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",
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
%HAS&IMAH 'T ISMAIL( %KHARIATI 'T TIRON( %ROHANA 'T ISMAIL(
PANITIA MATEMATIK KETUA PANITIA MATEMATIK GURU KANAN SAINS ) MATEMATIK
1
7/25/2019 Scheme of Work Add Maths T5 2016
2/25
SMK PUTERI TITIWANGSA&EARL& TEA*HING PLAN +OR ADDITIONAL MATHEMATI*S +ORM 5
205
WEEKS-
DATE
LEARNING O'JE*TI.ES
Students will be taught to
LEARNING OUT*OMES
Students will be able to
SUGGESTED
TEA*HING AND
LEARNING A*TI.ITIES
.ALUES AND
POINTS TO
NOTE
HOTS-
I/THINK-.LE
+ROG
- 1 -
2
- 1 5-
ALGE'RAI* *OMPONENT
A4 PROGRESSION
1. Undestand and use the !on!e"t o#aith$eti! "ogession.
Lee!
1.1 Identi#% !haa!teisti!s o#aith$eti! "ogessions.
1.& 'ete$ine whethe gi(ense)uen!e is an aith$eti!
"ogession.
Lee! 2
1.* 'ete$ine b% using #o$ula+a, s"e!i#i! te$s in aith$eti!
"ogessions-
b, the nu$be o# te$s inaith$eti! "ogessions
1. /ind +a, the su$ o# the #ist nte$s o#
aith$eti! "ogessions.
b, the su$ o# a s"e!i#i! nu$beo# !onse!uti(e te$s o#aith$eti! "ogessions
!, the (alue o# n, gi(en the su$o# the #ist n te$s o#aith$eti! "ogessions
Lee! 3
1.0 Sol(e "oble$s in(ol(ingaith$eti! "ogessions.
Use ea$"le #o$ eal2li#esituations3 s!ienti#i! oga"hing !al!ulato so#twae
to e"loe aith$eti!"ogessions.
S%ste$ati!4ae#ul3hadwo5ing3
!on#iden!e
6egin withse)uen!es tointodu!eaith$eti!al and
geo$eti!al"ogessions.
In!lude
ea$"les in
algebai! #o$.
In!lude the use
o# the #o$ulaTn7 Sn 2 Sn21
In!lude "oble$sin(ol(ing eal2li#e situations
Inte"eting3Identi#%ingelations3 Ma5ing
In#een!e3Tanslating3
Using o# I4T3Poble$ sol(ing3Mathe$ati!al!o$$uni!ation
4onstu!tion
i/T"ink
2/low Ma"2'ouble 6ubbleMa"
&
7/25/2019 Scheme of Work Add Maths T5 2016
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
*
7/25/2019 Scheme of Work Add Maths T5 2016
4/25
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
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
7/25/2019 Scheme of Work Add Maths T5 2016
5/25
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
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
7/25/2019 Scheme of Work Add Maths T5 2016
7/25
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
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$"aing and
4ontasting
?
7/25/2019 Scheme of Work Add Maths T5 2016
8/25
WEEKS-
DATE
LEARNING O'JE*TI.ES
Students will be taught toLEARNING OUT*OMES
Students will be able toSUGGESTED
TEA*HING AND
LEARNING A*TI.ITIES
.ALUES AND
POINTS TO
NOTE
HOTS-
I/THINK-.LE
+ROG
MID TERM 'REAK2-3 1 20-3
2-3 1 25-3 &. Undestand and use the!on!e"ts o# addition andsubta!tion o# (e!tos.
Lee!
2$ '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$"hasiBe +
I#Ia and
Ib ae
not "aallel and h
Ia 7 k
Ib 3 then h
7 k7 :.
i/T"ink
6ubble Ma"
/.LE +ROG
i/T"ink
Multi /lowMa"
@
7/25/2019 Scheme of Work Add Maths T5 2016
9/25
WEEKS-
DATE
LEARNING O'JE*TI.ES
Students will be taught toLEARNING OUT*OMES
Students will be able toSUGGESTED
TEA*HING AND
LEARNING A*TI.ITIES
.ALUES AND
POINTS TO
NOTE
HOTS-
I/THINK-.LE
+ROG
E$"hasiBe +a 2b 7a F>2b ,
7/25/2019 Scheme of Work Add Maths T5 2016
10/25
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
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$$uni!ation
1:
7/25/2019 Scheme of Work Add Maths T5 2016
11/25
WEEKS-
DATE
LEARNING O'JE*TI.ES
Students will be taught toLEARNING OUT*OMES
Students will be able toSUGGESTED
TEA*HING AND
LEARNING A*TI.ITIES
.ALUES AND
POINTS TO
NOTE
HOTS-
I/THINK-.LE
+ROG
3
- 1 -
TRIGONOMETRI*
*OMPONENT
T24 TRIGONOMETRI*
+UN*TIONS
1. Undestand the !on!e"t o#"ositi(e and negati(e angles$easued in degees andadians.
&. Undestand and use the si
tigono$eti! #un!tions o#an% angle
Lee!
1.1 Re"esent in a 4atesian "lane3
angles geate than *8:o &adians #o+a, "ositi(e angles
b, negati(e angles
&.1 'e#ine sine3 !osine and tangento# an% angle in a 4atesian "lane.
&.& 'e#ine !otangent3 se!ant and4ose!ant o# an% angle in a4atesian "lane
&.* /ind (alues o# the siTigono$eti! #un!tions o# an%angle.
&. Sol(e tigono$eti! e)uations
Use d%na$i! !o$"uteso#twae su!h as Geo$eteDsS5et!h"ad to e"loe anglesin 4atesian "lane.
Use d%na$i! !o$"ute
so#twae to e"loetigono$eti! #un!tions indegees and adians
Use s!ienti#i! o ga"hi!!al!ulatos to e"loe
tigono$eti! #un!tions o#an% angle.
4on#iden!ePatien!e4ae#ul
Use unit !i!le todete$ine the sine
o# tigono$eti!atios.
E$"hasise+sin 7 !os >: 2
,
!os 7 sin >: 2
,
tan 7 !ot>: 2 ,
!ose! 7 se! >: 2
,
se! 7!ose!>:2,
!ot 7 tan>: 2 ,
E$"hasise the useo# tiangles to #indtigono$eti!atios #o s"e!ial
angles *: : 3 0: and 8: : .
Inte"eting3Identi#%ingelations3Ma5ingIn#een!e3Tanslating3
Using o# I4T3Poble$sol(ing3Mathe$ati!al!o$$uni!ation
i/T"ink
26idge Ma"
2Tee Ma"
11
7/25/2019 Scheme of Work Add Maths T5 2016
12/25
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
- 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&
7/25/2019 Scheme of Work Add Maths T5 2016
13/25
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
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 $ulti"li!ation
ule.
Pedi!ting 4iti!althin5ingMa5ingin#een!es
Patien!e
Inte"eting3Identi#%ingelations3Ma5ing
In#een!e3Using o# I4T3
1*
7/25/2019 Scheme of Work Add Maths T5 2016
14/25
WEEKS-
DATE
LEARNING O'JE*TI.ES
Students will be taught toLEARNING OUT*OMES
Students will be able toSUGGESTED
TEA*HING AND
LEARNING A*TI.ITIES
.ALUES AND
POINTS TO
NOTE
HOTS-
I/THINK-.LE
+ROG
"e$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
7/25/2019 Scheme of Work Add Maths T5 2016
15/25
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
&. 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
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