

3 ; y x

1/2R T O

S E N

5.2 Inverse variation T R D

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

changes in another quantity involving inverse variation. T Tii. Determine from given information whether E B E

a quantity varies inversely as another quantity. S R S

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

equation involving two variables. A

iv. Find the value of a variable in an inverse variation K

when sufficient information is given.

v. Solve problems involving inverse variation for the

following cases :

y 1 , y 1 , y 1

x 2

x 3

x 1/2

5.3 Joint variationi. 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.

iv. Solve problems involving joint variation.


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

6 GRADIENT AND AREA UNDER GRAPH

6.1 Quantity represented by the gradient of a graph

i. State the quantity represented by 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 S

of a distance-time graph. E

iv. Find the speed for a period of time C

from a distance-time graph. O

v. Draw a graph to show relationship between T N

two variables representing certain measurements H D

and state the meaning of its gradient. I

R M

6.2 Quantity represented by the area under a graph. D I

i. State the quantity represented by the D

area under a graph. T T

ii. Find the area under a graph. E E

iii. Determine the distance by finding the area S R

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

a. v = k (uniform speed)

b. v = kt B

c. v = kt + h R

d. a combination of the above. E

iv. Solve problems involving gradient and area A

under a graph. K

# ENRICHMENT/REMEDIAL EXERCISE #

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

7 PROBABILITY II

7.1 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 probablity of an event.

S

7.2 Probability of the Complement of an Event E

i. State the complement of an event in : C

a. words O

b. Set notation T N

ii. Find the probability of the complement of an event. H D

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7.3 Probability of combined event R M

i. List the outcomes for event : D I

a. A or B as elements of set A B D

b. A and B as elements of set A B. T T

ii. Find the probability by listing the outcomes E E

of the combined event : S R

a. A or B T M

b. A and B

iii. Solve problems involving probability B

of combined event. R

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

8 BEARING

8.1 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 S

direction of B relative to another point A E

given the bearing of B from A. C

iv. State the bearing of point A from point B O

based on given information. T N

v. Solve problems involving bearing. H D

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# ENRICHMENT/REMEDIAL EXERCISE # R M

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1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 29 EARTH AS A SPHERE

9.1 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 longitude. S

E

9.2 Latitude C

i. Sketch a circle parallel to the equator. O

ii. State the latitude of a given points. T N

iii. Sketch and label a parallel of latitude. H D

iv. Find the difference between two latitudes. I

R M

9.3 Location of a place D I

i. State the latitude and longitude D of a given place. T T

ii. Mark the location of a place. E E

iii. Sketch and label the latitude and longitude S R

of a given place. T M

9.4 Distance on the surface of the earth B

i. Find the length of an arc of a great circle in R

nautical mile, given the subtended angle at the E

centre of the earth and vice versa. A

ii. Find the distance between two points measured K

along a meridian, given the latitudes of both points.

iii. Find the latitude of a point given the latitude of another point and the distance between the

two points along the same meridian.

iv. Find the distance between two points

measured along the equator, given the 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 the relation between the radius of the earth

and the radius of a parallel of latitude.

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1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2vii. 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

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. S

x. Find the shortest distance between two points E

on the surface of the earth. C

xi. Solve problems involving : O

a. distance between two points. T N

b. travelling on the surface of the earth. H D

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# ENRICHMENT/REMEDIAL EXERCISE # R M

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10 PLANS AND ELEVATIONS

10.1 Ortogonal projection

i. Identify ortogonal projection.

ii. Draw ortogonal projection, given an object

and a plane.iii. Determine the difference between an object and

its ortogonal projection with respect to edges

and angles. S

E

10.2 Plans and elevation C

i. Draw the plan of a solid object. O

ii. Draw : T N

a. the front elevation H D

b. side elevation I

of a solid object . R M

iii. Draw : D I

a. the plan D b. the front elevation T T

c. the side elevation E E

of a solid object to scale. S R

iv. Solve problems involving plan and elevation. T M

# ENRICHMENT/REMEDIAL EXERCISE # B

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Bil ARAS BIDANG & HASIL PEMBELAJARAN

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

1.1 Nombor dalam Asas Dua, Asas Lapan & Asas Lima P R

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

dalam asas : R K

i. dua T S

ii. lapan E U U A

iii. lima N J J A

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

dalam asas : A A A

H N N P

A E

N N

S G

P A D G

E T U A

N U A L

G

G S

A A

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PANITIA MATEMATIK SMK JUNJONG, 09000 KULIM, KEDAH

RANCANGAN PENGAJARAN TAHUNAN MATEMATIK TINGKATAN 5

PENGGAL SATU

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Bil ARAS BIDANG & HASIL PEMBELAJARAN

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1 NUMBER BASES C C

1.1 Number in base two, eight and five x U U

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

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

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

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

# Enrichment / Remedial Excercise # U O

N L

2 GRAPH OF FUNCTIONS (II) x A

2.1 Graphs of functions x B H

i. Draw the graph of a : x A

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

c. Cubic function :y = ax 3 + bx + cx + d and d. Reciprocal function : y = a/x. x U

ii. Find from a graph : x

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

2.2 Solution of an equation by graphical method x

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

iii. Find solutions using graphical method x

2.3 Region representing inequalities x

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

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

3.1 Combination of two transformations 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

# Enrichment / Remedial Excercise # X

YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEM

FEB MARCH APRIL MEI

FIRST TERM

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4 MATRICES C X C

4.1 Matrix U X U

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

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

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

ii. Solve problems involving equal matrices. T X S

4.3 Addition and subtraction on matrices A X E

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

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

4.4 Multiplication of a matrix N X L

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

4.5 Multiplication of two matrices B X 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 Xiii. Solve matrix equations involving multiplication of two matrices. U X

4.6 Identity matrix X

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

4.7 Inverse matrix I X

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

4.8 Simultaneous linear equations by using matrices 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 2

5 VARIATIONS X5.1 Direct variation - y ∞ x, 5.2 Inverse variation - y ∞ 1/ x and 5.3 Joint variation 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

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

# Enrichment / Remedial Excercise # X

FIRST TERM

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6GRADIENT AND AREA UNDER GRAPH C C X

6.1 Quantity represented by the gradient of a graph U U X

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

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

a. a table of distance-time values X

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

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

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

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

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

6.2 Quantity represented by the area under a graph. A X

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

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

a. v = k (uniform speed), b. v = kt and c. v = kt + h or a combination of the above. R Xiv. Solve problems involving gradient and area under a graph. U X

X

# ENRICHMENT/REMEDIAL EXERCISE # X

7 PROBABILITY II C U X X

7.1 Probability of an event 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

7.3 Probability of combined event 3 X X

i. List the outcomes for event : X X

a. A or B as elements of set A B X X

b. A and B as elements of set A B. 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

# ENRICHMENT/REMEDIAL EXERCISE # X X

FIRST TERM

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

8 BEARING C C X

8.1 Bearing U U X

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

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

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

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

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

given the bearing of B from A. H K X

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

v. Solve problems involving bearing. N L X

A X

# ENRICHMENT/REMEDIAL EXERCISE # H X

U

EARTH AS A SPHERE B J

9.1 Longitude A I

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

ii. Find the difference between two longitude. U N

9.2 Latitude 2

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

ii. Find the difference between two latitudes.

9.3 Location of a place C

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

9.4 Distance on the surface of the earth

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 the latitude/ longitude of a point given the latitude / longitude of another point andthe 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. Problems solving.



FIRST TERM

JAN FEB MARCH APRIL MEI

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



BIL BIDANG DAN HASIL PEMBELAJARAN RIL MEI

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 OBJ SUB

1 BENTUK PIAWAI X C C C C

x U U U U

I.ANGKA BEERTI x T T T T

II. BENTUK PIAWAI X I I I I

2 UNGKAPAN DAN PERSAMAAN KUADRATIK X T S S S

x A E E E

i. UNGKAPAN KUADRATIK x H K K K

ii. PEMFAKTORAN UNGKAPAN KUADRATIK X X U O O O

iii. PERSAMAAN KUADRATIK X N L L L

iv. PUNCA-PUNCA BAGI PERSAMAAN KUADRATIK U A A A

B J X H H H

3 SET / HIMPUNAN A I X

R A X

I. SET U N X

II. Subset, SET SEMESTA DAN PELENGKAP BAGI SET 1 X X

III. OPERASI KE ATAS SET C X

I

4 PENAAKULAN MATEMATIK N X U

A X J

i.PERNYATAAN X I

ii. PENGKUANTITI 'SEMUA' DAN 'SEBILANGAN' X A

iii. OPERASI MELIBATKAN 'BUKAN' , 'DAN' DAN 'ATAU'. X N

iv. IMPLIKASI. X

v. HUJAH X 2

vi. ARUHAN DAN DEDUKSI X

5 GARIS LURUS X

X

i. KECERUNAN BAGI GARIS LURUS X

ii. PINTASAN X

iii. PERSAMAAN GARIS LURUS X

iv. GARIS-GARIS SELARI X

FEBJAN FEB MARCH JUNE K

RANCANGAN PENGAJARAN DAN KONTRAKN PEMBELAJARAN TAHUNAN - MATEMATIK TING 4 2012RANCANGAN PENGAJARAN DAN KONTRAKN PEMBELAJARAN TAHUNAN - MATEMATIK TING 4 2012

SEMESTER PERTAMA



BIL BIDANG DAN HASIL PEMBELAJARAN MEI JUNE

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

6 STATISTIK C C X U U C C

i. SELANG KELAS, MOD & MIN BAGI DATA TERKUMPUL U U X J J U U

ii. HISTOGRAM T T X I I T T

iii. POLIGON KEKERAPAN I I X A A I I

iv. KEKERAPAN LONGGOKAN X N N

v. SUKATAN SERAKAN T S S S

A E 3 4 E E

7 KEBARANGKALIAN I H K K K P

U O O O E

i. RUANG SAMPEL N L L L R

ii. PERISTIWA A A A B

iii. KEBARANGKALIAN SUATU PERISTIWA B H H H I

A N

8 BULATAN 111 R CU A

I. TANGEN KEPADA BULATAN N

II. SUDUT ANTARA TANGEN DAN PERENTAS C G

III. TANGEN SEPUNYA.

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

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

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

I. NILAI BAGI sin θ, Kos θ & tan θ (0 ≤ θ < 360) I X X T L L E E E E T T T T T

II. GRAF BAGI sin, Kos Dan tan. A X X I A A P P P P 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

4 X X E K K I I I I 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

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

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

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

i. SUDUT ANTARA GARIS DAN SATAH H X X X N N N N H H H H H

ii. SUDUT ANTARA DUA SATAH X X X

JULY AUG SEPT OKT NOV D

RANCANGAN PENGAJARAN DAN KONTRAK PEMBELAJARAN TAHUNAN - MATEMATIK TIN

SEMESTER PERTAMA

JAN FEB MARCH APRIL



CATATAN



TARIKH : 10 JAN 2KELAS : 5 AL FARABY (1200-110), 5 AR RAZI (145-220), 5 AKY (1050 - 1125)TOPIK : NUMBER BASESlearning area / outcomes : To identify the concept of :

1.1 Number in base two, eight and five

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 2KELAS : 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 8

HARI 730-830 830-910 910-950 950-1030 030-110 1100-113 135-121 1210-124

AHAD P 5KHW R

740-820 820-900 900-940 940-1020 020-105 1050-112 125-120 1200-123

ISNIN 4AF E 5AK

SELASA 5AF H

RABU AKHAMIS T

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)

2.1 Graphs of func · Explore graphs of functions using graphing calcultor or

i. Draw the gra the Geometer's Sketchpad.

a. Llinear fun · Compare the characteristics of graphs of functions with

b. Quadratic different values of constants.

c. Cubic funct · Limit cubic functions to the following forms :

5AK

5

5KHW 5

5AR 5 KHW5AF 5 AR 4



d. Reciprocal y = ax 3

ii. Find from a g y = ax 3

+ b

2 a. the value y = x 3

+ bx + c

b. the value( y = -x 3

+ bx + c

iii. Identify : · Emphasise that :

a. the shape *For the region representing

b. the type o y < ax + b or y > ax + b,

and vice is drawn as a dashed line .iv. Sketch the g *For the region representing

quadratic, c the line y = ax + b is

2.2 Solution of an drawn as a solid line to indicate that

i. Find the poi all points on the

ii. Solve probl line y = ax + b are in the region.

LEARNING AREA /OU

iii. Find solutions using graphical method

2.3 Region representing inequalities

i. Determine whether a given point satisfies :

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

ii. Determine the position of a given point relative

to the equation y = ax + b.

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

y < ax + b .

iv. Shade the regions representing the inequalities :

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

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

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

v. Determine the region which satisfies two or more

simultaneous lnear inequalities.


TRANSFORMATIONS (III)

*Revision on Transformations (I) & (II)

- translation

- reflection

- rotation

- enlargeme · Explore combined transformation using the graphing

3.1 Combination o calculator, the Geometer's Sketchpad, or the overhead

i. Determine t projector and transparencies.3 ii. Draw the im · Investigate the characteristics of an object and its

iii. State the co image under combined transfomation.

of a point u · Limits isometric transformations to translations,

iv. Determine reflections and rotations.

is equivalent to combined transformation BA.

v. Specify a transformation which is equivalent

to the combination of two isometric

vi. Solve problems involving transformation.


D

TEACHING



LEARNING AREA /OU

MATRICES · Emphasise that matrices :

4.1 Matrix - are written in brackets.

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

EARNING CONT ii. Determine t is read as "an m by n matrix.

order of a m· Discuss equal matrices in terms of :

iii. Identify a s *the order

BIL 4.2 Equal matrices *the coresponding elements

i. Determine whether two matrices are equal.

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

4.3 Addition and s three row and three columns.

i. Determine whether addition or subtraction can be

performed on two given matrices.

ii. Find and per · Discuss :

of two matri *an identity matrix = square matrix

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

4.4 Multiplication · Discuss :

i. Multiply a m * AI = A

ii. Problems *IA = A

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

.

i. Determine · Emphasise that :

and state th *if matrix B is the inverse of matrix A, then matrix A is

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

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

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

of two matri · Discuss why :

4.6 Identity matrix *the use of inverse matrix is necessary. Relate to

i. Determine solving linear equations of type ax = b

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

4.7 Inverse matrix place on both sides of the equation

i. Determine · 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.

LEARNING AREA /OU

4.8 Simultaneous l · Simultaneous linear equations

i. Write simult ap + bq = h and cp + dq = k

ii. Find the ma in matrix form is

D

TEACHING

D

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ARNING CONT =

using the inverse matrix.

iii. Solve simul where a, b, c, d, h and k are constants, p and q are

BIL method. unknowns.

iv. Solve problems involving matrices.

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

simultaneous linear equations. VARIATIONS

5.1 Direct variation - y ∞ x

5.2 Inverse variati · Discuss the characteristics of the graph using the

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

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

changes in anot y x .

ii. Determine f · For the cases y x n . limit n to 2, 3 and ½.

a quantity v · If y x , then y = kx where k is the constant of

iii. Expressthe variation.

form of equ · Using :

iv. Find the val i. y = kx , or

joint variatio ii.

v. Solve proble to get the solution.

following ca · For the cases y x n .n = 2, 3 and ½, discuss the

- y characteristics of the graphs of y against xⁿ.

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

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

.

# Enrichment / Remedial E· For the cases ,

limit n to 2, 3 and ½.

LEARNING AREA /OU

GRADIENT AND · Use examples in various areas

6.1 Quantity repre such as technology and social science.

i. State the q · Compare and differentiate between

ARNING CONT of a graph. distance-time graph and speed-time graph.

ii. Draw the di · Emphasise that :

a. a table o gradient = change of distance = speed

BIL b. a relatio change of time

iii. Find and interpret the gradient

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

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

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

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

two variable may not represent any meaningful quantity.

and state th For examples :

6.2 Quantity repre The area under the distance-time graph.

D

TEACHING

a

pq hk

a

pq

hk

1 A

1 A

2

2

1

1

x

y

x

y

1 y

x

1

nyx



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

area under involving :

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

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

under the fo iii. a combination of the above.

a. v = k (

b. v = kt NOTES:

c. v = kt v represents speed,d. a comb t represent time,

iv. Solve proble h and k represent constants.

under a graph.


PROBABILITY II

7.1 Probability of an event

i. Determine the sample space of an

ii. Determine the probability of an event

iii. Solve problems involving probablity of an event.

7

LEARNING AREA /OU

7.2 Probability of t · Discuss equiprobable sample space through concrete

i. State the co activities and begin with simple cases such as

a. words tossing a fair coin.

ARNING CONT b. Set notat· Use tree diagrams to obtain sample space for tossing

ii. Find the pro a fair coin or tossing a fair die activities.

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

BIL 7.3 Probability of c p( A ) = 0.

i. List the out · Include events in real life situations such as

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

b. A and · Use real life situations to show the relationship between

ii. Find the pr i. A or B and A U B

of the com ii. A and B and A B.

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

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

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

of combine outcomes of combined events.

· Use two-way classification tables of events from

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

of combined events. Ask students to create tree

BEARING diagrams from these tables.

8.1 Bearing NOTES:

i. Draw and l Compass angle and bearing are written in

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

b. North-e measured in a clockwise direction from north.

ii. State the co Due north is considered as bearing 000° .

compass di For cases involving degrees and minutes, state

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

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

D

TEACHING



given the b For example, in map reading and navigation.

iv. State the beNOTES:

based on gi Begin with the case where bearing of point B

v. Solve proble from point A is given.


LEARNING AREA /OU

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

9.1 Longitude · Introduce the meridian through Greenwich in England

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

ARNING CONT ii. State the lon· Discuss that :

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

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

BIL given. both poles9.2 Latitude iii. Meridians with longitudes x°E (or W) and

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

ii. State the lati through both poles.

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

iv. Find the diff have the same latitude.

9.3 Location of a p· Use a globe or map to find locations of cities

i. State the lat around the world.

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

ii. Mark the loc given its location.

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

9.4 Distance on th cities or towns on the same meridian.

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

nautical mile is subtended by the arc between two given points

centre of th along the equator.

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

along a mer between the radius of the earth and radius

iii. Find the latit 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.

b. travelling on the surface of the earth.


D

TEACHING



LEARNING AREA /OU

ON FOR SPM / GEMPUR SPM

STANDARD

FORM . Discuss the significant of zero in a number.

. Discuss the uses of significant figures in everyday life

I.

Significan

t Figureand other areas.

ARNING CONT

II.

Standard

Form . Use the scientific calculator to explore standard form.

QUADRATIC

EXPRESSIONS

AND

EQUATIONS . Discuss the characteristics of quadratic expression or

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

i.

Quadrati

c

Expressio

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

1

ii.

Factorisa

tion of

Quadrati

c

Expressio

ns . Discuss the various methods to obtained the

iii.Quadrati

c

Equation

s desired products. Begin with a = 1.

iv.

Roots of

Quadrati

c

Equation

s . Discuss the number of roots of quadratic equations.

SETS . Discuss the relationship between sets and universal sets.2 . Discuss why {0} and {Ø} are not empty sets.

I.

Set . Discuss cases with :

TEACHING



II.

Subset,

Universal

set &

Comple

ment of

a set . A ∩ B = Ø,

III.Operatio

ns on Sets

. A ᶜ B .

MATHEMATI

CAL

REASONING . Focus on mathematical sentences.

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

3

i.

Stateme

nts .

ii.

Quantifie

rs ‘All’

and ‘

Some’

iii.

Operatio

n

involving

‘Not’ or

‘No’,

‘And’and ‘Or’

in

Stateme

nts.

iv.

Implicati

on

v.

Argumen

t

vi.

Deduction and

Induction

4

THE STRAIGHT

LINE

. Discuss the relationship between gradient and tan θ;

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



i.

Gradient

of a

Straight

Line . Find the ratio of vertical distance to horizontal distance

ii.

Intercept

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

iii.

Equation

of a

straight

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

iv.

Parallel

lines line with equation y = mx + c

5



9 10 11 12 13

1245-120 120-155 155-230

1235-110 110-145 145-220

5AR

KLINTEN

F

K

4 AFF

Rancangan Tahunan Matematik 2012

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Transcript of Rancangan Tahunan Matematik 2012