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    RPT : ADD MATH FORM 5

    RANCANGAN PELAJARAN TAHUNAN DAN

    PIAWAIAN LATIHAN AKADEMIK NEGERI JOHOR (PLAN-J)

    2012

    SEKOLAH : SEKOLAH MENENGAH KEBANGSAAN PADUKA TUAN

    SUBJECT : ADDITIONAL MATHEMATICS FORM : 5

    WEEK/DATE TOPIC SUB TOPIC LEARNING OUTCOMES PLAN JCOMPLETE

    DATE

    Progressions 1) Understand and usethe concept of

    arithmeticprogression.

    (i) Identify characteristics ofarithmetic progressions

    (ii) Determine whether a givensequence is an arithmeticprogression

    (iii) Determine by using formula:a) specific terms in arithmetic

    progressions,b) the number of terms in

    arithmetic progressions(iv) Find:

    a) the sum of the first n termsof arithmetic progressions,

    b) the sum of a specificnumber of consecutiveterms of arithmeticprogressions,

    c) the value ofn, given thesum of the first n terms ofarithmetic progressions

    (v) Solve problems involvingarithmetic progressions

    .

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    Progressions 2) Understand and usethe concept of

    geometricprogression

    (i) Identify characteristics ofgeometric progressions.

    (ii) Determine whether a givensequence is a geometricprogression.

    (iii) Determine by usingformula:a) specific terms in

    geometric progressions,b) the number of terms in

    geometric progressions.(iv) Find:

    a) the sum of the first n terms

    of geometric progressions,b) the sum of a specific

    number of consecutiveterms of geometricprogressions,

    c) the value ofn, given thesum of the first n terms ofgeometric progressions,

    Progressions 2. Understand and use

    the concept ofgeometricprogression

    (v) Find:

    a) the sum to infinity ofgeometric progressions,

    b) the first term or commonratio, given the sum toinfinity of geometricprogressions.

    (vi) Solve problems involvinggeometric progressions

    Linear Law 1) Understand and use (i) Draw lines of best fit by

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    the concept of linesof best fit.

    inspection of given data(ii) Write equations for lines of

    best fit(iii) Determine values of

    variables from:a) Lines of best fit,b) Equations of lines of best fit

    Linear Law 2) Apply linear law tonon-linear relations

    (i) Reduce non-linear relations to

    linear form.Determine values of constants

    of non-linear relations given

    a) lines of best fitb) data

    (iii) Obtain information froma) lines of best fitb) equations of lines of best

    fit

    Integration. 1) Understand and usethe concept ofintegration indefinite

    integral.

    (i) Determine integrals byreversing differentiation.

    (ii) Determine integrals of ax n

    where a is a constant and n isan integer,n 1.

    (iii) Determine integrals ofalgebraic expressions.

    (iv) Find constants of integration,c, in indefinite integrals

    (v) Determine equations of curvesfrom functions of gradients

    (vi) Determine by substitution theintegrals of expressions of the

    form (ax + b) n , where a and b

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    are constants, n is an integer

    and n -1

    Chinese New Year

    Integration 2) Understand and usethe concept ofdefinite integrals

    i) Find definite integrals ofalgebraic expressions

    (ii) Find areas under curves asthe limit of a sum of areas.

    (iii) Determine areas under curvesusing formula.

    Integration 2) Understand and usethe concept ofdefinite integrals

    (iv) Find volumes of revolutionswhen region bounded by acurve is rotated completelyabout thea) x-axis,b) y-axis

    as the limit of a sum ofvolumes.

    (iii) Determine volumes of

    revolutions using formula.

    Vector 1) U nderstand anduse the concept ofvector .

    (i) Differentiate between vectorand scalar quantities.

    (ii) Draw and label directed linesegments to represent vectors

    (iii) Determine the magnitude anddirection of vectorsrepresented by directedsegments

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    segments.l

    (iv) Determine whether twovectors are equal.

    (v) Multiply vectors by scalars.(vi) Determine wether two vectors

    are parallel.

    School Holiday

    Vector 2) Understand and

    use the concept ofaddition andsubtraction ofvectors

    (i) Determine the resultant vector

    of two parallel vectors(ii) Determine the resultant vector

    of two non-parallel vectorsusing:a) triangle law,b) parallelogram law.

    (iii) Determine the resultant vectorof three or more vectors usingthe polygon law

    (iv) Subtract two vectors whichare:

    a) Parallel,b) non-parallel.

    (v) Represent a vector as acombination of other vectors.

    (vi) Solve problems involvingaddition and subtraction ofvector

    Vector 3. Understand and usethe vectors in

    (i) Express vectors in the form:a) xi + yj

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    cartesian pane

    b)

    y

    x

    (ii) Determine magnitudes ofvectors

    (iii) Determine unit vectors in givendirections

    (iv) Add two or more vectors(v) Subtract two vectors(vi) Multiply vectors by scalars(vii)Perform combined operations

    on vectors(viii)Solve problems involving

    vectors

    Trigonome-tric Functions

    1) Understand theconcept of positiveand negative anglesmeasured indegrees andradians.

    (i) Represent in a Cartesianplane, angles greater than 3600 or 2 radians for:

    a) positive angles,b) negative angles

    (ii) Define sine, cosine andtangent of any angle in aCartesian plane

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    2) Understand and usethe six trigonometric

    functions of anyangle.

    (iii) Define cotangent, secant andcosecant of any angle in a

    Cartesian plane(iv) Find values of the six

    trigonometric functions of anyangle

    (v) Solve trigonometric equations

    Trigonome-tric Functions

    3) Understand and usegraphs of sine,cosine, and tangent

    functions..

    (i) Draw and sketch graphs oftrigonometric functions:a) y = c + a sin bx,

    b) y = c + a cos bx,c) y = c + a tan bxwhere a, b and c are constantsand b > 0

    (ii) Determine the number ofsolutions to a trigonometricequation using sketchedgraphs.

    (iii) Solve trigonometric equationsusing drawn graphs.

    Trigonome-tric Functions

    4) Understand and usebasic identities

    (i) Prove basic identities:a) sinA + cosA = 1,b) 1 + tanA = secA,c) 1 + cotA = cosecA

    (ii) Prove trigonometric identitiesusing basic identities

    (iii) Solve trigonometric equationsusing basic identities

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    Trigonome-

    tric Functions

    5) Understand and use

    addition formula anddouble-angleformula.

    (i) Prove trigonometric identities

    using addition formula forsin (A B), cos (A B) andtan (A B).

    (ii) Derive double-angle formulafor sin 2A, cos 2A and tan 2A.

    (iii) Prove trigonometric identitiesusing addition formula and/ordouble-angle formula.

    (iv) Solve trigonometric equations

    PermutationsandCombinations

    1) Understand and usethe concept ofpermutation.

    (i) Determine the total number ofways to perform successiveevents using multiplication rule

    (ii) Determine the number ofpermutations ofn differentobjects

    (iii) Determine the number ofpermutations ofn differentobjects taken rat a time

    (iv) Determine the number ofpermutations ofn different

    objects for given conditions.(v) Determine the number of

    permutations ofn differentobjects taken rat a time forgiven conditions

    PermutationsandCombinations

    2) Understand and usethe concept ofcombination

    (i) Determine the number ofcombinations ofrobjectschosen from n differentobjects.

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    (ii) Determine the number ofcombinations robjects chosen

    from n different objects forgiven conditions

    Mid Year Exam

    Mid Year Exam

    Mid Year Holidays

    Probability 1) Understand and usethe concept ofprobability

    (i) Describe the sample space ofan experiment.

    (ii) Determine the number ofoutcomes of an event.

    (iii) Determine the probability of anevent

    (iv) Determine the probability oftwo events:a) A or B occurring,

    b) A and B occurring

    Probability 2) Understand and use

    the concept ofprobability ofmutually exclusiveevents

    3) Understand and usethe concept ofprobability of

    (i) Determine whether two eventsare mutually exclusive

    (ii) Determine the probability oftwo or more events that aremutually exclusive.

    (i) Determine whether two eventsare independent

    (ii) Determine the probability of

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