1 absolute value:?
On the axis of (1) number, the distance between the point corresponding to a number and the origin is called the absolute value of the number. ?
The absolute value of a positive number is himself, the absolute value of a negative number is his opposite number, and the absolute value of 0 is 0, that is,
3 decomposition factor:?
(1) Changing a polynomial into the product of several algebraic expressions is called decomposing this polynomial. ⑵ Methods: ① extraction of common factor, ② use of formula, ③ grouping decomposition and ④ cross multiplication. 4 unary linear equation:?
(1) In an equation, there is only one unknown, and the exponent of the unknown is 1. Such an equation is called a linear equation. ⑵ Steps to solve the linear equation with one variable: remove the denominator, move the term, merge the similar terms, and change the unknown coefficient into 1. ⑶ Discussion on the solution of equation ax=b?
① When a≠0, the equation has a unique solution x = b/a;
② When a=0, 0b? When the equation has no solution;
③ When a=0 and b=0, the equation has countless solutions; At this time, any real number is the solution of the equation. ?
5 binary linear equation:?
(1) An equation group consisting of two binary linear equations is called binary linear equations. ?
(2) A set of unknown values applicable to a binary linear equation is called the solution of this binary linear equation.
(3) The common * * * solution of each equation in the binary linear equations is called the solution of this binary linear equations. (4) Methods of solving binary linear equations: ① substitution elimination method, ② addition and subtraction elimination method. 6 Inequality and Inequality Group (1) Inequality:?
The (1) operator is not equal to (>, ≡ and<). The connected formulas are called inequalities. ?
② Add or subtract the same algebraic expression on both sides of the inequality, and the direction of the inequality remains unchanged. ③ Both sides of inequality are multiplied or divided by a positive number, and the direction of inequality remains unchanged. ④ Both sides of inequality are multiplied or divided by the same negative number, and the unequal numbers are in opposite directions. (2) Solution set of inequality:?
(1) can make the value of an unknown inequality known as the solution of inequality. ?
(2) All solutions of an inequality with unknowns constitute the solution set of this inequality. ③ The process of finding the solution set of inequality is called solving inequality. (3) One-dimensional linear inequality:
An inequality with algebraic expression on both sides and only one unknown number, and the highest degree of the unknown number is 1, is called a linear inequality with one variable. ?
(4) One-dimensional linear inequalities:?
(1) Several linear inequalities about the same unknown quantity are combined into a linear inequality group. ② The common part of the solution set of each inequality in a linear inequality group is called the solution set of this linear inequality group. ?
③ The process of finding the solution set of inequality group is called solving inequality group. ?
8 function?
(1) variable: dependent variable, independent variable. ?
When using images to represent the relationship between variables, we usually use points on the horizontal axis as independent variables and points on the vertical axis as dependent variables. ?
(2) linear function: ① If the relationship between two variables Y and X can be expressed in the form of Y = KX+B (where B is a constant and K is not equal to 0), then Y is said to be a linear function of X. ② When b=0, Y is said to be a proportional function of X. (3) What are the images and properties of linear functions?
① Take the values of the independent variable X and the corresponding dependent variable Y of a function as the abscissa and ordinate of a point respectively, and trace the corresponding point in the rectangular coordinate system. A graph composed of all these points is called an image of a function. ② The image with the proportional function y=kx is a straight line passing through the origin. ?
(3) In a linear function, when k? 0，b？ O, and then pass through quadrants 2, 3 and 4; When k? 0，b？ 0, which passes through 1, 2, 4 quadrants; When k? 0，b？ 0, it passes through 1, 3, 4 quadrants; When k? 0，b？ 0, it passes through 1, 2, 3 quadrants. 4 when k? The values of 0 and y increase with the increase of x value, when k? The values of 0 and y decrease with the increase of x value. ?
(4) Quadratic function:
9 Symmetry of graphics?
(1) Axisymmetric graph: ① If a graph is folded along a straight line and the parts on both sides of the straight line can overlap each other, then the graph is called an axisymmetric graph, and this straight line is called an axis of symmetry. (2) The line segment determined by two points about the axis of symmetry on the axisymmetric graph is vertically bisected by the axis of symmetry. ?
(2) Centrally symmetric figure: ① On the plane, a figure rotates around a point 180 degrees. If the figures before and after rotation overlap, then this figure is called a central symmetric figure, and this point is called its symmetric center. ② The line segments connected by each pair of corresponding points on the central symmetric figure are equally divided by the symmetric center. 10 plane rectangular coordinate system
(1) In a plane, two mutually perpendicular number axes with a common origin form a plane rectangular coordinate system. The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, X axis and Y axis are collectively called coordinate axes, and their common origin O is called the origin of rectangular coordinate system.
(2) Sector statistical chart: ① A circle is used to represent the population, and each sector in the circle represents a different part of the population, and the size of the sector reflects the percentage of this part in the population. This kind of statistical chart is called departmental statistical chart. (2) In the sector statistical chart, the percentage of each part in the whole is equal to the ratio of the central angle of the sector corresponding to this part to 360 degrees. ?
(3) Advantages and disadvantages of various statistical charts: ① Bar chart: the specific figures of each item can be clearly displayed; 2 broken line statistical chart: it can clearly reflect the changes of things; (3) Department chart: It can clearly show the percentage of each part in the total.
(6) Weighted average: The importance of each data in a set of data may be different. Therefore, when calculating the average of this group of data, each data is often given a weight, which is the weighted average. ?
(7) Median and mode: ①N 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 Comparison of advantages and disadvantages: average value: all 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 affected by extreme values; Median: the calculation is simple, and it is less affected by extreme value, but it can't make full use of all data information; Pattern: when the number of repetitions of each data is roughly equal, the pattern often has no special meaning. ?
(8) Survey: ① A comprehensive survey of the respondents for a certain purpose is called a general survey, in which all the respondents are called the whole, and each object that constitutes the whole is called an individual. (2) Select some individuals from the population for investigation, which is called sampling investigation, and select some individuals from the population as a sample of the population. Sampling survey only investigates a small number of individuals in the population, so it has the advantages of small survey scope and saving time, manpower, material resources and financial resources, but its survey results are often not as accurate as those obtained by census. In order to obtain more accurate survey results, the main samples should be representative and extensive when sampling. ?
(9) Frequency and frequency: ① The frequency of each object and the ratio of the frequency of each object to the total frequency. (2) When the collected data take values continuously, we usually group the data properly first, and then draw the histogram of frequency distribution. ?
(10) data fluctuation: ① range refers to the difference between the largest data and the smallest data in a group of data. ② Variance is the average of the sum of squares of the difference between each data and the average. ③ The standard deviation is the arithmetic square root of variance. Generally speaking, the smaller the range, variance or standard deviation of a set of data, the more stable the set of data. ?
(1 1) Possibility of an event: ① There are some things that we can be sure will happen, which are called inevitable events; Some things we can be sure will not happen. These things are called impossible events. Inevitable events and impossible events are certain. There are many things that we are not sure will happen. These things are called uncertain events. (3) Generally speaking, the possibility of uncertain events is different. ?
(12) Probability: ① People usually use 1 (or 100%) to indicate the possibility of inevitable events and 0 to indicate the possibility of impossible events. The fairness of the game means that both sides have the same possibility of winning. (3) The probability of inevitable events is 1, and it is marked as p (inevitable events) =1; The probability of an impossible event is 0, and it is recorded as p (impossible event) = 0; If a is an uncertain event, then 0