Buku Wahana Matematika (IPA) Kelas 11 SMA

Materi Wahana Matematika (IPA)

Kata Sambutan ............................................................................................................................................. iii
Kata Pengantar ............................................................................................................................................. iv
Petunjuk Penggunaan Buku ....................................................................................................................... v
Daftar Simbol dan Notasi ............................................................................................................................ vii
Daftar Isi ........................................................................................................................................................ viii

BAB I STATISTIKA ............................................................................................................................. 1
1.1 Populasi, Sampel dan Data Statistika ............................................................................ 3
1.2 Menyajikan Data dalam Bentuk Tabel dan Diagram .................................................. 4
1.3 Menyajikan Data dalam Tabel Distribusi Frekuensi ................................................... 12
1.4 Ukuran Pemusatan (Tendensi Sentral) .......................................................................... 22
1.5 Ukuran Letak ....................................................................................................................... 32
1.6 Ukuran Penyebaran (Dispersi) ........................................................................................ 39
Rangkuman ................................................................................................................................. 47
Uji Kompetensi ........................................................................................................................... 49
Aktivitas Proyek ......................................................................................................................... 54

BAB II PELUANG .................................................................................................................................. 55
2.1 Aturan Pencacahan ........................................................................................................... 57
2.2 Ruang Sampel dan Kejadian ........................................................................................... 72
2.3 Peluang suatu Kejadian .................................................................................................... 75
2.4 Peluang Kejadian Majemuk ............................................................................................. 82
2.5 Peluang Kejadian Bersyarat ............................................................................................ 89
Rangkuman ................................................................................................................................ 94
Uji Kompetensi .......................................................................................................................... 96
Aktivitas Proyek ........................................................................................................................ 100

BAB III RUMUS-RUMUS TRIGONOMETRI .................................................................................... 101
3.1 Rumus Trigonometri untuk Jumlah dan Selisih Dua Sudut ....................................... 103
3.2 Rumus Trigonometri Sudut Ganda ................................................................................ 107
3.3 Rumus Perkalian Sinus dan Kosinus ............................................................................. 112
3.4 Rumus Trigonometri Jumlah dan Selisih Dua Sudut .................................................. 115
Rangkuman ................................................................................................................................ 119
Uji Kompetensi .......................................................................................................................... 120
Aktivitas Proyek ........................................................................................................................ 126

BAB IV LINGKARAN ........................................................................................................................... 127
4.1 Persamaan Lingkaran dengan Pusat O ........................................................................ 129
4.2 Persamaan Lingkaran dengan Pusat (a, b) ................................................................... 131
4.3 Persamaan Umum Lingkaran ......................................................................................... 133
4.4 Perpotongan Garis dan Lingkaran ................................................................................. 135
4.5 Garis Singung Lingkaran .................................................................................................. 137
Rangkuman ............................................................................................................................... 144
Uji Kompetensi .......................................................................................................................... 145
Aktivitas Proyek ......................................................................................................................... 151
LATIHAN ULANGAN UMUM SEMESTER 1 ....................................................................................... 153

BAB VSUKUBANYAK .......................................................................................................................... 161
5.1 Menghitung Nilai Suatu Sukubanyak ............................................................................ 163
5.2 Pembagian Sukubanyak ................................................................................................... 165
5.3 Teorema Sisa ...................................................................................................................... 168
5.4 Teorema Faktor .................................................................................................................. 172
5.5 Persamaan Sukubanyak .................................................................................................. 173
Rangkuman ................................................................................................................................ 176
Uji Kompetensi .......................................................................................................................... 178
Aktivitas Proyek ........................................................................................................................ 182

BAB VI KOMPOSISI FUNGSI DAN INVERS FUNGSI .................................................................. 183
6.1 Produk Cartesius dan Relasi ........................................................................................... 185
6.2 Fungsi atau Pemetaan ...................................................................................................... 188
6.3 Beberapa Fungsi Khusus ................................................................................................. 193
6.4 Sifat-sifat Fungsi ................................................................................................................ 200
6.5 Aljabar Fungsi .................................................................................................................... 204
6.6 Komposisi Fungsi ............................................................................................................... 206
6.7 Invers Fungsi ...................................................................................................................... 212
6.8 Fungsi Invers dari Fungsi Komposisi ............................................................................ 217
Rangkuman ................................................................................................................................ 221
Uji Kompetensi .......................................................................................................................... 222
Aktivitas Proyek ........................................................................................................................ 226

BAB VII LIMIT FUNGSI ......................................................................................................................... 227
7.1 Pengertian Limit ................................................................................................................ 229
7.2 Teorema Limit .................................................................................................................... 237
7.3 Laju Perubahan (Pengayaan) .......................................................................................... 242
7.4 Kekontinuan (Pengayaan) ................................................................................................ 244
7.5 Limit Tak Hingga (Pengayaan) ........................................................................................ 247
7.6 Limit di Tak Hingga ............................................................................................................ 250
7.7 Limit Fungsi Trigonometri ................................................................................................ 254
Rangkuman ................................................................................................................................ 259
Uji Kompetensi ........................................................................................................................... 261
Aktivitas Proyek ......................................................................................................................... 264

BAB VIII TURUNAN ................................................................................................................................. 265
8.1 Turunan Fungsi ................................................................................................................... 267
8.2 Teorema Turunan Fungsi Aljabar ................................................................................... 272
8.3 Turunan Fungsi Trigonometri .......................................................................................... 281
8.4 Persamaan Garis Singgung Kurva ................................................................................. 284
8.5 Kecepatan dan Percepatan ............................................................................................. 288
8.6 Aturan L’Hopital ................................................................................................................. 294
Rangkuman ................................................................................................................................ 297
Uji Kompetensi .......................................................................................................................... 299
Aktivitas Proyek ........................................................................................................................ 304

BAB IX NILAI EKSTRIM FUNGSI DAN TEKNIK MEMBUAT GRAFIK FUNGSI .................. 305
9.1 Fungsi Naik dan Fungsi Turun ......................................................................................... 307
9.2 Nilai Ekstrim ........................................................................................................................ 310
9.3 Ekstrim Mutlak pada Interval Tertutup ......................................................................... 318
9.4 Menggambar Grafik Fungsi Aljabar .............................................................................. 322
9.5 Masalah Pengoptimuman ................................................................................................ 325
Rangkuman ................................................................................................................................ 331
Uji Kompetensi .......................................................................................................................... 332
Aktivitas Proyek ........................................................................................................................ 336
LATIHAN ULANGAN UMUM SEMESTER 2 ........................................................................................ 338

Daftar Pustaka ............................................................................................................................................... 345
Glosarium ....................................................................................................................................................... 346
Indeks .............................................................................................................................................................. 349
Kunci ................................................................................................................................................................ 351