Summary of knowledge points of compulsory elective courses in senior high school mathematics

Part XII Statistics and Statistical Cases 1. Sampling method (1) Simple random sampling: Generally speaking, if the number of people in a group is n, a sample with a capacity of n is extracted from it by the method of not putting it back one by one, and the chances of each individual being extracted are equal, which is called simple random sampling. Note: ① The probability of each individual being drawn is; ② Common simple random sampling methods are: drawing lots; Random number method. ⑵ Systematic sampling: When the group is large, the group can be divided into several parts in a balanced way, and then an individual can be extracted from each part according to the preset rules to get the required samples. This sampling method is called systematic sampling. Note: Steps: ① numbering; ② subsection; ③ In the first paragraph, the number of individuals was determined by simple random sampling; (4) Extracting samples according to preset rules. ⑶ Stratified sampling: When the known population consists of several parts with obvious differences, in order to make the sample reflect the overall situation more comprehensively, the population is divided into several parts, and then sampling is carried out according to the proportion of each part in the population. This kind of sampling is called stratified sampling. Note: The number of individuals in each part = the number of individuals in this part. 2. Estimation of total feature number: (1) sample average; (2) sample variance; (3) Sample standard deviation =; 3. Correlation coefficient (judging the linear correlation between two variables): Note: (1) > 0, the variables are positively correlated; & lt0, the variables are negatively correlated; (2) ① The closer to 1, the stronger the linear correlation between the two variables; ② When it is close to 0, there is almost no linear correlation between the two variables. 4. Judgment of regression effect in regression analysis: (1) Sum of squares of total deviation: (2) Residual:; ⑶ Sum of squares of residuals:; (4) Regression sum of squares:-; 5] Correlation index. Note: ① The greater the knowledge, the smaller the sum of squares of residuals, and the better the model fitting effect; ② The closer to 1, the better the regression effect. 5. Independence test (classification variable relationship): The larger the random variable, the stronger the relationship between two classification variables, and vice versa. X. Derivative 1. The meaning of derivative: the slope of the tangent of the curve at this point (geometric meaning), instantaneous speed, marginal cost (cost is the derivative of the function to the dependent variable, and the output is the independent variable), (c is a constant), .2. Derivative of Polynomial Function and Monotonicity of Function: In an interval (all points are equal), it is increasing function in this interval. This function exists everywhere, and "left negative and right positive" takes the minimum value there. Note: ① Existence is a necessary and sufficient condition where the function takes the extreme value. (2) The method of finding the extreme value of a function: first find the domain, then find the derivative, find the boundary point of the domain, and find the extreme value by listing. In particular, we must consider the condition of giving the maximum (minimum) value of the function and the test of "Zuo Zheng Right Negative" (). (2) The maximum value of a function in a closed interval is the "maximum value" between the maximum value of the function in this interval and its endpoint value; The minimum value of a function in a closed interval is the "minimum value" between the minimum value of the function in this interval and its endpoint value; Note: the step of finding the maximum value of derivative: first find the definition domain, then find the point where the derivative is 0 and the derivative does not exist, and then compare the final value of the definition domain with the function value corresponding to the point where the derivative is 0, where the maximum value is the maximum value and the minimum value is the minimum value. The tangent of a point on the parabola of a quadratic parabola, but the tangent of a point on the parabola of a cubic curve contains two lines, one is the tangent of the point and the other is the intersection of the point and the curve. The combination of numbers and shapes can solve related problems such as equation inequality. XI。 Probability, Statistics and Algorithms Part XVI Science Elective Part 1. Permutation, combination and binomial theorem (1) permutation number formula: = n (n-1) (n-m+1) = (m ≤ n); ⑵ Combination number formula: (m ≤ n),; ⑶ The nature of combination number: (4) Binomial theorem: ① General term: ② Pay attention to the difference between binomial coefficient and coefficient; (5) The properties of binomial coefficient: ① binomial coefficient equal to the distance between two ends; ② If n is an even number, the binomial coefficient (+1) of the middle term is the largest; If n is an odd number, the binomial coefficient (sum+ 1) of the middle two terms is the largest; ③ (6) Pay attention to the assignment method when calculating the sum of binomial expansion coefficients or the sum of odd (even) coefficients. 2. Probability and Statistics (1) Random Variable Distribution Table: (1) Properties of Random Variable Distribution Table: pi ≥ 0, I = 1, 2, …; p 1+p2+…= 1； ② Discrete random variable: x1x2 … xn … pp1p2 … pn … Expectation: ex = x1p1+x2p2+…+xnpn+…; Variance: dx =；; Note:; ③ two-point distribution: X 0 1 expectation: ex = p；; Variance: dx = p (1