RAMALAN MATEMATIK SPM

E

x

e ee
E
f*G T

It

$

F? $
$$
na 1 1

d-

€ I

I

fig

T:

i z
."-

cp

p$ {1

P3 F*

{F FA
$E

s'E

€€ [E

ii g3

€F;sF
+

E $ !g
SR
$$

E
r

:?
EH

$i$r F
fo

.=

'-

3
(tt

$isi+g$a

b
=
's
:
k



3
l,

+

T

t

:a
*

R$Fa
$5

$$

$Fi F s
s'uF
I

Fag
FF
-iit
:E

g\
* tr

sFF
g$gE$
lFr
sE

i$EF
'
f

fi'

$$$

$g$F$+ii
se S $ s$

.
s
FF
$ FF3 H
$
g
Fs
F3 :

tr
Lp

"t-.

3
lv

F3

E$l

FS
->

3
0o

A
Y

g

3.

* o =. i

!

$:FE

F
b
=

gl

a=

ig
$r
E ts

$

q sE

tr
s
$$
s.t

E
nsF
\F

\

t!

t
F$iFl
$3:uuffi
I,
S=

'

T i E$ EFg

q

!F!5

te

$3

$F
+
!*

$fr

q

)F

P
)

5

s

G

TFi H a di sS'JF
AEs$s 3J

rP i E r
i oo

f

E

i$
$
XF.F. $s

,Hqit$g
,rr;$iFg

6.

$

$FEg-$

$F$$S
E
N
5:
$* E
BE
I::1FE=g
6e

S'w -

s

:

lr*
1l

-;,I

RF .

;a

sg

F3
I'S

sf
di tF

{F

SF

iF

h.g

FiE

$F

E'

** g

O-E

$3E
;.i ;;
st

Rg
FE i

{

x

l $i E _,
gs:

x Ei

|l

$ it

T

g
tr

g r!
5 E)
fi ' *

I I
s- E

4
sF
s Er
, "8

r

J-

F

3
tc

vl

s

q

$$
$g
Y:
ss.
riI **
$$
$g
i.:"

H=
sF
s3

$t
ts

5F'

s;
:X

$s

^d
to

'ct

sa

fF
* .8

ET

s E'
SE
3
tt

3
f

5i-

$$gs5-$i $F€E
$E
35
!e=l

F6 -

sa

! r=
=o

9f r
r0

B3
gg

*$asstg
o'5

*o

E

$1
Ee
*
F$
F*F€
6

{o

=t
80
o
o

-

o

a
3

*

> i;_

$E$

s
lr6

g
i$

s

i$
F$

D

E
O
e
s
G

3
o
!t

cr
Y
e

!
it
F

gE3 at #
iird
Jli

= \=>

!.l 4
r)i
^a
=T

F=
,3 L

z .t=

cl

ta x

*i =ts \

z.1'-,

i;:

;:s
?

=C '"-

-

Z

:-T

!

j

=.

d

r

-'deE

:'!
{J

sa )
a'-

'.)Z;
=

e:2

*:T
.: i.*
! po

3=l
'2=7ii

i 'X
lR

A7:
" 21=z
7' ,+

rF{
!S x

l-

I

t

qtC
s:'D

tt

D:

i :.F

It

FE

=t6

a

:.i:

-

Fs t

tF-

)i 7
I

-';

:j - t i> -

:o?

=-

i;n t

t+o

=€ 7s
:3- F

RE=

=a>

{=

:@

E, Vt 7'
= 2' . .

i= ^sF>

>B

*a
>3

.. +q
-t.'..

i

=,9
IF

=.€

;ir i

:-=:
: Pi

:

A.=

73c

ii.F=
=e

F9

Ei
lc

iF
:T

r

Ss
a(

+

-( -D
:".
3

€nz
Eal

F-

>=
a.,

-t

G:l

t)
a
(
t

s)

1
P
\

$

-a

€

o

X TF

>
-t

s

* ir

a
:

F n=Li d

€

sri

:!

t.:

g F s =g3 i H
i
"

i
S

=
6

E
+B
=

i
a
e

i
:
el
i
'^

s
*
B
:

35
* i'
:j
sJ.

E

t

s

:.F

9
P

ts
.=

='

F
=

--r- ;
F !4
-;,

3

*
3
d:.a
s:'

d+oB+
JQQ.

T8
+<
is.

=

::
i

;
;

*
6

}r

$

,t
\---F
\)

-

r

@

?
3
=
3

F
,c

c

"d

o

3

5

;

*

+
6
z;

*
:
:

\

S

;r

:

S5

-:

i:

s3'
dcv

='E
:;

dii'

*9.
s

C:F

6-

ls
:o
\tr-:

*I

7

*$

:.E E
L

E ,*+
:g 6
- a

e dFF
: *:"
+d

F
;
':

Fq
+-

t

S-

:=€ - =o
.t

E

i

o

S

+
:' oe'
o =C E'

,.

5
=

.

o

;-

C

v

'sE T
::*

.G

ot

s

{o

A

$g$$g: #;"r e=

si

.v

3s

z

B:*;{*eE$1E
gF

€
3

I l-

t l-

- .b - U

$ iu i [i3

q \<
llll

€$$tsE; E[
'$

- .!1,
nll

$g$

g aatr
*;-Y
O-O+

"3* r ; : 3 3 ? :.3.9 3
gls

s

*'Er,i

-o-o

? 7q?

;

{3;

= ; (l

FdJ
\ES

i s $ F&3 r $
i F E$F F
g
a
a-2*

sFC
r:h
::il
=:
!.p
!a

ZatO

sI

s oi

' g F**$ I

-o

3
6

+

i 3$,$ t

s lsi 5 r;E
3

€.s!

F

9i i

it

e

o
8J

$f,
s
g'E
D

EIl'

g

o

l$ig
$
:r :q
F $ ;;tg

E$g $$$ggE$$
i EEI IE e
FEiEiEB$
lgE$ii$
$iBt i Bi3 F $EgE
ig i* $ $
h5

d !i
ao
E[o '

3 { " 8 *r*r
;t;i

e;-

OrO

a
t,g
ri =

-:Et L :

i l =.

o6

rE

q9
It

g E.

a.,

#E

'(U
nB

C'E

sq

s1
tN

;e
xS
n+
t*

rE

i*

3*
3x

*OSE

I

e

o

€gE
sg€ s6

qiT ;
si;

gsgd

s€

E+ o

i

8S
*g

;

a

b

NJ

^q
p5'

P

irl

t9

g
6
tt

a
Io

6.
g
I

g.
x

3
af
=

g
o

ie

N

xt

N

t
3
D
;t
6
.F

i
rE
E
fi
ig i6 g= f
[g B 7 d
$ $ ;$
g:EE

I'i $$5

4

-l''

P

*'s?o

.ga

i

eI

e

g

F

!c
x
!!

0o
lr
tl

v
tl

EF
RE
ri
$T,
!r{
Fg

N
c

o

N

rit

o

o

n
o

s
*
E

N

@

N

6

9)

F

3t
(rl

E
P
F

)

tL

J,€

I

JE

Tf

I

N

$

T:.
5

"\'

f\.

:
li

(a)
.

. | 4--_

t ..{-_

rc#/\lrAev1

a Cartesian
Diagram 13.1 shorvspoint M and straight line -t:3 drarvn on
ptane.
=
puda sutttu satah
Rajah l3.l nteiunjukkan titik l+,tdan garis lttrus x 3 dilukis
Cartesart.
1,
i1

I

I

:

ra

I

i

!

I
I

i

I

'r_-_.1---.]
t;r
it:

i6

1
I

0
I

Mt j,-:t i
I

.

Diagram13-t
Raiah13.l

r-r\

reflection at
TransfomrationT is a translation I ." I *d transformationR is a
\4.J
the line -r = 3
penjelmaan T ialah satu fr.awlasi

{t1-2\
satu
i I dan penielmaan R ialah
i.4i

pantulan pada garis x=3
follorving
Statethe coordinaresof the image of point M (5,- 3) under the
transformations:
N-vatakankoordinotimejbagititikMdibawahpen"ielwtanbefilut:

(i)

T

pc-tis

(ii)

TR

[3 mcrkj]
f3 markahl

fY|t€1

(t)

_
Diagram l3.2 sho*s threetrape.zinm
Cartesianplane.
Rajah l3.2tnenuizjukkantiga trutpeziltmABCD, EFGH don.JKL*{ dilukis
pada sua&tsatah Cartes.

v
T

/.

4
/
M

Yj.

' i.,.

:

'i'li

'ti

B
',/

.-l;:lii

:.r*:.,,
i.:;ij:a
L\i:-: l

i.:r:;:_!:.
::.i.:-'l.
ita:,,.

{

L

D

-:'..!

:.:'

il'l::.'

,\

o

I

_
{i)

I

1

Diagram 13.2
^Rajah13.2

JKLMis the image of ABCD under the combined transformarionVU"
Describein full, the transformation:
JKIlvt ialah imej bagi ABCI] di baw,ahgobungm pe4jelnnanylJHursilran selengkaprqtapenj elmaan:

{ir)

(a\

Il,

(b,

v.

It is given that the trapezium ABCD representthe region of area 30 m2.
Calculatethe area,in m3, the shadedresion.
Diberi bahswo trepeEiumABCD ntewakili sustu ks*,asqt yang rwetupurywi

fuex3Am".
Hitung luu, dalam mz, kan,atan 3,ong herlorek.

Nqr1

f9 mYrksl
[9 wtrkahf

M l/ s ( o

s

s

i9

6.

t\,

E,L

€3
C:5

9UND
{ro5hr

$g$g$sFgFF
$F$$$iiF$T$
il-iFgEaiEig
s
s
*$u
$$gi,sF
ig
-3

5A

SE
EF

Eia;t

}D
oit

!wB{
-9-O

FF

95we
N
N

6

@

g- 3
s E:

Fg

1s

H6!$

e5
A.O
9r

+New

6
E
=.r

-5-O

i

hriravw
w{t9N

F,

s

i l !€

iE
*
P *+

ggs!

6 Fq

g
,r,
95U-

t\,

N

'3>

FsErr
G
D

iaxiB

-

aq
oD
t

rP

3
ata

s

-c.

9.

E

$$$g
$*rel
F

r
F$n$
.t
r

t.
(-

Ft
att

x

Ft

$FF
\

s

ed

,A FF
i
01

$Eg
EE

B3

€$

FB
F

P

Fe
t

I

3

n
D

;

Eg

pn

SL

FS
tc

t>
o

;

F
*

ra

g

)

r
)

3
(,t

P

ct

e

g$'gg$g$F
FEgg
FE i *$u
*$ F

$ F E5
$ r iF

EE
$E
t E*

€
F E$F F* F
€

pd

0.

*i$
F Eigg
CL
Ti l R
*i
rg. '

g

x

c'

8'
E
3

arl

g
T
D
!
(t

e

$EE

E$$

SKEMA PEMARKAHAN – SET SOALAN RAMALANKU MUNGKIN BENAR SPM 2016