Additional Mathematics Scheme of Work Form 4 (2012)

SEKOLAH MENENGAH AGAMA PERSEKUTUAN, LABU

ANNUAL SCHEME OF WORK - ADDITIONAL MATHEMATIC FORM 4 2012

TOPIC 1: FUNCTION

WEEK/DATE

SUB-TOPIC LEARNING OUTCOMESSUGGESTED TEACHING AND

LEARNING ACTIVITIES

MORAL VALUES/ TEACHING AIDS/USE OF TECHNOLOGY/ PEDAGOGICAL

APPROACHES

W1, W2 and W3

04 Jan-20 Jan

1. The concept of relations

Students will be able to Represent a relation using

a) arrow diagramsb) ordered pairsc) graphs

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

Classify a relation shown on mapped diagrams as: one to one, many to one, one to many or many to many relation.

Use pictures and role play to introduce the concept of relations.

Introduce set notation

Slide presentation

Love & respect Use of Power Point Presentations Website –

http://www.ugrad.math.ubc.ca/coursedoc/maths100/notes/zoo/ccomposite.html

2. The concept of functions

Recognize functions as a special relation.

Express functions using notation

Determine domain, object, image and range of a function.

Determine image of a function given the object and vice versa.

Works in groups to recognize functions as a special relation and determine domain, object, image and range of a function.

Slide presentation

Using Ms Excel to explore the image of function.

Worksheet Cooperation Rationality Cooperative Learning

Ms Power Point

1



WEEK SUB-TOPIC LEARNING OUTCOMESSUGGESTED TEACHING AND

LEARNING ACTIVITIES


APPROACHES3. The concept of

composite functions

3.1 Determine composition of two functions.

3.2 Determine 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 in slide presentation

Use algebraic method Works in pairs Use algebraic method

Cooperation

Power Point Presentation

Worksheet

4. The concept of inverse functions

4.1 Find object by inverse mapping given its image and function.

Use arrow diagrams in slide presentation

Use algebraic method Works in pairs

Freedom Power Point Presentation

Worksheet

TOPIC 2: QUADRATIC EQUATION


LEARNING ACTIVITIES


APPROACHESGeneral form of

Quadratic Equation

Students will be able to:1.1 Recognise quadratic equation

and express it in general form.

a) Discuss the characteristics of quadratic equation

b) Give handouts that have a lot of different kind of algebraic equation.

Moral Values/ CCTS : Co-operativeTeaching Aids : Graphic Calculator

WEEK SUB-TOPIC LEARNING OUTCOMES SUGGESTED TEACHING AND MORAL VALUES/ TEACHING AIDS/USE

2

LEARNING ACTIVITIESOF TECHNOLOGY/ PEDAGOGICAL

APPROACHES

W4 and W5

23 Jan-02 Feb

Solving a Quadratic Equation

1.2 Determine whether a given value is the root of a quadratic equation by a. substitutionb. inspection.

a) Discuss the number of roots of quadratic equation

b) give the questions which is x ≥ 1 and try to get the answer by using substitution and inspection.



1.3 Determine roots of a quadratic equation by trial and improvement method.

a) Discuss the number of roots of quadratic equation

b) give the questions which is x ≥ 1 and try to get the answer by using trial and improvement method.



Students will be able to:2.1 Determine the roots of a

quadratic equation by a. factorisationb. completing the squarec. using the formula.

a) Revise the technic of factorisation. b) Use computer software to discuss

the method of 2.1a and 2.1 b.

Moral Values/ CCTS : Co-operativeTeaching Aids : Computer Software

Form an Equation 2.2 Form a quadratic equation from given roots.

Discuss the reverse process of factorisation.


Nature of the roots Students will be able to:3.1 Determine types of roots of

quadratic equations from the value of b2 – 4ac.

Compare and observe the value of b2 – 4ac and types of roots by using table.

ax2+bx+c=0

a,b,c

x(use

formula)

b2 – 4ac Types

Moral Values : Co-operative, Rational thinkingTeaching Aids : Computer Software and LCDPedagogical Approaches : CCTS

WEEK SUB-TOPIC LEARNING OUTCOMES SUGGESTED TEACHING AND LEARNING MORAL VALUES/

3

ACTIVITIES

TEACHING AIDS/USE OF TECHNOLOGY/ PEDAGOGICAL APPROACHES

Nature of the roots 3.2 Solve problems involving b2 – 4ac in quadratic equations to:a. find an unknown value;b. derive a relation.

Groups discussion and presentation (different types of problem)

Moral Values : Co-operative, Rational thinking, hardworkingTeaching Aids : WorksheetPedagogical Approaches : Problem solving

TOPIC 3 : QUADRATIC FUNCTIONS


LEARNING ACTIVITIES


APPROACHES

W6 and W7

06 Feb-17 Feb

Quadratic Functions

Plotting Quadratic

Recognise quadratic function.

1.2 Plot quadratic function graphsa) based on given tabulated values.b) by tabulating values based on given functions.

Recognise shapes of graphs of

1. Identify various types of graphs:i) linear graphii) quadratic graphiii) inverse graphiv) cubic graph

2. Introduce the quadratic graph.Example :

i) y = x2

ii) y = 2x2

iii) y = 3x2

iv) y = x2 + cv) Identify everyday

situation involving quadratic graphs.

Example : i)roller coaster ii) pendulumiii) projectile motion

Cooperation

Honesty

Rationality

Self-reliance

4

W6 and W7

06 Feb-17 Feb

Function Graph quadratic functions.

Determine the maximum or minimum value of quadratic function by completing the square

Plotting quadratic function graph using tabulated values.

Sketching graph for quadratic function based on f(x) = ax2 + bx + c =0 , where a > 0 and a < 0 .Sketching graph for quadratic function

Diligence

Quadratic Inequality Determine the ranges of values of x that satisfies quadratic inequality

Graph sketchingNumber line

Cooperation

TOPIC 4 : SIMULTANEOUS EQUATIONS


LEARNING ACTIVITIES


APPROACHES

W8

20 Feb-

24 Feb

Simultaneous Equations.

Solve simultaneous

equations in two

unknowns: one

linear equation and

one non-linear

equation.

Solve simultaneous equations

using the substitution method.

Solve simultaneous equations involving real-life situations.

Use graphing calculators or dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of simultaneous equations.

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

Moral Value :

Self-reliance

Cooperation RationalityIntegrity

Teaching Aid :graphing calculators,dynamic geometry software

Pedagogical Approaches :

5

Cooperative learning,mastery learning.

TOPIC 5 : INDICES AND LOGARITHM


LEARNING ACTIVITIES


APPROACHES

W9, W11,W12

27 Feb-06 Apr

Indices and Law of Indices

Students will be able to:

1.1 Find the value of numbers given in the form of:a) integer indices.b) fractional indices.

1.2 Use laws of indices to find the value of numbers in index form that are multiplied, divided or raised to a power.

1.3 Use laws of indices to simplify algebraic expressions.

Use examples of real-life situations to introduce the concept of indices.

Use computer software such as the spreadsheet to enhance the understanding of indices.

Zero indices and negative indices should be explain.

Laws of indices

MS Excel

Suitable software

Rationality

Accuracy

Discipline

W1005 Mac -

Ujian 1

6

09 Mac

10 Mac -18 Mac

Cuti Sekolah Pertengahan Penggal 1

WEEK SUB-TOPIC LEARNING OUTCOMES SUGGESTED TEACHING AND LEARNING ACTIVITIES

MORAL VALUES/ TEACHING AIDS

Concept and Law of Logarithms

Students will be able to:2.1 Express equation in index

Definition of logarithm should be explain

MS Excel

Suitable software

7

W9, W11,W12

27 Feb-06 Apr

form to logarithm form and vice versa.

2.2 Find logarithm of a number.

2.3 Logarithm of numbers by using laws of logarithms.

2.4 Simplify logarithmic expressions to the simplest form.

where

Emphasis

Including cases, numbers are given in the form of

a) indicesb) numerical

Emphasis a) logarithm of a negative

number is not defined.b) logarithm of zero is not

defined.

Laws of logarithms

Rationality

Accuracy

Discipline

8


MORAL VALUES/ TEACHING AIDS

W9, W11,W12,W13

27 Feb-06 Apr

Change of Base of Logarithms

Students will be able to:3.1 Find the logarithm of a

number by changing the base of the logarithm to a suitable base.

3.2 Solve problems involving the change of base and laws of logarithms

Emphasis

Specially involving cases laws of logarithm and /or change of base of logarithm.

MS Excel

Suitable software

Rationality

Accuracy

Discipline

Solve Equations Involving Indices and Logarithms

Students will be able to:4.1 Solve equations involving

indices.

4.2 Solve equations involving logarithms.

Equations involving indices are solve by

a) comparing the indices and basesb) using logarithm

Equations involving indices and logarithm are restricted to one answer only.

MS Excel

Suitable software

Rationality

Accuracy

Discipline

9

TOPIC 6 : COORDINATE GEOMETRY


MORAL VALUES/TEACHING AIDS/USE OF TECHNOLOGY/PEDAGOGICAL APPROACHES

W14,W15,W16,W17

09 Apr-04 May

Coordinate geometry

Midpoint

Area of Triangle

1.1 Find the distance between two points using formula.

Use examples of real-life situations to find the distance between two points Accuracy,

GSP,

Contextual learning

2.1 Find the midpoint of two given points.

2.2 Find the coordinates of a point that divides a line according to a given ratio m : n.

-Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of midpoint of two given points

Systematic,

GSP

3.1 Find the area of a triangle based on the area of specific geometrical shapes.

3.2 Find the area of a triangle by using formula.

3.3 Find the area of a quadrilateral using formula.

-Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of area of polygons.

-Use for

substitution of coordinates into the formula.

Cooperation,

GSP,

Cooperative learning

10

W14,W15,W16,W17

09 Apr-04 May

Equation of Straight Line

4.1 Determine the x-intercept and the y-intercept of a line.

4.2 Find the gradient of a straight line that passes through two points.

4.3 Find the gradient of a straight line using the x-intercept and y-intercept.

Find the equation of a straight line given:

a) gradient and one point;

b) two points;

c) x-intercept and y-intercept.

4.5 Find the gradient and the intercepts of a straight line given the equation.

4.6 Change the equation of a straight line to the general form.

4.6 Find the point of intersection of two lines.

Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of equation of a straight line.

Cooperation,

GSP,

Cooperative learning

11

W14,W15,W16,W17

09 Apr-04 May

Equation Of Locus

5.1 Determine whether two straight lines are parallel when the gradients of both lines are known and vice versa.

5.2 Find the equation of a straight line that passes through a fixed point and parallel to a given line

5.3 Determine whether two straight lines are perpendicular when the gradients of both lines are known and vice versa.

5.4 Determine the equation of a straight line that passes through a fixed point and perpendicular to a given line.

5.5 Solve problems involving equations of straight lines.

Use examples of real-life situations to explore parallel and perpendicular lines.

Use graphic calculator and dynamic geometry software such as Geometer’s Sketchpad to explore the concept of parallel and perpendicular lines.

Graphic calculator,

GSP,

Compasses, protractor, set square

6.1 Find the equation of locus that satisfies 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 fixed points is constant.

6.2 Solve problems involving loci.

Use examples of real-life situations to explore equation of locus involving distance between two points.

Use graphic calculators and dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of parallel and perpendicular lines.

Abeyance,

Graphic calculator,

GSP

12

W18,W19,W20

07 May-

25 May

Peperiksaan Pertengahan Tahun

26 May-

10 June

Cuti Sekolah Penggal 1

13

TOPIC 7 : STATISTICS

WEEK SUB-TOPIC LEARNING OUTCOMES LEARNING SUGGESTED TEACHING AND ACTIVITIES

MORAL VALUES/TEACHING AIDS/USE OF TECHNOLOGY / PEDAGOGICAL APPROACHES

W21,

W22,

W23,

W24

11 June

-

06 July

Measures Of Central Tendency


1.1 Calculate the mean of ungrouped data.

1.2 Determine the mode of ungrouped data.

1.3 Determine the median of ungrouped data.

1.4 Determine 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.

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.

Teaching Aids

scientific calculators, graphic calculators and spreadsheets

Moral Values

cooperation, honesty

Pedagogical Approach

cooperative learningooperac

14


MORAL VALUES/TEACHING AIDS/USE OF TECHNOLOGY / PEDAGOGICAL

APPROACHES

W21,

W22,

W23,

W24

11 June

-

06 July

Students will be able to:1.7 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 for a set of data when:a) each data is changed

uniformly;b) extreme values exist;c) certain data is added or

removed.

i. Revision.

ii. Introducing formula

m = L+ ( N2

− F

f m) C

i. Revision

ii. Students work in group, calculate

mode, median and mean for a set of

data.

iii. Make changes to the data and then

every student in the group has to

calculate a new mode, median and

mean.

v. Students make conclusion.

Students should know how to calculate mode, median and mean.

15



APPROACHES

W21,

W22,

W23,

W24

11 June

-

06 July


1.10 Determine the most suitable measure of central tendency for given data.

i. Discussion of examples

ii. CD - presentation

iii. Written Exercise

Measures Of Dispersion

2.1 Find the range of ungrouped data.

2.2 Find the interquartile range of ungrouped data.

2.3 Find the range of grouped data.

2.4 Find the interquartile range of grouped data from the cumulative frequency table.

2.5 Determine the interquartile range of grouped data from an ogive.

2.6 Determine the variance ofa) ungrouped data;b) grouped data.

i. Intoducing the concept of Range of ungroup and group data.

ii. Discussion of concept by giving examples.


iv. CD- presentation

Students had learnt in Mathematics. (Refreshment)

- Introducing formula for variance.

Systematic

Moral ValueAccuracy

16

WEEK SUB-TOPIC LEARNING OUTCOMES SUGGESTED TEACHING AND LEARNING

ACTIVITIES


APPROACHES

W21,

W22,

W23,

W24

11 June

-

06 July

Students will be able to:2.7 Determine the standard

deviation of:a) ungrouped datab) grouped data.

2.8 Determine the effects on range, interquartile range, variance and standard deviation for a set of data when:a) each data is changed

uniformly; 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.

2.10

i. Intoducing the concept of standard

deviation of ungroup and group data.

ii. Discussion of concept by giving examples.


iv. CD- presentation

Standard deviation = √ var iance

Students investigate measures of central tendency and dispersion between two sets of data in real-life situations.

Moral Values Accuracy, systematic

Pedagogical ApproachesMastery learning, exploratory

Teaching AidsSpreedsheet

17

TOPIC 8 : CIRCULAR MEASURES

WEEK

SUB-TOPIC LEARNING OUTCOMESSUGGESTED T & L

ACTIVITIES

MORAL VALUES / TEACHING AIDS / USE OF TECHNOLOGY /

PEDAGOGICAL APPROACHS

W25,W26

09 July -20 July

Circular Measures Students will be able to :1.1 Convert measurements in

radian to degrees and vice versa.

Use dynamic geometry software such as Geometer’s Sketchpad to explore the concept of circular measure.

Moral Values : Rationality Integrity Courage Cooperation

Use of Technology : Geometer’s Sketchpad Power Point

Pedagogical Approachs Contextual Cooperative Learning

2.1 Determinea) length of arcb) radius; andc) angle subtended at the centre of a circle based on given information.2.2 Find perimeter of segments of

circles.2.3 Solve problems involving

lenghths of arcs.

Use examples of real-life situations to explore circular measure.

3.1 Determine a) area of sector;b) radius; andc) angle subtended at the centre of a circle based on given information.3.2 Find area of segments of circles3.3 Solve problems involving area

of sectors.

Use dynamic geometry software such as Geometer’s Sketchpad to explore the concept of circular measure.

18

TOPIC 9 : SOLUTION OF TRIANGLES

WEEK


ACTIVITIES



W27,W28

16 July -27 July

Solution of triangles 1.1 Verify sine rule1.2 Use sine rule to find unknown

sides or angles of a triangle1.3 Find unknown sides and angles

of a triangle in an ambiguous case

1.4 Solve problems involving the sine

Use dynamic geometry software such as the Geometer’s Sketchpad to explore the sine rule

Use examples of real-life situations to explore the sine rule

Diligence, cooperation, responsibility, helpfulness, self reliance, courageGSP, Power PointComputerCooperative LearningMastery learning

2.1 Verify cosine rule2.2 Use cosine rule to find unknown sides or angles of a triangle2.3 Solve problems involving cosine rule2.4 Solve problems involving sine and cosine rules

Use dynamic geometry software such as the Geometer’s Sketchpad to explore the cosine rule

Use example of real-life situations to explore the cosine rule

3.1 Find area of triangles using formula ½ ab sin C or its equivalent3.2 Solve problems involving three- dimensional objects

Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of area of triangles

Use examples of real-life situations to explore area of triangles

19

TOPIC 10 : DIFFERENTIATIONS

WEEK


ACTIVITIES



W29,W31,W32

06 Aug-

07 Sept

The Concept Of Gradients Of Curve And Differentiation

1.1 Determine The Value Of A Function When Its Variable Approaches A Certain Value.

1.2 Find The Gradient Of A Chord Joining Two Points On A Curve.

1.3 Find The First Derivative Of A Function Y = F(X), As The Gradient Of Tangent To Its Graph.

1.4 Find The Fist Derivative Of Polynomials Using The First Principles.

1.5 Deduce The Formula For First Derivative Of The Function Y = F(X) By Induction.

Using Graphic Calculator Using Gsp Values : Cautious Ccts : To Explore


W29,W31,W32

06 Aug-

07 Sept

First Derivative Of Polynomial Functions

2.1 Determine The First Derivative Of The Function Y = axn Using Formula.

2.2 Determine Value Of The First Derivative Of The Function Y = Axn For A Given Value Of X.

2.3 Determine First Derivative Of A Function Involving : Addition, Or Subtraction

Using Graphmatica Values : Collaborative, Cautious Ccts : To Interpret

Using Graphmatica Values : Collaborative, CautiousCcts : To Interpret


Diligence, cooperation, responsibility, helpfulness, self reliance, courage

20

W29,W31,W32

06 Aug-

07 Sept

Of Algebraic Terms.

2.4 Determine The First Derivative Of A Product Of Two Polynomials.

2.5 Determine The First Derivative Of A Quotient Of Two Polynomials.

2.6 Determine The First Derivative Of Composite Function Using Chain Rule.

2.7 Determine The Gradient Of Tangent At A Point On A Curve.

2.8 Determine The Equation Of Tangent At A Point On A Curve.

2.9 Determine The Equation Of Normal At A Point On A Curve.

Using Graphmatica Values : Collaborative, CautiousCcts : To Interpret

GSP, Power PointComputerCooperative LearningMastery learning

Maximum And Minimum Values

3.1 Determine Coordinates Of Turning Points Of A Curve

3.2 Determine Whether A Turning Point Is A Maximum Or A Minimum Point.

3.3 Solve Problems Involving Maximum Or Minimum Point.

Using Graphic Calculator Using Gsp To Determine The

Coordinate Of Turning Point Values : Accurate Ccts : To Interpret


21

1. Rates Of Change

2. Small Changes And Approximations

3. Second Derivative

4.1 Determine Rates Of Change For Related Quantities.

5.1 Determine Small Changes In Quantities.

5.2 Determine Approximate Values Using

Differentiation.6.1 Determine The Second

Derivative Of Function Y=F (X)

6.2 Determine Whether A Turning Point Is Maximum Or Minimum Point Of A Curve Using The Second Derivative.

Using Graphic Calculator Using Gsp Values : Accurate, Cautious Values : Cautious Ccts : To Interpret Values : Cautious Ccts : To Interpret Using Gsp Values : Cautious, Collaborative


W29,W31,W32

06 Aug-

07 Sept

W3013 Aug

-17 Aug

Ujian 2

18 Aug-

26 Aug Cuti Sekolah Pertengahan Penggal 2

22

TOPIC 11 : INDEX NUMBER

Week Topic Learning Outcomes Suggested Teaching & Learning Activities

Moral Values/ Teaching Aids/ Use Of Technology/ Pedagogical Approaches

W33

10 Sept-

14 Sept

Index Number Students will be able to:1.1 Calculate index number1.2 Calculate price index1.3 Find Q0 or Q1 given relevant

information

Use examples of real-life situations to explore index numbers

Moral Values :CooperationHonesty

Pedagogical Approaches :Cooperative LearningExploratoryContextual

2.1 Calculate composite index2.2 Find index number or

weightage given relevant information.

2.3 Solve problems involving index number and composite index

Use examples of real-life situations to explore composite index

Moral Values :Cooperation

Pedagogical Approaches :ExploratoryContextual

W3417 Sept

-21 Sept

Ulangkaji/Latihtubi Soalan SBP Akhir Tahun 2011

23

W35

24 Sept-

28 Sept


W3601 Oct

-05 Oct


W37,W38,W39

08 Oct-

26 Oct

Peperiksaan Akhir Tahun 2012

W40,W41

29 Oct-

09 Nov

Jadual Anjal (Jawab Untuk Jaya)

10 Nov-

2 Jan 2013

Cuti Sekolah Penggal 2

24

Documents

Additional Mathematics Scheme of Work Form 4 (2012)