Kumpulan Arsip Soal UN Matematika SMA Program IPA Tahun

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TAHUN 2002 s/d 201TAHUN 2002 s/d 201TAHUN 2002 s/d 201TAHUN 2002 s/d 2012222

Disusun Berdasarkan Topik Materi Per Bab

(Program(Program(Program(Program StudiStudiStudiStudi IPA)IPA)IPA)IPA)

Written by :

Karyanto, S.PdKaryanto, S.PdKaryanto, S.PdKaryanto, S.Pd ([email protected])

Edited and Distributed by :

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Arsip Soal UN Matematika IPA. Downloaded from http://pak-anang.blogspot.com Halaman ii

Daftar Isi

Halaman

Daftar IsiDaftar IsiDaftar IsiDaftar Isi ..................................................................................................................................................................................................................... ii

BAB 1.BAB 1.BAB 1.BAB 1. Pangkat, Akar dan LogaritmaPangkat, Akar dan LogaritmaPangkat, Akar dan LogaritmaPangkat, Akar dan Logaritma

A. Pangkat Rasional ......................................................................................................................................................................... 1

B. Bentuk Akar ................................................................................................................................................................................... 4

C. Logaritma........................................................................................................................................................................................ 8

BAB 2.BAB 2.BAB 2.BAB 2. Fungsi KuadratFungsi KuadratFungsi KuadratFungsi Kuadrat

A. Persamaan Kuadrat ................................................................................................................................................................. 11

B. Pertidaksamaan Kuadrat ...................................................................................................................................................... 12

C. Menyusun Persamaan Kuadrat Baru ............................................................................................................................... 15

D. Menentukan Persamaan Grafik Fungsi Kuadrat .......................................................................................................... 17

E. Kedudukan Garis Terhadap Kurva Parabola ................................................................................................................ 20

BAB 3.BAB 3.BAB 3.BAB 3. Sistem Persamaan LinearSistem Persamaan LinearSistem Persamaan LinearSistem Persamaan Linear

A. Sistem Persamaan Linear Dua Variabel (SPLDV) ....................................................................................................... 22

B. Sistem Persamaan Linear Tiga Variabel (SPLTV) ....................................................................................................... 22

BAB 4.BAB 4.BAB 4.BAB 4. Trigonometri ITrigonometri ITrigonometri ITrigonometri I

A. Trigonometri Dasar ................................................................................................................................................................. 27

B. Perbandingan Trigonometri Sudut Istimewa (30<, 45<, =0<) ................................................................................ 27

C. Perbandingan Trigonometri Sudut Berelasi ................................................................................................................. 27

D. Rumus-Rumus dalam Segitiga ............................................................................................................................................ 28

BAB 5.BAB 5.BAB 5.BAB 5. Trigonometri IITrigonometri IITrigonometri IITrigonometri II

A. Jumlah dan Selisih Dua Sudut .............................................................................................................................................. 34

B. Perkalian Sinus dan Kosinus................................................................................................................................................ 37

C. Penjumlahan dan Pengurangan Sinus, Kosinus dan Tangen .................................................................................. 38

D. Sudut Rangkap ........................................................................................................................................................................... 41

E. Persamaan Trigonometri ...................................................................................................................................................... 42

BAB =.BAB =.BAB =.BAB =. Logika MatematikaLogika MatematikaLogika MatematikaLogika Matematika

A. Negasi (Ingkaran) .................................................................................................................................................................... 4=

B. Operator Logika ........................................................................................................................................................................ 4=

C. Nilai Kebenaran Konjungsi, Disjungsi, Implikasi dan Biimplikasi ....................................................................... 4=

D. Konvers, Invers dan Kontraposisi ..................................................................................................................................... 4=

E. Pernyataan-Pernyataan yang Ekuivalen ........................................................................................................................ 4=

F. Kuantor Universal dan Kuantor Eksistensial ................................................................................................................ 47

G. Penarikan Kesimpulan ........................................................................................................................................................... 47

BAB 7.BAB 7.BAB 7.BAB 7. Dimensi TigaDimensi TigaDimensi TigaDimensi Tiga

A. Jarak ............................................................................................................................................................................................... 55

B. Sudut .............................................................................................................................................................................................. =2

C. Volume Bangun Ruang ........................................................................................................................................................... =9

Arsip Soal UN Matematika IPA. Downloaded from http://pak-anang.blogspot.com Halaman iii

BAB 8.BAB 8.BAB 8.BAB 8. StatistikaStatistikaStatistikaStatistika

A. Ukuran Pemusatan

1. Mean....................................................................................................................................................................................... 72

2. Median .................................................................................................................................................................................. 74

3. Modus .................................................................................................................................................................................... 75

B. Ukuran Letak

1. Kuartil.................................................................................................................................................................................... 78

BAB 9.BAB 9.BAB 9.BAB 9. PeluangPeluangPeluangPeluang

A. Kaidah Pencacahan

1. Aturan Perkalian ............................................................................................................................................................... 81

2. Permutasi ............................................................................................................................................................................. 82

3. Kombinasi ............................................................................................................................................................................ 83

B. Peluang Suatu Kejadian ......................................................................................................................................................... 85

BAB 10.BAB 10.BAB 10.BAB 10. LingkaranLingkaranLingkaranLingkaran

A. Persamaan Lingkaran ............................................................................................................................................................. 89

B. Persamaan Garis Singgung Lingkaran ............................................................................................................................. 89

BAB 11.BAB 11.BAB 11.BAB 11. Suku BanyakSuku BanyakSuku BanyakSuku Banyak

A. Teorema Sisa .............................................................................................................................................................................. 93

B. Teorema Faktor......................................................................................................................................................................... 93

C. Akar Rasional Persamaan Suku Banyak ......................................................................................................................... 93

BAB 12.BAB 12.BAB 12.BAB 12. Fungsi Komposisi dan Fungsi InversFungsi Komposisi dan Fungsi InversFungsi Komposisi dan Fungsi InversFungsi Komposisi dan Fungsi Invers

A. Domain Fungsi ........................................................................................................................................................................... 98

B. Komposisi Fungsi dan Invers Fungsi ............................................................................................................................... 98

BAB 13.BAB 13.BAB 13.BAB 13. Limit FungsiLimit FungsiLimit FungsiLimit Fungsi

A. Limit Fungsi Aljabar .............................................................................................................................................................. 105

B. Limit Fungsi Trigonometri ................................................................................................................................................. 108

C. Limit Mendekati Tak Berhingga ....................................................................................................................................... 112

BAB 14.BAB 14.BAB 14.BAB 14. Turunan Turunan Turunan Turunan (Derivatif)(Derivatif)(Derivatif)(Derivatif)

A. Rumus-Rumus Turunan Fungsi Aljabar dan Trigonometri .................................................................................. 113

B. Aplikasi Turunan Suatu Fungsi......................................................................................................................................... 11=

BAB 15.BAB 15.BAB 15.BAB 15. Integral (Anti Diferensial)Integral (Anti Diferensial)Integral (Anti Diferensial)Integral (Anti Diferensial)

A. Integral Tak Tentu

1. Rumus-Rumus Integral Tak Tentu Fungsi Aljabar dan Trigonometri ...................................................... 121

2. Penggunaan Integral Tak Tentu ............................................................................................................................... 127

B. Integral Tentu

1. Integral Tentu Fungsi Aljabar dan Trigonometri .............................................................................................. 128

2. Penggunaan Integral Tentu

a. Menentukan Luas Daerah ................................................................................................................................... 135

b. Menentukan Volume Benda Putar ................................................................................................................... 140

Arsip Soal UN Matematika IPA. Downloaded from http://pak-anang.blogspot.com Halaman iv

BAB 1=.BAB 1=.BAB 1=.BAB 1=. Program LinearProgram LinearProgram LinearProgram Linear

A. Persamaan Garis Lurus ........................................................................................................................................................ 14=

B. Himpunan Penyelesaian dari Pertidaksamaan Linear ........................................................................................... 14=

C. Fungsi Tujuan (Obyektif/Sasaran), Nilai Maksimum dan Nilai Minimum ..................................................... 147

BAB 17.BAB 17.BAB 17.BAB 17. MatriksMatriksMatriksMatriks

A. Transpose Matriks ................................................................................................................................................................. 154

B. Penjumlahan dan Pengurangan Matriks....................................................................................................................... 154

C. Perkalian Matriks dengan Bilangan Real B .................................................................................................................. 154

D. Perkalian Dua Buah Matriks .............................................................................................................................................. 154

E. Matriks Identitas .................................................................................................................................................................... 154

F. Determinan Matriks Berordo 2x2 ................................................................................................................................... 154

G. Invers Matriks .......................................................................................................................................................................... 155

H. Matriks Singular ...................................................................................................................................................................... 155

I. Persamaan Matriks ................................................................................................................................................................ 155

BAB 18.BAB 18.BAB 18.BAB 18. VektorVektorVektorVektor

A. Vektor Secara Geometri ....................................................................................................................................................... 1=1

B. Vektor Secara Aljabar ........................................................................................................................................................... 1=1

C. Perkalian Silang (DEF GHEIJKF) ....................................................................................................................................... 1=1

D. Proyeksi Vektor ....................................................................................................................................................................... 1=1

BAB 19.BAB 19.BAB 19.BAB 19. TransformasiTransformasiTransformasiTransformasi

A. Translasi (Pergeseran) ........................................................................................................................................................ 171

B. Refleksi (Pencerminan) ....................................................................................................................................................... 171

C. Rotasi (Perputaran) .............................................................................................................................................................. 171

D. Dilatasi (Perbesaran)............................................................................................................................................................ 172

E. Komposisi Transformasi ..................................................................................................................................................... 172

F. Luas Hasil Transformasi ...................................................................................................................................................... 172

BAB 20.BAB 20.BAB 20.BAB 20. Barisan dan DeretBarisan dan DeretBarisan dan DeretBarisan dan Deret

A. Barisan Aritmetika dan Geometri .................................................................................................................................... 178

B. Deret Aritmetika dan Geometri ........................................................................................................................................ 178

BAB 21.BAB 21.BAB 21.BAB 21. Fungsi Eksponen dan LogaritmaFungsi Eksponen dan LogaritmaFungsi Eksponen dan LogaritmaFungsi Eksponen dan Logaritma

A. Persamaan Eksponen ........................................................................................................................................................... 188

B. Pertidaksamaan Eksponen ................................................................................................................................................. 192

C. Persamaan Logaritma........................................................................................................................................................... 194

D. Pertidaksamaan Logaritma ................................................................................................................................................ 19=

Arsip Soal UN Matematika IPA. Downloaded from http://pak-anang.blogspot.com Halaman 1

1. PANGKAT, AKAR, DAN LOGARITMA

A. Pangkat Rasional

1) Pangkat negatif dan nol

Misalkan a ∈ R dan a ≠ 0, maka:

a) a-n

= na

1atau a

n =

na−

1

b) a0 = 1

2) Sifat-Sifat Pangkat

Jika a dan b bilangan real serta n, p, q bilangan bulat positif, maka berlaku:

a) ap × a

q = a

p+q

b) ap : a

q = a

p-q

c) ( )qpa = apq

d) ( )nba × = an×b

n

e) ( )n

n

b

an

b

a =

SOAL PENYELESAIAN

1. UN 2012/A13

Diketahui a = 4, b = 2, dan c = 2

1. Nilai

21)( −a x 3

4

−c

b = …..

A. 2

1 D.

16

1

B. 4

1 E.

32

1

C. 8

1 Jawab : C

2. UN 2012/C37

Diketahui ,2,2

1== ba dan c = 1 .Nilai dari

12

32 ..−

−

cab

cba adalah ….

A. 1

B. 4

C. 16

D. 64

E. 96

Jawab: B


SOAL PENYELESAIAN

3. UN 2012/B25

Nilai dari 22

132

bca

cba−

−

, untuk a = 2, b = 3

dan c = 5 adalah ...

A. 12581

B. 125144

C. 125432

D. 125

1296

E. 1252596

Jawab : B

4. UN 2012/E52

Jika di ketahui x = 31 , y =

51 dan z = 2 maka

nilai dari 423

24

−−

−−

zyx

yzx adalah…..

A. 32

B. 60

C. 100

D. 320

E. 640

Jawab : B

5. EBTANAS 2002

Diketahui a = 2 + 5 dan b = 2 – 5 .

Nilai dari a2 – b

2 = …

a. –3

b. –1

c. 2 5

d. 4 5

e. 8 5

Jawab : e

6. UN 2011 PAKET 12

Bentuk sederhana dari 417

643

84

7

−−−

−−

zyx

zyx = …

a. 3

1010

12y

zx d.

4

23

12x

zy

b. 34

2

12 yx

z e.

23

10

12 zy

x

c. 2

510

12z

yx Jawab : e


SOAL PENYELESAIAN

7. UN 2011 PAKET 46


27

6

24

−−−

−−

cba

cba = …

a. 53

54

ba

c d.

5

74

a

bc

b. 55

4

ca

b e.

ba

c

3

74

c. ca

b

3

4 Jawab : d

8. UN 2010 PAKET A

Bentuk sederhana dari

1

575

35

3

27−

−−

−−

��

�

�

��

�

�

ba

ba

adalah …

a. (3 ab)2

b. 3 (ab)2

c. 9 (ab)2

d. 2)(

3

ab

e. 2)(

9

ab

Jawab : e

9. UN 2010 PAKET B


423

)5(

)5(−−−

−

ba

ba

adalah …

a. 56 a

4 b

–18

b. 56 a

4 b

2

c. 52 a

4 b

2

d. 56 ab

–1

e. 56 a

9 b

–1

Jawab : a


B. Bentuk Akar

1) Definisi bentuk Akar

Jika a bilangan real serta m, n bilangan bulat positif, maka berlaku:

a) n aa n =1

b) n m

aa nm

=

2) Operasi Aljabar Bentuk Akar

Untuk setiap a, b, dan c bilangan positif, maka berlaku hubungan:

a) a � + b � = (a + b) �

b) a � – b � = (a – b) �

c) �� × = ��×

d) �� + = �� 2++

e) �� − = �� 2−+

3) Merasionalkan penyebut

Untuk setiap pecahan yang penyebutnya mengandung bilangan irrasional (bilangan yang tidak

dapat di akar), dapat dirasionalkan penyebutnya dengan kaidah-kaidah sebagai berikut:

a) b

ba

b

b

b

a

b

a =×=

b) ba

bac

ba

ba

ba

c

ba

c

−

−

−

−

++=×=

2

)(

c) ba

bac

ba

ba

ba

c

ba

c

−

−

−

−

++=×=

)(


SOAL PENYELESAIAN

1. UN 2012/A13


532

−

+

adalah…..

A. )10417(3

1−

B. )10415(3

2−−

C. )10415(3

2−

D. )10417(3

1−−

E. )10417(3

1+−

Jawab : E

2. UN 2012/C37

Bentuk 327

733

−

+ dapat disederhanakan

menjadi bentuk …

A. –25 – 5 21

B. –25 + 5 21

C. –5 + 5 21

D. –5 + 21

E. –5 – 21

Jawab : E

3. UN 2012/D49


322

−

−

adalah….

A.–4 – 3 6 D. 4 – 6

B. –4 – 6 E. 4 + 6

C. –4 + 6 Jawab : E

4. UN 2012/B25


25

+

−

A. )10411( +−−

B. )1041( +−−

C. )10411( −

D. )10411( +

E. )10411( +−

Jawab : C


SOAL PENYELESAIAN

5. UN 2011 PAKET 12


325

−

+ = …

a. 22

15520 + d.

22

15520

−

+

b. 22

15523 − e.

22

15523

−

+

c. 22

15520

−

− Jawab : e

6. UN 2011 PAKET 46


233

−

+ = …

a. )6313(23

1+−

b. )6313(23

1−−

c. )611(23

1−−−

d. )6311(23

1+

e. )6313(23

1+

Jawab : e

7. UN 2010 PAKET A


)53(

)32)(32(4

+

−+ = …

A. –(3 – 5 ) D. (3 – 5 )

B. –4

1(3 – 5 ) E. (3 + 5 )

C. 4

1 (3 – 5 ) Jawab : D

8. UN 2010 PAKET B


62

)53)(53(6

+

−+ =…

a. 24 + 12 6

b. –24 + 12 6

c. 24 – 12 6

d. –24 – 6

e. –24 – 12 6

Jawab : b

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Kumpulan Arsip Soal UN Matematika SMA Program IPA Tahun