Scheme of Work Add Maths T5 2016

7/25/2019 Scheme of Work Add Maths T5 2016

1/25

SMK PUTERI TITIWANGSA

JALAN TEMERLOH, 53200 KUALA LUMPUR

Disediakan !e", Dise#ak !e", Disa"kan !e",

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%HAS&IMAH 'T ISMAIL( %KHARIATI 'T TIRON( %ROHANA 'T ISMAIL(

PANITIA MATEMATIK KETUA PANITIA MATEMATIK GURU KANAN SAINS ) MATEMATIK

1


2/25

SMK PUTERI TITIWANGSA&EARL& TEA*HING PLAN +OR ADDITIONAL MATHEMATI*S +ORM 5

205

WEEKS-

DATE

LEARNING O'JE*TI.ES

Students will be taught to

LEARNING OUT*OMES

Students will be able to

SUGGESTED

TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

- 1 -

2

- 1 5-

ALGE'RAI* *OMPONENT

A4 PROGRESSION

1. Undestand and use the !on!e"t o#aith$eti! "ogession.

Lee!

1.1 Identi#% !haa!teisti!s o#aith$eti! "ogessions.

1.& 'ete$ine whethe gi(ense)uen!e is an aith$eti!

"ogession.

Lee! 2

1.* 'ete$ine b% using #o$ula+a, s"e!i#i! te$s in aith$eti!

"ogessions-

b, the nu$be o# te$s inaith$eti! "ogessions

1. /ind +a, the su$ o# the #ist nte$s o#

aith$eti! "ogessions.

b, the su$ o# a s"e!i#i! nu$beo# !onse!uti(e te$s o#aith$eti! "ogessions

!, the (alue o# n, gi(en the su$o# the #ist n te$s o#aith$eti! "ogessions

Lee! 3

1.0 Sol(e "oble$s in(ol(ingaith$eti! "ogessions.

Use ea$"le #o$ eal2li#esituations3 s!ienti#i! oga"hing !al!ulato so#twae

to e"loe aith$eti!"ogessions.

S%ste$ati!4ae#ul3hadwo5ing3

!on#iden!e

6egin withse)uen!es tointodu!eaith$eti!al and

geo$eti!al"ogessions.

In!lude

ea$"les in

algebai! #o$.

In!lude the use

o# the #o$ulaTn7 Sn 2 Sn21

In!lude "oble$sin(ol(ing eal2li#e situations

Inte"eting3Identi#%ingelations3 Ma5ing

In#een!e3Tanslating3

Using o# I4T3Poble$ sol(ing3Mathe$ati!al!o$$uni!ation

4onstu!tion

i/T"ink

2/low Ma"2'ouble 6ubbleMa"

&


3/25

WEEKS-

DATE

LEARNING O'JE*TI.ES

Students will be taught toLEARNING OUT*OMES

Students will be able toSUGGESTED

TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

3- 1 22- &. Undestand and use the !on!e"t

o# geo$eti! "ogession

Lee!

&.1 Identi#% !haa!teisti!s o#geo$eti! "ogessions

&.& 'ete$ine whethe agi(en se)uen!e is ageo$eti! "ogession.

Lee! 2

&.* 'ete$ine b% using#o$ula

a, s"e!i#i! te$s in geo$eti!"ogessions

b, the nu$be o# te$s ingeo$eti! "ogessions

&. /ind + a, the su$ o# the #ist nte$s o#

geo$eti! "ogessions

b, the su$ o# a s"e!i#i! nu$be o#!onse!uti(e te$s o# geo$eti!

"ogessions.

Lee! 3

&.0 /ind + a, the su$ to in#init% o#

geo$eti! "ogessions

b, the #ist te$ o !o$$onatio3 gi(en the su$ toin#init% o# geo$eti!

"ogessions.

&.8 Sol(e "oble$s in(ol(inggeo$eti! "ogessions

Use ea$"les #o$ eal2li#esituations3 s!ienti#i! oga"hing !al!ulatos - and!o$"ute so#twae toe"loe geo$eti!

"ogessions

'is!uss +

A s n 9 3 n

9: then S

r

a

1

S ead as

;su$ toin#init%1,3>&3*,3 >3038,3

>?3@331:,3..

Identi#%ingelationshi"3wo5ing out$entall%3!o$"aing and!ontasting3#inding all

"ossiblesolutions3aanging in.4haa!teiBing3

identi#% "attense(aluating.Poble$2sol(ing

/.LE +ROG

*


4/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

25- 1 26-

ALGE'RAI* *OMPONENT

A74 LINEAR LAW

1. Undestand and use the !on!e"t o#lines o# best #it.

&. A""l% linea law to non2lineaelations.

Lee!

1.8 'aw lines o# best #it b%ins"e!tion o# gi(en data.

Lee! 2

1.? Wite e)uations #o lines o# best

#it.1.@ 'ete$ine (alues o# (aiables

#o$+

a, lines o# best #itb, e)uations o# lines o# best #it.

Lee! 3

&.1 Redu!e non2linea elations tolinea #o$.

&.& 'ete$ine (alues o# !onstants o#non2linea elations gi(en+a, lines o# best #it

b, data.

&.* Cbtain in#o$ation #o$+a, lines o# best #it

b, e)uations o# lines o# best #it.

Use ea$"les #o$ eal2li#esituations to intodu!e the!on!e"t o# linea law.

Use ga"hing !al!ulatos o

!o$"ute so#twae su!h asGeo$eteDs S5et!h"ad toe"loe lines o# best #it.

Patien!eA!!ua!%

Neatness

=i$it data to

linea elationsbetween two(aiables.

Identi#% "attens34o$"aing and!ontasting3

4on!e"tualiBing

Tanslating3

4onstu!tion3Inte"eting3Pedi!ting.

i/T"ink

/low Ma"

/.LE +ROG


5/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

5

-2 1 5-2

*AL*ULUS *OMPONENT

*24 INTEGRATION

1. Undestand and use the

!on!e"t o# inde#inite integal.

Lee!

1.1 'ete$ine integals b% e(esing

di##eentiation.1.& 'ete$ine integals o# a n 3

whee a is a !onstant and n is an

intege3 n1.1.* 'ete$ine integals o# algebai!

e"essions.1. /ind !onstants o# integation3 !3 in

inde#inite integals.

Lee! 2

1.0 'ete$ine e)uations o# !u(es#o$ #un!tions o# gadients.

1.8 'ete$ine b% substitution theintegals o# e"essions o# the#o$ >a F b, n3 whee a and b ae

!onstants3 n is an intege n1.

Use !o$"ute so#twae su!h

as Geo$eteDs S5et!h"ad toe"loe the !on!e"t o#integation.

Patien!e 3

!o2o"eation3ational3s%ste$ati! anddiligen!e.

4oo"eation.E$"hasiBe!onstant o#integation.

ydx ead asintegation o# %with es"e!t to , >

b b

a a

kf x dx k f x=

=b

a

dxxf ,>

a

b

dxxf ,>

'ei(ation o##o$ulae note)uied.

=i$it to one!u(e.

Identi#%ingelationshi"s.Wo5ing out

$entall%.E(aluating.HisualiBingAnal%Bing'awingdiaga$sAanging inode.

Ma5ing!on!lusions.

*24 INTERGRATION

&. /ind (olu$e o# e(olutions when egion bounded b% a !u(e is Use d%na$i! !o$"ute =i$it (olu$es

8


7/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

22-2 1 2-2 otated !o$"letel% about the

>a, 2ais3>b, %2ais.

&.0 As the li$it o# a su$ o# (olu$es. 'ete$ine (olu$es o# e(olutions using #o$ula.

so#twae to e"loe (olu$es

o# e(olutions.

o# e(olution

about the 2aiso

%2ais.

6

26-2 1 -3 MA* TEST

0

23-3 1 27-3

GEOMETRI* *OMPONENT

G24 .E*TORS

1. Undestand and use the !on!e"to# (e!to.

Lee!

1.1 'i##eentiate between (e!to ands!ala )uantities.

1.& 'aw and label die!ted lineseg$ents to e"esent (e!tos.

1.* 'ete$ine the $agnitude anddie!tion o# (e!tos e"esented

b% die!ted line.1. 'ete$ine whethe two (e!tos

ae e)ual.Lee! 2

1.0 Multi"l% (e!tos b% s!alas.1.8 'ete$ine whethe two (e!tos

ae "aallel.

Use ea$"le #o$ eal2li#esituations and d%na$i!!o$"ute so#twae su!h asGeo$eteDs S5et!h"ad toe"loe (e!tos.

Patien!e 3!o2o"eation3ational3s%ste$ati! anddiligen!e.

Use notations+He!tos + ABa 3

I

3 a, A'$

Magnitude +

33I

ABa

ABa 3 .

Inte"eting3

Identi#%ing(e!tos3Ma5ingIn#een!e3Using o# I4T3Poble$sol(ing3Mathe$ati!al

!o$$uni!ationInte"eting3Identi#%ingelations3Ma5ingIn#een!e3Tanslating34o$"aing and

4ontasting

?


8/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

MID TERM 'REAK2-3 1 20-3

2-3 1 25-3 &. Undestand and use the!on!e"ts o# addition andsubta!tion o# (e!tos.

Lee!

2$ 'ete$ine the esultant (e!to o#two "aallel (e!tos.

Lee! 2

2$2 'ete$ine the esultant (e!to o#two non2"aallel (e!tos using +

>a, tiangle law>b, "aalleloga$ law.

2$3 'ete$ine the esultant (e!to o#

thee o $oe (e!tos using the"ol%gon law.

Lee! 3

2$ Subta!t two (e!tos whi!h ae +

>a, "aallel

>b, non2"aallel

2$5 Re"esent (e!tos as a!o$bination o# othe (e!tos.

2$ Sol(e "oble$s in(ol(ingaddition and subta!tion (e!tos

Use eal2li#e situations and$ani"ulati(e $ateials toe"loe addition andsubta!tion o# (e!tos.

Jeo (e!to+I: .

E$"hasise that aBeo (e!to has$agnitude o#Beo.E$"hasiBe

negati(e (e!to+ABAB =

In!lude negati(es!ala.

In!lude +>a, !ollinea

"oints>b, non2"aallel

non2Beo(e!tos.

E$"hasiBe +

I#Ia and

Ib ae

not "aallel and h

Ia 7 k

Ib 3 then h

7 k7 :.

i/T"ink

6ubble Ma"

/.LE +ROG

i/T"ink

Multi /lowMa"

@


9/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

E$"hasiBe +a 2b 7a F>2b ,


10/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

2

2-3/ -

*. Undestand and use (e!tos in

the 4atesian "lane.

Lee!

*.1 E"ess (e!tos in the #o$+a,

IIjyix +

b,

y

x

*.& 'ete$ine $agnitudes o# (e!tos.

Lee! 2

*.* 'ete$ine unit (e!tos in gi(endie!tions.

*. Add two o $oe (e!tos.*.0 Subta!t two (e!tos.*.8 Multi"l% (e!tos b% s!alas.

Lee! 3

*.? Pe#o$ !o$bined o"eations in(e!tos.

*.@ Sol(e "oble$s in(ol(ing (e!tos.

Use ea$"le #o$ eal2li#esituations3 !o$"ute so#twaeto e"loe (e!tos in the4atesian "lane.

Relate unit(e!tos

Ii and

I

j to 4atesian

!oodinates.E$"hasise+

(e!toIi 7

:

1

and

(e!toI

j 7

1

:

/o leaning

out!o$es *.& to*.?3 all (e!tos ae

gi(en in the #o$

IIjyix +

o

y

x.

=i$it !o$bined

o"eations toaddition3

subta!tion and$ulti"li!ation o#

(e!tos b% s!alas.

Poble$sol(ing3Mathe$ati!al!o$$uni!ation

1:


11/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

3

- 1 -

TRIGONOMETRI*

*OMPONENT

T24 TRIGONOMETRI*

+UN*TIONS

1. Undestand the !on!e"t o#"ositi(e and negati(e angles$easued in degees andadians.

&. Undestand and use the si

tigono$eti! #un!tions o#an% angle

Lee!

1.1 Re"esent in a 4atesian "lane3

angles geate than *8:o &adians #o+a, "ositi(e angles

b, negati(e angles

&.1 'e#ine sine3 !osine and tangento# an% angle in a 4atesian "lane.

&.& 'e#ine !otangent3 se!ant and4ose!ant o# an% angle in a4atesian "lane

&.* /ind (alues o# the siTigono$eti! #un!tions o# an%angle.

&. Sol(e tigono$eti! e)uations

Use d%na$i! !o$"uteso#twae su!h as Geo$eteDsS5et!h"ad to e"loe anglesin 4atesian "lane.

Use d%na$i! !o$"ute

so#twae to e"loetigono$eti! #un!tions indegees and adians

Use s!ienti#i! o ga"hi!!al!ulatos to e"loe

tigono$eti! #un!tions o#an% angle.

4on#iden!ePatien!e4ae#ul

Use unit !i!le todete$ine the sine

o# tigono$eti!atios.

E$"hasise+sin 7 !os >: 2

,

!os 7 sin >: 2

,

tan 7 !ot>: 2 ,

!ose! 7 se! >: 2

,

se! 7!ose!>:2,

!ot 7 tan>: 2 ,

E$"hasise the useo# tiangles to #indtigono$eti!atios #o s"e!ial

angles *: : 3 0: and 8: : .

Inte"eting3Identi#%ingelations3Ma5ingIn#een!e3Tanslating3

Using o# I4T3Poble$sol(ing3Mathe$ati!al!o$$uni!ation

i/T"ink

26idge Ma"

2Tee Ma"

11


12/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

- 1 5-

5

- 1 22-

3$ Undestand and use ga"hs o#sinus 3 !osines and tangent#un!tions.

. Undestand and use basi!

identities

Lee! 2

*.1 'aw and s5et!h ga"hs o#tigono$eti! #un!tions + >a, % 7 ! F a sin b >b, % 7 ! F a !os b >!, % 7 ! F a tan b

whee a3 b and ! ae !onstantsand b L :.

Lee! 2

*.& 'ete$ine the nu$be o#solutions to a tigono$eti!e)uation using s5et!hed ga"hs.

*.* Sol(e tigono$eti! e)uations

using dawn ga"hs.

Lee! 3

.1 Po(e basi! identities +

!, 1!ossin && =+ AA

d, AA && se!tan1 =+

e, AecA && !os!ot1 =+.& Po(e tigono$eti! identities

using basi! identities.

Use ea$"les #o$ eal2li#e

situations to intodu!ega"hs o# tigono$eti!#un!tions.

Use ga"hing !al!ulatosand d%na$i! !o$"uteso#twae su!h asGeo$eteDs S5et!h"ad to

e"loe ga"hs o#tigono$eti! #un!tions.

Use s!ienti#i! o ga"hing

!al!ulatos and d%na$i!s!o$"ute so#twae su!h asGeo$eteDs S5et!h"ad toe"loe basi! identities.

Use angles in

>a, degees>b, adians3in te$so# .

E$"hasise the!haa!teisti!s o#sine3 !osine andtangent ga"hs.In!lude

tigono$eti!#un!tionsin(ol(ing$odulus.

E!lude

!o$binations o#tigono$eti!

#un!tions.

6asi! identities

ae also 5nown asP%thagoeanidentities

In!lude leaningout!o$es &.1 and&.&.

'ei(ation o#addition #o$ulae

/.LE +ROG

1&


13/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

25- 1 26- 0. Undestand and use addition

#o$ulae and double2angle#o$ulae.

.* Sol(e tigono$eti! e)uation

using basi! identities

Lee! 3

0.1 Po(e tigono$eti! identitiesusing addition #o$ulae #o

( ) ( )BABA !os3sin and( )BAtan .

0.& 'ei(e double2angle #o$ulae

#o A&sin 3 A&!os and

A&tan .

0.* Po(e tigono$eti! identitiesusing addition #o$ulae andodouble2angle #o$ulae.

0. Sol(e tigono$eti! e)uations.

Use d%na$i! !o$"uteso#twae su!h as Geo$eteDsS5et!h"ad to e"loeaddition #o$ulae anddouble2angle #o$ulae.

not e)uied.

'is!uss hal#2angle#o$ulae.

E!lude +

xA!os F

cxb =sin 3

-5 1 -5

STATISTI*S *OMPONENT

S24 PERMUTATIONS AND

*OM'INATION

1. Undestand and use the !on!e"to# "e$utation.

Lee!

1.1 'ete$ine the total nu$be o#wa%s to "e#o$ su!!essi(e

e(ents using $ulti"li!ation ule.1.& 'ete$ine the nu$be o#

Use $ani"ulati(e $ateialsto e"loe $ulti"li!ation

ule.

Pedi!ting 4iti!althin5ingMa5ingin#een!es

Patien!e

Inte"eting3Identi#%ingelations3Ma5ing

In#een!e3Using o# I4T3

1*


14/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

"e$utations o# ndi##eent

obOe!ts.1.* 'ete$ine the nu$be o#"e$utation o# n di##eentobOe!ts ta5en rat a ti$e

Lee! 2

1. 'ete$ine the nu$be o#"e$utations o# n di##eentobOe!ts #o gi(en !onditions.

1.0 'ete$ine the nu$be o#"e$utations o# n di##eent

obOe!ts # ta5en rat a ti$e#o gi(en !onditions

Use eal2li#e situations and

!o$"ute so#twae to e"loe"e$utations

/o this to"i!+

a, Intodu!e the!on!e"t b% usingnu$ei!alea$"les.

b, 4al!ulatosshould onl% beused a#testudents ha(eundestood the!on!e"t.=i$it to * e(ents

E!lude !asesin(ol(ingidenti!al obOe!ts.

Poble$

sol(ing3Mathe$ati!al!o$$uni!ation

i/T"ink

4i!le Ma"

MID &EAR E8AMINATION

7/6

-5 1 26-5

MID &EAR 'REAK

30-5 1 -

205- 1 6-

S24 PERMUTATIONS AND

*OM'INATION

Inte"eting3Identi#%ingelations3

1


15/25

WEEKS-

DATE

LEARNING O'JE*TI.ES



TEA*HING AND

LEARNING A*TI.ITIES

.ALUES AND

POINTS TO

NOTE

HOTS-

I/THINK-.LE

+ROG

&. Undestand and use the !on!e"t

o# !o$bination

Lee!

&.1 'ete$ine the nu$be o#!o$binations o# obOe!ts !hosen#o$ n di##eent obOe!ts.

Lee! 2

&.& 'ete$ine the nu$be o#!o$binations o# obOe!ts !hosen#o$ n di##eent obOe!ts #o gi(en!onditions.

E"loe 4o$binations UsingReal2=i#e Situations And4o$"ute So#twae.

E"lain the!on!e"t o#"e$utations b%listing all "ossibleaange$ents.In!lude notationsa, n 7 n>n21,>n2&,>*,>&,>1,

b, : 71n ead as ;n

#a!toial

Scheme of Work Add Maths T5 2016

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