FUNCTIONAL SKILL

FUNCTIONAL SKILL

1. Offering Help or Things (menawarkan bantuan / menawarkan sesuatu)

Untuk menawarkan bantuan, dapat digunakan ungkapan-ungkapan berikut:

- May I help you? - Can I help you? - Could I help you? - How can I be of assistance to you? - How can I be of help to you? - What can I help you

- What can I do for you? - How can I assist you? - How can I help you? - Let me help you? - Do you want me to help you? - Shall I …?

Cara memberi tawaran seperti menawarkan makanan atau minuman dalam bahasa Inggris lazimnya dengan menggunakan ungkapan Would you like…?, Would you care for …?, why don’t you have…?, How about having …? May I offer you …?

Contoh:

Tawaran Respon

- Would you like some bread? Yes, please.

- Would you care for some coffee? No, thanks. I don’t drink coffee.

- Why don’t you have some biscuit, please? Thanks, I’d love to.

Jawaban untuk menerima tawaran antara lain: Yes please, Sure, Why not, Ofcourse, Certainly, I’d love to, It’s a good idea, That’s great. Untuk menolak tawaran digunakan ungkapan seperti: No, thanks, Please don’t bother, I’d love to but…, That’s great but…

1. 2. Introducing (memperkenalkan)

Memperkenalkan Dri	Memperkenalkan Orang Lain
- I’d like to introduce myself. - My I introduce myself? - Let me introduce myself! - I want to introduce myself	- I’d like you to meet … (nama) - This is my friend/boss/etc…(nama) - Have you met…(nama)? - May I introduce you to …(nama/jabatan) - Let me introduce you to …. - I want to introduce you to ….

1. Inviting (mengundang/mengajak)

Undangan/Ajakan	Menolak	Menerima
- let’s + V1 - Why don’t we …? - How about…? - I’d like to invite you to… - Would you like to…? - I wonder if you’d like to	- I’m sorry I can’t - I’d like to but… - I’m afraid I can’t - No, let’s not.	- I’d love to - I’d like very much - I’d be happy/glad to accept - Yes, I’d be delighted to. - That’s good ide

1. Expressing Thanks (terimakasih)

Ungkapan	Respon
Thank you Thank you very much Thanks. Thank you very much for… (kata benda) I’m grateful for…(kata benda/noun)	You are welcome. That’s all right Not at all Don’t mention it Thet’s all right Any time

1. Congratulations (ucapan selamat)

Ungkapan	Respon
Congratulations Congratulations on … I’d like to congratulate you. I’d like to congratulate you on… It was great to hear… It was to hear about…. Happy birthday to you. Happy new year. Good luck! Have a nice holiday	Thank you Thank you and the same to you Thank you. I need it. Thank you very much.

1. Sympathy (menyatakan rasa simpati)

Ungkapan-ungkapan perasaan simpati atas mala petaka/musibah yang dialami orang lain diantaranya:

• I’m sorry to hear that
• Oh, that’s too bad.
• How awful!
• How terrible!
• Poor!

1. Pleasure, Displeasure (senang & tidak senang)

Pleasure/senang	Displeasure/tidak senang
It’s really delightful/Iam delighted I’m satisfied That’s great That’s wonderful It’s really a great pleasure	I’m dissatisfied We are fed up with… I feel dosappointed She is extremely displeased

1. Satisfaction, Dissatisfaction ( kepuasan, ketidakpuasan)

Ketika kita akan mengungkapkan kepuasan atas kerja seseorang, kita dapat gunakan ungkapan:

• Well done!
• Great! Good work
• I am satisfied with your work
• You did well
• Your job is satisfactory
• I am so happy about this
• I’m glad to what you’ve done
• It’s really satisfying

Katika kita akan mengungkapkan ketidakpuasan atas kerja seseorang, kita dapat gunakan:

• I’m not satisfied with work
• You haven’t done well enough
• I am really dissappointed
• Sorry, but your work is not satisfactory
• Oh, no!
• It’s not very nice
• It’s really not good enough

1. Asking & Giving Opinion (meminta & memberi pendapat)

Asking Opinion	Giving opinion
How was the trip? How do you like your new house? How do you think of Rina’s idea? How do you feel about this dicition? What is your opinions of the movie? What are your feelings about it?	I think (that)…. In my opinion…. As I see, … If you ask me, I feel…

10. Agreement/approval, Disagreement/disapproval (setuju, tidak setuju)

Ketika kita merasa sependapat dengan opini orang lain, kita bisa mengatakan:

• So do I
• Yes, I agree with you
• It is certainly
• Exactly
• That’s what I want to say
• I am with you
• I am on your side

Ketika kita merasa tidak sependapat dengan opini orang lain, kita bisa mengatakan:

• Well, I don’t think so
• I don’t think that is true
• I disagree with …
• I wouldn’t say that
• Exactly not
• I can’t say so
• On contrary
• I don’t buy that idea

11. Fear, Anciety (ungkapan ketakutan, kegelisahan)

Fear	Respon
I am afraid I am feared I am scared I am terrified The sound is horrifying	Don’t be afraid There is nothing to be afraid of It is nothing
Anciety	Respon
I am worried about… I am anxious to know about… I wondered if… That made me worried I have been thinking about …. I am afraid if…	Take is easy Calm down I know you are worried but… It is not a big deal Don’t worry Stay cool

12. Pain, Relief (ungkapan kesakitan, kelegaan)

Pain	Relief
Ouch! That was hurt It is painful It hurts me I’ve got a backache/toothache/stomachache I feel sore all over My eyes hurt	I’m very relieved to hear… Finally, it was over I feel relieved I feel much better I’m glad it’s over That’s a great relief I’m extremely glad to hear… Thank goodness for that Marvellous What a relief!

13. Like/Love & Dislike/Hate (suka/cinta & tidak suka/benci)

Like	Dislike
I love it I like it I am keen on it I am crazy about it We all enjoy (benda/noun/gerund)…is my cup of tea	I don’t really like it I dislike it I am not really interested in… I can’t enjoy… (benda/noun/gerund)…is not my cup of tea I can’t stand I hate it

14. Embarrassment & Annoyance (Ungkapan rasa malu, kejengkelan)

Embarrassment	Annoyance
I am embarrassed I feel ashamed Oh my God Shame on me I don’t feel comfortable I feel awkward	I am annoyed I had enough with it I can’t bear it any longer You made me annoyed You are such a pain in the neck You made me sick

15. Request (permintaan)

Request	Acceptance	Refusal
Would it be possible for you to Would you be so kind as to Would you…,please? Would you mind …? Any chance of… Can you…?	I should be delighted to come By all means I have no objection I’d be happy to Sure Yeah OK No problem Mmm	I regret to say that we find ourselves unable to go I’m afraid it’s not possible I’m afraid not Sorry No, I won’t Not likely You must be joking

16. Complaint, Blame (keluhan,menyalahkan)

Complaint	Blame
I’m not at all satisfied with the service I really do/must objec to the service I take great exception to… I want to complain about… This is crazy!	You’re the one to blame It’s your fault! It’s your mistake! You’re wrong

17. Regret, Apology (penyesalan, meminta maaf)

Regret	Apology
Much to my regret Sadly, I …. Unfortunately I’m terribly sorry I honestly regret that I … Sorry, I …	Please accept my apologies for what I did Please forgive me for what I did I am extremely sorry I really must apologies May I offer you my sincerest apologies?

18. Possibility & Impossibility (kemungkinan & ketidakmungkinan)

Menyatakan Kemungkinan	Menanyakan Kemungkinan
I think there is possibility to … I sassume/believe… In all probability,… it is going to be possible for me to… that will probably … it’s quite possible …	Do you think he/it could…? Would you say we’re capable of…? Are you capable of…? Are you able to…? Do you have any experience of…? Can you…? Do you know how to…? Do you think you can…?

The Kind of Text in English Reading

No.	Jenis Teks	Contoh Teks
1.	Procedure	How to make Lemonade Ingredients: For each glass use: - 2 tablespoons of lemon juice. - 2 tablespoons of sugar. - 1 glass of water. Methods: 1. Slice a lemon in half and squeeze the juice into a cup. 2. Take out the seeds. 3. Pour two tablespoons of juice into glass. 4. Add sugar. 5. Add water and stir well. 6. Taste the lemonade. You may want to add more sugar or more lemon to make it taste just right. 7. Put it in ice cubes. A drop of red food coloring will make pink lemonade. A CONE-SHAPED BASKET Materials: - Heavy paper - Ribbon or string - A plate - A pencil - Paste Method: 1. Use a half circle of paper to make the cone basket. 2. Draw a whole circle on paper using a plate as the pattern to make a half circle. 3. Cut out the circle and fold it in half. 4. Cut the two halves apart along the fold. 5. Twist the half circle into a cone shape and it in place. 6. Use a ribbon or a string for the handle. Paste the ends of the ribbon in place. 7. Decorate your cone basket. How to make Popcorn crunch Materials: - 1,5 cups of sugar wheat cereal - 1 cup of golden syrup flaked almond - 0,5 cup of butter - 8 cup of popcorn already pop - 2 cups of puffed - 1 cup of toasted - 1 teaspoon of vanilla - 0,75 teaspoon of cinnamon Time: 10 minutes How to make it: Place sugar and golden syrup in a heatproof dish, stir and cook until sugar is dissolved (approximately four minutes on high). Add butter and cook for six minutes. While this is cooking, place popcorn, puff wheat cereal, and almonds into a separate bowl. Add cinnamon and vanilla to golden syrup mixture, combine syrup with popcorn, cereal and almonds and spread over a lighty greased 25 cetimeters x 30 centimeters baking tray. Allow to cool and then cut into pieces. Store in an airtight container. HOW TO MAKE PEANUT CRUNCH What you’ll need : v 1 cup of peanuts v 3 cups of brown sugar v 2 tablespoons of vinegar v 1 cup of water What to do : Place the sugar, water and vinegar into a large saucepan. Stir slowly over a low heat until the sugar is disolved Add peanuts , increase the heat and allow to boil Remove from the heat when the nuts have craked and the mixture appears golden brown Allow bubbles to settle Spoon into small paper patty cases or pour the mixture into a flat greased pan and mark into bite-size pieces.
2.	Recount	CLASS PICNIC Last Friday our school went to Centennial Park for a picnic First our teachers marked the rolls and the we got on the buses. On the buses, everyone was chatting and eating. When we arrived at the park, some students played cricket, some played cards but others went for a walk with the teachers. At lunchtime, we sat together and had our picnic. Finally, at two o’clock we left for school. We had a great day.
3.	Descriptive	‘ISSIS’ Cafe. ‘ISSIS’ is Javanese word meaning ‘cool’. So, besides the food, ISSIS Café offers a spacious, fully air-conditioned, cozy place. Located at Jl. Cilacap No. 8, Jakarta Pusat, ISSIS Café is famous for its European food, especially steak, barbecue ribs, salad, and soup. You might find this kind of food anywhere else, but there is no other place that offers great meals at better prices than ISSIS Café. You can enjoy a delicious imported sirloin steak for only Rp. 25,000 and ice cappuccino for only Rp. 5,500. There is also a salad bar with eight different vegetables. You can make your own salad which you can eat as much as you like, for only Rp. 12,000. The customers are mostly college students, office workers, and families.
4.	News Item	Undersea earthquake strikes off Maluku JAKARTA (AP): A strong earthquake struck in eastern Indonesian waters on Tuesday, a meteorological agency said. A local official said there was no threat of a destructive tsunami, and no damage or causalities were immediately reported. The quake, which had a preliminary magnitude of 6.1, was centered beneath the Banda Sea around 188 kilometers (117 miles) southwest of Ambon, the capital of Maluku province, the U.S. Geological Survey said on its Web site. The tremor was not felt by residents in the region and there were no reports of damage or casualties, said Aprilianto, an official at a Jakarta-based local Meteorological and Geophysics Agency.
5.	Report	Australia Australia is a large continent. It has six states and two territories. The capital city of Australia is Canberra. It is in the Australian Capital Territory. The population of Australia is about 20 million. The first inhabitants to live in Australia were Aboriginal people. After that people came from all over the world. The main language is English, however many other languages are spoken. There are many plants and animals that are only found in Australia, e.g. kangaroos, platypuses, gum trees and Waratahs. The main products and industries are wool, minerals, oil, coal, cereals and meat. Some famous landmarks are the Harbour Bridge, the Opera House and Uluru (Ayers Rock). 2. Drugs Drugs are chemical substances. There are three different types of drugs: stimulants, depressants and hallucinogens. Stimulants speed up the central nervous system. They increase heart rate, blood pressure and breathing. Examples are caffeine, nicotine, amphetamines, ecstasy and cocaine. Depressants slow down the central nervous system. They decrease heart and breathing rates. Alcohol, heroin and analgesics are common examples of these types of drugs. Hallucinogens change mood, thought and senses. LSD is the most well-known example of this type of drug. 3. A traditional market A traditional market is the type of market where people can bargain the prices. The items sold in traditional market are basically the same. They are fruits, vegetables, meat and fish, spices, dry good and household items. At the glances, the market may seem to be disorganized mess. Surrounding the market there are many small scale traders, usually selling fruits. This traders can not afford the cost of renting a stall inside the market. On the first floor of the market, there are permanent kiosks and stall selling textile, stationery, clothing, electronic goods, household appliances, gold shops, etc. On the second floor, people can buy meat and fish, fruits, vegetables, and dry goods. The sellers sell fruits and vegetables through the middle area. Meanwhile they sell dry goods in the edge area of the second floor
6.	Hortatory Exposition	Good morning, ladies and gentlemen Thank you very much for the House of Representatives which had invited me to give the speech concerning about the mystery sinetrons shown in many television presently. My name is Budi Santoso, a lecturer at University of Indonesia majoring in mass communication. Here, I represent the academics point of view about the subject we discuss this morning. As we know, there are many mystery sinetrons shown on Television stations presently. The sinetrons depict horrible scenes about the spirit world. It is described that spirits often disturb people by frightening them in the darkness, when they walk alone at night or at the cemetery. The spirits are pictured as frightening appearance such as white clothes flying corpse, shattered face copse etc. the show must be abandoned for several reasons. Firstly, it make a wrong perception of people especially children and women to do activity at nights, for example going to the wells, even cooking at kitchen alone. How do you fell if you always live in anxiety. Thirdly, such kind of sinetrons waste out time to think unreal phenomena while we are facing many kinds of living problems. In brief, for the reason, I think television station must stop showing mystery sinetrons. They are bad influences for people, frightening our children and destroying their belief to god. Thank you very much for your attention.
7.	Analytical Exposition	SHOULD CHILDREN WEAR HATS AT SCHOOL? (Statement of position): I believe that you should always wear a hat at school when you are playing outside , to stop you from getting sunburn. (Argument 1): Firstly, if you don’t wear a hat, you will get sunburn ant the sunburn is painful. (Argument 2): Secondly, sunburn could lead to skin cancer. Sunburn can lead to health problems later in life. Many older people suffer from skin cancer which can kill them. (Reinforcement of position statement): In my opinion all school students should wear hats.
8.	Spoof	One day, two villagers went to Jakarta. They went to the biggest mall and saw shiny silver walls that could open and move apart and back together. They were amazed when an old lady rolled in to the small room and the doors closed. A minute later, the doors opened and a young beautiful lady stepped out. The father said to his son “Go, get your mother now.” The ending of the story is funny because they thought that the doors can change an old lady into a young beautiful lady. Whereas the doors were actually elevator doors.
9.	Explanation	How to Fly a Hot Air Balloon A hot air balloon consists of a basket, four big gas tanks, a burner and the balloon or ‘envelope’ First, four nylon poles are put into sockets on top of the basket. The burner is then put on top of the poles. Next, the cables are connected to the burner frame. The cables also go under the basket in order to hold everything together. After this, the hoses from the full gas tanks must be connected to the burner so that pilot can test it. Next, the mouth of the balloon is held open by two people while it is filled with cold air from the fan until it is quite fat and tight. Now for the difficult bit. The pilot lies on the ground, half in the basket, turns on the gas burner, and points the flame into the ‘mouth’ of the balloon. This is so that the balloon slowly stands up. When the it is ready to go, a bit more air is heated up the in the balloon. This results in the air in the balloon to be hot enough to get the balloon to rise off the ground
10.	Discussion	Euthanasia Euthanasia is the act of intentionally causing the painless death of a sick person. In terms of a physician’s actions, it can be passive in that a physician plays no direct role in the death of the person or it can be active in that the physician does something directly to cause the death. Now the question: Do you think it is right for a physician to refuse to participate in active euthanasia? It is NEVER right for a physician or any one else to deliberately hasten a person’s death. This includes all forms of euthanasia-active and passive. To deliberately withhold food/fluids is to subject the person to a painful death-it is NOT a humane death. We are not in a position to determine the worth of a life. Every person has a soul-it is up to God to determine when he will take that soul from the shell that is the human body. We all have a duty to support life with ordinary means-food/fluids but we are not required to use extrordinary means-aggressive life support,dialysis,etc indefinitely. O.K. now, euthanasia (I think) is a type of suicide, whether or not you are sick. Physicians absolutley have the choice of NOT participating, in fact it should not be legal!!! Now if you put someone to death who was sick, or heck they dont even have to be sick, but you would look at your self everyday and be reminded of it. i bet you would feel like a murderer. If people want to die they can commit suicide in their own homes, makin someone else do it is not going to make it any better morally. Euthanasia is a sad, sad deal, please try to stop it. I believe if the person wants to die to end their life they should have the right to choose.I do not believe that the person should beable to have themselves killed if they’re not really suffering. Yes the person does have the right to kill him or herself. BUt the authourity stands in the way of that. If this is such a free country why can’t anyone participate in EUTHANASIA? If we have the right (at least in the U.S) to do whatever we want to with our lives, whether it be rich and famous or an alcoholic crack head, why is it that we can not decide when our life should end? It is ours, if we can kill the life that grows inside us, we should be allowed to also destroy the life that harbors others. Especially if that person is in pain and requests that some end their suffering. I don’t think you can allow one law with out the either. A life is a life, right? http://www-hsc.usc.edu/~mbernste/ethics.euthanasia.htm
11.	Review	Get Married Illustrating the current situation happening in Indonesia, Get Married presents the figures of unemployment. A few big-name celebrities show up in cameo roles. The movie tells about a true friendship of four youngsters Mae (Nirina Zubir), Guntoro (Desta ‘Club Eighties’), Eman (Aming), dan Beni (Ringgo Agus Rahman) who judge themselves as the most frustrated people in Indonesia. Soon, they turn out to be street kids and spend most of their times at street, bullying people who pass by. . Suddenly, it comes to a moment when Mae is persuaded to grant her parents’ wish to have a grandchild. Mae’s parents, (Meriam Bellina dan Jaja Mihardja) firmly state that Mae must get married in a little while. Soon, they are busy finding candidates who would marry their only daughter. However, along the process of finding the right one for Mae, the three male friends of Mae turn out to be brutal evaluators for the candidates. In the mean time, Mae falls badly in love with Rendy (Richard Kevin), a rich, handsome and kind-hearted man. Unfortunately Rendy, Mae, Guntoro, Eman, Beni are brought into a misunderstanding, and soon fights break out between the two groups of Mae and Rendy. Written based on some of youngsters’ real-life brotherhood experiences—this story will stir you to your emotional core while bringing out your sense of brotherhood. There are a lot of little things and big things that make this movie worth watching. The story is good, the banter is great, the relationships between the characters are great, and it’s a fun time at the movies. While some of the jokes are amusing, some of the fights go on a few bit too long. Adapted from: http://maliablog.wordpress.com
12.	Narratives	Snow Maiden Once upon a time there lived a couple in a village. They had got married for a long time, but so far they did not have a baby yet. Every single minute they prayed to God, begged for a baby, but it never came true. One day, they went to snow mountain. They made a girl from snow and they dressed her beautifully. When it got dark, they decided to go home and left the snow girl alone. The following morning, someone knocked the door. \”Any body home?\”, she said. The old woman inside opened the door and asked, \”Who are you?\” The girl said \”I\’m Snow Maiden, your daughter\”. The old woman was surprised and happy. \”Oh really? Thanks God! Come in, please!\” Since that meeting, they lived happily. Snow Maiden was beautiful, kind, diligent and helpful. Her parents and all of her friends loved her very much One day, Snow Maiden played with her friends. They played fire. At first, Snow Maiden just looked at their play. Suddenly, her friends asked her to jump on the fire. Of course she refused it because one thing that made her afraid was the fire. It\’s because Snow Maiden was made of snow, so she should avoid the fire. But her friends kept on forcing her to jump on. Finally, she could not do anything then she did it. She jumped on the fire and she melted. Her friends was so sorry about this, they cried and cried hoping Snow Maiden could live again, but it was useless. Snow Maiden would not be back anymore. Her mother tried to entertain Snow Maiden\’s friends and asked them to make a new Snow Maiden. They went to a snow mountain and started making it. They expected to have the new Snow Maiden. Days passed but their dreams never came true. Malin Kundang Once upon time, there was a boy named Malin Kundang. He lived with his mother in a very poor condition. They looked fire wood in the forest nearly to make a living. Malin Kundang was so unsatisfied with their bad luck. That’s why he decided to go to another city to look for a better life. Not long afterwards, Malin asked his mother’s permission to go to a big city. He promised to come back soon with much money. His mother permitted him and always prayed for him. In his journey, Malin Kundang joined a merchant in a big ship. Actually, Malin was a diligent boy. He worked hard to get much money and everything changed. He became a rich merchant. His business partner asked him to marry his daughter. Malin agreed. Then Malin and his business partner’s daughter got married. They had honeymoon and traveled all over the world. Many years later, Malin’s ship anchored in his village. Many villagers welcome his arrival and admired his glorious ship. Furthermore, they wanted to see his success. Malin’s mother heard that her son had come back. She was very glad and eager to see him. With a happy smile in her lips, she went to the seashore to meet her son. Do you know what happened when she met Malin? He pretended that he didn’t know her. Of course she was very very sad and disappointed. In her desperation she cried to God to punish Malin. She cursed Malin Kundang and his ship to be a stone. Since then, people can see the big stone in the beach.

BILANGAN BULAT

BILANGAN BULAT

Pernahkah kalian memerhatikan termometer? Termometer adalah alat yang digunakan untuk mengukur suhu suatu zat. Pada pengukuran menggunakan termometer, untuk menyatakan suhu di bawah 0oC digunakan tanda negatif. Pada tekanan 1 atmosfer, suhu air mendidih 100oC dan membeku pada suhu 0oC. Jika air berubah menjadi es, suhunya kurang dari 0oC. Misalkan, es bersuhu –7oC, artinya suhu es tersebut 7oC di bawah nol.

Tujuan pembelajaranmu pada bab ini adalah:

• - dapat memberikan contoh bilangan bulat
• - dapat menyatakan sebuah besaran sehari-hari yang menggunakan bilangan negatif;
• - dapat menentukan letak bilangan bulat pada garis bilangan;
• - dapat menyelesaikan operasi tambah, kurang, kali, bagi, dan pangkat bilangan bulat termasuk operasi campuran;
• - dapat menentukan sifat-sifat perkalian dan pembagian bilangan negatif dengan negatif dan positif dengan negatif;
• - dapat menaksir hasil perkalian dan pembagian bilangan bulat;
• - dapat menghitung kuadrat dan pangkat tiga serta akar kuadrat dan akar pangkat tiga bilangan bulat;
• - dapat menemukan dan menggunakan sifat penjumlahan, pengurangan, perkalian,
• pembagian, dan perpangkatan bilangan bulat untuk menyelesaikan masalah.

Kata-Kata Kunci:

• - bilangan bulat positif
• - bilangan bulat negatif
• - penjumlahan bilangan bulat
• - pengurangan bilangan bulat
• - perkalian bilangan bulat
• - pembagian bilangan bulat
• - perpangkatan dan akar bilangan bulat

1. Bilangan bulat terdiri dari bilangan bulat negatif, nol, dan bilangan bulat positif.

2. Sifat-sifat penjumlahan pada bilangan bulat.

a. Sifat tertutup

Untuk setiap bilangan bulat a dan b, berlaku a + b = c dengan c juga bilangan bulat.

b. Sifat komutatif

Untuk setiap bilangan bulat a dan b, selalu berlaku a + b = b + a.

c. Sifat asosiatif

Untuk setiap bilangan bulat a, b, dan c selalu berlaku (a + b) + c = a + (b + c).

d. Mempunyai unsur identitas

Untuk sebarang bilangan bulat a, selalu berlaku a + 0 = 0 + a. Bilangan nol (0) merupakan unsur identitas pada penjumlahan.

e. Mempunyai invers

Untuk setiap bilangan bulat a, selalu berlaku a + (–a) = (–a) + a = 0. Invers dari a adalah –a, sedangkan invers dari –a adalah a.

3. Jika a dan b bilangan bulat maka berlaku a – b = a + (–b).

4. Operasi pengurangan pada bilangan bulat berlaku sifat tertutup.

5. Jika p dan q bilangan bulat maka
1) p x q = pq;
2) (–p) x q = –(p x q) = –pq;
3) p x (–q) = –(p x q) = –pq;
4) (–p) x (–q) = p x q = pq.

6. Untuk setiap p, q, dan r bilangan bulat berlaku sifat
a. tertutup terhadap operasi perkalian;
b. komutatif: p x q = q x p;
c. asosiatif: (p x q) x r = p x (q x r);
d. distributif perkalian terhadap penjumlahan: p x (q + r) = (p x q) + (p x r);
e. distributif perkalian terhadap pengurangan: p x (q – r) = (p x q) – (p x r).

7. Unsur identitas pada perkalian adalah 1, sehingga untuk setiap bilangan bulat p berlaku p x 1 = 1 x p = p.

8. Pembagian merupakan operasi kebalikan dari perkalian.

9. Pada operasi pembagian bilangan bulat tidak bersifat tertutup.

10. Apabila dalam suatu operasi hitung campuran bilangan bulat tidak terdapat tanda kurung, pengerjaannya berdasarkan sifat-sifat operasi hitung berikut.

a. Operasi penjumlahan (+) dan pengurangan (–) sama kuat, artinya operasi yang terletak di sebelah kiri dikerjakan terlebih dahulu.
b. Operasi perkalian ( x ) dan pembagian (:) sama kuat artinya operasi yang terletak di sebelah kiri dikerjakan terlebih dahulu.
c. Operasi perkalian ( x ) dan pembagian (:) lebih kuat daripada operasi penjumlahan (+) dan pengurangan (–), artinya operasi perkalian ( x ) dan pembagian (:) dikerjakan terlebih dahulu daripada operasi penjumlahan (+) dan pengurangan (–).

PENGENALAN ALJABAR

PENGENALAN ALJABAR

Pada arena balap mobil, sebuah mobil balap mampu melaju dengan kecepatan (3x + 10) km/jam selama 0,5 jam. Berapakah kecepatannya jika jarak yang ditempuh mobil tersebut 200 km?

A. BENTUK ALJABAR DAN UNSUR-UNSURNYA

Perhatikan ilustrasi berikut:
Banyak boneka Rika 5 lebihnya dari boneka Desy. Jika banyak boneka Desy dinyatakan dengan x maka banyak boneka Rika dinyatakan dengan x + 5. Jika boneka Desy sebanyak 4 buah maka boneka Rika sebanyak 9 buah. Bentuk seperti (x + 5) disebut bentuk aljabar.

Bentuk aljabar adalah suatu bentuk matematika yang dalam penyajiannya memuat huruf-huruf untuk mewakili bilangan yang belum diketahui. Bentuk aljabar dapat dimanfaatkan untuk menyelesaikan masalah dalam kehidupan sehari-hari. Hal-hal yang tidak diketahui seperti banyaknya bahan bakar minyak yang dibutuhkan sebuah bis dalam tiap minggu, jarak yang ditempuh dalam waktu tertentu, atau banyaknya makanan ternak yang dibutuhkan dalam 3 hari, dapat dicari dengan menggunakan aljabar.

Contoh bentuk aljabar yang lain seperti 2x, –3p, 4y + 5, 2x2 – 3x + 7, (x + 1)(x – 5), dan –5x(x – 1)(2x + 3). Huruf-huruf x, p, dan y pada bentuk aljabar tersebut disebut variabel. Selanjutnya, pada suatu bentuk aljabar terdapat unsur-unsur aljabar, meliputi variabel, konstanta, faktor, suku sejenis, dan suku tak sejenis.

Agar kalian lebih jelas mengenai unsur-unsur pada bentuk aljabar, pelajarilah uraian berikut:

1. Variabel, Konstanta, dan Faktor
Perhatikan bentuk aljabar 5x + 3y + 8x – 6y + 9. Pada bentuk aljabar tersebut, huruf x dan y disebut variabel. Variabel adalah lambang pengganti suatu bilangan yang belum diketahui nilainya dengan jelas. Variabel disebut juga peubah. Variabel biasanya dilambangkan dengan huruf kecil a, b, c, ..., z.

Adapun bilangan 9 pada bentuk aljabar di atas disebut konstanta. Konstanta adalah suku dari suatu bentuk aljabar yang berupa bilangan dan tidak memuat variabel. Jika suatu bilangan a dapat diubah menjadi a = p X q dengan a, p, q bilangan bulat, maka p dan q disebut faktor-faktor dari a.

Pada bentuk aljabar di atas, 5x dapat diuraikan sebagai 5x = 5 X x atau 5x = 1 X 5x. Jadi, faktor-faktor dari 5x adalah 1, 5, x, dan 5x. Adapun yang dimaksud koefisien adalah faktor konstanta dari suatu suku pada bentuk aljabar. Perhatikan koefisien masing-masing suku pada bentuk aljabar 5x + 3y + 8x – 6y + 9. Koefisien pada suku 5x adalah 5, pada suku 3y adalah 3, pada suku 8x adalah 8, dan pada suku –6y adalah –6.

2. Suku Sejenis dan Suku Tak Sejenis
a) Suku adalah variabel beserta koefisiennya atau konstanta pada bentuk aljabar yang dipisahkan oleh operasi jumlah atau selisih.

Suku-suku sejenis adalah suku yang memiliki variabel dan pangkat dari masing-masing variabel yang sama. Contoh: 5x dan –2x, 3a2 dan a2, y dan 4y, ...

Suku tak sejenis adalah suku yang memiliki variabel dan pangkat dari masing-masing variabel yang tidak sama. Contoh: 2x dan –3x2, –y dan –x3, 5x dan –2y, ...

b) Suku satu adalah bentuk aljabar yang tidak dihubungkan oleh operasi jumlah atau selisih. Contoh: 3x, 2a2, –4xy, ...

c) Suku dua adalah bentuk aljabar yang dihubungkan oleh satu operasi jumlah atau selisih. Contoh: 2x + 3, a2 – 4, 3x2 – 4x, ...

d) Suku tiga adalah bentuk aljabar yang dihubungkan oleh dua operasi jumlah atau selisih. Contoh: 2x2 – x + 1, 3x + y – xy, ...

Bentuk aljabar yang mempunyai lebih dari dua suku disebut suku banyak.

B. OPERASI HITUNG PADA BENTUK ALJABAR

1. Penjumlahan dan Pengurangan Bentuk Aljabar
Pada bentuk aljabar, operasi penjumlahan dan pengurangan hanya dapat dilakukan pada suku-suku yang sejenis. Jumlahkan atau kurangkan koefisien pada suku-suku yang sejenis.

2. Perkalian
Perlu kalian ingat kembali bahwa pada perkalian bilangan bulat berlaku sifat distributif perkalian terhadap penjumlahan, yaitu a X (b + c) = (a X b) + (a X c) dan sifat distributif perkalian terhadap pengurangan, yaitu a X (b – c) = (a X b) – (a X c), untuk setiap bilangan bulat a, b, dan c. Sifat ini juga berlaku pada perkalian bentuk aljabar.

3. Perpangkatan
Coba kalian ingat kembali operasi perpangkatan pada bilangan bulat. Operasi perpangkatan diartikan sebagai perkalian berulang dengan bilangan yang sama. Hal ini juga berlaku pada perpangkatan bentuk aljabar. Pada perpangkatan bentuk aljabar suku dua, koefisien tiap suku ditentukan menurut segitiga Pascal. Misalkan kita akan menentukan pola koefisien pada penjabaran bentuk aljabar suku dua (a + b)n, dengan n bilangan asli.
Perhatikan uraian berikut:


Pada segitiga Pascal tersebut, bilangan yang berada di bawahnya diperoleh dari penjumlahan bilangan yang berdekatan yang berada di atasnya.

4. Pembagian
Hasil bagi dua bentuk aljabar dapat kalian peroleh dengan menentukan terlebih dahulu faktor sekutu masing-masing bentuk aljabar tersebut, kemudian melakukan pembagian pada pembilang dan penyebutnya.

5. Substitusi pada Bentuk Aljabar
Nilai suatu bentuk aljabar dapat ditentukan dengan cara menyubstitusikan sebarang bilangan pada variabel-variabel bentuk aljabar tersebut.

6. Menentukan KPK dan FPB Bentuk Aljabar
Coba kalian ingat kembali cara menentukan KPK dan FPB dari dua atau lebih bilangan bulat. Hal itu juga berlaku pada bentuk aljabar. Untuk menentukan KPK dan FPB dari bentuk aljabar dapat dilakukan dengan menyatakan bentuk-bentuk aljabar tersebut menjadi perkalian faktor-faktor primanya. Perhatikan contoh berikut:


C. PECAHAN BENTUK ALJABAR

Di bagian depan kalian telah mempelajari mengenai bentuk aljabar beserta operasi hitungnya. Pada bagian ini kalian akan mempelajari tentang pecahan bentuk aljabar, yaitu pecahan yang pembilang, atau penyebut, atau kedua-duanya memuat bentuk aljabar.

1. Menyederhanakan Pecahan Bentuk Aljabar
Suatu pecahan bentuk aljabar dikatakan paling sederhana apabila pembilang dan penyebutnya tidak mempunyai faktor persekutuan kecuali 1, dan penyebutnya tidak sama dengan nol. Untuk menyederhanakan pecahan bentuk aljabar dapat dilakukan dengan cara membagi pembilang dan penyebut pecahan tersebut dengan FPB dari keduanya.

2. Operasi Hitung Pecahan Aljabar dengan Penyebut Suku Tunggal
a. Penjumlahan dan pengurangan
Pada bab sebelumnya, kalian telah mengetahui bahwa hasil operasi penjumlahan dan pengurangan pada pecahan diperoleh dengan cara menyamakan penyebutnya, kemudian menjumlahkan atau mengurangkan pembilangnya. Kalian pasti juga masih ingat bahwa untuk menyamakan penyebut kedua pecahan, tentukan KPK dari penyebut-penyebutnya. Dengan cara yang sama, hal itu juga berlaku pada operasi penjumlahan dan pengurangan bentuk pecahan aljabar. Perhatikan contoh berikut:

b. Perkalian dan pembagian
Perkalian pecahan aljabar tidak jauh berbeda dengan perkalian bilangan pecahan. Perhatikan contoh berikut:

c. Perpangkatan pecahan bentuk aljabar
Operasi perpangkatan merupakan perkalian berulang dengan bilangan yang sama. Hal ini juga berlaku pada perpangkatan pecahan bentuk aljabar. Perhatikan contoh berikut:

LOGARITMA

Logaritma adalah operasi matematika yang merupakan kebalikan dari eksponen atau pemangkatan.

Rumus dasar logaritma:

Mencari nilai logaritma:
Cara untuk mencari nilai logaritma antara lain dengan menggunakan:
>Tabel
>Kalkulator (yang sudah dilengkapi fitur log)

Kegunaan logaritma:
Logaritma sering digunakan untuk memecahkan persamaan yang pangkatnya tidak diketahui. Turunannya mudah dicari dan karena itu logaritma sering digunakan sebagai solusi dari integral. Dalam persamaan bn = x, b dapat dicari dengan pengakaran, n dengan logaritma, dan x dengan fungsi eksponensial.

Rumus Logaritma:

Sains dan teknik:
Dalam sains, terdapat banyak besaran yang umumnya diekspresikan dengan logaritma. Sebabnya, dan contoh-contoh yang lebih lengkap, dapat dilihat di skala logaritmik.

* Negatif dari logaritma berbasis 10 digunakan dalam kimia untuk mengekspresikan konsentrasi ion hidronium (pH). Contohnya, konsentrasi ion hidronium pada air adalah 10−7 pada suhu 25 °C, sehingga pH-nya 7.

* Satuan bel (dengan simbol B) adalah satuan pengukur perbandingan (rasio), seperti perbandingan nilai daya dan tegangan. Kebanyakan digunakan dalam bidang telekomunikasi, elektronik, dan akustik. Salah satu sebab digunakannya logaritma adalah karena telinga manusia mempersepsikan suara yang terdengar secara logaritmik. Satuan Bel dinamakan untuk mengenang jasa Alexander Graham Bell, seorang penemu di bidang telekomunikasi. Satuan desibel (dB), yang sama dengan 0.1 bel, lebih sering digunakan.

* Skala Richter mengukur intensitas gempa bumi dengan menggunakan skala logaritma berbasis 10.

* Dalam astronomi, magnitudo yang mengukur terangnya bintang menggunakan skala logaritmik, karena mata manusia mempersepsikan terang secara logaritmik.

Penghitungan yang lebih mudah:
Logaritma memindahkan fokus penghitungan dari bilangan normal ke pangkat-pangkat (eksponen). Bila basis logaritmanya sama, maka beberapa jenis penghitungan menjadi lebih mudah menggunakan logaritma:

Sifat-sifat diatas membuat penghitungan dengan eksponen menjadi lebih mudah, dan penggunaan logaritma sangat penting, terutama sebelum tersedianya kalkulator sebagai hasil perkembangan teknologi modern.

Untuk mengkali dua angka, yang diperlukan adalah melihat logaritma masing-masing angka dalam tabel, menjumlahkannya, dan melihat antilog jumlah tersebut dalam tabel. Untuk mengitung pangkat atau akar dari sebuah bilangan, logaritma bilangan tersebut dapat dilihat di tabel, lalu hanya mengkali atau membagi dengan radix pangkat atau akar tersebut.

Beberapa contoh software Aplikasi

Software aplikasi adalah suatu software (perangkat lunak) yang sudah siap pakai/jadi, dan hanya dipergunakan untuk mengolah data tertentu.

-Software pengolah kata :
1.Microsoft Word
2.Wordstar
3.WordPerfect
4.OpenOffice Writer

-Software pengolah lembar kerja (spreadsheet) :
1.Microsoft Excel
2.Lotus 123
3.OpenOffice Calc
4.Quattro Pro

-Software presentasi :
1.Microsoft PowerPoint
2.Presentation, Impress
3.Macromedia Flash

-Software pengolah database :
1.Microsoft Access
2.Base
3.SQL Server

-Software Internet Browser :
1.Internet Explorer
2.Mozilla Firefox
3.Opera, Safari
4.Google Chrome
5.Netscape Navigator

-Software desain grafis :
1.Adobe Photoshop
2.Corel Draw
3.ACDSee
4.Paint
5.Photopaint
6.Photoshine

-Software antivirus :
1.Norton Internet Security
2.AVG Free
3.Kaspersky
4.PCMAV
5.Norton 360
6.Nod32
7.Norton AntiVirus
8.Avira
9.McAfee
10.Avast!

-Software extractor / pengolah archive :
1.WinZip
2.WinRAR
3.KGB Archiver
4.WinACE

-Software Video Editing :
1.Pinnacle Studio Plus
2.Ulead Movie Studio
3.Adobe After Effect
4.Adobe Premiere

-Software burning CD / DVD :
1.Nero Burning ROM / Nero StartSmart
2.WinISO
3.Daemon Tools
4.UltraISO
5.CloneCD
6.CloneDVD
7.Alcohol 120%

-Software music / video player :
1.Windows Media Player
2.iTunes
3.Real Player
4.Winamp
5.Media Monkey

-Software game :
1.Warcraft III
2.Platypus
3.Feeding Frenzy 2
4.GTA
5.PES 2012

-Software pengaturan tampilan :
1.Vista Transformation Pack
2.WinFlip
3.ViStart
4.Bricopack Vista Inspirat
5.DesktopX

-Software Messenger :
1.Windows Messenger
2.Yahoo! Messenger

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-Selanjutnya anda bisa tanya Om google -

Beberapa jenis Motherboard dan Processor

1.Motherboard Processor Pentium I














-CPU Intel Pentium MMX, 166 MHz
-Motherboard QDI VX III (3 ISA, 4 PCI, 4 SIMM, 1 DIMM)
-Chipset Intel Triton 82430VX
-BIOS Award Modular (07/07/97)
-Motherboard id 07/07/97-i430VX-NS306-2A59GQ1EC-00
-Chipset Intel Triton 82430VX
-BIOS Award Modular BIOS v4.51PG
-BIOS message P5I430VX/250DM Explorer II BIOS V3.5S 07/09/97
-chipset North Bridge Intel 82437VX



2.Motherboard Processor Pentium II















-Chip Set Intel
-Video Chip Set None
-Maximum Onboard Memory 384MB (EDO & SDRAM supported)
-Maximum Video Memory None
-Cache 256/512KB (located on Pentium II CPU)
-BIOS AMI Dimensions 305mm x 244mm
-I/O Options 32-bit PCI slots (5), floppy drive interface, green PC connector, IDE interfaces (2), parallel port, PS/2 mouse port, serial ports (2), IR connector, USB connectors (2), ATX power connector, AGP slot
-NPU Options None

3.Motherboard Processor Pentium III














-Chipset Intel 82443BX PAC
-Memory Capacity Two DIMM sockets for up to 512 MB SDRAM (16 MB minimum)
-Memory Type/Size Supports Intel
4-clock, 72-bit ECC or 64-bit
non-ECC, unbuffered 66-MHz or 100-MHz DIMMs
-DIMM Sizes 16 MB, 32 MB, 64 MB, 128 MB, 256 MB
-Memory Voltage 3.3V only
-USB Two stacked USB connectors
-BIOS Type 4 Mb bootblock Flash,AMI BIOS 4Mb Flash
-Special Features Plug and Play, IDE drive auto-configure,
Advanced Power Management (APM) 1.2,
ACPI 1.0, DMI 2.0 ECC/Parity support,
LS120 support, Multilingual support

4.Motherboard Processor Pentium IV















-RAM Dual Channel atau Quad Channel ECC Registered & FBDIMM
-Chassis Model tower,rackmount dan blade
-Graphics Controller On-board
-Power Connector 24-pin & 8-pin auxiliary 500 watt - 750 watt
-Socket Processor Dual Socket atau Lebih Processor Intel Xeon atau Itanium
-Slot PCI Tersedia PCI-X dan 64-bit

5.Motherboard Dual Core













-Max CPU Configuration 1
-TCASE 74.1°C
-Package Size 37.5mm x 37.5mm
-Processing Die Size 82 mm2
-Processing Die Transistors 228 million
-Sockets Supported LGA775
-Halogen Free Options Available Yes
-Clock Speed 2.7 GHz
-L2 Cache 2 MB
-Bus/Core Ratio 13.5
-FSB Speed 800 MHz
-Instruction Set 64-bit
-Embedded Options Available No
-Supplemental SKU No
-Lithography 45 nm
-Max TDP 65 W
-VID Voltage Range 0.8500V–1.3625V

6.Motherboaard Core 2 Duo














- LGA775 Core 2 Duo
- Chipset Intel G31, ICH7
- Front Side Bus 1600(O.C)/1333/1066/800 MHz
- Dual 2 DDR2 1600(O.C)/1333/1066/800
- 1x PCIe x16, 1x PCIex1,2 x PCI;Support Intel next generation 45nm CPU; Support Enhanced Intel Speed Step Technology (EIST)
- VGA, Audio, PCIe LAN


7.Motherboard Intel Core 2 Quad














-CPU Socket LGA 775
-Multi-Core Quad-Core
-Operating Frequency 2.66GHz
-Cache 6MB L2
-64 bit Support Yes
-Cooling Device Heatsink and Fan