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Skip to main content. Log In Sign Up. Ngoc Anh Nguyen. The music of English Too Fast, Too Furious

Subject Matter - Reference: Geometry for High-school Textbook. Sheets of paper, Protractor, Puzzles. Deliver the 1st m worksheet to ask the students to fill in the I k C name of objects in a R C given picture. Work in pair to finish the task in 3 mins. Line CD: Secant an extended chord, a straight line cutting the circle at two points.

Work in pair to finish radius distance the task in 3 mins tangent points T: A…………… 5 of a circle touches the circle at one point and the distance from the center of the circle to the tangent is equal to the radius of the circle.

State problem 15 Problem 1. In the coordinate min plane, given a point I a; b S: Find the solution to the s and a positive real number problem R. What is the formulae to Solution: M is on the circle calculate the distance if and only if the distance between two points?

Standard form of the equation of a circle The circle with center I a; b and radius R is the set T. State the equation of a of all points x; y satisfying circle officially. Determine the coordinate of the center and the radius of a circle in the following cases: Deliver the 3rd worksheet.

Finish the task 2 2 iv. Correct the answer. Convert the given Ans: Completing the square and the radius in each form of x and y, we cases. Problem 2. Convert the given equation 2 be the equation equation to the standard of a circle. In this case, form of equation. Then, to calculate the radius. Write the left-hand the center and the length side of the equation 2 in of the radius in this case. Examples T. Deliver the 4rd Example 1. Given two worksheet. Find the equation of the S.

Finish the task in 5 circle with the diameter AB. The center of the circle T. What is the center of segment AB, then the the circle? Hence, of the midpoint of a the equation of the circle segment?

Given three s points A 1;2 ; B 2;5 ; C 4;1. Find the equation of the circumcircle of the triangle ABC. Notice the character of Ans: Locate the center of a right triangle. Notice that then the triangle ABC is right triangle at A. Find the equation of a circle which touches the x- and y-axes and passes through the point A - 1; 3 Ans: Let I be the center of the circle with coordinates a; b.

Under what condition that a line touches a circle? Case 1: Summary the lesson 4 - Review the terms learned during the lesson through mins flashcards. Find the equation of the circle C centered at I 1; 2 and tangent to the line d with the equation: Exercise 2: Find the equation of the circle C passing through three points A - 2; 4 ; B 5; 5 ; C 6; - 2.

Given the circle C: Find the points of intersection of the line and the circle. Exercise 4: Let C be the circle with the center I on the line d: Find the equation of the circle. Sheets of paper.

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Procedure T: Student ; Q: Direction vector of a line T: State the definition of 20 direction mins vector of a line. A non — zero vector is a vector does a direction vector of a line d if the line line have? What is the relation Notes: Given the line d passing S: Answer all through a point M x ; y and get a the questions. What is the condition for the point M x; y to lie on the line d? M iff and are collinear, it means there exists a parameter t such that , then we have T: Find the solutions.

Theorem The point M x; y is on the line d if and Q: Which vector equality can Note: State the - By equating t values, we obtain the equation parametric equations of a line officially. We call this equation the Cartesian equation of the line. How do we calculate the gradient of the line? Examples Example 1: Find the vector of d and two points on d. Find the parametric equations of the line d passing through the points A 1; 2 and B 2; - 1.

The line d passing through the points A and B then it has direction T: Is the vector 1; Example 3: Find the coordinates of H. What is the Ans: What equation can we Substituting into the parametric deduce? AH is also the shortest distance from A to the line d.

Read the following passage and find out one of the application of parametric equation. Homework Exercise 1: Find k. Exercise 3: Find the initial position of each yacht.

Show that the speed of each yacht is constant and state the speeds. If they start at 6: Prove that the paths of the yachts are right angles to each other. Geometric Sequences Course: A-level Date: Process Standards: Geometric sequences 6. Summing geometric series 6. Convergent geometric series 6. Using sigma notation Lesson Objective s: Language Objectives: Skill Focus: Vocabulary Focus: Solve problems relating G.

Terms; Sequences; Series; G. Outline of the lesson: Recap the lesson, hand out assignment, and talk briefly the content of the next. A sequence in which you get from one term to the next by multiplying by a constant is called a geometric sequence. Example 1 Show that the numbers 4, 12, 36, form a geometric sequence. If the sequence is continued, find a the next two terms, b the twentieth term. So the numbers form a geometric sequence. Correct to 4 sifnificant figures, this is million.

How many terms are there altogether? This means that is the seventh term of the sequence. A general definition for this kind of sequence is: You should notice two points about this definition.

First, since the letter r is conventionally used for the common ratio, a different letter, i , is used for the suffixed. Secondly, the ratios 0 and 1 are excluded. However, r can be negative; in that case the terms are alternatively positive and negative. Example 3 The first two terms of a geometric sequence are 10 and Show that the first term greater than is the fiftieth.

Each term of the sequence is greater than the preceding term. You therefore have to show that the 49th term is less than , and that the 50th term is greater than So the first term greater than is the fiftieth. Example 4 Show that there are two geometric sequences whose first term is 5 and whose fifth term is For each of these sequences, find the tenth term.

The two sequences are 5, 10, 20, 40, 80, …. Homework C Homework Questions — Geometric Sequences 1. For each of the following geometric sequences find the common ratio and the next two terms. Find the number of terms in each of these geometric progressions. Different numbers x, y and z are the first three terms of a geometric progression with common ratio r, and also the first, second and fourth terms of an arithmetic progression. Different numbers x, y and z are the first three terms of a geometric progression with common ratio r, and also the first, second and fifth terms of an arithmetic progression.

Related Rates Course: Lesson Objective s: Solve problems in which there are two quantities whose rates of change are related. Learn new terms in related rates problems. Give the general strategy in solving related rates problems. Recap the lesson and talk briefly the content of the next. Connected Rates of Change: Use of the Chain Rule Consider one or two following introductory examples.

Introductory example 1 Police are 30 feet from the side of the road. Their radar sees your car approaching at 80 feet per second when your car is 50 feet away from the radar gun. The speed limit is 65 miles per hour which translates to 95 feet per second. Are you speeding? First, draw a diagram of the setup. Let D be the distance between the police and the car and x be the distance from the car to the foot of the altitude from the police to the road. In this kind of problems, it is important to follow the following steps: Step 1: We then use the chain rule to link what we are told with what we want: Now, plug in the instantaneous numerical values: As the cone forms, the height, h cm, remains equal to the base radius, r cm, of the heap.

Give your answer to 2 significant figures. Find the rate at which the area is increasing at the instant when the radius is 50cm. You are told … You want to find … remember to look at the units for clues.

Step 2: The linking equation, using the chain rule is: In part a we had an expression for. Find the rate at which the radius is decreasing at the instant when the radius of the balloon is 2cm. Give your answer correct to 2 significant figures. The formula relating to volumes of spheres is: Permutations and Combinations Course: Mathematics Date: Permutations 6.

Combinations 6. Examples 6. Exercises Academic Standards: Standard 1 — Counting Techniques Students develop an understanding of combinatorial reasoning, using various types of diagrams and the fundamental counting principle to find numbers of outcomes and related probabilities. They also use simulations to solve counting and probability problems.

Performance Objectives: Permutations and combinations will also be on a paper and pencil test that will be assessed at the end of the chapter.

Students should also recognize when to use permutations or combinations instead of the other counting techniques when solving a problem. This assignment will be due at the beginning of the next class. The goal of the daily assessment is to give extra practice and test the knowledge and understanding of the lesson of that day.

In the homework assignment the students will be applying permutations and combinations to solve various problems. This will help give the teacher feedback to where the students are at. There middle of the chapter to help test the students overall knowledge of the lessons. Advanced Preparation by Teacher: The teacher should be prepared to teach the lesson and have all the accommodation ready for the gifted and talented students.

The teacher should have the agenda, homework assignment, and bell ringer ready when students come to class. The teacher should already have the groups divided out on paper for when the teacher chooses groups. The teacher should have all the examples ready when students come to class, with appropriate solutions. Essential Questions: Some questions on the SAT begin: Use the Fundamental Counting Permutation, Combination, principle permutations to count counting principle Procedure: Bell Ringer: A bowl contains ten red balls and ten blue balls.

A woman selects balls at random without looking at them. How many balls must she select to be sure of having at least three balls of the same color? How many balls must she select to be sure of having at least three blue balls?

It is good to provide a little review before you start a new lesson. The agenda for the day should also be written on the board for the students when they come in.

While the students are working on the bell ringer activity the teacher should use the time to take attendance and make any further preparations for the lesson. When the students have finished the bell ringer activity it is important for the teacher to go over that activity. Make sure that all of student are on the same page before you begin the new lesson. The teacher should begin with an example on the board. The teacher knows that the answer is way too large for the students to be able to write down all the possibilities, but the teacher should let the students try anyway for about 2 to 3 minutes.

The teacher should ask the students what the highest number they came up with was, and then the teacher should tell them the answer is Step by Step Procedure: Then teacher should explain exactly what each one of those words means.

Activity — have the students put in the people in the first and 2nd place race and see how many possibilities that they get. It is best to start with the question, how many ways can I award 1st and 2nd place to 4 people? The reaction that students may initially have is 4! Or So, let them place the people and record the answers. They should get 12possibilities. Ask the students to use the same pieces, but answer, what if there was 1st, 2nd, and 3rd place to award for those 4 people?

Now there are 24 possibilities. What if there is only 1st place? Now there are only 4 possibilities. When you take sub-groups from an original group the possibilities change depending on the size of the sub-group. This does use the Fundamental Counting principle, but it extends it to something called a permutation. The formula for Permutation is defined to be when we n! If there are 4 people and you need to pick a 1st, and 2nd place winner, how many ways that be done?

Start with asking the question, how many ways can we take four people and put them in teams of 2? They many do a permutation and answer Have them work the people and record the possibilities to see. With those same people, have them calculate a team of 1 and then a team of 3?

Have them compare their results to those when we did 1 , 2 , and 3rd st nd place. Why is this different? Combinations n is the total group and r is the number in the sub- n! The other way it is written is Cnr or C n,r. See if students can find it on their calculator. Focus on canceling out the factorials and doing order of operations properly.

A permutation is a set of distinct objects is am ordered arrangement of these objects. A combination is a set of unordered elements from the total set. The teacher should ask the students if they see the difference between the two definitions. The teacher should ask the student what they think it means, and how it affects the problem.

The teacher should then give a simple example of a permutation problem followed by a simple example of combination problem no need to solve yet. The teacher should then explain the difference between the two problems and why the first is a permutation and the second is a combination.

Once the teacher feels that the class understands the difference between the two, then it is time to move on to formulas. The formula for permutation is n!

The teacher should then go over some examples and teach the students how to apply the formula. Then the teacher should have the students do some examples by themselves at their desk. Example 2 Suppose that there are eights runners in a race.

The winner receives a gold medal the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. How many different ways are there to award these medals, if all possible outcomes of the race can occur and there are no ties?

Example 3 Suppose that a saleswoman has to visit eight different cities. She must begin her trip in a specified city, but she can visit the other seven cities in any order she wishes. How many possible orders can the saleswoman use when visiting the cities? The first city is locked in but the order seven can be chosen however she wants them to be. Thus the answer is 7! Since we have a block of 3 that have to occur, the other six letters can be in any order, thus the answer is 6!

Now the teacher should do the same with combinations. The teacher should explain the combinations formula, which is: The teacher should then go over examples as a class then have the students do one example by themselves. Example 5 How many ways are there to select five players from a member tennis team to make a trip to a match at another school?

How many ways are there to select a first prize winner, second-prize winner, and a third-prize winner from five different people who have entered a contest? Example 7 A group of 30 people have been trained as astronauts to go on the first mission to Mars.

How many ways are there to select a crew of six people to go on this mission assuming that all crew members have the same job? The positions of r 1s in a bit string of length n form an r-combination of the set 1,2,3, Hence, there are C n,r bit strings of length n that contain exactly r 1s.

Now the teacher should divide the class into six groups of 3 or 4. First position the men and then consider possible positions for the women. The teacher should then go over those problems with the class as a whole and answer in questions they might have.

Then the teacher should have the each group go to the board and teach the class how to solve their problem. The group will first have to decide which counting technique to use to solve their given problem.

Examples 10 1 How many license plates can be made using either three digits followed by three letters or three letters followed by three digits? Most sentences have multiple nouns, some sentences have only a single noun. The first letter is capitalized. Michael Jordan person, athlete Pepsi Cola drinks, soda , New York city Nouns that refer to a general class of person, place, entity are common nouns and they are not capitalized: Count nouns are countable. Adams book nut bean Mass nouns name undifferentiated mass, things that are not usually considered countable..

Remember that the article is not stressed, so don't listen for its full value! Also, ask native speakers to help you when you don't know whether or not to use the article. Some Rules using Articles Singular count nouns: My daughter wants to buy a dog this weekend. Indefinite-Could be any dog The dog in the backyard is very cute. Definite-The one in the backyard He requested a puppy for his birthday.

He wanted the puppy he played with at the pet shop. She ordered a hamburger without onions. Did you drink the coke I just ordered? Plural count nouns: Use "the" or Nothing, never 'a'. Come and look at the children. Do you like reading the grammar rules on this page? Non-count nouns: He has experience.

Writing in a second language is especially challenging. Have you studied the history of South Africa?

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History reminds us that events repeat themselves. Can I turn over to another channel? The verbs change form to show the various tenses. Some verbs are regular in their changes, some are irregular. See a list of Irregular Verbs.

I watch television everyday. I visit my cousin all the time. In general, the simple present expresses events or situations that exist always, usually, habitually; they exist now, they have existed in the past, and will probably exist in the future.

Simple Past Tense It snowed yesterday. I watched television last night. I visited my cousin last year. At one particular time in the past, this happened. It began and ended in the past. I will watch television tonight. I will visit my cousin later. At one particular time in the future, this will happen. He is asleep at the moment. His sleep is in progress at the present time, and will probably continue.

I arrived at He was still asleep. His sleep began before and was in progress at a particular time in the past. It probably continued. He will go to sleep at We will arrive around The action of sleeping will begin before we arrive, and it will be in progress at a particular time in the future.

His sleep will probably continue. I finished eating something before now. The exact time is not important. First I finished eating. Later they arrived. My eating was completely finished before another time in the past Future Perfect Tense I will have already eaten when they arrive. First I will finish eating.

Later they will arrive. My eating will be completely finished before another time in the future. Event in progress: Before now, up to now How long? Before another event in the past How long? For two hours Future Perfect Progressive Tense I will have been studying for two hours by the time you arrive. Before another event in the future How long?

It gives us information about the actions, events, or state of being. Verbs can be categorized into four groups: They just connect to the subject and give more information about the subject. For example: We are writing an e-mail. We are students. Your new book seems interesting. Seems is a linking verb. I see you. The soup tastes good. The flowers we have picked from the backyard smell so nice. The flowers we have picked from the backyard are so nice.

The sentence doesn't lose its meaning, so the verb smell in the first sentence is a linking verb. He looked at me with fear in his face. He was at me with fear in his face.

The second sentence doesn't make sense, so the verb look in the first sentence is an action verb. Most common linking verbs are: There are some verbs that can both be used as action and linking verbs. Helping Verbs A helping verb, also called an Auxiliary verb, has no meaning on its own but helps the main verb in functional and grammatical way.

Daniel is drawing a picture. Daniel is the subject, "is" is the helping verb, drawing is the main verb action in progress , a picture is the object. Some common helping verbs are: For Example: Tony gave me some flowers My sister sent me a postcard. I brought you a bottle of wine.

Prepositional phrase with For Verbs Examples bake They baked bread for me. Active I gave some money to him yesterday. Active Some money was given to him yesterday. Passive He was given some money yesterday. Passive I will buy her a book tomorrow. A book will be bought for her tomorrow. She will be bought a book tomorrow. The teacher gave her a warning. A warning was given to her by a teacher. She was given a warning by the teacher. The nurse will tell you the decision.

The decision will be told to you by the nurse. You will be told the decision by the nurse. They are going to provide us with accommodation.

The accommodation is going to be provided for us. We are going to be provided with accommodation. My sister sent me a card. A card was sent to me by a sister. I was sent a card by my sister. He sold the old man an alarm clock.

An alarm clock was sold to the old man. The old man was sold an alarm clock. The Rule: Whether they take objects or not. I saw. I saw a bird. I baked. I baked some cake. We played soccer. Now that we can ask the question "what did you play? My son bought me a watch for my birthday. They gave me a pay raise. In the two sentences above the words in bold are indirect objects and the underlined words are direct objects; so, the verbs "buy and give" are transitive. They awarded a gold medal to the top 10 students.

The young girl brought some flowers to her mother. In the two sentences above the words in bold are direct objects and the underlined words are indirect objects; so, the verbs "award and bring" are transitive. Sandra cried. The room flooded. We swam. The birds flew. He jumped. When the fire alarm rang, we all ran out of the building as fast as we could.

The little girl was sitting on the corner. The Sun rises in the East. The earthquake happened yesterday at around 3 am. See more about prepositional and adverbial phrase: Adverbials Note: The hurricane happened in Not The hurricane was happened The athlete ran so fast that he broke the world record. Not the athlete was run The little boy broke the vase.

The vase was broken by the little boy. You have spoiled everything again. Put the meat in the fridge so that it doesn't spoil. List of common intransitive verbs: We were to meet them here. You can use my car tomorrow.

Can - Can't informal polite request Can I borrow your book? Could impossibility negative That can't have been true! Cats can't swim. I didn't have to go to class lack of necessity negative yesterday.

I had to go to class have got to necessity I have got to go to class today yesterday. You must not open that door. Mary must have beensick Shemust be sick. I ought to have studied last advisability I ought to study tonight. She must be sick. I can play the piano.

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I can have a dog in my apartment. When I was a kid, I could run for hours. Infinitives An infinitive is a verb used as a noun. They can be used as a subject or an object of a sentence. It is made by adding "—to" to the beginning of a verb. After certain verbs: I want to find a job. After an object: I want you to help me.

After certain adjectives: I'm happy to help you. After certain expressions with 'it': It's important to practice English. To show purpose: I went to the mall to buy some shoes.

Use the objective case for pronouns that are subjects or objects of infinitives. We wanted him to go with us. When the infinitive or the infinitive phrase is used as a noun after verbs like hear, let, help, make, see and watch, the to is not used.

Correct Incorrect He made her correct the paper. He made her to correct the paper. We all heard her tell the story. We all heard her to tell the story. She let me try on her shoes. She let me to try on her shoes. I am surprised by him coming to my party. He is happy about her finding a new job. I have a BMW. The roses smell nice. Sometimes we can use the same verbs in a progressive tense, yet with a different meaning.

I am having a BMW soon. Here the verb "have" doesn't indicate possession, it has a meaning of "buying". I am tasting the soup. Here the verb "taste" indicates an action so it is an action verb. The flowers look beautiful. Elroy had his car washed.

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I had my dad carry my backpack. I had my horse carry the body. The teacher made me do extra work.

Melisa got her hair cut. Elizabeth had her nails done. Chaps got his house painted. Gary had his ring polished. He had himself kicked out of school. I had my tooth extracted yesterday. I made my little brother say sorry. Fred got his friend to do his homework. Charlie had the carpenter repair the table. Dora had her hairdresser cut her hair. The bank was robbed. Harvard University was founded in English is spoken in many countries around the world.

I was told that you didn't go to work today. In a passive sentence, If we want to mention what caused or who did the action, we use the agent by Charles Dickens wrote many novels.

Many novels were written by Charles Dickens. Most children are strongly influenced their parents. The jam sandwiches were made white bread. Jake was dismissed his boss. The show was presented Mr.

The parcels were tied string. The meal was eaten chopsticks. The song was performed Madonna. This awful mess was made Carol's dog. The football fans were observed the police. My hair was cut a top stylist. The goal was scored Liverpool's youngest player. The beds were made up dean sheets. The supermarket trolley was filled cat food. My camera was loaded a black and white film. Who was the radio invented ? The cyclist was knocked down a bus. The car was fixed a mechanic.

The glass was cut a special tool. Her hair is colored henna. The roast was flavored wine. Music will be played the local band. I love you. I hear you. More Examples: Do you hear that noise outside? Are you hearing that noise outside? I hope everything will be all right.

I am hoping everything will be all right. I prefer tea to coffee. I am preferring tea to coffee. Non continuous verbs express thoughts and feelings and they are used with simple present tense. Non Progressive Verbs List appear believe belong care cost dislike exist expect feel forget have hate hear hope imagine include know like look love mind need own prefer realize remember see seem smell suppose taste understand want Some of the non continuous verbs are used in progressive tense but their meaning changes.

I see there is a man in front of the door. Sense of vision The doctor is seeing a patient. Dating a patient What do you think he will do? Your opinion? What is he thinking about? What's in his mind? They don't have a car. Don't possess We are having our breakfast right now. Eating You look tired, have a rest for a few hours. The rose smells wonderful. The woman is smelling the flowers in the garden. The cake tastes terrific. The cook is tasting the soup. I expect she'll pass the exam. We are expecting guests to the dinner tonight.

He used to live here. He was used to live here. When I was young, I would go fishing every Sunday. No, I didn't use to go there. I used to not go there. He would smile every time I mentioned her name. We would have breakfast on the roof. I told you the bus would arrive on time. Unreal Situations You would look better with short hair. I would buy a lottery ticket if I were you. It would be great if we had money but unfortunately we don't.

The old man asked a question. That is a good book. I found an old, black, cotton sweater. They are usually used in pairs. The woman, beautiful and smart, knew what she was doing. The winner, tired but happy, waved and smiled.

They come at the end of the sentence and they modify the subject. The tickets are expensive. She looked old. The oven felt hot. He was young and shy. A nice big house. A big square table.

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A lovely little town. An old plastic pipe. An expensive Scotch whiskey. A tall young woman. Intelligent young Danish scientist.

Because his job is boring at least to him , it caused him to be bored. I don't want to be with him because he is a boring person. Because your offer is interesting at least to him , it drew his attention.

He engages attention, you want to know him better. Expresses a quality without a comparison The twins are smart. The tree is tall. The book is old. Used to compare things to each other. Form Use Example Shorter adjectives er hotter area, warmer water 1 syllable or 2 longer adjectives more interesting subject, more more 2 or more syllables comfortable couch adjectives that end with ed , ing , 's' even if they are more I am more tired , more boring book 1 syllable Fred is taller than Barney.

He is the more aggressive of the two. Barney is smarter than Fred. Climbing is more tiring than running. The inflectional suffix for superlative degree is est. Longer superlatives usually take most instead of est. This is the brightest room in the house. Duncan is the tallest player on the team. Britney is the most beautiful girl in the class. There is no comparison.

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Dead, perfect, round You can't be deader than someone else who is only dead. Some Absolute Adjectives: But they are misusing absolute adjectives.

The prime minister said he strongly supported the NATO plan. Though she is pretty beautiful, her behaviors make her unattractive. My brother speaks English very well. He is very smart. A lion is a far more dangerous animal than a hyena. I am a lot faster than you think. My son is a bit sick today so he couldn't go to school. They mainly modify verbs. They tell us how, where, when Carol drives carefully.

How does she drive? I looked for her everywhere. Where did you look for her? She came to London yesterday. When did she come to London? Adverbs are generally divided into seven groups: Forming Adverbs They are generally made from adjectives.

Many adverbs of manner and degree are formed by putting -ly at the end of an adjectives. The weather was awfully cold. You should treat people gently. Please, drive the car slowly. Chuck passed the test easily. My mom brushes my hair gently every day. When an adjectives ends in -e, we keep -e and add -ly. Our army fought bravely. When an adjective ends in -ic, we add -ally.

Systematic - systematically Phonetic - phonetically We searched the attic systematically. Burns wanted us to write the words phonetically. Expresses a quality without a comparison. Ivan walks slowly. Expresses a higher or lower degree than the positive. Ida walks faster than Ivan. Brad walks the slowest. Adverbs having the same form as adjectives: Kenyans always win prizes in marathons because they run the fastest of all. Adverbs formed with —ly.

Elizabeth speaks English the most fluently. They do everything worse than us. Adverbs modify verbs, adjectives or other adverbs. And even more confusingly, some words sometimes act as adjectives, and sometimes act as adverbs.

Ask yourself which word is being described: Sarah was a little sleepy. This is the larger of the two rooms. This white one is the smallest of the three puppies. Good vs well Good is an adjective. The adverb is well. He runs very fast. She works very hard. The train arrived late. She hardly spoke to me. I don't think they should get married yet. They hardly know each other. Common adjectives: They are always followed by nouns or pronouns.

You bought the car for pounds. How cheap! Prepositions of place, position and direction. Prepositions of time.

Prepositions for other relationships. And, unlike most rules, this rule has no exceptions. They are always followed by a "noun", never followed by a verb. By "noun" we include: He lives in England. Henry is looking for you. The newspaper is under your green book. Pascal is used to English people.

She isn't used to working. We ate before coming. Subject Pronouns 2. Object Pronouns 3. They are used as the subject of a verb. They do the action. It is cold. It is the subject of is She paid today. They are always the object of the verb, preposition, or infinitive. She paid him today. I wanted her to come to the cinema with me. I am the subject of wanted; her is the object of wanted; him is the object of the preposition with Possessive Pronouns Mine, yours, his, hers, its, ours, theirs.

They show ownership, answering the question "Whose? Whose car is it? It is my car. It is mine. We use possessive pronouns as subject or object of a verb. Notice that "its" usually used as possessive pronoun. This is my tie - This is mine. Her umbrella is beautiful. These are his shoes. These are their wallets. It is my book. That is our school. This is our house.

That is my radio. Those tickets are Kimberley's. This is Henry's suitcase. They are my mother's keys. It's Lucy's chocolate. My cousins' grades are better. Elizabeth's cakes are delicious. It's in example 'l' is short form of It is and should not be confused with its. My cousins' grades in 'm' is not the same as my cousin's grades. In fact it means grades of my cousins and it is plural so we use the plural possessive pronoun theirs.

Apostrophe in It's and Possession 1. Carol loved chocolate more than him. Carol loved chocolate more than she loved him. Carol loved chocolate more than he. Carol loved chocolate more than he loved chocolate. You can avoid misunderstandings by writing: Carol loved chocolate more than James did. Carol loved chocolate more than she loved James. Myself, yourself, himself, herself, itself, ourselves, yourselves, themselves.

Use the right mirror pronoun to match the subject: He hit himself with the slingshot. They rescued themselves by selling their house. Reflexive pronouns may be used to emphasis. He himself finished all that work. I prepared the dinner by myself alone.

I solved the puzzle all by myself. Did you have fun? Please help yourself to some food. Go and get whatever you want How do you feel yourself?

We also use these and those when talking about more than one objects. This book is in my hand. That book is over there on the desk. These coins are in my hand. Those coins are over there on TV set. Convert from singular form to plural or plural to singular as in the examples below. This exercise is easy. These exercises are easy. Those socks are Sara's.

That sock is Sara's. These flowers are on the floor. That flower is on the floor. Transitions help fluency in writing and speaking.

Coordinating Conjunctions Coordinating conjunctions are short and simple transitions that are composed of two or three letters. They are used to avoid short, choppy, run-on etc. Correlative Conjunctions Transitions that always appear in pairs and link sentence elements together are called correlative conjunctions.

Subordinating Conjunctions Subordinating conjunctions connect the dependent clause of a sentence with the independent clause and show the relationship between the two.

We use a comma in between if the subordinator when, before, because, although Although it was raining, she went out for a walk. She went out for a walk although it was raining.

Because she was tired, she went straight to the bed. She went straight to the bed because she was tired. After she had made a phone call, she left home. She left home after she had made a phone call. In other words, cohesive devices make our content coherent. Overusing cohesive devices or not using them enough might affect the reader negatively. Here is a list of words and phrases used as cohesive devices: Phrase And Both Still Notwithstanding Adj.

Comparison similarly equally in the same way compared with like I can speak Spanish; similarly, my brother can speak Spanish. First I loved its museums. Secondly, I loved its people. Finally I loved its tourist attractions. Giving Examples for example for instance such as as follows namely I like small pets such as cats and birds.

Generalizing in general generally in most cases most of the time on the whole In general, people don't like getting up early. They are similar in meaning but they are used differently. Richard worked on his project all night although he was tired. They don't spend much money although they are rich. Andrew passed the exam although he didn't study at all.

Amber wants to go out although she is sick. Although it rained a lot, the students enjoyed their holiday. Berk won the prize in spite of the difficult conditions. They went on holiday in spite of the bad weather conditions.

Steve waited outside for 2 hours in spite of the cold. We arrived on time in spite of the traffic jam. In spite of all her careful plans, Laura made a lot of mistakes.

They didn't want to buy anything in spite of having a lot of money. There are two types of relative clauses 1 Defining 2 Non-defining Defining Relative Clauses Specify a particular noun. Use who, that The girl who is the best in our class is Nayad. The ring that was stolen from my room hasn't been found yet. Non-defining Relative Clauses They are used with an already defined noun, so; they just give extra information and we usually put commas around.

No need to define my father. Johnson is happy, he got the highest grade on the test. Johnson, who got the highest grade on the test, is happy. A dentist is a person. He gives dental treatment. We know a lot of people. They live in Minnesota. A vegetarian is a person. Do you know the man? He discovered Africa. The teacher was very strict. We had him last semester. The relative pronoun comes just after the word it refers to. The man was drunk. He caused the accident. The man who was drunk caused the accident.

That man is my uncle. He is coming towards us. This is the horse. I like him. It also kicked me yesterday. The nails are rusty. They are in the tool-box.