SOW Additional Mathematics Form 5 2014

8/9/2019 SOW Additional Mathematics Form 5 2014

1/12

SCHEME OF WORK ADD MATHS FORM 5 2014

WEEKS

LEARNINGOBJECTIVESPupils will betaught to

SUGGESTED TEACHINGAND LEARNING

ACTIVITIES

LEARNING OUTCOMESPupils will be able to

POINTS TO NOTE VOCABULARY

Learning Area: PROGRESSIONSWEEK 1!1"#!1

WEEK $!1"1 !1

1. Understand anduse the concept ofarithmeticprogression

Use examples from real-lifesituations, scientific orgraphing calculators andcomputer software toexplore arithmeticprogressions.

i"THINK:Tree Map

HOT% Questions

i) Identify characteristics of rithmetic!rogressions.ii) "etermine whether a gi#en se$uence is anarithmetic progression.iii) "etermine %y using formula&

a) specific terms in arithmetic progressions, %) the num%er of terms in arithmeticprogressions.i#) 'ind&

a) the sum of the first n terms of arithmeticprogressions,

%) the sum of a specific num%er ofconsecuti#e terms of arithmeticprogressions,

c) the #alue of n, gi#en the sum of the firstn terms of arithmetic progressions,#) (ol#e pro%lems in#ol#ing arithmeticprogressions.

egin with se$uences tointroduce arithmetic andgeometric progressions.Include examples inalge%raic form.

Include the use of theformula

T n= Sn Sn1

Include pro%lemsin#ol#ing real-lifesituations.

se$uenceseriescharacteristicarithmeticprogressioncommondifferencespecific termfirst termnth termconsecuti#e

WEEK &1&!1"1'!1

*. Understand anduse the concept ofgeometricprogression.

Use examples from real-lifesituations, scientific orgraphing calculators+ andcomputer software toexplore geometricprogressions.

i) Identify characteristics of geometricprogressions.

ii) "etermine whether a gi#ense$uence is a geometric progression.

iii) "etermine %y using formula&a) specific terms in geometric progressions,%) the num%er of terms in geometricprogressions.

Include examples inalge%raic form.

discuss& s n , r n 0

then S= a1 r

S read as /sum toinfinity0Include recurring

decimals.imit to * recurring digits

geometricprogressioncommon ratio

1


2/12


WEEKS



ACTIVITIES



such as 2.3, 2.14 5WEEK ()!1" $!1

i"THINK:Tree Map

HOT% Questions

i#) 'ind&a) the sum of the first n terms of geometricprogressions,%) the sum of a specific num%er ofconsecuti#e terms of geometricprogressions,c) the #alue of n, gi#en the sum of thefirst n terms of geometric progressions,

#) 'ind&a) the sum to infinity of geometricprogressions,%) the first term or common ratio, gi#enthe sum to infinity of geometric progressions.

#i) (ol#e pro%lems in#ol#e arithmeticprogressions

6xclude&a) com%ination ofarithmetic progressionsand geometricprogressions,

%) cumulati#e se$uences

such as,1), *, 3), 7, 4, 8),9, :, ;, 12), 5

sum to infinity

recurringdecimal

Learning Area: LINEAR LAWWEEK #*!1"&1!1

WEEK $1! "'!

1. Understand anduse the concept oflines of %est fit.

Use examples from real-lifesituations to introduce theconcept of linear law.

Use graphing calculators or computer software such as

etchpad toexplore lines of %est fit.

i) "raw lines of %est fit %y inspection ofgi#en data.

ii) ?rite e$uations for lines of %est fit.iii) "etermine #alues of #aria%les from&a) lines of %est fit,

%) e$uations of lines of %est fit.

imit data to linearrelations %etween two#aria%les.

line of %est fitinspection#aria%lenon-linear relationlinear form

reduce

WEEK *1)! "1$!

*. pply linear lawto nonlinearrelations.

HOT% Questions

i) @educe non-linear relations to linear form.ii) "etermine #alues of constants of non-

linear relations gi#en&a) lines of %est fit, %) data.

iii) A%tain information from&a) lines of %est fit, %) e$uations of lines of%est fit.

WEEK +,', 1)

1%- MONTHLY TEST .1+! "#!&/

2


3/12


WEEKS



ACTIVITIES



1*! "'!& Learning Area: INTEGRATIONWEEK 111)!&"1$!&

1. Understand anduse the concept ofindefinite integral.

Use computer softwaresuch as etchpad to explore theconcept of integration.

i"THINK:u%%le Map

i) "etermine integrals %y re#ersingdifferentiation.

ii) "etermine integrals of a x n , where ais a constant and n is an integer, n B C1.

iii) "etermine integrals of alge%raicexpressions.

i#) 'ind constants of integration, c , inindefinite integrals.

#) "etermine e$uations of cur#es fromfunctions of gradients.

#i) "etermine %y su%stitution the integrals of expressions of the form (ax +b)n , wherea and b are constants, n is an integer and nB C1.

6mphasiDe constant ofintegration.

ydx read as/integration of y withrespect to x 0

imit integration of

u n dx where u =ax+b .

integrationintegralindefiniteintegralre#erseconstant of integrationsu%stitution

WEEK 11*!&" &!&

*. Understand anduse the concept ofdefinite integral.

Use scientific or graphingcalculators to explore theconcept of definiteintegrals.

Use computer software andgraphing calculator toexplore areas under cur#esand the significance ofpositi#e and negati#e#alues of areas.

Use dynamic computersoftware to explore#olumes of re#olutions.

i) 'ind definite integrals of alge%raicexpressions.

ii) 'ind areas under cur#es as the limit of asum of areas.

iii) "etermine areas under cur#es usingformula.

i#) 'ind #olumes of re#olutions when region%ounded %y a cur#e is rotated completelya%out thea) x -axis,%)y -axisas the limit of a sum of #olumes.

#) "etermine #olumes of re#olutions using

Include

a

b

kf ( x)dx= k a

b

f ( x)dx

a

b

f ( x)dx= b

a

f ( x)dx

"eri#ation of formulae notre$uired.

imit to one cur#e.

"eri#ation of formulae notre$uired.

imit #olumes ofre#olution a%out the x -axis or y -axis.

definite integrallimit#olumeregionrotatedre#olutionsolid of re#olution

3


4/12


WEEKS



ACTIVITIES



formula.WEEK 1&(!&"&)!&

MID SEMESTER BREAK . !&"&)!&/

Learning Area: VECTORWEEK 1(

1!("$!(1. Understand anduse the concept of#ector.

Use examples from real-lifesituations and dynamiccomputer software such asetchpad toexplore #ectors.

i"THINK:

'low Map

i) "ifferentiate %etween #ector and scalar$uantities.

ii) "raw and la%el directed line segments torepresent #ectors.

iii) "etermine the magnitude and direction of #ectors represented %y directed linesegments.

i#) "etermine whether two #ectors aree$ual.

#) Multiply #ectors %y scalars.#i) "etermine whether two #ectors are

parallel.

Use notations&Eector& a , AB, a , AB .Magnitude&Fa F, | AB| , Fa0, FAB0.Gero #ector& 26mphasise that a Dero#ector has a magnitudeof Dero.6mphasise negati#e#ector&H AB BAInclude negati#e scalar.

Include&a) collinear points%) non-parallel non-Dero#ectors.6mphasise& If a and b arenot parallel and ha kb ,then h k 2.

differentiatescalar #ector directed linesegmentmagnitudedirectionDero #ector negati#e #ector parallelnon-parallelcollinear pointsnon-Derotriangle lawparallelogramlawresultant #ector polygon law

WEEK 1#*!("1&!(

*. Understand anduse the concept ofaddition andsu%traction of#ectors.

Use real-life situations andmanipulati#e materials toexplore addition andsu%traction of #ectors.

i) "etermine the resultant #ector of twoparallel #ectors.

ii) "etermine the resultant #ector of two non-parallel #ectors using&a) triangle law,%) parallelogram law.

iii) "etermine the resultant #ector of three or more #ectors using the polygon law.

i#) (u%tract two #ectors which are&a) !arallel,

6mphasise&a C b a J Hb)

4


5/12


WEEKS



ACTIVITIES



HOT% Questions

%) non-parallel.#) @epresent a #ector as a com%ination ofother #ectors.

#i) (ol#e pro%lems in#ol#ing addition andsu%traction of #ectors

WEEK 1$1(!(" )!(

3. Understand anduse #ectors in theKartesian plane.

Use computer software toexplore #ectors in theKartesian plane.

i) 6xpress #ectors in the form&a) xi J yj

%) ( x y)ii) "etermine magnitudes of #ectors.iii) "etermine unit #ectors in gi#en

directions.i#) dd two or more #ectors.#) (u%tract two #ectors.#i) Multiply #ectors %y scalars.#ii) !erform com%ined operations on

#ectors.#iii) (ol#e pro%lems in#ol#ing #ectors

@elate unit #ector i and jto Kartesian coordinates.6mphasise&

Eector i (10 ) andEector j

(0

1

)to 3.9, all #ectors aregi#en in the form xi J yj or ( x y) .

imit com%inedoperations to addition,su%traction andmultiplication of #ectors%y scalars.

Kartesian planeunit #ector

Learning Area: TRIGONOMETRIC UNCTIONWEEK 1*

1!(" *!(1. Understand theconcept of positi#eand negati#eangles measured indegrees andradians.

Use dynamic computersoftware such asetchpad toexplore angles in Kartesianplane.

i) @epresent in a Kartesian plane, anglesgreater than 382L or * radians for&a) positi#e angles,%) negati#e angles.

Kartesian planerotating raypositi#e anglenegati#e anglecloc>wiseanticloc>wiseunit circle$uadrantreference angletrigonometric

5


6/12


WEEKS



ACTIVITIES



functionNratiosine cosinetangent cosecantsecant cotangent

WEEK 1++!("(!#

*. Understand anduse the sixtrigonometricfunctions of anyangle.

Use dynamic computersoftware to exploretrigonometric functions indegrees and radians.Use scientific or graphingcalculators to exploretrigonometric functions ofany angle.

i) "efine sine, cosine and tangent of anyangle in a Kartesian plane.

ii) "efine cotangent, secant and cosecant of any angle in a Kartesian plane.

iii) 'ind #alues of the six trigonometricfunctions of any angle.

i#) (ol#e trigonometric e$uations.

Use unit circle todetermine the sign of trigonometric ratios.6mphasise&sin O cos ;2L C O)cos O sin ;2LC O)tan O cot ;2L C O)cosec O sec ;2L C O)

sec O cosec ;2LC O)cot O tan ;2LC O)6mphasise the use of triangles to findtrigonometric ratios for special angles 32L, 74Land 82L.

3. Understand anduse graphs of sine,cosine and tangentfunctions.

Use examples from real-lifesituations to introducegraphs of trigonometricfunctions.Use graphing calculators

and dynamic computersoftware such asetchpad toexplore graphs oftrigonometric functions.

i) "raw and s>etch graphs of trigonometricfunctions&a) y c + a sin bx ,%)y c + a cos bx ,c) y c + a tan bx

where a , b and c are constants and b P 2.ii) "etermine the num%er of solutions to atrigonometric e$uation using s>etchedgraphs.

Use angles ina) degrees%) radians, in terms of .6mphasiDe thecharacteristics of sine,

cosine and tangentgraphs.Include trigonometricfunctions in#ol#ingmodulus.6xclude com%inations oftrigonometric functions.

Modulusdomainranges>etchdraw

periodcyclemaximumminimumasymptote

WEEK1', ), 1#!#" #!# MID YEAR E2AMINATION .#!#" &!#/

6


7/12


WEEKS



ACTIVITIES



WEEK, &, ($!#"1#!$

MID YEAR HOLIDAY

WEEK #1$!$" !$

7. Understand anduse %asic identities.

Use scientific or graphingcalculators and dynamiccomputer software such asetchpad toexplore %asic identities.

i) !ro#e %asic identities&a) sin * A J cos * A 1,%) 1 J tan * A sec * A,c) 1 J cot * A cosec * A.

ii) !ro#e trigonometric identities using %asicidentities.

iii) (ol#e trigonometric e$uations using%asic identities.

asic identities are also>nown as !ythagoreanidentities.Include learningoutcomes *.1 and *.*.

%asic identity!ythagoreanidentity

4. Understand anduse additionformulae anddou%le-angleformulae.

Use dynamic computersoftware such asetchpad toexplore addition formulaeand dou%le-angle formulae.

i) !ro#e trigonometric identities usingaddition formulae for sin A B), cos A B)and tan A B).

ii) "eri#e dou%le-angle formulae for sin * A,cos * A and tan * A.

iii) !ro#e trigonometric identities usingaddition formulae andNor dou%le-angleformulae.

i#) (ol#e trigonometric e$uations.

"eri#ation of additionformulae not re$uired."iscuss half-angleformulae.6xcludea cos x J b sin x c ,where c B 2.

addition formuladou%le-angleformulahalf-angleformula

Learning Area: PERMUTATION AND COMBINATIONWEEK $

&!$" '!$1. Understand anduse the concept of

permutation.

Use manipulati#e materialsto explore multiplication

rule.Use real-life situations andcomputer software such asspreadsheet to explorepermutations.

i) "etermine the total num%er of ways toperform successi#e e#ents using

multiplication rule.ii) "etermine the num%er of permutations ofn different o%Rects

iii) "etermine the num%er of permutations of n different o%Rects ta>en r at a time.

i#) "etermine the num%er of permutations of n different o%Rects for gi#en conditions.

#) "etermine the num%er of permutations ofn different o%Rects ta>en r at a time for gi#enconditions.

a) Introduce the concept%y using numerical

examples.%) Kalculators shouldonly %e used afterstudents ha#eunderstood the concept.

imit to 3 e#ents.6xclude cases in#ol#ingidentical o%Rects.6xplain the concept ofpermutations %y listing allpossi%le arrangements.Include notations&

multiplicationrulesuccessi#ee#entspermutationfactorial

7


8/12


WEEKS



ACTIVITIES



i"THINK:"ou%le %u%le map

HOT% Questions

a) nS n n C 1) n C *)5 3) *) 1)%) 2S 1nS read as / n factorial06xclude cases in#ol#ingarrangement of o%Rects ina circle.

arrangementorder

WEEK *&)!$"$!*

*. Understand anduse the concept ofcom%ination.

6xplore com%inations usingreal-life situations andcomputer software.i"THINK:"ou%le %u%le map

HOT% Questions

i) "etermine the num%er of com%inations ofr o%Rects chosen from n different o%Rects.

ii) "etermine the num%er of com%inations ro%Rects chosen from n different o%Rects forgi#en conditions.

6xplain the concept of com%inations %y listing allpossi%le selections.Use examples to illustrate

C r= P rn

r !

n

com%inationselection

Learning Area: PROBABILITYWEEK +*!*"1&!*

1. Understand anduse the concept ofpro%a%ility.

Use real-life situations tointroduce pro%a%ility.Use manipulati#e materials,computer software, andscientific or graphingcalculators to explore theconcept of pro%a%ility

i) "escri%e the sample space of anexperiment.

ii) "etermine the num%er of outcomes of ane#ent.

iii) "etermine the pro%a%ility of an e#ent.

i#) "etermine the pro%a%ility of two e#ents&a) A or B occurring,%) A and B occurring.

Use set notations."iscuss&a) classical pro%a%ility

theoretical pro%a%ility)%) su%Recti#e pro%a%ilityc) relati#e fre$uencypro%a%ility experimentalpro%a%ility).6mphasise&

Anly classical pro%a%ilityis used to sol#epro%lems.6mphasise& ! AUB) ! A) J ! B) C! A B)using Eenn diagrams.

experimentsample spacee#entoutcomee$ually li>elypro%a%ilityoccur classicaltheoretical

pro%a%ilitysu%Recti#erelati#efre$uencyexperimental

WEEK '1(!*" )!*

*. Understand anduse the concept ofpro%a%ility ofmutually exclusi#ee#ents.

Use manipulati#e materialsand graphing calculators toexplore the concept ofpro%a%ility of mutuallyexclusi#e e#ents.

i) "etermine whether two e#ents aremutually exclusi#e.

ii) "etermine the pro%a%ility of two or moree#ents that are mutually exclusi#e.

Include e#ents that aremutually exclusi#e andexhausti#e.

imit to three mutuallyexclusi#e e#ents.

mutuallyexclusi#ee#entexhausti#eindependent

8


9/12


WEEKS



ACTIVITIES



Komputer to simulateexperiments in#ol#ingpro%a%ility of mutuallyexclusi#e e#ents.

tree diagrams

3. Understand anduse the concept ofpro%a%ility ofindependente#ents.

Use manipulati#e materialsand graphing calculators toexplore the concept ofpro%a%ility of independente#ents.Use computer software tosimulate experimentsin#ol#ing pro%a%ility of

independent e#ents.i"THINK:u%%le map

HOT% Questions

i) "etermine whether two e#ents areindependent.

ii) "etermine the pro%a%ility of twoindependent e#ents.

iii) "etermine the pro%a%ility of threeindependent e#ents.

Include tree diagrams.

Learning Area: PROBABILITY DISTRIBUTIONSWEEK &)

1!*" *!*1. Understand anduse the concept of%inomialdistri%ution.

Use real-life situations tointroduce the concept of%inomial distri%ution.Use graphing calculatorsand computer software toexplore i) ist all possi%le#alues of a discrete random

#aria%le.ii) "etermine thepro%a%ility of an e#ent in a%inomial distri%ution.

i) ist all possi%le #alues of a discreterandom #aria%le.

ii) "etermine the pro%a%ility of an e#ent in a%inomial distri%ution.

iii) !lot %inomial distri%ution graphs.

i#) "etermine mean, #ariance and standardde#iation of a %inomial distri%ution.#) (ol#e pro%lems in#ol#ing %inomial

distri%utions.

Include thecharacteristics of

ernoulli trials.'or learning outcomes1.* and 1.7, deri#ation offormulae not re$uired.

discrete random#aria%leindependent trial

ernoulli trialsinomial

distri%utionmean

#ariancestandardde#iation

*. Understand anduse the concept ofnormal distri%ution.

Use real-life situations andcomputer software such asstatistical pac>ages toexplore the concept ofnormal distri%utions.

i) "escri%e continuous random #aria%lesusing set notations.

ii) 'ind pro%a%ility of z -#alues for standardnormal distri%ution.

"iscuss characteristicsof&a) normal distri%utiongraphs%) standard normal

continuousrandom #aria%lenormaldistri%utionstandard normal

9


10/12


WEEKS



ACTIVITIES



i"THINK:Tree map

HOT% Questions

iii) Kon#ert random #aria%le of normaldistri%utions, , to standardised #aria%le, ! .

i#) @epresent pro%a%ility of an e#ent usingset notation.

#) "etermine pro%a%ility of an e#ent.#i) (ol#e pro%lems in#ol#ing normal

distri%utions.

distri%ution graphs.! is called standardiDed#aria%le.

Integration of normaldistri%ution function todetermine pro%a%ility isnot re$uired.

distri%utionz -#aluestandardised#aria%le

WEEK &1+!*"&!+ HARI RAYA AIDIL ITRI HOLIDAY

Learning Area: MOTION ALONG A STRAIGHT LINEWEEK &(!+"1)!+

1. Understand anduse the concept ofdisplacement.

Use real-life examples,graphing calculators andcomputer software such asetchpad toexplore displacement.

i) Identify direction of displacement of aparticle from a fixed point.

ii) "etermine displacement of a particle froma fixed point.

iii) "etermine the total distance tra#elled %ya particle o#er a time inter#al using graphicalmethod.

6mphasise the use of thefollowing sym%ols&s displacement" #elocitya accelerationt timewhere s , " and a arefunctions of time.6mphasise the difference%etween displacementand distance."iscuss positi#e,

negati#e and Derodisplacements.Include the use ofnum%er line.

particlefixed pointdisplacementdistance#elocityaccelerationtime inter#al

*. Understand anduse the concept of#elocity.

Use real-life examples,graphing calculators anddynamic computer softwaresuch as etchpad to explore theconcept of #elocity.

i) "etermine #elocity function of a particle %ydifferentiation.

ii) "etermine instantaneous #elocity of aparticle.

6mphasise #elocity asthe rate of change of displacement.Include graphs of #elocityfunctions."iscuss&a) uniform #elocity

Instantaneous#elocity#elocityfunctionuniform #elocityrate of changemaximum

10


11/12


WEEKS



ACTIVITIES



iii) "etermine displacement of a particlefrom #elocity function %y integration.

%) Dero instantaneous#elocityc) positi#e #elocityd) negati#e #elocity.

displacementstationary

3. Understand anduse the concept ofacceleration 3

Use real-life examples andcomputer software such asetchpad toexplore the concept ofacceleration.

i"THINK:'low map

HOT% Questions

i) "etermine acceleration function of aparticle %y differentiation.

ii) "etermine instantaneous acceleration ofa particle.

iii) "etermine instantaneous #elocity of aparticle from acceleration function %yintegration.

i#) "etermine displacement of a particle

from acceleration function %y integration.#) (ol#e pro%lems in#ol#ing motion along astraight line.

6mphasise accelerationas the rate of change of#elocity."iscuss&a) uniform acceleration%) Dero accelerationc) positi#e accelerationd) negati#e acceleration.

Maximum #elocityMinimum #elocityUniformacceleration

Learning Area: LINEAR PROGRAMMINGWEEK &&11!+"1*!+

1. Understand anduse the concept ofgraphs of linearine$ualities.

Use real-life examples,graphing calculators anddynamic computer softwaresuch as etchpad to explore linearprogramming.

i) Identify and shade the region on the graphthat satisfies a linear ine$uality.

ii) 'ind the linear ine$uality that defines ashaded region.

iii) (hade region on the graph that satisfiesse#eral linear ine$ualities.

i#) 'ind linear ine$ualities that define ashaded region.

6mphasise the use ofsolid lines and dashedlines.

imit to regions defined%y a maximum of 3 linearine$ualities not includingthe x -axis and y -axis).

inear programminglinear ine$ualitydashed linesolid lineregiondefinesatisfy

*. Understand anduse the concept oflinearprogramming.

i) (ol#e pro%lems related to linearprogramming %y&a) writing linear ine$ualities and e$uationsdescri%ing a situation,%) shading the region of feasi%le solutions,c) determining and drawing the o%Recti#efunction ax J by k where a , b and k areconstants,d) determining graphically the optimum #alueof the o%Recti#e function.

Aptimum #alues refer tomaximum or minimum#alues.Include the use of#ertices to find theoptimum #alue.

feasi%le solutiono%Recti#efunctionparallel lines#ertex#erticesoptimum #aluemaximum #alueminimum #alue

11


12/12


WEEKS



ACTIVITIES



3. Karry out proRectwor>. Use scientific calculators,graphing calculators orcomputer software to carryout proRect wor>.!upils are allowed to carryout proRect wor> in groups%ut written reports must %edone indi#idually.!upils should %e gi#en theopportunities to gi#e oralpresentations of theirproRect wor>.

HOT% Questions

i) "efine the pro%lemNsituation to %e studied.ii) (tate rele#ant conRectures.iii) Use pro%lem-sol#ing strategies to sol#e

pro%lems.i#) Interpret and discuss results.#) "raw conclusions andNor generalisations

%ased on critical e#aluation of results.#i) !resent systematic and comprehensi#e

written reports.

6mphasise the use of!olya=s four-steppro%lemsol#ing process.Use at least twopro%lemsol#ingstrategies.6mphasise reasoningand effecti#emathematicalcommunication.

KonRecturesystematiccriticale#aluationmathematicalreasoning

Rustificationconclusiongeneralisationmathematical

WEEK &(1+!+" (!+

REVISION

WEEK ,&$, &*#!+"1(!'

SPM TRIAL E2AM#!+"1 !'

WEEK &+1#!'" 1!'

MID SEMESTER BREAK

WEEK &'!'" +!'

REVISION

WEEK (),(1, ( , (&,

(('!'" !11

PECUTAN CLASS

WEEK (#,($, (*

&!11" &!11SPM E2AMINATION )1& .&!11" !1 /

12

SOW Additional Mathematics Form 5 2014

Documents

Transcript of SOW Additional Mathematics Form 5 2014