1. 1 positive and negative numbers
A number with a negative sign "-"in front of a number that is not 0 is called a negative number.
It has the opposite meaning to negative number, that is, I learned that numbers other than 0 are called positive numbers (sometimes "+"is added before positive numbers as needed).
1.2 rational number
Positive integers, 0 and negative integers are collectively called integers, and positive and negative fractions are collectively called fractions.
Integers and fractions are collectively called rational numbers.
Numbers are usually represented by points on a straight line, which is called the number axis.
Three elements of number axis: origin, positive direction and unit length.
Take any point on a straight line to represent the number 0, and this point is called the origin.
Numbers with only two different signs are called opposites. (Example: the reciprocal of 2 is-2; The reciprocal of 0 is 0)
The distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A, and it is recorded as |a|.
The absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0. Two negative numbers, the larger one has the smaller absolute value.
Addition and subtraction of rational number 1.3
Rational number addition rule:
1. Add two numbers with the same sign, take the same sign, and then add the absolute values.
2. Add two different symbols with different absolute values, take the symbol of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value. Two opposite numbers add up to 0.
When a number is added with 0, it still gets this number.
Rule of rational number subtraction: subtracting a number is equal to adding the reciprocal of this number.
Multiplication and division of rational number 1.4
Rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0.
Two numbers whose product is 1 are reciprocal.
Rational number division rule: dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.
Divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Divide 0 by any number that is not equal to 0 to get 0. mì
The operation of finding the product of n identical factors is called power, and the result of power is called power. In the n power of a, a is the base and n is the exponent.
The odd power of a negative number is negative and the even power of a negative number is positive. Any power of a positive number is a positive number, and any power of 0 is 0.
Scientific counting method is used to express numbers greater than 10 as the n power of a× 10.
From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number.
Chapter II One-variable Linear Equation
2. 1 From Formula to Equation
An equation is an equation with unknowns.
All equations contain only one unknown (element) X, and the exponent of the unknown X is 1 (degree). Such an equation is called a linear equation with one variable. Solving the equation is to find the value of the unknown quantity that makes the left and right sides of the equation equal, and this value is the solution of the equation.
Properties of the equation:
1. Add (or subtract) the same number (or formula) on both sides of the equation, and the result is still the same.
2. Both sides of the equation are multiplied by the same number, or divided by the same number that is not 0, and the results are still equal.
2.2 Starting from the Ancient Algebra Books-Discussion on the Linear Equation of One Variable (1)
Moving the sign of the term on one side of the equation to the other side is called moving the term.
The third chapter is the preliminary understanding of graphics.
3. 1 color graphics
Geometry is also called solid for short. What surrounds the body is the surface.
3.2 Lines, rays and line segments
Axiom of line segment: Of all the connecting lines between two points, the line segment is the shortest (between two points, the line segment is the shortest).
The length of the line segment connecting two points is called the distance between these two points.
3.3 Angle measurement
1 degree =60 minutes 1 minute =60 seconds 1 fillet =360 degrees 1 flat angle = 180 degrees.
3.4 Angle comparison and operation
If the sum of two angles is equal to 90 degrees (right angle), they are said to be complementary angles, that is, each angle is the complementary angle of another angle.
If the sum of two angles is equal to 180 degrees (flat angle), it is said that the two angles are complementary, that is, each angle is the complement of the other angle.
The complementary angles of equal angles (same angles) are equal.
The complementary angles of equal angles (same angles) are equal.
Chapter IV Data Collection and Arrangement
Collecting, sorting, describing and analyzing data is the basic process of data processing.
Chapter V Intersecting Lines and Parallel Lines
5. 1 intersection line
The vertical angles are equal.
One and only one straight line is perpendicular to the known straight line.
Of all the line segments connecting a point outside the straight line with a point on the straight line, the vertical line segment is the shortest (in short, the vertical line segment is the shortest).
5.2 parallel lines
After a point outside the straight line, there is one and only one straight line parallel to this straight line.
If both lines are parallel to the third line, then the two lines are also parallel to each other.
Conditions of parallel lines:
Two straight lines are cut by a third straight line. If congruent angles are equal, two straight lines are parallel.
Two straight lines are cut by a third straight line. If the internal angles are equal, two straight lines are parallel.
Two straight lines are cut by a third straight line. If they are complementary, then these two straight lines are parallel.
5.3 Properties of parallel lines
Two parallel lines are cut by a third straight line and have the same angle.
Two parallel lines are cut by a third line, and their inner angles are equal.
Two parallel lines intersect with the third straight line, which complement each other.
A statement that judges a thing is called a proposition.
Chapter VI Plane Cartesian Coordinate System
6. 1 plane rectangular coordinate system
A word containing two numbers represents a definite position, where the two numbers represent different meanings. We call this number pair consisting of two numbers A and B in sequence an ordered pair.
Chapter VII Triangle
7. 1 Line segment related to triangle
Triangles are stable.
7.2 Angle related to triangle
The sum of the internal angles of a triangle is equal to 180 degrees.
The outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
The outer angle of a triangle is greater than any inner angle that is not adjacent to it.
7.3 sum of polygons and their internal angles
Is the sum of the internal angles of the N-polygon equal to: (n-2)? 180 degrees
The sum of the outer angles of a polygon is equal to 360 degrees.
Chapter VIII Binary Linear Equations
8. 1 binary linear equations
An equation contains two unknowns (X and Y) whose exponents are 1. Equations like this are called binary linear equations.
Two binary linear equations are combined to form a system of linear equations with two unknowns.
The values of two unknowns that make the values on both sides of the binary linear equation equal are called the solutions of the binary linear equation.
The common * * * solution of two equations of binary linear equations is called the solution of binary linear equations.
8.2 elimination
The idea of solving the unknowns one by one from more to less is called elimination thought.
Chapter 9 Inequality and Unequal Groups
9. 1 inequality
Formulas that indicate the size relationship with less than sign or greater than sign are called inequalities.
The value of the unknown quantity that makes the inequality valid is called the solution of the inequality.
The value range of x that can make inequality hold is called the solution set of inequality, which is called the solution set for short.
An inequality whose unknown number is 1 is called a linear inequality of one variable.
The essence of inequality:
Add (or subtract) the same number (or formula) on both sides of the inequality, and the direction of the inequality remains unchanged.
Both sides of inequality multiply (or divide) the same positive number, and the direction of inequality remains unchanged.
When both sides of the inequality are multiplied (or divided) by the same negative number, the direction of the inequality changes.
The difference between any two sides in a triangle is less than the third side.
The sum of any two sides in a triangle is greater than the third side.
9.3 One-dimensional linear inequality system
When two linear inequalities are combined, a unitary linear inequality is formed.
Chapter 10 Real Numbers
10. 1 square root
If the square of a positive number x is equal to a, then this positive number x is called the arithmetic square root of a, and 2 is the root index.
The arithmetic square root of A is pronounced as "root number A", and A is called radix.
The arithmetic square root of 0 is 0.
If the square of a number is equal to a, then this number is called the square root or quadratic root of a.
The operation of finding the square root of a number is called square root.
10.2 cube root
If the cube of a number is equal to A, then this number is called the cube root or cube root of A. ..
The operation of finding the cube root of a number is called finding the cube root.
10.3 real number
Infinitely cyclic decimals are also called irrational numbers.
Rational numbers and irrational numbers are collectively called real numbers.
Expanding: Knowledge Points of Junior One Chinese
First, the narrator (three kinds of people):
1, the first person ("first person") can give people a cordial, natural and true feeling. Writing "I" in the first person is most suitable for describing the psychological activities of the characters. What you see, hear, do and feel can be expressed through the description of psychological activities. When writing "he" in the first person, it is most appropriate to write the appearance, language and movements of the characters, because it is more objective to write "he" with the impression of "I". The first person's description of my appearance and his psychological activities must be accompanied by imitation to convince readers. To write "I", you can write: "You can imagine how red my face was." To write about his psychological activities, you can write: "I feel relaxed." )
2, the second person said (role: enhance the lyricism and intimacy of the article, and facilitate emotional communication. )
3, the third person (role: can show colorful life more directly and objectively, not limited by time and space, and reflect reality more flexibly and freely. )
Second, the narrative way (or "narrative order") (3):
1, described in chronological order-described in chronological order. The structural pattern of sequence type is: total narrative+sub-narrative (sub-narrative 1+ sub-narrative 2+ sub-narrative 3+ sub-narrative n)+ ending. Function: The narrative is clear.
2, flashback-the end of the event mentioned earlier in the article or an important chapter in its development process, write the end or chapter, and then write it in chronological order. Function: This kind of brushwork can arouse suspense and attract readers.
3. Interpolation (supplementary narrative is a kind of interpolation)-For the full text, interpolation is only a fragment. After interpolation, the article returns to the original event narrative. This kind of narration is not the main part of narration, and generally does not happen in the mainstream time range. If this episode is deleted, it will weaken the profundity of the theme, but it will not obviously affect the integrity of the main plot. Function: Make the plot more complete, the structure more rigorous and the content more substantial. Supplementary function: supplement and explain the above contents, and make some explanations for the following.
(There is an unusual narrative called "telling the story straight", which is commonly known as "two flowers bloom, each with a flower", which means telling two or more things that happen at the same time, so that the clues are clear and handled properly. )
Third, description:
Generally speaking, description has the following functions: ① Reproduce natural scenery. ② Describe the appearance and inner world of the characters. ③ Explain the natural and social environment of the characters' activities.
1. Five description methods of characters: portrait (appearance) description, language description, action description, psychological description and expression description.
Function: better show the inner world and personality characteristics of the characters. Depicting characters' personalities, reflecting their psychological activities and promoting the development of stories. Wait a minute. When answering specifically, you should be clear about your personality and psychology.
2. Two kinds of environmental descriptions: the description of natural environment-describing the natural scenery in detail, creating an atmosphere, and setting off the emotions and thoughts of the characters. Contrast the mood of the characters, render the atmosphere, etc.
Description of social environment-explain the background of people's activities, point out the time and place of events, render the atmosphere, and better express people.
3. Front description and side description: The front directly shows people and things; Highlight people and things from the side.
4. Detail description: Describe the characters' personalities, reflect their psychological activities and promote the development of the story. It can also describe the voice of a character and receive special effects.
Fourth, rhetoric:
1, metaphor: make the language vivid and increase the color of the language. Turn plain into vivid, abstruse into simple, abstract into concrete image.
2, personification: write things into adults, so that the language image is vivid. Give things human form and emotion (personification), describe vivid images and express rich meanings.
3, parallelism: enhance the language momentum, strengthen the expression effect. The narrative is thorough and detailed; Good at lyric.
4. exaggeration: highlight something or emphasize a certain feeling. Set off the atmosphere, enhance the appeal and enhance the association; Create an atmosphere, reveal the essence and inspire people.
5. Rhetorical question: it plays an important role and enhances the positive (negative) tone.
6. Questioning: Ask yourself and answer yourself, ask questions, and arouse readers' attention and thinking.
7. Duality: make the language concise and neat, and have a sense of music; Lyric and hearty; Easy to recite and remember.
8. Repetition: Repeated emphasis is impressive; Writing about scenery is lyrical and infectious; Connect the front with the bottom and distinguish the levels.
Note: The functions of various rhetorical devices (methods) are simply given above. When answering questions, be sure to combine the specific content to avoid being empty.
Verb (abbreviation of verb) structure arrangement:
Layout planning skills: cut to the chase, echo from beginning to end, show great plans, pave the way, deepen layer by layer, over-spread, set clues; Compact structure and complete symmetry; Lift the ground and take care of it; Set suspense, create waves, connect and merge, and have twists and turns. Whether the relationship between materials and the center is properly handled and whether the primary and secondary details are appropriate; Whether the materials are typical, authentic, novel and powerful.
Narrative texts are often arranged according to the passage of time, the transformation of space, the change of scenes and the logical order of thinking. The clues of prose conception generally include: taking emotion as the clue; Take reason as a clue; Take things as clues; Take spatial location as a clue.
Clarify the function of sentences in different positions in the text from the structure;
1, the first sentence-lead out the full text, outline and lead out the following to pave the way for the following;
2, the last sentence-summary of the full text, deepen the theme, take into account the above, echo before and after, meaning endless, memorable.
3, into a sentence-connecting the preceding with the following, transition, undertaking the above, leading to the following;
4. Central sentence-point out the center and reveal the main idea;
5, the finishing touch-point out the center of the full text and lead the full text; The sentence is profound, thought-provoking and enlightening after reading.
6, emotional sentences-express strong inner feelings, express your chest directly;
7. Contradictory sentence-it is self-contradictory literally, but the author has profound meaning. Reveal profound connotations and express profound opinions.
(1) The structural features of narrative (prose)
(1) Organize materials in chronological order or in the order of occurrence and development of events.
(2) according to the transformation of observation points to arrange material, such as my castle in the air.
(3) Arrange the materials according to the layout of the site, such as "Visiting Ancient Inner Mongolia".
(4) Arrange the structure according to the nature of materials, such as "trivial memories".
⑤ Arrange the materials according to the author's cognitive process or emotional changes. Like litchi honey.
⑥ Arrange materials according to what the author has seen, heard, felt and thought as writing clues.
Sixth, the expression began to analyze the meaning of the sentence:
Five ways of expression: narration, description, explanation, lyricism and discussion.
Explanation: when expressing ideas in words, there is a problem of methods or means, which people are used to calling expression.
For example, narration, description and lyricism are the main factors, and argumentation and explanation are the main factors.
1, the discussion in narrative often plays the role of finishing touch, revealing the purpose and significance of narrative;
2. Narratives in argumentative essays often play the role of illustrations;
3. The description and writing style in the explanatory text have played a role in making the works more vivid.
4. The writing method of alternating narration and discussion makes the explanation and discussion of the article relaxed and lively, and it is both interesting and enlightening to read. The narrative in the article serves the discussion, which is based on narrative and provides factual basis for the discussion, making the argument well-founded and convincing.
Seven, punctuation:
1, five uses of quotation marks: ① table quotation ② table irony or negation ③ table specific title ④ table emphasis or emphasis ⑤ special meaning.
2. Five uses of dashes: ① table annotation; ② table insertion; ③ table sound interruption; ④ table topic change; ⑤ table meaning change.
3. Six usages of ellipsis: ① Omit the contents of the table; ② Intermittent predication; (3) the table is incomplete because of grabbing the vernacular; 4 emotional contradictions; 5 thinking jump; ⑤ Thinking is in progress.
Eight, ten common writing skills:
Symbol, contrast, foil, contrast, foreshadowing, care (echo), direct (indirect) description, promotion and suppression (to promote first, to suppress first), lyrical with scenery, metaphorical with things.
Symbol expresses the essential characteristics of a person and a social phenomenon through the concrete image of a certain feature. Example: Haiyan symbolizes the image of a proletarian revolutionary pioneer with great wisdom and courage.
Compare two opposite things or two opposite aspects of a thing, and highlight the main features of the main thing or thing. Example: Haiyan compares the tall image of Haiyan with the cowardly images of sea ducks, seagulls and penguins, highlighting the distinctive characteristics of Haiyan's courage and courage to fight.
The main features of ontology are set off from two angles. Example: Praise for Poplar begins with a description of the growth environment of poplars-the majestic northwest plateau, which sets off the tall image of poplars standing proudly.
Lyricism by borrowing scenery is to express the author's sincere thoughts and feelings by describing concrete and vivid natural scenery or life scenes.
For example, from "Hundred Herbs Garden" to "San Tan Yin Yue", the article vividly depicts the colorful scenery of the Hundred Herbs Garden and the boring life scene in "San Tan Yin Yue" from different angles and levels, showing the author's thoughts and feelings of loving nature, enjoying a free and happy life and being dissatisfied with feudal education that restricts children's physical and mental development.
Metaphor is used to describe things, highlight the characteristics of things, and express the author's noble thoughts and sentiments with metaphor. Example: Praise of the Poplar compares the northern soldiers and civilians with poplars, and compares the tenacious spirit of the northern soldiers and civilians fighting bloody battles for the liberation of China with the characteristics of poplars' integrity, simplicity, seriousness, honest and frank and striving for the upper reaches.
First suppress and then promote, first deny or belittle the image of things, then dig deep into the characteristics and internal meaning of things, then affirm and praise things, and emphasize the characteristics of things more prominently. Example: Praise poplars. Say poplars are not "good women" first, and then praise them as "good husbands", which highlights the external image and internal charm of poplars.
Nine, some commonly used terms (questions) of test paper topics:
1. Answer what is the function of something in the article, which can be considered from three aspects. The first is the content, such as deepening the theme and emphasizing feelings; Second, the structure, such as transition and echo; Third, language, such as fascinating and lively.
2, ideological-basically refers to the central idea or theme of the article.
3, thoughts and feelings-the ideological tendency of the author or the characters in the work, such as good and evil, likes and dislikes, praise and blame, etc.
Extracurricular reading refers to reading content other than textbooks (teaching materials). No matter what you read in class or after class.
4, sentiment-refers to the heartfelt feelings, understanding, sentiment, etc.
5. Writing skills-candidates should be clear that the narrow sense of writing skills is "expression", and the broad sense of writing skills refers to all the skills of writing articles, such as expression, rhetoric, suppression before promotion, symbol, straight to the point, and expression of will.
6. Means of expression-in a broad sense, it is a special sentence organization method used by the author in writing words and expressing thoughts and feelings.
By analyzing a work, we can grasp its special performance from point to surface. First of all, there are many rhetorical skills in words and sentences, including metaphor, symbol, exaggeration, parallelism, duality, contrast, personification, allusions and so on. When grasping its expressive techniques as a whole, we should pay attention to different styles of works: lyric prose has rich and colorful expressive techniques, such as borrowing scenery to express emotion, supporting things to express emotion, combining cadence and symbolism, etc. Narrative writing skills such as beginning and end coordination, finishing touch, clever use of rhetoric, proper details, combination of narration and discussion, positive and negative comparison, etc. Argumentative writing skills such as quoting classics, clever analogy, reverse seeking differences, positive and negative comparison, analogy reasoning, etc. Novel description, comparison, bedding and reference, suspense and interpretation, real writing and imaginary writing.
The analysis of expression is a very general topic. Pay attention to the requirements of solving complete geographical problems when answering questions, and answer them concisely and accurately. For some topics, such as appreciating writing skills, it is necessary to accurately grasp the context, theme and genre style of the article, and choose the most important answer. It is not necessary to cover everything, such as the various methods of shaping characters in novels, such as the various methods of expressing emotions in prose, and try to get points.
7. Note: We should know some commonly used procedures (sentence patterns), such as what to embody, what to emphasize, what to strengthen, what to create and what to express, as well as deepen and clarify the theme.
X. Others: "A trip of two or three miles, four or five smoke villages. There are six or seven pavilions with 90 flowers. "
Two common narrative clues: object line and emotional line.
Two language types: spoken and written. Language features generally refer to easy-to-understand spoken language, rigorous and elegant written language, and distinctive, vivid, vivid and perceptual features of literary language. When analyzing, it is generally analyzed from rhetoric. )
Two kinds of lyricism: 1 Direct lyricism refers to the author's direct expression of his feelings about something or situation. Because the author comes forward directly, the direct lyrical language often has a strong subjective color. (1) Choose an image to express feelings; (2) Express feelings directly to the image.
2. Indirect lyricism means that the author does not come forward directly, but expresses his feelings in other ways, and the language is calm and objective. (1) Lyric by characters. (2) Lyric through a specific tone.
Three emotional colors: positive, negative and neutral.
Three principles of language use: conciseness (sentences are concise and clear, and there is generally a word limit. ), coherent and decent (civilized and polite, humanized. )。
Three interpretation sequences: (1) time sequence, (2) spatial order,
(3) Logical order. There are six logical sequences: ① general ← to individual ← ② phenomenon ←→ essence ③ cause ←→ result ④ generalization ←→ concrete ⑤ part ←→ whole ⑤ main ←→ secondary.
Four literary genres: novel, poetry, drama and prose.
The novel has three elements: the characters (the main characters depend on whether the theme of the novel can be expressed), the plot (beginning/development/climax/ending) and the environment (natural environment/social environment). )
Characters mainly master the reading skills of depicting characters through appropriate description methods and angles and reflecting their thoughts and personalities.
Plot mainly understands the basic content of each part, as well as the methods and skills to understand and analyze the plot of the novel.
The plot of the novel consists of four parts: beginning, development, climax and ending.
Begin to explain the background and pave the way for the following.
Develop the characters' personalities and embody their individuality.
The climax shows conflict and reveals the theme.
The ending deepens the theme and leaves some thoughts.
Environment mainly understands the role of natural environment and social environment.
The natural environment describes the natural landscape, exaggerates the atmosphere, sets off emotions, predicts the fate of characters, reveals the essence of society and promotes the development of plots.
The social environment describes the social situation, explains the background of the story, reveals the social essence, and paves the way for the following content.
Four usages of sentences: declarative sentences, interrogative sentences, imperative sentences and exclamatory sentences.
Six elements of narrative: time, place, people, cause, process and result of events.
Six kinds of ill sentences: ① Incomplete components; ② Improper collocation; ③ Improper use of related words; 4 inconsistent; ⑤ Improper word order; ⑤ Misuse and abuse of function words (prepositions).
Seven interpretation methods: example, analogy, comparison, number of columns, classification, definition and quotation.
A complete collection of Chinese knowledge points for students to learn. I hope the students' Chinese scores are getting better and better!