Yearlylessonplanaddmathf42010

Week/Learning

Area

Learning objectives

Learning outcomesSuggested activities

Points to noteTeaching

Strategies/ Skills

QUADRATICEQUATIONS

Week1 & 2

1. Understand the concept of quadratic equation and its roots.

1.1 Recognise a quadratic equation and express it in general form.

1.2 Determine whether a given value is the root of a quadratic equation bya) substitution;b) inspection.

1.3 Determine roots of quadratic

equations by trial and

improvement method.

Use graphing

calculators or computer software such as the Geometer’s Sketchpad and spreadsheet to explore the concept of quadratic equations.

.

Questions for 1.2(b) are given

in the form of (x + a)(x + b) =

0; a and b are numerical

values.

Noble value :Cooperation

TGA:Flashcard

Pedagogy :Activity/

Cooperative Learning

CCTS:Classification.

2. Understand the concept of quadratic equations.

2.1 Determine the roots of a quadratic equation bya) factorisation;b) completing the

squarec) using the formula.

Discuss when (x p)(x q) = 0, hence x – p = 0 or x – q = 0. Include case when p = q.

Derivation of formula for 2.1c is not required.

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

Value :Cooperation

TGA :Manila CardPedagogy :

Inquiry Finding, Constructisme

CCTS:Refresh idea

1

Week/Learning

Area

Learning objectives



Strategies/ Skills

2.2 Form a quadratic equation from given roots.

(xp)(xq)=0, that is x2(pq)xpq=0.

Involve the use of:

+ = and

= , Where and

are roots of the quadratic equationax2 +bx +c =0

and trial & error

Pedagogy:Mastery Learning

QUADRATICFUNCTIONS

Week 3 & 4

1. Understand the concept of quadratic functions and their graphs

1.1 Recognise quadratic functions

1.2 Plot quadratic functions graphsa) based on given

tabulated values b) by tabulating values based on given functions

1.3 Recognise shapes of graphs of quadratic functions

1.4 Relate the position of quadratic function graphs with types of roots for

f (x) = 0.

Use computer software or graphing calculator.(ex; GSP, Graphmatica or Microsoft Excel to explore the graphs of quadratic functions)

Use example of everyday situations to introduce graphs of quadratic functions.

Discuss the general shape of quadratic function.Introduce the term of parabola, minimum, maximum point and axis of symmetry for quadratic curves.

Discuss cases where and for

Mastery Learning

Contextual

2

Week/Learning

Area

Learning objectives



Strategies/ Skills

2. Find maximum and minimum values of quadratic functions

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

Use computer software or graphing calculator.(ex; GSP, Graphmatica or Microsoft Excel to explore the graphs of quadratic functions)

Discuss the general form of completing the square

Mastery Learning

Self-Access Learning

3. Sketch graphs of quadratic functions.

3.1 Sketch quadratic functions by determining the maximum or minimum point and two other points.

Use graphing calculator or dynamic geometry software such as the GSP or Graphmatica to reinforce the understanding of graphs of quadratic functions.

Emphasis the marking of maximum or minimum point and two other points on the graphs drawn or by finding the axis of symmetry and the intersection with the y – axisDetermine other points by finding the intersection with x-axis (if it exists )

Contextual

4. Understand and use the concept of quadratic inequalities.

4.1 Determine the ranges of values of x that satisfies quadratic inequalities

Use graphing calculator or dynamic geometry software such as the GSP or Graphmatica to reinforce the understanding of graphs of quadratic inequalities

Emphasis on sketching graphs and use number lines when necessary.

Contextual

3

Week/Learning

Area

Learning objectives



Strategies/ Skills

SIMULTANEOUS EQUATIONS

Week 5

Students will be taught to:

1. Solve simultaneous equations in two unknowns: one linear equation and one non - linear equation.

Students will be able to :

1.1Solve simultaneous equations using the the substitution method

1.2Solve simultaneous equations involving real life situations

Use graphing calculator or dynamic geometry software such as the Geometers Sketchpad to explore the concept of simultaneous equations

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

Limit non linear equations up to second degree only

Problem solving, discovery method, trial and improvement method.

ICT, relating, reasoning, Mathematical Communication, Mathematical Connections

FUNCTIONS

Week6 , 7 &8

1. Understanding the concept of relations.

1.1 Represent

relations using a)arrow diagrams b) ordered pairs c) graphs

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

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

Use pictures, role-play and computer software to introduce the concept of relations.

Discuss the idea of set and introduce set notation.

Contextual

4

Week/Learning

Area

Learning objectives



Strategies/ Skills

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.

Use graphing calculators and computer software to explore the image of functions.

Represent functions using arrow diagrams, ordered pairs or graphs.

e.g. f : x 2x f (x) = 2x"f : x 2x" is read as "function f maps x to 2x".

f (x) = 2x is read as “2x is the image of x under the function f ”.

Include examples of functions that are not mathematically based.

Cooperative learning

Examples of functions include algebraic (linear and quadratic), trigonometric and absolute value.

Define and sketch absolute value functions.

3. Understand the 3.1 Determine

5

Week/Learning

Area

Learning objectives



Strategies/ Skills

concept

of composite functions.

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

Use arrow diagrams or algebraic method to determine composite functions.

Involve algebraic functions only.

Images of composite functions include a range of values. (Limit to linear composite functions)

Mastery learning

b) given composite function given the other related function.

.

c)

d) 4. Understand the concept of inverse functions.

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

Limit to algebraic functions.

Exclude inverse of composite functions.

Emphasise that inverse of a function is not necessarily a function.

Mastery learning

9 e) Test 1

INDICES AND 1. Understand and use 1.1 Find the value of numbers Use examples of Discuss zero index and

Teaching

6

Week/Learning

Area

Learning objectives



Strategies/ Skills

LOGARITHMS

Week 10

the concept of indices and laws of indices to solve problems.

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.

real-life situations to introduce the concept of indices.

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

negative indices.Aids/materialsScientific calculator,Geometer’s Sketchpad, geometric set

CCTSIdentifying relationship

Teaching StrategiesMastery LearningMultiple intelligentContextual learning

2. Understand and use the concept of logarithms and laws of logarithms to solve problems

2.1 Express equation in index form to logarithm form and vice versa.

2.2 Find logarithm of a number.

2.3 Find logarithm of numbers by using laws of logarithms.

2.4 Simplify logarithmic expressions to the simplest form.

Use scientific calculators to enhance the understanding of the concept of logarithm.

xplain definition of logarithm.N = ax ; loga N = x with a >

0, a ≠ 1.Emphasise that:loga 1 = 0; loga a = 1.

Emphasise that:a) logarithm of negative

numbers is undefined;b) logarithm of zero is

undefined.

Discuss cases where the given number is ina) index formb) numerical form.Discuss laws of logarithms

7

Week/Learning

Area

Learning objectives



Strategies/ Skills

Week 113 Understand and use

the change of base of logarithms to solve problems.

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.

Discuss:

loga b =

Vocabulary

base

integer indices

fractional indices

index form

raised to a power

law of indices

index form

logarithm form

logarithmundefined

134. Solve equations

involving indices and logarithms.

4.1 Solve equations involving indices.

4.2 Solve equations involving logarithms.

Equations that involve indices and logarithms are limited to equations with single solution only.

Solve equations involving indices by: a) comparison of indices

and bases;

b) using logarithms

COORDINAT

GEOMETRY

Week 14

1. Find distance between two points

1.1

Find the distance between two points using formula

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

Use the Pythagoras’ Theorem to find the formula for distance between two points.

Moral ValuesCooperativePatriotismRespect

Teaching Aids/ Material ChartArrow diagramCCTSAnalogyRelationsImagine

2. Understand the concept of division of a line segment.

2.1 Find the midpoint of two given points.

Limit to cases where m and n are positive.

Derivation of the

8

Week/Learning

Area

Learning objectives



Strategies/ Skills

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

formula

is

not required.

Teaching StrategiesContextual

Week 15

3. Find areas of polygons

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

3.2Find the area of a triangle by using formula.

1321

1321

2

1

yyyy

xxxx

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.

Limit to numerical values.

Emphasise the relationship between the sign of the value for area obtained with the order of the vertices used.

Emphasise that when the area of polygon is 0, the given points are collinear.

Moral ValuesCooperative

Teaching Aids/ Material Grid Board

Teaching StrategiesContextualGenerate ideasThinking Skills

4. Understands use the concept of equation of a straight line.

4.1

Determine the x – intercept and y-intercept of a line

4.2

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

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

Moral ValuesHonestyAccuracy

Teaching Aids/ MaterialCharts, Graphical CalculatorCharts

9

1321

1321

2

1

yyyy

xxxx

Week/Learning

Area

Learning objectives



Strategies/ Skills

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

4.4Find the equation of a straight line given:

a) gradient and one point

b) two point

c) x-intercept and y-intercept

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

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

4.7 Find the point of intesection of two lines.

Answer for learning outcomes 4.4 (a) and 4.4(b) must be stated in the simplest form

involve

changing the equation into gradient and intercept form

Solve simultaneous linear equations using the graph method.

Teaching StrategiesMastery LearningContextual ApproachMastery Approach

Moral ValuesAccuracy

Teaching Aids/ Material Graph paper

Teaching StrategiesSelf Access Learning

16 5.Understand and use the concept of parallel and perpendicular lines.

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

5.2 Find equation of a

Use example of real-life situations to explore parallel end perpendicular lines.

Emphasize that for parallel lines:

Emphasize that for perpendicular lines :

Moral ValuesCooperationGratitudeCarefulSystematic

Teaching Aids/

10

Week/Learning

Area

Learning objectives



Strategies/ Skills

straight line that passes through a fixed point and parallel to a given line.

5.3 Determine whether two straight lines are perpendicular when 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 graphic calculator and dynamic geometry software such as Geometer’s Sketchpad to explore the concept of parallel and perpendicular lines.

Derivation of is not required.

Material Exact SystematicICTGrid Board

Teaching StrategiesSelf Access LearningLearn How to StudyMultiple IntelligentConstructivism approach

6. Understand and use the concept of equation of locus involving distance between two points.

6.1 Find the equations 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 calculator and dynamic geometry software such as Geometer’s Sketchpad to explore the concept


Teaching Aids/ Material Exact SystematicICTGrid Board

11

Week/Learning

Area

Learning objectives



Strategies/ Skills

of loci. 17 1. Understand and use

the concept of measures of central tendency to 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.

1.4 Determine the modal class of grouped data from frequency distribution tables.

1.5 Find the mode from histograms.

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.

Discuss grouped data and ungrouped data.

Involve uniform class intervals only.


Teaching Aids/ Material Exact SystematicICTGrid Board

Teaching StrategiesSelf Access LearningLearn How to StudyMultiple IntelligentConstructivism approach

1.6 Calculate the mean of grouped data.

1.7 Calculate the median of grouped data from cumulative frequency distribution tables.

Derivation of the median formula is not required.

Teaching Strategies

Self Access LearningLearn How to StudyMultiple Intelligent

12

Week/Learning

Area

Learning objectives



Strategies/ Skills

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.

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

Ogive is also known as cumulative frequency curve.

Involve grouped and ungrouped data

Constructivism approach

18 2. Understand and use the concept of measures of dispersion to solve problems.

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.

Determine upper and lower quartiles by using the first principle.

Vocabulary

measure of central tendency

mean

mode

median

ungrouped data

frequency distribution table

modal class

uniform class intervalhistogram

13

Week/Learning

Area

Learning objectives



Strategies/ Skills

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

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.

Emphasise that comparison between two sets of data using only measures of central tendency is not sufficient.

Mid Term Examination Week 19 - 20

CIRCULARMEASURES

Week


1. Understand

Students will be able to:

Convert measurements in radians to degrees and vice

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

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

Moral ValuesRational, patience

14

Week/Learning

Area

Learning objectives



Strategies/ Skills

21&22 the concept of radian

versa. of circular measure.

Or

Use worksheets of Polya's method to explore the concept of circular measures

Include measurements in radians expressed in terms of

Teaching Aids/materialsScientific calculator,Geometer’s sketchpad, geometric set

CCTSCompare and contrast

Teaching StrategiesContextual

VocabularyRadian,Degree

2. Understand and use the concept of length of arc of a circle to solve problems.

Determinea) length of arcb) radiusc) angle subtended

at the center of a circle.

Based on given information.

Find the perimeter of segments of circles

Solve problems involving lengths of arc.

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

Or

Use an experiment method to enhance the concept of length of an arc of a circle.

Moral ValuesDiligence, cooperate

Teaching Aids/materialsScientific calculator,Geometer’s Sketchpad, geometric set

CCTSIdentifying

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Week/Learning

Area

Learning objectives



Strategies/ Skills

relationship

CIRCULAR MEASURES

23


3. Understand and use the concept of area of sector of a circle to solve problems .

Students will be able to: 3.1 Determine :

a) area of sectorb) radius and c) angle subtended at

the centre of a based on given information

3.2 Find area of segments of circles.

3.3 Solve problems involving area of sectors.

Use Geometer’s Sketchpad to differentiate between area of a sector and area of segments of circles.

Or

Use worksheets of Polya's method to explore the concept of area of sector of a circle.

Moral ValuesDiligencecooperationfreedom

Teaching Aids/materialsScientific calculator,Geometer’s Sketchpad, geometric set

CCTSIdentifying informationProblem solving

Teaching StrategiesMastery LearningMultiple Intelligent

VocabularyAreaSector

DIFFERENTI

1. Understand and use the concept of gradients of

Level 11.1 Determine value of

a function when its Use graphing calculator or dynamic

Idea of limit to a function can be

Moral value : accurately

16

Week/Learning

Area

Learning objectives



Strategies/ Skills

ATION

Week24 - 27

curve and differentiation.

variable approaches a certain value.

1.2 Find gradient of a chord joining two points on a curve

Level 21.3 Find the first

derivative of a function y=f(x) as gradient of tangent to its graph

1.4 Find the first derivative for polynomial using first principles.

1.5 Deduce the formula for first derivative of function

y = axn by induction.

geometry software such as Geometer’s Sketchpad to explore the concept of differentiation.

illustrated using graphs.

Concepts of first derivative of a function are explained as a tangent to a curve can be illustrated using graphs.

Limit y = axn,a , n are constants n = 1,2,3.Notation f’(x)

equivalent to when

y= f(x).F’(x) read as “f prime x”.

Pedagogy : ContextualVocabulary : limit, tangent, First derivative, gradient, induction, curve , fixed point

Moral value : rationalPedagogy : Mastery Learning

2. Understand and use the concept of first derivative of polynomial functions to solve problems.

Level 22.1 Determine 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

Formula y = axn , then

= naxn-1

a, n are constant and n integer.y is a function of x.

Moral value : rationalPedagogy : Mastery Learning

17

Week/Learning

Area

Learning objectives



Strategies/ Skills

2.3 Determine first derivative of a function involvinga. addition orb. subtraction

algebraic terms.2.4 Determine first

derivative of a product of two polynomials.

2.5 Determine first derivative of a quotient of two polynomials

2.6 Determine first derivative of composite function using chain rule.

2.7 Determine gradient of tangent at a point on a curve.

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

2.9 Determine equation of normal at a point on a curve

Find when y=f(x) +

g(x) or y=f(x) – g(x), f(x) and g(x) is given

When y=uv, then

When y= , then

y=f(u) and u=g(x), then

Limit cases in learning outcomes 2.7 – 2.9 to rules Introduced in 2.4 – 2.6.

Pedagogy : Creative thinking

ABM : OHP

Vocabulary: product, quotient,Composite function, chain rule,Normal.

Moral value : independents, cooperationPedagogy: Mastering learning.

3. Understand and use the concept of

Level 23.1 Determine

Use graphing calculator or dynamic Emphasis the use of

Moral Values :Independendan

18

Week/Learning

Area

Learning objectives



Strategies/ Skills

maximum and minimum values to solve problems.

coordinates ofturning points of a curve.

3.2 Determine whether a turning points is a maximum or minimum point

Level 33.3 Solve problems involving maximum or minimum values

geometry software such as Graphmatica software to explore the concept of maximum and minimum values.

first derivative to determine turning points.

Exclude points of inflexion

Limit problems to two variables only.

tCooperation

CCTS:Identifying relationshipTeaching Strategies :Mastery Learning

4. Understand and use the concept of rates of change to solve problems

Level 24.1 Determine rates of change for related quantities

Use graphing calculator with computer base ranger to explore the concept of rates of change.

Limit problems to 3 variables only

Moral Values :Cooperation

CCTS:Identifying relationshipTeaching Strategies :Problem solvingContextual

5. Understand and use the concept of small changes and approximations to solve problems

Level 25.1 Determine small changes in quantities5.2 Determine approximate values using differentiation

y dyx dx

Exclude cases involving percentage change

Moral Values :SincereHardworking

19

Week/Learning

Area

Learning objectives



Strategies/ Skills

CCTS:

Teaching Strategies :Mastery Learning

6. Understand and use the concept of second derivative to solve problems

Level 26.1 Determine 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.

Introduce d 2 y as dx2

d dy ordx dx

f’’(x) =

Moral Values :IndependendantCooperation

CCTS:Identifying relationshipTeaching Strategies :Mastery Learning

Week

28 - 30

SOLUTION OF TRIANGLES

1. Understand and use the concept of sine rule to solve problems

1.1 Verify sine rule

1.2 Use sine rule to

Using GSP to verify the sine rule.

Discuss the acute Include obtuse-

Sine ruleAcute-angled triangleObtuse-angled triangleAmbiguous

20

Week/Learning

Area

Learning objectives



Strategies/ Skills

2. Understand and use the concept of cosine rule to

find unknown sides or angles of a triangle.

1.3 Find unknown sides and angles of a triangle in an ambiguous case.

1.4 Solve problems involving the sine rule.

2.1 Verify cosine rule

2.2 Use cosine rule to find unknown sides or

angle triangle and obtuse angle triangle.

Discuss on ambiguity cases where

i) non-included angle is given

ii) a < bQuestions involving real-life situations

Use GSP to explore the concept of cosine rule

Cosine rule

-Teams Work-Brainstorming

Discuss the acute angle triangle and obtuse angle triangle.

- Teams Work

angled triangles

Include obtuse-angled triangles Cosine rule

21

Week/Learning

Area

Learning objectives



Strategies/ Skills

solve problems

3. Understand and use the formula for area of

triangles to solve problems

angles of a triangle.

2.3 Solve problems involving cosine rule

Level 32.4 Solve problems involving sine and cosine rules

Level 23.1 Find area of triangle using formula

or its

equivalent

Level 33.2 Solve problems involving three-dimensional objects

Discussion

Non-rutin question

Area of triangle =

Related to suitable content

-Teams work

Three-dimensional object

INDEX NUMBER

Week 31 &


1. Understand and use the concept of index

Students will be able to:

1.1 Calculate index number.1.2 Calculate price index.1.3 Find Q0 or Q1 given

Explain index number. Index number has no units and no % symbol.

Q1 and Q0 must be of the same unit.

Moral values Accurate

Teaching aids/ Materials:

22

Week/Learning

Area

Learning objectives



Strategies/ Skills

33 number to solve problems.

relevant information.

Quantity at base time.

Quantity at specific time.

Use example of real-life situations to explore index numbers.

Newspaper

Vocabulary: Index number, Price index, quantity at base time, quantity at

specific time.

Pedagogy: Contextual

2. Understand and use the concept of composite index to solve problems

2.1 Calculate composite index.2.2 Find index number or weightage given relevant information.2.3 Solve problems involving index number and composite index

Explain weightage and composite index.

Use examples of real-life situations to explore composite index.

W can be simplifiedto the smallest numberaccording to ratio.

Moral Values: Accurate

Vocabulary:Composite indexWeightage

34 Revision ( Final SBP form 4 2006)

35 Revision ( Final Melaka Form 42006)

36 Revision ( Final SBP 2005)

37 Pep PMR / Akhir Tahun

38 Final Exam SBP

39 Final Exam SBP

23

Week/Learning

Area

Learning objectives



Strategies/ Skills

40 Progression

41 Progression

42 Progression

24

Yearlylessonplanaddmathf42010

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