students' modul (pmr matematik pemulihan)
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ANALYSIS OF PMR QUESTIONS (2001 2006)
(FOR THE CHOOSEN TOPICS)
TOPIC PAPER 1 PAPER 2
01 02 03 04 05 06 01 02 03 04 05 06
1 Directed
Numbers
- 1 - 1 - - - - 1 1
2 Fraction 2 2 1 1 - 1 2 1 1 -
3 Linear equation 1 1 2 - 1 - 1 1 1
4 Linear
inequalities
2 2 2 2 1 - - - 1 1
5 Squares, ubes,
Square roots,
ube roots
2 1 2 - - 1 1 1 1 1
6 Loci 1 1 1 1 1 - - - 1 1
! "rans#ormations 1 2 2 1 2 2 2 2 2
$ Scale dra%in& - 1 1 1 - - - - - 1
' Statistics 3 3 5 5 4 1 1 1 2 1
10 Solid &eometr(
)net*
1 1 2 1 1 1 - - 1 -
11 onstruction - - - - - 1 1 1 1 1
12 +ra o##unctions
1 1 1 1 2 - - - 1 1
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MODUL PEMULIHAN MATEMATIK PMR (STF)
.riters /
1 n aa oani bt i
2 7n 8od mir ama bin Sudin
3 7n 8od Foi bin 9amri
4 7n :smail bin %an& Non&
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TOPIC : DIRECTED NUMBERS
Duration / 2 ours
Imp!"#$" $"%& :
1 ;nderstand te question
2 Determine te si&n to te numbers and te oeration used
3 :# t%o same si&ns meet ten it %ill be ositi =
= )? * > ?
? )= * > ?
4 Follo% te @AD8S la% / @A )@racBet #Allo%ed b(*, D8 )Di
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SECTION ONE
MODULE 1 DIRECTED NUMBERS
T'& *%&"$ p#p%! +$&&"& , 10 *%&"$&- A$&.%! #// *%&"$&- !"% *!
#$&.%!& +/%#!/ $ "'% &p#+% p!3%3- S'. *! .!4$5- T'% *% ,
+#/+*/#"! & $" #//.%3-
1 alculate te ) 2 marBs *
2 alculate te ) 2 marBs *
3 alculate te ) 2 marBs *
4 Find te ) 2 marBs *
5 alculate te ) 2 marBs *
6 Find te ) 2 marBs *
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! alculate te ) 2 marBs *
$ alculate te ) 2 marBs *
' Find te ) 2 marBs *
10 alculate te ) 2 marBs *
SECTION TO
MODULE 1 DIRECTED NUMBERS
T'& *%&"$ p#p%! +$&&"& , 10 *%&"$&- A$&.%! #// *%&"$&- !"% *!
#$&.%!& +/%#!/ $ "'% &p#+% p!3%3- S'. *! .!4$5- T'% *% ,
+#/+*/#"! & $" #//.%3-
1 Find te ) 2 marBs *
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2 alculate te ) 2 marBs *
3 alculate te ) 2 marBs *
4 Find te ) 2 marBs *
5 alculate te ) 2 marBs *6 Find te ) 2 marBs *
! alculate te ) 2 marBs *
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$ alculate te ) 2 marBs *
' Find te ) 2 marBs *
10 alculate te ) 2 marBs *
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TOPIC : FRACTION
Duration / 1 our
Imp!"#$" $"%& :
1 Determine te t(e o# #raction ? a roer #raction or an imroer #raction
2 :# it is a mied number ten it sould be con )2 G 4* = )3 G 3* > 1!
3 4 )3 G 4* 12
)iii* 5 - 3 > )5 G 4* - )3 G 6* > 20 - 1$ > 2 > 1
6 4 )6 G 4* 24 24 12
)i )3 G1 = 2* - )2 G3* > 5 - 6 > -1
3 5 )3 G 5* 15 15
) 2 G 3 > 6 > 3
5 4 5 G 4 20 10
) 2 G 4 > 2 G 4 > $
5 4 5 3 5 G 3 13
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TOPIC : FRACTIONS
SET 1
F$3 "'% #/*% , %#+' , "'% ,//.$5-
1 =
+
3
2
2
1
12
!2 =
3
1-
5
4
15
!
3 =
5
2-
4
3
14
54 =
5
3
3
2-
5
4
5 =
5
32
5
2-
3
12 6 =
6
5
3
2-
10
11
! =
4
3-
2
11
3
11 $ =
+
3
2
6
1
2
11
' =
+
4
1
5
12
3
210 =
$
1
4
11-
2
11
TOPIC : FRACTIONS
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SET 2
1 alculate te
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5 alculate te
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TOPIC : SQUARES SQUARE ROOTS CUBES AND CUBE ROOTS
SET 1 : SQUARES AND CUBES
Duration / 1 our
Imp!"#$" $"%& :
1 S*#!%&? a number is multil( b( itsel#
aaa =2
examples/ 11112 == '3332 ==
'
4
3
2
3
2
3
22
=
=
or'
4
33
22
3
2
3
2
2
22
=
=
=
( ) 040202020 2 ==
Note/ i* squares to one decimal lace t%o decimal laces
ii* te squares o# an( number is al%a(s ositi
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)&*3
5
3
)*3
5
2
)i* ( )23 54 + )* ( ) 32 45
2 Find te
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Imp!"#$" $"%& :
1 S*#!% !"& /
aaaa ==2
examples/ 11111 2 === 3333' 2 ===
3
2
3
2
33
22
'
4
3
2
==
=
Note/ te square roots o# a #raction can be #ound b( #indin& te square
roots o# te numerator and te denominator searatel(
( ) 10101010010 2 ===
( ) 50505050250 2 ===
Note/ square roots to t%o decimal laces one decimal lace
2 C*7% !"&/
aa =3 3
examples / 111111 3 333 ===
4444464 3 333 ===
5
3
5
3
555
333
125
2!3
3
33 =
=
=
( ) 10101010100010 3 333 ===
( ) 40404040400640 3 333 ===
Note/ cube roots to tree decimal laces one decimal lace
Q*%&"$&/
1 alculate te
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)&* 3 64 )* 3 512
)i* 3 3430 )* 3 1250
)B* 3 0640 )l* 3 1250
2 alculate te
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4 )a* Find te
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! )a* Find te
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! Follo% te @AD8S la% / @A )@racBet #Allo%ed b(*, D8 )Di 4 x = 2 - 2 > 4 - 2
x > 2
)ii* x - 3 > 4 x - 3 = 3 > 4 = 3
x > !
)iii* 3x > 2 3 > 2
3 3
x > 2
3
)i ! x G 5 > ! G 5
5 5
x > 35
LINEAR EQUATIONS ( SET 1 )
A$&.%! #// *%&"$&- !"% *! #$&.%!& +/%#!/ $ "'% &p#+% p!3%3- S'.
*! .!4$5- T'% *% , +#/+*/#"! & $" #//.%3-
1 Sol 16 )b* 2m = 3 > 4
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c*3
a> - 5 )d* 3( ? 6 > 15
)4 marBs*
2 Sol 6 )b*
2
m- 3 > 4
c* 5n = 4 > 24 )d* 6 ? 4( > 22
)4 marBs*
3 Sol 2m )b* 5( > 4 ? 3(
c* 3n ? 4 > n = 2 )d* 4 ? 6 > = 6
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)4 marBs*
4 Sol $ )b* B = 2 > ? 2) B - 4 *
)3 marBs*
5 Sol 10 ? 4m )b*2
10+m> 3m
)4 marBs*
LINEAR EQUATIONS ( SET 2 )
A$&.%! #// *%&"$&- !"% *! #$&.%!& +/%#!/ $ "'% &p#+% p!3%3- S'.
*! .!4$5- T'% *% , +#/+*/#"! & $" #//.%3-
2 Sol 1$ )b* 2a - 4 > $
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c*!
x> - 3 )d* 4( = 4 > 20
)4 marBs*
2 Sol 20 )b*4
y- 3 > 4
c* 3n = 4 > - 20 )d*3
5a> 10
)4 marBs*
3 Sol 2m )b* 2( > 15 ? 3(
c* 6a ? $ > a = 2 )d* 3# > 5# - 14
)4 marBs*
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4 Sol 12 )b* 2n - 2 > 4 ) n - 4 *
)3 marBs*
5 Sol 2 )b* 2 ) m ? 1 * > $ ? 3m
)4
marBs*
TOPIC : LINEAR INEQUALITIES
Duration / 1 ours
Imp!"#$" $"%& :
1 n inequalities is a matematical statement tat describes one eression is
&reater tan or less tan anoter in
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- J is read as K&reater tan
- M is read as Kless tan
- is read as K&reater tan or equal to
- O is read as Kless tan or equal to
3 linear inequalities in one unBno%n is a relationsi bet%een an unBno%n in
te #irst de&ree and a number4 "e condition o# an inequalit( is uncan&ed %en a number is added to or
subtract #rom bot sides o# te inequalit(
5 "e condition o# an inequalit( is uncan&ed %en an inequalit( is multilied
or di
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c* 3m J - 12 )d* 3# = 5 O 20
e* 3a = 2 20 )#*6
k -3
) 4marBs *
2 Sol
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a* 2m = 3 J -3 )b* ' ? 2B O -1
c* 5 -2
xJ 4 )d*
4
f= 3 1
) 4 marBs *
4 Sol
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6 List all te inte&er
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- examples/1 /2
1 dra%in& is t%o times bi&&er tan obect
1 / 2 dra%in& is t%o times smaller tan obect
Scale 1 /2
1 Len&t o# te side o# te dra%in&
len&t o# te corresondin& side o# te obect3 e
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2 Dia&ram 2 so%s a traeium
16 m
6 m
10 m
An te &rid in te ans%er sace, dra% dia&ram 2 usin& te scale 1 / 200 "e
&rid as equal squares %it sides o# 1 cm
H3 marBsI
Dia&ram 2
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3 Dia&ram 3 so%s a circle %it radius 6 cm
An te &rid in te ans%er sace, dra% dia&ram 3 usin& te scale 1 / 2 "e &rid
as equal squares %it sides o# 1 cm
H3 marBsI
4 Dia&ram 4 so%s a ea&on
' cm
' cm
15 cm
6 cm
21 cm
An te &rid in te ans%er sace, dra% dia&ram 4 usin& te scale 1 / 2 "e &ridas equal squares %it sides o# 1 cm
Dia&ram 3
Dia&ram 4
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H3 marBsI
5 Dia&ram 5 so%s a traeium
4 cm
3 cm
5 cm
An te &rid in te ans%er sace, dra% dia&ram 5 usin& te scale 1 /2
1 "e
&rid as equal squares %it sides o# 1 cm
H3 marBsI
Dia&ram 5
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6 Dia&ram 6 so%s a ea&on
3 cm
4 cm
4 cm 5 cm
3 cm
An te &rid in te ans%er sace, dra% dia&ram 6 usin& te scale 1 /2
1 "e
&rid as equal squares %it sides o# 1 cm
H3 marBsI
! Dia&ram ! so%s a ea&on
Dia&ram 6
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10 m
6 m
16 m
An te &rid in te ans%er sace, dra% dia&ram ! usin& te scale 1 / 200 "e
&rid as equal squares %it sides o# 1 cm
H3 marBsI
$ Dia&ram $ so%s a combined sae o# an isosceles and a al#-circle
Dia&ram !
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15 cm
1$ cm
An te &rid in te ans%er sace, dra% dia&ram $ usin& te scale 1 / 3 "e &rid
as equal squares %it sides o# 1 cm
H3 marBsI
' Dia&ram ' so%s a combined sae o# a square and a al#-circle
3 cm
An te &rid in te ans%er sace, dra% dia&ram ' usin& te scale 1 /2
1 "e
&rid as equal squares %it sides o# 1 cm
H3 marBsI
Dia&ram '
Dia&ram $
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11 Dia&ram 11 so%s a #i&ure dra%n on a square &rids Dra% te scale dra%in&
o# te #i&ure b( usin& te scale 1 /2
1 H3
marksI
Answer :Dia&ram 11
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TOPIC : SOLID 8EOMETRY (NET)
Duration / 1 our
Imp!"#$" $"%& :
1 Determine te dia&ram
2 Determine te number and sae o# te sur#ace
3 Determine te scale/-
e& / #ull scale dra%in& same sie
4 ;se (ta&oras ratio %ere needed e& / 3, 4, 5 or 6, $, 10 etc
5 &eometric solid can a
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Dra% a #ull scale, te net o# te cuboid on te &rid in te ans%er sace "e
&rid as equal squares %it sides o# 1 unit
H3 marBsI
3 Dia&ram 3 so%s a rism
Dra% a #ull scale, te net o# te rism on te &rid in te ans%er sace "e
&rid as equal squares %it sides o# 1 unit
H3 marBsI
4 Dia&ram 4 so%s a cone %it diameter 6 units
6 units
4 unitsDia&ram 3
3 units
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5 units
Dra% a #ull scale, te net o# te cuboid on te &rid in te ans%er sace "e
&rid as equal squares %it sides o# 1 unit
H3 marBsI
5 Dia&ram 5 so%s a ri&t c(linder "e radius o# te c(linder is 35 units and
its ei&t is 4 units
Dra% a #ull scale, te net o# te c(linder on te &rid in te ans%er sace "e
&rid as equal squares %it sides o# 1 unit
H3 marBsI
Dia&ram 5
Dia&ram 4
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6 Dia&ram 6 so%s a cuboid
Dra% a #ull scale, te net o# te cuboid on te &rid in te ans%er sace "e
&rid as equal squares %it sides o# 1 unit H3 marksI
Answer/
! Dia&ram ! so%s te net o# a solid
5 units
4 units Dia&ram 6
3 units
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Name te solid H1 marBI
Answer :
$ Dia&ram $ so%s a cube "e len&t o# te side is 4 cm
Dra% a #ull scale, te net o# te cube on te &rid in te ans%er sace "e &rid
as equal squares %it sides o# 1 unit H3 marksI
Answer/
' Dia&ram ' so%s te net o# a solid
4 units Dia&ram $
Dia&ram !
Dia&ram '
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Name te solid H1 marBI
Answer :
TOPIC : TRANSFORMATIONS
Duration / 3 ours
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Imp!"#$" $"%& :
1 trans#ormation is a one-to-one corresondence bet%een oints on a lane
2 Four t(e o# trans#ormation /)a* "ranslation
- a trans#ormation %ere all oints on te lane are mo
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TRANSLATION
1 8arB te ima&e o# te oint under te #ollo%in& translations
i*
4
4
ii*
53
iii*
2
6
i
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REFLECTION
1 :n te dia&ram, dra% te ima&e o# under a re#lection in tey-ais
2 :n te dia&ram, dra% te ima&e o# " under a re#lection in
a* tex-ais
b* tey-ais
c* te liney>x
d* "e liney > 2
3 Dra% te ais re#lection @ i# R is te ima&e o# L under a re#lection
4 :n te dia&ram, is te ima&e o# Q under a re#lection
Describe te re#lection
R
x
K
K
KL
L
L
y
x
y
T
2
0 2
;2
;2
6
6
6P
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5 :n te dia&ram, Q is te ima&e o# under a trans#ormation A
Describe #ull( te trans#ormation A
5 :n te dia&ram, R is te ima&e o# L under a trans#ormation M
Describe #ull( te trans#ormation M-
TOPIC : TRANSFORMATIONS
SET A
b* 8arB %it te s(mbol te intersection o# te locus T and U
ns%er/
@
S A Q
D
3 Dia&ram in te ans%er sace so%s a square @D T, U and 9 are treemo
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a* An te dia&ram, dra%/
i* "e locus o# T suc tat T > T
ii* "e locus o# U suc tat U > UD
iii* "e locus o# 9 suc tat 9 > 97
b* ence, marBs %it te s(mbol te intersection o# te locus T and U
7
ns%er/ @
D
4 Dia&ram in te ans%er sace so%s a rectan&ular @D T and U are t%o
mo
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i* "e locus o# tat is constantl( 1 cm #rom te strai&t line VR
ii* "e locus o# @ tat is constantl( 2 cm #rom te strai&t line V8
b* ence, marBs %it te s(mbol te intersection o# te locus and @
ns%er/V R
8 L
6 Dia&ram in te ans%er sace so%s a rectan&ular @D U and 9 are t%o
mo
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1 Dia&ram in te ans%er sace so%s a square @D dra%n on a &rid o# equal
squares %it sides o# 1 unit T, U and 9 are tree mo RL
B* "e locus o# @ tat is constantl( 3 cm #rom te strai&t line V8
ii* "e locus o# U suc tat it is equidistant #rom strai&t lines VR
and
V8
b* ence, marBs %it te s(mbol te intersection o# te locus and @
ns%er/
V R
8 L
3 Dia&ram in te ans%er sace so%s #our squares, RVN, RQLV, NV8S and
VL8 , @ and are tree mo
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i* te locus o# suc tat V > 2 cm
ii* te locus o# @ suc tat it is equidistant #rom oints and V
iii* te locus o# suc tat it is constantl( 1 cm #rom te strai&t line NL
i 4 cm
* "e locus o# 9 suc tat it is equidistant #rom strai&t lines @
and D
b* ence, marBs %it te s(mbol te intersection o# te locus T and U
ns%er/ @
D
5 Dia&ram in te ans%er sace so%s an equilateral trian&le @ o# sides 6
cmT and U are t%o mo
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a* An te dia&ram, dra%
i* "e locus o# T suc tat its distance #rom oint and are te same
ii* "e locus o# U suc tat its distance #rom oint @ is 3 cm
b* ence, marBs %it te s(mbol te intersection o# te locus T and U
ns%er/
@
6 Dia&ram belo% so%s a rectan&ular QS , @ and are tree mo
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1 Dia&ram in te ans%er sace so%s a rectan&ular @D U and 9 are t%o
moT
ii* "e locus o# U suc tat it is equidistant #rom strai&t lines D
and @
b* ence, marBs %it te s(mbol te intersection o# te locus T and U
ns%er/
@
D
3 Dia&ram in te ans%er sace so%s a trian&le TU9 , @ and are tree
mo
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a* i* "e locus o# suc tat it is mo 35 cm
iii* "e locus o# suc tat it is equidistant #rom oints U and 9
b* ence, marBs %it te s(mbol te intersection o# te locus and
ns%er/
T
U
9
5 Dia&ram in te ans%er sace so%s #our squares, RVN, RQLV, NV8S and
VL8 , @ and are tree mo
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i* te locus o# suc tat V > VN
ii* te locus o# @ suc tat it is equidistant #rom oints and
iii* te locus o# suc tat it is constantl( 2 cm #rom te strai&t line S
i @;
iii* "e locus o# suc tat it is equidistant #rom strai&t lines "S and S
; " S
ns%er/
Q
TOPIC : 8EOMTRICAL CONSTRUCTIONS
Duration / 3 ours
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Imp!"#$" $"%& :
1 onstruct line se&ment
- usin& a ruler, dra% a strai&t line
- marB a oint on te line and label - usin& a air o# comasses, set it to te radius needed
- %it te centre o# te marBed oint, dra% an arc to cut te strai&t line
2 onstruct an&les 60o
- #ollo% stes in )1*
- %it te centre o# te marBed oint, dra% a bi& arc to cut te strai&t line
- usin& te same radius and te intersection o# te arc and te strai&t line as
te centre, dra% anoter arc
- oint te #irst oint and te intersection o# t%o arcs to &et 60 oan&le
3 onstruct an&le bisector- usin& a ruler, dra% t%o strai&t lines %ic intersect eac oter
- %it te intersection as te centre, dra% arcs to cut bot lines
- %itout can&in& te radius and te oints o# intersection o# te line and arc,
dra% arcs tat cut eac oter
- oint te intersection o# t%o lines and te intersection o# t%o arc
4 onstruct erendicular bisector
- #ollo% stes in )1*
- set te comasses to a radius sli&tl( o
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SECTION ONE
MODULE THREE CONSTRUCTION
T'& *%&"$ p#p%! +$&&"& , 10 *%&"$&- A$&.%! #// *%&"$&- !"% *!
#$&.%!& +/%#!/ $ "'% &p#+% p!3%3- S'. *! .!4$5-
1 onstruct a bisector #rom te an&elbelo%
a
c
b
d
2
@
n&le @
@
n&le @
@
n&le @
n&le @
@
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2 onstruct 60W an&le #rom te oint
An te line belo%
a
b
c
d
e
#
3
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SECTION TO
1 onstruct 30W an&le #rom te oint An te line belo%
a
b
c
d
e
#
4
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2 onstruct erendicular line ) '0W*
#rom te oint on te line belo%
a
b
c
d
e
#
5
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SECTION TREE
1 onstruct 45W #rom te oint on
te line belo%
a
b
c
d
e
#
6
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2 onstruct erendicular line ) '0W*
#rom te oint belo%
a
b
c
d
e
#
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SECTION ONE
MODULE 1 STATISTICS
T'& *%&"$ p#p%! +$&&"& , @ *%&"$&- A$&.%! #// *%&"$&- !"% *!
#$&.%!& +/%#!/ $ "'% &p#+% p!3%3- S'. *! .!4$5- T'% *% ,
+#/+*/#"! & $" #//.%3-
1 "able so%s te membersi o# 4 societies in a scool :n te square &rid ro
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2 "able so%s te membersi o# 4 clubs in a scool :n te square &rid ro
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Using ! unit equal 2 pencils on y - axis raw a line graph"
ns%er/
4 T#7/% so%s t(es o# #ruit tree &ro%n in Sale Arcard
Using ! unit equal !0 trees on y - axis raw a bar chart
Tp% , F!*"&N*m7%! , T!%%&Durian40ambutan!0Lan&sat100
TABLE
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ns%er/
5 T#7/% so%s te a
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SECTION TO
MODULE 1 STATISTICS
T'& *%&"$ p#p%! +$&&"& , @ *%&"$&- A$&.%! #// *%&"$&- !"% *!
#$&.%!& +/%#!/ $ "'% &p#+% p!3%3- S'. *! .!4$5- T'% *% ,
+#/+*/#"! & #//.%3-
1 T#7/%so%s te number o# co-curricular acti
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2 T#7/% so%s te number o# students %o liBe #our t(es o# drinBs
"e in#ormation #or "ea is so%n #ull( in te ie cart in te ans%er sace
)a* omlete te table in ans%er sace
)b* omlete te ie cart to reresent all te in#ormation in T#7/%H# marksI
Answer:
3 T#7/%so%s te number o# students %o liBe la( #our t(es o# sorts
"e in#ormation #or u&b( is so%n #ull( in te ie cart in te ans%er sace
T%#
'0W
"(es o# DrinBsNumber o# Studentsn&le o# te
Sector8ilo15o##ee'Nesca#e6"ea10
TABLE
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)a* omlete te table in ans%er sace
)b* omlete te ie cart to reresent all te in#ormation in T#7/%
H# marksI
Answer:
4 T#7/%so%s te number o# students %o liBe in
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Answer:
4 T#7/%so%s te ercenta&es o# students %o #ul#ill teir leisure time %it
acti
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"(es o# cti
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SECTION THREE
MODULE 1 STATISTICS
T'& *%&"$ p#p%! +$&&"& , @ *%&"$&- A$&.%! #// *%&"$&- !"% *!
#$&.%!& +/%#!/ $ "'% &p#+% p!3%3- S'. *! .!4$5- T'% *% ,
+#/+*/#"! & #//.%3-
1 T#7/% so%s te number o# ma&aines in te readin& corner o# tree classes
"e in#ormation #or te @iaBsana lass is so%n #ull( in te icto&ra in te
ans%er sace
omlete te icto&ra to reresent all te in#ormation in T#7/%
H# marksI
Answer:
C/#&&N*m7%! ,
M#5#$%&mana60@iaBsana40emerlan&100
TABLE
N*m7%! , m#5#$%& $ "'% !%#3$5 +!$%!-
mana
@iaBsana
emerlan&
reresents 20 booBs
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2 T#7/% so%s te number o# student a
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3 T#7/% so%s te number o# Durian tree in tree illa&e
"e in#ormation #or te lass is so%n #ull( in te icto&ra in te ans%er
sace
omlete te icto&ra to reresent all te in#ormation in T#7/%
H# marksI
Answer:
>//#5%N*m7%! , D*!#$ "!%%65@45100
TABLE
N*m7%! , D*!#$ "!%% $ "'!%% //#5%-
@
reresents 20 tree
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4 T#7/% so%s te a
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5 T#7/% so%s te total net ro#it o# sellin& #or #i
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TOPIC : 8RAPH OF FUNCTION
Duration / 3 ours
Imp!"#$" $"%& :
1 a #unction is a relationsi bet%een t%o
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TOPIC : 8RAPHS OF FUNCTIONS
S7" 1
Dra% te -ais and te (-ais and marB te scales
1 ;sin& a scale o# 2+m " 1 *$" $ "'%x;#?&and 2 +m " 2 *$" $ "'%y;
#?&-
2 ;sin& a scale o# 2+m " 1 *$" $ "'%x;#?&and 2 +m " @ *$" $ "'%y;
#?&-
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3 ;sin& a scale o# 2+m " 1 *$" $ "'%x;#?&and 2 +m " 10 *$" $ "'%y;
#?&-
4 ;sin& a scale o# 1+m " 1 *$" $ "'%x;#?&and 1 +m " @ *$" $ "'%y;
#?&-
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1 Use the graph paper pro&ie to answer this question"
"able 1 so%s te
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TOPIC : 8RAPHS OF FUNCTIONS
S7" 2
1 Use the graph paper pro&ie to answer this question""able 1 so%s te
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4 Use the graph paper pro&ie to answer this question"
"able 1 so%s te
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TOPIC : 8RAPHS OF FUNCTIONS
S7" 3
1 Use the graph paper pro&ie to answer this question"
"able 1 so%s te
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ENHANCEMENT QUESTIONS
Duration / 1 our
"e questions are based on te toics tat a
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and 04
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! :n dia&ram 2, is te ima&e o# " under trans#ormation
Describe in #ull trans#ormation H2 marksI
Answer :
)" Dia&ram 3 so%s a sae o# an arro%
2 cm
3 cm 5 cm
2 cm
2 cm
An te &rid in te ans%er sace, dra% dia&ram 3 usin& te scale 1 /2
1 "e
&rid as equal squares %it sides o# 1 cm H3 marksI
Answer :
$
$
4
6
2
62 4
" Dia&ram 2
Dia&ram 3
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'
"e data in dia&ram 4, so%s scores obtained b( 20 students in a 8atematics test
1! 1$ 15 16 20 20 1! 16 16 151$ 1' 1! 15 20 1! 1$ 1' 16 1!
)a* ;sin& te data, comlete te #requenc( table in te ans%er sace
)b* State te mode H3 marksI
Answer :
)a*
Scores 15 16 1! 1$ 1' 20
Frequenc(
)b*
10 Dia&ram 5 so%s a rism
Dra% a #ull scale, te net o# te rism on te &rid in te ans%er sace "e
&rid as equal squares %it sides o# 1 unit H3 marksI
Answer/
6 units
4 units Dia&ram 5
3 units
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11 *et squares an protractors are not allowe for this question
Dia&ram 6 so%s a strai&t line+,
)a* ;sin& onl( a ruler and a air o# comasses,)i* construct trian&le+,, startin& #rom te strai&t line+,, suc tat
o-+, 60= and,> 6 cm
)ii* "en construct te erendicular line trou& te oint
)b* @ased on te dia&ram constructed in )a*, measure te erendicular distance
bet%een ointand te strai&t line+,
H. marksI
Answer/
12 Use the graph paper to answer this question
"able belo% so%s te
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@( usin& a scale o# 2 cm to 1 unit on tex-ais and 2 cm to 5 units on tey-ais,
dra% te &ra o# #unction
H# marksI
/raph for question !2"
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