I. Vocabulary

I simple past tense

The simple past tense indicates the action or state of a past time, and is often used with adverbials indicating the past time. Like yesterday, last weekend, last Saturday and so on. Basic sentence pattern: subject+verb past tense+others. What did you do last week? What did you do last week?

I played football last weekend. I played football.

★ Formation of the past tense of regular verbs

In general, -ed is added to the end of the verb prototype. Example: Play—Played.

3. Add -d directly to verbs ending in e, for example, dance—danced.

3. For stressed closed syllable words with only one consonant at the end, first double the consonant letters and then add -ed. For example, stop-stop.

4. For verbs ending in "consonant +y", change "y" to "i" and add -ed, for example, study-studied.

★ Past tense of some irregular verbs

Am/is-was-was-was-was-was-was-was-was-was-was-was-was-go-go swimming-fly-fly-

Begin-begin think-think find-found run-ranbuy-buy-buy twin-won give-giving-sangleave-leftware (listening) heart wear-wear

Ⅱ simple present tense

The simple present tense indicates the behavior or state of being that often occurs in a period of time including the present time, and indicates the habitual or objective facts and truth. Often used with oft, always, naturally, some times, every day, etc. Basic sentence patterns are divided into two situations:

● Subject (non-third person)+verb prototype+others. Example: What do you usually do on weekends? I usually do my homework on weekends.

● Subject (third person)+third person singular form of verb+others. Example:

What does Sarah usually do on weekends? What does Sarah usually do on weekends?

She usually does her homework on weekends.

★ The Changing Rule of the Third Person Singular Form of Verbs

Generally, -s is added directly after the verb. Like playing-playing.

2. verbs ending in s, x, ch and sh+es. For example: watch-watch

3. Verbs ending in consonants plus Y, change Y to I, and then add es, such as fly-flies.

3. Individual verbs with irregular changes need to be memorized separately, such as do-does go-goes.

Ⅲ present continuous tense

The present continuous tense indicates what the speaker is doing now. Basic sentence pattern: subject +be+ verb -ing+ others.

For example:-What are you doing? What are you doing?

I'm doing my home.-I'm doing my homework.

★ The changing law of verb present participle

1. Generally, add ing directly after the word, for example; Wash-wash

For verbs ending in the silent letter e, remove e and add ing. For example, make-making.

3. For stressed closed syllable words with only one consonant at the end, double the last consonant and add ing. Like swimming-swimming.

Ⅳ simple future tense

The simple future tense indicates the action or state of a certain time or period in the future. Often used with future time, such as tomorrow, next week, this afternoon, etc. We usually use the prototype of the verb will, be going to+, to express the general future tense. Basic sentence pattern: subject+will+verb prototype+others. Or subject +be to+ verb prototype+other.

I will go to Beijing tomorrow. I'm going to Beijing tomorrow. I plan to travel to Beijing tomorrow.

Comparative degree of ⅴ adjectives

Composition of comparative degree of adjectives

1. generally add -er at the end of the word. For example, high-higher.

4. for words ending in e, add-r. For example, late-—late

3. For words that end with stressed closed syllables and have only one consonant at the end, you should double the consonants and add -er.

For example, big-bigger

2. change y to I, and then add -er to the disyllabic words ending in consonants and y. For example, easy—easy

2. Irregular changes

Good-better-worse-worse-more/less.

Usage of comparative degrees of three adjectives

Express the comparison between the two (people or things). Basic sentence pattern: A+be+ comparative +than+B

Example: Mike is taller than me. Mike is taller than me.

A+be+ number+unit+comparative +than+B

For example, Zhang Peng is 4 centimeters taller than Mike. Zhang Peng is 4 centimeters taller than Mike.

ⅵ pronoun

Personal nominative objective adjective possessive pronoun noun possessive pronoun

First person singular plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural plural

I, we, we, I, we, my, our, our.

The second person calls you you, you, you, you, you, you, you, you, you, you.

What is the third person?

she

Is it him?

she

this is his

she

This is theirs.

she

This is theirs.

VII noun

1) master the changing law of noun plural;

1. Most nouns are plural, and s is added directly at the end. Example: Books-Books

2. generally add the example of es. End with s, sh, x, ch; Watch-watch

3. for nouns ending in consonants and y, change y into I and add es. Examples; Family-family

4. For nouns ending in F and Fe, in most cases, F and Fe are generally changed into the case of V plus es; Leaves-leaves

5. Nouns ending in the letter O become plural, and in most cases, S is added, but in some cases, ES is added; Piano-piano

Photo-photo radio-radio tomato-tomato

There are exceptions to the above situation, such as; Some nouns ending in -f are pronounced as /s/ only when they are plural. Bay-bay

2) Irregular plural forms of nouns need to be memorized separately. For example: feet-feet-men-women-women.

Children-children sheep-sheep people-people.

Ⅷ number

Numerals are divided into cardinal words and ordinal cardinal words, which are used to indicate the number of countable nouns, such as one, two, three and four. Ordinal numbers indicate order, such as: first, seond. Third, fourth, etc. It can be abbreviated to Arabic numerals with two letters at the end, for example: 1st, 2nd, 3rd.

Ordinal number is converted from cardinal number, which means "first". . . . . . One "

1-3 is the first, second, third and third respectively, which is irregular.

4- 19 is usually composed of cardinal words plus th, and the special ones are: 55, 88 and 99.

, one twelfth

The suffix -ty of integer numbers should be changed to tie first and then -th. For example (example)

The twentieth session.

Two digits only change the last numeral into an ordinal number, and the previous numeral still retains its cardinal form.

For the first time in the 21st century.

The expression of ⅸ month

The month can be used alone or together with the year and day. The first letter of the month word is always capitalized.

1. Add the preposition in before the month, which means "in ..."

January has thirty-one days.

There are thirty-one days in January

When month is used with year, it is preceded by the preposition in, which means "in"

The meaning of "month" is like (example)

The 2008 Olympic Games will be held in August 2008.

The 2008 Olympic Games will be held in August 2008.

If a specific date is specified, it will be preceded by the preposition on. For example (example)

Every year1February 25th is Christmas.

Christmas is on February 25th every year, 65438.

I'm going to visit the Great Wall on April 6th, 2007.

I will visit the Great Wall on April 6th, 2007.

★ Knowledge expansion ★ The date order in English is month, day and year, which is completely different from that in Chinese.

▲ abbreviation of month

English abbreviation of month English full name of month English abbreviation English full name

January January July July July

February February February August August

March March March September September September

April April October October October October

May May November November November November

June June June December December December

▼ Attention ▼

In English, May itself is three letters, so there is no abbreviation. June and July can be abbreviated to the first three letters or not. The abbreviations of September are generally the first four letters, and the abbreviations of other months are the first three letters.

The usage of some special interrogative words.

● What to ask questions about unknown things. For example:

What's your name? My name is Amy. What's your name? My name is Amy.

Question: What is this? This is a desk. ..

Ask occupation: What do you do? = What are you? What do you do? I'm a teacher? I am a teacher.

Asking about the illness: What's the matter? I have a headache. What's the matter with you? I have a headache.

Ask hobbies: What are your hobbies? I like reading. What's your hobby? I like reading. (Note: When two verbs appear in a sentence continuously, the latter verb should be changed into gerund form, that is, the -ing of the verb.

What's your favorite food? My favorite food is hot dogs. What's your favorite thing? I like hot dogs.

Q: What time is it? = What time is it? It's seven o'clock. What time is it now? It's seven o'clock.

What color are bananas? It is yellow. What color are bananas? It is yellow.

● Where to ask questions. For example: Where is my pen? It is on the desk.

● Which is used to choose one of two or more things, such as which season do you like best? I like summer best. Which season do you like best? I like summer best. What's your favorite season? My favorite season is summer. What's your favorite season? I like summer best.

● why is used to ask the reason. Because it is usually used to answer. For example: Why do you like summer? Because I can swim. Why do you like summer? Because I can swim in summer.

When is used to ask the time, which translates as "when". What time do you get up every day? I usually get up at six. What time do you get up every day? I usually get up at six in the morning.

● How is mainly used to ask questions such as ways, means and methods. How, how, in what way, for example: how do you go to school? I go to school by bus. How do you go to school? I go to school by bus. In addition, how has the following other uses:

Greetings: How are you? I'm fine, thank you. How are you? I'm fine, thank you.

Weather forecast: What's the weather like in Beijing? It's sunny. What is the weather like in Beijing? It's sunny.

Ask Age: How old are you? M 1 1 year. How old are you? I am eleven years old.

Ask height: How tall are you? My height 160 cm. How tall are you? My height 160 cm.

Q: How much does Mike weigh? He weighs 40 kilograms. How much does Mike weigh? He weighs 40 kilograms.

Size: How big are your feet? I wear size 16? How big are your feet? I wear shoes of size 16.

Question area: How big is your classroom? S 30 ㎡。 How big is your classroom? 30 square meters.

Q: How many books do you have? I have 12. How many books do you have? I have twelve copies.

(After how many, add the plural form of countable nouns)

Ask the price: How much is the shirt? S yuan. How much is that shirt? 30 yuan.

How do you feel? I feel sad. How do you feel? I am sad.

The seventh article

Articles are divided into definite articles and indefinite articles.

The indefinite article includes a, an stands for a, and modifies singular nouns. A is used before the countable noun singular at the beginning of consonant phoneme, such as a book, an is used before the countable noun singular at the beginning of vowel phoneme, and apple is an apple.

▲ the definite article "the" is used before a specific noun or the above nouns. You can modify both countable nouns and uncountable nouns, and there is no limit to singular and plural numbers.

Demonstrative pronouns this, that, these, those

This and these both indicate that there is something near the speaker. This is used to modify the singular and these are used to modify the plural.

That and that both mean something far from the speaker, that is used to modify the singular and that is used to modify the plural.

▲ Note: this and that can also modify uncountable nouns.

Second, sentence patterns.

★ The method of changing affirmative sentences into general interrogative sentences.

If there are be verbs am, is, are, was and were in the sentence, put them directly at the beginning of the sentence. If the personal pronoun in a sentence is the first person, it is converted into the second person, and if it is the second person or the third person, it remains unchanged. That is, I, we become you; ; My, our becomes your, and then copy down the remaining words in the sentence. For example, I was at home yesterday.

There are no be verbs in the sentence, but modal verbs can, may, must, will, etc. Put modal verbs can, may, must, will, etc. At the beginning of the sentence. If the personal pronoun in a sentence is the first person, it will be converted into the second person. If the personal pronoun is in the second person or the third person, it remains the same. That is, I, we become you; ; My, our becomes your, and then copy down the remaining words in the sentence. Modal verbs should be followed by verb prototypes. I can play football. Can you play football?

3. If there is no be verb or modal verb in the sentence, change it with the help of verbs, that is, add do, does or did at the beginning of the sentence. If the personal pronoun in a sentence is the first person, it is converted into the second person, and if it is the second person or the third person, it remains unchanged. That is, I, we become you; ; My, our becomes your, and then copy down the remaining words in the sentence. But in the process of copying, we should change the verbs back to their original forms. The choice of auxiliary verbs should change according to the change of sentence tense and subject. Example: She cleaned her home last night. Did she do her homework last night?

★ Rules for answering general questions

Generally speaking: affirmative answer: yes, personal pronoun+corresponding auxiliary verb or be verb or modal verb. In other words, whoever guides this general question will be used to answer it.

Negative answer: no, personal pronoun+corresponding auxiliary verb or be verb or modal verb and not.

★ The method of changing affirmative sentences into negative sentences

If there are be verbs am, is, are, was, was and modal verbs can, may, must, will, etc. In the sentence, add not after be verbs am, is, are, were and modal verbs can, may, must, will, etc. Example: I can play basketball. I can.

If there is no be verb or modal verb in the sentence, use verbs to change it, that is, add Don, not and dot before the verb and after the subject, and then copy down the remaining words in the sentence. But in the process of copying, we should change the verbs back to their original forms. The choice of auxiliary verbs should change according to the change of sentence tense and subject. He played football yesterday. I didn't play football yesterday.

The difference between there be sentence pattern and have:

This sentence pattern means that there is something somewhere. The basic sentence pattern is: there is+something+place. And there is an adjacency principle in sentence structure, that is, when the noun closest to the be verb is singular, the be verb is IS, and when it is plural, the be verb is are. There is an English book and two Chinese books on the desk. There are two Chinese books and an English book on the desk. There are two Chinese books and an English book on the desk.

▲ Note: Several commonly used prepositions indicating places are,

In is in ... or added before some taxi locations. For example, in Beijing, it is in Beijing.

On the table, for example, on the table.

The back is the back, for example, the back of the door is the back of the door.

Close is close, for example, close to the window is close to the window.

For example, next to the post office next to the post office. Next to the post office.

For example, the tree is in front of our classroom.

For example, under the table.

⒉have/has indicates that someone owns something and indicates affiliation. Basic sentence pattern: subject (not the third person) +have+ something.

Or subject (third person) +has+ something. For example, I have a new bike. I have a new bike.

She has a new dress. She has a new dress. In addition, have has other uses, such as

Have lunch, drink some coke and have a headache.

Have fun, have fun.

Usage of it's time for and It's time to

Both of these sentence patterns mean "what to do", but it's time to add nouns. For example, it's time for lunch. It's time for lunch

It's time to add verbs. For example, it's time to get up. Time to get up.

★ Words indicating the week

Monday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday and Sunday (note: use the preposition on before week, and the first letter must be capitalized)

★ If there are four seasons.

Spring Spring summer summer Autumn/Autumn Winter Winter (use preposition before the season)

Review of primary school mathematics

Chapter I Number and Number Operation

A concept

(1) integer

The meaning of 1 integer

Natural numbers and 0 are integers.

2 natural number

When we count objects, 1, 2, 3 ... the numbers used to represent the number of objects are called natural numbers.

There is no object, which is represented by 0. 0 is also a natural number.

3 counting unit

One, ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million, one hundred million ... are all counting units.

The propulsion rate between every two adjacent counting units is 10. This counting method is called decimal counting method.

4 digits

Counting units are arranged in a certain order, and their positions are called numbers.

Divisibility of 5 numbers

When the integer A is divided by the integer b(b ≠ 0), the quotient is an integer with no remainder, so we say that A is divisible by B, or that B is divisible by A. ..

If the number A is divisible by the number B (b ≠ 0), then A is called a multiple of B, and B is called a divisor of A (or a factor of A). Multiplication and divisor are interdependent.

Because 35 is divisible by 7, 35 is a multiple of 7, and 7 is a divisor of 35.

The divisor of a number is finite, in which the smallest divisor is 1 and the largest divisor is itself. For example, the divisor of 10 is 1, 2,5, 10, where the smallest divisor is 1 0 and the largest divisor is 10.

The number of multiples of a number is infinite, and the smallest multiple is itself. The multiple of 3 is: 3, 6, 9, 12 ... The minimum multiple is 3, but there is no maximum multiple.

Numbers in units of 0, 2, 4, 6 and 8 can be divisible by 2, for example, 202, 480 and 304 can be divisible by 2. .

Numbers in units of 0 or 5 can be divisible by 5, for example, 5,30,405 can be divisible by 5. .

The sum of the numbers in each bit of a number can be divisible by 3, so this number can be divisible by 3. For example, 12,108,204 can all be divisible by 3.

The sum of each digit of a number can be divisible by 9, and so can this number.

A number divisible by 3 may not be divisible by 9, but a number divisible by 9 must be divisible by 3.

The last two digits of a number can be divisible by 4 (or 25), and this number can also be divisible by 4 (or 25). For example,16,404 and 1256 can all be divisible by 4, and 50,325,500 and 1675 can all be divisible by 25.

The last three digits of a number can be divisible by 8 (or 125), and this number can also be divisible by 8 (or 125). For example,1168,4600,5000, 12344 can all be divisible by 8, and 1 125,13375,5000 can all be/kloc-.

A number divisible by 2 is called an even number.

Numbers that are not divisible by 2 are called odd numbers.

0 is also an even number. Natural numbers can be divided into odd and even numbers according to their divisibility by 2.

A number with only two divisors of 1 is called a prime number (or prime number), and the prime numbers within 100 are: 2, 3, 5, 7,1,13, 17.

If a number has other divisors besides 1 and itself, then it is called a composite number. For example, 4, 6, 8, 9 and 12 are all complex numbers.

1 is not a prime number or a composite number, and natural numbers are either prime numbers or composite numbers except 1. If natural numbers are classified according to the number of their divisors, they can be divided into prime numbers, composite numbers and 1.

Every composite number can be written as the product of several prime numbers. Every prime number is a factor of this composite number, which is called the prime factor of this composite number. For example, 15=3×5, and 3 and 5 are called prime factors of 15.

Multiplying a composite number by a prime factor is called prime factor decomposition.

For example, decompose 28 into prime factors.

The common divisor of several numbers is called the common divisor of these numbers. The largest one is called the greatest common divisor of these numbers. For example, the divisor of 12 is 1, 2, 3, 4, 6,12; The divisors of 18 are 1, 2,3,6,9 and 18. Where 1, 2,3,6 are the common divisors of 12 and 1 8, and 6 is their greatest common divisor.

The common divisor is only 1, which is called prime number. There are the following situations:

1 is coprime with any natural number.

Two adjacent natural numbers are coprime.

Two different prime numbers are coprime.

When the composite number is not a multiple of the prime number, the composite number and the prime number are coprime.

When the common divisor of two composite numbers is only 1, these two composite numbers are coprime. If any two numbers are coprime, they are said to be coprime.

If the smaller number is the divisor of the larger number, then the smaller number is the greatest common divisor of these two numbers.

If two numbers are prime numbers, their greatest common divisor is 1.

The common multiple of several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers. For example, the multiple of 2 is 2,4,6,8, 10, 12, 14, 16, 18. ...

The multiple of 3 is 3,6,9, 12, 15, 18 ... where 6, 12, 18 ... are the common multiples of 2 and 3, and 6 is their least common multiple. .

If the larger number is a multiple of the smaller number, the larger number is the least common multiple of the two numbers.

If two numbers are prime numbers, then the product of these two numbers is their least common multiple.

The common divisor of several numbers is finite, while the common multiple of several numbers is infinite.

(2) Decimals

The meaning of 1 decimal

Divide the integer 1 into 10, 100, 1000 ... a tenth, a percentage, a thousandth ... can be expressed in decimals.

One decimal place indicates a few tenths, two decimal places indicate a few percent, and three decimal places indicate a few thousandths. ...

Decimal system consists of integer part, decimal part and decimal part. The point in the number is called the decimal point, the number to the left of the decimal point is called the integer part, and the number to the right of the decimal point is called the decimal part.

In decimals, the series between every two adjacent counting units is 10. The propulsion rate between the highest decimal unit "one tenth" of the decimal part and the lowest unit "one" of the integer part is also 10.

2 Classification of decimals

Pure decimals: Decimals with zero integer parts are called pure decimals. For example, 0.25 and 0.368 are pure decimals.

With decimals: decimals whose integer part is not zero are called with decimals. For example, 3.25 and 5.26 are all decimals.

Finite decimals: The digits in the decimal part are finite decimals, which are called finite decimals. For example, 4 1.7, 25.3 and 0.23 are all finite decimals.

Infinite decimal: The digits in the decimal part are infinite decimal, which is called infinite decimal. For example: 4.33...3. 145438+05926 ...

Infinite acyclic decimal: the decimal part of a number with irregular arrangement and unlimited digits. Such decimals are called infinite cyclic decimals. For example: ∈

Cyclic decimal: the decimal part of a number, in which one or several numbers appear repeatedly in turn, is called cyclic decimal. For example: 3.555 … 0.0333 …12.15438+009 …

The decimal part of cyclic decimal is called the cyclic part of cyclic decimal. For example, the period of 3.99 ... is "9", and the period of 0.5454 ... is "54".

Pure cyclic decimal: the cyclic segment starts from the first digit of the decimal part, which is called pure cyclic decimal. For example: 3.111.5656 ...

Mixed cycle decimal: the cycle section does not start from the first digit of the decimal part. This is called mixed cyclic decimal. 3. 1222 …… 0.03333 ……

When writing a cyclic decimal, for simplicity, the cyclic part of the decimal only needs one cyclic segment, and a dot is added to the first and last digits of this cyclic segment. If there is only one number in the circle, just click a point on it. For example: 3.777 ... Jane writing 0.5302302 ... Jane writing.

(3) scores

1 significance of the score

Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction.

In the score, the middle horizontal line is called the dividing line; The number below the fractional line is called the denominator, indicating how many copies the unit "1" is divided into on average; The number below the fractional line is called the numerator, indicating how many copies there are.

Divide the unit "1" into several parts on average, and the number representing one part is called fractional unit.

2 Classification of scores

True fraction: The fraction with numerator less than denominator is called true fraction. The true score is less than 1.

False fraction: Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. False score is greater than or equal to 1.

With fraction: False fraction can be written as a number consisting of integer and true fraction, which is usually called with fraction.

3 Reduction and comprehensive score

Changing a fraction into a fraction equal to it, but with smaller numerator and denominator, is called divisor.

The denominator of a numerator is a fraction of a prime number, which is called simplest fraction.

Dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called the total score.

4) Percentage

1 indicates that one number is the percentage of another number, which is called percentage, also called percentage or percentage. Percentages are usually expressed as "%". The percent sign is a symbol indicating percentage.