kumpulan soal

SOAL-SOAL SBMPTN MATEMATIKA DASAR

PER BAB TAHUN 2015 - 2017

1

www.purwantowahyudi.com

DAFTAR HALAMAN

PERSAMAAN dan FUNGSI KUADRAT …………………………… BARISAN dan DERET ………………………………………………… PERTIDAKSAMAAN ………………………………………………… STATISTIKA ………………………………………………………… AKAR PANGKAT ……………………………………………………

3 6 ! 1" 17

FUNGSI KOMPOSISI dan IN#ERS ………………………………… SISTEM PERSAMAAN LINEAR …………………………………… LOGARITMA ………………………………………………………… PELUANG ……………………………………………………………… MATRIKS ……………………………………………………………… BANGUN RUANG ……………………………………………………… LIMIT …………………………………………………………………… INTEGRAL ………………………………………………………………

1! 21 25 26 2$ 32 37 3$

2


SBMPTN 2015

A. -3 B. -1

C. 1 D. 2

E. 3

Jawab :

 −





ax – b = 0  misal akar ke 1 = dan akar ke 2 = 2 Rumus umum ersamaan kuadra!  Ax " Bx " C = 0 # A $aka: A = 1 % B = - a dan C = - b  akar-akar

berkebalikan maka

&unakan rumus : x 1 " x 2 = x 1 " x 2 = -

b a

= -

masukkan rumus x 1 " x 2 =

B A

= -

−

1

 = 

 "  = a 

a

. 

b a

=a

= 1 maka

dan x 1 . x 2 = # x 1 . x 2 =

 = 

a

=

0

 =  c

a C A

=

−

b

1

= - b = 1

 b

= -1



'ala( sa!u akar adala( ada la( bilan)an bula! *si!i+ arena

c

≠

 maka

 bilan)an

bula! *si!i+ = 1%2%3% ,

akar ) lain adala( /u)a bilan)an bula! *si!i+

$aka x 1 " x 2  0  a  0 $aka De!erminanna D

(−) −  − ≥ 0 ≥ 0 ( +2 ++ 2)(≥ −0 2)2) ≥ 0 AC . 1 . -b

b

 suda(

""" •

•

≥0

didaa! di a!as b = -1% maka

 − ≥ 0 

- - - - - - - """ •

-2

•

•

0

•

•

•

2 3


≤ −2≥ 2 ≥ 2

Didaa! nilai ) memenu(i adala( a arena nilai a  0 maka ) berlaku adala( a  nilai ) berlaku adala( 2%3%  , nilai !erke4il a adala( 2 maka nilai !erke4il un!uk a – b = 2 – -1 = 3  E

≥2

SBMPTN 2015 -A. 35 B. 33

Jawab : 7uas

C. 30 D. 26

E. 2

∆  = − 9  − 9

8 alas x !in))i  ki!a li(a! )ambar beriku! ber iku!

9un)si  = mem*!*n) n) di sumbu x maka  = 0  mem*!* 0= di(asilkan n x =3 dan x = -3  x- 3   x " 3  = 0  di(asilka Didaa! !i!ik A adala( 3% 0 dan !i!ik B adala( -3%0  -3%0  $em*!*n) sumbu  maka x = 0  = 0 –    = - maka !i!ik Cna adala( 0% - didaa!kan )ra+ik sbb: ;an/an) alas AB = 3 " 3 = 5
∆   =

 D

4


SBMPTN 2016

> Jawab:

?=

 −  −

2x – 3

+x =

2x – 3 =

?=

 −

"a x " a

+x =

 −

"a x " a

+=15 - @ - 3 = 15 15 - "a  " a  = 15 – 35 – a " a  =- 20 "

a

a = 2 a= B SBMPTN 2016

5


Jawab

 +  +  = √ 7

0

2

Ax " Bx " C = 0 # A ≠ 0 x1= 6  akarna *si!i+ A = 1 % B = a bilan)an bula! dan C = b real ne)a!i+

b bilan)an real ne)a!i+ ne)a!i+ maka x 2 adala( ne)a!i+ x 1 " x 2 = 6-

√ 7

B

a

=-

A

1

" x 2 = - a

= - a

 a

adala( bilan)an bilan)an bula!

arena a adala( bilan)an bula! maka x 2 = m " $asukkan nilai x 2 ke dalam ersamaan : 6-

√ 7 √ 7 √ 7 √ 7 √ 7√ 7 "m"

x 1 . x 2 =

C

A

= - a

=b0

 6

 b

"m=-a

 a

√ 7

 m

adala( sua!u bilan)an bula!

= -6 – m

real ne)a!i+

6 -

 m "

  0

6 -

 adala( *si!i+ maka m "

m-

√ 7

  0

m= -3% -% -% , a = -6 – m  a = -% -3% -2% , nilai !erke4il a adala( -  /awabanna adala( B

'B$;< 201

A. 12 B. 15

C. 20 D.2

E. 2@

6


Jawab: " 3% k " 1% k = k"3%



 suku

ke 3%  dan  barisan )e*me!ri k

 =  +  ! " =

#$ = #& ' = ' = #% #$ ' ' = + 1 2k "1 == 1"3% + 3k =  +  !  = 1  = %  = 2 !  = 1   "   "   =  = 12 

Ra!i* = r =





'uku er!ama = a # suku kedua = ar 'uku ke!i)a= a

 =

  a =

*() = *$ = 15

$aka a = 15 dan ar = 15. 8 = @  suku er!ama dan kedua Jumla( dua suku er!ama = a " ar = 15 " @ = 2  /awabanna adala( D SBMPTN 2017

A. 1 B. 20 Jawab: Beda = b = 3 = a " n-1 b



C. 21 D.22

 ,



"

E. 23

= 2@

a " 2. 3 " a " 5 . 3 = 2@ 2a " 2 = 2@  2a =   a = 2 $aka suku ke 6 = = a " 5.b = 2 " 5. 3 = 20

,

 /awabanna

adala( B

SBMPTN 2017

A. 12 B. 130

C. 1@0 D.211

E. 36 7


Jawab:

   " "

" "

13 343   (  + ,  r "

= 65 "

  

 a

" ar " a = 161  a

= 65 " a " a



=

(  +  +-+ -) =

, ,

65

 diba)i

:

 = 65

,

161 = 161

/  maka r = 

1 men/adi

,

(  5  6 ) = (   / ) = ( / ) = 15 $% &:)  ($% : )  (  ( 6 % :* ) $aka " = = % % = 6:  :  a=

= 161 

8

**  ( ) % = * =211 

 /awabanna

adala( D

SBMPTN 2015

A. F G R% F  -1 a!au F  0 H B.  F G R% F  0 a!au F  2 H C.  F G R% F  -1 a!au F  2 H D.  F G R% F  -1 a!au 0F  3 H E.  F G R% -1  F  0 a!au F  3 H Jawab:

 ;  − 2   – x " 2  0 : % 0  :: & 0 ' ()*+,da.a/aan )*a a*)na a*)na )*a )*a +anda  () )(:) & 0  P)/a+ n4   -1 dan   3 8 dan  '/a.an n,a,-n,a,n9a

<

0

8


- - - "" - - - - """ •

•

•

•

•

•

•

•

-1 0 3 P)n9)).a,ann9a adaa - 1 %  % 0 a+a  & 3

:a;aann9a adaa E

SBMPTN 2016

 ≤  :    −  ≤ 0 :( +2 + 2) − ( − )( )( + )

( − )( + 2) ≤ 0 ( +−2)−(+ +2)9 ≤ 0 2  + 9 ( − )( +2 + 2) ≤ 0 >a*, n,a,-n,a, 9? )*a d,   - $@2 8   3 dan   -2

<

<

 3 dan  -2

- - - "" " " - - - - - - - - """ • • •

-2

•

•

-2

•

•

•

•

0

•

3

≤ − /

a!au -2  x  3

 /awabanna

adala( B

9


SBMPTN 2106

Jawab :

<

<

<

;enebu! e4a(an 0  x 2 dan x 1 Jawaban ) memenu(i x = 2 dan x = 1 sala( ai!u B% C dan D
    F = -1 didaa!   

In!uk x  1 ambil nilai x = 0 didaa!  1 Benar

Jawabanna adala( A

 Benar

Jawaban al!erna!i+ a)ak an/an) Jika x -2 0% x 2

≥ ≥  −2  − 2 ;  − − −  : : ( − ) − ( − 2)2) ; 0 ( − 2)( 2)( − ) : ; 0 (:)(:)  0

- - - - - - - -- """ • •

•

•

-2

•

•

•

•

•

0 1 2 10


32 ilai x 2 !idak !idak berlaku Jika x  2

−  ; 2:− −  − − :( :) − (2−)(−)  − −  − (2(2 − ) ; 0 : ; 0 (:)(:) : ; 0 (:)(:)  0

Ba!as nilai x =2% x = 1 dan x = 32 - - - -- - " - - - - • •

•

•

•

•

•

•

•

0 1 2 32 ilai ) memenu(i adala( x  1 dan F  2% nilai x  2 !idak memenu(i maka maka ) memenu(i adala( nilai x  1  A 'B$;< 2015

Jawab : F = 0 berlaku karena bukan enebu! enebu! 'e(in))a un!uk x 2 didaa! F–2

≥  − >   − > ( +  )( −2 −2)

– x " 2  0 – x - 2  0  0 ;embua! n*l x =-1 a!au x = 2 11


" " " " "" - - -- - " "" • •

•

•

•

•

•

-1 0 2 asilna -1x2

•

•

 !idak

memenu(i karena !idak memenu(i x

≥

2

In!uk x  2 2- F  " x - 2  0 " x - 5  0  0 ;embua! n*l x = - 3 a!au x = 2

 − >   − > ( +  )( −2 −2)

"" " - - - - - - - - - " " " " "" • •

•

•

-3 asilna

•

•

•

0 -3x2

•

•

2  D

SBMPTN 2017

A. - B. -3

C. -1 D. 3

E. 

Jawab : - 2x – a  a –  2x   " a

:"  x  "  

imunan enelesaian K2x – a K   adala( x K -1  x   H Ambil nilai x = -1 dan x =  'e(in))a :

:" = -1 

 −? −= ?

= -2 3 12


" =  

? += 

= @

Jawabanna adala( D SBMPTN 2017

A. 2 B.  Jawab :

C. 5 D. @

E. 10

 "  x = 12 !i!ik *!*n) d)n sb x /ika  = 0% didaa! !i!ik 3% 0 !i!ik *!*n) d)n sb  /ika x = 0% didaa! !i!ik 0% 12

alas

alas

 " 2x = @ !i!ik *!*n) d)n sb x /ika  = 0% didaa! !i!ik % 0 !i!ik *!*n) d)n sb  /ika x = 0% didaa! !i!ik 0% @ 7uasna adala( daera( ) diarsir berben!uk se)i!i)a. 7uas = 8 alas . !in))i !in))i Alas= 12 – @ = 
!in))i

13


STATISTIKA SBMPTN 2015

A. 5%33 B. 5%0 Jawab:

C. 5%6 D. 6%00

E. 6%2

1 2

3

1. menun/ukkan /umla( siswa an) mendaa!kan nilai 5 ai!u 1 " 2 = 3 siswa 2. menun/ukkan /umla( siswa an) mendaa!kan nilai 6 ai!u  siswa 3. menun/ukkan /umla( /umla ( siswa an) mendaa!kan mendaa!ka n nilai @ ai!u 3 siswa

Ra!a-ra!a =

(  ) )(  ,),)(@) = ,A = 6.00  A

 /awabanna

adala( D

14


SBMPTN 2015 Dike!a(ui ra!a-ra!a dari  nilai en)ama!an sama den)an dua kali medianna% Jika /umla( nilai en)ama!an an) lebi( ke4il dariada median adala( 105 dan /umla( nilai en)ama!an an) lebi( lebi( besar dariada median median adla( 200% maka ra!a-ra!a dari  nilai nilai en)ama!an !ersebu! adala(,. adala(,. A. 2 C. 35 E. 0

B. 30

D. 50

Jawab :

B = 2 C1 = DEFGH/ IJ   ! ! ! " ! ,! @! /  "  ++  ++  ++   , @ / 2 C1 = 2" A /&AA K " 0L + " + 200 7"A " ,  BB A @AA / /  nilai

$isalkan  da!ana adala( % $aka adala( medianna = 105 dan = 200

ra!a-ra!a 2 kali medianna %

=

= = 305

=

= 1@

$aka ra!a-ra!ana adala( = = =

=

= 35  C

SBMPTN 2016

15


Jawab : misalkan dari 2 siswa an) men)iku!i u/ia susulan ) memer*le( nilai !erke4il adala( x dan nilai an) !erbesar adala(  dimana x 1 dan  10

BB

Ra!a-ra!a = = =

A . ,M = @A   M =6  

2@0 " x "  = 2 F "  = 1 ? = 1 – x  karena 

≤

10 maka 1 – x

≥

≤

≤

≥

10  x



In!uk x =  maka  = 10 % /an)kauanna 10 –  = 5 In!uk x =  maka  = % /an)kauanna  –  =  In!uk x = 5 maka  = @% /an)kauanna @ – 5 = 2 In!uk x = 6 maka  = 6  !idak meme memenu(i nu(i karena nilaina (arus !idak sama 'e(in))a /an)kauan da!ana adala( 3  C SBMPTN 2017

A. 

C. 

B.

D. 5

/ 

E.

 

Jawab: $isal % % % % adala( da!a bera! badan  bali!a = median = <*!al bera! badan  bali!a = 

     "  BB   " %N  +   ?  +  L      %O $  " !  =

= = " 5 % % %

M)d,an 

P

" 5

%



 se!ela(

di!amba(kan bali!a ke 5 

 =  )  (  

 median !idak beruba( maka = diba)i 2 (asilna sama 

$aka selisi( bera! bali!a !erak(ir den)an bali!a ke  adala( 

" 5 -



= 5 D

16


AKAR PANGKAT SBMPTN 2015

A. -2 B. -1 Jawab :

C. 0 D. 1

E. 2

 √  √ QQ QQ :(  √  √ QQ) QQ) =  √  √ Q Q :  √  √ Q:Q: Q) : :  = -1 B = : 

SBMPTN 2016

Jawab :



$aka  



 √ 2  √ 2 √ S)&:(RS)T& ( R%S&S: RT&S R R&  RT%ST& = (RS)%(RS)T%

= 2



=



(√ )) %:(√ )) T% (√ )) (*√ )) √  : $*√  √  √  %T* $√  = . √  =  =  UO* √  / .√  /. @

=

 A

17


FUNGSI KOMPOSISI dan IN#ERS SBMPTN 2015

A. - C. -1 E. 2 B. -2 D. 1 Jawab: = = = - - =  maka arena = = 1  = -1 $aka didaa! : = = -  C

VV((−−)) −V−V(()) ( ) V ( ( V − V ( ? V(−?) −V(?) V(?) V( ( V(−) V(?)  =



SBMPTN 2015

: @  B. @

:"  : D. 

A.

C.

E.

 

/aa "   -5

Maa =

V::(Z) K W:XY V (Z) 2Z − 02Z VV::(()) 2 V([) [ = 2 =

 12



 2

 2

=  maka  2 2  9 C 2 

W:X Y

 12

=

=



\:P P

/aa  '  

]:P P

= x

D

18


SBMPTN 2016

D

SBMPTN 2016

V^::([)([) ^_T*:(M)([) 

= x "  ,1 = 2x - 1

2x =

F=

" 1



,.2 19


Dari 1 dan 2

T*(M)   T*(M) A _T*(M)   _ _ : V ([) =  " _T*=()    = =  $aka 2 V : () = 2 . = ^: () +  = ^: () +  

 A

SBMPTN 2017

A. - L  F  L B. F 0

< −  :": √  − √ :" − 

C. F D. F

<≥

1 1

E. F  1

Jawab : +. ) = un!uk un!uk

`

.

 nilai

:

 nilai

1 2  x  1

≥

) (arus memenu(i adala( x 1 ,1

) (arus memenu(i adala( x

 E

<

1 ,,2

SBMPTN 2017

A. 0 B. 1

C. 2 D. 3

E. 

(abc) = adc(])e ]P +P P) ]]P af] =dcg(])e adc(])e ]P  -3'

 !

-3

C 6  !

 -3

 2

A?a* n,a, /a.,// /aa +*nan  -6   0

0

adc(])e

 0

d,/a.an ) daa/ ()*.a/aan = - 3

2022

>

20


SISTEM PERSAMAAN LINEAR SBMPTN 2015

A. -3 B. -2 Jawab :

C. -1 D. 3

E. 

 ( +2 + 2) −L 2( −[ − [) =   3x

" 5 – 2x " 2 = 5  x " 2 = 0 ,,..1

2 ( +[ + [) L− ([ ([ +) + ) = 2  2x

" 2 – 3 – 3 = 12  2x –  = 1 ,..,2 'ubs!i!usi 1 dan 2 x " 2 = 0 x 2 2x –  = 1 x 1

 2x

"  = 0 2x -  = 1  = -1   = -3

F " 2 = 0 F = -2 x = -2 . -3 = 5 $aka x "  = 5 " -3 = 5 – 3 = 3

 D

21


SBMPTN 2015

A. 10.000 C. 1.000 E. 300.000 B. [email protected] D. 22.000 Jawab:  *ran) siswa = A% B% C% D A " B " C " D = R. 00.000%-  D = 00.000 – A"B"C A = 8 B " C " D   A = 8  00.000 – A  = 0.000 – 8 A A " 8 A = 0.000 32 A = 0.000  A = 300.000 B = 13 A " C " D   B = 13  00.000 – B  = 300.000 – 13 B B " 13 B = 300.000 3 B = 300.000  B = 22.000 C = 1 A " B " D   C = 1  00.000 – C  = 22.000 – 1 C C " 1 C = 22.000  C = 22.000  B = [email protected] D = 00.000 – A"B"C = 00.000 – 300.000 " 22.000 " [email protected] = 00.000 – 60.000 = 1.000  C SBMPTN 2016

22


Jawab :

;erse)ian/an) ABCD !erba)i 2 ba)ian ) sama maka A$ = C = d MA$ seban)un den)an MBC

Rh = kR I =ij ki :I " $aka

d = 12 – d 5d = 12  d = 2

 )radien  C

SBMPTN 2016

Jawab : 3x "  = b ,,..1 4x – d = 1 ,,.2 masukkan x% = 1%1 ke 1 3 " 1 = b  b =   ersamaan 1 men/adi 3x "  =  ,.3 $asukkan x% = a% -2 ke 3 23


3a – 2 = 1 3a = 3  a = 1 masukkan x% = 1%1 ke 2 4 – d = 1 , masukkan x% = a% -2 ke 2 dimana dimana a = 1 4 " 2d = 1 ,....

 x%

= 1% -2

subs!  dan  4–d=1 4 " 2d = 1 -3d = 0

 d

=0

$asukkan nilai d = 0 ke 

 4

" 2. 0 = 1  4 = 1

Didaa! nilai a =1% b =% 4 = 1 dan d = 0 $aka a " b " 4 " d = 1 "  " 1 " 0 = 5

 B

SBMPTN 2017

A. 00 B. 20

C. 3 D. 0

E. 5

Jawab: ' = <*!al b*b*! semua ikan ' = 5 – 0.02x . x = 5x – 0.02



A)ar maksimum maka ' di!urunkan dide++erensialkan 'N = 5 – 0.0 x = 0 0.0 x = 5  x = 10 $aka !*!al b*b*! ikan maksimum = 5 . 10 – 0.02 . 10 = 00 – 0 = 0

 D

24


LOGARITMA SBMPTN 2015

A. 23 B. 32

( 2lmn) ( 2lmn)

Jawab :  = a l*) x

C. 32 D. 

2

3

x

k

l*) b = l*) p = l*) q

=

1 3 1 2

l*) y =

k

a

n

( lmn)

≠

1

l*) b ,,.2

*%  *

2 

 

=

 O

=

p 2

E. 

a y = x ,1

⇔

den)an a  0 dan a an

( lmn) ( 2lmn)



3

l*) q =

o = (2*%) = 2% = x p = (*) = % = 

22  3

3 2

l*) 3

% = %

2

l*) 3 =

/ 

2

l*) 3

 D

SBMPTN 2016 7*)ari!ma dan Barisan Dere!

A.  B. 2 Jawab : Beda suku = 2 = " 2 a l*)b + 2 = a

C. 0 D. -2

E. - 

        ( + 2) ( + 2)   + > + > 

l*)

=

-

a

=

l*) b " a

a

-

l*)2b + 

l*) b2b + 

= b2b +  = 2

" b

–  = 0 b " 2  b – 2  = 0

25


b = -2  !idak memenu(i% b = 2 /umla( !i)a suku = 5 masukkan nilai b = 2 a l*) 2 " a l*)  " a l*) @ = 5 a

l*)2..@ =

a

 memenu(i

l*) 5 = 5

=  2 −  = = 5 2

2. 2 – 2 =  – 2 = 2

B

PELUANG

'B$;< 201

A. 15 B. 1

C. 2 D. 8

E. 32

Jawab : Banak kemun)kinan ruan) samle di!en!ukan den)an men))unakan ermu!asi: <*!al buku 5 den)an  buku ma!ema!ika dan 1 buku b uku ek*n*mi dan 1 buku ba(asa

(R) (q) r = . ". r = 30 n' = rrr rrr

;A =

'usunan a)ar !idak ada !i)a a!au lebi( buku d)n /udul sama beruru!an den)an /udul ) sama !idak dibedakan: $isal # $= buku ma!ema!ika% E= buku Ek*n*mi# B= buku Ba(asa emun)kinan 1 : $$E% $$% B A =

r rrr

$$E% $$% B 3 *sisi $$E = 1# $$ = 1# B = 1

= 3.2.1 = 5

26


emun)kinan 2 : $$% B% E$$ 'ama s! di a!as A =

r = 3.2.1 = 5 rrr

<*!al nA = 5 " 5 = 12 Jadi ;A =

 =  A "

 C

'B$;< 2015

A. 1 B. 10@ Jawab:

C. 62 D. 35

sR sR tR

E. 3

tR

$isalkan : ;ria dari '$A A = # Pani!a dari '$A A = ;ria dari bukan '$A A = ;% Pani!a dari bukan '$A A = P emun)kinan emun)kina n 1 sd 5 :  1.

sRtst Rsts sR tR ssts RtststRs RtstRs st R stsRts st R ststsR stst sts

dan

!idak b*le( beru!uran



dan !e!a di *sisina% kemun)kinan uru!an ) !er/adi ;= 3 P= 2  3Q.2Q = 12 Be)i!u ula den)an  kemun)kinan di bawa( ini.

2. 3. . . 5.

R R

'e(in))a !*!al kemun)kinan uru!an ) !er/adi adala( 5 x 12 = 62

 C

27


SBMPTN 2017 'ebua( bilan)an )an/il  an)ka dike!a(ui memua! !ea!  an)ka )an/il dan !idak memiliki an)ka berulan) ser!a !idak memua! an)ka 0. Banak bilan)an berbeda den)an 4iri !ersebu! adala( A. 1.250 C. 1.20 E. 2.200 B. 1.320 D. 1.20

Jawab :N FFFFF &JJJJ J&JJJ JJ&JJ JJJ&J

 susunan

an)ka-an)ka &= &ena%J= &e na%J= &an/il  !erdiri dari  )an/il dan 1 )ena an)ka !erak(ir  ke  (arus )an/il 1%3%%6%  an)ka

 

ili(an

 susunan

susunan !erdiri dari  an)ka )an/il dan 1 an)ka )ena 'usunan  an)ka ) mun)kin



r = . r =  rr rr

misal ambil susuan &JJJJ Jumla( kemun)kinan kemun)kinan  an)ka er!ama =  . . 3. 2. = 5 an)ka )ena   an)ka 2%%5%@ an)ka )an/il er!ama  suda( !erakai 1 se(in))al !ersisa  an)ka an)ka )an/il kedua  suda( !erakai 2 se(in))al !ersisa 3 an)ka an)ka )an/il ke!i)a  suda( !erakai 3 se(in))al !ersisa 2 an)ka

Banakna bilan)an berbeda = 5 .  .  = 120 4ara

 D

SBMPTN 2017

A. .250 B. .20

C. .320 D. .00

E. 6.200

28


Jawab: FFFFF &&JJJ J&&JJ JJ&&J JJJ&J &J&JJ &JJ&J

  susunan

an)ka-an)ka &= &ena%J= &an/il  !erdiri dari  )an/il dan 2 )ena an)ka !erak(ir  ke   (arus )an/il 1%3%%6%  an)ka

 

ili(an

5 susunan

'usunan  an)ka ) mun)kin



r = . . r = 5 rr  .r

misal ambil susuan &&JJJ Jumla( kemun)kinan  an)ka er!ama =  . 3.  .3 = 1 an)ka )ena   an)ka 2%%5%@ an)ka )ena kedua  suda( !erakai 1 se(in))al !ersisa 3 an)ka an)ka )an/il er!ama  suda( !erakai 1 se(in))al s e(in))al !ersisa  an)ka an)ka )an/il kedua  suda( !erakai 2 se(in))al !ersisa 3 an)ka Banakna bilan)an berbeda = 1. 5 .  = 320 4ara

 C

MATRIKS

'B$;< 201

A. 5 B. 10

C. 20 D. 30

E. 50

Jawab:

u2 >v < A=

 de!

A = @ – a

 memunai

@

de! A = 15 de!  de!

A =

iners berar!i de! A

<

0 maka @ – a

<

0  a

: () 

wxy(R) .wxy(i) xy(i)

29


 de!

A. de! A =

 @-a

 @-a =  =   5 – 15a " – 15a " 50 = 0 





 =  =  wxy(i) 

Sn)a! rumus erkalian dua akar =

  .

z R

= = 50 =

  .

 E

SBMPTN 2016

Jawab : A.

B=

u0  v { 0| u2 2+ v 0 .

=

AB !idak memunai iners maka de!KABK = 0 2a. 2b – ab"1 = 0 ab – ab – a = 0 3ab – a = 0 a 3b – 1 = 0  dari s*al a 0 karena a 0 maka 3b – 1 = 0 3b = 1  b = 13 B

<

<

30


SBMPTN 2017

A. 2 B. 

C.  D. @

E. 

Jawab:

u0 v } u 0v  }  0  0 u 0  v u  v u0  v u20 2L v u 90v u?0 ?0 v u? 2?v u?0 ?0 v 

A=

2A"3



adala( meruba( baris men/adi k*l*m

= 1 S

 2




=

" 3

= 1

"

=

=

a = 1  a = 3 3b = 0  b = 0 $aka

   "

=

" 0 = 

 E

SBMPTN 2017

A. - B. -3
C. 0 D. 3

u0 0v u2v u>2v u2 v u>2v

E. 

=

=

 a

Maa /a+*,. A 

= 2 dan b = 2

u02 20v 31


u02 20v u[v u2L v u2[2v u2L v =

=

 x

= 3 dan  = 5

S),n??a  C 9  3 C 6  -3

B

BANGUN RUANG SBMPTN 2015

A. 22% B. 

C. 50 D. 56%

E. 0

Jawab :

7uas daera( ) diarsir = 7uas

∆

∆

AE9 " 7uas

∆~•

7uas AE9 = 8 E9 x AB = 8 ..  = 22.

32


7uas

∆~•

= 8 & x AD = 8 3 . 1 = 22.

7uas daera( ) diarsir = 22. " 22. = 

 B

SBMPTN 2016

A  A  ( B  B   C ( >  >   C ( B>  B  > aC(-( a     C 2( 2(     C a (  A 2A     C a E 33


SBMPTN 2017

  B. /

 / D. @

A.

C.

Jawab:

E.

 

∆

arena ABC sama kaki maka AB = BC = a  a = misal  A = 7 = 7B = 13 a B$ = $ = C = 13 a 7uas ABC = 8 BC . AB =8a.a

∆

=8

∆



= x





= 2x

7uas $ = 8 $. B

       = = / / B = . a . a 

34


SBMPTN 2017

√ √ KK

√ √ 22722

A. 2

C. 2

B. 2

D. 

√ 

E. 

Jawab :

∆

AB; seban)un den)an

    

$aka =

 x

= 1@

∆

T9;

 x

=2

ET = 5 – T9 = 5 – 2 = 

∆(€•) + (€) (•) L > (•) (•) (•) ∆  (•) (‚) (‚•) L √ KKKK √ > . 22 √ > . √ 2222 = √ 2222 ET siku-siku di E maka : =

" = 35 " 15 =

= 2

DT siku-siku di  = =

TD =

" " 2 = @@

=

=

2

 C

35


SBMPTN 2017 Dike!a(ui kubus ABCD.E9& den)an ; dan T ber!uru!-!uru! adala( !i!ik !en)a( & dan BC. Jika an/an) rusuk kubus !ersebu! adala(  4m% maka /arak ; ke T adala( ,. Cm

√ √ L

√ √ 2

A. 2

C. 5

B. 2

D. 5

√ L

E. 5

Jawab :

&; adala( !i!ik !en)a( & = 8 .  = 2

 () (~) = (~) >∆ 2 (~s) +(s) (~) (s) (s) = √ 2>2> √ > .L. L √ > √ L √ L "

= " = 20 ;er(a!ikan &;T siku-siku di & =

 " 20 =

2

;T =

=

=

.

= 2

 B

36


LIMIT

SBMPTN 2016

]P:Y ƒ„… (]P)(]:P) ƒ„… (]−P) ƒ„… ] † −P ]P ] † −P ]P ] † −P P]) ƒ„… ( ] † −P ‡P ] :Y ƒ„… ˆ]P + ‰ ƒ„… ] † −P ]P ] † ‡ ƒ„… P ˆ] ] † ‡ + ‰ ƒ„… P ˆ] ] † P + ‰ 



 -2 -2  -"

Sa/a .a:a d)n?an a*a LH4(,+a 2  -2  -" 



 -"

/aa

 a    -" '1

 "a    2 '2

S+,+., '1 dan '2 a    -" "a    2 -3a -6 a 2 a    -"   -a - "  - 2-"  -6 /aa a C   2 C '-6  2  6  !

E

37


SBMPTN 2017

A. -1 B. – 12

C. 0 D. 1

E. 32

Jawab: ura mem*!*n) di sumbu  maka x = 0% di !i!ik 0% 1 maka = 1



+x = a " bx " 4 Didaa! 4 = 1

 masukkan

'ara! limi! adala( berben!uk :

c(]) ƒ„… Š  ‹Œ   ƒ„… ] † ‡ ]:‡ ] † ‡ ]:‡ 

A A

x=0

 maka

+x = +1 = a " b " 1 = 0

 a

" b = -1 ,. 1

 -"

$emer)unakan 7N*i!al didaa!

ŠŒ  ‹ ƒ„… ] †‡ ‡

 2a    -" …'2

'ubs!i!usi 1 dan 2 a " b = -1 2a " b = - -a = 3  a = -3 a " b = -1

maka

 b

= -a – 1 b = 3 – 1 = 2

QŽ =  = -1  :

 A

38


INTEGRAL SBMPTN 2017

A.

Jawab :

* $ * : $    √  u − v dx =  ( .&  - % .  ) dx : = (  -   ) dx & %)    ((:  = &  "C   - (: % )    : *  =   - *  "C :   N * *  :  = ,   " 2  " C   √  "  " C A = , √  

39


kumpulan soal

Recommend Documents