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