Yearly Plan Add Math f4 2013

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    Topic A4: SIMULTANEOUS EQUATIONS---3 weeks

    1 1. Solve simultaneous equations in twounknowns: one linear equation andone non-linear equation.

    1.1 Solve simultaneous equations using thesubstitution method.

    4 Limit non-linear equations up tosecond degree only.

    2-3 1.2Solve simultaneous equations involving real-life situations.

    Additional Exercises

    2

    2

    Topic ASS1: INDEX NUMBER---2 week

    41. Understand and use the concept of index

    number to solve problems1.1 Calculate index number.1.2 Calculate price index.

    Find Q0 orQ1 given relevant information.

    11

    Q0 = Quantity at base time.Q1 = Quantity at specific time.

    5

    2. Understand and use the concept ofcomposite index to solve problems

    2.1 Calculate composite index.

    2.2 Find index number orweightage given relevantinformation.

    2.3 Solve problems involving index number andcomposite index.

    Additional Exercises orpast year questions

    2

    2

    2

    Explain weightage and compositeindex.

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

    First Term

    6 1. Understand the concept of relations. 0.1 Represent relations usinga) arrow diagramsb) ordered pairs

    c) graphs

    1 Discuss the idea of set andintroduce set notation.

    1

    Yearly Plan Additional Mathematics Form 4

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    0.2 Identify domain, co domain, object, image andrange of a relation.

    1.3 Classify a relation shown on a mapped

    diagram as: one to one, many to one, one tomany or many to many relation.

    1

    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 afunction.

    2.4 Determine the image of a function given the

    object and vice versa.

    1

    1

    Represent functions using arrow

    diagrams, ordered pairs orgraphs, e.g.

    ( ) xxfxxf 2,2: = xxf 2: is read asfunction fmaps x to 2x.

    ( ) xxf 2= is read as 2x isthe image of x under the

    function f.

    7 3. Understand the concept 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 givencomposite function given the other relatedfunction.

    1

    1

    2

    Involve algebraic functions only.

    Images of composite functions

    include a range of values. (Limit tolinear composite functions).Define composite functions

    84. Understand the

    concept of inversefunctions.

    4.1 Find the object by inverse mapping given itsimage and function.

    4.2 Determine inverse functions using algebra.

    4.3 Determine and state the condition for existence

    1

    1

    Limit to algebraic functions.

    Exclude inverse of composite

    functions.

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    of an inverse functionAdditional Exercises

    1

    1

    Emphasise that the inverse of a

    function is not necessarily afunction.

    Topic A2 : Quadratic Equations ---3 weeks

    9 1. Understand the concept of quadraticequations and their roots.

    1.1 Recognise a quadratic equation and express itin general form.

    1. 2 Determine whether a given value is the rootof a quadratic equation by

    a) substitution;

    b) inspection.

    1.3 Determine roots of quadratic equations by

    trial and improvement method.

    1

    1

    Questions for 1..2(b) are givenin the form of( ) ( ) 0=++ bxax ; a and b arenumerical values.

    10

    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.

    2.2 Form a quadratic equation from given roots.

    1

    1

    2

    Discuss when( ) ( ) 0= qxpx , hence

    0=px or 0=qx .

    Include cases when p = q.

    Derivation of formula for 2.1cis not required.

    3. Understand and use the conditionsfor quadratic equations to have

    a) two different roots;b) two equal roots;c) no roots.

    3.1 Determine types of roots of quadratic equations

    from the value of acb 42 .

    3.2 Solve problems involving acb 42 in

    2 Explain that no roots means noreal roots.

    3

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    11 quadratic equations to:a) find an unknown value;b) derive a relation.

    Additional Exercise

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    Topic A3 : Quadratics Functions---3 weeks

    12 1. Understand the concept of quadraticfunctions and their graphs.

    1.1 Recognise quadratic functions 1

    1.2 Plot quadratic functiongraphs:

    a)based on given tabulatedvalues;

    1 b) by tabulating values

    2 based on given functions.

    2

    2

    1.3 Recognise shapes of graphs of quadraticfunctions. 1

    Discuss the form of graph ifa > 0 and a < 0 for

    ( ) cbxaxxf ++= 2

    Explain the term parabola.

    1.4 Relate the position of quadratic function

    graphs with types of roots for ( ) 0=xf . 1 Relate the type of roots with the

    position of the graphs.

    13 2. Find the maximum and minimum

    values of quadratic functions.

    2.1 Determine the maximum or minimum value

    of a quadratic function by completing thesquare.

    2

    Students be reminded of the steps

    involved in completing square andhow to deduce maximum orminimum value from the functionand also the corresponding valuesof x.

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    3. Sketch graphs of quadratic functions. 3.1 Sketch quadratic function graphs by determiningthe maximum or minimum point and two other

    points.

    2Emphasise the marking ofmaximum or minimum point andtwo other points on the graphs

    drawn or by finding the axis ofsymmetry and the intersection withthey-axis.

    Determine other points by finding

    the intersection with the x-axis (ifit exists).

    14 4. Understand and use

    the concept of quadratic inequalities.

    4.1 Determine the ranges of values ofx that satisfies

    quadratic inequalities. 2

    Emphasise on sketching graphs

    and use of number lines whennecessary.

    Topic G1. Coordinate Geometry---5 weeks

    1. Find distance between two points. 1.1 Find the distance between two points ( )11 , yx ,

    ( )22 , yx using formula

    1 Use the Pythagoras Theorem tofind the formula for distance

    between two points.

    152.Understand the concept of division

    of line segments2.1Find the midpoint of two given points.

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

    12

    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 areaof specific geometrical shapes.

    3.2 Find the area of a triangle by using formula.

    13

    13

    21

    21

    2

    1

    yy

    xx

    yy

    xx

    1

    1

    Limit to numerical values.Emphasise the relationship

    between the sign of the value forarea obtained with the order of the

    vertices used.Emphasise that when the area of

    polygon is zero, the given points

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    3.3 Find the area of a quadrilateral usingformula.

    are collinear.

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    4 Understand and use the concept ofequation of a straight line.

    4.1 Determine the x-intercept and the y-intercept ofa line.

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

    4.3 Find the gradient of a straight line using thex-

    intercept and y-intercept

    4.4 Find the equation of astraight line given:

    a) gradient and one point;b) two points;

    c) x-intercept andy-intercept.

    4.5Find the gradient and the intercepts of astraight line given the equation.

    4.6Change the equation of a straight line to thegeneral form

    4.7Find the point of intersection of two lines.

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    1

    1

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    Answers for learning outcomes4.4(a) and 4.4(b) must be stated in

    the simplest form.

    Involve changing the equationintogradient and intercept form

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    18 5. Understand and use the concept ofparallel and perpendicular lines.

    5.1 Determine whether two straight lines areparallel 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 agiven line.

    5.3 Determine whether two straight lines are

    perpendicular when the gradients of bothlines are known and vice versa.

    5.4 Determine the equation of a straight line that

    passes through a fixed point andperpendicular to a given line.

    5.5 Solve problems involving equations ofstraight lines.

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    1

    1

    1

    2

    Emphasise that for parallel lines:

    21 mm = .

    Emphasise that for perpendicular

    lines

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

    PEPERIKSAAN PERTENGAHAN TAHUN 2013(13-23 mei 2013)

    21 6 Understand and use the concept of equation of locus involving distance

    between two points.

    6.1 Find the equation of locus that satisfies thecondition 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.

    1

    1

    2

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    Topic T1: Circular Measures---3 weeks

    22 1. Understand the concept of radian. 1.1 Convert measurements inradians to degrees andvice versa.

    1 Discuss the definition of oneradian.rad is the abbreviation of radian.Include measurements in radiansexpressed in terms of .

    rad = 1800

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

    bulatan

    2.1 Determine:i) length of arc;ii) radius; andiii) angle subtended at the centre of a circle

    based on given information.

    2 Major and minor arc lengthsdiscussed

    Emphasize that the angle must bein radian.Students can also use formula

    S= 2360

    xj

    when the angle

    given is in degree

    23

    2.2 Find perimeter of segments of circles.

    Solve problems involving lengths of arcs

    1

    1

    24

    3. Understand and use the concept of

    area of sector of a circle to solveproblems

    3.1 Determine the:

    a) area of sector;b)radius; and

    c)angle subtended at the centre of a circlebased on given information.

    3.2 Find the area of segments of circles.

    3.3 Solve problems involving areas of sectors

    2

    2

    2

    Emphasize that the angle must be

    in radian.Area of major sektor need to be

    discussedStudents can also use formula

    L=2

    360

    xj

    if the angle given

    is in degree.

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    Topic A5 : INDICES AND LOGARITHMS---4 weeks

    Second Term

    25 1. Understand and use the concept of

    indices and laws of indices to solveproblems.

    1.1 Find the value of numbers given in the form

    of:i. integer indices.ii. fractional indices.

    1.2 Use laws of indices to find the value of numbers

    in index form that are multiplied, divided orraised to a power.

    1

    1

    Discuss zero index and negative

    indices.

    1.3 Use laws of indices to simplify algebraicexpressions 1

    2. Understand and use the concept oflogarithms and laws of logarithmsto solve problems.

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

    2.2 Find logarithm of a number

    1Emphasise that:loga 1 = 0; logaa = 1.

    Emphasise that:

    a) logarithm of negative numbersis undefined;

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

    number is in:a) index form

    b) numerical form.

    UJIAN BULANAN 2 (17-19 JULAI 2013)

    27 2.3 Find logarithm of numbers by using laws of logarithms

    2.4 Simplify logarithmic expressions to thesimplest form.

    2

    1

    Discuss laws of logarithms

    3 Understand and use the change ofbase of logarithms to solve problems.

    3.1 Find the logarithm of a number by changingthe base of the logarithm to a suitable base.

    1 Discuss:

    ab

    b

    alog

    1log =

    28 3.2 Solve problems involving the change of baseand laws of logarithms.

    2

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    4. Solve equation involving indices andlogarithms

    4.1 Solve equations involving indices. 2 Equations that involve indices andlogarithms are limited to equationswith single solution only.

    Solve equations involving indicesby:a) comparison of indices and

    bases;b) using logarithms.

    29 . 4.2 Solve equations involving logarithms.

    Additional/reinforcement Exercises on thistopic

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    Topic S1: Statistics ---4 Weeks

    30

    31

    1 Understand and use the concept ofmeasures 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 data1.4Determine the modal class of grouped data from

    frequency distribution tables.1.5 Find the mode from histograms.

    1.6 Calculate the mean of grouped data1.7 Calculate the median of grouped data from

    cumulative frequency distribution tables.

    1.8 Estimate the median ofgrouped data from an ogive

    1.9 Determine the effects on

    mode, median and mean fora set of data when:

    i) each data is changeduniformly;

    ii) extreme values exist;iii) certain data is added or

    removed

    1.10 Determine the most suitablemeasure of central tendency

    1

    2

    1

    1

    2

    1

    Discuss grouped data andungrouped data.

    Involve uniform class intervalsonly.

    Derivation of the median formulais not required.

    Ogive is also known as cumulativefrequency curve

    Involve grouped and ungroupeddata

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    for given data.

    32 2. Understand and use the concept ofmeasures of dispersion to solve

    problems.

    2.1 Find the range of ungrouped data.

    2.2 Find the interquartilerange of ungrouped data.

    2.3 Find the range of grouped data

    1

    2.4 Find the interquartile range of grouped datafrom the cumulative frequency table

    2.5 Determine theinterquartile range of

    grouped data from anogive.

    2.6Determine the variance of

    a)ungrouped data;b)grouped data.

    2.7 Determine the standarddeviation of:

    ii) ungrouped datagrouped data.

    1

    1

    2

    Determine the upper and lowerquartiles by using the first

    principle.

    2.8 Determine the effects on range, interquartilerange, 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 anddispersion between two sets of data.

    2

    2Emphasise that comparison

    between two sets of data usingonly measures of central tendencyis not sufficient.

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    Topic AST1: SOLUTION OF TRIANGLES---2 weeks

    291. Understand and use the concept of

    sine rule to solve problems.1.1Verify sine rule.

    1.2Use sine rule to findunknown sides or angles of atriangle.

    1.3Find the unknown sides and

    angles of a triangle involvingambiguous case

    1.4Solve problems involving thesine rule.

    1

    1

    1

    1

    Include obtuse-angled triangles

    30

    2. Understand and use the concept ofcosine rule to solve problems.

    2.1 Verify cosine rule.2.2 Use cosine rule to find

    unknown sides or anglesof a triangle.

    2.3 Solve problemsinvolving cosine rule.

    2.4Solve problemsinvolving sine andcosine rules

    1

    1

    2

    Include obtuse-angled triangles

    31 3. Understand and use the formula forareas of triangles to solve problems.

    3.1 Find the areas of triangles using the formula

    Cab sin2

    1or its equivalent

    3.2.Solve problemsinvolving three-dimensional objects.

    1

    2

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    Additional Exercises

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    Topic K1 : Differentiation---5 Weeks

    34 1. Understand and use the concept ofgradients of curve and

    differentiation.

    1.1Determine the value of a function when itsvariable approaches a certain value.

    1.2Find the gradient of a chord joining twopoints on a curve.

    1.3Find the first derivative of a function( )xfy = , as the gradient of tangent to its

    graph.

    1.3 Find the first derivative of polynomials using

    the first principles.1.4 Deduce the formula for first derivative of the

    function( )xfy =

    by induction.

    1

    1

    2

    Idea of limit to a function can beillustrated using graphs.

    The concept of first derivative of afunction is explained as a tangentto a curve can be illustrated usinggraphs.

    Limit to naxy = ;

    a, n are constants, n = 1, 2, 3.

    Notation of ( )xf' is equivalent

    todx

    dywhen ( )xfy = ,

    ( )xf'

    read as fprime x.

    35 2. Understand and use the concept of firstderivative of polynomial functions tosolve problems.

    2.1 Determine the first derivative of the functionnaxy = using formula.

    2.2 Determine value of the first derivative of the

    function naxy = for a given value ofx.

    1

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    2.3Determine first derivative ofa function involving:a) addition, or

    b) subtractionof algebraic terms.

    2.4Determine the first derivative of a product of

    two polynomials.2.5 Determine the first derivative 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 a curve.2.8Determine the equation of tangent at a point

    on a curve.

    2.9 Determine the equation of normal at a pointon a curve

    1

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    1

    1

    1

    1

    1

    3. Understand and use the concept ofmaximum and minimum values tosolve problems.

    3.1 Determine coordinates of turning points of acurve.3.2 Determine whether a turning point is amaximum or a minimum point.

    2

    Emphasise the use of firstderivative to determine the turning

    points.Limit problems to two variables

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    3.3 Solve problems involving maximum orminimum values.

    1

    only.Exclude points of inflexion.

    Limit problems to two variablesonly

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

    4.1 Determine rates of change for relatedquantities.

    1 Limit problems to 3 variables only.

    5. Understand and use the concept of small

    changes and approximations to solveproblems.

    5.1 Determine small changes in quantities5.2 Determine approximate values using

    differentiation.

    1 Exclude cases involvingpercentage change.

    6. Understand and use the concept ofsecond derivative to solve problems.

    6.1 Determine the second derivative of ( )xfy = .6.2 Determine whether a turning point is

    maximum or minimum point of a curve usingthe second derivative

    1

    1

    Introduce 2

    2

    dx

    ydas

    dx

    dy

    dx

    dor

    ( ) ( )( )xfdx

    dxf ''' =

    PROJECT WORK

    3

    WEEKs

    OUTSI

    DE

    SCHOO

    L

    HOURS

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    Carry out project work In carrying out the project work1.1Define the problem/situation to be studied.

    1.2 State relevant conjectures1.3 Use problem solving strategies to solve problems1.4 Interpret and discuss results.

    1.5 Draw conclusions and/ormake generalisations based

    on critical evaluation ofresults.

    1.6 Present systematic and comprehensive writtenreports.

    Usescientific

    calculators,graphing

    calculators

    orcomputer

    software tocarry out

    projectwork.

    Students

    are allowedto carry out

    projectwork in

    groups butwrittenreportsmust be

    doneindividuall

    y.

    Studentsshould be

    givenopportunityto give oralpresentatio

    n of theirproject

    work.

    Emphasise the use of Polyas four-step problem solving process.

    Use at least two problem solvingstrategies.

    Emphasise reasoning and effective

    mathematical communication.

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