PENYELESAIAN KODE A

Penyelesaian A

1.        √18 - √32 + √50 + √72 = 3√2 – 4√2  + 5√2  + 6√2 = 10√2 (A)

2.        p + 1 = x → p = x – 1

4(x – 1)² – 2(x – 1) – 3 = 0

4x² – 8x + 4 – 2x + 2 – 3 = 0

4x² – 10x + 3 = 0 (C)

3.        (– 8)² – 4(m – 1)(8m) ≥ 0

64 – 32m² + 32m ≥ 0

m² – m – 2 ≤ 0

(m – 2)(m + 1) ≤ 0

m = 2 atau m =  – 1

– 1 ≤ m ≤  2 (C) 

4.        y = a(x – 3)² – 2

f(0) = 16→ 16 = a(9) – 2

                    a = 2

y = 2(x – 3)² – 2 = 2x² – 12x + 16 (D)                    

5.        Semua peserta Ujian Nasional berdoa sebelum mengerjakan soal (E)

6.        p →  ~q ≡ p →  ~q

~r → q  ≡ ~q → r

                    ~ r          r          

                    ~  p     (A)

7.        x+ y + z = 12                               3x + 2y – z = 8

2x – y + 2z = 12                           2x + 2y +2z = 24

3x + 3z = 24                                 x – 3z = – 16

                             3x + 3z = 24

                             x – 3z =  – 16

                                         x = 2 → z = 6 → y = 4

x.y.z = 2.4.6 = 48  (B)

8.        2 cos (2x + 150⁰) = Ö3

cos (2x + 150⁰) = ½V3

cos (2x + 150⁰) = cos 30⁰

1.         2x + 150⁰ = 30⁰ + k.360⁰                                          2. 2x + 150⁰ = – 30⁰ + k.360⁰

2x =  – 120⁰ + k.360⁰                                                    2x = – 180⁰ + k.360⁰

x = – 60⁰ + k.180⁰                                                           x = – 90⁰ + k.180⁰

                         HP= {90⁰, 120⁰}   (B)

 

9.        Panjang vertikal = 10 tan 30⁰ = 10/3 V3

Sudut puncak kelapa = 45^o

(10/3 V3) : sin 45⁰  = x : sin 120⁰

        10.V3.V3 = 3.x.V2

x = 5√2 (D)

10.    Jarak C ke BDG = 1/3 diagonal ruang = 3 cm (D)

11.    TP = CP =  = 2

Sudut ADB dengan ABC adalah sudut CED = α

Cos α =  =

Tan α = 2√2

12.     5.4.7.6.5 = 4200

13.    1 3 3 1

Paling sedikit dua gambar = 4/8 = ½ (E)

14.    300000 =

300 p + 300w = 320p + 285w

15w = 20p

3w = 4p

 p : w = 3 : 4   (D)

15.    Mo = 85,5 +  = 85,5 + 3 = 88,5 (B)

16.    Tan 105⁰  = Tan (60 + 45)⁰

=  .

=

= – 2  –  (B)

17.    Cos 3x + Cos x = 2 Cos 2x cos x = 2 (1 – 2 sin²x) Cos x = 2 (1 – 2.16/25).3/5 = - 42/125 (C)

18.    (x + 1)² + (y – 3)² = 1

x² + y² + 2x – 6y + 9 =0 (D)

19.     3x – y + (x + 3) – 2(y – 1) – 20 = 0

4x – 3y – 15 = 0 (A)

20.    x⁴ – 3x³ – 5x² + x – 6        = (x² + bx + c)(x² – x  – 2) + (px + q)

                                         = x⁴ – x³ – 2x² + bx³ – bx² – 2bx + cx² – cx – 2c + px + q

                                         =  x⁴ – (1 – b)x³ – (2 + b – c)x² – (2b + c – p)x – 2c + q

1 – b = 3              2 + b – c = 5        p – c – 2b = 1                         q – 2c = – 6 

b = – 2                             c = – 5                   p = – 8                             q = – 16 

jadi sisanya :  – 8 x – 16 (D)

21.       2a + b =8

– 3a + b = – 7

5a = 15

a = 3

b = 2

jadi didanya : 3x + 2 (E)

22.    6(5p + 4) – 3 = 81

30p + 24 = 84

p =   2  (D)

23.    5yx + 3y = 2x – 1

2x – 5yx = 3y + 1

x =   = , jadi a = –3 dan b = 5 maka 2a + b = – 6 + 5 = – 1 ( A)

24.         =  

                                         =                  

                                         =  6          (B)

25.      =  =            ( C )

26.    f(x) = cos⁵ (4x – 2)

f’(x) = 5cos⁴(4x – 2).sin (4x – 2)(– 4) = – 10 cos³ (4x – 2) sin (8x – 4).  (E)                         

27.    L = a² + 4at = 108

V= a²t = a²(108 – a²)/4a = 27a – a³/4

V’ = 27 – ¾ a² = 0

         27 = ¾ a²

         a² = 4.9

         a  = 6    (A) 

28.    y = x³ – 3x² + x + C

– 3 = 8 – 12 + 2 + C

C =  – 1

Jadi persamaan kurva itu :y = x³ – 3x² + x – 1  ( B )

29.    ò sin⁵ x. cos x dx = ò sin⁵ x d(sin x) = 1/6  sin⁶ x + C    (A)

30.    V = π  =  π{( + 16 + 18)} = 40  π      (A)

31.    102 + 105 + 108 + ... + 399

399 = 102 + (n – 1)3

297 = (n – 1)3

99 = n – 1

n = 100

Sn = 50.501 = 25.050 (C)

32.    ar⁵ : ar² = 10 2/3 : 36

r³ = 8/27

r = 2/3

a = 9.9

S~ = 9.9/(1 – 2/3) = 9.9.3 = 243 (B)

33.      

Titik	A	B	C
Koordinat	(30,0)	(0,63)	(8,55)
500x + 300y	15.000.000	18.900.000	4.000.000+16.500.000 =20.500.000

34.    3 = 2 + 2p → p = ½

5 = q + 4 → q = 1

p + q` = 3/2  (A)

35.    6 – 4 – 2x = 0 → x = 1 (E)

36.    Proyeksi vektor ortogonal  pada   = (4  + 8 – 24)/24 {2 – 2+ 4}

= – + - 2                                                            

                                         

37.    rotasi dengan pusat (0,0) sejauh +90^o →  y = – x’ dan x  =  y’

                                         x – 2y + 4 = 0 → y’ + 2x’ + 4 = 0

pencerminan terhadap garis y = x → y’ = x’’ dan x’  = y’’

                             x’’ + 2y’’ + 4 = 0

Jadi bayangannya adalah x + 2y + 4 = 0

38.    L_bayangan = ½ .6.4 = 12  

39.     ⁵log(x² – 7x – 1)  –  ⁵log (4 – 3x) = 0

x² – 7x – 1 = 4 – 3x

x² – 4x – 5 = 0

(x – 5)(x + 1) = 0

x = 5 (tm) atau x = – 1   (D )

40.    3^2x+1 –10.3^x + 3 = 0, diketahui akar- akarnya adalah x₁ dan x₂ dimana           x₁ <  x₂. Nilai dari 2x₁ – 3x₂

3a² – 10a + 3 = 0

(3a – 1)(a – 3) = 0

a = 1/3 atau a = 3

x = – 1 atau x = 1

      2x₁ – 3x₂ = – 2 – 3 =  – 5

PENYELESAIAN KODE B

Penyelesaian KODE B:

1.   √18 + √32 - √50 + √72 = 3√2 + 4√2 – 5√2 + 6√2 = 8√2(D)

2.        p + 2 = x → p = x – 2

3(x – 2)² – 2(x – 2) – 5 = 0

3x² – 12x + 12 – 2x + 4 – 5 = 0

3x² – 14x + 11 = 0 (C)

3.        (– 8)² – 4(k – 1)(8k) < 0

64 – 32k² + 32k < 0

k² – k – 2 > 0

(k – 2)(k + 1) > 0

k = 2 atau k =  – 1

k< – 1 atau k > 2 (D) 

 4.        y = a(x – 3)² – 2

f(0) = 25→ 25 = a(9) – 2

                    a = 3

y = 3(x – 3)² – 2 = 3x² – 18x + 25 (D)

                    

5.        Semua peserta Ujian Nasional berdoa sebelum mengerjakan soal (E)

6.        ~p → q ≡ ~p →  q

r → ~q  ≡ q → ~r

                   r          r          

                      p     (B)

7.        6x – 4y + 2z = 18                         -x + 3y+ z = 6

2x + y – 2z = 23                           3x – 2y + z = 9

8x – 3y = 41                                 4x – 5y = 3

                             8x – 3y = 41

                             8x – 10y = 6

                                         y = 5 → x = 7 → z = – 2

x.y.z = 7.5.(– 2) =  – 70  (A)

8.        2 sin (2x +150⁰) = 1 

Sin (2x + 150⁰) = ½

Sin (2x + 150⁰) = sin 30⁰

1.         2x + 150⁰ = 30⁰ + k.360⁰                                          2. 2x + 150⁰ = 150⁰ + k.360⁰

2x =  – 120⁰ + k.360⁰                                                    2x = k.360⁰

x = – 60⁰ + k.180⁰                                                           x = k.180⁰

                         HP= {120⁰, 180⁰}   (B)

9.        CA = 30 mil dan CB = 40 mil

AB² = 30² + 40² – 2.30.40 cos 120⁰

        = 900 + 1600 + 1200

        = 3700

AB = 10√37 (B)

10.    Jarak E ke AFH = 1/3 diagonal ruang = 5√3 cm (B)

11.    DE = CE = √(36 - 9) = 3√3

Sudut ADB dengan ABC adalah sudut CED = α

Cos α = (27 + 27 - 36)/2.9.3 = 1/3

Tan α = 2√2

12.     7.6.5.5.4 = 4200

13.    1 3 3 1

Paling banyak dua angka = 7/8 (E)

14.    300.000 = (285.000p + 320.000w)/(p + w)...........ruas kanan dan kiri dibagi 1.000

300 p + 300w = 285p + 320w

15p = 20w

3p = 4w

 p : w = 4 : 3   (E)

15.    Me = 85,5 + 5(25-23)/10 = 85,5 + 1 = 86.5 (B)

16.    Tan 15⁰  = tan (60 – 45)⁰

= (√3 - 1)/(1 + √3) . (√3 - 1)/(√3 - 1)

= (4 - 2√3)/2

= 2 – √3 

17.    sin 3x + sin x = 2 sin 2x cos x = 4 sin x cos² x = 4. 3/5 . 16/25 = 192/125 (D)

18.    (x + 3)² + (y – 1)² = 1

x² + y² + 6x – 2y + 9 =0

19.     – x + 3y – 2(x – 1) + (y + 3) – 20 = 0

3x – 4y + 15 = 0 (C)

20.    x⁴ – 3x³ – 5x² + x – 6        = (x² + bx + c)(x² + x – 2) + (px + q)

                                         = x⁴ + x³ – 2x² + bx³ + bx² – 2bx + cx² + cx – 2c + px + q

                                         =  x⁴ + (1 + b)x³ – (2 – b – c)x² – (2b – c – p)x – 2c + q

b + 1 =  – 3              2 – b – c = 5        p + c – 2b = 1                       q – 2c = – 6 

b = – 4                                 c = 1                      p = – 8                            q = – 4 

jadi sisanya : – 8x – 4 (E)

21.       2a + b = 24

– 5a + b = 10

7a = 14

a = 2

b = 20

jadi didanya : 2x + 20 (D)

22.    6(5p + 4) – 3 = – 39

30p + 24 = – 36

p =  – 2  (A)

23.    yx + 2y = 3x – 5

3x – yx = 2y + 5

x = (2y + 5)/(3 - y) = (-2y - 5)(y - 3), jadi a = –2 dan b = 1 maka 3a + b = – 6 + 1 = – 5 ( A)

24. lim  x² /{1 - √( x² + 1)} =  lim  x² /{1 - √( x² + 1)}.{1 + √( x² + 1)}/{1 + √( x² + 1)}                            

        x →0                                 x →0              

                                     = lim  x² {1 + √( x² + 1)}/{1 - x² - 1)}

                                         x →0 

                                     = (1  + 1)/(-1)     

                                     =  – 2          (A)

25. lim   x sin 3x/(1 - cos 4x)  = lim (x sin 3x) / (2 sin² 2x) = (1.3)/(2.2.2) = 3/8 (C)

      x →0                                  x →0         

26.    f(x) = sin³ (3 – 2x)

f’(x) = 3sin²(3 – 2x).cos (3 – 2x)(– 2) = – 3 sin (6 – 4x) sin (3 – 2x)  (E)

27.    L = a² + 4at = 432

V= a²t = a²(432 – a²)/4a = 108a – a³/4

V’ = 108 – ¾ a² = 0

         108 = ¾ a²

         a² = 4.36

         a  = 12    (D) 

28.    y = x³ – 6x² + 5x + C

– 4 = 8 – 24 + 10 + C

C = 2

Jadi persamaan kurva itu :y = x³ – 6x² + 5x + 2 ( C )

29.    ∫ sin³ x. cos x dx =∫ sin³ x d(sin x) = ¼ sin⁴ x + C    (A)

30.    V = π (1/5 x⁵ + 2x³ + 9x) =  π{2(1/5 + 2 + 9)} = 22 2/5 π      (D)

31.    1005 + 1010 + 1015 + ... + 2000

2000 = 1005 + (n – 1)5

995 = (n – 1)5

199 = n – 1

n = 200

Sn = 100.3005 = 300.500

32.    ar⁵ : ar² = 2/3 : 18

r³ = 1/27

r = 1/3

a = 9.18

S~ = 9.18/(1 – 1/3) = 9.18.3/2 = 243 (B)

33.     anulir

34.    3 = 2 + 2p → p = ½

7 = q + 4 → q = 3

p.q` = 3/2  (A)

35.    8 – 2x – 2 = 0 → x = 3 (A)

36.    Proyeksi vektor ortogonal a pada  b   = (– 3  + 2 + 10)/9 {i + 2j - 2k}

= i + 2j - 2k                                                      

37.    rotasi dengan pusat (0,0) sejauh +270^o → y = x’ dan x  = – y’

                                         2x – y + 4 = 0 → – 2y’ – x’ + 4 = 0

pencerminan terhadap garis y = x → y’ = x’’ dan x’  = y’’

                             – 2x’’ – y’’ + 4 = 0

Jadi bayangannya adalah 2x + y – 4 = 0

38.  hasil translasinya adalah A'(-2,2), B'(1,2) dan C(1,4)
       hasil dilatasinya A"(-4,4), B"(2,4) dan C"(2,8)

L_bayangan = 1/2.6.4 = 12

39.     ⁵log(x² – 7x – 1)  –  ⁵log (4 – 3x) = 0

x² – 7x – 1 = 4 – 3x

x² – 4x – 5 = 0

(x – 5)(x + 1) = 0

x = 5 (tm) atau x = – 1   (D )

40.    5. 5^2x –26.5^x + 5 = 0

5a² – 26a + 5 = 0

(5a – 1)(a – 5) = 0

a = 1/5 atau a = 5

x = – 1 atau x = 1

       3x₁ – 4x₂ = – 3 – 4 =  – 7   (B)

KUNCI LATIHAN UJIAN

KUNCI JAWABAN

LATIHAN UJIAN NASIONAL

MATEMATIKA (B)

1	D	6	B	11	A	16	A	21	D	26	E	31	B	36	D
2	C	7	A	12	D	17	D	22	A	27	D	32	B	37	C
3	D	8	B	13	E	18	D	23	A	28	C	33		38	B
4	D	9	D	14	E	19	C	24	A	29	A	34	A	39	D
5	E	10	B	15	B	20	E	25	C	30	D	35	A	40	B

KUNCI JAWABAN

LATIHAN UJIAN NASIONAL

MATEMATIKA (A)

1	A	6	A	11	A	16	B	21	E	26	E	31	C	36	E
2	C	7	B	12	D	17	C	22	D	27	A	32	B	37	A
3	C	8	B	13	E	18	D	23	A	28	B	33	D	38	D
4	D	9	D	14	D	19	A	24	B	29	A	34	A	39	D
5	E	10	D	15	B	20	D	25	C	30	A	35	E	40	B