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 4 1 NUMBER BASES R M M S I I i. State zero, one, two, three……. T D D as a number in base: a. two M S Y Y b. eight F I E E E c. five I D C A A ii. State the value of adigit of a number in R T O R R base : S E N 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 a. two S R S I O 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 a. two O E 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 # 1.1 Number in base two, eight and five
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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".
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
YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2012)
YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2012)
YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2012)
YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2012)
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 :
1.1 Number in base two, eight and five
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
# Enrichment / Remedial Excercise #
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 :
YEARLY TEACHING PLAN AND LEARNING CONTRACT : FORM 5 MATHEMATICS (2011)
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.
# Enrichment / Remedial Excercise #
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,
2.2 Solution of an equation by graphical method
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
3.1 Combination of two transformations
is equivalent to combined transformation BA.
v. Specify a transformation which is equivalent
to the combination of two isometric
vi. Solve problems involving transformation.
# Enrichment / Remedial Excercise #
LEARNING AREA /OUTCOMES
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
4.3 Addition and subtraction on 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.
*if matrix B is the inverse of matrix A, then matrix A is
also the inverse of matix B, AB = BA = I
4.6 Identity matrix
solving linear equations of type ax = b
4.7 Inverse matrix
LEARNING AREA /OUTCOMES
· 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 ,
LEARNING AREA /OUTCOMES
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
4.8 Simultaneous linear equations by using matrices
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
limit n to 2, 3 and ½.
TEACHING AND
LEARNING
6.1 Quantity represented by the gradient of a graph
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
LEARNING AREA /OUTCOMES
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
6.2 Quantity represented by the area under a graph.
i. a straight line which is parallel to the x-axis.
a. v = k (uniform speed)
b. v = kt
c. v = kt + h
7.1 Probability of an event
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.
# ENRICHMENT/REMEDIAL EXERCISE #
LEARNING AREA /OUTCOMES
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
9.3 Location of a place
9.4 Distance on the surface of the earth
b. travelling on the surface of the earth.
# ENRICHMENT/REMEDIAL EXERCISE #
LEARNING AREA /OUTCOMES
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.