2015 Scheme of Work Add Maths F5

8/10/2019 2015 Scheme of Work Add Maths F5

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progressions.

L!"!# 32.5 'ind "

a# the sum to in$nity ofgeometric progressions

# the $rst term orcommon ratio* given thesum to in$nity ofgeometric progressions.

2.6 (o!ve pro!ems invo!vinggeometric progressions.

#)umu!ativesequences such as*71#* 72*3#* 7&*5*6#*78*9*:*10#*4..

WEEK

TOPICS /LEARNING

OBJECTIVES[students will be

taught to:]

LEARNING OUTCOMES[students will be able to:]

POINTS TO NOTE

W$

W526.01 /06.02

A% LINEAR LAW

1. Understand anduse the conceptof !ines of est$t.

2. pp!y !inear !awto non/!inearre!ations.

L!"!# 1

1.6Draw !ines of est $t yinspection of given data.

L!"!# 21.8;rite equations for !ines of

est $t.1.9Determine va!ues of

varia!es from"a# !ines of est $t# equations of !ines of est

$t.

L!"!# 32.1atience

ccuracy?eatness

imit data to !inearre!ations etween twovaria!es.

W6

W&0:.02 28.02

C2INTEGRATION

1. Understandand use theconcept ofinde$niteintegra!.

L!"!# 11.1Determine integra!s y

reversing [email protected] integra!s of a- n *

where a is a constant and n is

an integer* nA1.

1.3Determine integra!s ofa!geraic e-pressions.

1.&'ind constants of integration*c* in inde$nite integra!s.

L!"!# 21.5Determine equations of

curves from functions ofgradients.

1.6Determine y sustitution

>atience *co/operation*rationa!* systematicand di!igence.

)ooperation.mphasiBe constant ofintegration.

ydx read as Cintegrationof y with respect to -

imit integration ofnu dx

w hereu a- .


3/9

the integra!s of e-pressions ofthe form 7a- # n* where aand are constants* n is an

integer nA1.

C2INTERGRATION

2. Understand anduse theconcept ofde$niteintegra!.

L!"!# 22.1 'ind de$nite integra!s of

a!geraic e-pressions.

L!"!# 32.2 'ind areas under curves as

the !imit of a sum of areas.2.3 Determine areas under

curves using formu!a.2.& 'ind vo!ume of revo!utions

when region ounded y acurve is rotated comp!ete!yaout the7a# -/a-is*7# y/a-is.

2.5 s the !imit of a sum of

vo!umes. Determine vo!umesof revo!utions using formu!a

Inc!ude

( ) ( )b b

a a

kf x dx k f x dx=

=b

a

dxxf )(

a

b

dxxf )(

Derivation of formu!aenot required.imit to one curve.

imit vo!umes of

revo!ution aout the -/a-is ory/a-is.

W'02.03 06.03

S T U D ( W E E K / R E V I S I O N

W100:.03 13.03

TEST PERFORMANCE 1

1&.03 22.03

MID TERM HOLIDA(

WEEK

TOPICS /LEARNING


taught to:]


POINTS TO NOTE

W11

W1323.03 10.0&

G2 VECTORS1. Understand and

use the conceptof vector.

2. Understand and

use theconcepts of

addition andsutraction of

vectors.

L!"!# 11.1 Di@erentiate etween

vector and sca!ar quantities.

1.2 Draw and !ae! directed !inesegments to representvectors.

1.3 Determine the magnitudeand direction of vectorsrepresented y directed !ine.

1.& Determine whether twovectors are equa!.

L!"!# 21.5 Eu!tip!y vectors y sca!ars.1.6 Determine whether two

vectors are para!!e!.

L!"!# 12.1 Determine the resu!tant

vector of two para!!e!vectors.

>atience *co/operation* rationa!*systematic and

di!igence.Use notations"

Fectors " ABa ,~

* ),

AB*Eagnitude "

,,~

ABa

ABa , .

Gero vector"~0 .

mphasise that a Bero

vector has magnitudeof Bero.

mphasiBe negative

vector" ABAB =

Inc!ude negative sca!ar.


4/9

L!"!# 22.2 Determine the resu!tant

vector of two non/para!!e!vectors using "7a# triang!e !aw7# para!!e!ogram !aw.

2.3 Determine the resu!tantvector of three or morevectors using the po!ygon!aw.

L!"!# 32.&(utract two vectors which

are "7a# para!!e!7# non/para!!e!

2.5


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inequa!ities.L!"!# 21.& 'ind !inear inequa!ities that

de$ne a shaded region.2 Understand and

use theconcept of !inearprogramming.

L!"!# 32.1 (o!ve pro!ems re!ated to

!inear programming y"a# writing !inear inequa!ities

and equations descriing asituation*

# shading the region offeasi!e so!utions*

c# determining and drawingthe oHective function ax by k where a* b and k areconstants*

d# determining graphica!!y theoptimum va!ue of theoHective function.

W1%

0&.05 09.05

S T U D ( W E E K / R E V I S I O N

W1& W20

11.05 2:.05

MID (EAR E+AM

30.05 1&.06

MID (EAR HOLIDA(

W21

W23

15.06

03.08

T2TRIGONOMETRICFUNCTIONS

1. Understand theconcept ofpositive andnegative ang!esmeasured indegrees andradians.

2. Understand anduse the si-trigonometric

functions of anyang!e

L!"!# 11.1


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&. Understand anduse asicidentities

5. Understand anduse additionformu!ae anddou!e/ang!eformu!ae.

L!"!# 23.2Determine the numer of

so!utions to a trigonometricequation using s+etched

graphs.

3.3 (o!ve trigonometricequations using drawngraphs.

L!"!# 3&.1>rove asic identities "

c# 1cossin 22 =+ AA

d# AA 22 sectan1 =+

e# AecA 22 coscot1 =+

&.2>rove trigonometric identitiesusing asic identities.

&.3(o!ve trigonometric equationusing asic identities

L!"!# 35.1 >rove trigonometric

identities using additionformu!ae for

( ) ( )BABA cos,sin and( )BAtan .

5.2 Derive dou!e/ang!eformu!ae for A2sin * A2cos and A2tan .

5.3 >rove trigonometricidentities using addition

formu!ae andLor dou!e/ang!eformu!ae.

5.& (o!ve trigonometricequations.

invo!ving modu!us.-c!ude cominationsof trigonometricfunctions.,asic identities are a!so+nown as >ythagoreanidentities

Inc!ude !earningoutcomes 2.1 and 2.2.Derivation of additionformu!ae not required.Discuss ha!f/ang!eformu!ae.-c!ude "

xAcos cxb =sin *

W2$

06.08

10.08

S2PERMUTATIONS, COMBINATION

1. Understand anduse the conceptof permutation.

L!"!# 11.1 Determine the tota!

numer of ways to performsuccessive events usingmu!tip!ication ru!e.

1.2 Determine the numer ofpermutation of ndi@erentoHects.

1.3 Determine the numer ofpermutation of n di@erent

oHects ta+en rat a time

L!"!# 21.& Determine the numer of

permutations of n di@erentoHects for given conditions.

1.5 Determine the numer ofpermutations of n di@erent

oHects f ta+en rat a time forgiven conditions

>redicting )ritica!thin+ingEa+ing inferences>atience

'or this topic"a# Introduce theconcept y usingnumerica! e-amp!es.# )a!cu!ators shou!don!y e used afterstudents haveunderstood theconcept.imit to 3 events

-c!ude cases invo!vingidentica! oHects.

2. Understand anduse the conceptof comination


cominations of r oHectschosen from n di@erent

-p!ain the concept ofpermutations y !istinga!! possi!earrangements.


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oHects.


cominations of r oHectschosen from n di@erentoHects for given conditions.

Inc!ude notationsa# nM n7n/1#7n/2#473#72#71## 0M 1nM read as n factoria!

-c!ude cases invo!vingarrangement of oHectsin a circ!e.-p!ain the concept ofcominations y !istinga!! possi!e se!ections.Use e-amp!es to

i!!ustrate rnC

!r

Prn

WEEK

TOPICS /LEARNING


taught to:]


POINTS TO NOTE

W25

W2613.08 2&.08

S3 PROBABILIT(

1. Understandand use theconcept ofproai!ity

2. Understand anduse the conceptof proai!ity ofmutua!!ye-c!usiveevents.

3. Understand anduse the conceptof proai!ity ofindependentevents.

L!"!# 11.1 Descrie the samp!e space

of an e-periment.1.2 Determine the numer of

outcomes of an event1.3 Determine the proai!ity of

an event.

L!"!# 21.& Determine y using formu!a"

a# speci$c terms in arithmeticprogressions%

# the numer of terms inarithmetic progressions.

L!"!# 22.1Determine whether two

events are mutua!!ye-c!usive.

2.2Determine the proai!ity oftwo or more events that aremutua!!y e-c!usive.

L!"!# 33.2 Determine whether two

events are independent.3.2 Determine the proai!ity

of two independent events.3.3 Determine the proai!ity

of three independent events.

con$dence

Use set notationsDiscuss"a. )!assica! proai!ity7theoretica! proai!ity#ca! progressions.. (uHective proai!ityc. re!ative frequencyproai!ity

7e-perimenta!proai!ity#mphasiBe"=n!y c!assica!proai!ity is used toso!ve pro!ems

mphasiBe"

)(

)()(

)(

BAP

BPAP

BAP

+

=

Using Fenn Diagrams.Inc!ude events that aremutua!!y e-c!usive ande-haustive.imit to three mutua!!ye-c!usive events.Inc!ude tree diagrams.

W2%

W2&28.08

08.09

S$ PROBABILIT(DISTRIBUTIONS

1. Understand anduse the conceptof inomia!distriution.

L!"!# 1

1.1 ist a!! possi!e va!ues of adiscrete random varia!e.

L!"!# 21.2 Determine the proai!ity of

an event in a inomia!distriution.

Nonesty* fairness*

carefu!* independent

Inc!udes thecharacteristics of,ernou!!i tria!s.'or !earning outcomes1.2 and 1.&* derivations


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2. Understandand use theconcept ofnorma!distriutions

1.3 >!ot inomia! distriutionsgraphs.

1.& Determine mean* variance*and standard deviations of ainomia! distriutions

L!"!# 31.5 (o!ve pro!ems invo!ving

inomia! distriution.

L!"!# 12.1 Descrie continuous random

varia!es using set notations.2.2 'ind proai!ity of B/va!ues

for standard norma!distriution.

L!"!# 22.3 )onvert random varia!e of

norma! distriutions* O* tostandardiBed varia!e* G.

L!"!# 32.&


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use the conceptof ve!ocity.

3. Understand anduse the conceptof acce!eration.

2.1 Determine ve!ocity functionof a partic!e y [email protected] Determine instantaneousve!ocity of a partic!e.

L!"!# 32.3 Determine disp!acement ofa

partic!e from ve!ocityfunction y

integration

L!"!# 23.1Determine acce!eration

function of a partic!e ydi@erentiation.

L!"!# 33.2Determine instantaneous

acce!eration of a partic!e.3.3Determine instantaneousve!ocity of a partic!e fromacce!eration function yintegration.

3.&Determine disp!acement of apartic!e from acce!erationfunction y integration.

3.5(o!ve pro!ems invo!vingmotion a!ong a straight !ine.

the rate of change ofdisp!acement

v dt

ds

Inc!ude graphs ofve!ocity functionsDiscuss"a# uniform

ve!ocity

# Bero instantaneousc# positive ve!ocityd# negative ve!ocity

s dt

dv

mphasis acce!erationas the rate ofchange of ve!ocity.Discuss "

a# uniformacce!eration

# Beroacce!eration

c# positiveacce!eration

d# negativeacce!eration

W31

2&.09 29.09

STUD( WEEK / REV IS ION

W32 W3$

01.0: 19.0:

SPM TR IAL E+AM

W 35 W3'

29.0: 30.10

REVIS ION - MOCK E+AM .OTHER STATES PAPERS

W$0

02.11 03.12

SPM 2015

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2015 Scheme of Work Add Maths F5