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QUESTION 3(a)
NON-ROUTINE PROBLEM
Year : 2
Learning outcome : Solve prolem! involving multiplication "it#in 2$ %$ & an' (
time! in real li)e !ituation!*
+ue!tion ,:
l)ie u.! a mo'el car an' a mo'el plane to ma/e* T#e car #a! t"o !et! o) ,0
!tic/er! an' t#e plane #a! t#ree !et! o) ,( !tic/er!*
1o" man. !tic/er! are t#ere altoget#er
,* Un'er!tan' t#e prolem
• mo'el car an' a mo'el plane
• Mo'el car 3 2 !et! 4 , !et 3 ,0 !tic/er! 5
• Mo'el plane 3 % !et! 4 , !et 3 ,( !tic/er! 5
• Total o) all t#e !tic/er! )or ot# o) t#e mo'el!
2* 6evice t#e plan
• 6ra" t#e 'iagram
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%* 7arr. out t#e plan
4 ,0 !tic/er! 8 2 5 9 %&
4 ,( !tic/er! 8 % 5 9 &(
%& !tic/er! &( !tic/er! 9 0; !tic/er! <
&* 7#ec/ t#e an!"er
• U!e t#e inver!e met#o' : ''ition Su!traction
Multiplication 6ivi!ion
0; !tic/er! 3 &( !tic/er! 9 %& !tic/er!
%& !tic/er! = 2 9 ,0 !tic/er!
&( !tic/er! = % 9 ,( !tic/er!
1717151717
3rd SET2nd SET1st SET2nd SET1st SET
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Year : &
Learning outcome : Solve !utraction an' a''ition prolem! up to ,>> >>>
+ue!tion 2:
Mari!!a love! to collect ottle cap!* S#e #a! 2? 0(> ottle cap!* 1er !i!ter give! #er
anot#er %0 (>> ottle cap!* I) Mari!!a give! a"a. (> (>> ottle cap! )or rec.cling$
#o" man. ottle cap! 'oe! !#e #ave no"
,* Un'er!tan' t#e prolem
• Mari!!a #a! 9 2? 0(> ottle cap!
• 1er !i!ter give! 9 %0 (>> ottle cap!
• S#e give! a"a. 9 (> (>> ottle cap!
2* 6evice t#e plan
• 6ra" t#e 'iagram
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%* 7arr. out t#e plan
&* 7#ec/ t#e an!"er
• U!e t#e inver!e met#o' : ''ition Su!traction
,% 0(> (> (>> 9 ?& (>>
?& 2(> 3 %0 (>> 9 2? 0(>
Mari!!a #a!
2? 0(> ottlecap!
1er !i!ter give!
%0 (>> ottlecap!
(> (>> ottlecap!
Rec.cle2? 0(> ottle cap! %0 (>> ottle
cap! 9 ?& 2(> ottle cap!
?& (>> ottle cap! 3 (> (>> ottle
cap! 9 ,% 0(> ottle cap!
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QUESTION 3(b)
IN@ESTIATION IN MT1EMTI7S
Year : (
Learning outcome: calculating t#e area o) compo!ite-t"o 'imen!ional !#ape
4triangle5
+ue!tion ,:
7alculate t#e area o) triangle in 6iagram ,
,* Un'er!tan' t#e prolem
• rea o) a !mall o8 i! , cm
• T#ere are o8e! )or t#e a!e
• T#ere are ? o8e! )or t#e #eig#t
2* 6evice t#e plan
• U!ing t#e )ormula o) t#e area o) triangle
%* 7arr. out t#e plan
1eig#t$ # 9 ,cm 8 ,cm 8
9 cm
Ba!e$ 9 ,cm 8 ,cm 8 ?
9 ? cm
rea o) triangle 9 C 8 #eig#t$ # 8 a!e$
9 C 8 cm 8 ? cm
9 2& cm
, cm
, cm
6IARM ,
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&* 7#ec/ t#e an!"er
• rea o) triangle 9 C 8 #eig#t$ # 8 a!e$
2& cm 9 C 8 cm 8 a!e$
2& cm 9 & cm
Ba!e$ 9 2& cm = & cm
9 ? cm
OR
2& cm 9 C 8 #eig#t$ # 8 ? cm
2& cm 9 % cm
1eig#t$ # 9 2& cm = % cm
9 cm
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Year : (
Learning outcome: Solve prolem! involving volume o) compo!ite %-6 !#ape!*
+ue!tion 2:
T#e area o) t#e a!e o) a cuoi'al gla!! container i! 02> cmD* T#e #eig#t o) t#e
container i! 2& cm* o) t#e container i! )ille' . t#e "ater* 7alculate t#e volume o)
"ater in t#e container in cmF*
,* Un'er!tan' t#e prolem
• T#e area o) t#e a!e o) t#e container 9 02> cmD
• T#e #eig#t o) t#e container 9 2& cm
• i! )ille' . "ater
• Gin' t#e volume o) t#e "ater in cmF
2* 6evice t#e plan
• U!e t#e 'iagram
• U!e t#e )ormula o) volume o) t#e cuoi'
%* 7arr. out t#e plan
02> cmD
T#e #eig#t$# o) )ille' "ater 9 8 2& cm
9 ? cm
@olume o) cuoi' 9 rea o) a!e$ cmD 8 #eig#t$ cm
9 02> cmD 8 ? cm
9 & %2> cmF
&* 7#ec/ t#e an!"er
02> cmD
2& cm
)ille' .
"ater
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T#e #eig#t$# o) )ille' "ater 9 & %2> cmF = 02> cmD
9 ? cm
QUESTION 3(c)
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PPLI7TION
Year : ,
Learning outcome: Solve !imple prolem involving mone. in realli)e !ituation!*
+ue!tion , :
Siti u.! a gla!! o) orange Huice an' t"o piece! o) ca/e! at #er !c#ool canteen ever.
'a.* I) t#e Huice i! RM ,*%> an' a piece o) ca/e i! RM >*>$ #o" muc# 'oe! !#e
!pen' to u. t#e 'rin/ an' t#e ca/e! )or )ive 'a.!
,* Un'er!tan' t#e prolem
• Price o) t#e orange Huice : RM ,*%>
• Price o) a piece o) ca/e : RM >*>• Siti u.! 2 piece! o) ca/e! ever. 'a.
• Total o) mone. !#e !pen'! )or ( 'a.!
2* 6evice t#e plan
• U!e a tale
• U!e t#e 'iagram
%* 7arr. out t#e plan
ITEM +UNTITY PRI7E PER ITEM TOTL
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ORNAE UI7E
, RM ,*%> RM ,*%>
7JE
2 RM >*> RM ,*?>
TOTL RM 2*;>
Price o) orange Huice an' t"o piece! o) ca/e! per 'a. 9 RM 2*;>
Price )or ( 'a.! 9 RM 2*;> 8 (
9 RM ,&*(>
&* 7#ec/ t#e an!"er
• U!e t#e inver!e met#o' : Multiplication 6ivi!ion
Price per 'a. 9 RM ,&*(> = (
9 RM 2*;>
Price per piece o) ca/e 9 RM ,*?> = 2
9 RM >*>
Year : ,
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Learning outcome: Solving prolem in real li)e !ituation u!ing a''ition an'
!u!traction "it# t#e #ig#e!t numer i! ,>*
+ue!tion 2 :
#ma' u.! ,> can'ie! at # Seng !#op* 1e t#en give! % can'ie! to #i! rot#er an'
anot#er % can'ie! to S#i/in* 1o" man. !"eet! t#at #e #a! no"
,* Un'er!tan' t#e prolem
• #ma' u.! 9 ,> can'ie!
• 1e give! to #i! rot#er 9 % can'ie!
• 1e give! to S#i/in 9 ? can'ie!
2* 6evice t#e plan
• 6ra" t#e 'iagram
%* 7arr. out t#e plan
,> can'ie! 3 % can'ie! 3 % can'ie!
9 & can'ie!
&* 7#ec/ t#e an!"er
• U!e inver!e met#o' : Su!traction ''ition
!utract
!utract
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#ma'K! can'ie! 9 & % %
9 ,> can'ie!
QUESTION 3(d)
AMES
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Year : 2
Learning outcome: Solving prolem involving multiplication "it#in , to ( an' a''ition
al!o !u!traction*
+ue!tion , :
In a )ootall tournament$ t#e rule! in or'er )or a team to e a "inner i! . getting t#e
#ig#e!t point!* ( point! "ill e given to t#e team t#at i! "in )or t#e matc#* T#e team
t#at i! lo!e "ill get , point an' )or t#e tie matc#$ 2 point! "ill e given* ImranK! team
#a! "on % matc#e!$ lo!e )or one time an' , tie matc#* 'amK! team "in 2 matc#$
lo!e 2 time! an' , tie matc#* #at i! t#e 'i))erence et"een ot# o) t#e teamK!
point!
,* Un'er!tan' t#e prolem
• in 9 ( point!
• Lo!e 9 , point
• Tie 9 2 point!
• ImranK! team 9 in : % time!
Lo!e : , time
Tie : , time
• 'amK! team 9 in : 2 time!
Lo!e : 2 time
Tie : , time
2* 6evice t#e plan
•
U!e t#e tale
%* 7arr. out t#e plan
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Team in Point! Lo!e Point! Tie Point!
Imran % % 8 ( 9 ,( , , 8 , 9 , , , 8 2 9 2
'am 2 2 8 ( 9,> 2 2 8 , 9 2 , 2 8 2 9 &
ImranK! team 9 ,( , 2
9 ,
'amK! team 9 ,> 2 &
9 ,?
6i))erence! et"een ot# team! 9 , 3 ,?
9 2 point! <
&* 7#ec/ t#e an!"er
• U!e t#e inver!e met#o' : ''ition Su!traction
ImranK! team 9 2 point! ,? point!
9 , point!
Year : ,
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Learning outcome: !olving prolem in real li)e involving a''ition an' !u!traction
+ue!tion 2 :
Gi'a$ I.lia$ S.ira$ ia#$ Mira an' Gare love to pla. a game* ll o) t#em are 'ivi'e' into
2 group! "#ic# contain % people in eac# group* In t#e game$ i! given ; all!* T#e.
#ave to t#ro" t#e all! into a a!/et* Gi'a$ I.lia an' S.ira are in Team "#ile ot#er!
are in Team B* I) Team can t#ro" & all! into t#e a!/et an' Team B cannot get (
all! to get into t#e a!/et$ )in' t#e total o) t#e all! t#at ot# team can t#ro" into t#e
a!/et*
,* Un'er!tan' t#e prolem
• Team can t#ro" into t#e a!/et 9 & all!
• Team B cannot t#ro" into t#e a!/et 9 ( all!
• T#e total o) all! t#at ot# team can t#ro" into t#e a!/et
2* 6evice a plan
• U!e t#e 'iagram
%* 7arr. out t#e plan
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T#e all! t#at can e t#ro"n . team B 9 re' all
9 & all!
T#e total o) t#e all! t#at can e t#ro"n . ot# team! 9 & &
9 all! <
&* 7#ec/ t#e an!"er
• U!ing inver!e met#o' : ''ition Su!traction
T#e all! t#at can e t#ro"n . team B 9 3 &
9 & all!
QUESTION 2(a)
Re' all 9 can t#ro"
into t#e a!/et
Yello" all 9 cannot
t#ro" into t#e a!/et
Team Team B
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Price )or ? apple! an' ,> orange! i! RM ,%* I) t#e price )or eac# o) t#e 2 apple! i!
RM ,*(>* #at i! t#e price )or % orange!
Solution :
Price )or an apple 9 RM ,*(> 2
9 RM >*0(
Price )or ? apple! 9 RM >*0( 8 ?
9 RM &*(>
Price )or ? apple! an' ,> orange! 9 RM ,%
Price )or ,> orange! 9 RM ,% 3 ? apple!
9 RM ,% 3 RM &*(>
9 RM *(>
Price )or an orange 9 RM *(> ,>
9 RM >*(
Price )or % orange! 9 RM >*( 8 %
9 RM 2*((
QUESTION 2(b)
REGER TO T1E RELI
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7i/gu Ja!!im #a! ,0? pencil!* S#e give! 2? pencil! to Mut#u* T#e alance o) t#e
pencil! are 'ivi'e' euall. to Siti$ Tan an' S#anti* 7alculate t#e pencil! t#at Siti get!*
SOLUTION :
Aive! to Siti
7i/gu Ja!!imK!
pencil! 9 ,0? 2? pencil!
Balance are
'ivi'e'
Mut#u
S#antiTan
Siti
Siti
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Balance 9 ,0? 3 2?
9 ,(>
SitiK! pencil! 9 ,(> %
9 (> pencil! <
QUESTION 2(c)
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T#ere i! a o8 contain! re' all!$ green all!$ .ello" all! an' lue all!* >*% o) t#e
all! are re' all!$ >*& are green all! an' ot#er! are lue an' .ello" all!* T#e !um
o) lue all! are t"ice t#e !um o) t#e .ello" all!* T#e numer o) re' all! are ,0
more t#an lue all!* 1o" man. all! are t#ere in t#e o8
QUESTION 2(d)
AreenRe'Yello"Blue
>*&>*%
2 : ,
2 : ,&=,>%=,>
Numer o) re' all! i! ,0 more
t#an lue all!
,0
SOLUTION :
, part o) re' 9 ,0 all!
,> part! 9 ,> 8 ,0
9 ,0> all!
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alil #a! RM *>>* T#e total o) mone. t#at alil$ Ma#mu' an' Bor#an #ave i! RM
%>*>>* T#e total o) mone. t#at alil$ Ma#mu' an' 6a#lan #ave i! RM &>*>>* I) t#e
total o) mone. t#at )our o) t#em #ave i! RM (2*>>$ "#at i! t#e total o) mone. t#at
Ma#mu' #a!
6IARM ,
6IARM 2
6IARM %
RM %>*>>
Bor#anMa#mu'alil
RM %>*>> 3 RM *>>
9 RM 22*>>
RM *>>
RM &>*>>
6a#lanMa#mu'alil
RM *>>
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RM (2*>>
Bor#an 6a#lanMa#mu'alil
RM (2*>> 3 RM&>*>>
9 RM ,2*>>
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l
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