Positive numbers: positive numbers are greater than 0Negative numbers: negative numbers less than 00 are neither positive nor negative; positive numbers are greater than negative numbersIntegers include: positive integers, 0, negative integers

Fractions include: positive fractions, negative fractions

Rational numbers include: integers, fractions/finite decimals, infinitely recurring decimals

Numerical axes: take a point on a straight line and express it as 0 (origin), select the unit length, specify the direction to the right on the line as the positive direction

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

Two numbers differ only by their sign, and one of them is the opposite of the other; two opposite numbers of each other

The opposite of 0 is 0

On the Two points on the number axis, representing opposite numbers, are located on either side of the origin and are equidistant from the origin

The two points on the number axis represent numbers where the one on the right is always greater than the one on the left

Absolute value: the distance between the point on the number axis that corresponds to a number and the origin

The absolute value of a positive number is itself; the absolute value of a negative number is its opposite; and the absolute value of 0 is 0

Two negative numbers compare the size, the absolute value of the larger instead of small

Rational numbers addition law: the same number is added, no change in the sign, the absolute value of the addition

Different sign is added, the absolute value of the absolute value of equal to get 0; unequal, in line with the same and absolute value of the larger, the absolute value of the subtraction

A number plus 0, is still the same number

Additions exchange law: A + B = B + A

The law of addition: (A + B) + C = A + (B + C)

The law of subtraction of rational numbers: subtracting a number is the same as adding the opposite of that number

The law of multiplication of rational numbers: multiplying two numbers with the same sign yields a positive result, while a different sign is negative, and absolute values are multiplied together; multiplying any number by 0 yields a product of 0

The two rational numbers that yield a product of 1 are the inverses of each other; 0 has no inverse

The law of multiplicative exchange: AB=BA

The law of multiplicative union: (AB)C=A (BC)

The law of multiplicative distribution: A (B+C) =AB+AC

The law of division of rational numbers: two rational numbers divided by the same number get positive, the negative of a different number, and the absolute value divides them

0 divides any number that is not 0 gets 0; 0 does not be a divisor

Multiplication: the operation of finding the product of n identical factors a; the result is called a power; a is the base; n is the exponent; an is pronounced as the nth power of a

Rational number mixing algorithms: multiplication, then multiplication and division, then addition and subtraction; parentheses come first

Irrational numbers: infinite irreducible decimals, positive and negative.

Arithmetic square root: the square of a positive number x is equal to a, i.e., x2 = a, then x is the arithmetic square root of a, pronounced "root a."

The arithmetic square root of 0 is 0

Square root: the square root of a number x is equal to a, i.e., x2 = a, then x is the square root of a (also called: Quadratic root)

A positive number has two square roots that are opposite to each other; 0 has only one, which is itself; negative numbers do not have a square root

Squaring: the operation of finding the square root of a number; a is called the number to be squared

Cubic root: the cube of a number x is equal to a, i.e., x3 = a, and then x is a cubic root of a (also known as: cubic root)

Each number has only one cubic root; positive numbers are positive; 0's are 0's; negative numbers are negative

Cubing: the operation of finding the cubic root of a number; a is called the number being cubed

Real Numbers: a collective term for rational and irrational numbers, including rational numbers, irrational numbers. Opposites, inverses, absolute values have the same meaning and rational numbers. The real numbers have the same arithmetic rules as the rational numbers. After the calculation of the irrational numbers appearing with a root sign to simplify, so that the number of the square does not contain the denominator and open all the factors

Two, formula

Algebraic formula: the basic operation symbols to connect the numbers or letters of the formula; separate numbers or letters is also an algebraic formula

Monomials: the product of the number and the letter; separate numbers or letters are also monomials; the numerical factor is called the coefficients of the monomials <

Polynomial: the sum of several monomials; each monomial is called a term of the polynomial; those containing no letters are called constant terms

Number of monomials: the sum of the exponents of all the letters of a monomial; the number of times a single nonzero number is 0

Number of polynomials: the number of times the term with the highest number of times

Terms of a kind: terms containing the same number of letters and whose exponents are identical

Terms of a kind: terms whose numbers or letters contain the same number and whose exponents are also the same

Merging like terms: combining like terms into one term; when combining like terms, the coefficients are added, and the letters and the exponents of the letters remain the same

Rule for removing parentheses: parentheses are preceded by a plus sign, and the symbol of the removing parentheses operation remains unchanged

Parentheses are preceded by a minus sign, and the sign of the removing parentheses (the first level of the operation) operation changes

Multiple parentheses, which are formed from inside the parentheses Start to go

Integer: monomials and polynomials collectively

Integer addition and subtraction operations: first remove the parentheses, and then merge like terms, know the formula is the simplest

Multiplication of powers of the same base: multiplication of powers of the same base, the base remains unchanged, and the exponents are added together, such as am ?6 ?1an = am + n (m, n is a positive integer)

Multiplication of powers: Multiplication of powers, base remains unchanged, and the exponents are multiplied together, such as am ?6 ?1an = am + n (m, n is positive integer)

Power multiplication: power multiplication, base remains unchanged, and the exponent is added together, such as am? , n is a positive integer, a ≠ 0, and m>n); a0 = 1 (a ≠ 0); a-p = 1/ap (a ≠ 0, p is a positive integer)

Multiplication of integers: monomials and monomials, add the coefficients, powers of the same letter separately, and the remaining letters together with their exponents remain unchanged as the factors of the product

Monomials and polynomials. By the law of distributions go from a monomial to each term of a polynomial, then add the products

Polynomials and polynomials, multiply each term of one polynomial by each term of the other, then add the products

Square difference formula: the product of the sum of two numbers and the difference between those two numbers is equal to their squared 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

Integer division: monomials are divided by the coefficients and powers of the same base as factors of the quotient; for a letter contained only in the divisor, it is a factor of the quotient together with its exponent

Polynomials divided by monomials are divided by the monomials, and then the quotient is added together

Decomposition of factoring: factorize a polynomial into the product of several integers in the Form

Common-factorization: the polynomial contains the same factor in each term

Presenting the common factor: each term of the polynomial contains a common factor, present this common factor, and reduce the polynomial to the product of the two factors

Complete equality: formulas such as a2 - 2ab + b2 and a2 + 2ab + b2

The use of formulas: the multiplication formula is reversed, used to factorize certain polynomials

Fractions: the whole formula A divided by the whole formula B, expressed as A/B. A is the numerator of the fractional formula; B is the denominator of the fractional formula (B is not 0)

Basic properties of fractions: fractions of the molecule and the denominator of the fractional formula are multiplied by (or divided by) the same integer not equal to 0, the value of the fractional formula remains unchanged

Approximate fractions : a fraction of the numerator and denominator of the common factor of the common factor of the transformation

The simplest fractions: the numerator and denominator do not have a common factor of the fraction

Fractional multiplication and division rule: fractional multiplication, the numerator multiplied by the numerator for the numerator, the denominator multiplied by the denominator as the denominator

Division of fractions, the division of the formula, the molecules and denominators of the formula reversed position and then multiply the formula with the divisor

Fractional addition and subtraction rules: the same Denominator fractional addition and subtraction, the denominator remains unchanged, the numerator is added; different fractions first through the denominator, and then add and subtract

Through the denominator: according to the basic properties of the fractional formula, different denominators fractional into the same denominator fractional process; through the denominator is often taken to the simplest denominator

Fractional equations: equations with unknowns in the denominator

Incremental roots: make the denominator of the original fractional equation of the original equation of the root of the denominator is 0; solve fractional equations must be tested

Three, equations (groups)

Equation: equations with the equal sign to indicate equality; equations have transferability

Equation: equations containing unknowns

One-variable equations: an equation that contains only one unknown (yuan), and the unknown exponent of 1 (times)

Equation properties: both sides of the equation at the same time Adding (or subtracting) the same algebraic formula at the same time results in an equation

Multiplying both sides of an equation by the same number (or dividing by the same non-zero number) at the same time results in an equation

Translocation: a distortion that involves moving from one side of an equation to the other

Divisible equations: equations containing two unknowns and containing unknowns whose exponent is 1 (times)

One solution of a quadratic equation: the value of a set of unknowns that fits into a quadratic equation

Solution of a system of quadratic equations: the common **** solution of the individual equations of a system of quadratic equations; they occur in pairs

Substitution elimination: abbreviated to "Substitution method", the method of transforming a system of quadratic equations into a single equation by expressing one of the unknowns of one of the equations in terms of an algebraic formula containing the other unknown and substituting it into the other equation, thus eliminating one of the unknowns

Additive and subtractive elimination method: abbreviated as "additive and subtractive elimination method "by adding (subtracting) two equations to eliminate one of the unknowns

Image method: according to the relationship between the solution of the quadratic equation and the image of the primary function, find out the coordinates of the intersection of the two straight lines to find the solution

Integrated equations: equations on both sides of the equal sign on the unknowns

Integrated equations: equations that contain only one unknown, the first two sides of the equations. unknown, reduced to ax2 + bx + c = 0 (a ≠ 0, a,b,c are constants)

Matching method: the method of obtaining the roots of a quadratic equation by matching into a perfect square

Formulas method: for ax2 + bx + c = 0 (a ≠ 0, a,b,c are constants), when b2 - 4ac ≥ 0 (when b2-4ac ≤ 0, the equation has no solution), the use of quadratic equations to find the roots of the formula to solve the method

Decomposition of the factorization method: also known as the "cross multiplication method", when the quadratic equation of one side of 0, the other side of the equation can be decomposed into the product of the two factors, the method of solving for the roots of the equation

Decomposition of the equation: also known as "the cross multiplication method", the method of solving for the roots of the equation

Four, inequality (group)

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

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

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

Inequality: with the symbol "<" (or "≤"), "≤", "≤", "≤", "≤", "≤", "≤", "≤", "≤", "≤", "≤". "), ">" (or "≥"); inequality is transitive (except "≠")

Basic Inequality Properties: both sides of the inequality are added to (or subtracted from) the same integer, the direction of the inequality sign remains unchanged

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

Both sides of the inequality are multiplied (or divided) by the same negative number, the direction of the inequality sign changes

Solutions to the inequality: the values of the unknowns that make the inequality valid

Solutions to the set: an Collective term for all solutions to an inequality containing an unknown

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

One-variable inequality: an inequality whose left and right sides are integers, which contains only one unknown, and whose highest number of unknowns is 1

Set of one-variable inequalities: a set of one-variable inequalities that consists of several one-variable inequalities with respect to the same unknown combined

Set of one-variable inequalities: an inequality with respect to a single unknown that consists of several one-variable inequalities combined

The solution set of a set of one-variable inequalities: the common *** part of the solution set of each inequality in a set of one-variable inequalities

Solution of a set of inequalities: the process of finding the solution set of an inequality

The solution set of a set of one-variable inequalities: the same big take the big one, and the same small take the small one, and the size of the difference is no solution

Five, function

Function: there are two variables, x and y, and there are two variables, x and y, which are the same. Given the x value corresponds to find a y value

Function image: a function of the independent variable x and the corresponding value of the dependent variable y as the point of the horizontal and vertical coordinates, respectively, in the right-angled coordinate system to trace out its corresponding points, so the points composed of the image

Variables include: the independent variable and dependent variable

Relationships: a method of expressing the relationship between the variables, according to the value of any one of the value of the independent variable to find the value of the corresponding dependent variable

Tabular method: represents the change of the dependent variable with the change of the independent variable

Image method: a method to represent the relationship between the variables, more intuitive

Plane right-angled coordinate system: in the plane, composed of two mutually perpendicular and have a common **** origin of the number of axes; two axes of the plane right-angled coordinate system is divided into 4 part: the upper right is the first quadrant, the lower right is the fourth quadrant, the upper left is the second, the lower left is the third

Coordinates: over a point to the x-axis, y-axis as a vertical line, the foot of the vertical line in the x-axis, y-axis corresponding to the number of a, b, then (a, b)

Coordinates plus and minus, the graph of the size and shape of the same; coordinate multiplication and division, the graph of the graph will be changed

Once a function: If two variables x, y of the Relationship can be expressed in the form of y = kx + b (k, b is a constant, k ≠ 0)

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

Photographs of a primary function: k>0 straight line to the left; k<0 straight line to the right. With the x-axis (-b/k, 0); with the y-axis (0, b)

Inverse proportional function: if the relationship between two variables x, y can be expressed in the form y = k/x (k is a constant, k ≠ 0), x is not 0

Image of the inverse proportional function: k<0 bisecting the curve in the second and fourth quadrants, and y decreases as x increases in each quadrant

k>0 hyperbola in one and three quadrants, in each quadrant, y increases as x increases

quadratic function: the relationship between two variables x, y is expressed as a function of y = ax2 + bx + c (a ≠ 0, a, b, c are constants)

quadratic function of the image: the image of the function is a parabola; a>0, the opening upward with a minimum value of and a<0 has a maximum value downward

The image of y = a(x-h)2 + k, the direction of the opening, the axis of symmetry, and the coordinates of the vertices are related to a,h,k

The intersection of the image of the quadratic function y = ax2 + bx + c with the x-axis is the root of ax2 + bx + c = 0: 0, 1, and 2 roots

VI, Trigonometry

Tangent (slope ratio): the ratio of the opposite side of an acute angle A to its neighbor in Rt△ABC is noted as tan A; the larger tan A is, the steeper the ladder is

Sine: the ratio of the opposite side of ∠A to its hypotenuse is noted as sin A; the larger sin A is, the steeper the ladder is

Cosine: the ratio of the neighbor of ∠A to its hypotenuse is noted as cos A; the smaller cos A is, the The steeper the ladder

The tangent, sine, and cosine of an acute angle A are all trigonometric functions of ∠A

Elevation angle: the acute angle that the line of sight makes with the horizontal when observing a high target from a low point

Pitch angle: the acute angle that the line of sight makes with the horizontal when observing a low target from a high point

Special trigonometric values

tan

sin

cos

30o

45o

1

60o

VII. Statistics and Probability

Scientific notation: notation in which a number is written in the form a*10n

Statistical graphs: graphs that graphically represent the data collected

Fan chart: a circle and fan to represent the relationship between the whole and the part, the size of the fan reflects the size of the percentage of the part of the whole; in a fan chart, the percentage of the whole for each part is equal to the ratio of the corresponding fan's central angle to 3600

Bar chart: a chart that clearly shows the exact number of items in each

Bar chart: a chart that clearly reflects the changes in things

Line chart: a chart that clearly reflects the changes

Certain events include: certain events that will definitely occur (P = 1) and impossible events that will definitely not occur (P = 0)

Uncertain events: events that may or may not occur (0<P<1); uncertain events occur with different degrees of likelihood; the probability of an uncertain event: can be obtained by dividing the outcome of the event by the so-called probability of the event. To find the theoretical probability

Effective number: for an approximate number, from the first number on the left that is not 0, to the exact number of digits until the number of digits

Fairness of both sides of the game: both sides of the same likelihood of winning

Arithmetic mean: referred to as the "average", the most commonly used, subject to the extreme values of Weighted average

Median: data arranged by size, in the middle of the number, simple to calculate, less affected by the extreme value

Plural: a group of data in the most frequent data, less affected by the extreme value of the impact of the other data is not very related

Mean, plural, median are representatives of the data, depicting a group of data of the "average level" of the "average"

Census: a comprehensive survey of the objects to be examined for a certain purpose; the whole of the objects to be examined is called the whole, and each object to be examined is called an individual

Sampling: a survey of some of the individuals taken from the whole; a portion of the individuals drawn from the whole is called a sample (representative)

Random survey: survey according to the principle of equal opportunity, each individual in the overall survey has the same probability

Frequency: the number of times each object occurs

Frequency: the ratio of the number of times each object occurs to the total number of times

Level of variance: a set of data in the largest data and the smallest data difference, portraying the degree of dispersion of the data

Covariance: the average of the squares of the differences between the data and the mean

Variance: each data The average of the squares of the differences from the mean, portraying the degree of dispersion of the data

Calculation formula for variance s2 = [(x1-x)2+ (x2-x)2+......+(xn-x)2]/n = (x12+x22+......+ xn2-nx2)/n

Standard variance: the arithmetic square root of the variance portrays the degree of dispersion of the data

The smaller the variance, variance, and standard deviation of a set of data, the more stable that set of data will be

Using tree diagrams or tables to conveniently find the probability of an event occurring

Two contrasting images in which the same unit of length on the axes represent the same meaning consistent, with vertical coordinates drawn from 0