Eight-grade mathematics knowledge points
data analysis
1, average
① Generally speaking, for n numbers x 1x2...xn, we take (x 1+x2+? +xn) is called the arithmetic average of the n numbers, and the average for short is recorded as.
② In practical problems, the "importance" of each data in a set of data may be different, so when calculating the average of this set of data, each data is often given a weight, which is called weighted average.
2. Median and mode
① Median: generally, n data are arranged in order of size, and the data in the middle position (or the average of the two data in the middle) is called the median of this group of data.
② The data with the highest frequency in a group of data is called the pattern of this group of data.
③ Average, median and mode are all statistics that describe the trend in data set.
(4) When calculating the average, all the data participate in the operation, which can make full use of the information provided by the data, so it is commonly used in real life, but it is easily influenced by extreme values.
⑤ Median has the advantage of simple calculation and little influence by extreme value, but it can't make full use of all data information.
⑥ When the number of repetitions of each data is roughly equal, the pattern often has no special meaning.
3. Analyze the concentration trend of data from the statistical chart.
4. Degree of data dispersion
① In real life, people not only pay attention to the concentration trend of data, but also pay attention to the degree of dispersion of data, that is, the degree of deviation from the concentration trend. The difference between the data in a set of data and the minimum data (called range) is a statistic that describes the degree of data dispersion.
② Mathematically, the dispersion degree of data can also be described by variance or standard deviation.
③ Variance is the average of the square of the difference between each data and the average.
(4) where x 1, the mean of x2 ... xn, s2 is the variance, and the standard deviation is the arithmetic square root of variance.
⑤ Generally speaking, the smaller the range, variance or standard deviation of a set of data, the more stable it is.
Sorting out the knowledge points of eighth grade mathematics
Addition and subtraction of fractions
1. Although general fractions and reduction are aimed at fractions, they are two opposite variants. Reduction is for one score, while general scores are for multiple scores. The approximate fraction is a simplified fraction, and the general fraction is a simplified fraction, thus unifying the denominator of the fraction.
2. Both general score and approximate score are deformed according to the basic properties of the score, and their similarity is to keep the value of the score unchanged.
3. The general denominator is written in the form of unexpanded continuous product, and the numerator multiplication is written in polynomial to prepare for further operation.
4. Total score basis: the basic nature of the score.
5. The key to general division is to determine the common denominator of several fractions.
Usually, the product of the powers of all factors of each denominator is taken as the common denominator, which is called the simplest common denominator.
6. By analogy, get the total score of this score:
Changing several fractions with different denominators into fractions with the same mother equal to the original fraction is called the general fraction of fractions.
7. The rules for adding and subtracting fractions with the same denominator are: adding and subtracting fractions with the same denominator and adding and subtracting numerators with the same denominator.
Addition and subtraction of fractions with the same denominator, denominator unchanged, addition and subtraction of molecules, that is, the operation of fractions is transformed into the operation of algebraic expressions.
8. Fraction addition and subtraction law of different denominators: Fractions of different denominators are added and subtracted, first divided by fractions of the same denominator, and then added and subtracted.
9. Fractions with the same denominator are added and subtracted, and the denominator remains the same. Add and subtract molecules, but pay attention to each molecule as a whole, and put parentheses in due course.
10. For the addition and subtraction between the algebraic expression and the fraction, the algebraic expression is regarded as a whole, that is, it is regarded as a fraction with the denominator of 1, so as to divide.
1 1. For addition and subtraction of fractions with different denominators, first observe whether each formula is the simplest fraction. If the fraction can be simplified, it can be simplified first and then divided, which will simplify the operation.
12. As the final result, if it is a score, it should be the simplest score.
Summary of Mathematics Review Methods in Grade Two of Junior High School
First, junior high school math exam review method:
Mathematician Hua once said: "Cleverness lies in learning, and genius lies in diligence." Diligence is good training, and one effort is one talent.
1. Review must be diligent.
Diligent hands-on: Don't look at the questions, count them, and write down the knowledge points that you can't, and write them down in a notebook.
Diligent: No, you must ask the teacher if you have any questions. Time waits for no one, there is no time to waste. And learn to discuss problems with classmates.
Be diligent: Be sure to listen to the teacher's review class. Don't think that this problem is solved, and the teacher can slip the number. You should know that you can learn new things by looking back on the past.
Think hard: be good at thinking and think positively-absorb and store information.
Exercise your legs regularly: Don't take part in too intense exercise to prevent injuries from affecting your study, but keep exercising, jog for 30 minutes every day and report to the country.
2. Junior high school math review should also emphasize two points:
One is to do, and the other is to use your head.
Thinking is to learn to observe and analyze problems, learn to think, don't just do problems, find the connection between known and unknown, ask more why, and know more about what knowledge points to test.
Hands-on is to practice more, do more problems, and never leave your mouth. Students just stick to the subject. These two points should be remembered and adhered to. Only through thinking and action can the efficiency of the brain be fully exerted. This is also the teacher's experience.
Step 3 do it with your heart three times
Listen carefully in class: listen to the teacher's knowledge about methods and so on
Hand-made: do it according to the teacher's idea and see if the effect is good.
Think carefully: think about why you did it and what knowledge you took.
4. Pay attention to the simple learning process
Reading a textbook well is the main basis for teaching and senior high school entrance examination;
The knowledge of note-taking methods is the crystallization of teachers' years of experience, and everyone prepares a set of wrong questions;
Do a good job of cleaning up a problem set, which is to broaden the knowledge;
These seemingly ordinary and simple, but it is a true portrayal of the teacher's personal experience and careful observation of our senior high school entrance examination and college entrance examination. In fact, what they repeat every day is not what the teacher just said.
There is no magical power, only ordinary. The most valuable thing is persistence.
If resources are available, find several sets of final exam questions in previous years, all from your own county and other counties (the test sites are similar). Within the specified time, find out the bottom, be familiar with the questions in each chapter, and practice the efficiency of doing the questions yourself. Many students make mistakes in exercises for the first time. If they don't correct and reflect in time, but only correct their answers, then they don't really understand where they are wrong or how to apply this knowledge, which will eventually lead to similar problems in the future.
Zhejiang education printing plate second grade mathematics knowledge related articles;
★ Eight Grade Mathematics Knowledge Points Zhejiang Education Edition Volume II
★ The first volume of mathematics knowledge points induction of the second grade teaching edition.
★ Zhejiang Education Publishing House, Grade 8, Volume II, Mathematics Final Review Materials
★ Guidance and summary of mathematics learning methods in senior two.
★ Guidance of eighth grade mathematics learning methods
★ Summary of knowledge points in the first volume of eighth grade mathematics published by People's Education Press
★ Summary of mathematical knowledge points in the first volume of the eighth grade
★ Zhejiang Education Edition Senior One Mathematics Knowledge Points
★ Summary of knowledge points in the first volume of Mathematics in the second day of the People's Education Edition
★ Appreciation of Math Mind Map in Senior Two.