ADDITIONAL MATHEMATICS LESSON PLAN

FORM FIVE 2009

TERM 1 : 5.1.2009 - 29.5.2009 (20 WEEKS)

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

1 Students will be able to:

1 - 3 A6

PROGRESSIONS

1. Understand and use the concept of arithmetic progression.

Use examples from real-life situations, scientific or graphing calculators; and computer software to explore geometric progressions.

1.1 Identify characteristics of

arithmetic progressions.

1.2 Determine whether a given

sequence is an arithmetic

progression.

1.3 Determine by using formula:

a) specific terms in arithmetic

progressions

b) the number of terms in

arithmetic progressions.

1.4 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

the arithmetic progressions.

1.5 Solve problems involving

arithmetic progressions.

Begin with sequences to

introduce arithmetic and

geometric progressions.

Include examples in

algebraic form.

Include the use of the

formula 1−−= nnn SST

Include problems involving

real-life situations

Constructivism

Constructivism

Thinking Skills

Exploratory

Problem Solving

Identifying patterns

Identifying patterns

Making inferences

Making inferences

Finding all possible solutions

Self-Reliance

Self-Reliance

Freedom

Freedom

Self-Reliance

Compassion

Courage

Sequence

Series

Characteristic

Arithmetic progression

Common difference

Specific term

First term

thn term

consecutive

1

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

2. Understand and use the concept of geometric progression.

Use examples from real-life situations, scientific or graphing calculators; and computer software to explore geometric progressions.

2.1 Identify characteristics of

geometric progressions.

2.2 Determine whether a given

sequence is a geometric

progression.

2.3 Determine by using formula:

a) specific terms in geometric

progressions

b) the number of terms in

geometric progressions.

2.4 Find :

a) the sum of the first n terms of

geometric progressions.

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

the geometric progressions.

2.5 Find :

a) the sum to infinity of

geometric progressions.

Include examples in

algebraic form.

Discuss :

As 0, →∞→ nrn

then r

aS

−=∞ 1

Constructivism

Constructivism

Thinking Skills

Exploratory

Constructivism

Identifying patterns

Identifying patterns

Making inferences

Making inferences

Making generalizations

Self-Reliance

Self-Reliance

Freedom

Freedom

Rationality

Geometric progression

Common ratio

Sum to infinity

Recurring decimal

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

2

b) the first term or common

ratio, given the sum to

infinity of geometric

progressions.

2.6 Solve problems involving

geometric progressions

∞S read as ‘sum to infinity’.

Include recurring decimals.

Limit to 2 recurring digits such as 0.3, 0.15,...

Exclude:

a) combination of arithmetic progressions and geometric progressions.

b) cumulative sequences such as (1), (2,3), (4,5,6), (7,8,9,10), …

Mastery Learning

Finding all possible solutions

Compassion

courage

4CHINESE NEW YEAR HOLIDAY

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

3

Students will be taught to:

2 Students will be able to:

5 - 6 A7

LINEAR LAW

1 Understand and use the concept of lines of best fit.

Use examples from real-life situations to introduce the concept of linear law.

Using graphing calculators or computer software such as the Geometer’s Sketchpad to explore lines of best fit.

1.1 Draw lines of best fit by inspection of given data.

1.2 Write equations for lines of best fit.

1.3 Determine values of variables from :a) line of best fit

b) equations of lines of best fit.

Limit data to linear relations between two variables.

Constructivism

Constructivism

Multiple Intelligent

Integrating ICT

Finding all possible solutions

Identifying relations

Representing and Interpreting Data

Effort

Reasoning

Determination

Line of best fit

Inspection

Variable

Non-linear relation

Linear form

reduce

2 Apply linear law to non-linear relations

2.1 Reduce non-linear relations to linear form.

2.2 Determine values of constants of non-linear relations given :a) line of best fit

b) data

2.3 Obtain information from: a) line of best fit

b) equations of lines of best fit.

Mastery Learning

Thinking Skills

Mastery Learning

Identifying Patterns

Identifying Relations

Representing and Interpreting Data

Problem Solving

Able to act independently

Reasoning

Effort

Prudence

4

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

7 C2

INTEGRATION

1 Understand and use the concept of indefinite integral

Use computer software such as Geometer’s Sketchpad to explore the concept of integration.

1.1 Determine integrals by

reversing differentiation.

1.2 Determine integrals of nax ,

where a is a constant and n is

an integer, 1−≠n

1.3 Determine integrals of algebraic expressions.

1.4 Find constants of integration, c , in indefinite integrals.

1.5 Determine equations of curves from functions of gradients.

1.6 Determine by substitution the integrals of expressions of

the form ( ) nbax + , where

a and b are constants, n is an

integer and 1−≠n

Emphasize constant of integration.

∫ dxy read as ‘ integration

of y with respect to x ‘

Limit integration of

dxu n∫ , where

baxu +=

Thiking Skills

Thiking Skills

Identifying relations

Recognising and representing

Identifying relations

Recognising and representing

Cooperation, Compassion, Diligence

Moderation, Diligence

Courage

Rationality

Honesty

IntegrationIntegral

Indefinite integral

Reverse

Constant of integration

5

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

8 2 Understand and use the concept of definite integral

Use scientific or graphing calculators to explore the concept of definite integrals.

Use computer software and graphing calculators to explore areas under curves and the significance of positive and negative values of areas.

Use dynamic computer software to volumes of revolutions.

2.1 Find definite integrals of

algebraic expressions.

2.2 Find the areas under curves

as the limit of a sum of

areas.

2.3 Determine areas under curves

using formula.

2.4 Find volumes of revolutions

when region bounded by a

curve is rotated completely

about :

a) the x-axis

b) the y-axis

as the limit of a sum of

volumes.

2.5 Determine volumes of

revolutions using formula.

Include:

∫ ∫=b

a

b

a

dxxfkdxxkf )()(

∫ ∫−=b

a

a

b

dxxfdxxf )()(

Derivation of formulae not required.

Limit to one curve.

Derivation of formulae nor required.

Limit volumes of revolution about the x-axis or y-axis.

Integrating ICT

Multiple Intelligent

Mastery learning

Problem solving

Recognising and representing

Simulation

Logical reasoning

Simulation

Logical reasoning

Rationality

Justice

Self-reliance

Freedom, Respect

Self-reliance, Honesty

Substitution

Define integral

Limit

Volume

Region

Rotated

Revolution

Solid of revolution

9 TEST 1

6

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

10 G2

VECTORS

1 Understand and use the concept of vector

Use examples from real-life situations and dynamic computer software such as Geometer’s Sketchpad to explore vectors.

1.1 Differentiate between vectors and scalar quantities.

1.2 Draw and label directed line segments to represent vectors.

1.3 Determine the magnitude and the

direction of vectors represented

by directed line segments.

1.4 Determine whether two vectors

are equal.

1.5 Multiply vectors by scalars.

1.6 Determine whether two vectors

are parallel.

Use notations:

Vector: a, AB , a,

AB .

Magnitude:

ABa ,~

Zero vector: ~0

Emphasize that a zero has a magnitude of zero.

Emphasize negative vector:

BAAB =−

Include negative scalar

Include:

a) collinear points

b) non-parallel non-zero vectors

Emphasize :

If ~a and

~b are not

parallel and ~~bkah =

, then h=k=0

Constructivism Comparing & differentiating

Drawing diagrams

Identifying relations

Camparing & differentiating

Identifying relations

Comparing & differentiating

Rationality

Open & logical mind

Differentiate

Scalar

Vector

Directed line segment

Magnitude

Direction

Parallel

Non-parallel

Collinear points

Non-zero

a , AB

7

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

SCHOOL HOLIDAY (MID TERM 1) : 14.3.2009 – 22.3.2009

11 2.Understand and use the concept of addition and subtraction of vectors.

Use real-life situations and manipulative materials to explore addition and subtraction of vectors.

2.1 Determine the resultant vector of

two parallel vectors.

2.2 Determine the resultant vector of two non-parallel vectors using :

a) triangle law

b) parallelogram law

2.3 Determine the resultant vector of three or more vectors using the polygon law.

2.4 Subtract two vectors which

a) parallel

b) non-parallel

2.5 Represent vectors as a combination of

other vectors.

Solve problems involving addition and subtraction of vectors.

Emphasize:

( )~~~~baba −+=−

Constructivism

Mastery learning

Thinking skill

Problem Solving

Drawing diagram

Identifying relations

Identifying

Relations

Drawing diagram

Recognizing & representing

Self-reliance

Self confident

Triangle law

Parallelogram law

Resultant vector

Polygon law

8

9

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOMES POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

12 3 Understand and use vectors in the Cartesian plane.

Use computer software to explore vectors in the Cartesian plane.

3.1 Express vectors in the form:

a) ~~jyix +

b)

y

x

Relate unit vector ~i

and ~j to Cartesian

coordinates.

Emphasise:

Vector

=

0

1~i and

Vector

=

1

0

~j

Intergrating ICT

Arranging sequentially

unity Cartesian plane

unit vector

3.2 Determine magnitudes of vectors.

3.3 Determine unit vectors in given

directions.

3.4 Add two or more vectors.

3.5 Subtract two vectors

3.6 Multiply vectors by scalars.

3.7 Perform combined operations on

vectors.

3.8 Solve problems involving vectors.

For learning outcomes 3.2 to 3.7 , all vectors are given in the form

~~jyix + or

y

x.

Limit combined operations to addition , subtraction and multiplication of vectors by scalars.

Problem solving

10

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

13 -

15

T2

TRIGONOMETRIC FUNCTIONS

1 Understand the concept of positive and negative angles measured in degrees and radians.

Use dynamic computer software such as Geometer’s sketchpad to explore angles in Cartesian plane.

1.1 Represent in a Cartesian plane, angles greater than 360o or 2π radians for:

a) positive angles

b) negative angles

Self-Access Learning

Drawing diagrams

Responsible Cartesian plane

rotating ray

positive angle

negative angle

clockwise

anticlockwise

2 Understand and use the six trigonometric functions of any angle.

Use dynamic computer software to explore trigonometric functions in degrees and radians.

Use scientific or graphing calculators to explore trigonometric functions of any angle.

2.1 Define sine, cosine and tangent of any angle in a Cartesian plane.

2.2 Define cotangent, secant and

cosecant of any angle in a Cartesian

plane.

2.3 Find values of the six trigonometric

functions of any angle.

2.4 Solve trigonometric equations.

Use unit circle to determine the sign of trigonometric ratios.

Emphasise:

sin θ = cos (90o - θ )

cos θ = sin (90o - θ )

tan θ = cot (90o - θ )

cosecθ = sec (90o -θ )

secθ = cosec(90o - θ )

cot θ= tan (90o - θ )

Emphasise the use of triangles to find trigonometric ratios for special angles 30o , 45o

and 60o.

Constructivism

Making generalizations

Dedication unit circle

quadrant

reference angle

trigonometric function/ratio

sine

cosine

tangent

cosecant

secant

cotangent

special angle

11

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

3 Understand and use graphs of sine, cosine and tangent functions.

Use examples from real-life situations to introduce graphs of trigonometric functions.

3.1 Draw and sketch graphs of trigonometric functions:

a) y = c + a sin bx

b) y = c + a cos bx

c) y = c + a tan bxwhere a,b, and c are constants and

b > 0.

Use angles in

a) degrees

b) radians, in terms of πEmphasize the characteristics of sine. Cosine and tangent graphs. Include trigonometric functions involving modulus.

Constructivism

Integrating ICT

Mastery Learning

Identifying patterns

Drawing diagrams

Comparing & differentiating

Diligence

Self-Reliance

Modulus

Domain

Range

Sketch

Draw

Period

cycle

. Use graphing calculators and dynamic computer software such as Geometer’s Sketchpad to explore graphs of trigonometric functions.

3.2 Determine the number of solutions

to a trigonometric equations using

sketched graphs.

3.3 Solve trigonometric equations

using drawn graphs.

Exclude combinations of trigonometric functions.

Constructivism

Integrating ICT

Thinking Skills

Working out mentally

Finding all possible solutions

Logical reasoning

Rationality

Diligence

Maximum

Minimum

asymptote

4 Understand and use basic identities.

Use scientific or graphing calculators and dynamic computer software such as Geometer’s Sketchpad to explore basic identities.

4.1 Prove basic identities:

a) sin2 A + cos2 A = 1

b) 1 + tan2 A = sec2 A

c) 1 + cot2 A = cosec2 A

4.2 Prove trigonometric identities

using basic identities.

4.3 Solve trigonometric equations

using basic identities.

Basic identities are also known as Pythagorean identities.

Include learning outcomes 2.1 and 2.2.

Thinking skills

Integrating ICT

Thinking skills

Problem solving

Identifying relations

Drawing diagrams

Logical

Reasoning

Classifying

Self reliance

Moderation

Tolerance

Basic identity

Pythagorean identity

12

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

5 Understand and use addition formulae and double-angle formulae.

Use dynamic computer software such as Geometer’s Sketchpad to explore addition formulae and double-angle formulae.

5.1 Prove trigonometric identities

using addition formulae for

sin ( A ± B), cos ( A ± B) and

tan ( A ± B).

5.2 Derive double-angle formulae for

sin 2A, cos 2A and tan 2A.

5.3 Prove trigonometric identities

using addition formulae and/or

double-angle formulae.

5.4 Solve trigonometric equations.

Derivation of addition formulae not required.

Discuss half-angle formulae.

Exclude

A cos x + b sin x = c,

where .0≠c

Thinking skills

Exploratory

Thinking skills

Contextual

Problem solving

Self access learning

Problem solving

Identifying patterns

Identifying relations

Identifying relations

Finding all possible solutions

Diligence

Self-reliance

Self-reliance

Cooperation

Diligence

Addition formulae

Double-angle formulae

Half-angle formulae

13

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

16-17

S2

PERMUTATIONS AND COMBINATION

1 Understand and use the concept of permutation.

Use manipulative materials to explore multiplication rule.

Use real-life situation and computer software such as spreadsheet to explore permutations.

1.1 Determine the total number of ways to perform successive events using multiplication rule.

1.2 Determine the number of permutations of n different objects.

1.3 Determine the number of permutations of n different objects taken r at a time.

1.4 Determine the number of

permutations of n different

objects for given conditions.

1.5 Determine the number of

permutations of n different

objects taken r at a time for

For this topic:

a) Introduce the concept by

using numerical values.

b) Calculators should only

be used after the student

have understood the

concept.

Limit to 3 events.

Exclude cases involving identical objects.

Explain the concept of permutations by listing all possible arrangements.

Include notations:

a)

( ) ( ) 123...21! ⋅⋅−−= nnnn

b) 1!0 = !n read as ‘ n factorial’

Exclude cases involving arrangement of objects in a circle.

Thinking skill

Problem solving

Constructivism

Integrating ICT

Thinking skill

Problem solving

Constructivism

Integrating ICT

Identifying patens

Finding all possible solutions

Classifying

Simulation

Identifying patens

Finding all possible solutions

Classifying

Simulation

Cooperation

Self reliance

Systematic

Justice

Cooperation

Self reliance

Justice

Multiplication rule

Successive

Events

Permutation

Factorial

Arrangement

order

14

given conditions.

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

18-19 MID YEAR EXAM WEEK

20 2 Understand and use the concept of combination.

Explore combinations using real-life situations and computer software.

Use scientific or graphing calculators to explore trigonometric functions of any angle.

2.1 Determine the number of

combinations of r objects chosen from n different objects.

2.2 Determine the number of

combinations of r objects chosen from n different objects for given conditions.

2.3 Determine the number of

permutations of n different objects for given conditions.

2.4 Determine the number of Permutations of n different objects taken r at a time for given conditions.

Explain the concept of combinations by listing all possible selections.

Use examples to illustrate

!r

PC r

n

rn =

Thinking skill

Integrating ICT

Constructivism

Identifying relations

Finding all possible solutions

Classifying

Simulation

Rationality

Logical thinking

Cooperation

Combination

Selection

15

MID YEAR SCHOOL HOLIDAYS : 30.5.2009 – 14.6.2009

16

Term II : 15.6.2008 – 20.11.2009 (22 week)

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

1-2

S3

PROBABILITY

1 Understand and use the concept of probability

Use real-life situations to introduce probability.

Use manipulative materials, computer software and scientific or graphing calculators to explore the concept of probability.

1.1 Describe the sample space of an experiment.

1.2 Determine the number of outcomes of an event.

1.3 Determine the probability of an event.

1.4 Determine the probability of two events:

a) A or B occurring

b) A and B occurring

Use set notations.

Discuss:

a) classical probability

(theoretical probability)

b) subjective probability

c) relative frequency probability

(experimental probability)

Emphasize:

Only classical probability is used to solve problems

Emphasize :

( ) ( ) ( )( )BAP

BPAPBAP

∩−+=∪

Using Venn Diagrams.

Thinking skills

Contextual

Thinking skills

Drawing diagram

Identifying patens

Simulation

Making inference

Making generalization

Cooperation

Rationality

Systematic

Experiment

Sample space

Event

Outcome

Equally likely

Probability

Occur

Classical probability

Theoretical probability

Subjective probability

Relative

frequency probability

Experimental probability

2 Understand and use the concept of probability of mutually exclusive events.

Use manipulative materials and graphing calculators to explore the concept of probability mutually exclusive events.

2.1 Determine whether two events are mutually exclusive.

2.2 Determine the probability of two or more events that are mutually exclusive.

Include events that are mutually exclusive and exhaustive.

Limit to three mutually exclusive events.

Contextual

Constructivism

Identifying relations

Identifying patens

Drawing diagrams

Rationality

Mutually exclusive event

exhaustive

17

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

3 Understand and use the concept of probability of independent events.

Use manipulative materials and graphing calculators to explore the concept of probability of independent events.

Use software to stimulate experiments involving probability of independent events.

3.1 Determine whether two events are independent.

3.2 Determine the probability of two independent events.

3.3 Determine the probability of

three independent events.

Include tree diagram Integrating ICT

Mastery learning

Integrating ICT

Classifying

Identifying patens

Comparing and differentiating

Self reliance

Rationality

Rationality

Independent

Tree diagrams

18

19

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

20

3 - 4

S4

PROBABILITY DISTRIBUTIONS

1 Understand and use the concept of binomial distribution.

WEEK LEARNING OBJECTIVES

Use real-life situations to introduce the concept of binomial distribution.

Use graphing calculators and computer software to explore binomial distribution.

SUGGESTED TEACHING AND LEARNING ACTIVITIES

Use real-life situations and computer software

1.1 List all possible values of a

discrete random variable.

1.2 Determine the probability of an event in a binomial distribution.

1.3 Plot binomial distribution graphs.

1.4 Determine mean, variance and

standard deviation of a binomial

distribution.

1.5 Solve problems involving binomial distributions.

Include the characteristics of Bernoulli trials.

For learning outcomes 1.2 and 1.4 , derivation of formulae are not required.

Mastery Learning

Cooperative Learning, Integrating ICT

Constructivism,

Integrating ICT

Contextual, Integrating ICT

Contextual, Problem solving

Recognising and representing

Identifying patterns, predicting.

Identifying relations, drawing diagrams

Comparing and differentiating

Making inferences.

Rational, accuracy.

Diligence.

Neatness, careful.

Freedom by law, accuracy, careful.

Ability to act independently, self motivated

Discrete random

Variable

Independent trial

Bernoulli trials

Binomial distribution

Mean

Variance

Standard deviation

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

2.1 Describe continuous random

variables using set notations.

2.2 Find probability of z-values for

standard normal distribution.

Discuss characteristics of:

a) normal distribution graphs.

b) standard normal distribution graphs.

Z is called standardized variable

Integration of normal distribution function to

Constructivism,

Cooperative Learning

Contextual, Multiple Intelligence

Contextual, mastery learning

Identifying patterns, comparing and differentiating

Identifying relations.

Recognising and representing, identifying

Honesty, accuracy.

Rational, accuracy, careful.

Neatness, self-reliance, effort

Continuous random variable

Normal distribution

Standard normal distribution

z-values

standardized variable

21

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

5 AST2

MOTION ALONG A STRAIGHT

1 Understand and use the concept of displacement.

Use real-life examples, graphing calculators or computer software such as Geometer’s Sketchpad to explore displacement.

1.1 Identify direction of displacement

of a particle from a fixed point.

1.2 Determine displacement of a particle from a fixed point.

1.3 Determine the total distance

traveled by a particle over a time

interval using graphical method.

Emphasize the use of the following symbols:

s = displacement

v = velocity

a = acceleration

t = time

where s , v , and a are functions of time.

Emphasize the difference between displacement and distance.

Discuss positive, negative and zero displacement.

Include the use of number line.

Contextual

ConstructivismExploratory

Masterylearning

IdentifyingpatternsDrawing diagrams

Comparing and differentiatingDrawing diagrams

Comparing and differentiatingIdentifying relations

Rational

Systematic

Cooperation

ParticleFixed pointDisplacementDistanceVelocityAccelerationTime interval

2 Understand and use the concept of velocity.

Use real-life examples, graphing calculators or computer software such as Geometer’s Sketchpad to explore velocity.

2.1 Determine velocity function of a

particle by differentiation.

2.2 Determine instantaneous

velocity of a particle.

2.3 Determine displacement of a

particle from velocity function by

Integration.

Emphasize velocity as the rate of change of displacement.

Include graphs of velocity functions.

Discuss:

a) uniform velocity

b) zero instantaneous velocity

c) positive velocity

d) negative velocity

Constructivism

Mastery learning

Mastery

learning

Identifying relations

Identifying relations

Drawing diagrams

Finding all possible solutions

Rational

Cooperation

Systematic

Instantaneous

velocity

Velocity

function

Uniform velocity

Rate of change

Maximum displacement

stationary

22

WEEK LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

3 Understand and use the concept of acceleration.

Use real-life examples, graphing calculators or computer software such as Geometer’s Sketchpad to explore the concept of acceleration.

3.1 Determine acceleration function of

a particle by differentiation.

3.4 Determine instantaneous

acceleration of a particle.

3.5 Determine instantaneous velocity

of a particle from acceleration

function by integration.

3.4 Determine displacement of a

particle from acceleration function

by integration.

3.5 Solve problems involving motion

along a straight line.

Emphasize acceleration as the rate of change of velocity.

Discuss:

a) uniform acceleration

b) zero acceleration

c) positive acceleration

d) negative acceleration

Mastery learning

Mastery learning

Multiple Intelligence

Thinking skills

Multiple intelligence

Identifying relations

Identifying relations

Identifying relations

Finding all possible solutions

Making generalization

Rational

Confident

Systematic

Maximum velocity

Minimum velocity

Uniform acceleration

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WEEK

LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

Students will be taught to:

Students will be able to:

6-7

ASS2

LINEAR PROGRAMMING

1 Understand and use the concept of graphs of linear inequalities

Use real-life examples, graphing calculators or computer software such as Geometer’s Sketchpad to explore linear programming.

1.1 Identify and shade the region on the graph that satisfies a linear inequality.

1.2 Find the linear inequality that defines a shaded region.

1.3 Shade the region on the graph that satisfies several linear inequalities.

1.4 Find linear inequalities that define a shaded region.

Emphasize the use of solid lines and dashed lines.

Limit to regions defined by a maximum of 3 linear inequalities not including the x-axis and y-axis.

Constructivism

Integrating ICT

Constructivism

Constructivism

Integrating ICT

Constructivism

Identifying Relations

Representing and Interpreting Data

Drawing Diagrams

Representing and Interpreting Data

Reasoning

Able to act independently

Reasoning

Able to act independently

Linear programming

Linear inequality

Dashed line

Solid line

Region

Define

satisfy

2 Understand and use the concept of linear programming.

2.2 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

Optimum values refer to maximum or minimum values.

Include the use of vertices to find the optimum value.

Contextual

Cooperative Learning

Contextual

Multiple Intelligent

Cooperative Learning

Future Learning

Contextual

Constructivism

Recognizing and Representing

Drawing Diagrams

Representing and Interpreting Data

Problem Solving

Collaboration

Steadfastness

Responsible

Open and logical mind

Feasible solution

Objective function

Parallel lines

Vertex

Vertices

Optimum value

Maximum value

Minimum value

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objective function.

WEEK

LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOME POINTS TO NOTE GENERICS CCTS MORAL VALUE

VOCABULARY

8-9 SPM REVISION

SCHOOL HOLIDAYS (MID TERM 2) : 22.08.2009 - 30.08.2009

10 INTENSIVE REVISION

11 - 13 SPM TRIAL EXAM

14 HOLIDAY (HARI RAYA PUASA)

15 - 20 INTENSIVE REVISION

21-22 SPM EXAM 2009

YEAR END SCHOOL HOLIDAYS : 21.11.2009 - 03.01.2010

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SEKOLAH MENENGAH KEBANGSAAN CONVENT BUKIT NANAS

KUALA LUMPUR

RANCANGAN TAHUNANMATA PELAJARAN

MATEMATIK TAMBAHAN TINGKATAN 5TAHUN 2007

Disediakan oleh : Disemak oleh : Disahkan oleh :

…………………………............ ……………………………….. …………………………… …………………………

(PN. MA SIEW LANG ) (PN. PARIDAH BT YAACOB) (PN. CHUA POI LANG) (PN. LEE CHII YUANN)

Penyelaras Ketua Panitia Matematik Guru Kanan Sains dan Pengetua

Matematik Tambahan Matematik

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