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F5 add maths year plan 2013
1. SMK JENJAROM, KUALA LANGAT
SCHEME OF WORKS
ADDITIONAL MATHEMATICS FORM 5
2013
Week
(Date)
Topic
(Learning Area)
Sub-topic
(Learning Outcomes)
Remarks
1-- 4
CHAPTER :1
PROGRESSIONS
1.1 Understand and use the
concept of arithmetic
progression
1. Identify characteristics of arithmetic progressions.
2. Determine whether a given sequence is an arithmetic
progression.
3. Determine by using formula :
a) specific terms in arithmetic progressions;
b) the number of terms in arithmetic progressions.
4. Find :
a) the sum of the first n terms of arithmetic progressions.
b) the sum of a specific number of consecutive terms of
arithmetic progressions.
c) the value of n, given the sum of the first n terms of
arithmetic progressions.
5 Solve problems involving arithmetic progressions.
Include the use of
formula
Tn = Sn – Sn-1
Problems involving real-
life situations
1.2 Understand and use the
concept of geometric
progression
1 Identify characteristics of geometric progressions.
2. Determine whether a given sequence is an geometric
progression.
3. Determine by using formula :
a) specific terms in geometric progressions;
b) the number of terms in geometric progressions.
4 Find :
a) the sum of the first n terms of geometric progressions.
2. Week
(Date)
Topic
(Learning Area)
Sub-topic
(Learning Outcomes)
Remarks
b) the sum of a specific number of consecutive terms of
geometric progressions.
c) the value of n, given the sum of the first n terms of
geometric progressions.
5. Find :
a) the sum to infinity of geometric progressions.
b) the first term or common ratio, given the sum to infinity of
geometric progressions.
6. Solve problems involving geometric progressions.
Discuss: As n → α, rn
→
0, then
Sα =
r
a
−1 .
Exclude: combination of
arithmetic progressions
and geometric
progressions.
5 –6
CHAPTER 2 :
LINEAR LAW
2.1 Understand and use the
concept of lines of best fit.
2.2 Apply linear law to non-
linear relations.
`
1. Draw lines of best fit by inspection of given data.
2. Write equations for lines of best fit.
3 Determine values of variables from :
a) lines of best fit
b) equations of lines of best fit.
2.1 Reduce non-linear relations to linear form.
2.2 Determine values of constants of non-linear relations given :
a) lines of best fit
b) data.
2.3 Obtain information from :
a) lines of best fit
b) equations of lines of best fit.
Limit data to linear
relations between two
variables.
3. Week
(Date)
Topic
(Learning Area)
Sub-topic
(Learning Outcomes)
Remarks
7 -- 10
CHAPTER 3 :
INTEGRATION
3.1 Understand and use the
concept of indefinite
integral.
1. Determine integrals by reversing differentiation.
2. Determine integrals of axn
, where a is a constant and n is an
integer, n ≠ -1.
3. Determine integrals of algebraic expressions.
4. Find constants of integration, c, in indefinite integrals.
5. Determine equations of curves from functions of gradients.
6. Determine by substitution the integrals of expressions of the
form (ax + b)n
, where a and b are contants, n is an integer
and
n ≠ -1.
Limit intregration of
∫ dxun
, where u = ax +
b
3.2 Understand and use the
concept of indefinite
integral.
1 Find definite integrals of algebraic expressions.
2 Find areas under curves as the limit of a sum of areas.
3 Determine areas under curves using formula.
4 Find volumes of revolutions when region bounded by a curve
is rotated completely about the
a) x-axis
b) y-axis
as the limit of a sum of volumes.
5 Determine volumes of revolutions using formula.
Include
∫ ∫=
a
b
a
dxxfkdxxkf )()(
∫ ∫−=
b
a
a
b
dxxfdxxf )()(
Deriavation of formula not
required.
Lomit volume of
revolution about the x axis
or y axis.
12 – 15
CHAPTER 4:
VECTORS
4.1 Understand and use the
conceptof vector
1. Differentiate between vector and scalar quantity.
2. draw and label directed line segments tu represent
vectors.
3. Determine the magnitude and direction of vectors
represented by directed line segments.
4. Determine whether two vectors are equal.
5. Multiply vectors by scalars
6. Determine whether two vectors are parallel.
Use notations:
Vector: a, AB
Zero vector : 0
Emphasis negative
vector: -AB = BA
Include negative scalar.
Week 7
1st Monthly Test
First Semester Break
Week 11
4. Week
(Date)
Topic
(Learning Area)
Sub-topic
(Learning Outcomes)
Remarks
4.2 Understand and use the
concept of addition and
subtraction of vectors
1. Determine the resultant vector of two parallel vectors.
2. Determine the resultant vector of two non-parallel
vectors using:
a. triangle law
b. parallelelogram law
3. Determine the resultant vector of three or more vectors
using the polygon law.
4. Subtract two vectors which are:
a. parallel
b. non-parallel
5. Solve problems involving addition and subtraction of
vectors.
4.3 Understand and use
vectors in the Cartesian
plane
1 Express vectors in the form:
a. x i + y ) b.
2 Determine magnitudes of vectors.
3 Determine unit vectors in given directions.
4 Add two or more vectors.
5 Subtract two vectors.
6 Multiply vectors by scalars.
7 Perform combined operations on vectors.
8 Solve problems involving vectors.
Relate unit vector i and j
to Cartesian coordinates.
Emphasise:
vector i =
0
1
and
vector j =
1
0
xy
Week 15
Second Monthly Test
5. Week
(Date)
Topic
(Learning Area)
Sub-topic
(Learning Outcomes)
Remarks
16 – 19
CHAPTER 5 :
TRIGONOMETRIC
FUNCTIONS
5.1 Understand the concept of
positive and negative
angles measured in
degrees and radians.
1. Represent in a Cartesian plane, angles greater than 3600
or
2π radians for:
a. positive angles
b. negative angles
5.2 Understand and use the
six trigonometric
functions of any angle
1. Define sine, cosine and tangent of any angle in a Cartesian
plane
2. Define cotangent, secant and cosecant of any angle in a
Cartesian plane
3. Find values of the six trigonometric functions of any angle
4. Solve trigonometric equations
Emphasis :
Sin θ = cos (90 – θ), cos θ=
sin (90 – θ) , tan θ = cot
(90 – θ), cosec θ= sec (90 –
θ), sec θ = cosec ( 90-θ),
cot θ = tan (90 – θ).
Emphasis the use of
triangles to find trigo ratio
for special angles 300
, 450
,
60 0
.
5.3 Understand and use
graphs of sine, cosine and
tangent functions.
1. Draw and sketch graphs of trigometric functions
a. y = c + a sinbx,
b. y = c + a cosbx,
c. y = c + a tan bx where a, b and c are constant and b >
0.
2. Determine the number of solutions to a trigonometric
equation using sketched graphs.
3. Solve trigonometric equations using drawn graphs.
Use angles in (a)
degrees, (b) radians, in
term of Л.
Include trigonometric
functions involving
modulus.
Exclude combinations of
trigonometric functions.
5.4 Understand and use basic
identities
1. Prove basicidentities
a. sin2
A + cos2
= 1
b. 1 + tan2
+A = sec2
A
6. Week
(Date)
Topic
(Learning Area)
Sub-topic
(Learning Outcomes)
Remarks
c. 1 + cot2
A = cosec2
A
2. Prove trigonometric identities using basic identities.
3. Solve trigonometric equations using basic identities.
5.5 Understand and use
addition formulae and
double-angle formulae
1. Prove trigonometric identities using addition formulae for
sin (A + B), cos (A + B) and tan (A + B).
2. Derive double-angle formulae for sin 2A, cos 2A and tan
2A.
3. Prove trigonometric identities using addition formulae
and/or double-angle formulae.
4. Solve trigonometric equations.
Derivation of addition
formulae not required.
Discuss half-angle
formulae.
Ecclude A cos x + b sin
x = c, where c ≠ 0.
25 – 27
CHAPTER: 6
PERMUTATION
AND COMBINATIONS
6.1 Understand and use the
concept of permutation
1. Determine the total number of ways to perform successive
events using multiplication rule.
2. Determine the number of permutation of n different objects.
3. Determine the number of permutation of n different object
taken r at a time.
4. Determine the number of permutation of n different objects
for given conditions.
5. Determine the number of permutation of n different objects
taken r at a time for given conditions.
Exclude cases involving
identical objects.
Exclude cases involving
arrangement of objects
in a circle.
6.2 Understand and use the
concept of combination
1 Determine the number of combinations r objects chosen
from n different objects
2 Determine the number of combination r objects chosen from
n different objects for given conditions
Use examples to
illustrate
!r
p
c r
n
r
n
=
Week 20 – 22: Mid Year Exam
Week 23--24: Semester Break
7. Week
(Date)
Topic
(Learning Area)
Sub-topic
(Learning Outcomes)
Remarks
28 – 29
CHAPTER 7
PROBABLITY
7.1 Understand and use the
concept of probability.
1. Describe the sample space of an expriment.
2. Determine the number of outcome of an event.
3. Determine the probability of an event
4. Determine the probability of two event:
- a) A or B occurring
- b) A and B occurring
Discuss :
a) classical probability
(Throretical probability)
b) subjective probability
c) relative frequency
probability
( experimental prob.).
Emphasis : only
classical Prob is used to
solve problems.
7.2 Understand and use the
concept of probability of
mutually exclusive events.
1 Determine whether two events are mutually exclusive.
2. Determine the probability of two or more evebts that are
mutually exclusive.
Include events that are
mutually exclusive and
exhaustive.
Limits to three mutually
exclusive events.
7.3 Understand and use the
concept of probability of
independent events.
1 Determine whether two events are independent.
2 Determine the probability of two independent events.
3 Determine the probability of three independent events.
Include tree diagrams.
30 – 32
CHAPTER 8 :
PROBABILITY
DISTRIBUTIONS
8.1 Understand and use the
concept of binomial
distribution.
1. List all possible values of a discrete random variable.
2. Determine the probability of an event in a binomial
distribution.
3. Plot binomial distribution graph.
4. Determine mean variance and standard deviation of a
binomial distribution.
5. Solve problems involving binomial distributions.
8. Week
(Date)
Topic
(Learning Area)
Sub-topic
(Learning Outcomes)
Remarks
8.2 Understand and use the
concept of normal
distribuation.
1 Describe continuous random variables using set notation.
2 Find probability of z values for standard normal distribution.
3 Convert random variable of normal distributions X to
standardised variable,Z.
4 Represent probability of an event using set notation.
5 Determine probability of an event.
6 Solve problems involving normal distributions.
Intregration of normal
distribution function to
determine probability is
not required.
33 – 34
CHAPTER 9:
MOTION ALONG A
STRAIGHT LINE
9.1 Understand and use the
concept of displacement
1. Identify direction of displacement of a particle from a fixed
point.
2. Determine displacement of a particle from a from a fixed
point.
3. Determine the total distace travelled by a particle over a
time interval using graphical method.
Emphasis the use of the
following sumbols: s,v,a
and t. Where s,v and a
are functions of time.
Emphasis the difference
between displacement
and distance.
Discuss positive,
negative and zero
displacements.
9.2 Understand and use the
concept of velocity
1 Determine velocity function of a particle by differentiation .
2 Determine instantaneous velocity of a particle
3 Determine displacement of a particle from velocity function
by intergration.
Emphasis velocity as the
rate of change of
velocity.
Discuss :
a) uniform velocity
b) zero instantaneous
velocity.
c) positive velocity
d) negative velocity.
9. Week
(Date)
Topic
(Learning Area)
Sub-topic
(Learning Outcomes)
Remarks
9.3 Understand and use the
concept of acceleration.
1 Determine acceleration function of a particle by
differentiation
2 Determine instantaneous acceleration of a particle.
3 Determine instantaneous velocity of a particle from
acceleration function by intergration.
4 Determine displacement of a particle from acceleration
function by integration.
5 Solve problems involving motion along a staright line.
Emphasis acceleration
as the rate of change of
velocity.
Discuss :
a) uniform acceleration
b) zero acceleration
c) positive acceleration
d) negative acceleration.
33—34
CHAPTER 10:
LINEAR PROGRAMMING
10.1 Understand and use the
concept of graphs of
linear inequalities.
1. Identity and shade the region on the graph that satisfies a
linear inequality
2. Find the linear inequlity that defines a shaded region.
3. Shade region on the graph that satisfies several linear
inequalities.
4. Find linear inequalities that defines a shaded region.
Emphasis the use of
solid lines and dashed
lines.
10.2. Understand and use
theconcept of linear
programming
1 Solve problems related to linear
programming by:
a) writing linear inequalities and equations describing a
situation.
b) shading the region of feasible solutions.
c) determining and drawing the objective function ax + by
= k where a, b and k are constants.
d) determining graphically the optimum value of the
objective function.
Optimum values refer to
maximum or minimum
values.
Include the use of
vertices to find the
optimum value.
