# rpt add math frm 5_2011

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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

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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

(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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independent events two independent events.

(iii) Determine the probability ofthree independent events.

ProbabiltyDistributions

1) Understand and use

the concept ofbinomial distribution

(i) List all possible values of adiscrete random variable.

(ii) Determine the probability of an

event in a binomial distribution(iii) Plot binomial distribution

graphs.(iv) Determine mean, variance and

standard deviation of abinomial distribution

(v) Solve problems involvingbinomial distributions.

Probabilty

Distributions

2) Understand and use

the concept ofnormal distribution

(i) Describe continuous random

variables using set notations(ii) Find probability of z-values for

standard normal distribution.(iii) Convert random variable of

normal distributions, X, tostandardised variable, Z.

(iv) Represent probability of anevent using set notation.

(v) Determine probability of anevent

(vi) Solve problems involving

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normal distributions

Motion AlongA StraightLine

1) Understand and usethe concept ofdisplacement

2) Understand and usethe concept ofvelocity.

(i) Identify direction ofdisplacement of a particle froma fixed point

(ii) Determine displacement of aparticle from a fixed point.

(iii) Determine the total distancetravelled by a particle over atime interval using graphicalmethod.

i) Determine velocity function of

a particle by differentiation.(ii) Determine instantaneous

velocity of a particle(iii) Determine displacement of a

particle from velocity functionby integtration

Motion AlongA StraightLine

3) Understand and usethe concept ofacceleration

(i) Determine accelerationfunction of a particle bydifferentiation

(ii) Determine instantaneous

acceleration of a particle(iii) Determine instantaneous

velocity of a particle fromacceleration function byintegration

(iv) Determine displacement of aparticle from accelerationfunction by integration

(v) Solve problems involvingmotion along a straight line.

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Linear

Programming

1) Understand and use

the concept ofgraphs of linearinequalities

(i) Identify and shade the region

on the graph that satisfies alinear inequalities

(ii) Find the linear inequality thatdefines a shaded region.

(iii) Shade region on the graphthat satisfies several linearinequalities.

(iv) Find linear inequalities thatdefine a shaded region.

LinearProgramming

2) Understand and usethe concept of linearProgramming

(i) Solve problems related tolinear programming by:a) writing linear inequalitiesandequations describing asituation,b) shading the region offeasible solutions,c) determining and drawing theobjective function ax + by = kwhere a, b and k are

constants,d) determining graphically theoptimum value of theobjective function.

SPM Trial Exam

Intensif RevisionTrial Exam Paper from other state

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Past year questions

SPM Exam. 2012