Yearly Plan ADD MATHS Form 4 (2012)

8/3/2019 Yearly Plan ADD MATHS Form 4 (2012)

1/17

WeekNo

Learning ObjectivesPupils will be taught

to.....

Learning Outcomes

Pupils will be able to

Suggested Teaching & Learning

activities/Learning Skills/ValuesPoints to Note

14 6 Jan

Orientation Form 4 (4 10Jan)

Topic 2 : Quadratic Equations

29 13 Jan

1. Understand the conceptof quadratic equationsand their roots.

1.1 Recognise a quadraticequation and express it ingeneral form.1. 2 Determine whether a givenvalue is the root of a quadraticequation by

a) substitution;b) inspection.

1.3 Determine roots of quadraticequations by trial andimprovement method.

Use graphing calculators or computersoftware such as the GeometersSketchpad and spreadsheet to explorethe concept of quadratic equations

Values : Logical thinkingSkills : seeing connection, usingtrial and improvement method.

Questions for 1..2(b) aregiven in the form of

( ) ( ) 0=++ bxax ; a and bare numerical values.

316 20

Jan

2. Understand theconcept of quadraticequation

2.1 Determine the roots of aquadratic equation bya) factorisation;

b) completing the square

c) using the formula.

2.2 Form a quadratic equation fromgiven roots.

Ifx=p andx= q are the roots, then the

quadratic equation is ( ) ( ) 0= qxpx ,that is ( ) 02 =++ pqxqpx .Involve the use of:

b

a + = and

a

c=

where and are roots of the

quadratic equation 02 =++ cbxax

Skills : Mental process, trial and

improvement method

Discuss when

( ) ( ) 0= qxpx , hence0=px or 0=qx .

Include cases whenp = q.

Derivation of formula for 2.1cis not required.

316 20

Jan

3. Understand and usethe conditions forquadratic equations tohave

a) two different roots;b) two equal roots;

c) no roots.

a)dua punca berbeza;

3.1 Determine types of roots of

quadratic equations from the value

of acb 42 .3.2 Solve problems involving

acb 42 in quadratic equationsto:a) find an unknown value;

b) derive a relation.

Additional Exercises

Giving quadratic equations with the

following conditions : 042 > acb

042 = acb , 042


2/17

WeekNo


to.....

Learning Outcomes




and comparison

423 27

Jan

23 24 Jan Cuti Umum Chinese New Year

25 Jan Cuti Peristiwa

26 27 Cuti Berganti

Topic 4 : Simultaneous Equations

530 Jan

3 Feb

1. Solve simultaneousequations in twounknowns: one linearequation and one non-linear equation.

1.1 Solve simultaneous equationsusing the substitution method.

1.2 Solve simultaneous equationsinvolving real-life situations.


Use graphing calculators or Geometers

Sketchpad to explore the concept of

simultaneous equations.

Value: Systematic

Skills: interpretation of mathematical

problem

Use examples in real-life situations suchas area, perimeter and others.

Pedagogy: Contextual LearningValues : Connection betweenmathematics and other subjects

Revise through solving

simultaneous linear equations

before entering into second

degree equations.

Limit non-linear equations up to

second degree only.

Topic 11: Index Number

6

6 10 Feb* 6 Feb

HariKeputera-an NabiMuhdS.A.W

1. Understand and use the

concept of index numberto solve problems

2. Understand and use theconcept of compositeindex to solve problems

1.1 Calculate index number.

1.2 Calculate price index.

1.3 Find Q0 orQ1 given relevant

information.

2.1 Calculate composite index.

2.2 Find index number orweightage given relevantinformation.

2.3 Solve problems involving index

number and composite index.

Additional Exercises orpast year questions

Use examples of real-life situations to

explore index numbers.Skill : Analise, problem solvingValue : Systematic, thrifty

Use examples of real-life situations toexplore composite index. Eg Compositeindex of share.

Skill : Analise, problem solvingValue : SystematicUse daily life examples:

e.g monthly expenditure;national budget; etc

Q0 = Quantity at base time.

Q1 = Quantity at specific time.

Explain weightage and

composite index using real life

examples like monthly

expenditure in bar chart or pie

chart etc

2


3/17

WeekNo


to.....

Learning Outcomes




Topic 1 : FUNCTION

713 17

Feb

1. Understand theconcept of relations.

1.1 Represent relations usingarrow diagrams, ordered pairs &graphs

1.2 Identify domain, codomain, object,image and range of a relation.

1.3 Classify a relation shown on amapped diagram as: one to one,many to one, one to many or manyto many relation.

Use pictures, role-play and computersoftware to introduce the concept ofrelations.Skill : Interpretation, observe connectionbetween domain, codomain, object,image and range of a relation.

Use of daily life examples.

Values : systematic

Discuss the idea of set andintroduce set notation.

Emphasis :(a) f(x) as image(b) x as object

713 17Feb

2. Understand the concept

of functions.

2.1 Recognise functions as a special

relation..2.2 Express functions using function

notation.

2.3 Determine domain, object, image

and range of a function.

2.4 Determine the image of a function

given the object and vice versa.

Give examples of finding images given

the object and vice versa.(a) Given f : x4x x2. Find image of

5.

(b) Given function h : x 3x 12. Find

object with image = 0.

Use graphing calculators and computer

software to explore the image of

functions.

Represent functions using

arrow diagrams, ordered pairsor graphs, e.g.

( ) xxfxxf 2,2: = xxf 2: is read as

function fmapsxto 2x.

( ) xxf 2= is read as 2xis the image ofx under the

function f.

Include examples of functions

that are not mathematically

based.

Examples of functions includealgebraic (linear and quadratic),

3


4/17

WeekNo


to.....

Learning Outcomes




trigonometric and absolutevalue.

Define and sketch absolute

value functions.

820 24Feb

20 24Feb

KejohananSukan

TahunanSekolah

3. Understand theconcept of compositefunctions.

3.1 Determine composition of two

functions.

3.2 Determine the image of composite

functions given the object and vice

versa

3.3 Determine one of the functions in a

given composite function given the

other related function.

Use arrow diagrams or algebraic

method to determine compositefunctions.

Give examples of finding images given

the object and vice versa for composite

functions. For example :

Given f : x 3x 4. Find

(a) ff(2),

(b) range of value of x if ff(x) > 8.

Give examples for finding a function

when the composite function is given

and one other function is also given.

Involve algebraic functions only.

Images of composite functions

include a range of values. (Limit

to linear composite functions).

Define composite functions

Students do not need to find ff(x)

first then substitute x=2.

927 Feb

2 Mac

4. Understand the conceptof inversefunctions.

4.1 Find the object by inverse mapping

given its image and function.

4.2 Determine inverse functions using

algebra.

4.3 Determine and state the condition

for existence of an inverse function


Use sketches of graphs to show the

relationship between a function and its

inverse.

Examples :

Given f: x 23 + x , find1f

Limit to algebraic functions.

Exclude inverse of composite

functions.

Emphasise that the inverse of

a function is not necessarily a

function.

105 9 Mac

Mid Term Semester 1Examination

111018 Mac

Mid Term Semester 1

School Holiday

1219 23 Mac

Correction for Examination (Mid-Term Semester 1)

Topic 3 : Quadratics Functions

4


5/17

WeekNo


to.....

Learning Outcomes




1219 23 Mac

1. Understand theconcept of quadraticfunctions and theirgraphs.

1.1 Recognise quadratic functions.

1.2 Plot quadratic function graphs:a) based on given tabulated

values;

b) by tabulating values basedon given functions.

1.3 Recognise shapes of graphs ofquadratic functions.

1.4 Relate the position of quadraticfunction graphs with types of

roots for ( ) 0=xf .

Use graphing calculators or Geometers

Sketchpad to explore the graphs of

quadratic functions.

a) f(x) = ax2 + bx + c

b) f(x) = ax2 + bxc) f(x) = ax2 + c

Pedagogy : Constructivism

Skills : Making comparison & making

conclusion

Use examples of everyday situations tointroduce graphs of quadratic functions.

Contextual learning

Recall the type of roots if :

a) b2 - 4ac > 0

b) b2 - 4ac < 0

c) b2 - 4ac = 0

Discuss the form of graph if

a > 0 and a < 0 for( ) cbxaxxf ++= 2

Explain the term parabola.

Relate the type of roots with theposition of the graphs.

1326 30 Mac

2. Find the maximum andminimum values ofquadratic functions.

2.1 Determine the maximum orminimum value of a quadraticfunction by completing the

square.

Use graphing calculators or dynamicgeometry software such as theGeometers Sketchpad to explore the

graphs of quadratic functions

Skills : Mental process , interpretation

Students be reminded of the

steps involved in completing

square and how to deduce

maximum or minimum valuefrom the function and also the

corresponding values of x.

3. Sketch graphs of

quadratic functions.

3.1 Sketch quadratic function graphs

by determining the maximum or

minimum point and two other

points.

Use graphing calculators or dynamic

geometry software such as theGeometers Sketchpad to reinforce theunderstanding of graphs of quadraticfunctions.

Steps to sketch quadratic graphs:

a) Determining the form or

b) Finding maximum or minimum point

Emphasise the marking ofmaximum or minimum point andtwo other points on the graphsdrawn or by finding the axis ofsymmetry and the intersectionwith the y-axis.

Determine other points by

finding the intersection with thex-axis (if it exists).

5


6/17

WeekNo


to.....

Learning Outcomes




and axis of symmetry.

c) Finding the intercept with x-axis and y-

axis.

d) Plot all points

e) Write the equation of the axis of

symmetry

142 6April

4. Understand and usethe concept of quadraticinequalities.

4.1 Determine the ranges of values of

xthat satisfies quadratic

inequalities.

Use graphing calculators or dynamicgeometry software such as theGeometers Sketchpad to explore theconcept of quadratic inequalities.

Emphasise on sketching graphs

and use of number lines when

necessary.

Topic 5 : Indices and Logarithms

142 6April

6 AprilGoodFriday

1. Understand and use

the concept of indicesand laws of indices tosolve problems.

1.1 Find the value of numbers

given in the form of:integer indices.

fractional indices.1.2 Use laws of indices to find the

value of numbers in index form thatare multiplied, divided or raised toa power.

1.3 Use laws of indices to simplifyalgebraic expressions


introduce the concept of indices.

Use computer software such as thespreadsheet to enhance theunderstanding of indices.Pedagogy : ConstructivismSkill : making inference, use of lawsValue : systematic, logical thinking

Discuss zero index and negative

indices.

Can show the following

0

1

m ma a

ma

ma

=

= =

159 13April


the concept oflogarithms and lawsof logarithms to solveproblems.

2.1 Express equation in index form

to logarithm form and viceversa.

2.2 Find logarithm of a number.

Use scientific calculators to enhance the

understanding of the concept of logarithm.Explain definition of logarithm.N= ax; logaN=xwith a > 0, a 1.

Value : Systematic, abide by the laws

Pedagogy:Mastery learning

Emphasise that:

loga 1 = 0; logaa = 1.

Emphasise that:a) logarithm of negative numbers

is undefined;b) logarithm of zero is undefined.Discuss cases where the givennumber is in:a) index formb) numerical form.

6


7/17

WeekNo


to.....

Learning Outcomes




2.3 Find logarithm of numbers byusing laws of logarithms

2.4 Simplify logarithmic expressionsto the simplest form.

Activities : Demonstration

Value : systematic and organised

Skill : recognising pattern and

relationship, application of laws

Discuss laws of logarithms

16

16 20April

3. Understandand use the change ofbase of logarithms tosolve problems.

3.1 Find the logarithm of a numberby changing the base of thelogarithm to a suitable base.

3.2 Solve problems involving thechange of base and laws oflogarithms.

Activities : Demonstration, Questions andanswers

Pedagogy: Mastery learning, problem

solving

Discuss:

ab

b

alog

1log = ,

loglog

log

ca

c

bb

a=

Topic 7: Statistics

17

23 27April

1723 27April

1. Understand and use theconcept of measures ofcentral tendency tosolve problems.

1.1 Calculate the mean of ungrouped

data.1.2 Determine the mode of ungrouped

data.

1.3 Determine the median of

ungrouped data

1.4Determine the modal class of

grouped data from frequency

distribution tables.

1.5 Find the mode fromhistograms.

1.6 Calculate the mean of grouped

data1.7 Calculate the median of grouped

data from cumulative frequency

distribution tables.

1.8 Estimate the median of

grouped data from an ogive

1.9 Determine the effects on

mode, median and mean fora set of data when:

i) eachdata is changed uniformly;

ii) extreme values

Use scientific calculators, graphing

calculators and spreadsheets to exploremeasures of central tendency.

Students collect data from real-life

situations to investigate measures of

central tendency.

Eg. 1) Length of leaves in school

compound

2) Marks for Add maths in the class.

Values : Cooperative; honest , logical

thinkingSkill : classification, making conclusion

Pedagogy :

1. Contextual learning

2. Constructivism

3. Multiple intelligence

Use Geometers Sketchpad to show the

effects on mode, median, mean for a set

of data when each data is changed

uniformly

Discuss grouped data and

ungrouped data.

Involve uniform class intervals

only.

Derivation of the median formula

is not required.

Ogive is also known as

cumulative frequency curve.

Involve grouped and ungrouped

data

7


8/17

WeekNo


to.....

Learning Outcomes




exist;

iii) certain data is added or

removed

1.10 Determine the most suitable

measure of central tendency for

given data.

Skills : Classification; observing

relationship, course and effect, able to

analise and make conclusion

1830 April

4 May

1 MayHari

Pekerja

2. Understand and usethe concept ofmeasures ofdispersion to solveproblems.

2.1 Find the range of ungroupeddata.

2.2 Find the interquartilerange of ungrouped data.

2.2 Find the range of groupeddata

2.3 Find the interquartile rangeof grouped data from thecumulative frequency table

2.5 Determine the interquartile rangeof grouped data from an ogive.

2.6 Determine the variance of

a) ungrouped data;

b) grouped data.

2.7 Determine the standarddeviation of:

(i) ungrouped data

(ii) grouped data.

Activities :

Teacher gives real life examples where

values of mean, mode and median are

more or less the same and not sufficient

to determine the consistency of the data

and that lead to the need of finding

measures of dispersion.

Values :1. Honest

2. cooperative

Pedagogy : Contextual learning

Determine the upper and lower

quartiles by using the first

principle.

197 11

May

2.8 Determine the effects onrange, interquartile range, varianceand standard deviation for a set ofdata when:

a) each data is changed uniformly;

Skills :

1. Compare and contrast

2. Classification

3. Problem Solving

4. Sorting data from small to big

8


9/17

WeekNo


to.....

Learning Outcomes




b) extreme values exist;

c) certain data is added or

removed.

2.9 Compare measures of central

tendency and dispersion between

two sets of data.

Pedagogy : Contextual learning

Values : Logical thinking Emphasise that comparisonbetween two sets of data using

only measures of centraltendency is not sufficient.

20 2114 25

MayMid Year Examination

22 2326 May-10 Jun

Semester 1 School Holiday

2411 15

JunCorrection for Mid Year Examination Paper

Topic 6: Coordinate Geometry

24

11 15Jun

1. Find distance betweentwo points.

2. Understand the conceptof division of linesegments

1.1 Find the distance between two

points ( )11, yx , ( )22 , yx using formula.

2.1 Find the midpoint of two givenpoints.

2.2 Find the coordinates of a pointthat divides a line according toa given ratio m : n.

Skill : Use of formula

Skill : Use of formulaValue : Accurate & neat work

Use the Pythagoras Theorem to

find the formula for distance

between two points.

Limit to cases where m and n

are positive.

.

25

18 22Jun

3. Find areas of polygons. 3.1 Find the area of a trianglebased on the area of specificgeometrical shapes.

3.2 Find the area of a triangle byusing formula.

Values : Systematic & neat

Skills : use of formula , recognise

relationship and patterns

Limit to numerical values.

Emphasise the relationship

between the sign of the value for

area obtained with the order of

the vertices used.

9


10/17

WeekNo


to.....

Learning Outcomes




1

2x1

x2

y1

y2

x3 x1y3

y1

3.3 Find the area of a quadrilateralusing formula.

Derivation of the formula:

++

3123

12133211

2

1

yxyx

yxyxyxyx is

not required.

Emphasise that when the area of

polygon is zero, the given points

are collinear.

25

18 22Jun

4. Understand and usethe concept ofequation of a straightline.

4.1 Determine thex-intercept andthe y-intercept of a line.

4.2 Find the gradient of a straightline that passes through twopoints.

4.3 Find the gradient of a straightline using thex-intercept andy-intercept.

4.4 Find the equation of astraight line given:

a) gradient and one point;

b) two points;

c) x-intercept and y-intercept.

4.5 Find the gradient and theintercepts of a straight line giventhe equation.

4.6 Change the equation of astraight line to the generalform.

Use dynamic geometry software such as

the Geometers Sketchpad to explore the

concept of equation of a straight line.

Skills : Drawing relevant diagrams, using

formula, recognising relationship,

compare and contrast.

Values : Neat & systematic

Pedagogy: Contextual learning

Finding point of intersection of two lines

by solving simultaneous equations.

Answers for learning outcomes4.4(a) and 4.4(b) must be statedin the simplest form.

Involve changing the equation

into gradient and intercept form

10


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WeekNo


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Learning Outcomes




4.7 Find the point of intersectionof two lines.

2625 29Jun


the concept ofparallel and perpen-dicular lines.

5.1 Determine whether two straight

lines are parallel when thegradients of both lines areknown and vice versa.

5.2 Find the equation of a straightline that passes through a fixedpoint and parallel to a givenline.

5.3 Determine whether two straightlines are perpendicular whenthe gradients of both lines areknown and vice versa.

5.4 Determine the equation of a

straight line that passes througha fixed point and perpendicularto a given line.

5.5 Solve problems involvingequations of straight lines.


explore parallel and perpendicular lines.

Skill: Use of formula; making comparison

Use graphic calculators and dynamic

geometry software such as the

Geometers Sketchpad to explore the

concept of parallel and perpendicular -

lines.

Students to be exposed to SPM examtype of questions.

Values : hard work, cooperative

Pedagogy : Mastery learning

Emphasise that for parallel lines:

21 mm = .

Emphasise that for perpendicularlines

121 =mm .Derivation of 121 =mm is notrequired.

27

2 6 July

6. Understand and usethe concept ofequation of locus

involving distancebetween two points.

6.1 Find the equation of locus thatsatisfies the condition if:a) the distance of a moving point

from a fixed point is constant;b) the ratio of the distances of a

moving point from two fixedpoints is constant

6.2 Solve problems involving loci.


Use examples of real-life situations toexplore equation of locus involvingdistance between two points.

Value : Patience, hard working

Pedagogy: contextual learning

Skill : drawing relevant diagrams

Topic 8 : Circular Measures

28

9 13July

1. Understand theconcept of radian.

1.1 Convert measurements inradians to degrees and

vice versa.

Use dynamic geometry software such as

the Geometers Sketchpad to explore the

concept of circular measure.Students measure angle subtended at the

Discuss the definition of oneradian.

rad is the abbreviation ofradian.

11


12/17

WeekNo


to.....

Learning Outcomes




centre by an arc length equal the length of

radius. Repeat with different radius.

Skill : contextual learning

Value : Accurate, making conclusion.

Include measurements in

radians expressed in terms of .

rad = 1800

289 13

July


the concept of length of

arc of a circle to solve

problems.

bulatan

2.1 Determine:i) length of arc;

radius; andiii) angle subtended at thecentre of a circle

based on given information.

2.2 Find perimeter of segments ofcircles.

2.3 Solve problems involving

lengths of arcs.

Use examples of real-life situations toexplore circular measure.Derivation of S = j by use of ratio or bydeduction using definition of radian.Skill : Making conclusion or deduction,application of formula

Solving problems with help of diagrams

Value : Accurate

Major and minor arc lengths

discussed

Emphasize that the angle must

be in radian.

Students can also use formula

S= 2360

xj

when the angle

given is in degree

Perimeter of segment

= 2j sin2 +j

2916 20

July

3. Understand and usethe concept of area ofsector of a circle tosolve problems

3.1 Determine the:a) area of sector;

b) radius; andc) angle subtended at the

centre of a circlebased on given information.

3.2 Find the area of segments of

circles.

3.3 Solve problems involving areasof sectors.


Deriving the formula L= j2

Using ratio

Skill : Drawing relevant diagrams,

recognising relationship & making

conclusion

Value : Systematic & logical

Emphasize that the angle mustbe in radian.

Area of major sector need to be

discussed

Students can also use formula

L=2

360

xj

if the angle given

is in degree.

Topic 10: Solution of Triangles

12


13/17

WeekNo


to.....

Learning Outcomes




3023 27

July

3130 July 3

Aug

1. Understand and usethe concept of sinerule to solveproblems.

1.1 Verify sine rule.

1.2 Use sine rule to find unknown

sides or angles of a triangle.

1.3 Find the unknown sides and

angles of a triangle involvingambiguous case

1.4 Solve problems involving the sine

rule.

Use dynamic geometry software such asthe Geometers Sketchpad to explore thesine rule.

Use examples of real-life situations toexplore the sine rule.

Skill : Interpretation of problemValue : Accuracy

Include obtuse-angled triangles

2. Understand and usethe concept of cosinerule to solve problems.

2.1 Verify cosine rule.2.2 Use cosine rule to find unknown

sides or angles of a triangle.2.3 Solve problems involving cosine

rule.2.4 Solve problems involving sine

andcosine rules

Use dynamic geometry software such asthe Geometers Sketchpad to explore thecosine rule.Use examples of real-life situations toexplore the cosine rule.Acticities : Demonstration

Skill : Interpretation of datas givenValue : Accuracy.

Include obtuse-angled triangles

326 10

August

3. Understand and use theformula for areas oftriangles to solveproblems.

3.1 Find the areas of triangles using

the formula Cab sin2

1or its

equivalent.

3.2.Solve problems involving three-

dimensional objects.


Use dynamic geometry software such asthe Geometers Sketchpad to explore theconcept of areas of triangles.Use dynamic geometry software such asthe Geometers Sketchpad to explore theconcept of areas of triangles.Skills: Recognising Relationship,

Analising dataUse examples of real-life situations to

explore area of triangles.

3313 17August

EXAMINATION (MID-TERM SEMESTER 2)

3418 26

September

SCHOOL HOLIDAY MID-TERM SEMESTER 2

19 20 Sept Cuti Umum Hari Raya Puasa Aidil Fitri

3527 31

Aug

Correction for Examination (Mid-Term Semester 2)

13


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Learning Outcomes




Topic 9 : Differentiation

3527 31

Aug

31 AugustHari

Kebangsaan

362 - 7 Sept

1. Understand and usethe concept ofgradients of curve and

differentiation.

1.1 Determine the value of a functionwhen its variable approaches acertain value.

1.2 Find the gradient of a chordjoining two points on a curve.

1.3 Find the first derivative of a

function ( )xfy = , as thegradient of tangent to its graph.

1.4 Find the first derivative ofpolynomials using the firstprinciples.

1.5 Deduce the formula for firstderivative of the function( )xfy = by induction.

Use graphing calculators or dynamicgeometry software such as GeometersSketchpad to explore the concept of

differentiation.

Skills : Logical Thinking, relationship,application of rules, making inference,making deduction

Pedagogy : Constructivism

Activities : Explanation & demonstration

Values : accuracy, systematic, tolerance ,patient

Idea of limit to a function can beillustrated using graphs.

The concept of first derivative ofa function is explained as atangent to a curve can beillustrated using graphs.

Limit to naxy = ; a, n are

constants, n = 1, 2, 3.

Notation of ( )xf' is equivalent

todx

dywhen ( )xfy = ,

( )xf' read as fprimex.

3710 - 14

Sept


concept of first

derivative of polynomial

functions to solve

problems.

2.1 Determine the first derivative of

the function naxy = using

formula.2.2 Determine value of the first

derivative of the functionnaxy = for a given value ofx.

2.3 Determine first derivative of a

function involving:a) addit ion, orb) subtractionof algebraic terms.

2.4 Determine the first derivative ofa product of two polynomials.

2.5 Determine the first derivative ofa quotient of two polynomials.

2.6 Determine the first derivative ofcomposite function using chainrule.

2.7 Determine the gradient of

tangent at a point on a curve.2.8 Determine the equation of

Pedagogy : ConstructivismSkills : Logical Thinking, relationship,application of rules, making inference,making deductionValue : Logical thinking, Perserverance

Activities : Explanation and demonstrationby teacher

14


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Learning Outcomes




tangent at a point on a curve.2.9 Determine the equation of

normal at a point on a curve.

Limit cases in Learning Outcomes 2.7through 2.9 to rules introduced in 2.4through 2.6

3817 - 21

Sept

17 SeptCuti Umum

HariMalaysia

3. Understand and usethe concept of maximumand minimum values tosolve problems

3.1 Determine coordinates of turningpoints of a curve.

3.2 Determine whether a turningpoint is a maximum or a minimumpoint.

3.3 Solve problems involving

maximum or minimum values.

Use graphing calculators or dynamicgeometry software to explore the conceptof maximum and minimum valuesPedagogy : ConstructivismValue : Rational

Skills : Interpretation of problem;Application of approprate method/formulaValue : Logical thinking

Emphasise the use of firstderivative to determine the

turning points.

Limit problems to two variables

only.

Exclude points of inflexion.

Limit problems to two variables

only.

4. Understand and usethe concept of rates ofchange to solveproblems.

4.1 Determine rates of change forrelated quantities.

Use graphing calculators with computerbase ranger to explore the concept ofrates of change.Skills : Interpretation of problem;Application of approprate method/formula

Limit problems to 3 variables

only.

392 - 7 Sept


concept of small

changes and

approximation to solve

problems.

6. Understand and use theconcept of second

derivative to solve

problems.

5.1 Determine small changes in

quantities

5.2 Determine approximate valuesusing differentiation.

6.1 Determine the second derivative

of ( )xfy = .6.2 Determine whether a turning point

is maximum or minimum point of a

curve using the second derivative


Skills : Interpretation of problem;Application of approprate method/formulaValue : Accuracy

Mathematical logic

Value : systematic problem solving

Exclude cases involving

percentage change.

Introduce2

2

dxyd as

dxdy

dxd

or

( ) ( )( )xfdx

dxf ''' =

INTENSIVE REVISION (Chapter 4 , 10 & 11)

Week No. Topic Learning Outcomes : Suggested Teaching and Learning activities

15


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WeekNo


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Learning Outcomes




401 5 Oct

CHAPTER 4(Simultaneous Equation)

Solve the Simultaneous Equation using Substitution

Method

Drilling the basic algebraic skill such as :

Algebraic Expansion

Algebraic Expression

Linear Equation

Drilling through Pass Year questions Year 2003 2011

418 12 Oct

CHAPTER 10(Solution of Triangles)

Solve the problems involve the triangles in 2 Dimension Drilling through Pass Year question Year 2003 2011

4215 19 Oct

CHAPTER 11(Index Number)

Solve the problems involve Index Number Drilling through Pass Year questions Year 2003 2011

43-4422 Oct

2 Nov

End Year Examination

45

5 9 NovCorrection for Examination (End Year Examination)

4612 Nov 31 Dec

END YEAR SCHOOL HOLIDAY

(19 Nov Peperiksaan SPM bermula)

16

Checked by :

..(NORZITA BINTI WAHAB)Head of Science & MathsDepartment, SMK Merbau

Checked by :

..(TANG CHENG MUN)

Senior Assistant 1SMK Merbau, Miri

Prepared by :

..(WONG MEE LING)Subject teacher

Approved by :

..(ANG SIEW JIN)Senior Principal

SMK Merbau, Miri


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Yearly Plan ADD MATHS Form 4 (2012)

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