LKPD Pertidaksamaan Rasional

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 berkaitan dengan 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. Bentuk Umum Umum dari persamaan kuadrat adalah ________________________ _________________________________ _________ 2. Relasi penghubung penghubung pada pertidaksamaan pertidaksamaan yaitu _______________________ _________________________________ __________

KEGIATAN INTI Permasalahan 1 Tentukan himpunan penyelesaian dari pertidaksamaan berikut !   + 3 < 10

Penyelesaian : a.

Pertidaksamaan diubah menjadi bentuk umum.  ______________________  _________________________________ ______________________ ______________________ ______________________ ___________________ ________ b. Ruas Kiri difaktorkan  ______________________  _________________________________ ______________________ ______________________ ______________________ ____________________ _________  ______________________  ___________________________________ ______________________ ______________________ ______________________ __________________ _________ c. Menentukan akar-akar atau pembuat nol ( mencari nilai x )  ______________________  _________________________________ ______________________ ______________________ ______________________ ____________________ _________  ______________________  _________________________________ ______________________ ______________________ __________________________ ____________________ _____  ______________________  _________________________________ ______________________ ______________________ ______________________ ____________________ _________ d. Selanjutnya membuat garis bilangan dan menentukan tanda ( +/- ) pada interval yang dibatasi akar-akar.  ______________________  _________________________________ ______________________ ______________________ __________________________ ____________________ _____  ______________________  _________________________________ ______________________ ______________________ ______________________ ____________________ _________  ______________________  _________________________________ ______________________ ______________________ ______________________ ____________________ _________  ______________________  _________________________________ ______________________ ______________________ ______________________ ____________________ _________  ______________________  ___________________________________ ______________________ ______________________ ______________________ __________________ _________  ______________________  _________________________________ ______________________ ______________________ ______________________ ____________________ _________  ______________________  _________________________________ ______________________ ______________________ ______________________ ____________________ _________  ______________________  _________________________________ ______________________ _________________________ _________________________ _________________ ______  ______________________  _________________________________ ______________________ ______________________ ______________________ ____________________ _________ e. Menentukan penyelesaian berdasarkan tanda

Oleh karena _____________ < __  bertanda _____________ _____________

maka selang yang yang memenuhi adalah selang yang

Jadi,  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________

Permasalahan 2 Tentukan nilai x yang memenuhi 2  + 3 ≤ 2 ! Penyelesaian : Lakukan langkah seperti penyelesaian permasalahan 1  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ _______________________ _____________________ _________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________

 _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ _______________________ _____________________ _________

Jadi, nilai x yang memenuhi adalah  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________

Permasalahan 3 Tentukan himpunan penyelesaian pertidaksamaan berikut : a.   > 5 − 6 !  b. 



≥ 5 − 6

Penyelesaian : Lakukan langkah seperti penyelesaian permasalahan 1  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ _______________________ _____________________ _________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________

 _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ _______________________ ______________________ _____________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________  _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________ __________

 _____________________  ________________________________ ______________________ ______________________ ______________________ _____________________  __________   ______________________  ________________________________ _____________________ ______________________ ______________________ _____________________ __________

Pertidaksamaan kuadrat adalah ............................................... .................................................................... ......................................... .................... .......................................... ................................................................ ............................................ ........................................... ........................................... ...................................... ................ .......................................... ................................................................ ............................................ ........................................... ........................................... ...................................... ................ .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... Ada beberapa bentuk umum pertidaksamaan kuadrat yaitu .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... .......................................... ............................................................... ............................................ ............................................. ........................................... ..................................... ................ .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... .......................................... ................................................................ ............................................ ........................................... ........................................... ...................................... ................ Langkah-langkah penyelesaian Pertidaksamaan Kuadrat yaitu .......................................... ............................................................... ........................................... ............................................. ............................................ ..................................... ................ .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... .......................................... ................................................................ ............................................ ........................................... ........................................... ...................................... ................ .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... .......................................... ............................................................... ........................................... ........................................... ........................................... ....................................... ................. .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ............... .......................................... ............................................................... ........................................... ............................................ ............................................. ...................................... ...............