LKPD Pertidaksamaan irasional satu variabel

LEMBAR KERJA PESERTA DIDIK

Mata pelajaran

: Matematika

Kelas/semester Kelas/semester

: .............../ 1

Materi Pokok

: Pertidaksamaan Pertidaksamaan Rasional & Irasional Satu Variabel

Alokasi Waktu

: 30 menit

Kelompok : _________  Nama : 1. 2. 3. 4.

 ______________________  _________________________ ___  ______________________  _________________________ ___  ______________________  _________________________ ___  ______________________  _________________________ ___

:

Kompetensi Kompetensi Dasar 3.2 Menjelaskan dan menentukan penyelesaian pertidaksamaan rasional dan irasional satu variabel. 4.2 Menyelesaikan masalah yang yang berkaitan berkaitan dengan pertidaksamaan rasional dan irasional satu variabel. Indikator 4.2.1 Mengidentifikasi bentuk rasional dan irasironal pada penyelesaian pertidaksamaan rasional dan irasional satu variabel. 3.2.2 Menyelesaikan masalah konsep pertidaksamaan rasional dan irasional satu variabel. 4.2.1 Menyelesaikan masalah kontekstual berkaitan dengan pertidaksamaan rasional dan irasional satu variabel.

Petunjuk : 1. Berdoalah sebelum mengerjakan. 2. Bacalah setiap petunjuk dengan seksama. 3. Diskusikan dengan kelompok pertanyaan yang ada kemudian jawablah pertanyaan tersebut. 4. Tanyakan kepada guru, jika ada ada yang kurang kurang jelas.

1. Sebutkan Sebutkan bentuk bentuk Umum Umum dari pertidaksam pertidaksamaan aan kuadrat kuadrat ! ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... .........................................................................................................................................

KEGIATAN INTI Permasalahan 1 −

Tentukan himpunan penyelesaian dari pertidaksamaan

+3

≥2 !

Penyelesaian : a.

Pertidaksamaan diubah menjadi bentuk umum ( membuat ruas kanan m enjadi nol)

 … ≥ 0 

≥ 0 ≥ 0 ≥ 0

b.

c.

Menentukan syarat agar terdefinisi yaitu penyebut tidak sama dengan 0. ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... Menentukan nilai-nilai yang membuat pembilang bernilai nol dan penyebut bernilai nol

Pembuat nol dari pembilang adalah ................ = 0  = ..... Pembuat nol dari penyebut adalah ................ = 0  = ..... d. Meletakkan nilai-nilai yang pembuat nol pada garis bilangan dan menentukan tanda ( +/- ) pada selang/interval yang terbentuk.

.....

.....

..... .....

.....

Garis bilangan di atas terdiri atas 3 selang . Tentukan satu bilangan pada tiap-tiap selang, lalu substitusikan ke dalam pertidaksamaan. 1) Untuk selang  < ...... Misalkan diambil  = .... ,lalu substitusikan ke pertidaksamaan rasional diperoleh ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... Sehingga selang bertanda .........

2) Untutk selang ..... <  < ..... Misalkan diambil  = .... ,lalu substitusikan ke pertidaksamaan rasional diperoleh ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... Sehingga selang bertanda ......... 3) Untuk selang  > ....... Misalkan diambil  = .... ,lalu substitusikan ke pertidaksamaan rasional diperoleh ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... Sehingga selang bertanda .........

e. Menentukan penyelesaian berdasarkan tanda

Oleh karena ____________ ≥ __  bertanda _____________

maka selang yang memenuhi adalah selang yang

Jadi,_______________________________________________________________________   ___________________________________________________________________________

Setelah bisa mengerjakan permasalahan 1, lanjutkan mengerjakan permasalahan 2

Permasalahan 2 −8

Tentukan nilai x yang memenuhi

−

≤1

Penyelesaian : Lakukan langkah seperti penyelesaian permasalahan 1  ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________   ___________________________________________________________________________

 ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________   ___________________________________________________________________________   __________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________  ___________________________________________________________________________   ___________________________________________________________________________

Pertidaksamaan rasional adalah ........................................................................................ ................................................................................................................................................... ............................................................................................................................................... ................................................................................................................................................. Ada beberapa bentuk umum pertidaksamaan rasional yaitu ................................................................................................................................................... ............................................................................................................................................... ................................................................................................................................................. ................................................................................................................................................... ............................................................................................................................................... ................................................................................................................................................. Langkah-langkah penyelesaian Pertidaksamaan Rasional yaitu ................................................................................................................................................... ............................................................................................................................................... ................................................................................................................................................. ................................................................................................................................................... ............................................................................................................................................... ................................................................................................................................................. ................................................................................................................................................... ............................................................................................................................................... .................................................................................................................................................