matematika

PENYELESAIAN KODE A

2011-12-22T03:18:00.001-08:00

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. Semuapeserta 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 sin⁵x. cos x dx = ò sin⁵x 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. Proyeksivektor ortogonal pada = (4 +8 – 24)/24 {2 – 2+ 4}

= – + - 2

37. rotasidengan 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, diketahuiakar- akarnya adalah x₁dan 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

2011-12-19T02:28:00.000-08:00

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. Semuapeserta 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 cos²x = 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. ∫ sin³x. cos x dx =∫ sin³x 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. Proyeksivektor ortogonal a pada b = (– 3 + 2 + 10)/9 {i + 2j - 2k}

= i + 2j - 2k

37. rotasidengan 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

2011-12-18T21:58:00.001-08:00

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

KUNCIJAWABAN

LATIHANUJIAN 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

2011-12-05T07:09:00.001-08:00

DAFTAR NILAI ULANGAN AKHIR SEMESTER 1

NO	XII IPA-3	NILAI	NO	XII IPA-4	NILAI
1	ABDURRAHMAN F.A.H.	50	1	ADE RAHMA DEWANTRI	61
2	AISYAH RUBINA SATRIANI	69	2	ADHITYA SETIAWAN W	53
3	ANANDA SAKA PRAYOGO	61	3	ADI ARIEF WICAKSONO	74
4	ANI SULASTRI	69	4	ADITYA SURYA ADMOKO	60
5	ARI LISTYA NINGRUM	56	5	AFRIDA NUR WIDASTI	73
6	ARIESTYA RAHADIYAN	51	6	ANDRI PRIHANTO	64
7	ATIK MAYASRI	61	7	ARYA AJISAKA	46
8	AUFA HAQQU HABLILLAH	63	8	ATIKA DWI HARJANTI	60
9	CLAUDIA CHINDY CLARASATI	63	9	BELLINDA WAHYU R	68
10	DIKTYO ROBBY ROHIMAWAN	73	10	CYNTHIA PUTRI PURWADI	65
11	DINA OKTAVIA UTAMI	63	11	DICKA CATUR PUTRA	65
12	DISHA YUDHA SESHA	53	12	GREDY ARYOCAKSONO W	56
13	EKO YUNI SETIAWAN	72	13	HAYYU HANDARWATI	64
14	FARIZ ADITYA PURNAMA P	65	14	KARISNA S.	62
15	INDI HARTINI	63	15	MAHENDRA SHENAPUTRA	57
16	ISNAN ROHMIA ASNA NUR`AIN	66	16	MARANTIKA SOLONINGTYAS	61
17	KEVIN ADI WIRANATA	44	17	MARLINDA CESNA DEWI	62
18	LISTY AVRI CHRISTIANA	74	18	NABILA FII SABILILLAH	50
19	MEI LESTARI	79	19	NANDA EKA SRI SEJATI	74
20	MERINDA SYUKURILLA	73	20	NANING STYANINGSIH	66
21	MUHAMMAD NUR PRAMUDYA P	40	21	NIKEN FARAHDIBA	75
22	NIZA ANJARI	66	22	NOVRYA BAGUS SAPUTRO	94
23	NORMA SEPTIANA	78	23	NUR KASANAH	74
24	NOVA CHINTYA VERONICA	65	24	OLGA PRAMUDITA MAJID	68
25	NUR ANUGRAHANI	61	25	PATRA DEWI SAFANA	63
26	RAHMAT DHARMAWAN	77	26	PRATIWI MANGGALAWATI	66
27	ROSIANI AMI AGUSTIN	70	27	RISKY KARTIKA SARI	58
28	SAGA DERMAWAN DWI L	50	28	RIYAD	62
29	SIWI RESIKA	57	29	RIZKI MA`RIFAH	74
30	SRI YUNIARTI	58	30	SALSABILAH	62
31	VITA DYAH PUSPITASARI	50	31	VANIA UTAMI	64
			32	WINA CHANDRA FERDYANA	65
			33	ZULFIKAR MAHMUD	76

	CATATAN : BAGI SISWA YANG NILAINYA DIBAWAH 70 SILAHKAN MENGERJAKAN SOAL REMIDI SEMESTERAN
	DI BLOG INI (http://matematika-sman2solo.blogspot.com)

2011-12-05T01:54:00.001-08:00

DAFTAR NILAI ULANGAN AKHIR SEMESTER 1

NO	XII IPA-1	NILAI	NO	XII IPA-2	NILAI
1	AFIFAH SHAFA SHELVIANA	52	1	AFINA NAHARINDYA V	59
2	ANGGA WISESA	68	2	AJI KURNIAWAN	54
3	ANINDITA GANGGA DEWI	30	3	ALDILLA ARIFATUNURRILAH	69
4	ARDIATAMA PUTRA	57	4	ALFIAN ARSYADI SUNANTO	73
5	CITRA AYU SURYA PUTRI	65	5	AMANDA BOY ARVIAN ATMAJA	59
6	DEWANTI ENDAH C	70	6	AMANDA MAYANG SARI S	63
7	DEWI SANG ARIFTI	38	7	ANDI ADAM HASANUDIN	60
8	DIAN RATRI RAHAYU	61	8	ANDREAN FAJAR ROKIM	74
9	EMA TRIE SWARI	50	9	BINTANG RAMADHAN S	72
10	ENDAH APRILLIANI	49	10	DEANISA KORIFIAS	66
11	ENDAH SULISTYANINGSIH	60	11	DEREK TRANKA PRAKOSO	29
12	ENNO CITRA HARMONY	39	12	DIAN PRADIPTA	55
13	ERLANGGA YUDHA M	59	13	ERNA NURSANTI	58
14	FARIDA AYU DEWAYANTI	72	14	ERY PERMANA YUDHA	73
15	GABRA MICHAEL GANDHI	58	15	GILANG FADILANA	70
16	HERU ISYA MAULANA	64	16	HILDA HARDIANTI	59
17	IGNASIUS HARI KURNIAWAN	58	17	IKA NURKUMALASARI	58
18	MARIA MARGARETHA DEBBY L	59	18	IRVAN ARDIYANTO	50
19	MEIRIZA SENGEORIS	55	19	ISNAINI FITRI FATIMAH	50
20	NOVIANDIRA LARASATI	63	20	ITTAQI DEA OKTARINA	41
21	PRANITA WIDYANTI	60	21	MUHAMMAD BIMO AGUNG K	61
22	RADEN AJENG DINASTI P.P.S.	64	22	MUHAMMAD S.A.A.	58
23	RAHMANIA SHALIHAH	68	23	MUHAMMAD WAQSHIT	39
24	RATNA MENTARI WULAN SUCI	65	24	NABILLA TURISTA LASTANTA	61
25	RENI ENDAH SUWARNO	50	25	NUR ATTIKA	53
26	RENY NUGRAHENI OKTAVIA	32	26	PASULIH ADITYA ETMI	65
27	RIAN KRIS WIDIANTO	51	27	RISTY INTAN PUSPITA	40
28	SESILIA ADVENITA HARYANTI	52	28	SIGIT DWI WIBOWO	50
29	VICTOR BAGASWINADI	51	29	SUCI ARDIANA RAHMAWATI	60
30	WACHID SEDYO PRAKOSO	63	30	VRISHELLA SETIADI PUTRI	56
31	YOLANDA PUTRI PERDANA A	51	31	YOGI LINTANG SARI	48

	CATATAN : BAGI SISWA YANG NILAINYA DIBAWAH 70 SILAHKAN MENGERJAKAN SOAL REMIDI SEMESTERAN
	DI BLOG INI (http://matematika-sman2solo.blogspot.com)

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

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

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

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

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

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