Positive number: positive number greater than 0: negative number less than 00 is neither positive nor negative; Integers whose positive number is greater than negative number include: positive integer, 0, negative integer.

Scores include: positive scores and negative scores.

Rational numbers include integers, fractions/finite decimals and infinite cyclic decimals.

Number axis: take a point on the straight line to indicate 0 (origin), select the unit length, and specify the right direction on the straight line as the positive direction.

Any rational number (real number) can be represented by a point on the number axis, and points and numbers are in one-to-one correspondence.

Two numbers differ only in sign, one of which is opposite to the other; Two opposite numbers

The antonym of 0 is 0.

On the number axis, two points representing the opposite number are located on both sides of the origin, and the distance from the origin is equal.

The number represented by two points on the number axis is always larger on the right than on the left.

Absolute value: the distance between the point corresponding to a number and the origin on the number axis.

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.

Comparing the sizes of two negative numbers, the absolute value is larger but smaller.

Rational number addition rule: same sign addition, same sign addition, absolute value addition.

When the symbols are added together, the absolute value is equal to 0; Unequal, consistent with the same absolute value, absolute value subtraction.

A number plus 0 or this number.

Additive commutative law: A+B = B+A.

Additive associative law: (A+B)+C=A+(B+C)

Rule of rational number subtraction: subtracting a number is equal to adding the reciprocal of this number.

Rational number multiplication rule: two numbers are multiplied, the same sign is positive, the negative sign is negative, and the absolute value is multiplied; Multiply any number by 0, and the product is 0.

Two rational numbers whose product is 1 are reciprocal; 0 has no reciprocal.

Multiplicative commutative law: AB=BA

Law of multiplicative association: (AB)C=A (BC)

Multiplication and distribution law: A (B+C) =AB+AC.

Rational number division rule: divide two rational numbers, the same sign is positive, the different sign is negative, and the absolute value is divided.

Divide 0 by any number except 0 to get 0; 0 cannot be partitioned.

Power: the operation of finding the product of n identical factors a; The result is called power; A is the cardinal number; N is an exponent; An is pronounced as the power of n.

Rational number mixed algorithm: first calculate the power, then multiply and divide, then add and subtract; What's in brackets counts first.

Irrational number: infinite acyclic decimal, with positive and negative points.

Arithmetic square root: the square of a positive number X is equal to A, that is, X2 = A, then X is the arithmetic square root of A, which is pronounced as "root number A"

The arithmetic square root of 0 is 0.

Square root: The square root of a number X is equal to A, that is, X2 = A, then X is the square root of A (also called square root).

Positive numbers have two opposite square roots; There is only one 0, which is yourself; Negative numbers have no square root.

Square root: the operation of finding the square root of a number; A is called the root sign.

Cubic root: the cube of a number X is equal to A, that is, x3 = A, then X is the cube root of A (also called cube root).

Each number has only one cube root, and a positive number is a positive number; 0 is 0; A negative number is a negative number.

Publisher: the operation of finding the cube root of a number; A is called the root sign.

Real number: the collective name of rational number and irrational number, including rational number and irrational number. Inverse number, reciprocal number and absolute value have the same meaning and are all rational numbers. The arithmetic of real numbers is the same as that of rational numbers. After calculation, the irrational number with root sign should be simplified, so that the root sign does not contain denominator and open factor.

Second, the type

Algebraic expression: an expression that connects numbers or letters with basic operation symbols; A single number or letter is also algebraic.

Monomial: the product of numbers and letters; Individual numbers or letters are also monomials; The numerical factor is called the coefficient of a single item.

Polynomial: the sum of several monomials; Each monomial is called a polynomial term, and those without letters are called constant terms.

The number of times of the monomial: the exponential sum of all letters in the monomial; The degree of a single nonzero number is 0.

Number of items: the number of items with the most times.

Similar items: items with the same letters and the same index.

Merge similar items: merge similar items into one item; When merging similar items, the coefficients are added, and the letters and their indexes remain unchanged.

Rule of bracket removal: there is a plus sign before brackets, and the symbol of bracket removal operation remains unchanged.

The parentheses are preceded by a minus sign, and the sign of the first-level operation changes after the parentheses are removed.

Multiple brackets, starting with the brackets inside.

Algebraic expression: a general term for monomials and polynomials.

Algebraic expression addition and subtraction: first remove brackets, and then merge similar items until the formula is the simplest.

Multiplication with the same base: multiplication with the same base, constant base, exponential addition, such as am? 6? 1an = am+n (both m and n are positive integers)

Power: the power multiplied by the base and exponent, such as (am) n = AMN (m both m and n are positive integers).

Power of product: the power of the product is equal to the product of the powers of the factors in the product, such as (ab) n = anbn (n is a positive integer).

Same base powers's division: same base powers is divided, the base number is unchanged, and the exponent is subtracted, such as am ÷ n = am-n (m, n is a positive integer, a≠0, m >；; n)； A0 = 1(a≠0)； A-p = 1/AP (a ≠ 0, p is a positive integer)

Power of algebraic expression: monomial and monomial, the coefficients and powers of the same letter are added separately, and the other letters, together with their exponents, remain unchanged as the factors of the product.

Monomial and polynomial, according to the distribution law, form the terms of polynomial with monomial, and then add the products.

Polynomials and polynomials, first multiply each term of one polynomial by each term of another polynomial, and then add the products.

Square difference formula: the product of the sum of two numbers and the difference between the two numbers is equal to their square difference (A+B) (A-B) = A2-B2.

Complete square formula: (a-b) 2 = (b-a) 2 = A2-2AB+B2.

(a+b)2=(-a-b)2=a2+2ab+b2

Algebraic division: monomial division, which is divided by the coefficient and the same base power as the factor of quotient; For the letter only contained in the division formula, it is used as the factor of quotient together with its index.

Polynomials are divided by monomials. First, divide each term of the polynomial by the monomial, and then add the obtained quotients.

Factorization: transforming a polynomial into the product of several algebraic expressions.

Common factor: the same factor contained in all terms of a polynomial.

Raise the common factor: every term of a polynomial contains a common factor. Raise this common factor and turn the polynomial into the product of two factors.

Completely flat mode: formulas in the form of A2-2ab+B2 and A2+2ab+B2.

Using formula method: the multiplication formula is reversed and some polynomials are decomposed into factors.

Fraction: algebraic expression A is divided by algebraic expression B, which means A/B. A is a fractional molecule; B is the denominator of the fraction (b is not 0).

The basic properties of a fraction: both the numerator and denominator of the fraction are multiplied by (or divided by) the same algebraic expression that is not equal to 0, and the value of the fraction remains unchanged.

Reduce: reduce the distortion of the common factor of the numerator and denominator of the fraction.

Simplest fraction: a fraction in which the numerator and denominator have no common factor.

Fractional multiplication and division: fractional multiplication, numerator multiplication as numerator, denominator multiplication as denominator.

Fractional division: the numerator and denominator of division are reversed and then multiplied by the divisor.

Fraction addition and subtraction rules: fractions with the same denominator are added and subtracted, the denominator is unchanged, and the numerator is added; The score is divided first, then added and subtracted.

General score: according to the basic properties of scores, different denominator scores are converted into the same denominator score; General points usually adopt the simplest common denominator.

Fractional equation: An equation with unknowns in the denominator

Finding the root: the root of the original fractional equation whose denominator is 0; Solving fractional equation must be tested.

Third, the equation (group)

Equality: an equality equation represented by an equal sign; The equation is transitive.

Equation: An equation with unknown numbers.

Unary linear equation: An equation contains only one unknown (element), and the exponent of the unknown is 1 (degree).

The nature of the equation: an equation with the same algebraic expression added (or subtracted) on both sides at the same time will still result in an equation.

Multiplying both sides of an equation by the same number (or dividing by the same non-zero number) will still get an equation.

Moving term: the deformation from one side of the equation to the other.

Binary linear equation: an equation containing two unknowns with the number of terms 1.

Binary linear equations: A system of equations consisting of two linear equations with two unknowns.

Solution of binary linear equation: a set of unknown values suitable for binary linear equation

The solution of binary linear equations: the common solution of each equation in binary linear equations; They came in pairs.

Substitution elimination method: referred to as "substitution method" for short, it is a method that the unknown number of one equation is expressed by an algebraic expression containing another unknown number and substituted into another equation, thus eliminating an unknown number and transforming a binary linear equation group into a univariate linear equation group.

Addition and subtraction elimination method: referred to as "addition and subtraction", a method of adding (subtracting) two formulas to eliminate one of the unknowns.

Mirror method: according to the relationship between the solution of binary linear equation and the mirror image of linear function, find out the method to solve the coordinates of the intersection of two straight lines.

Integral equation: an integral equation with unknown numbers on both sides of the equal sign.

One-dimensional quadratic equation: an integral equation with only one unknown number, which is transformed into AX2+BX+C = 0 (A ≠ 0, A, B and C are constants).

Matching method: a method of obtaining the roots of a quadratic equation with one variable by completely flat matching.

Formula method: For AX2+BX+C = 0 (A ≠ 0, A, B and C are constants), when B2-4ac ≥ 0 (when B2-4ac ≤ 0, the equation has no solution), it can be solved by the root formula of a quadratic equation with one variable.

Factorization: also known as "cross multiplication", when one side of a quadratic equation is 0 and the other side can be decomposed into the product of two linear factors, the method of finding the root of the equation.

Fourth, inequality (group)

Not greater than: equal to or less than, and the symbol "≤" is read as "less than or equal to"

Not less than: greater than or greater than, and the symbol "≥" is read as "greater than or equal to"

Inequality: a formula connected by the symbol ""(or "≥"); Inequalities are transitive (except "800";

The basic property of inequality: add (or subtract) the same algebraic expression on both sides of inequality, and the direction of inequality remains unchanged.

Both sides of the inequality are multiplied (or divided) by the same positive number, and the direction of the inequality remains the same.

When both sides of the inequality are multiplied (or divided) by the same negative number, the direction of the inequality will change.

Solution of inequality: the value of an unknown quantity that can make inequality hold.

Solution set: the collective name of all solutions of an unknown inequality.

Solving inequality: the process of finding the solution set of inequality

One-dimensional linear inequality: the left and right sides of the inequality are algebraic expressions, which contain only one unknown number, and the highest degree of the unknown number is 1.

One-dimensional linear inequality group: it consists of several one-dimensional linear inequalities about the same unknown quantity.

Solution set of linear inequality group: the common part of the solution set of each inequality in linear inequality group.

Solving inequality groups: the process of finding inequality solution sets

The solution set of a linear inequality group: the same size takes the maximum, the same size takes the minimum, and the different sizes have no solution.

Verb (abbreviation for verb) function

Function: There are two variables X and Y, and a given X value corresponds to a given Y value.

Function image: an image that takes the values of independent variable X and corresponding dependent variable Y of a function as the abscissa and ordinate of points respectively, and tracks their corresponding points in rectangular coordinate system.

Variables include: independent variables and dependent variables

Relationship: a method to express the relationship between variables, and calculate the value of the corresponding dependent variable according to the value of any independent variable.

Tabular method: It indicates that the dependent variable changes with the change of the independent variable.

Image method: a method to express the relationship between variables, which is more intuitive.

Plane rectangular coordinate system: on the plane, it consists of two mutually perpendicular number axes with a common origin; The two coordinate axes divide the plane rectangular coordinate system into four parts: the first upper right quadrant, the fourth lower right quadrant, the second upper left quadrant and the third lower left quadrant.

Coordinate: If a point is perpendicular to the X axis and Y axis respectively, and the numbers A and B corresponding to the X axis and Y axis are perpendicular, then (a, b).

Coordinate addition and subtraction, graphics size and shape unchanged; Coordinate multiplication and division, the graph will change.

Linear function: If the relationship between two variables X and Y can be expressed in the form of Y = KX+B (k, b is constant, k≠0).

Proportional function: when y = kx+b (k, b is constant, k≠0) and b = 0, that is, y = kx, its image passes through the origin.

Linear function image: k>0 straight line to the left; K<0 goes straight to the right. And x axis (-b/k, 0); And y axis (0, b)

Inverse proportional function: If the relationship between two variables X and Y can be expressed in the form of Y = K/X (where K is constant and k≠0), then X is not 0.

Inverse proportional function image: k

The hyperbola of k>0 is in the first and third quadrants. In each quadrant, Y increases with the increase of X..

Quadratic function: the relationship between two variables X and Y is expressed as a function of Y = AX2+BX+C (A ≠ 0, A, B and C are constants).

The image of quadratic function: the function image is a parabola; A>0, the opening has a minimum upward.

For the image with Y = A (X-H) 2+K, the opening direction, symmetry axis and vertex coordinates are related to a, h, k H and k.

The intersection of the image of quadratic function Y = AX2+BX+C and the X axis is the root of AX2+BX+C = 0: 0, 1, 2.

Six, trigonometric function

Tangent (slope): in Rt△ABC, the ratio of the opposite side to the adjacent side of acute angle A is recorded as tan A；; ; The bigger the tan, the steeper the step.

Sine: the ratio of the opposite side to the hypotenuse of ∠A is recorded as sin A；; ; The greater the sin, the steeper the ladder.

Cosine: the ratio of the adjacent side to the hypotenuse of ∠A is recorded as cos A；; ; The smaller the cos A, the steeper the step.

The tangent, sine and cosine of acute angle a are trigonometric functions of ∠ a.

Elevation angle: the acute angle formed by the line of sight and the horizontal plane when observing a higher target from a lower position.

Depression angle: the acute angle formed by the line of sight and the horizontal line when observing a low target from a height.

Special trigonometric function value

Dark color

commit a crime

cosine

30o

45 degrees

1

60o

Seven. Statistics and probability

Scientific notation: a notation in which a number is written as * 10n.

Statistical chart: a chart that visually represents the collected data.

Sector statistical chart: circle and sector are used to represent the relationship between the whole and the part, and the size of the sector reflects the percentage of the part in the whole; In the fan-shaped statistical chart, the percentage of each part in the whole is equal to the ratio of the central angle of the corresponding fan-shaped part to 3600.

Bar chart: clearly show the specific figures of each item.

Broken line statistical chart: clearly reflect the changes of things.

Deterministic events include: inevitable events that will definitely happen (P = 1) and impossible events that will definitely not happen (P = 0).

Uncertain events: events that may or may not occur (0

Significant digits: for approximation, from the first digit on the left that is not 0 to the nearest digit.

Both sides of the game are fair: both sides have the same possibility of winning.

Arithmetic average: referred to as "average" for short, it is the most commonly used and is greatly influenced by extreme value; weighted average

Median: the number in the middle of the data arranged by size, which is simple to calculate and less affected by extreme values.

Mode: the data with the highest frequency in a group of data is less affected by extreme values and has little to do with other data.

Average, mode and median are all representatives of data and describe the "average level" of a group of data.

Census: conduct a comprehensive census of the inspected object for a certain purpose; All subjects are called whole, and each subject is called individual.

Sampling survey: select some individuals from the population for investigation; Some individuals extracted from the population are called samples (representatives)

Random survey: According to the principle of equal opportunity, the probability of each individual in the population is the same.

Frequency: The number of times each object appears.

Frequency: the ratio of the number of times an object appears to the total number of times.

Grade difference: the difference between the largest data and the smallest data in a group of data, which describes the degree of data dispersion.

Variance: the average value of the square of the difference between each data and the average value, which describes the degree of dispersion of the data.

The variance calculation formula S2 = [(x1-x) 2+(x2-x) 2+…+(xn-x) 2]/n = (x12+x22+…+xn2-nx2)/n.

Standard Variance: The arithmetic square root of variance describes the degree of data dispersion.

The smaller the grade difference, variance and standard deviation of a set of data, the more stable this set of data is.

The probability of an event can be easily found by using a tree diagram or table.

In two contrast images, the meaning of the same unit length on the coordinate axis is the same, and the ordinate is drawn from 0.