Ranadd Math Form 4yearplan2009

8/13/2019 Ranadd Math Form 4yearplan2009

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SCHEME OF WORK ADDITIONAL MATHEMATICS FORM 4 YEAR 2009

1ST Term : 05.01.09 29.05.09 ( 20 wee!"

A1. LEARNIN# AREA: F$NCTIONSNO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED

TEACHIN# AND

LEARNIN#

ACTI'ITIES

LEARNIN# O$TCOMES OINTS TO NOTE MORAL 'AL$ES

) #ENERICS

CCTS 'OCA%$LARY

Students will be

taught to:

Students will be able to:

1 - 3 1.

Understand

the conceptof relations.

Use pictures, role-

play and computer

software tointroduce the

concept of

relations.

1.1 Represent relations using

a) arrow diagrams

b) ordered pairs

c) graphs

1.2 Identify domain, codomain,obect, image and range of a

relation.

1.3 !lassify a relation shown on a

mapped diagram as" one to one,

many to one, one to many or

many to many relation.

#iscuss the idea of set and

introduce set notation.

!ooperation

$rderly

Contextual

Rationality

!omparison

and

distinguish

#ifferentiating

function

relation

obect

image

range

domain

codomain

map

ordered pair

arrow diagram

2.

Understand

the conceptof functions.

2.1 Recogni%e functions as a special

relation.

Represent functions using

arrow diagrams, ordered pairs or

graphs.

Respect

Reasoning

!ollating &

!ategori%ing

1



A1. LEARNIN# AREA: F$NCTIONS

NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED

TEACHIN# AND

LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY

Students will betaught to:


Use graphing

calculators and

computer

software to

e'plore the image

of functions.

2.2 ('press functions using

function notation.

2.3 #etermine domain, obect,

image and range of a

function.

2. #etermine the image of a

function gi*en the obect and

*ice *ersa.

.

e.g. f " x 2 x

f + x) 2 x

f " x 2 x is read as

function f maps x to 2 x.

f + x) 2 x is read as 2 x is

the image of x under the

function f ”.

Include e'amples of functionsthat are not mathematically

based.

('amples of functions

include algebraic +linear and

/uadratic), trigonometric and

absolute *alue.

#efine and s0etch absolute

*alue functions.

$rderly

Constructivism

elf-Reliance

Mastery

Learning

!ourage

Rationality

!onceptualise

Identifying!haracteristics

!onceptualise

notation

2



A1. LEARNIN# AREA: F$NCTIONS

3



NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED

TEACHIN# AND

LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY

Students will be

taught to:


3.

Understand

the concept

of

composite

functions.

Use arrow

diagrams or

algebraic method

to determine

composite

functions.

3.1 #etermine composition of

two functions.

3.2 #etermine the image of

composite functions gi*en the

obect and *ice *ersa.

3.3 #etermine one of the

functions in a

gi*en composite function

gi*en the other

related function.

In*ol*e algebraic functions

only.

Images of composite

functions include a range of

*alues. +imit to linear

composite functions).

#iligence

Constructivism

Mastery

Learning

#iligence

elf-Reliance

conceptuali%e

relational

a0ing

4nalogies

composite

function

in*erse

mapping

.

Understand

the concept

of in*erse

functions.

.1 5ind the obect by in*erse

mapping gi*en its image and

function.

imit to algebraic functions.

('clude in*erse of composite

functions.

#iligence

4ccuracy

Constructivism

Mastery

Learning

conceptuali%e

relational

NO. OF

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ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



4



5



A2. LEARNIN# AREA: *$ADRATIC E*$ATIONS

6



NO. OF

WEEKS

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O%&ECTI'ES

S$##ESTED

TEACHIN# AND

LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY

Students will be taught to: Students will be able to:

6 7 1. Understand

the concept of

/uadratic

e/uation and

its roots.

Use graphing

calculators or

computer

software such

as the

8eometer9s

0etchpad and

spreadsheet to

e'plore theconcept of

/uadratic

e/uations.

1.1 Recogni%e a /uadratic

e/uation and e'press it in

general form.

1.2 #etermine whether a gi*en

*alue is the root of a

/uadratic e/uation by

a) substitution:

b) inspection.

1.3 #etermine roots of

/uadratic e/uations by trial

and impro*ement method.

;uestions for 1.2+b) are

gi*en in the form of + x <

a)+ x < b) =: a and b

are numerical *alues.

Rationality

Mastery

Learning

elf confident

Exploratory

Rational

>atience

Constructivism

>attern

Identificatio

n

!ritici%e

#ecision

a0ing

ogical

Reasoning

/uadratic

e/uation

general form

root

substitution

inspection

trial andimpro*ement

method

NO. OF

WEEKS

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ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY


7



8



A+. LEARNIN# AREA: *$ADRATIC F$NCTIONS

9



NO. OF

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ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



? - @ 1.

Understand

the concept

of /uadratic

functions

and their

graphs.

Use graphing

calculators or

computer

software such as

8eometer9s

0etchpad to

e'plore the

graphs of

/uadratic

functions.

Use e'amples of

e*eryday

situations to

introduce graphs

of /uadratic

functions.

1.1 Recogni%e /uadratic

functions.

1.2 >lot /uadratic function graphs

a) based on gi*en tabulated

*alues:

b) by tabulating *alues

based on gi*en functions.

1.3 Recogni%e shapes of graphs

of /uadratic functions.

1.4 Relate the position of quadratic

function graphs with types of

roots for f (x)

0.

#iscuss cases where

a A = and a B = for

f+') a x2 < b x < c =

!ooperation

Constructivism

Contextual

#rawingCabulating

8enerating

Ideas

Identifying

characteristics

/uadratic function

tabulated *alues

a'is of symmetry

parabola

ma'imum point

minimum point

completing the

s/uare

a'is of symmetry

NO. OF

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/ GENERICS

CCTS 'OCA%$LARY



2. 5ind the Use graphing 2.1 #etermine the ma'imum or 10





A+. LEARNIN# AREA: *$ADRATIC F$NCTIONS

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AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



1= 3. 0etch

graphs of

/uadratic

functions.

Use graphing

calculators or

dynamic geometry

software such as

the 8eometer9s

0etchpad to

reinforce the

understanding of

graphs of /uadratic

functions.

3.1 0etch /uadratic function

graphs by determining the

ma'imum or minimum point

and two other points.

(mphasi%e the mar0ing of

ma'imum or minimum point

and two other points on the

graphs drawn or by finding

the a'is of symmetry and the

intersection with the y-a'is.

#etermine other points by

finding the intersection with

the '-a'is +if it e'ists).

#iligence

Constructivism

Maing

connections

Relating to

something

0etch

Intersection

Dertical line

;uadratic

ine/uality

Range

Eumber line

.

Understand

and use the

concept of

/uadratic

ine/ualities.

Use graphing

calculators or

dynamic geometry

software such as

the 8eometer9s

0etchpad to

e'plore the concept

of /uadratic

ine/ualities.

.1 #etermine the ranges of

*alues of x that satisfies

/uadratic ine/ualities.

(mphasi%e on s0etching

graphs and use of number

lines when necessary.

Rationality

!he use of

technology

a0ing

inferences

MID,TERM HOLIDAYS : 14.0+.09 , 22.0+.09

12



A4. LEARNIN# AREA: SIM$LTANEO$S E*$ATIONS

NO. OF

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ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



11 -

121. ol*e

simultaneous

e/uations in

two

un0nowns"

one linear

e/uation and

one non-

lineare/uation.

Use graphing

calculators or

dynamic geometry

software such as

the 8eometer9s

0etchpad to

e'plore the

concept of

simultaneouse/uations.

Use e'amples in

real-life situations

such as area,

perimeter and

others.

1.1 ol*e simultaneous e/uations

using the substitution method.

1.2 ol*e simultaneous e/uations

in*ol*ing real-life situations.

imit non-linear e/uations up

to second degree only.!ooperation

!ourage

!areful

"roblem

solving

Maing

inference

Mainganalogy

!reating

!reating

ental

>ictures

Relating to

omething

a0ing

4nalogies

#rawing

!onclusions

simultaneous

e/uations

intersection

substitution

method

13



A5. LEARNIN# AREA: INDICES AND LO#ARITHMS

NO. OF

WEEKS

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ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



13 -

1F1.

Understand

and use the

concept of

indices and

laws of

indices to

sol*e

problems.

Use e'amples of

real-life

situations to

introduce the

concept of

indices.

Use computer

software such asthe spreadsheet to

enhance the

understanding of

indices.

1.1 5ind the *alue of numbers

gi*en in the form of"

a) integer indices.

b) fractional indices.

1.2 Use laws of indices to find the

*alue of numbers in inde'

form that are multiplied,

di*ided or raised to a power.

1.3 Use laws of indices to simplify

algebraic expressions.

#iscuss %ero inde' and

negati*e indices.4wareness

Gardwor0ing

elf reliance

Respect

Contextuallearning

8enerating

ideas

Relating to

something

Identifying

characteristics

base

integer indices

fractional

indices

inde' form

raised to a

power

law of indices

2.

Understand

and use the

concept of

logarithms

and laws oflogarithms

to sol*e

problem

Use scientific

calculators to

enhance the

understanding of

the concept of

logarithm.

2.1 ('press e/uation in inde'

form to logarithm form and

*ice *ersa.

('plain definition of

logarithm.

# a x : loga # x with a A

=, a H 1.

(mphasi%e that"

loga 1 =: loga a 1.

elf reliance

Contextual

learning

>redicting

a0ing

hypotheses

inde' form

logarithm

form

logarithm

undefined

14




NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED

TEACHIN# AND

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ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



2.2 5ind logarithm of a number. (mphasi%e that"

a) logarithm of negati*e

numbers is undefined:

b) logarithm of %ero is

undefined.

#iscuss cases where the gi*en

number is in

a) inde' form

b) numerical form.

Respect

Identify the

relation

Multiple

intelligence

>attern

identification

inde' form

logarithm form

logarithm

undefined

2.3 5ind logarithm of numbers by

using laws of logarithms.

2. implify logarithmic

e'pressions to the simplest

form.

#iscuss laws of logarithms

3.

Understand

and use the

change of

base oflogarithms

to sol*e

problems.

3.1 5ind the logarithm of a

number by changing the base

of the logarithm to a suitable

base.

3.2 ol*e problems in*ol*ing thechange of base and laws of

logarithms.

#iscuss"

loga b ablog

1Respect

Identify the

relation

Cooperative

learning

Relating to

something

>roblemsol*ing

15




NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED

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ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



. ol*e

e/uations

in*ol*ing

indices and

logarithms.

.1 ol*e e/uations in*ol*ing

indices.

.2 ol*e e/uations in*ol*ing

logarithms.

(/uations that in*ol*e

indices and logarithms are

limited to e/uations with

single solution only.

ol*e e/uations in*ol*ing

indices by"

a) comparison of indices

and bases: b) using logarithms.

#iligence

"roblem solving

Masterylearning

>roblem

sol*ing

16



#1. LEARNIN# AREA: COORDINATE #EOMETRY

NO. OF WEEKS LEARNIN#

O%&ECTI'ES

S$##ESTED

TEACHIN# AND

LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



17 - 1? 1. 5ind

distance

between

two

points.

Use

e'amples of

real-life

situations to

find the

distance

between two

points.

1.1 5ind the distance between

two points using formula.

Use the >ythagoras9 Cheorem

to find the formula for

distance between two points.

ystematic

4ccuracy

Cranslation

Mastery

learning

!reate ental

>ictures

distance

midpoint

coordinate

ratio

2.

Understa

nd the

concept

of

di*ision

of a line

segment.

2.1 5ind the midpoint of two

gi*en points.

2.2 5ind the coordinates of a

point that di*ides a line

according to a gi*en ratio

m " n.

imit to cases where m and n

are positi*e.

#eri*ation of the formula

++

++

nm

myny

nm

mxnx 2121 , is not

re/uired.

#etermine

relation

Rational

!omparing

#ifferentiating

Masterylearning

Identifying

!haracteristics

Relating to

omething

1@ -1 I#-J(4R (K4IE4CI$E

17




NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY

Students will betaught to: Students will be able to:

2= 3. 5ind areas

of polygons.

Use dynamic

geometry software

such as the

8eometer9s

0etchpad to

e'plore the concept

of area of

polygons.

Use

for substitution of

coordinates into the

formula.

3.1 5ind the area of a triangle

based on the area of specific

geometrical shapes.

3.2 5ind the area of a triangle by

using formula.

3.3 5ind the area of a/uadrilateral using formula.

imit to numerical *alues.

(mphasi%e the relationship

between the sign of the *alue

for area obtained with the

order of the *ertices used.

#eri*ation of the formula"

2

1+ x1 y2 < x2 y3 < x3 y1 6 x2 y1 6

x3 y2 6 x1 y3) is notre/uired.

(mphasi%e that when the area

of polygon is %ero, the gi*en

points are collinear.

Rational

Luilding

diagram

!lassification

#etermine the

patterns

Mastery

learning

!ollating

and

!ategori%ing

e/uencing

a0ing

4nalogies

area

polygon

geometrical

shape

/uadrilateral

*erte'

*ertices

cloc0wise

anticloc0wise

modulus

collinear

MID,YEAR HOLIDAYS : +0.05.09 - 14.0.09

18

1321

1321

2

1

y y y y

x x x x






NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY


4. 5ind the gradient and the

intercepts of a straight line

gi*en the e/uation.

4.# !hange the e/uation of a

straight line to the general

form.

.? 5ind the point of

intersection of two

lines.

!ooperation

Colerance

4ccuracy

!ategori%e

Constructivism

#ifferentiating

Relating to

omething

4naly%ing

F.

Understand

and use the

concept of

parallel and

perpendicu-

lar lines.

Use e'amples of


to e'plore parallel

and perpendicular

lines.

F.1 #etermine whether two

straight lines are parallel

when the gradients of both

lines are 0nown and *ice

*ersa.

F.2 5ind the e/uation of a

straight line that passes

through a fi'ed point and parallel to a gi*en line.

(mphasi%e that for parallel

lines"

m1 m 2.

(mphasi%es that for

perpendicular lines

m 1 m 2 61.#eri*ation of m 1 m 2 61

is not re/uired.

!onnection

Rational

!omparison

(*aluating

Relating toomething

parallel

perpendicular

20




NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY


Use graphic calculator

and dynamic

geometry software

such as

8eometer9s

0etchpad to

e'plore the

concept of parallel

and perpendicular

lines.

F.3 #etermine whether two

straight lines are

perpendicular when the

gradients

of both lines are 0nown and

*ice *ersa

F. #etermine the e/uation of a

straight line that passes

through a fi'ed point and

perpendicular to a gi*enline.

. ol*e problems in*ol*ing

e/uations of straight lines.

!ooperation

Colerance

4ccuracy

!ategori%e

Constructivism

Relating to

omething

(*aluating

ol*e

>roblemsa0e

#ecisions

e/uation of

locus

mo*ing point

loci

7.

Understand

and use the

concept of

e/uation of

locus

in*ol*ingdistance

between two

points

Use e'amples of


to e'plore e/uation

of locus in*ol*ing

distance between

two points.

7.1 5ind the e/uation of locus

that satisfies the condition

if"

a) the distance of a mo*ing

point from a fi'ed point is

constant$ b) the ratio of the distances of

a mo*ing point from two

fi'ed points is constant.

7.2 ol*e problems in*ol*ing

loci.

Gardwor0ing

!omparison

Cooperative

4nalysing(*aluating

ol*e

problems

21



S1. LEARNIN# AREA: STATISTICS

NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED

TEACHIN# AND

LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



Understand

and use the

concept of

measures of

central

tendency to

sol*e

problems.

Use

scientific

calculators,

graphing

calculators

and

spreadsheets

to e'plore

measures ofcentral

tendency.

tudents

collect data

from real-

life

situations to

in*estigate

measures ofcentral

tendency.

1.1 !alculate the mean of ungrouped data.

1.2 #etermine the mode of ungrouped

data.

1.3 #etermine the median of ungrouped

data.

1. #etermine the modal class of grouped

data from fre/uency distribution tables.

1.F 5ind the mode from histograms.

1.7 !alculate the mean of grouped data.1.? !alculate the median of grouped data

from cumulati*e fre/uency distribution

tables.

1.@ (stimate the median of grouped data

from an ogi*e.

1. #etermine the effects on mode, median

and mean for a set of data when"

a) each data is changed uniformly:

b) e'treme *alues e'ist:

c) certain data is added or remo*ed.

1.10 %etermine the most suitable measure of

central tendency for gi&en data.

#iscuss grouped data and

ungrouped data.

In*ol*e uniform class

inter*als only.

#eri*ation of the medianformula is not re/uired.

$gi*e is also 0nown ascumulati*e fre/uency

cur*e.

In*ol*e grouped and

ungrouped data

!ooperation

Eeat

In order

Rule &Regulation

oderate

Rule &Regulation

>recise

Rational

Contextual

!ourteous

conduct and

speed

$pen and

logical mind

Contextual

8ather &

!lassify

Interpret

Interpret

Interpret

Co infer

a0egenerali%ation

measure of

central

tendency

mean

mode

median

ungrouped

data

fre/uency

distribution

table

modal class

uniform class

inter*al

histogram

F MONTHLY TEST 2

22



S1. LEARNIN# AREA: STATISTICSNO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY

Students will be

taught to:


7 - ? 2.

Understand

and use

theconcept of

measures

of

dispersion

to sol*e

problems.

2.1 5ind the range of ungrouped

data.

2.2 5ind the inter/uartile range of

ungrouped data.

2.3 5ind the range of grouped data.

2. 5ind the inter/uartile range of

grouped data from thecumulati*e fre/uency table.

2.F #etermine the inter/uartile

range of grouped data from an

ogi*e.

2.7 #etermine the *ariance of

a) ungrouped data:

b) grouped data.

2.? #etermine the standard

de*iation of"

a) ungrouped data

b! grouped data.

#etermine upper and

lower /uartiles by using

the first principle.

Independent

!onfident

Eeat

Constructivism

!ourage

Contextual

Co compare

&

differentiate

(*aluate , to

compare &differentiate

standard

de*iation

class inter*al

upper /uartile

lower /uartile

*ariance

23



S1. LEARNIN# AREA: STATISTICS

NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY


2.@ #etermine the effects on range,

inter/uartile range, *ariance and

standard de*iation for a set of

data when"

a) each data is changed

uniformly:

b) e'treme *alues e'ist:

c) certain data is added or

remo*ed.

2. !ompare measures of central

tendency and dispersion

between two sets of data.

(mphasi%e that

comparison between two

sets of data using only

measures of central

tendency is not sufficient.

Rules &

regulation

Rational

Mastery

learning

a0e analogy

Co identify

a0e

generali%ation

24



T1. LEARNIN# AREA: CIRC$LAR MEAS$RES

NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY


@ -

1=1.

Understand

the concept

of radian.

Use dynamic

geometry software

such as the

8eometer9s

0etchpad to

e'plore the

concept of circular

measure.

1.1 !on*ert measurements in

radians to degrees and *ice

*ersa.

#iscuss the definition of

one radian.

radM is the abbre*iation

of radian.

Include measurements in

radians e'pressed in terms

of i .

!ooperati

on

4ccuracy

!onte'tual

#rawin

g

#iagra

m

Interpre

tation

radian

degree

2.

Understand

and use the

concept of

length of

arc of a

circle to

sol*e

problems.

Use e'amples of


to e'plore circular

measure.

2.1 #etermine"

a) length of arc:

b) radius: and

c) angle subtended at the

centre of a circle

based on gi*en information.

2.2 5ind perimeter of segments of

circles.


lengths of arcs.

!ourage

#iligence

astery

earning

Rational

Gonesty

Independence

elf confident

Reasoning

!onstructi*ism

elf 4ccess

Disuali%e

8enerate

ideas

length of arc

angle

subtended

circle

perimeter

segment

25



T1. LEARNIN# AREA: CIRC$LAR MEAS$RES

NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



3.

Understand

and use the

concept of

area of

sector of a

circle to

sol*e

problems.

3.1 #etermine the"

a) area of sector:

b) radius: and

c) angle subtended at the

centre of a circle

based on gi*en information.

3.2 5ind the area of segments of

circles.

3.3 ol*e problems in*ol*ing areas

of sectors.

#iligence

astery

earning

!ourage

Rational

$pen

logical

mind

!omparison

5ormul

ate

Reason

ing

4nalyst

8enerate

idea#rawing

diagram

area

sector

MID,TERM HOLIDAYS : 21.0/.09 , +0.0/.09

26



27



C1. LEARNIN# AREA: DIFFERENTIATIONNO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY

Students will be

taught to:


11 6

1F1.

Understand

and use the

concept of

gradients of

cur*e and

differentiati

on.

Use graphing

calculators or

dynamic geometry

software such as

8eometer9s

0etchpad to

e'plore the concept

of differentiation.

1.1 #etermine the *alue of a

function when its *ariable

approaches a certain *alue.

1.2 5ind the gradient of a chord

oining two points on a cur*e.

1.3 5ind the first deri*ati*e of a

function y f + x), as the gradient

of tangent to its graph.

1. 5ind the first deri*ati*e of

polynomials using the first

principles.

1.F #educe the formula for first

deri*ati*e of the function y

f + x) by induction.

Idea of limit to a function

can be illustrated using

graphs.

Che concept of first

deri*ati*e of a function is

e'plained as a tangent to a

cur*e can be illustrated

using graphs.

imit to y axn:

a, n are constants, n

1, 2, 3.

Eotation of f $ + x) is

e/ui*alent todx

dy when y

f + x),

f 9N+ x) read as f prime xM.

!onfidence

4ccuracy

>atience

Rational

Constructivis

m

!onscientious

!onfidence

Cooperative

(*aluating

8enerate

ideas

5inding

relation

Interpreting

a0ing

conclusion

limit

tangent

first deri*ati*e

gradient

induction

cur*e

fi'ed point

28




WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY

Students will be

taught to:


2.

Understand

and use the

concept of

first

deri*ati*e of

polynomial

functions to

sol*e

problems.

2.1 #etermine the first deri*ati*e of

the function y axn using

formula.

2.2 #etermine *alue of the first

deri*ati*e of the function y

axn for a gi*en *alue of x.

2.3 #etermine first deri*ati*e of a

function in*ol*ing"

a) addition, or

b) subtractionof algebraic terms.

2. #etermine the first deri*ati*e of

a product of two polynomials.

2.F #etermine the first deri*ati*e of

a /uotient of two polynomials.

2.7 #etermine the first deri*ati*e of

composite function using chain

rule.

(ffort

Rational

!areful

!onfidence

!onscientious

Mastery

learning

8enerate

ideas

(*aluating

4pplications

Identify

relation

Identify

relation

>roblem

sol*ing

C1. LEARNIN# AREA: DIFFERENTIATIO

29






WEEKS

LEARNIN# O%&ECTI'ES S$##ESTED

TEACHIN# AND

LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LAR

Y


. Understand and

use the concept of

rates of change to

sol*e problems.

Use graphing

calculators with

computer base

ranger to

e'plore the

concept of rates

of change.

.1 #etermine rates of change

for related /uantities.

imit problems to 3

*ariables only.

!ooperation

#iligence

Mastery

Learning

8enerate ideas

5inding

relations

rates of

change

F. Understand and

use the concept of

small changes andappro'imations to

sol*e problems.

F.1 #etermine small changes in

/uantities.

F.2 #etermine appro'imate*alues using differentiation.

('clude cases in*ol*ing

percentage change.

!onfidence

Self access

Learning

4nalysing data

a0inginference

appro'imat

ion

7. Understand and

use the concept of

second deri*ati*e to

sol*e problems.

7.1 #etermine the second

deri*ati*e of function y f

+ x).

7.2 #etermine whether a

turning point is ma'imum

or minimum point of a

cur*e using the secondderi*ati*e.

Introduce2

2

dx

yd as

dx

dy

dx

d or

f M+ x) ( )( ) x f

dx

d ′ .

Rational

Self access

learning

!ooperation

Self access

learning

5inding

relations

a0ing

inference

>roblem sol*ing

second

deri*ati*e

17 6 1@ END,OF,YEAR EAMINATION

31



AST1. LEARNIN# AREA: SOL$TION OF TRIAN#LESNO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY

Students will be

taught to:


1 6

2=1.

Understand

and use the

concept of

sine rule to

sol*e

problems.

Use dynamic

geometry software

such as the

8eometer9s

0etchpad to

e'plore the sine

rule.

Use examples of real"

life situations toexplore the sine rule.

1.1 Derify sine rule.

1.2 Use sine rule to find un0nown

sides or angles of a triangle.

1.3 5ind the un0nown sides and

angles of a triangle in*ol*ing

ambiguous case.

1. ol*e problems in*ol*ing the

sine rule.

Include obtuse-angled

triangles.

Rational

Constructivism

!he use of

!echnology

%naly&e

Contextual

Exploratory

4ccuracy

Mastery Learning

Using

arithmetic,algebra,

formula

#rawing

diagrams

>roblem

sol*ing

sine rule

acute-angled

triangle

obtuse-angled

triangle

ambiguous

2.

Understand

and use the

concept of

cosine rule

to sol*e

problems.

Use dynamic

geometry software

such as the

8eometer9s

0etchpad to

e'plore the cosine

rule.

2.1 Derify cosine rule.

2.2 Use cosine rule to find

un0nown sides or angles of a

triangle.

Include obtuse-angled

triangles

Rational

%naly&e

!ooperation

Contextual

Identif

ying

pattern

s

#rawi

ng

diagra

ms

cosine rule

32



AST1. LEARNIN# AREA: SOL$TION OF TRIAN#LES

NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



Use e'amples of

real-life

situations to e'plore

the cosine rule.


cosine rule.

2. ol*e problems in*ol*ing sine

and cosine rules.

elf-Reliance

#iligence

Identifying

patterns

>roblems

sol*ing

elf-4ccess

earning

3.

Understand

and use the

formula for

areas of

triangles to

sol*e

problems.

Use dynamic

geometry software

such as the

8eometer9s

0etchpad to

e'plore the concept

of areas of

triangles.

Use e'amples of


to e'plore area of

triangles.

3.1 5ind the area of triangles using

the formula2

1ab sin C or its

e/ui*alent.

3.2 ol*e problems in*ol*ing three-

dimensional obects.

!ooperation

Identify shapes

Mastery

learning

'uture

Learning

Using

arithme

tic,

algebra,

formul

a

>roble

m

sol*in

g

three-

dimensional

obect

33



ASS1. LEARNIN# AREA: INDE N$M%ER

NO. OF

WEEKS

LEARNIN#

O%&ECTI'ES

S$##ESTED TEACHIN#

AND LEARNIN#

ACTI'ITIES


/ GENERICS

CCTS 'OCA%$LARY



21 -

221.

Understand

and use the

concept of

inde'

number to

sol*e

problems.

Use e'amples of


to e'plore inde'

numbers.

1.1 !alculate inde' number.

1.2 !alculate price inde'.

1.3 5ind (= or ( 1 gi*en rele*ant

information.

('plain inde' number.

( = ;uantity at base

time.

( 1 ;uantity at

specific time.

4ccuracy

!ooperation

Cooperative

>redicting

a0ing

inferences

Related to

something

a0ing

hypotheses

inde' number

price inde'

/uantity at

base time

/uantity at

specific time

2.

Understand

and use the

concept ofcomposite

inde' to

sol*e

problems

Use e'amples of


to e'plore

composite inde'.

2.1 !alculate composite inde'.

2.2 5ind inde' number or

weightage gi*en rele*ant

information.

2.3 ol*e problems in*ol*ing inde'

number and composite inde'.

('plain weightage and

composite inde'.

Independence

Oindness

ynthesi%ing

4nalysin

g

ol*e problems

composite

inde'

weightage

END,OF,YEAR HOLIDAYS : 21.11.09 , 0+.01.09

34

Documents

Ranadd Math Form 4yearplan2009