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Xiaoshengchu Chinese review materials people's education edition
The formula that defines the theorem must be remembered.
Volume and surface area
Area of triangle = base × height ÷2. The formula S= a×h÷2.
Area of square = side length × side length formula S= a2
Area of rectangle = length× width Formula S= a×b
Area of parallelogram = base× height Formula S= a×h
Trapezoidal area = (upper bottom+lower bottom) × height ÷2 Formula S=(a+b)h÷2
Sum of internal angles: sum of internal angles of triangle = 180 degrees.
The surface area of a cuboid = (length× width+length× height+width× height )× 2 Formula: S=(a×b+a×c+b×c)×2.
Surface area of cube = side length × side length ×6 Formula: S=6a2.
Cuboid volume = length× width× height formula: V = abh
Volume of cuboid (or cube) = bottom area × height formula: V = abh.
Volume of cube = side length × side length × side length formula: V = a3.
Circumference = diameter × π formula: L = π d = 2π r
Area of circle = radius × radius× π formula: s = π R2.
Surface (side) area of cylinder: The surface (side) area of cylinder is equal to the perimeter of bottom multiplied by height. Formula: s = ch = π DH = 2π RH.
Surface area of cylinder: the surface area of cylinder is equal to the perimeter of the bottom multiplied by the height plus the area of the circles at both ends. Formula: S=ch+2s=ch+2πr2.
Volume of cylinder: the volume of cylinder is equal to the bottom area multiplied by the height. Formula: V=Sh
Volume of cone = 1/3 bottom× product height. Formula: V= 1/3Sh
arithmetic
1, additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged.
2. Additive associative law: A+B = B+A.
3. Multiplicative commutative law: a× b = b× a.
4. Multiplicative associative law: a × b × c = a ×(b × c)
5. Multiplicative distribution law: a× b+a× c = a× b+c.
6. The nature of division: a ÷ b ÷ c = a ÷(b × c)
7. Nature of division: In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged. O is divided by any number that is not O. Simple multiplication: the multiplicand and the end of the multiplier are multiplied by O. You can multiply 1 before o first, and zero does not participate in the operation, and add a few zeros at the end of the product.
8. Division with remainder: dividend = quotient × divisor+remainder
Equations, Algebras and Equality
Equation: An equation in which the value on the left of the equal sign equals the value on the right of the equal sign is called an equation. Basic properties of the equation: When both sides of the equation are multiplied (or divided) by the same number at the same time, the equation is still valid.
Equation: An equation with an unknown number is called an equation.
One-dimensional linear equation: An equation with an unknown number of degree 1 is called a one-dimensional linear equation. Example method and calculation of learning linear equation of one variable. That is, an example is given to illustrate that the formula is replaced by χ and calculated.
Algebra: Algebra means replacing numbers with letters.
Algebraic expression: Expressions expressed by letters are called algebraic expressions. For example 3x = AB+C.
mark
Fraction: divide the unit "1" into several parts on average, and the number representing such a part or points is called a fraction.
Comparison of fraction size: Compared with the fraction of denominator, the numerator is large and the numerator is small. Compare the scores of different denominators, divide them first and then compare them; If the numerator is the same, the denominator is big and small.
Addition and subtraction of fractions: add and subtract fractions with the same denominator, only add and subtract numerators, and the denominator remains the same. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
Fraction multiplied by integer, numerator is the product of fractional and integer multiplication, denominator remains unchanged.
Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.
Law of fractional addition and subtraction: Fractions with the same denominator are added and subtracted, only the numerator is added and subtracted, and the denominator remains the same. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
The concept of reciprocal: 1 If the product of two numbers is 1, we call one of them the reciprocal of the other. These two numbers are reciprocal. The reciprocal of 1 is 1, and 0 has no reciprocal.
A fraction divided by an integer (except 0) is equal to this fraction multiplied by the reciprocal of this integer.
The basic properties of a fraction: the numerator and denominator of a fraction are multiplied or divided by the same number (except 0), and the size of the fraction.
The law of division of fractions: dividing by a number (except 0) is equal to multiplying the reciprocal of this number.
True fraction: The fraction with numerator less than denominator is called true fraction.
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 a score: write a false score as an integer, and a true score is called with a score.
The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged.
Calculation formula of quantitative relationship
Unit price × quantity = total price 2, single output × quantity = total output
Speed × time = distance 4, work efficiency × time = total workload.
Appendix+Appendix = and one addend = and+another addend.
Negative-negative = differential negative = negative-differential negative = negative+difference.
Factor × factor = product One factor = product ÷ another factor.
Frequency divider/frequency divider = frequency divider = frequency divider/frequency divider = quotient × frequency divider
Length unit:
1 km = 1 km 1 km = 1000 m
1 m = 10 decimeter 1 decimeter =10 cm1cm =10 mm.
Area unit:
1 km2 = 1 00ha1hectare =10000m2
1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter 1 square centimeter = 100 square millimeter
1 mu = 666.666 square meters.
volume unit
1 m3 = 1000 cubic decimeter
1 cm3 = 1000 cm3
1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter.
Unit right
1 ton = 1 000kg1kg = 1 000g = 1 kg =1kg.
compare
What is the ratio? When two numbers are divided, it is called the ratio of two numbers. For example, the first and second terms of the ratio of 2÷5 or 3:6 or 1/3 are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
What is proportion? Two formulas with equal ratios are called proportions. For example, 3: 6 = 9: 18
The basic property of proportion: in proportion, the product of two external terms is equal to the product of two internal terms.
Solution ratio: the unknown term in the proportion is called solution ratio. Such as 3: χ = 9: 18.
Proportion: two related quantities, one of which changes and the other changes. If the ratio (i.e. quotient k) corresponding to these two quantities is constant, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. For example: y/x=k( k must be) or kx = y.
Inverse proportion: two related quantities, one of which changes and the other changes accordingly. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. For example: x×y = k( k must be) or k/x = y.
per cent
Percentage: a number that indicates that one number is a percentage of another number, which is called percentage. Percentages are also called percentages or percentages.
To convert decimals into percentages, just move the decimal point two places to the right and add hundreds of semicolons at the end. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%. To convert percentages to decimals, simply remove the percent sign and move the decimal point two places to the left.
When a fraction is converted into a percentage, the fraction is generally converted into a decimal (three decimal places are generally reserved when it is not used up), and then the decimal is converted into a percentage. In fact, to turn a fraction into a percentage, you must first turn the fraction into a decimal and then multiply it by 100%.
Divide the percentage into components, and rewrite the percentage into components first, so that the quotation that can be lowered can be made into the simplest score.
We should learn to decompose fractions into components and fractions into decimals.
Multiples and divisors
Maximum common divisor: The common divisor of several numbers is called the common divisor of these numbers. There is a finite common factor. The largest one is called the greatest common divisor of these numbers.
Least common multiple: The common multiple of several numbers is called the common multiple of these numbers. There are infinite common multiples. The smallest one is called the least common multiple of these numbers.
Prime number: the common divisor has only 1 two numbers, which is called prime number. Two adjacent numbers must be prime numbers. Two consecutive odd numbers must be coprime. 1 and any number coprime.
Comprehensive score: the difference between scores of different denominators is changed into the same denominator score equal to the original score, which is called comprehensive score. (Common divisor is the least common multiple)
Decrement: divide the numerator and denominator of a fraction by the common divisor at the same time, and the fraction value remains unchanged. This process is called dropping points.
Simplest fraction: The numerator and denominator are fractions of prime numbers, which are called simplest fraction. At the end of the score calculation, the score must be converted into the simplest score.
Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number).
Composite number: a number. If there are other divisors besides 1 and itself, such numbers are called composite numbers. 1 is neither prime nor composite.
Prime factor: If a prime number is a factor of a certain number, then this prime number is the prime factor of this number.
Prime factor decomposition: A composite number is represented by the complementary way of prime factors, which is called prime factor decomposition.
Multiple characteristics:
Characteristics of multiples of 2: You are 0, 2, 4, 6, 8.
Characteristics of multiples of 3 (or 9): The sum of the numbers on each digit is multiples of 3 (or 9).
Characteristics of multiples of 5: You are 0, 5.
Characteristics of multiples of 4 (or 25): The last two digits are multiples of 4 (or 25).
Characteristics of multiples of 8 (or 125): the last three digits are multiples of 8 (or 125).
Characteristics of multiples of 7 (1 1 or 13): the difference (big-small) between the last three digits and other digits is a multiple of 7 (1 1 3).
Characteristics of multiples of 17 (or 59): the difference (big-small) between the last three digits and the rest digits is a multiple of 17 (or 59).
Characteristics of multiples of 19 (or 53): the difference (big-small) between the last three digits and other seven digits is a multiple of 19 (or 53).
Characteristics of multiples of 23 (or 29): The difference (big-small) between the last four digits and the other five digits is multiples of 23 (or 29).
Of the two numbers in the multiple relation, the greatest common divisor is smaller and the smallest common multiple is larger.
The coprime relation between two numbers, the greatest common divisor is 1, and the least common multiple is the product.
When two numbers are divided by their greatest common divisor, the quotient is coprime.
The product of two numbers and the least common multiple is equal to the product of these two numbers.
The common divisor of two numbers must be the greatest common divisor of these two numbers.
1 is neither prime nor composite.
A prime number greater than 3 divided by 6 must get 1 or 5.
Odd and even numbers
Even numbers: Numbers are numbers of 0, 2, 4, 6 and 8.
Odd number: The number is not 0, 2, 4, 6 or 8.
Even even = even Qiqi = Qiqi.
Even numbers add up to even numbers, and odd numbers add up to odd numbers.
Even × even = even × odd = odd × even = even.
The sum of two adjacent natural numbers is odd, and the product of adjacent natural numbers is even.
If one number in the multiplication is even, then the product must be even.
Odd ≠ even number
separable
If c | a, c | b, then c | (a b)
If, then b | a, c | a
If b | a, c | a and (b, c)= 1, then BC | a.
If c | b, b | a, then c | a
decimal
Natural number: an integer used to represent the number of objects, called natural number. 0 is also a natural number.
Pure Decimal: Decimal in units of 0.
With Decimal: Decimal with more than 0 digits.
Cyclic decimal: a decimal, starting from a certain bit of the decimal part, and one or several numbers are repeated in turn. Such decimals are called cyclic decimals. Like 3. 14 14 14.
Acyclic decimal: a decimal, starting from the decimal part, without one number or several numbers appearing repeatedly. Such a decimal is called acyclic decimal. Like 3. 14 1592654.
Infinite cycle decimal: a decimal, from the decimal part to the infinite digits, and one or several numbers are repeated in turn. Such decimals are called infinite cyclic decimals. For example, 3. 14 14 14 ...
Infinite acyclic decimal: a decimal, from decimal part to infinite digits, is called infinite acyclic decimal without one number or several numbers appearing repeatedly. Such as 3. 14 1592654. ...
profit
Interest = principal × interest rate × time (time is usually in years or months, which should correspond to the unit of interest rate).
Interest rate: The ratio of interest to principal is called interest rate. The ratio of interest to principal for one year is called annual interest rate. The ratio of interest to principal in January is called monthly interest rate.
There is also a website, you don't need to register, you can have a look.
This is the skill of writing and reading articles. I hope it will help you.
Chinese reading comprehension plays an increasingly important role in Chinese teaching. It is not only an important way for students to acquire knowledge and information daily, but also an inevitable need for students' all-round development and an essential skill to adapt to the future information society.
Judging from the trend of the reform and development of the Chinese senior high school entrance examination in primary schools, the proportion of reading comprehension questions is gradually increasing, and the number of subjective questions is on the rise. But students lose more points in this item in the exam. Often in the exam, when encountering reading questions, most students show fear of difficulties and don't know where to start. They are confused, confused, incomplete, unable to answer questions, and often lose points on questions that could have been done, resulting in unsatisfactory results.
In fact, reading comprehension questions are not as difficult as some students think. As long as the problem-solving requirements are clear, certain problem-solving ideas are followed, and some problem-solving methods are mastered, most problems can still be answered correctly. Mastering the problem-solving requirements and ideas of reading comprehension will eliminate the fear of difficulties, and the so-called problem will be solved with half the effort.
Below, I will talk about my own teaching experience and my humble opinion on the answering skills of Chinese reading comprehension.
First, calmly examine the questions and avoid carelessness.
When answering reading questions, don't panic, calm down and follow the idea of from easy to difficult, from shallow to deep, from easy to difficult, and gradually open your mind. Carelessness is a taboo in learning, and Chinese reading comprehension is no exception. When examining a question, you should read every word, every word, every sentence and even every punctuation carefully, see the requirements of the question clearly and analyze the main points of the question clearly, just like the numbers in the math question. Careless students often miss correct answers. For example, some students explained the added words when they asked for phonetic notation. You can often see similar situations in exams. Carelessness is an important reason why some students lose points in this item. So be careful when you do the questions.
Second, carefully study the paragraphs and perceive the content of the article as a whole.
The written materials of reading comprehension questions are mainly used to test students' reading speed, understanding ability and memory ability. Some use a sentence, some use a paragraph or an entire article. It has a wide range of contents and different themes.
Usually when reading an article, you need to read it quickly the first time. First of all, you should focus on whether the genre of the article is narrative or expository. When answering a question, don't write down the answer in a hurry without completely reading the article. It's best to read the article from beginning to end first, and have an overall understanding and understanding of the article. Secondly, we should clarify the thinking of the article. Generally speaking, every paragraph and sentence of the article, in the final analysis, is to clarify the center and return to the main idea of the article. Usually learn to bid for articles and summarize the meaning of each paragraph.
Some students want to use the "sequential reading method", that is, read the passage first, then read the topic, and then read the passage to find the correct answer. Some students use the "backward reading method", that is, read the topic first, then read the passage, and finally find the answer. I am in favor of "reading backwards", because this reading method is reading with questions, with clear purpose and easy concentration, and can grasp the information closely related to solving problems in time, thus saving reading time.
Therefore, the central step to solve this kind of problem is reading, which depends on both the short passage and the topic. Pay attention to reading skills and improve reading efficiency. On the basis of the above points, we can judge and answer the questions given at the back of the article by "one-time judgment", "one-by-one analysis" and "exclusion" respectively.
Third, skillfully use "original words" to determine the problem-solving space.
On the basis of reading the full text, put the questions to be answered in the reading article, then browse the questions to be answered, and determine the reading space to solve the problems after preliminary thinking. Some questions need to be answered in the original text, so we can answer them in the original text, and then we can "extract information directly from the article" to answer the questions.
If it doesn't explicitly ask for an answer in the original words of the article, we can also "extract information directly from the article" to answer the question. If students are required to answer in their own words, we can also ask students to translate the original words in the text, in other words. Try to dig out the hidden information and deep meaning of the original sentence. Some topics need to be combined with the full text, dig out the implied information of sentences, and seek perfect answers after careful thinking.
The openness of Chinese test questions requires that the answers can be well-founded and the answers are the best. Chinese vocabulary is so rich and emotional, so when reading, we should analyze it carefully and deeply. When answering questions, we should carefully consider the choice of words and sentences, and use words accurately according to the characteristics of different genres and contexts.
Fourth, choose the right method and try to make the answer meaningful.
There are still some ways to do reading comprehension questions. In teaching, students can be guided to choose different methods to answer according to different questions. I'll summarize it roughly into four types here.
1, in the context. That is, thinking in context. This method is suitable for "understanding the meaning of words; Understand profound sentences; Find synonyms, antonyms, experience scenes, etc.
2. Experience the scene. It is to let students and the author exchange roles, think and answer questions from the author's standpoint. This method is especially suitable for answering questions and understanding the author's thoughts and feelings.
3. Contact life. That is, jump out of the text, expand the scope of thinking, and think about related things: such as the text you have learned, the accumulation of knowledge, and whether life experience can help you solve problems. This method is especially suitable for talking about one's feelings, experiences or understanding of profound sentence topics.
4. Combination center. This is the most important way to solve the reading problem. Every question is thought from the center of the article, and the answer has a foothold.
Generally speaking, "being in context" is the most basic way of thinking, and this method should be considered first when encountering problems; When the method in context still can't answer, we can think with the method of "situational experience"; If the previous method still can't solve the problem, you can think about the problem by "connecting with the reality of life" in order to get a more accurate answer; "Combination Center" is a method that can't be ignored when thinking about problems. Only by thinking about the problem in the center can the answer be correct.
The so-called "reasoning" is to let students tell a truth according to the problem, tell a truth, or "justify themselves." As long as students are well-founded and well-founded, they can be graded as appropriate. At the same time, students should pay attention to organizing standardized language answers and writing carefully. After the answer is basically considered mature, you need to pay attention to the language of expression. Simple and clear language can achieve twice the result with half the effort; Repetition is verbose, irrelevant and often leads to thankless efforts. After answering the questions, if time permits, you should reread the full text and review it with confidence. After all the answers are finished, return to the original text with the results of reading comprehension, check whether there are any omissions in the answers, study their internal relations and logical relations, and make inferences and judgments for each topic to ensure correctness.
Fifth, reasonably control the time for answering questions, which is easy first and then difficult.
When solving problems, don't look at reading comprehension questions, but look for answers from reading comprehension articles, because this method is difficult to improve reading comprehension, especially for articles with deep reading comprehension. First of all, we should browse, read and understand the full text and have a general understanding of it. After reading, you should remember the main points of reading comprehension, the important conclusions of reading comprehension and some key names, places, definitions and figures in reading comprehension (different names and places can be marked in the article with a pencil for easy search). At the same time, we should master the problem-solving speed of reading comprehension and effectively control the answering time of reading comprehension. It is a common method to do reading comprehension questions first. When you encounter reading comprehension problems, don't get into trouble and waste too much time. If you can't do the reading comprehension questions for a while, you should give up decisively so as not to affect the answers to other more confident reading comprehension questions. After all the reading comprehension questions are solved, if you still have time, come back and do the abandoned reading comprehension questions.
In short, I think that in the training of Chinese reading comprehension, only by following the correct educational laws and giving students the correct problem-solving methods and skills can students learn easily and relax, and they can really get twice the result with half the effort and get good results in Chinese reading teaching.
The above is just a little experience from the author's teaching, and his views are superficial and can only be discussed with colleagues.
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