(1) Positive and negative numbers: the necessity of negative numbers; A quantity with opposite meaning.

⑵ Classification of rational numbers: integers and fractions are collectively called rational numbers; Integers include positive integers, zero and negative integers, and fractions include positive fractions and negative fractions.

(3) reciprocal, reciprocal and absolute value:

Only two numbers with different signs are anti-numbers, and the anti-number of a is-a;

The quotient obtained by dividing a number by 1 is the reciprocal of this number, and zero has no reciprocal;

The absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of zero is zero.

(4) Number axis: origin, positive direction and unit length are the three elements of number axis.

5] Comparison of rational numbers:

Method 1: zero is greater than all positive numbers and less than all negative numbers;

Two negative numbers, the larger one has the smaller absolute value.

Method 2: On the number axis, the number represented by the right point is always greater than that represented by the left point.

real number

First, knowledge combing:

1, the classification of real numbers. Rational number (positive rational number, 0, negative rational number), irrational number (infinite cycle decimal)

2. Related concepts of real numbers:

(1) square root: Generally speaking, if the square of a number is equal to, then this number is called the square root of. Positive numbers have two square roots, negative numbers have no square roots, and the square root of 0 is 0.

(2) Arithmetic square root: the positive square root of a positive number and the square root of zero are collectively called arithmetic square roots.

(3) Cubic root: the cube of a number is equal to A, and this number is called the cube root of A.

3. Real numbers correspond to points on the number axis one by one. Will represent some irrational numbers on the number axis.

Key points of knowledge

1. An integral equation that contains only one unknown quantity and the unknown quantity has one degree is called a linear equation with one variable.

2. The general steps to solve the linear equation are:

(1) denominator removal (2) bracket removal (3) moving items (4) merging similar items (5) converting unknown coefficients into "1"

3. The solution of unary linear equation ax=b:

(1) ax=b has a unique solution when a≠0.

(2) When a=0 and b≠0, ax=b has no solution.

(3) When a=0 and b=0, ax=b has infinite solutions.

Key points of knowledge:

1. Definition of factorization: A polynomial is transformed into the product of several _ _ _ _ _ _ _. Factorization and multiplication of algebraic expressions are mutual _ _ _ _ _ _.

2. The basic method of factorization:

(1) Extraction of common factor method (the first method to be considered), application of formula method, grouping decomposition method and cross multiplication.

(2) Formula: A2-B2 = _ _ _ _ _ _ _ A2AB+B2 = _ _ _ _ _ _,

a3+b3=____ ____，a3-b3=___ ____。

3. The general steps of factorization

Let's see if there are any common factors first, and if there are, put them forward immediately; Then look at the binomial formula, if binomial, use the square difference, cubic or cubic difference formula; If it is a trinomial, use the complete square formula or cross multiplication; If more than four formulas are decomposed in groups, it is necessary to pay attention to the decomposition until it can no longer be decomposed.

First, knowledge combing:

1, rational number addition, subtraction, multiplication, division, multiplication algorithm, mixed operation

2. Operation method: exchange method, correlation method, distribution method and bracket removal method.

The addition rule of (1) rational numbers;

1. Add two numbers with the same symbol, take the same symbol, and add the absolute values;

2. Add two numbers with different absolute values, take the sign of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value;

3. Add a number to zero and still get this number;

4. Two opposite numbers add up to zero.

(2) the subtraction rule of rational numbers:

Subtracting a number is equal to adding the reciprocal of this number.

Supplement: delete brackets and add brackets:

Rules for removing brackets: When there is a "+"in front of brackets, remove brackets and the "+"in front, and everything in brackets remains unchanged; When there is a "-"in front of the bracket, remove the bracket and the "-"in front, and all items in the bracket will be changed.

Parenthesis rule: put parentheses after the "+"sign, and everything in parentheses remains unchanged; Put brackets after the "-"sign, and all items in brackets should be changed.

(3) the multiplication rule of rational numbers:

① Multiply two numbers, the same sign is positive, the different sign is negative, and the absolute value is multiplied;

(2) Any number multiplied by zero will get zero;

③ Multiply several numbers that are not equal to zero. The sign of the product is determined by the number of negative factors. When the negative factor is odd, the product is negative. When the number of negative factors is even, the product is positive;

④ Multiply several rational numbers, and if one of them is zero, the product is zero.

(4) the division rule of rational numbers:

Rule 1: divide two rational numbers, the same sign is positive, the different sign is negative, and divide the absolute value;

Rule 2: dividing by a number is equal to multiplying the reciprocal of this number.

5. Power of rational number: the operation of finding the product of n identical factors is called power, and the result of power is called power.

Any positive power is positive; The odd power of a negative number is negative and the even power of a negative number is positive.

[6] rational number operation order:

First calculate the power, then multiply and divide, and finally add and subtract; If there are brackets, count them first and then count them out.

Once you run the law:

① commutative law of addition;

② the associative law of addition;

③ Commutative law of multiplication;

④ Multiplicative associative law;

⑤ Distribution law of multiplication to addition;

Note: Division has no distribution law.

3. scientific notation: express a number as a (1 ≤ a)

4. Exact numbers and divisors: numbers that are completely consistent with the reality are called exact numbers, and numbers that are close to the reality are called divisors. There are two ways to get the approximate value (1). For example, if 84960 is accurate to 10000 digits, you can get (2) significant digits: all digits from the first non-zero digit on the left to the last digit are called the significant digits of this number. For example, keep two significant digits of 84960:

Review outline of the seventh grade last semester

Unit 1 The Origin of China Civilization

The ancient inhabitants of China

Humans evolved from apes, and whether they can make tools is the fundamental difference between humans and animals.

The earliest ancient humans discovered in China;

Yuanmou people lived in Yuanmou County, Yunnan Province about1700,000 years ago.

Progress chart of comparison between cavemen and Beijingers;

A social organization that represents the concept of fire in the tool manufacturing of culture, physique and body.

Peking man kept some features of ape-man from 700,000 to 200,000 years ago, made rough stone tools, and set primitive people on fire naturally.

Neanderthals are about 30 thousand years ago, and their appearance is basically the same as that of modern people. He mastered polishing and drilling techniques to make artificial fires.

Know how to love beauty

Bury blood-related clans after death.

Lesson 2 primitive farming life

Two representatives of China's primitive farming life;

A place where primitive humans discovered production, activities, tools, houses and appliances.

The original inhabitants of Hemudu planted rice in Yuyao City, Zhejiang Province in the Yangtze River valley about 7000 years ago.

Raise livestock, grind stone tools, cultivate land, dry fence houses (wells), make pottery, jade, musical instruments and learn to spin.

The original inhabitants of Banpo were about five or six thousand years ago.

Shaanxi in the Yellow River Basin

Xi' an grows millet vegetables, raises pigs and dogs; Painted pottery with grinding stone tools and semi-basement houses is widely used for fishing and hunting (with the earliest text prototype on it)

China is the first country in the world to grow rice and millet (and also the first country to invent porcelain).

Dawenkou culture: polarization between the rich and the poor (root: development of productive forces)

★ Lesson 65438+0,2 Look at the corrected questions and the original test paper in Fine Analysis.

Lesson 3 China's ancestors

1. Why do China people often proudly call themselves "descendants of the Chinese people"?

1, Yan Di and Huangdi are the ancestors of the Chinese nation: Huangdi Tribe and Yan Di Tribe defeated Chiyou in Zhuolu and formed an alliance from then on. After a long period of development, the future Huaxia nation was formed. Huaxia nationality is the predecessor of the Han nationality and the backbone of the Chinese nation.

2. Huangdi: the ancestor of mankind. Build palaces, make clothes, dig wells, and invent boats and cars. (Lei Zu sericulture reeling, Cangjie word-making, Linglunle)

Second, abdication system: the way to democratically elect the leaders of tribal alliances (the leaders elected by abdication system are Yao, Shun and Yu). )

Dayu went to the mansion three times, but he didn't enter, which contributed to the water control.

Unit 2 the emergence of the state and social changes

Lesson 4 The Rise and Fall of Xia, Shang and Zhou Dynasties

First, the replacement of Xia, Shang and Zhou Dynasties.

The establishment of dynasties, the time of death, the capital, the founding monarch and the king of the country.

Xia Dynasty, about 2070 BC, about 65438 BC+0600 BC, Yucheng Yujie.

From 65438 BC to 1046 BC, the Shang Dynasty moved its capital many times, and Pan Geng moved its capital to Tang Yin.

65438 BC+0046 BC 7765438 BC+0 BC Haojiang, Zhou Youwang, Zhou Wuwang.

Zhou Pingwang, Luoyi, 770 BC, Eastern Zhou Dynasty.

Second, why can Shang Tang defeat Xia He?

Jay and Zhou are cruel and unpopular; The benevolence and righteousness of Shang Tang and Wu Wang won the hearts of the people; Appoint sages (Yi Yin, Jiang Shang) to unite with small neighboring countries.

Three. Xia, Shang and Zhou politics

1, Kay: Inherited his father's business and became the second generation king of Xia Dynasty. Since then, the hereditary system has replaced the abdication system, and the "public world" has become the "home world".

2. The establishment of various state institutions (including government agencies, military, criminal law and prisons, etc.). ) The Xia Dynasty marked the emergence of early countries.

3. The enfeoffment system in the Western Zhou Dynasty (purpose: to consolidate the rule)

Content: ① The son of heaven distributed the land and people to relatives and heroes and made them princes.

(2) Duties of princes: obey the orders of the Emperor of Zhou; Pay tribute to the emperor; Defend the territory in peacetime and lead troops to fight against the emperor in wartime. Significance: the remote areas were developed and the rule was strengthened, making the Western Zhou Dynasty a powerful country.

Lesson 5 Brilliant Bronze Civilization

The prosperity of agriculture, animal husbandry, handicrafts and commerce has formed a splendid bronze civilization in Xia, Shang and Zhou Dynasties.

First, the superb craftsmanship of bronzes (famous artists: Simu Wuding, Siyang Fangzun)

The characteristics of bronze casting in Shang and Zhou dynasties are: large scale, many varieties, fine craftsmanship and wide distribution.

Second, the development of agriculture and animal husbandry: The Xia, Shang and Western Zhou Dynasties were mainly agricultural societies with basically complete varieties.

Third, the miserable life of slaves: the splendid civilization at this time is at the expense of the miserable life of slaves.

Lesson 6 Disputes during the Spring and Autumn Period and the Warring States Period

First, the spring and autumn hegemony.

1. Famous overlords: Qi Huangong (logo: Kwai Meng), (logo: victory in the battle of Chengpu),.

2. What are the reasons why Qi Huangong and Jin Wengong became the hegemons? (Reform: developing production, training the army and rectifying internal affairs)

Qi Huangong appointed Guan Zhong as prime minister, carried out reforms, and won the hegemony of Chu Jin with the slogan of "respecting the king and rejecting foreign countries".

3. Impact: bring all kinds of disasters to society; However, in the war for hegemony, some vassal States were eliminated and some countries with vast territory appeared.

Second, the Seven Heroes of the Warring States: Qi, Chu, Yan, Han, Zhao, Wei and Qin (pay attention to the position)

Famous battles: the battle of Guiling, the battle of Maling and the battle of Changping (the battle of Changping, the six eastern countries were unable to resist Qin Jun's attack)

★ Idioms related to this lesson: Stay out of it, submit to humiliation, encircle Wei to save Zhao, and talk on paper (pay attention to which war it is).

Lesson 7 the era of great change

First of all, economically

1, iron farm tools and the popularization of Niu Geng (Niu Geng is a revolution in the history of agricultural development)

2. The famous Dujiangyan: Li Bing, the prefect of Shu County, Qin State Location: the middle reaches of Minjiang River in Chengdu Plain

Significance: Dujiangyan eliminated the flood of Minjiang River, irrigated a large area of farmland, and made Chengdu Plain gain the reputation of "Land of Abundance".

Second, politically-Shang Yang's political reform.

① Time: 356 BC ② Character: Shang Yang carried out political reform with the support of Qin Xiaogong.

Objective: To establish feudal rule, develop feudal economy and be invincible in hegemony.

④ Content and influence:

content

affect

Reward farming

Reward production (people who produce more grain and cloth can avoid corvee) economic development and the country is rich. In short, Shang Yang's reform established a feudal system, which made Qin the most prosperous country in the late Warring States period and laid the foundation for Qin to unify the whole country.

Reward the military (according to the size of the military, the title of Hotan Prefecture). The combat effectiveness of the army is enhanced and the soldiers are strong.

Recognize private ownership of land, allow free trading and establish feudal land ownership.

Establish a county system: the monarch directly sends officials to govern and strengthen centralization

Lesson 8 and Lesson 9 The Prosperity of China Culture

First, the evolution of the text

Time, Shang and Zhou Dynasties, Late Western Zhou Dynasty, Warring States Period

Oracle Bone Inscriptions Copper Seal Bamboo Slips and Silk Books

Materials tortoise shell, animal bones, bronze bamboo slips, silks.

The history of China's writing began in Shang Dynasty (Oracle Bone Inscriptions is a relatively mature writing).

Two. Achievements in astronomy, calendar, medicine and literature

The earliest solar eclipse recorded in astronomical ancient books took place in the Xia Dynasty.

There are many records about solar and lunar eclipses in Oracle Bone Inscriptions in Shang Dynasty, which are very reliable by modern scientists.

Calendar According to legend, there was a calendar in Xia Dynasty, and the calendar in Shang Dynasty was more complete.

During the Warring States period, 24 solar terms were defined in one year.

Bian Que, a famous doctor of medicine, has always been used by Chinese medicine.

Literature Qu Yuan and His Masterpiece Li Sao

The music "Bell and Drum Music" prevailed in chimes unearthed in Suizhou, Hubei Province during the Spring and Autumn Period and the Warring States Period.

Third, a hundred schools of thought contended during the Spring and Autumn Period and the Warring States Period.

Ideological Content of Representative Works in School Period

The political thought of Confucian Analects in the Spring and Autumn Period-Benevolence, Love and Rule by Virtue.

Educational thought: teach students in accordance with their aptitude, be modest and eager to learn, and learn new things by reviewing old ones.

Mencius in the Warring States period ruled the country with benevolence, paid taxes lightly and used resources sustainably.

Everything in Laozi's Tao Te Ching in the Taoist Spring and Autumn Period is antagonistic, and the opposing sides can be transformed into each other.

During the Warring States Period, Zhuangzi let nature take its course and ruled by doing nothing.

Universal Love by Mozi in the Warring States Period: I hope people can help each other and love each other.

"Non-aggression": Oppose the war of aggression and support the just war.

Legalist Han Feizi advocated reform; Advocate the rule of law; Put forward the establishment of a feudal country with absolute monarchy and centralization.

Sun Tzu's art of war, a strategist "know yourself and know yourself, and you won't be defeated."

★ Solve the problem with three viewpoints: Confucianism: persuasion education; Tao: Let nature take its course; Law: strict regulations and effective punishment

Unit 3 the establishment of a unified country

Lesson 10 "The King of Qin swept Liuhe"

A, the unification of the qin dynasty:

22 BC1Capital: Xianyang Founding Emperor: Qin Shihuang Ying Zheng.

Significance: It ended the infighting situation that lasted for hundreds of years since the Spring and Autumn Period and the Warring States Period, and created a new situation of unification. Since then, reunification has been the mainstream of China's historical development.

Second, measures to consolidate reunification.

Impact of measures

The political system of centralization and absolutism has been used in China for more than two thousand years, which has had a far-reaching impact on the history of China.

Economic unity, currency and weights and measures have great influence on promoting economic and cultural exchanges and safeguarding national unity.

Cultural unity writing

Burning books to bury Confucianism destroys culture and limits people's thinking.

The Military Construction of the Northern Great Wall and the Development of Southern Xinjiang

(Unifying Lingnan and Building Lingqu) The Qin Dynasty has a vast territory and became the first unified multi-ethnic centralized country in the history of China.

★ Qin Shihuang's evaluation: a monarch with great achievements in China history (historical facts); But there is also a cruel side (historical facts); The overall work is greater than the excess.

Lesson 1 1 "Killing Qin without virtue"

First, the tyranny of the Qin dynasty

(1) Heavy corvee and taxes (two-thirds) (2) Severe criminal law (3) More cruel (Zhao Gao "refers to a deer as a horse").

The tyranny of the Qin dynasty seriously damaged the social economy, increased the burden and pain of the people, and aroused the people's resistance.

Second, Chen Guang Uprising (Uprising)

Time: 209 BC Uprising Location: Xiangguan, osawa: Slightly rooted in the tyranny of Qin.

Significance: The first large-scale peasant uprising in China's history, and their revolutionary pioneering spirit inspired millions of working people in later generations to rise up against brutal rule.

Third, the peasant rebels overthrew the Qin Dynasty.

Xiang Yu: The Battle of Julu defeated Qin Jun's main force. (burn one's bridges)

Liu Bang: The rulers of the Qin Dynasty surrendered to Liu Bang, and the Qin Dynasty perished.

The dispute between Chu and Han: 206 BC-202 BC,

★ Related idioms: Xiang Zhuang dances sword, which means stories such as Pei Gong, Chu River and Han Dynasty, besieged on all sides, farewell to my concubine, etc. : Hongmen Banquet.

Establishment of the Western Han Dynasty: In 202 BC, Liu Bang established the Han Dynasty with Chang 'an as its capital. Liu bang is the emperor gaozu.

Unified Han dynasty

First, the rule of Wenjing (historically, the rule of Wendi Jingdi was called "the rule of Wenjing")

1. reason: ① situation in the early Han dynasty: economic depression and ethnic poverty. (2) Summarize the lessons of Qin Dynasty's death from tyranny.

2. Measures: ① Pay attention to the development of agricultural production and reduce people's burden; 2 advocating economy; (3) advocate "remoulding people by virtue"

Second, the unification of Emperor Wu of Han Dynasty

Impact of background measures

The political vassal States that were enfeoffed in the early Han Dynasty still had considerable power to "push the favor order" and weaken the enfeoffment right. (Zhu's suggestion) The vassal states are no longer able to confront the central authorities.

think

Schools of thought are still active. They criticized the emperor's policies and accused the central authorities, which was very unfavorable to centralization. "oust a hundred schools of thought and respect Confucianism alone"; (Dong Zhongshu's suggestion)

The Five Classics of Confucianism is the main textbook of imperial academy.

Confucianism became the orthodox thought of feudal culture.

During the period of Emperor Wu of the Han Dynasty, the Western Han Dynasty achieved great unification and entered its heyday, which was also the first heyday of China's feudal era.

Fourth, the establishment of the Eastern Han Dynasty: the capital was established in 25 AD: Luoyang, and the founding emperor: Emperor Guangwu Liu Xiu.

Economic development in Han dynasty

1. Harnessing the Yellow River: In the Western Han Dynasty, Emperor Wu of the Han Dynasty ordered the harnessing of the Yellow River; In the Eastern Han Dynasty, Ming Di sent Wang Jing to preside over the river repair.

Agricultural progress: In the Western Han Dynasty, methods such as plowing the wall (turning over the soil and breaking the soil), plowing the car (sowing tools), and two cows lifting the bar appeared.

Second, silk weaving: using jacquard machine; The dyeing technology is also very high, and silk is liked by foreigners.

Smelting technology: Du Fu-shi invented the water grate (a tool for iron processing) in the Eastern Han Dynasty, which was 1000 years earlier than that in Europe. Iron weapons replace bronze weapons.

Third, economic measures to strengthen centralization: Emperor Wu of the Han Dynasty restored the right to coin and the right to operate salt and iron to the central government, and unified the casting of five baht (economic unity). Business prosperity: East and West Beijing (Xijing Chang 'an, Tokyo Luoyang); Professional business district: city. (But the rulers practice "emphasizing agriculture and restraining commerce")

The Rise of Xiongnu and Its Peace War with Han Dynasty