Rancangan Pengajaran Tahunan Addmath

2. YEARLY PLAN FOR FORM 5 ADDITIONAL MATHEMATICS YEAR 2024 KSSM
WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
WEEK 1
PROGRAM MINGGU PERTAMA PERSEKOLAHAN
(11/03/2024 – 15/03/2024)
ELECTIVE PACKAGE: APPLICATION OF SOCIAL SCIENCE
TOPIC : 7.0 Linear Programming
2
MARCH
(18/3-22/3)
7.1
Linear
Programming
Model
Pupils are able to:
7.1.1
Form a mathematical model for a
situation based on the constraints
given and hence represent the
model graphically.
PL Descriptor
1 Demonstrate the basic
knowledge of linear
programming model.
2 Demonstrate the
understanding of linear
programming model.
3 Apply the understanding of
linear programming model
to perform simple tasks.
4 Apply appropriate
knowledge and skills of
linear programming in the
context of simple routine
problem solving.
5 Apply appropriate
knowledge and skills of
linear programming in the
context of complex routine
problem solving.
6 Apply appropriate
knowledge and skills of
Notes:
Real-life situations need to be involved
throughout this topic.
Exploratory activities involving optimization need
to be carried out.
Round Table
7.2
Application of
Linear
Programming
Pupils are able to:
7.2.1
Solve problems involving linear
programming graphically.
Notes:
The terms constraints, scattered region, objective
function and optimum value need to be involved.
Round Table

3. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
linear programming in the
context of non-routine
problem solving in a
creative manner.
LEARNING AREA: GEOMETRY
TOPIC : 1.0 Circular Measure
3
MARCH
(25/3 - 29/3)
1.1
Radian
Pupils are able to:
1.1.1
Relate angle measurement in radian
and degree.
PL Descriptor
1 Demonstrate the basic
knowledge of circular
measure.
2 Demonstrate the
understanding of circular
measure.
3 Apply the understanding of
circular measure to perform
simple tasks.
4 Apply appropriate
knowledge and skills of
circular measure in the
context of simple routine
problem solving.
5 Apply appropriate
knowledge and skills of
circular measure in the
context of complex routine
problem solving.
6 Apply appropriate
knowledge and skills of
circular measure in the
context of non-routine
Notes:
Real-life situations need to be involved throughout
this topic.
The definition of one radian needs to be discussed.
Measurement in radian can be expressed:
a) in terms of .
b) Without involving .
Gallery Walk
1.2
Arc Length of
a Circle
Pupils are able to:
1.2.1
Determine
i) arc length,
ii) radius, and
iii) Angle subtended at the centre
of a circle.
1.2.2
Determine perimeter of segment of
a circle.
1.2.3
Solve problems involving arc
length.
Notes:
Derivation of the formula needs to be
discussed.
The use of sine rule and cosine rule can be
involved.
Gallery Walk
4
APRIL
(1/4 - 5/4)
1.3
Area of Sector
of a Circle
Pupils are able to:
1.3.1
Determine
i) area of sector,
Notes: Gallery Walk

4. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
problem solving in a
creative manner.
ii) radius, and
iii) Angle subtended at the centre
of a circle.
1.3.2
Determine the area of segment of a
circle.
1.3.3
Solve problems involving areas of
sectors.
Derivation of the formula needs to be
discussed.
The use of the following formulae can be
involved:
a) Area of triangle =
b) Area of triangle =
1.4
Application of
Circular
Measures
Pupils are able to:
1.4.1
Solve problems involving circular
measure.
Circle Map
HARI RAYA AIDILFITRI & CUTI TAMBAHAN KPM
(08/04/2024 – 12/04/2024)
WEEK 5
UJIAN INTERVENSI
(15/04/2024 – 19/04/2024)
LEARNING AREA: CALCULUS
TOPIC : 2.0 Differentiation
6
APRIL
(22/4 - 26/4)
2.1
Limit and its
Relation to
Differentiatio
n
Pupils are able to:
2.1.1
Investigate and determine the value
of limit of a function when its
variable approaches zero.
PL Descriptor
1 Demonstrate the basic
knowledge of
differentiation.
Notes:
Real-life situations need to be involved throughout
this topic.
Pop Corn

5. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
2.1.2
Determine the first derivative of a
function f(x) by using the first
principle.
2 Demonstrate the
understanding of
differentiation.
3 Apply the understanding of
differentiation to perform
simple tasks.
4 Apply appropriate
knowledge and skills of
differentiation in the
context of simple routine
problem solving.
5 Apply appropriate
knowledge and skills of
differentiation in the
context of complex routine
problem solving.
6 Apply appropriate
knowledge and skills of
differentiation in the
context of non-routine
problem solving in a
creative manner.
Graphing calculator or dynamic geometry software
need to be used throughout this topic.
Exploratory activities using table of values and
graphs when the value of the variables approaches
zero from two opposite directions need to be
involved.
The notation of needs to be introduced.
Exploratory activities to determine the first
derivative of a function using the idea of limit
needs to be involved.
When , .
The relation between the first derivative and the
gradient of a tangent should be emphasized.
2.2
The First
Derivative
Pupils are able to:
2.2.1
Derive the formula of first
derivative inductively for the
function , a is a constant
and n is an integer.
2.2.2
Determine the first derivative of an
algebraic function.
Notes:
Differentiation notations , and
where ( ) is a function of x, need to be
involved.
Further exploration using dynamic geometry
software to compare the graphs of f(x) and f’(x)
(gradient function graph) can be carried out.
Think Pair Share

6. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
2.2.3
Determine the first derivative of
composite function.
2.2.4
Determine the first derivative of a
function involving product and
quotient of algebraic expressions.
Chain rule needs to be involved.
The use of idea of limit to prove the chain rule can
be discussed.
The use of the idea of limit to prove product rule
and quotient rule can be discussed.
7
APRIL
(29/4 - 3/5)
8
MAY
(6/5 - 10/5)
2.3
The Second
Derivative
Pupils are able to:
2.3.1
Determine the second derivative of
an algebraic function.
Notes:
and need
to be emphasized.
Bridge Map
2.4
Application of
Differentiatio
n
Pupils are able to:
2.4.1
Interpret gradient of tangent to a
curve at different points.
2.4.2
Determine equation of tangent and
normal to a curve at a point.
2.4.3
Solve problems involving tangent
and normal.
2.4.4
Determine the turning points and
their future.
2.4.5
Solve problems involving
maximum and minimum values
and interpret the solutions.
Notes:
The following matters need to be involved:
a) Sketching tangent method
b) Second derivative method
c) Point of Inflection
Suggested activity:
Graph sketching can be involved.
The use of chain rule needs to be emphasized.
Three Stay One
Stay

7. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
2.4.6
Interpret and determine rates of
change for related quantities.
2.4.7
Solve problems involving rates of
change for related quantities and
interpret the solutions.
2.4.8
Interpret and determine small
changes and approximations of
certain quantities.
2.4.9
Solve problems involving small
changes and approximations of
certain quantities.
Problems involved are limited to two variables.
LEARNING AREA: CALCULUS
TOPIC : 3.0 Integration
9
JUNE
(13/05 - 17/5)
3.1
Integration as
the Inverse of
Differentiatio
n
Pupils are able to:
3.1.1
Explain the relation between
differentiation and integration.
PL Descriptor
1 Demonstrate the basic
knowledge of integration.
2 Demonstrate the
understanding of
integration.
3 Apply the understanding of
integration to perform
simple tasks.
4 Apply appropriate
knowledge and skills of
integration in the context of
Suggested activities:
The use of dynamic software is encouraged
throughout this topic.
Notes:
Real-life situations need to be involved throughout
this topic.
Exploratory activities need to be carried out.
Bridge Map
3.2
Indefinite
Integral
Pupils are able to:
3.2.1
Derive the indefinite integral
formula inductively.
3.2.2
Notes:
Limited to , a is a constant, n is an
integer and .
Gallery Walk

8. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
simple routine problem
solving.
5 Apply appropriate
knowledge and skills of
integration in the context of
complex routine problem
solving.
6 Apply appropriate
knowledge and skills of
integration in the context of
non-routine problem
solving in a creative
manner.
10
JUNE
(20/5 - 24/5)
Determine indefinite integral for
algebraic functions.
3.2.3
Determine indefinite integral for
functions in the form of
, where a and b are constants, n is
an integer and .
3.2.4
Determine the equation of curve
from its gradient function.
The following integrations need to be involved.
a)
b)
Suggested activities:
Substitution method can be involved.
3.3
Definite
Integral
Pupils are able to:
3.3.1
Determine the value of definite
integral for algebraic functions.
Notes:
The following characteristics of definite integral
need to be emphasized.
a)
b)
The use of diagrams needs to be emphasised.
Exploratory activities need to be carried out.
Pop Corn
3.3.2
Investigate and explain the relation
between the limit of the sum of
areas of rectangles and the area
under the curve.
3.3.3
Determine the area of a region.
When n approaches , approaches 0,
area under the curve
Circle Map

9. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
3.3.4
Investigate and explain the relation
between the limits of the sum of
volumes of cylinders and the
generated volume by revolving a
region.
3.3.5
Determine the generated volume of
a region revolved at the x-axis or
the y-axis.
The meaning of the positive and negative signs for
the value of area needs to be discussed.
Area of region between two curves needs to be
involved.
When n approaches , approaches 0,
generated volume
When n approaches , approaches 0,
generated volume
Generated volume for region between two curves
is excluded.
3.4
Application of
Integration
Pupils are able to:
3.4.1
Solve problems involving
integration.
CUTI PENGGAL 1 SESI 2024/2025
(25/05/2024 – 02/06/2024)
CUTI UMUM: HARI KEPUTERAAN DYMM YDP AGONG
(03/0620/24)

10. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
WEEK 11 – 13
(04/06/2024 – 21/06/2024)
PEPERIKSAAN PERTENGAHAN TAHUN
LEARNING AREA: STATISTICS
TOPIC : 4.0 Permutation and Combination
14
JUNE
(24/6 - 28/6)
4.1
Permutation
Pupils are able to:
4.1.1
Investigate and make
generalisation about multiplication
rule.
4.1.2
Determine the number of
permutations for
i) n different objects
ii) n different objects taken r at a
time.
iii) n objects involving identical
objects.
4.1.3
Solve problems involving
permutations with certain
conditions.
PL Descriptor
1 Demonstrate the basic
knowledge of permutation
and combination.
2 Demonstrate the
understanding of
permutation and
combination.
3 Apply the understanding of
permutation and
combination to perform
simple tasks.
4 Apply appropriate
knowledge and skills of
permutation and
combination in the context
of simple routine problem
solving.
5 Apply appropriate
knowledge and skills of
permutation and
combination in the context
of complex routine problem
solving.
6 Apply appropriate
knowledge and skills of
permutation and
Notes:
Real-life situations and tree diagrams need to be
involved throughout this topic.
The calculator is only used after the students
understand the concept.
Multiplication rule:
If a certain event can occur in m ways and another
event can occur in n ways, then both events can
occur in ways.
The notation n! needs to be involved.
Formula needs to be emphasised.
Cases involving identical objects or arrangement
of objects in a circle limited to one condition.
Double Bubble
Map
4.2
Combination
Pupils are able to:
4.2.1
Compare and contrast permutation
and combination.
4.2.2
Notes:
The relation between combination and
permutation, needs to be discussed.
Hot Seat

11. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
combination in the context
of non-routine problem
solving in a creative
manner.
Determine the number of
combinations of r objects chosen
from n different objects at a time.
4.2.3
Solve problems involving
combinations with certain
conditions.
LEARNING AREA: STATISTICS
TOPIC : 5.0 Probability Distribution
15
JULY
(1/7 - 5/7)
5.1
Random
Variable
Pupils are able to:
5.1.1
Describe the meaning of random
variable.
5.1.2
Compare and contrast discrete
random variable and continuous
random variable.
5.1.3
Describe the meaning of
probability distribution for discrete
random variables.
5.1.4
Construct table and draw graph of
probability distribution for discrete
random variable.
PL Descriptor
1 Demonstrate the basic
knowledge of random
variables.
2 Demonstrate the
understanding of
probability distribution.
3 Apply the understanding
of probability distribution
to perform simple tasks.
4 Apply appropriate
knowledge and skills of
probability distribution in
the context of simple
routine problem solving.
5 Apply appropriate
knowledge and skills of
probability distribution in
the context of complex
routine problem solving.
6 Apply appropriate
knowledge and skills of
probability distribution in
Notes:
Real-life situations need to be involved throughout
this topic.
Set builder notations for discrete random variable
and continuous random variable need to be
involved.
Example of representation for discrete random
variable:
Example of representation for continuous random
variable:
Tree diagram and probability formula need to be
used to introduced the concept of probability
distribution for discrete random variable.
Suggested activities:
Simple experiments can be involved such as
tossing coins or dice to explain the concept of
probability distribution for discrete variable.
Traffic Light

12. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
the context of non-routine
problem solving in a
creative manner.
Probability Distribution is a table or a graph that
displays the possible values of a random variable,
along with respective probabilities.
5.2
Binomial
Distribution
Pupils are able to:
5.2.1
Describe the meaning of binomial
distribution.
5.2.2
Determine the probability for an
event for binomial distribution.
5.2.3
Interpret information, construct
table and draw graph of binomial
distribution.
5.2.4
Determine and describe the value
of mean, variance and standard
deviation for a binomial
distribution.
5.2.5
Solve problems involving binomial
distributions.
Notes:
The characteristics of Bernoulli trials need to be
discussed.
The relation between Bernoulli trials and Binomial
distribution need to be emphasised.
Tree diagram needs to be used to study the values
of probability for the binomial distribution.
Formula need not be
derived.
Mean as an expected average value when an event
happens repeatedly needs to be emphasised.
Interpretation of solutions needs to be involved.
Pop Corn
16
JULY
(9/7 – 12/7)
5.3
Normal
distribution
5.3.1
Investigate and describe the
properties of normal distribution
graph.
5.3.2
Describe the meaning of standard
normal distribution.
Notes:
Sketches of graphs and the importance of the
normal distribution graph features need to be
emphasised.
The properties of random variation and the Law of
Large Numbers need to be discussed.
Double Bubble
Map

13. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
5.3.3
Determine and interpret standard
score, Z.
5.3.4
Determine the probability of an
event for normal distribution.
5.3.5
Solve problems involving normal
distributions.
The importance of converting normal distribution
to standard normal distribution needs to be
emphasised.
The relation between normal distribution graph
and standard normal distribution graph need to be
discussed.
The use of the Standard Normal Distribution Table
needs to be emphasised.
The use of calculator, mobile application or
website can be involved.
Skills to determined the standard score, Z when
given the probability value needs to be involved.
ELECTIVE PACKAGE: APPLICATION OF SCIENCE AND TECHNOLOGY
TOPIC : 8.0 Kinematics of Linear Motion
17
JULY
(15/7 – 19/7)
8.1
Displacement,
Velocity and
Acceleration
as a Function
of Time
Pupils are able to:
8.1.1
Describe and determine
instantaneous displacement,
instantaneous velocity, instantaneous
acceleration of a particle.
8.1.2
Determine the total distance
travelled by a particle in a given
period of time.
PL Descriptor
1 Demonstrate the basic
knowledge of
displacement, velocity and
acceleration.
2 Demonstrate the
understanding of
displacement, velocity and
acceleration.
3 Apply the understanding
of displacement, velocity
and acceleration to
perform simple tasks.
4 Apply appropriate
knowledge and skills of
kinematics of linear
motion in the context of
Notes:
Number lines and sketches of graphs need to be
involved throughout this topic.
The following need to be emphasised:
i) Representations of s = displacement, v =
velocity, a = acceleration and t = time
ii) The relation between displacement, velocity
and acceleration.
iii) Scalar quantity and vector quantity
iv) The difference between
● distance and displacement
● Speed and velocity
The meaning of
● positive, negative and zero displacement,
● positive, negative and zero velocity,
● positive, negative and zero acceleration,
need to be discussed.
Think Pair
Share

14. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
simple routine problem
solving.
5 Apply appropriate
knowledge and skills of
kinematics of linear
motion in the context of
complex routine problem
solving.
6 Apply appropriate
knowledge and skills of
kinematics of linear
motion in the context of
non-routine problem
solving in a creative
manner.
Simulation needs to be used to differentiate
between positive displacement and negative
displacement.
The displacement function is limited to linear and
quadratic.
8.2
Differentiatio
n in
Kinematics of
Linear Motion
Pupils are able to:
8.2.1
Relate between displacement
function, velocity function and
acceleration function.
8.2.2
Determine and interpret
instantaneous velocities of a particle
from displacement function.
8.2.3
Determine and interpret
instantaneous acceleration of a
particle from velocity function and
displacement function.
Notes:
The following relations need to be emphasised:
Interpretation of graphs need to be involved.
Maximum displacement, initial velocity and
constant velocity need to be emphasised.
Maximum velocity, minimum velocity and
constant acceleration need to be emphasized.
Think Pair
Share
18
JULY
(22/7 – 26/7)
8.3
Integration in
Kinematics of
Linear Motion
Pupils are able to:
8.3.1
Determine and interpret
instantaneous velocity of a particle
from acceleration function.
8.3.2
Determine and interpret
instantaneous displacement of a Notes:
Total distance needs to be involved.
Think Pair
Share

15. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
particle from velocity function and
acceleration function.
8.4
Application of
Kinematics of
Liner Motion
Pupils are able to:
8.4.1
Solve problems of kinematics of
linear motion involving
differentiation and integration.
Round Table
Circle Map
LEARNING AREA: TRIGONOMETRY
TOPIC : 6.0 Trigonometric Functions
19
JULY
(29/7 – 2/8)
6.1
Positive
Angles and
Negative
Angles
Pupils are able to:
6.1.1
Represent positive angles and
negative angles in a Cartesian
Plane.
PL Descriptor
1 Demonstrate the basic
knowledge of trigonometric
functions.
2 Demonstrate the
understanding of
trigonometric functions.
3 Apply the understanding of
trigonometric functions to
perform simple tasks.
4 Apply appropriate
knowledge and skills of
trigonometric functions in
the context of simple
routine problem solving.
5 Apply appropriate
knowledge and skills of
trigonometric functions in
the context of complex
routine problem solving.
6 Apply appropriate
knowledge and skills of
Notes:
Angle in degrees and radians greater than or
radian need to be involved throughout this
topic.
The following needs to be emphasised:
a) the position of angles in quadrants.
b) the relation between units in degrees and
radians in terms of .
Suggested activities:
Dynamic software can be used to explore positive
angles and negative angles.
Pop Corn
6.2
Trigonometric
Ratios of any
Angle
6.2.1
Relate secant, cosecant and
cotangent with sine, cosine and
tangent of any angle in a Cartesian
plane.
Suggested activities:
Exploratory activities involving the following
complementary angles need to be carried out:
a)
b)
c)
Presentation

16. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
trigonometric functions in
the context of non-routine
problem solving in a
creative manner.
6.2.2
Determine the values of
trigonometric ratios for any angle.
d)
e)
f)
Notes:
The use of triangles to determine trigonometric
ratios for special angles , and
need to be emphasised.
20
AUGUST
(5/8 – 9/8)
6.3
Graph of
Sine, Cosine
and Tangent
Functions
Pupils are able to:
6.3.1
Draw and sketch graphs of
trigonometric functions:
i)
ii)
iii)
where a, b and c are constants and
b>0.
6.3.2
Solve trigonometric equations
using graphical method.
Notes:
The effect of the changes in constants a, b and c
for graphs of trigonometric functions need to be
discussed.
The absolute value of trigonometric functions
needs to be involved.
Suggested activities:
Dynamic software can be used to explore graphs
of trigonometric functions.
Trigonometric equations for y that are not
constants need to be involved.
Sketches of graphs to determine the number of
solutions need to be involved.
One Stay Three
Stay
6.4
Basic
Identities
Pupils are able to:
6.4.1
Derive basic identities:
i)
ii)
Notes:
Exploratory activities involving basic identities
using right-angled triangle or unit circle need to be
carried out.
Gallery Walk

17. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
iii)
6.4.2
Prove trigonometric identities
using basic identities.
21
AUGUST
(12/8 – 16/8)
6.5
Addition
Formulae and
Double Angle
Formulae
Pupils are able to:
6.5.1
Prove trigonometric identities
using addition formulae for
, and
.
6.5.2
Derive double angle formulae for
sin 2A, cos 2A and tan 2A.
6.5.3
Prove trigonometric identities
using double-angle formulae.
Suggested activities:
Calculator can be used to verify addition formulae.
Notes:
Half-angle formulae need to be discussed.
Gallery Walk
6.6
Application of
Trigonometric
Functions
6.6.1
Solve trigonometric equations.
6.6.2
Solve problems involving
trigonometric functions.
Circle Map
REVISION
WEEK 22
(19/08/2024 - 23/08/2024)

18. WEEK
CONTENT
STANDAR
DS
LEARNING STANDARDS PERFORMANCE LEVEL NOTES
SUGGESTED
ADDITIONAL
ACTIVITIES
WEEK 23 - 25
(26/08/2024 - 13/09/2024)
PEPERIKSAAN PERCUBAAN SPM
CUTI PENGGAL 2 SESI 2024/2025
(14/09/2024 - 22/09/2024)
26 - 27
SEPTEMBE
R -
OKTOBER
(23/9 - 4/10)
DISCUSSION OF SPM TRIAL/ STATE EXAMINATION PAPERS
28 - 35
OCTOBER -
NOVEMBE
R
(7/10 - 29/11)
UBBM/UBBI/AMALI SAINS SPM 2024
REVISION / EXTRA CLASS
WEEK 36 - 37
(02/12/2024 - 13/12/2024)
SPM 2024
WEEK 38 - 42
(016/12/2024 - 24/01/2025)