annual teaching plan addmath form 4 2012

8/2/2019 Annual Teaching Plan Addmath Form 4 2012

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ANNUAL TEACHING PLAN

ADDITIONAL MATHEMATICS FORM 4

WEEK/

CHAPTER/

DATE

LEARNING

OBJECTIVES

Pupils will be

taught to..

SUGGESTED

TEACHING AND

LEARNING

ACTIVITIES

LEARNING OUTCOMESPupils will be able to..

POINTS TO NOTE VOCAB

CHAPTER 1

FUNCTIONS

WEEK 1

46 Jan

1. Understand theconcept of relations

Use pictures, role-play and

computer software to

introduce the concept of

relations

i.Represent relations using:a) arrow diagramsb) ordered pairsc) graphs

ii. identify domain, object, image and range of the relationiii. classify the relation shown on a mapped diagrams as:

one-to-one, many-to-one, one-to-many or many-to-manyrelation

Discuss the idea of set and introduce setnotation

FunctionRelationObject

ImageRangeDomain

CodomainMapOrdered pairArrow diagram

2. Understand theconcept of

functions

Use graphing calculators orcomputer software to

explore the image of

functions

i.

Recognise functions as a special relationii. Express functions using functions notationiii. Determine domain, object, image and range of a functioniv. Determine the image of a function given the object and

vice versa

Represent functions using arrow diagrams,ordered pairs of graphs, e.g.

f :x 2x

f(x) = 2x

f :x 2xis read as function fmapsx

to 2x.f(x) = 2x is read as 2x is the image ofxunder the functionf

Include examples of functions that are notmathematically based.Examples of functions include algebraic

(linear and quadratic), trigonometric andabsolute value.Define and sketch absolute valuefunctions.

Notation

WEEK 2

913 Jan


composite

functions

Use arrow diagrams or

algebraic method to

determine the composite

functions.

i. Determine composition of two functionsii. Determine the image of composition function given the

object and vice versaiii. Determine one of the functions in a given composition

function given the other related functions

Involve algebraic functions onlyImage of composite functions include a

rage of values. (Limit to linear compositefunctions)

Inverse mapping

Composite function

WEEK 3

1620 Jan

4. Understand theconcept of inverse

functions

Use sketches of graphs to

show the relationshipbetween a function and its

inverse

i. Find the object by inverse mapping given its image andfunction.ii. Determine inverse functions using algebra.

iii. Determine and state the condition for existence of aninverse function

Limit to algebraic functions.

Exclude inverse of composite functionsEmphasise that inverse of a function is notnecessarily a function

WEEK 4

2327 JanCHINESE NEW YEAR

CHAPTER 2

QUADRATIC

EQUATIONS


quadratic equations

Use graphing calculators or

computer software such as

Geometers Sketchpad and

i. Recognise a quadratic equations and express it in generalform

ii. Determine whether a given value is the root of aQuadratic for 1.2(b) are given in form of;

a and b are numerical values.

Quadratic equationGeneral form

Root


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WEEK 5

30 Jan3 Feb

and their roots. spreadsheet. quadratic equation by:a. Substitution. Inspection

iii. Determine roots of quadratic equations by trial andimprovement method.

SubstitutionInspectionTrial and improvement

method

WEEK 6

610 Feb


quadratic equations

i. Determine the roots of quadratic equations by:a. Factorisationb. Completing the squarec. Use the formula

ii. Form a quadratic equation from given roots.

Discuss when(xp)(xq) = 0 hence

xp = 0 orxq = 0Include cases whenp = qDerivation of formula for 2.1(c) is notrequired.Ifx =p andx = q are the roots,

then the quadratic equation is(xp)(xq)=0, that is

x2(pq)x +pq = 0

Involve the use of:

+ = -

and =

where and areroots of the quadraticequationax2 + bx + c = 0

WEEK 7

1317 Feb

3. Use the conditions forquadratic eqns to

havea.2 different roots;b.2 equal roots;c.no roots

i. Determine types of roots of quadratics from the value ofb24ac.

ii. Solve problems involvingb24ac in quadratic equations to:a. find an unknown value,b. derive a relation.

b24ac > 0

b24ac = 0

b24ac < 0Explains no roots means no real roots

Discriminant

Real root

CHAPTER 3

QUADRATIC

FUNCTIONS

WEEK 82023 Feb


quadratic fns andtheir graphs.

Using graphing calculator

or computer software suchas Geometers Sketchpad

i. Recognise quadratic functions.ii. Plot quadratic function graphs;

a. based on given tabulated values,b.

by tabulating values based on given functionsiii. Recognise shapes of graphs of quadratic functions.

iv. Relate the position of quadratic function graphs withtypes of roots for f(x) = 0

Discuss cases where a > 0 and a < 0 forf(x) = ax2 + bx + c

Quadratic function

Tabulated valuesAxis of symmetry

ParabolaMax and min ptCompleting the square

WEEK 9

27 Feb2 Mar

2. Find the max andminimum values

Using computer software such

as Geometers SketchpadUse examples of real lifesituations such as area,perimeter and others.

i. Determine the maximum or minimum value of aquadratic function by completing the square.

WEEK 10

59 MarCENTRALISED TEST 1 (5 - 9 Mar 2012)

MID-FIRST SEMESTER BREAK (10 18 Mar 2012)

WEEK 11

1923 Mar

3. Sketch graphs ofquadratic functions.

Using computer software such

as Geometers SketchpadUse examples of real life

situations such as area,perimeter and others.

i. Sketch quadratic function graphs by determining themaximum or minimum point and two other points.

Emphasise the marking of maximum or

minimum point on the graphs drawn or byfinding the axis of symmetry and the

intersection with they-axis.Determine other points by finding theintersection with thex-axis (if it exists)

SketchIntersection

Vertical lineQuadratic

InequalityRangeNumber line

WEEK 12

26 Apr

4. Understand and usethe concept of

quadratic

inequalities.

i. Determine the ranges of values ofx that satisfiesquadratic i nequalities.

Emphasise on sketching graphs and use ofnumber lines when necessary.


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CHAPTER 4

SIMULTANEOUS

EQUATION

WEEK 13

913 Apr

1. Solve simultaneousequations in 2

unknowns:

1 linear &1 non-

linear equation.

i. Solve simultaneous equations using the substitutionmethod.

ii. Solve simultaneous equations involving real lifesituations.

Limit non-linear equations up to second

degree only.

Simultaneousequations

IntersectionSubstitution method

CHAPTER 5

INDICES &LOGARITHMS

WEEK 14

1620 Apr


indices and laws of

indices.

Use examples of real life

situations to introduce theconcept of indices.

Use computer software such

as spreadsheet.

i. Find the values of numbers given in the form of:a. Integer indices,. Fractional indices.ii. Use laws of indices to find the values of numbers in

index form that are multiplied, divided or raised to apower.

iii. Use laws of indices to simplify algebraic expression.

Discuss zero index and negative indices

Base

Integer indicesFractional indicesIndex form

Raised to a powerLaw of indices

WEEK 152327 Apr

2. Understand and usethe concept and

laws of logarithms

to solve problems.

Use scientific calculators to

enhance understanding of

the concept of logarithms.

i. Express equation in index form to logarithm form andvice versa.

ii. Find logarithm of a number.iii. Find logarithm of numbers by using laws of logarithsm.iv. Simplify logarithmic expressions to the simplest form.

Explain definition of logarithm.

N= ax; logaN=x with a > 0, a1.Emphasise that:

. Logarithm of negative numbers isundefined;

. Logarithm of zero is undefined.Discuss cases where the given number is

in: index form, numerical form.Discuss laws of logarithms.

Index formLogarithm formLogarithm

Undefined

WEEK 16

30 Apr 4 May

3. Understand and usethe change of baseof logarithms

i. Find the logarithm of a number by changing the base ofthe logarithm to a suitable base.

ii. Solve problems involving the change of base and laws oflogarithms.

Discuss

log a b =

4. Solve equationsinvolving indices

and logarithms

i. Solve equations involving indices.ii. Solve equations involving indices.

Equations that involve indices andlogarithms are limited to equations with

single solution only.

Solve equations

involving indices by:a.comparison of

indices and bases,

b. using logarithmsCHAPTER 6

COORDINATE

GEOMETRY

WEEK 17 711/5

1. Find distancebetween two points


situations to find the distancebetween two points.

i. Find the distance between two points using formula. Use the Pythagoras Theorem to find theformula for distance between two points.

WEEK 18 - 19

14 - 25 MayFIRST SEMESTER EXAM (12 24 May 2012)

FIRST SEMESTER BREAK (26 May - 10 June 2012)

WEEK 20

1115 June

2. Understand theconcept of divisionof line segments.

i. Find the midpoint of two given points.ii. Find the coordinates of a point that divides a line rationm:n.

Limit to cases where m and n are positive.

Derivation of formula

isnot required.

WEEK 21

1822 June

3. Find areas ofpolygon.

Use dynamic geometry

software such as GeometersSketchpad.

Use

|

| for

substitution of coordinates into

the formula.

i. Find the area of a triangle based on the area of specificgeometrical shapes.

ii. Find the area of a triangle by using formula.iii. Find the area of a quadrilateral by using formula.

Limit to numerical values.Emphasis the relationship between the

sign of the value for area obtained with theorder of the vertices used.Derivation of the formula is not required.

Emphasise that when the area of a polygonis zero, the given points are collinear.

Area, PolygonGeometrical shape

QuadrilateralVertex, VerticesClockwise

AnticlockwiseModulus, Collinear


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WEEK 22

2529 Jun


equation of a

straight line.


software such as

Geometers Sketchpad.

i. Determine thex-intercept and they-intercept of a line.ii. Find the gradient of a straight line that passes through

two points.

iii. Find the gradient of straight line using thex-intercept andy-intercept.

iv. Find the equation of a straight line given:a. gradient and one point, b. points,c. x andy-intercepts

v. Find the gradient and the intercepts of a straight linegiven the equation.

vi. Change the equation of a straight line to the general formvii. Find the point of intersection of two lines.

Answers for learning outcomes 4.4a. and4.4b. must be stated in the simplest form.Involve changing the equation into

gradient and intercept form

x-intercept

y-interceptGradientStraight lineGeneral form

Intersection

Gradient formIntercept form

WEEK 23

26 July


parallel and

perpendicular lines.

i. Determine whether two straight lines are parallel whenthe gradients of both lines are known and vice versa.

ii. Find the equation of a straight line that passes through afixed point and parallel to a given line.

iii. Determine whether two straight lines are perpendicularwhen the gradients of both lines are known &vice versa.

iv. Determine the equation of a straight line that passesthrough a fixed point and perpendicular to a given line.

v. Solve problems involving equations of straight lines.

Emphasise that for parallel lines:m1 = m2Emphasise that for perpendicular lines:

Derivation ofm1m2 = -1 is not required.

ParallelPerpendicular

WEEK 24

913 July

6. Use concept ofequation of locus

involve distancebetween 2 points

i. 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 pointfrom two fixed points is constant.

ii. Solve problems involving loci.

Equation of locus

Moving point

Loci

CHAPTER 7

STATISTICS

WEEK 25

1620 July


measures of central

tendency to solve

problems.

i. Calculate the mean, mode, median of ungrouped data.ii. Determine the modal class of grouped data from

frequency distribution tables.iii. Find the mode from histograms.iv. Calculate the mean, and median of grouped data from

cumulative frequency distribution tables.v. Estimate the median of grouped data from an ogive.vi. 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.vii. Determine the most suitable measure of central tendency

for given data.

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.

Involve grouped and ungrouped data.VOCAB: MidpointCumulative frequency

Distribution tableOgive, Range, InterquartileMeasures of dispersion

Measure of central

tendencyMean. Mode, MedianUngrouped data

FrequencyDistribution tableModal class

Uniform classInterval, HistogramExtreme valueLower boundary

WEEK 26

2327 July


measures of

dispersion to solve

problems.

i. Find the range of ungrouped data.ii. Find the interquartile range of ungrouped data.iii. Find the range of grouped data.iv. Find the interquartile range of grouped data from the

cumulative frequency table.v. Determine interquartile range of grouped data fromogive.vi. Determine the variance of grouped and ungrouped data.vii. Determine the standard deviation of ungrouped and

grouped data.

Determine the upper and lower

quartiles by using the first principle.

Emphasise that comparison between

two sets of data using only measures

of central tendency is not sufficient.

Standard deviation

Class interval

Upper quartile

Lower quartile

Variance


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viii.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 to removed.

ix. Compare measures of central tendency and dispersionbetween two sets of data.

CHAPTER 8

CIRCULAR

MEASURE

WEEK 27

30 July3 Aug

1. Understand theconcept of radian.

Use dynamic geometrysoftware such as the

Geometers Sketchpad

i. Convert measurements in radians to degrees and viceversa.

Discuss the definition of one radian. radis the abbreviation of radian.

Include measurements in radians

expressed in terms of .

Radian

Degree

WEEK 28

610 AugCENTRALISED TEST 2 (6 10 Aug 2012)

WEEK 29

1317 Aug


length of arc of a

circle to solve

problems.


situations

i. Determine:a. length of arcb. radius,c. angle subtended at the centre of a circle based on

given information.ii. Find perimeter of segments of circles.iii. Solve problems involving lengths of arcs.

Length of arc

Angle subtended

Circle

Perimeter

Segment

3. Understand and usethe concept of area

of sector of a circleto solve problems.

i. Determine thearea of sector, radius, and angle subtended at the centre ofa circle based on given

ii. Find the area of segments of circles.iii. Solve problems involving areas of sectors.

Area

Sector

MID-SECOND SEMESTER BREAK (18 26 Aug 2011)

CHAPTER 9

DIFFEREN-

TIATION

WEEK 30

2731 Aug


gradients of curve

and differentiation


software such as

Geometers Sketchpad.

i. Determine the value of a function when its variableapproaches a certain value.

ii. Find the gradient of a chord joining two points on a curveiii. Find the first derivative of a functiony =f(x), as the

gradient of tangent to its graph.iv. Find the first derivative of polynomials using the first

principle.

v. Deduce the formula for first derivative of the functiony =f(x) by induction.

Idea of limit to a function can beillustrated using graphs.The concept of first derivative of a

function is explained as a tangent to acurve and can be illustrated using graphs.Limit toy = axn, a, n are constants, n = 1,

2, 3,

Notation off(x) is equivalent to

Wheny =f(x),f(x) read as fprime ofx

Limit

Tangent

First derivative

Gradient

Induction

Curve

Fixed point

WEEK 31037Sept

2.

Understand and usethe concept of first

derivative of

polynomial

functions to solve

problems.

i. Determine the 1st derivative ofy = axn using formula.ii. Determine value of the first derivative of the function for

a given value ofx.

iii. Determine first derivative of a function involvinga. addition, or b. subtraction of algebraic terms.iv. Determine 1st derivative of a product and quotient of 2

polynomials.v. Determine the first derivative of composite function using

chain rule.vi. Determine the gradient and equation of tangent at a point

on a curve.

vii. Determine the equation of normal at a point on a curve.

Limit cases in LO 2.5 through 2.7 to rules

introduced in 2.5 through 2.6

ProductQuotient

Composite

Function

Chain rule

Normal


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WEEK 32

1014 Sept

3. Understand and usethe concept of max

and min values to

solve problems.

i. Determine coordinates of turning points of a curve.ii. Determine whether a turning point is a max or min point.iii. Solve problems involving max or min values.

Emphasise the use of first derivative to

determine the turning points.Exclude points of inflexion.Limit problems to two variables only.

Turning point

Maximum and

minimum point

WEEK 33

1521 Sept

. Understand and usethe concept of rates

of change to solve

problems,


software such as

Geometers Sketchpad

i. Determine rates of change for related quantities . Limit problems to 3 variables only. Rate of changes5. Use the concept of

small changes and

approximations to

solve problems.

i. Determine small changes in quantities. Exclude cases involving percentagechange.

Approximation


second derivative to

solve problems.

i. Determine the second derivative ofy =f(x).ii. Determine whether a turning point is max or min point of

a curve using the second derivative.Introduce

as

orf(x) = (f(x)) Second derivative

CHAPTER 10

SOLUTION OF

TRIANGLES

WEEK 34

2428 Sept

1. Understand and usethe concept of sine

and cosine rule to

solve problems.


software such as

Geometers Sketchpad

i. Verify sine and cosine rule.ii. Use sine and cosine rule to find unknown sides or angles.iii. Find the unknown sides and angles of a triangle involving

ambiguous case.iv. Solve problems involving the sine rule.v. Find areas of triangles using formula ab sin C

Include obtuse-angled triangles.

Sine rule

Acute-angled triangleObtuse-angled triangleAmbiguous

Cosine rule, 3D object

CHAPTER 10

INDEX NUMBER

WEEK 35

37 Oct

1. Understand and usethe concept of indexnumber to solve

problems. Use examples of real life

situations to explore index

numbers.

i. Calculate index number.ii. Calculate price index.iii. Find Q0or Q1 given relevant information.

Explain index number.Q0 = Quantity at base time.Q1 = Quantity at specific time.

Index number

Price indexQuantity at base timeQuantity at specifictime


composite index tosolve problems

i. Calculate compostite index.ii. Find index number or weightage give relevant

informationii. Solve problems involving index number and composite

index.

Explain weightage and composite index

WEEK 36-38

824 OctSECOND SEMESTER EXAM (9 24 Oct 2012)

WEEK 39

29 Oct2 NovREVISION

WEEK 4059 Nov

annual teaching plan addmath form 4 2012

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