211365169 Kunci Jawaban Dan Pembahasan MAT XIB IPA

8/18/2019 211365169 Kunci Jawaban Dan Pembahasan MAT XIB IPA

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2/131

1Matematika Kelas XI Program IPA

K o m p e

t e n s

i

D a s a r

M a

t e r i

P o

k o k

/

P e m

b e

l a j a r a n

K e g

i a t a n

P e m

b e

l a j a r a n

I n d i k a

t o r

P e n c a p a

i a n

K o m p e

t e n s

i

P e n

i l a

i a n

T e

k n

i k

B e

n t u k

I n s t r u m e n

C o n

t o h I n s

t r u m e n

A l o k a s

i

W a

k t u

A l a t d a n

S u m

b e r

B e

l a j a r

N i l a

i d a n

M a

t e r i y a n g

D i i n

t e g r a s

i k a n

4 . 1

M e n g g u n a k a n

a l g o r i t m a

p e m b a g i a n

s u k u

b a n y a k

u n t u k m e n e n -

t u k a n h a s i l b a g i

d a n s i s a p e m -

b a g i a n .

S u k u

B a n y a k

S i l a

b u s

B a b I S u

k u

B a n y a

k

S e

k o

l a h

: . . .

K e

l a s

/ S e m e s

t e r

: X I / 2

M a

t a P e

l a j a r a n

: M a

t e m

a t i k a

S t a n

d a r

K o m p e

t e n s

i : 4 .

M

e n g g u n a k a n a t u r a n s u k u b a n y a k d a l a m p e n y e l e s a i a n m a s a l a h .

T e s

4 . 1 . 1

M a m p u m e n d e -

f i n i s i k a n s u k u

b a n y a k .

4 . 1 . 2

M a m p u m e n e n -

t u k a n n i l a i s u k u

b a n y a k .

4 . 1 . 3


t u k a n h a s i l o p e -

r a s i s u k u b a -

n y a k .

4 . 1 . 4


t u k a n h a s i l b a g i

d a n s i s a p e m -

b a g i a n

s u k u

b a n y a k .

T e r t u l i s

1 .

B u k u P R M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,

I n t a n P a r i w a r a ,

h a l a m a n 1 – 2 0

2 .

B u k u P G M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n 1 – 3 8

3 .

B u k u B S E M a

h i r

M e n g e m

b a n g -

k a n

K e m a m p u -

a n

M a

t e m a

t i k a

u n

t u k K e

l a s

X I

S M A / M A I P A ,

W

a h y u d i n

D j u m a n t a d a n

R .

S u d r a j a t ,

D e p d i k n a s

–

M e n j e l a s k a n p e

-

n g e r t i a n s u k u b a n y a k .

–

M e n e n t u k a n u n s u r -

u n s u r s u a t u

s u k u

b a n y a k .

–

M e n e n t u k a n

n i l a

i

s u k u b a n y a k d e n g a n

c a r a s u b s t i t u s i .

–

M e n e n t u k a n

n i l a

i

s u k u b a n y a k d e n g a n

c a r a H o r n e r .

–

M e n e n t u k a n

h a s

i l

p e n j u m l a h a n s u k u

b a n y a k .

–

M e n e n t u k a n h a s i l p e

-

n g u r a n g a n

s u k u

b a n y a k .

–

M e n e n t u k a n h a s i l p e r -

k a l i a n s u k u b a n y a k

.

–

M e n e n t u k a n

h a s

i l

b a g i d a n s i s a p e m

-

b a g i a n s u k u b a n y a

k

d e n g a n

c a r a

b e r -

s u s u n .

( * )

–

M e n e n t u k a n

h a s

i l


-


k

o l e h ( x – k ) d e n g a n

c a r a H o r n e r . ( * )

–

M e n e n t u k a n

h a s

i l


-


k

o l e h ( a x + b ) d e n g a n


8 × 4 5

m e n i t

1 .

T e n t u k a n n i l a i s u k u

b a n y a k b e r i k u t u n t u k

n i l a i x y a n g d i s e b u t -

k a n m e n g g u n a k a n


a .

f ( x ) = 3 x

5 –

2 x

4

+ x

2

+ 2 x + 4

u n t u k x = – 2 .

b . g ( x ) = 2 x 4 –

5 x

3

+ x u n t u k x = 3 .

c . p ( x ) = 6 x

3 –

x 2

+

x

+

7

u n t u k

x =

2 .

D i k e t a h u i :

p ( x ) = x 3 +

5 x 2 – 3 x + 1 0

q ( x ) = x 4 –

x 3 +

2 x – 6

T e n t u k a n :

a .

p ( x ) + q ( x ) ,

b .

p ( x ) – q ( x ) ,

c .

4 q ( x ) – 3 p ( x ) .

3 .

T e n t u k a n h a s i l b a g i

d a n s i s a p e m b a g i a n

b e r i k u t .

a .

( 2 x

4 –

3 x

3 +

3 x

2 +

x – 8 ) : ( x –

)

b .

( 4 x

5 –

2 x

3 +

5 x +

6 ) : ( 2 x – 3 )

P e n d i d i k a n

k a r a k t e r

( * ) K r i t i s


3/131

2 Silabus

T e s

T e r t u l i s

4 . 2


t e o r e m a s i s a

d a n

t e o r e m a

f a k t o r d a l a m

p e m e c a h a n

m a s a l a h .

S u k u

B a n y a k

–

M e n e n t u k a n

h a s

i l


-


k

o l e h a x

2 +

b x + c y a n g

d a p a t

d i f a k t o r k a n

d e n g a n c a r a H o r n e r .

–

M e n j e l a s k a n t e o r e

-

m a s i s a .

–

M e n j e l a s k a n t e o r e

-

m a f a k t o r .

–

M e n e n t u k a n

s i s a

p e m b a g i a n

s u k u

b a n y a k o l e h

s u k u

b a n y a k b e r d e r a j a

t

s a t u .

–

M e n e n t u k a n

s i s a

p e m b a g i a n

s u k u

b a n y a k o l e h

s u k u

b a n y a k b e r d e r a j a

t

d u a d e n g a n m e m i s a

l -

k a n s i s a n y a a x + b .

–

M e n e n t u k a n f a k t o r -

f a k t o r d a r i s u a t u s u k u

b a n y a k .

4 . 2 . 1


t u k a n s i s a p e m -

b a g i a n

s u k u

b a n y a k m e n g -

g u n a k a n t e o r e -

m a s i s a .

4 . 2 . 2


t u k a n

f a k t o r -

f a k t o r

s u a t u

s u k u b a n y a k .

4 .

T e n t u k a n h a s i l b a g i

d a n s i s a p e m b a g i a n

s u k u b a n y a k b e r i k u t .

a .

( 3 x

4 –

2 x

3 +

x 2

– 4 x + 5 ) : ( x – 3 )

( 3 x + 1 )

b .

( 2 x 4 –

3 x 3 +

5 x – 4 )

: ( x 2

– 4 )

1 .

D i k e t a h u i

s u k u

b a n y a k f ( x ) d i b a g i

g ( x ) = x

2 –

4 x + 3

b e r s i s a

2 x

–

4 .

T e n t u k a n :

a . n i l a i f ( 3 ) ;

b . s i s a p e m b a g i a n

f ( x ) o l e h ( x – 1 ) .

2 .

S i s a

p e m b a g i a n

s u k u

b a n y a k

f ( x )

o l e h ( x + 2 ) a d a l a h 8 .

S i s a p e m b a g i a n s u k u

b a n y a k t e r s e b u t o l e h

( 2 x – 1 ) a d a l a h – 4 .

T e n t u k a n s i s a p e m -

b a g i a n s u k u b a n y a k

t e r s e b u t o l e h

2 x

2

+ 3 x – 2 .

3 .

T e n t u k a n

f a k t o r -

f a k t o r

d a r i

s u k u

b a n y a k

f ( x ) = x

4 –

5 x

3 +

2 0 x

– 1 6 .

1 .

B u k u P R M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n 1 – 2 0

2 .

B u k u P G M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n 1 – 3 8

3 .

B u k u B S E M a

h i r

M e n g e m

b a n g -

k a n

K e m a m p u -

a n

M a

t e m a

t i k a

u n

t u k K e

l a s

X I

S M A / M A I P A ,

W

a h y u d i n


R .

S u d r a j a t ,

D e p d i k n a s

8 × 4 5

m e n i t

K o m p e

t e n s

i

D a s a r

M a

t e r i

P o

k o k

/

P e m

b e

l a j a r a n

K e g

i a t a n

P e m

b e

l a j a r a n

I n d i k a

t o r

P e n c a p a

i a n

K o m p e

t e n s

i

P e n

i l a

i a n

T e

k n

i k

B e

n t u k

I n s t r u m e n

C o n

t o h I n s

t r u m e n

A l o k a s

i

W a

k t u

A l a t d a n

S u m

b e r

B e

l a j a r

N i l a

i d a n

M a

t e r i y a n g

D i i n

t e g r a s

i k a n

P e n d i d i k a n

k a r a k t e r

( * ) J u j u r


4/131


S i l a

b u s

B a

b I I F u n g s i K

o m p o s

i s i d a n

F u n g s i

I n v e r s

S e

k o

l a h

: . . .

K e

l a s

/ S e m e s

t e r

: X I / 2

M a

t a P e

l a j a r a n

: M a

t e m

a t i k a

S t a n

d a r

K o m p e

t e n s

i : 5 .

M

e n e n t u k a n k o m p o s i s i d u a f u n g s i d a n i n v e r s s u a t u f u n g s i .

K o m p e

t e n s

i

D a s a r

M a

t e r i

P o

k o k

/

P e m

b e

l a j a r a n

K e g

i a t a n

P e m

b e

l a j a r a n

I n d i k a

t o r

P e n c a p a

i a n

K o m p e

t e n s

i

P e n

i l a

i a n

T e

k n

i k

B e

n t u k

I n s t r u m e n

C o n

t o h I n s

t r u m e n

A l o k a s

i

W a

k t u

A l a t d a n

S u m

b e r

B e

l a j a r

N i l a

i d a n

M a

t e r i y a n g

D i i n

t e g r a s

i k a n

5 . 1

M e n e n t u k a n

k o m p o s i s i

f u n g s i d a r i d u a

f u n g s i .

F u n g s i

K o m p o s i s i

2 3

T e s

5 . 1 . 1


f i n i s i k a n f u n g s i .

5 . 1 . 2

M a m p u m e n y e -

l e s a i k a n o p e -

r a s i a l j a b a r f u n g -

s i .

5 . 1 . 3


t u k a n

d a e r a h

a s a l

s u a t u

f u n g s i .

5 . 1 . 4


f i n i s i k a n f u n g s i

k o m p o s i s i .

5 . 1 . 5


t u k a n

f u n g s i

k o m p o s i s i d a r i

d u a a t a u t i g a

f u n g s i .

5 . 1 . 6


l e s a i k a n m a s a -

l a h s e h a r i - h a r i

y a n g m e l i b a t k a n

f u n g s i .

T e r t u l i s

1 .

B u k u P R M a

t e -

m a

t i a K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n 2 1 – 3 6

2 .

B u k u P G M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n 3 9 – 7 0

3 .

B u k u B S E M a

h i r

M e n g e m

b a n g -

k a n

K e m a m p u -

a n

M a

t e m a

t i k a

u n

t u k K e

l a s

X I

S M A / M A I P A ,

W

a h y u d i n


R .

S u d r a j a t ,

D e p d i k n a s

–

M e n j e l a s k a n p e n g e r -

t i a n f u n g s i .

–

M e m b e d a k a n s i f a t -

s i f a t f u n g s i ( f u n g s i

i n j e k t i f , f u n g s i s u r -

j e k t i f , d a n

f u n g s i

b i j e k t i f ) .

–

M e m b e r i k a n c o n t o h

f u n g s i b i j e k t i f .

–

M e n g h i t u n g

s u a t u

n i l a i f u n g s i j i k a d i -

k e t a h u i r u m u s n y a .

–

M e n u l i s k a n r u m u

s

o p e r a s i p e n a m b a h

-

a n , p e n g u r a n g a n

,

p e r k a l i a n ,

d a n p e m

-

b a g i a n d u a f u n g s i .

–

M e n y e l e s a i k a n

o p e r a s i p e n a m b a h

-

a n , p e n g u r a n g a n

,

p e r k a l i a n ,

d a n p e m

-

b a g i a n d u a f u n g s i .

–

M e n y e b u t k a n s y a r a

t

a g a r s u a t u f u n g s i t e r -

d e f i n i s i .

–

M e n y i m p u l k a n d a e r a h

a s a l s u a t u f u n g s i b e r -

d a s a r k a n s y a r a t a g a

r

f u n g s i t e r s e b u t t e r -

d e f i n i s i .

–

M e n e n t u k a n i r i s a n

d a e r a h

a s a l

d u a

f u n g s i .

1 .

D i k e t a h u i f ( x ) = x 2 –

5 ,

( f

g ) ( x ) = 9 x

2 +

1 2 x

– 1 , d a n h ( x ) = x + 1 0 .

R u m u s

f u n g s i

( g

h ) ( x – 1 ) = . . . .

a .

3 x + 3 2

b .

3 x + 2 9

c .

3 x + 2 5

d .

3 x + 1 2

e .

3 x + 2

2 .

D i k e t a h u i

f ( x ) =

+

d a n

g ( x ) =

+ −

.

a .

T e n t u k a n d a e r a h

a s a l f u n g s i h ( x )

j i k a h ( x ) =

.

b .

T e n t u k a n d a e r a h

a s a l f u n g s i k ( x )

j i k a k ( x ) =

.

8 × 4 5

m e n i t

P e n d i d i k a n

k a r a k t e r

( * ) K r i t i s


5/131

4 Silabus

T e s

T e r t u l i s

5 . 2

M e n e n t u k a n

i n v e r s

s u a t u

f u n g s i .

F u n g s i

I n v e r s

–


t i a n f u n g s i k o m p o s i s

i .

–

M e n j e l a s k a n s i f a t -

s i f a t k o m p o s i s i f u n g s

i .

( * )

–

M e n u l i s k a n

r u m u

s

f u n g s i k o m p o s i s i d a

r i

d u a a t a u t i g a f u n g s i .

–

M e n g h i t u n g s u a t u n i l a i

f u n g s i k o m p o s i s i d a

r i

d u a a t a u t i g a f u n g s i .

–

M e n u l i s k a n

r u m u

s

f u n g s i y a n g t e r m u a t

d a l a m s o a l c e r i t a .

–

M e n g h i t u n g

s u a t

u

n i l a i f u n g s i y a n g t e r -

m u a t d a l a m s o a l c e r i t a .

–


t i a n f u n g s i i n v e r s .

–

M e n j e l a s k a

n

l a n g k a h - l a n g k a

h

m e n e n t u k a n i n v e r

s

s u a t u f u n g s i .

–

M e n e n t u k a n i n v e r

s

s u a t u f u n g s i s e s u a i

l a n g k a h - l a n g k a

h

y a n g d i p e l a j a r i .

( * )

–


s

s u a t u f u n g s i d e n g a

n

r u m u s p r a k t i s .

–

M e n g h i t u n g

s u a t

u

n i l a i i n v e r s f u n g s i .

–

M e n g g a m b a r g r a f i k

i n v e r s s u a t u f u n g s i .

–


t i a n i n v e r s d a r i f u n g s i

k o m p o s i s i .

–


s

s u a t u f u n g s i k o m p o

-

s i s i

b e r d a s a r k a

n

p e n g e r t i a n n y a .

5 . 2 . 1


f i n i s i k a n f u n g s i

i n v e r s .

5 . 2 . 2


t u k a n

i n v e r s


5 . 2 . 3


f i n i s i k a n i n v e r s

d a r i f u n g s i k o m -

p o s i s i .

5 . 2 . 4


t u k a n

i n v e r s

s u a t u

f u n g s i

k o m p o s i s i .

5 . 2 . 5


l e s a i k a n m a s a -

l a h s e h a r i - h a r i

y a n g m e l i b a t k a n

i n v e r s

s u a t u

f u n g s i .

1 .

B u k u P R M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n 2 1 – 3 6

2 .

B u k u P G M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n 3 9 – 7 0

3 .

B u k u B S E M a

h i r

M e n g e m

b a n g -

k a n

K e m a m p u -

a n

M a

t e m a

t i k a

u n

t u k K e

l a s

X I

S M A / M A I P A ,

W

a h y u d i n


R .

S u d r a j a t ,

D e p d i k n a s

8 × 4 5

m e n i t

3 .

D i b e r i k a n

f u n g s i

f ( x ) = x

2 –

2 x – 4 ,

g ( x ) = 3 x + 9 ,

d a n

( g

f ) ( a ) = 6 .

a .

T e n t u k a n n i l a i a

j i k a

a

a d a l a h

b i l a n g a n p o s i t i f .

b .

T e n t u k a n

n i l a i

( f

g ) ( 2 ) .

1 .

I n v e r s d a r i f u n g s i

h ( x ) =

+ −

+

2

a d a l a h . . . .

a .

h – 1 ( x ) =

+ −

;

x ≠ 2

b .

h – 1 ( x ) =

+ +

;

x ≠ – 2

c .

h – 1 ( x ) =

+ −

;

x ≠ 4

d .

h – 1 ( x ) =

− −

;

x ≠ 4

e .

h – 1 ( x ) =

− +

;

x ≠ – 4

2 .

D i k e t a h u i f ( x ) = 1 2 x + 1

d a n

g ( x ) =

−

;

x ≠ 3 .

D a e r a h a s a l

f u n g s i ( g

f ) – 1

a d a l a h

. . . .

K o m p e

t e n s

i

D a s a r

M a

t e r i

P o

k o k

/

P e m

b e

l a j a r a n

K e g

i a t a n

P e m

b e

l a j a r a n

I n d i k a

t o r

P e n c a p a

i a n

K o m p e

t e n s

i

P e n

i l a

i a n

T e

k n

i k

B e

n t u k

I n s t r u m e n

C o n

t o h I n s

t r u m e n

A l o k a s

i

W a

k t u

A l a t d a n

S u m

b e r

B e

l a j a r

N i l a

i d a n

M a

t e r i y a n g

D i i n

t e g r a s

i k a n

P e n d i d i k a n

k a r a k t e r

( * ) T e l i t i


6/131


–


s

s u a t u f u n g s i k o m p o

-

s i s i d e n g a n

c a r

a

y a n g s a m a d e n g a

n

m e n e n t u k a n i n v e r

s


–

M e n g h i t u n g

s u a t

u

n i l a i i n v e r s f u n g s i

k o m p o s i s i .

–

M e n u l i s k a n

r u m u

s

i n v e r s s u a t u f u n g s i

y a n g t e r m u a t d a l a m

s o a l c e r i t a .

–

M e n g h i t u n g

n i l a i

i n v e r s s u a t u f u n g s i

d a l a m s o a l c e r i t a .

K o m p e

t e n s

i

D a s a r

M a

t e r i

P o

k o k

/

P e m

b e

l a j a r a n

K e g

i a t a n

P e m

b e

l a j a r a n

I n d i k a

t o r

P e n c a p a

i a n

K o m p e

t e n s

i

P e n

i l a

i a n

T e

k n

i k

B e

n t u k

I n s t r u m e n

C o n

t o h I n s

t r u m e n

A l o k a s

i

W a

k t u

A l a t d a n

S u m

b e r

B e

l a j a r

N i l a

i d a n

M a

t e r i y a n g

D i i n

t e g r a s

i k a n

a .

{ x | x ≠ –

, x ∈ R }

b .

{ x | x ≠ –

, x ∈ R }

c .

{ x | x ≠ 0 , x ∈ R }

d .

{ x | x ≠

, x ∈ R }

e .

{ x | x ≠ 1 , x ∈ R }

3 .

D i k e t a h u i f ( x ) = 2 x + 1 3

d a n g – 1 ( x + 1 ) = 1 2 x – 7 .

T e n t u k a n :

a . g – 1 ( x )

b .

f – 1 ( x )

c .

( f

g ) – 1 ( x )

d .

( g

f ) – 1 ( x )


7/131

6 Silabus

T e s

6 . 1

M e n j e l a s k a n

s e c a r a i n t u i t i f

a r t i l i m i t f u n g s i

d i s u a t u t i t i k

d a n d i t a k h i n g -

g a .

L i m i t F u n g s i

6 . 1 . 1


f i n i s i k a n

l i m i t

f u n g s i d i s u a t u

t i t i k .

6 . 1 . 2


t u k a n n i l a i l i m i t

f u n g s i b e r d a s a r -

k a n

g a m b a r

g r a f i k f u n g s i .

6 . 1 . 3


f i n i s i k a n

l i m i t

f u n g s i d i t a k

h i n g g a .

6 . 1 . 4


t u k a n l i m i t f u n g s i

d i t a k

h i n g g a

b e r d a s a r k a n

g a m b a r g r a f i k

f u n g s i .

T e r t u l i s

1 .

B u k u P R M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n 4 1 – 5 8

2 .

B u k u P G M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n

8 3 –

1 2 3

3 .

B u k u B S E M a

h i r

M e n g e m

b a n g -

k a n

K e m a m p u -

a n

M a

t e m a

t i k a

u n

t u k K e

l a s

X I

S M A / M A I P A ,

W

a h y u d i n


R .

S u d r a j a t ,

D e p d i k n a s

–

M e n j e l a s k a n p e

-

n g e r t i a n l i m i t f u n g s i d i

s u a t u

t i t i k

s e c a r

a

i n t u i t i f .

–

M e n e n t u k a n n i l a i l i m

i t

f u n g s i d i s u a t u t i t i k

j i k a d i d e k a t i d a r i k i r i

b e r d a s a r k a n g a m b a

r


–


i t


j i k a

d i d e k a t i d a r i

k a n a n b e r d a s a r k a

n

g a m b a r g r a f i k f u n g s

i .

–

M e n e n t u k a n

l i m

i t



r


–


t i a n l i m i t f u n g s i d i t a

k

h i n g g a s e c a r a i n t u i t i f .

–


i t

f u n g s i j i k a v a r i a b e l

m e m b e s a r

t a n p

a

b a t a s b e r d a s a r k a

n

g a m b a r g r a f i k f u n g s

i .

–


i t

f u n g s i j i k a v a r i a b e l

m e n g e c i l t a n p a b a t a

s


r


8 × 4 5

m e n i t

U n

t u k m e n

j a w a

b

s o a

l

n o m o r

1 s a m p a

i d e n g a n

3

p e r h a

t i k a n

g a m

b a r

g r a

f i k f u n g s

i f ( x

) b e r i

k u

t .

1 .

→

f ( x ) = . . .

a .

1

d .

3

b .

1

e .

3

c .

2

2 .

→ → → →

f ( x ) = . . .

a .

0

d .

1

b .

1

e .

t i d a k

c .

2

a d a

3 .

→

∞

f ( x ) = . . .

a . – ∞

d . ∞

b . – 2

e .

t i d a k

c .

0

a d a

S i l a

b u s

B a b I I I L i m i t F u n g s

i

S e

k o

l a h

: . . .

K e

l a s

/ S e m e s

t e r

: X I / 2

M a

t a P e

l a j a r a n

: M a

t e m

a t i k a

S t a n

d a r

K o m p e

t e n s

i : 6 .

M

e n g g u n a k a n k o n s e p l i m i t f u n g s i d a n t u r u n a n f u n g s i d a l a m p e m e c a h a n

m a s a l a h .

K o m p e

t e n s

i

D a s a r

M a

t e r i

P o

k o k

/

P e m

b e

l a j a r a n

K e g

i a t a n

P e m

b e

l a j a r a n

I n d i k a

t o r

P e n c a p a

i a n

K o m p e

t e n s

i

P e n

i l a

i a n

T e

k n

i k

B e

n t u k

I n s t r u m e n

C o n

t o h I n s

t r u m e n

A l o k a s

i

W a

k t u

A l a t d a n

S u m

b e r

B e

l a j a r

N i l a

i d a n

M a

t e r i y a n g

D i i n

t e g r a s

i k a n

X

Y

6 5 4 3 2 1

– 3 – 2 – 1 0

1

2

3

4

5

6

– 1

– 2

f ( x )

P e n d i d i k a n

k a r a k t e r

( * ) K e r j a

k e r a s


8/131


T e s

T e r

t u l i s

6 . 2


s i f a t l i m i t f u n g s i

u n t u k

m e n g -

h i t u n g b e n t u k

t a k t e n t u f u n g s i

a l j a b a r d a n t r i -

g o n o m e t r i .

L i m i t F u n g s i

–


s i f a t l i m i t f u n g s i d i

s a t u t i t i k .

–


c a r

a

m e n y e l e s a i k a n l i m

i t


m e n g g u n a k a n c a r

a

s u b s t i t u s i l a n g s u n g .

–


c a r

a


i t



a

m e m f a k t o r k a n .

–


c a r

a


i t


d e n g a n m e n g a l i k a

n

b e n t u k s e k a w a n .

–

M e n g g u n a k a n s i f a t -

s i f a t l i m i t u n t u k m e n g

-

h i t u n g l i m i t f u n g s i .

–

M e n y e l e s a i k a n p e r -

m a s a l a h a n y a n g b e r -

k a i t a n d e n g a n l i m

i t

f u n g s i d i s u a t u t i t i k .

–


s i f a t l i m i t f u n g s i d i t a

k

h i n g g a .

–


c a r

a


i t

f u n g s i d i t a k h i n g g

a


a

s u b s t i t u s i l a n g s u n g .

–


c a r

a


i t


a


a

m e m b a g i

d e n g a

n

p a n g k a t t e r t i n g g i .

–


c a r

a


i t


a


a

m e n g a l i k a n d e n g a

n

b e n t u k s e k a w a n .

6 . 2 . 1



f u n g s i a l j a b a r d i

s u a t u t i t i k .

6 . 2 . 2


l e s a i k a n p e r m a -

s a l a h a n

y a n g

b e r k a i t a n

d e -

n g a n l i m i t f u n g s i

d i s u a t u t i t i k .

6 . 2 . 3



f u n g s i a l j a b a r d i

t a k h i n g g a .

6 . 2 . 4



s a l a h a n

y a n g

b e r k a i t a n

d e -


d i t a k h i n g g a .

6 . 2 . 5



f u n g s i t r i g o n o -

m e t r i d i s u a t u

t i t i k .

6 . 2 . 6



s a l a h a n

y a n g

b e r k a i t a n

d e -


t r i g o n o m e t r i .

1 .

B u k u P R M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n 4 1 – 5 8

2 .

B u k u P G M a

t e -

m a

t i k a

K e

l a s

X I

S e m e s

t e r

2 ,


h a l a m a n

8 3 –

1 2 8

3 .

B u k u B S E M a

h i r

M e n g e m

b a n g -

k a n

K e m a m p u -

a n

M a

t e m a

t i k a

u n

t u k K e

l a s

X I

S M A / M A I P A ,

W

a h y u d i n


R .

S u d r a j a t ,

D e p d i k n a s

1 .

N i l a i

→ → → →

− − − −

− − − −

− − − −

= . . . .

a .

d .

4

b .

e . ∞

c .

2

2 .

J i k a

→

=

4 ,

n i l a i a y a n g m e m e -

n u h i a d a l a h . . . .

a .

2

d . – 1

b .

1

e . – 2

c .

0

3 .

N i l a i

→

∞ ∞ ∞ ∞ ( ( x – 2 )

–

−

) = . . .

a . – 4

d .

0

b . – 3

e .

4

c . – 2

4 .

→

= . . .

a .

5

d .

b .

e .

c .

5 .

T e n t u k a n n i l a i l i m i t

b e r i k u t .

a .

→ → → →

− −

b .

→

−

−

−

1 2 × 4 5

m e n i t

K o m p e

t e n s

i

D a s a r

M a

t e r i

P o

k o k

/

P e m

b e

l a j a r a n

K e g

i a t a n

P e m

b e

l a j a r a n

I n d i k a

t o r

P e n c a p a

i a n

K o m p e

t e n s

i

P e n

i l a

i a n

T e

k n

i k

B e

n t u k

I n s t r u m e n

C o n

t o h I n s

t r u m e n

A l o k a s

i

W a

k t u

A l a t d a n

S u m

b e r

B e

l a j a r

N i l a

i d a n

M a

t e r i y a n g

D i i n

t e g r a s

i k a n

P e n d i d i k a n

k a r a k t e r

( * ) R a s a

I n g i n

T a h u


9/131

8 Silabus

K o m p e

t e n s

i

D a s a r

M a

t e r i

P o

k o k

/

P e m

b e

l a j a r a n

K e g

i a t a n

P e m

b e

l a j a r a n

I n d i k a

t o r

P e n c a p a

i a n

K o m p e

t e n s

i

P e n

i l a

i a n

T e

k n

i k

B e

n t u k

I n s t r u m e n

C o n

t o h I n s

t r u m e n

A l o k a s

i

W a

k t u

A l a t d a n

S u m

b e r

B e

l a j a r

N i l a

i d a n

M a

t e r i y a n g

D i i n

t e g r a s

i k a n

6 .

J i k a

→

∞

(

+ + + +

–

( 2 x – 1 ) ) =

, c a r i l a h

n i l a i a y a n g m e m e -

n u h i .

7 .

T e n t u k a n n i l a i l i m i t

b e r i k u t .

a .

→

− − − −

b .

→ → → →

− − − −

–




i t

f u n g s i d i t a k h i n g g a .

–

M e n j e l a s k a n t e o r e m a

l i m i t a p i t .

–


c a r a


i t

f u n g s i t r i g o n o m e t r i .

–


i t

f u n g s i t r i g o n o m e t r i d i

t i t i k n o l .

–


c a r a


i t



–


i t



–




i t

f u n g s i t r i g o n o m e t r i .


10/131


11/131

10 Silabus

3 .

J i k a f ( x ) = ( x + 1 )

+ + + +

m a k a f ′ ( x ) =

. . . .

a .

+ +

b .

+ +

c .

+ +

d .

+ +

e .

+ +

4 .

D i k e t a h u i

g ( x ) =

−

. N i l a i

g (

+ + + +

) = . . . .

a .

−

d . –

b .

+

e . –

c .

5 .

J i k a f ( x ) =

+ + + +

,

g ( x ) =

− − − −

, d a n

h = g

f , t u r u n a n d a r i

h a d a l a h . . . .

a .

+ + + +

b .

+ + + +

c .

+ + + +

d .

+ + + +

e .

+ + + +

K o m p e

t e n s

i

D a s a r

M a

t e r i

P o

k o k

/

P e m

b e

l a j a r a n

K e g

i a t a n

P e m

b e

l a j a r a n

I n d i k a

t o r

P e n c a p a

i a n

K o m p e

t e n s

i

P e n

i l a

i a n

T e

k n

i k

B e

n t u k

I n s t r u m e n

C o n

t o h I n s

t r u m e n

A l o k a s

i

W a

k t u

A l a t d a n

S u m

b e r

B e

l a j a r

N i l a

i d a n

M a

t e r i y a n g

D i i n

t e g r a s

i k a n


12/131


2 × 4 5

m e n i t

6 .

D i k e t a h u i

f ( x )

=

a x

2 +

b x + 6 .

J i k a

f ′ ( – 1 ) =

– 1 1

d a n

f ′ ( 2 ) = 7 ,

t e n t u k a n

n i l a i f ( 1 ) .

7 .

D i k e t a h u i y = 3 t 2

d a n

x = 2 t 2

+ t – 1 .

J i k a

t < 0 ,

t e n t u k a n n i l a i

d

i x = 2 .

1 .

J i k a y = c o s

4 x

m a k a

= . . . .

a .

t a n x

b .

2 t a n x

c . – 4 t a n x

d . – 2 c o t a n x

e . – 4 c o t a n x

2 .

D i k e t a h u i

g ( x ) =

− − − −

. N i l a i

( g (

π ) ) = . . . .

a .

1

d . –

b .

e . – 1

c .

0

3 .

D i k e t a h u i f ( x ) = s i n

2 x

d a n f ′ ′ ( x ) = 1 u n t u k

0 ° ≤ x ≤ 1 8 0 ° . N i l a i x

y a n g m e m e n u h i a d a -

l a

211365169 Kunci Jawaban Dan Pembahasan MAT XIB IPA

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