Buku Mahir Matematika Kelas 11 SMK

Materi Mahir Matematika

Kata Sambutan................................................................................................................................... iii
Kata Pengantar................................................................................................................................... iv
Daftar Isi ............................................................................................................................................. v

Bab 1 Logika Matematika
1.1 Mendeskripsikan Pernyataan dan Bukan Pernyataan (Kalimat Terbuka)...................................... 2
1.1.1 Pernyataan........................................................................................................................ 2
1.1.2Kalimat terbuka................................................................................................................. 3
1.1.3Kalimat tertutup ................................................................................................................3
1.2 Mendeskripsikan Ingkaran, Konjungsi, Disjungsi, Implikasi, Biimplikasi dan Ingkarannya ........... 5
1.2.1 Pernyataan majemuk........................................................................................................ 5
1.2.2Ingkaran atau negasi......................................................................................................... 5
1.2.3 Konjungsi .......................................................................................................................... 7
1.2.4 Disjungsi........................................................................................................................... 9
1.2.5Implikasi ........................................................................................................................... 11
1.2.6Biimplikasi ........................................................................................................................ 13
1.3 Mendeskripsikan Konvers, Invers, dan Kontraposisi................................................................... 15
1.4 Menerapkan Modus Ponens, Modus Tollens, dan Prinsip Silogisme dalam Menarik Kesimpulan . 16
1.4.1 Modus ponens.................................................................................................................. 17
1.4.2Modus tollens...................................................................................................................17
1.4.3 Silogisme .......................................................................................................................... 17
Rangkuman......................................................................................................................................... 19
Evaluasi.............................................................................................................................................. 20

Bab 2 Fungsi
2.1 Mendeskripsikan Perbedaan Konsep Relasi dan Fungsi.............................................................. 24
2.1.1 Relasi...............................................................................................................................24
2.1.2 Fungsi atau pemetaan...................................................................................................... 24
2.1.3Sifat-sifat fungsi............................................................................................................... 25
2.2 Menerapkan Konsep Fungsi Linear............................................................................................. 28
2.2.1Bentuk umum fungsi linear ............................................................................................... 28
2.2.2Menggambar grafik fungsi linear....................................................................................... 29
2.2.3 Persamaan garis lurus yang melalui sebuah titik dengan gradien diketahui....................... 31
2.2.4 Persamaan sebuah garis lurus yang melalui dua buah titik ............................................... 31
2.2.5Dua buah garis saling sejajar............................................................................................ 32
2.2.6Dua buah garis saling tegak lurus ..................................................................................... 33
2.2.7Menentukan koordinat titik potong dua buah garis lurus.................................................... 34
2.2.8 Jarak (materi pengayaan).................................................................................................. 34
2.3 Menggambarkan Fungsi Kuadrat................................................................................................. 38
2.3.1Bentuk umum fungsi kuadrat ............................................................................................ 38
2.3.2Menentukan titik potong grafik sumbu koordinat............................................................... 38
2.3.3Menentukan nilai ekstrim, sumbu simetri, dan titik puncak (titik balik) .............................. 39
2.3.4Menggambar grafik fungsi kuadrat.................................................................................... 40
2.3.5 Menentukan fungsi kuadrat............................................................................................... 41
2.4 Menerapkan Konsep Fungsi........................................................................................................ 44
2.4.1 Fungsi permintaan (demand) ............................................................................................. 44
2.4.2 Fungsi penawaran (supply) ................................................................................................ 46
2.4.3Titik keseimbangan pasar................................................................................................. 48
2.4.4 Pengaruh perpajakan dalam fungsi permintaan dan fungsi penawaran............................... 49
2.4.5 Pengaruh subsidi dalam fungsi permintaan dan fungsi penawaran.................................... 51
2.4.6 Model biaya linear (Pengayaan)........................................................................................ 52
2.4.7Titik pulang pokok .............................................................................................................53
Rangkuman................................................................................................................................ 55
Evaluasi.............................................................................................................................................. 56

Bab 3 Barisan dan Deret
3.1 Mengidentifikasi Pola, Barisan, dan Deret Bilangan..................................................................... 60
3.1.1 Pola bilangan, barisan, dan deret...................................................................................... 60
3.1.2Notasi Sigma (Pengayaan).......................................................................................... 61
3.2 Menerapkan Konsep Barisan dan Deret Aritmetika...................................................................... 63
3.2.1Barisan aritmetika............................................................................................................. 63
3.2.2 Deret aritmetika................................................................................................................ 64
3.3 Menerapkan Konsep Barisan dan Deret Geometri....................................................................... 66
3.3.1 Barisan geometri............................................................................................................... 66
3.3.2 Deret geometri.................................................................................................................. 67
3.3.3 Deret geometri takhingga.................................................................................................. 68
Rangkuman................................................................................................................................ 70
Evaluasi.............................................................................................................................................. 71

Bab 4 Geometri Dimensi Dua
4.1 Mengidentifikasi Sudut................................................................................................................ 74
4.1.1 Unsur-unsur dalam bangun datar....................................................................................... 74
4.1.2 Pengukuran sudut............................................................................................................. 74
4.2 Menentukan Keliling Bangun Datar dan Luas Daerah Bangun Datar............................................ 76
4.2.1Jenis-jenis bangun dimensi dua........................................................................................ 76
4.2.2Luas bangun datar dengan sistem koordinat..................................................................... 83
4.2.3Rumus-rumus keliling dan luas bangun dimensi dua......................................................... 84
4.3 Menerapkan Transformasi Bangun Datar..................................................................................... 87
4.3.1 Refleksi (pencerminan)..................................................................................................... 87
4.3.2 Translasi (pergeseran)....................................................................................................... 91
4.3.3 Rotasi (perputaran)........................................................................................................... 92
4.3.4 Dilatasi............................................................................................................................. 93
Rangkuman................................................................................................................................ 96
Evaluasi.............................................................................................................................................. 98
Soal Akhir Buku .................................................................................................................................. 103

Daftar Pustaka.................................................................................................................................... 107
Glosarium................................................................................................................................... 108
Indeks........................................................................................................................................ 111