percubaan matematik 2014 [skema].doc

8/11/2019 Percubaan Matematik 2014 [Skema].doc

1/14

KERTAS JAWAPANEXCEL II - 2011

MATEMATIK SPM KERTAS 2

Question Solution an Ma!" S#$e%e Marks

1

St!ai&$t otte linex '( #o!!e#tl) !a*n

Re&ion #o!!e#tl) s$ae+

Note ,1+ A##et soli line .'(/ a*a! K12+ A*a! P1 to s$ae !e&ion oune ) t*o #o!!e#t lines+

K1

P2 3

00

y = 8

y

x

y = x + 2


2/14

2 p q' - o rp- 12q' or3p 12q'-12 o! e4ui5alent

Note ,Atte%t to e4uate t$e #oe66i#ient o6 one o6 t$e un"no*ns/ a*a! K1-7q' 13 or 7p ' 21 ore4ui5alent

OR

p ' 11 3 qorq -1 - p

1or e4ui5alent

Atte%t to %a"e one o6 t$e un"no*ns as t$e su8e#t/ a*a! K1-7q' 13 or 7p ' 21 ore4ui5alent

OR

=

11

11

3

939:1:919::

1

q

p

Note ,A*a! K1 i6

1+

qp '

;

inversematrix

11 or

=

11

1

31

q

p

2+


3/14

3 2d2 =d 1> ' 0

:2d 9:d (9 ' 0 ore4ui5alent

d' or 1+?

d' (

Note ,1+ A##et *it$out @'0

2+ A##et t$!ee te!%s on t$e sa%e sie/ in an) o!e!

+


4/14

5:a9

:9

6:a9

:9

Ienti6) BFC o! CFB

oBFC

BFC

7>+23

1

(tan

=

= or e4ui5alent

o! 23 37D

137

222

(0

=0

137

222

(0

=0

?0

13137

22

(0

=0 or 77

7

22

(0

3?

777

22

(0

3?1313

2

11313

7

22

(0

=0+

7?+2? or3

17?

Note,

1+ A##et 6o! K %a!"+2+ Co!!e#t ans*e! 6!o% in#o%lete *o!"in&/ a*a! KK2

P1

K1

N1

K1

K1

N1

KI

K1

N1

3

13 7 7


5/14

>:a9

:9 :i9

:ii9

:2/S9/ :3/ S9/ :?/ S9/ :2/M9/:3/ M9/:?/M9F

:2/ S9/ :3/ S9F

(

2

1

:2/S9/ :2/ M9/ :3/ M9/ :?/S9/ :?/M9F

(

?

Note, A##et ans*e! *it$out *o!"in& 6o! K1N1

P1

K1

N1

K1

N1

=+ :a9

:9

p ' -k' 2:-(9 :9k' -21

P1

P1

K2

7 :a9

:9

:#9

All GG Se%ua

I6 3x' 1 / t$enx' 0 GGJi"a 3x' 1/ %a"a x' 0+

I6 x' 0/ t$en 3x

' 1 GGJi"a x' 0/ %a"a 3x' 1

/

Note , seen/ a*a! K1

P1

P1

P1

K2

5

5

7


6/14

Note,

1+

2+


7/14


8/14

!a$ o! Question 12Graf untuk Soalan12

y= 4x- 10

y= 3x2+ x+4

x

y= -30

-2.7

-2.5

1.7 3.5

11 2 43

4

0

y

3

1

3

2

1

2

4

5

4

2

3

y= -2x-2

= -

x


9/14

1:a9:i9 :>/39 P1

:ii9 :(/19Note,Point :3/19 %a!"e on ia&!a%/ a*a! P1+

P2

:9 :i9 Clo#"*ise !otation o6 =00 aout t$e #ent!e : 1/9 orPuta!an =00 a!a$ 8a% aa usat :1/9+

P

Note,1+ P2 , Rotation =00 anti#lo#"*ise orRotation at #ent!e :1/9 or

Puta!an =00 la*an a!a$ 8a%orPuta!an aa usat :1/9

2+ P1 , Rotation orPuta!an+

:ii9 Enla!&e%ent at #ent!e o! :0/29 *it$ s#ale 6a#to! 2 or

Pe%esa!an aa usat atau :0/ 29 an 6a"to! s"ala2+

Note,1+ P2 , Enla!&e%ent #ent!e :0/29 orEnla!&e%ent s#ale 6a#to! 2 or

Pe%esa!an usat :0/29 orPe%esa!an 6a"to! s"ala2+

2+ P1 , Enla!&e%ent orPe%esa!an

P (

:#9 a!ea o6EHJ' :2 92X a!ea o6ABC

= 3 X =0

A!ea o6EHJ ' (0 unit 2

A!ea o6 t$e s$ae !e&ion' (0 - =0

' 270 unit 2

K2

N1

12


10/14

13:a9

Class inte!5alSelan kelas

Mioint!itik tena"

!e4uen#)#ekerapan

0 = 3+? 30 3=

33+? 2?0 ?= ?3+? >(0 (= (3+? 1070 7= 73+? 11>0 >= >3+? 3=0 == =3+? 2

Class inte!5al , all t$e ans*e!s a!e #o!!e#t P1

!e4uen#) , all t$e ans*e!s a!e #o!!e#t P1!e4uen#) , all t$e ans*e!s a!e #o!!e#t P1

:9 ?+=32?+>33?+7311?+(310?+?3>?+332?+3 ++++++

(?+? or (?2

K2

N1

:#9

Note,1+ Allo* t*o %ista"es 6o! K1+

i+e+ %i oint *!on&l) #oie o! *!on& %ultili#ation2+ In#o%lete *o!"in& 6ollo*e ) #o!!e#t ans*e!/ a*a! KK2

i+e+2(20

' (?+?

A.es !a*n in #o!!e#t i!e#tion *it$ uni6o!% s#ales 6o!23+? . 103+? an 0 ) 11

;7 oints #o!!e#tl) lotte usin& t$e #o!!e#t %ioints+

:23+?/09 an :103+?/09 lotteS%oot$ an #ontinuous st!ai&$t line asses t$!ou&$ all #o!!e#t oints usin&t$e &i5en s#ales

P1

K2

K1

N1

?

:9 ( P1 1

12


11/14

Graph !r "#$s%&!' 14

1

24(5

3

4

5

8

)

10

11

34(5 44(5 54(5 74(5 84(564(5 )4(5 104(5

2

7

6


12/14

1?:a9

Co!!e#t s$ae *it$ !e#tan&leABC$% an se%i #i!#le A


13/14

1?:9 :i9

Co!!e#t s$ae *it$ t!aeBiu%JCSHan!e#tan&le#$CJ an'%$(All soli lines+

%' CS=SH=(# $%&$#J

Measu!e%ents #o!!e#t to 2+0 #% :one *a)9 anS'(%$C ///// an = 1=0#

K1

K1e K1

N2 eK1K1 3

1?:9 :ii9

LM

3 #%

J2 #%

3 #%

#% 3 #%

K

D S

H

P +? #% C

#%

E

1 #%

#%

7 #%$A

(

H

#

)

G


14/14

Co!!e#t s$ae *it$ !e#tan&le)GH( an GA$H*All soli lines+

Note, I&no!eE#

Ean# 8oine *it$ as$e line to 6o!% !e#tan&le GE#H

A$AG G) E

Measu!e%ents #o!!e#t to 2+0 #% :one *a)9 an all an&les at5e!ti#es o6 !e#tan&les = 1=0

K1

K1e K1

K1

N2 eK1K1

?12

1( :a9 : )(0 / E1?0 9 GG : +(0 / !1?0 9

Note , 1?0 o! E o! !/ a*a! P1

P1P2

:92:=0 (09 (0

(00 n+%+

K1

N1 2

:#9

(0#os(09200: +

Note, + 9200: o! usin& (0#os / a*a! K1

1?00 n+%+

K2

N1

:i9

:ii9

(00 7 o! 3200

(0(0

7(00

S10

K2

K1

N1

12

percubaan matematik 2014 [skema].doc

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