Buku Matematika Untuk SMA/MA Jilid 3 (Prodi IPA) Kelas 12 SMA

Materi Matematika Untuk SMA/MA Jilid 3 (Prodi IPA)

Kata Sambutan ...................................................................................................................... iii
Kata Pengantar ...................................................................................................................... iv
Apakah Keunggulan Buku Ini? ............................................................................................... v
Daftar Simbol ......................................................................................................................... ix

BAB 1 INTEGRAL ................................................................................................ 1
A. Pengertian Integral .................................................................................... 2
B. Integral Tak Tentu ...................................................................................... 4
C. Integral Tertentu ......................................................................................... 13
D. Menentukan Luas Daerah ......................................................................... 21
E. Menentukan Volume Benda Putar ............................................................ 26
Rangkuman ........................................................................................................ 31
Ulangan Bab 1 .................................................................................................. 33

BAB 2 PROGRAM LINEAR ................................................................................. 35
A. Sistem Pertidaksamaan Linear Dua Variabel .......................................... 36
B. Model Matematika...................................................................................... 39
C. Nilai Optimum Suatu Fungsi Objektif ....................................................... 41
Rangkuman ........................................................................................................ 47
Ulangan Bab 2 .................................................................................................. 48

BAB 3 MATRIKS .................................................................................................. 51
A. Pengertian Matriks ..................................................................................... 52
B. Operasi Hitung pada Matriks .................................................................... 57
C. Determinan dan Invers Matriks ................................................................. 69
D. Penerapan Matriks dalam Sistem Persamaan Linear ............................. 76
Rangkuman ........................................................................................................ 79
Ulangan Bab 3 .................................................................................................. 80

BAB 4 VEKTOR ................................................................................................... 83
A. Pengertian Vektor ...................................................................................... 84
B. Operasi pada Vektor ................................................................................. 89
viiiviii Matematika Aplikasi SMA dan MA Kelas XII Program Studi Ilmu Alam
C. Perbandingan Vektor ................................................................................. 98
D. Perkalian Skalar Dua Vektor dan Proyeksi Vektor ................................... 100
Rangkuman ........................................................................................................ 104
Ulangan Bab 4 .................................................................................................. 107

BAB 5 BARISAN, DERET, DAN NOTASI SIGMA .............................................. 109
A. Barisan dan Deret Aritmetika ................................................................... 110
B. Barisan dan Deret Geometri .................................................................... 114
C. Notasi Sigma dan Induksi Matematika ..................................................... 120
D Aplikasi Barisan dan Deret ....................................................................... 124
Rangkuman ........................................................................................................ 127
Ulangan Bab 5 .................................................................................................. 129

BAB 6 TRANSFORMASI GEOMETRI................................................................ 131
A. Translasi .................................................................................................... 132
B. Refleksi ...................................................................................................... 138
C. Rotasi ........................................................................................................ 146
D. Dilatasi ....................................................................................................... 151
E. Komposisi Transformasi dengan Matriks ................................................. 153
Rangkuman ........................................................................................................ 156
Ulangan Bab 6 .................................................................................................. 158

BAB 7
FUNGSI, PERSAMAAN, DAN PERTIDAKSAMAAN EKSPONEN DAN
LOGARITMA ............................................................................................. 161
A. Grafik Fungsi Eksponen dan Fungsi Logaritma ...................................... 162
B. Persamaan dan Pertidaksamaan Eksponen ............................................ 165
C. Persamaan dan Pertidaksamaan Logaritma ............................................ 173
Rangkuman ........................................................................................................ 179
Ulangan Bab 7 .................................................................................................. 181
Tugas Akhir ....................................................................................................... 184

Glosarium........................................................................................................... 187
Pustaka Acuan ................................................................................................... 190
Kunci Jawaban .................................................................................................. 191
Indeks ................................................................................................................. 193