yearly plan add maths form 4

7/30/2019 Yearly Plan Add Maths Form 4

http://slidepdf.com/reader/full/yearly-plan-add-maths-form-4 1/26

Week

No

Learning Objectives

Pupils will be taught

to.....

Learning Outcomes

Pupils will be able to…

Suggested Teaching & Learning

activities/Learning Skills/Values

Points to Note

Topic/Learning Area Al : FUNCTION --- 3 weeks

1. Understand the

concept of relations.

1 Represent relations using

2 arrow diagrams

3 ordered pairs

4 graphs

5 Identify domain, co domain,

object, image and range of a

relation.

1.3 Classify a relation shownon a mapped diagram as: oneto one, many to one, one tomany or many to manyrelation.

Use pictures, role-play and

computer software to introduce the

concept of relations.

Skill : Interpretation, observe

connection between domain, codomain, object, image and range of

a relation.

Use of daily life examples

Values : systematic

Discuss the idea of set and introduce

set notation.

Emphasis :

(a) f(x) as image

(b) x as object

2. Understand theconcept 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 : x → 4x – 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 pairs or graphs,

e.g.

( ) x x f x x f 2,2: =→“ x x f 2: → ” is read as “function

f maps x to 2 x”.

• “ ( ) x x f 2= ” is read as “2 x is the

image of x under the function f ”.

Include examples of functions that

are not mathematically based.

Examples of functions includealgebraic (linear and quadratic),

trigonometric and absolute value.

Define and sketch absolute value

1



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

functions.

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 theother related function.

• Use arrow diagrams or algebraic

method to determine composite

functions.

• 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.

Example :

Given f : x→2x – 1. find function

g if

a. The composite function fg is

given as fg : x →7 – 6x b. composite function gf is given as

gf : x → 5/2x.

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.

4. Understand theconcept of inversefunctions.

4.1 Find the object by inverse

mapping given its image and

function.

• Limit to algebraic functions.

• Exclude inverse of composite

functions.

2



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

4.2 Determine inverse functions

using algebra.

4.3 Determine and state the

condition for existence of an

inverse function

Additional Exercises

Use sketches of graphs to show the

relationship between a function and

its inverse.

Examples :

Given f: x 23 +→ x , find1− f

• Emphasise that the inverse of a

function is not necessarily a

function.

Topic A2 : Quadratic Equations ---3 weeks

1. Understand the

concept of quadraticequations andtheir roots.

1.1 Recognise a quadratic

equation and express it ingeneral form.

1. 2 Determine whether agiven value is the root of aquadratic equation by

6 substitution;

a) inspection.

1.3 Determine roots of quadratic equations by

trial and improvementmethod.

Use graphing calculators or

computer software such as theGeometer’s Sketchpad andspreadsheet to explore the conceptof quadratic equations

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

Questions for 1..2(b) are given in

the form of ( ) ( ) 0=++ b xa x ; aand b are numerical values.

2. Understand theconcept of

quadraticequations.

2.1 Determine the roots of aquadratic equation by

a) factorisation;

b) completing the

If x = p and x = q are the roots, thenthe quadratic equation is

( ) ( ) 0=−− q x p x , that is

( ) 02 =++− pq xq p x .

Discuss when

( ) ( ) 0=−− q x p x , hence 0=− p x

or 0=− q x .

Include cases when p = q.

3



Week

No

Learning Objectives


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Learning Outcomes




Points to Note

square

c) using the formula.

2.2 Form a quadratic equation

from given roots.

Involve the use of:

b

aα β + = − and a

c

=αβ

where α and β are roots of thequadratic equation

02 =++ cbxax

Skills : Mental process, trial andimprovement method

Derivation of formula for 2.1c is

not required.

3. Understand anduse the conditionsfor quadraticequations to have

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 equations to:

a) find an unknown value;

b) derive a relation.


Giving quadratic equations with thefollowing conditions : 042 >− acb

042 =− acb , 042 <− acb

and ask pupils to find out the type of

roots the equation has in each case.

Using Geometer’s Sketchpad to show

the relationship between the values of

acb 42 − and the types of roots

Values: Making conclusion,connection and comparison

Explain that “no roots” means “noreal roots”.

4



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

Topic A3 : Quadratics Functions---3 weeks


quadraticfunctions and

their graphs.

1.1 Recognise quadraticfunctions

1) Use graphing calculators or

Geometer’s Sketchpad to explore the

graphs of quadratic functions.

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

b) f(x) = ax2 + bx

c) f(x) = ax2 + c

pedagogy : Constructivism

Skills : making comparison

& making conclusion

1.2 Plot quadratic functiongraphs:

a)based on giventabulated

values;

1 b) by tabulating values

2 based on given functions.

1) Use examples of everyday

situations to introduce graphs of

quadratic functions.

• Contextual learning

1.3 Recognise shapes of graphs of quadratic

functions.

Discuss the form of graph if

a > 0 and a < 0 for

( ) cbxax x f ++= 2

Explain the term parabola.

1.4 Relate the position of quadratic function graphswith types of roots for

Recall the type of roots if :

a) b2 – 4ac > 0

b) b2 – 4ac < 0

Relate the type of roots with

the position of the graphs.

5



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

( ) 0= x f .c) b2 – 4ac = 0

2. Find themaximum and

minimum valuesof quadratic

functions.

2.1 Determine the maximumor minimum value of a

quadratic function bycompleting the square.

Use graphing calculators or dynamicgeometry software such as the

Geometer’s Sketchpad to explore thegraphs of quadratic functions

Skills : mental process ,

interpretation

Students be reminded of the steps

involved in completing square and

how to deduce maximum or

minimum value from 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.


dynamic geometry software suchas the Geometer’s Sketchpad to

reinforce the understanding of graphs of quadratic functions.

Steps to sketch quadratic graphs:

a) Determining the form“∪” or

“∩”

b) finding maximum or minimum

point 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

Emphasise the marking of

maximum or minimum point andtwo other points on the graphs

drawn or by finding the axis of symmetry and the intersection with

the y-axis.

Determine other points by finding

the intersection with the x-axis (if it

exists).

4. Understand and usethe concept of

quadratic inequalities.

4.1 Determine the ranges of

values of x that satisfies

quadratic inequalities.


dynamic geometry software such as

the Geometer’s Sketchpad to

Emphasise on sketching graphs and

use of number lines when necessary.

6



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

explore the concept of quadratic

inequalities

1. Solvesimultaneousequations in twounknowns: one

linear equationand one non-

linear equation.

1.1 Solve simultaneousequations using thesubstitution method.


Geometer’s Sketchpad to explore the

concept of simultaneous equations.

Value: systematic

Skills: interpretation of mathematical

problem

Revise through solving simultaneous

linear equations before entering into

second degree equations.

Limit non-linear equations up to

second degree only.

1.2Solve simultaneousequations involving real-

life situations.


Use examples in real-lifesituations such as area, perimeter

and others.

Pedagogy: Contextual LearningValues : Connection between

mathematics and other subjects

7



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

Topic G1. Coordinate Geometry---5 weeks

1. Find distance between two

points.

1.1 Find the distance between

two points ( )11, y x ,

( )22 , y x using formula

Skill : Use of formula

Use the Pythagoras’ Theorem to find

the formula for distance between two

points.

2.Understand the

concept of division of linesegments

2.1Find the midpoint of two

given points.

2.2Find the coordinates of a point that divides a lineaccording to a given ratiom : n.

Skill : Use of formula

Value : Accurate & neat work

Limit to cases where m and n are positive.

Derivation of the formula

++

++

nm

myny

nm

mxnx 2121 ,

is not required.

3 Find areas of polygons.

3.1 Find the area of a triangle based on the area of specific geometricalshapes.

3.2 Find the area of a triangle

by using formula.

13

13

21

21

2

1

y y

x x

y y

x x

3.3 Find the area of aquadrilateral usingformula.

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.

Derivation of the formula:

−−

−++

3123

12133211

21

y x y x

y x y x y x y xis not

required.

Emphasise that when the area of

polygon is zero, the given points are

collinear.

8



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

4 Understand anduse the conceptof equation of astraight line.

4.1 Determine the x-interceptand the y-intercept of aline.

4.2 Find the gradient of a

straight line that passesthrough two points.

4.3 Find the gradient of astraight line using the x-

intercept and y-intercept

4.4 Find the equation of astraight line given:

a) gradient and one point;

b) two points;

c)x-intercept and y-

intercept.4.5Find the gradient and the

intercepts of a straight linegiven the equation.

4.6Change the equation of astraight line to the generalform

4.7Find the point of intersection of two lines.

Use dynamic geometry software suchas the Geometer’s Sketchpad toexplore the concept of equation of astraight line.

Skills : drawing relevant diagrams,

using formula, recognisingrelationship, compare and contrast.

Values : Neat & systematic

Pedagogy: contextual learning

Finding point of intersection of twolines by solving simultaneousequations

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

Involve changing the equation intogradient and intercept form

9



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

5. Understand and

use the conceptof parallel and

perpendicular

lines.

5.1 Determine whether two

straight lines are parallelwhen the gradients of

both lines are known and

vice versa.

5.2 Find the equation of astraight line that passes

through a fixed point and parallel to a given line.

5.3 Determine whether two

straight lines are perpendicular when thegradients of both lines areknown and vice versa.

5.4 Determine the equation of a straight line that passesthrough a fixed point and

perpendicular to a givenline.

5.5 Solve problems involvingequations of straightlines.

Use examples of real-life situations to

explore parallel and perpendicular lines.

Skill: Use of formula; makingcomparison

Students to be exposed to SPMexam type of questions.

Values : hard work, cooperative

Pedagogy : Mastery learning

Emphasise that for parallel lines:

21 mm = .

Emphasise that for perpendicular lines

121

−=mm .

Derivation of 121 −=mm is not

required.

10



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

6 Understand and

use the conceptof equation of locus involving

distance between two

points.

6.1 Find the equation of locus that satisfies the

condition if:

a)the distance of a moving point from a fixed point isconstant;

b) the ratio of the distancesof a moving point fromtwo fixed points isconstant

6.2 Solve problems involvingloci.



explore equation of locus involvingdistance between two points.Use graphic calculators and dynamic

geometry software such as theGeometer’s Sketchpad to explore the

concept of parallel and perpendicular lines.

Value : Patience, hard working

Pedagogy: contextual learningSkill : drawing relevant diagrams

11



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

Topic T1: Circular Measures---3 weeks


radian.

1.1 Convert measurements in

radians to degrees andvice versa.

Use dynamic geometry software such

as the Geometer’s Sketchpad to

explore the concept of circular

measure.

Students measure angle subtended at

the centre by an arc length equal the

length of radius. Repeat with different

radius.

Skill : contextual learning

Value : Accurate, making conclusion.

Discuss the definition of one radian.“rad” is the abbreviation of radian.

Include measurements in radians

expressed in terms of π.

π rad = 1800

2. Understand and use

the concept of length

of arc of a circle to

solve problems.

bulatan

2.1 Determine:

i) length of arc;

radius; and

iii) angle subtended atthe centre of a circle

based on given information.

Use examples of real-life situations toexplore circular measure.Derivation of S = j θ by use of ratio or

by deduction using definition of radian.Skill : Making conclusion or deduction, application of formula

Major and minor arc lengthsdiscussedEmphasize that the angle must be inradian.Students can also use formula

S= 2360

x jπ

°×

°when the angle

given is in degree

2.2 Find perimeter of segments of circles.2.3 Solve problemsinvolving lengths of arcs.

Solving problems with help of diagrams

Value : Accurate

Perimeter of segment

= 2j sin2

θ +jθ

12



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

3. Understand and

use the conceptof area of sector of a circle to

solve problems

3.1 Determine the:

a) area of sector;

b)radius; and

c)angle subtended at thecentre of a circle

based on given information.

3.2 Find the area of segmentsof circles.

3.3 Solve problems

involving areas of sectors.


Deriving the formula L= ½ j2 θ

Using ratio

Skill : drawing relevant diagrams ,

recognising relationship & makingconclusion

Value : Systematic & logical

Emphasize that the angle must be in

radian.Area of major sektor need to bediscussed

Students can also use formula

L=2

360

x jπ

°×

°if the angle given is

in degree.

21Area of sector =

2 j θ ,

emphasize that mustbe in radianθ

Area of segment = ( )21sin

2 j θ θ −

1. Understand anduse the concept

of indices andlaws of indicesto solve

problems.

1.1 Find the value of numbersgiven in the form of:

integer indices.

fractional indices.

1.2 Use laws of indices to findthe value of numbers inindex form that aremultiplied, divided or raised to a power.


introduce the concept of indices.

Use computer software such as the

spreadsheet to enhance the

understanding of indices.

Pedagogy : Constructivism

Skill : making inference, use of laws

Value : systematic, logical thinking

Discuss zero index and negative

indices.

Can show the following

0 m ma a −=

1

m

m

a= =

1.3 Use laws of indices tosimplify algebraicexpressions

13



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

2. Understand and

use the conceptof logarithmsand laws of

logarithms tosolve problems.

2.1 Express equation in index

form to logarithm formand vice versa.

2.2 Find logarithm of anumber

Use scientific calculators to enhance

the understanding of the concept of logarithm.

Explain definition of logarithm.

N = ax; loga N = x with a > 0, a ≠ 1.

Value : systematic, abide by the laws

Pedagogy:Mastery learning

Emphasise that:

loga 1 = 0; loga a = 1.

Emphasise that:

a) logarithm of negative numbers isundefined;

b) logarithm of zero is undefined.Discuss cases where the given

number is in:a) index form

b) numerical form.

2.3 Find logarithm of

numbers by using laws of logarithms

2.4 Simplify logarithmicexpressions to thesimplest form.

Activities : Demonstration

Value : systematic and organised

Skill : recognising pattern andrelationship, application of laws

Discuss laws of logarithms

14



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

2 Understand and

use the changeof base of logarithms to

solve problems.

3.1 Find the logarithm of a

number by changing the base of the logarithm to asuitable base.

Aktivities : Demonstration

Questions and answersPedagogy: Mastery learning, problem solving

Discuss:

ab

b

alog

1log = ,

loglog

log

ca

c

bb

a=

3.2 Solve problems involvingthe change of base andlaws of logarithms.

Aktivities : DemonstrationPedagogy: Mastery learning

, problem solving.

4. Solve equations

involvingindices and

logarithms

4.1 Solve equations

involving indices.

Aktivities : Demonstration

Pedagogy: Mastery learning

, problem solving.

Equations that involve indices andlogarithms are limited to equationswith single solution only.

Solve equations involving indices

by:a) comparison of indices and bases;b) using logarithms.

. 4.2 Solve equations involvinglogarithms.

Additional/reinforcementExercises on this topic

Values : Systematic & logicalthinking

15



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

Topic S1: Statistics ---4 Weeks

1 Understand anduse the conceptof measures of central tendencyto solve

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 from

histograms.

1.6 Calculate the mean of

grouped data

1.7 Calculate the median of

grouped data from

cumulative frequency

distribution tables.

1.8 Estimate the median of

grouped data from an ogive

Use scientific calculators, graphing

calculators and spreadsheets to

explore measures 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

thinking

Skill : classification, making

conclusion

Pedagogy :

1. Contextual learning

2. Constructivism

3. Multiple intelligence

Discuss grouped data and ungrouped

data.

Involve uniform class intervals only.

Derivation of the median formula is

not required.

Ogive is also known as cumulativefrequency curve.

16



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

1.9 Determine the effects on

mode, median and mean for a set of data when:

i) each data is changed uniformly;

ii) extreme valuesexist;

iii) certain data is added or

removed

1.10 Determine the most suitable

measure of central tendency

for given data.

Use Geometer’s Sketchpad to show

the effects on mode, median, meanfor a set of data when each data is

changed uniformly

Skills : Classification; observing

relationship, course and effect, able to

analise and make conclusion

Involve grouped and ungrouped data

2. Understand anduse the conceptof measures of dispersion tosolve problems.

2.1 Find the range of ungrouped data.

2.2 Find the interquartilerange of ungrouped data.

2.2 Find the range of

grouped data

Activities :1. Teacher gives real life exampleswhere values of mean, mode adnmedium are more or less the same andnot sufficient to determine theconsistency of the data and that leadto the need of finding measures of

dispersion

2.3 Find the interquartilerange of grouped datafrom the cumulativefrequency table

2.5 Determine the

Values :1. Honest2. cooperative

Determine the upper and lower quartiles by using the first principle.

17



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

interquartile range of grouped data from an

ogive.

2.6Determine the variance of

a)ungrouped data;

b)grouped data.

2.7 Determine the standarddeviation of:

(i) ungrouped data

(ii) grouped data.

Pedagogy : Contextual learning

2.8 Determine the effects onrange, interquartile range,variance and standarddeviation for a set of datawhen:

a) each data is changeduniformly;

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.

Skills :1. Compare and contrast2. Classification3. Problem Solving4. Sorting data from small to big

Pedagogy : Contextual learning

Values : Logical thinking Emphasise that comparison betweentwo sets of data using only measures

of central tendency is not sufficient.

18



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

1. Understand anduse the conceptof sine rule tosolve problems.

1.1Verify sine rule.

1.2Use sine rule to find

unknown sides or angles of a

triangle.

1.3Find the unknown sides and

angles of a triangle involving

ambiguous case

1.4Solve problems involving the

sine rule.

Use dynamic geometry software suchas the Geometer’s Sketchpad toexplore the sine 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 cosine rule tosolve problems.

2.1 Verify cosine rule.

2.2 Use cosine rule to findunknown sides or anglesof a triangle.

2.3 Solve problemsinvolving cosine rule.

2.4Solve problemsinvolving sine andcosine rules

Use dynamic geometry software suchas the Geometer’s Sketchpad toexplore the cosine rule.


explore the cosine rule.

Acticities : DemonstrationSkill : Interpretation of datas givenValue : Accuracy.

Include obtuse-angled triangles

19



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

3. Understand and usethe formula for areas of triangles to

solve problems.

3.1 Find the areas of triangles

using the formula C ab sin2

1

or its equivalent

3.2.Solve problems

involving three-dimensional objects.


Use dynamic geometry software suchas the Geometer’s Sketchpad toexplore the concept of areas of

triangles.

Use dynamic geometry software suchas the Geometer’s Sketchpad to

explore the concept of areas of triangles.

Skills : Recognising RelationshipAnalising data

Use examples of real-life situations toexplore area of triangles.

Value : Systematic

20



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

Topic ASS1: INDEX NUMBER---1 week


the concept of index number to

solve problems

1.1 Calculate index number.

1.2 Calculate price index.

Find Q0 or Q 1 given relevant

information.


explore index numbers.Skill : Analise, problem solving

Value : Systematic, thrifty Q0 = Quantity at base time.Q1 = Quantity at specific time.


the concept of composite index tosolve problems

2.1 Calculate composite index.

2.2 Find index number or weightage given relevantinformation.

2.3 Solve problems involving

index number and composite

index.Additional Exercises or

past year questions


explore composite index. EgComposite index of share.

Skill : Analise, problem solvingValue : SystematicUse daily life examples:e.g monthly expenditure;national budget; etc

Explain weightage and composite

index using real life examples likemonthly expenditure in bar chart or

pie chart etc

21



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note


the concept of firstderivative of

polynomial

functions to solve

problems.

2.1 Determine the firstderivative of the function

nax y = using formula.

2.2 Determine value of thefirst derivative of the

function nax y = for a

given value of x.

2.3Determine first derivativeof

a function involving:

a) addition, or

b) subtractionof algebraic terms.

2.4Determine the firstderivative of a product of two polynomials.

2.5 Determine the firstderivative of a quotient of

two polynomials.

2.6Determine the first

derivative of compositefunction using chain rule.

2.7Determine the gradient of

tangent at a point on acurve.

Pedagogy : Constructivism

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

Value : Logical thinking,Perserverance

Activities : Explanation anddemonstration by teacher

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

23



Week

No

Learning Objectives


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Learning Outcomes




Points to Note

2.8Determine the equation

of tangent at a point on acurve.

2.9 Determine the equationof normal at a point on a

curve

3. Understand and

use the conceptof maximum

and minimumvalues to solve

problems.

3.1 Determine coordinates of

turning points of a curve.

3.2 Determine whether a

turning point is a maximumor a minimum point.

3.3 Solve problems involving

maximum or minimum

values.

Use graphing calculators or dynamic

geometry software to explore theconcept of maximum and minimum

valuesPedagogy : Constructivism

Value : rational

Skills : Interpretation of problem; Application of appropratemethod/formula

Emphasise the use of first derivative

to determine the turning points.

Limit problems to two variables

only.Exclude points of inflexion.

Limit problems to two variables only

4. Understand anduse the concept

of rates of change to solve

problems.

4.1 Determine rates of change for related

quantities.

Value : logical thinkingUse graphing calculators withcomputer base ranger to explore the

concept of rates of change.Skills : Interpretation of problem; Application of appropratemethod/formula

Limit problems to 3 variables only.

5. Understand and

use the concept of

small changes and

approximations to

solve problems.

5.1 Determine small changes in

quantities

5.2 Determine approximatevalues using

Skills : Interpretation of problem; Application of appropratemethod/formulaValue : Accuracy

Exclude cases involving percentagechange.

24



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

differentiation.


the concept of

second derivative

to solve problems.

6.1 Determine the second

derivative of ( ) x f y = .

6.2 Determine whether a

turning point is maximum or

minimum point of a curve

using the second derivative


Mathematical logic

Value : systematic problem solving

Introduce2

2

dx

yd as

dx

dy

dx

d or

( ) ( )( ) x f dx

d x f ''' =

25



Week

No

Learning Objectives


to.....

Learning Outcomes




Points to Note

PROJECT WORK

Carry out project work In carrying out the project work

1.1Define the problem/situation

to be studied.

1.2 State relevant conjectures

1.3 Use problem solving strategies

to solve problems

1.4 Interpret and discuss results.

1.5 Draw conclusions and/or

make generalisations based

on critical evaluation of

results.

1.6 Present systematic and

comprehensive written reports.

Emphasise the use of Polya’s four-step problem solving process.

Use at least two problem solving strategies.

Emphasise reasoning and effective mathematical communication.

26

yearly plan add maths form 4

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