Definition of rational number (1): a number consisting of integers and fractions. Include positive integer, 0, negative integer, positive fraction and negative fraction. Can be written as the ratio of two integers.
(2) Number axis: In mathematics, numbers can be represented by points on a straight line, which is called number axis.
(3) Inverse number: Inverse number is a mathematical term, which means that two numbers with equal absolute values and opposite signs are opposite to each other.
(4) Absolute value: Absolute value is the distance from a point corresponding to a number on the exponential axis to the origin. The absolute value of a positive number is itself, and the absolute value of a negative number is its inverse; The absolute value of 0 is 0, two negative numbers, the larger absolute value is smaller.
(5) Addition and subtraction of rational numbers
Add the same symbol to the same symbol and add the absolute values. For the addition of different symbols, take the sign of the addend with large absolute value, and subtract the sign with small absolute value from the sign with large absolute value.
(6) Multiplication of rational numbers
Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value.
Multiply any number by 0, and the product is 0. For example: 0× 1=0
(7) Division of rational numbers
Dividing by a number that is not zero is equal to multiplying the reciprocal of this number.
Divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Divide by 0
For any number that is not 0, you get 0.
(8) Power of rational number
The operation of finding the product of n identical factors is called power, and the result of power is called power. Where a is called the base and n is called the exponent. When a. When it is regarded as the result of the n power of A, it can also be read as "the n power of A" or "the n power of A"
Algebraic expression (1) Algebraic expression: it is a general term for monomials and polynomials and is a part of rational formulas. In rational expressions, there can be five operations: addition, subtraction, multiplication, division and multiplication, but in algebraic expressions, the divisor cannot contain letters.
(1) monomial: An algebraic expression composed of the product of numbers or letters is called a monomial, and a single number or letter is also called a monomial.
(2) Polynomial: An algebraic expression formed by adding several monomials is called polynomial.
③ Coefficient: The sum of the indices of all the letters in a monomial is called its number.
④ Times: The sum of the indexes of all variables in a single item is called the times of this single item.
⑤ Term: Each monomial that constitutes a polynomial is called a polynomial term.
⑥ Degree of Polynomial: The degree of the term with the highest degree in the polynomial is called the degree of the polynomial.
⑦ Similar terms: In polynomials, terms with the same letters and the same index of the same letters are called similar terms.
⑧ Merging similar terms: Merging similar terms in polynomials into one term is called merging similar terms.
(2) Addition and subtraction of algebraic expressions
Algebraic expression addition and subtraction operation, if you encounter parentheses, first remove the parentheses, and then merge similar items.
Definition of one-dimensional linear equation (1):
One-dimensional linear equation refers to an equation with only one unknown number, the highest order of which is 1, and both sides are algebraic expressions, which is called one-dimensional linear equation. Finding the value of the unknown quantity in the equation is called the solution of the equation.
(2) the steps of solving a linear equation with one variable
(1) Denominator: Turn the coefficient into an integer.
(2) stent removal
③ Shift term: shift the sign of an item on one side of the equation to the other side.
④ Merge similar items.
⑤ The coefficient is 1.
Intersecting lines and parallel lines (1)
In the same plane, there are two positional relationships between two straight lines: intersecting and parallel. If two straight lines have only one common point, they are said to intersect.
(2) Vertical line
One of the four angles formed by the intersection of two straight lines is a right angle, that is, the two straight lines are perpendicular to each other, one of which is called the perpendicular of the other straight line, and the intersection point is called the vertical foot.
(3) Equilibrium angle
Two straight lines A and B are cut by a third straight line C (or the intersection of C of A and B). On the same side of the cutting line C, cut the corners on the same side of the two straight lines A and B.. We call these two angles congruent angles.
(4) Internal dislocation angle
Two straight lines are cut by a third straight line, and the two corners are on both sides of the cutting line and sandwiched between the two cut straight lines. Diagonal lines with this positional relationship are called inscribed angles.
(5) ipsilateral internal angle
The two angles at which two straight lines intersect with the third line are called inner angles on the same side, which are located on the same side of the cutting line and within the cutting line.
(6) Parallel lines
In geometry, two straight lines that never intersect (and never coincide) on the same plane are called parallel lines.
The nature of parallel lines: ① Two lines are parallel, and the included angle is equal; ② Two straight lines are parallel and the internal dislocation angles are equal; ③ The two straight lines are parallel and complementary.
(7) Translation
Translation means that all points on the map move equidistantly along a straight line in the same plane. This kind of graphic movement is called graphic translation movement, which is called translation for short.
Square root of real number (1)
Square root is also called quadratic square root, which is expressed as √ ~ where the non-negative square root is called arithmetic square root. Positive numbers have two real square roots in opposite directions, while negative numbers have no square roots.
(2) Cubic root
If the cube of a number is equal to A, then this number is called the cube root of A, also called the cube root.
Cubic root property
(1) In the range of real numbers, there is only one cube root of any real number.
② Within the range of real numbers, negative numbers cannot be squared, but they can be squared.
The cube root of 0 is 0.
(3) Real numbers
Real number is a general term for rational number and irrational number. Real numbers are closed, ordered, transitive, dense and complete.
Definition of Binary Linear Equations (1)
Binary linear equation refers to an equation with two unknowns (such as X and Y), and the degree of the unknowns is 1. Two combined linear equations with two unknowns are called binary linear equations.
(2) The solution method of binary linear equation
① Substitution in elimination method.
② Method of addition, subtraction and elimination.
Three Expressions of Quadratic Function (1)
The general formula of quadratic function is: y=ax? +bx+c(a≠0).
Vertex of quadratic function: y=a(x-h)? The coordinate of +k vertex is (h, k)
Intersection point of quadratic function: y=a(x-x? )(x-x？ ) function and image intersect at (x? 0) and (x? ,0)
(2) Properties of quadratic function
① The image of quadratic function is a parabola, and parabola is an axisymmetric figure. The symmetry axis is a straight line x=-b/2a.
② Quadratic coefficient A determines the opening direction and size of parabola.
③ Both the first-order coefficient b and the second-order coefficient a*** determine the position of the symmetry axis.
④ The constant term c determines the intersection of parabola and Y axis. The parabola intersects the y axis at (0, c).
(3) Symmetry axis formula of quadratic function
Quadratic function image is an axisymmetric figure. The symmetry axis is a straight line x=-b/2a.
The only intersection of the symmetry axis and the quadratic function image is the vertex p of the quadratic function image.
Especially when b=0, the symmetry axis of the quadratic function image is the Y axis (that is, the straight line x=0).
A and B have the same sign, and the symmetry axis is on the left side of Y axis;
A and B are different symbols, and the symmetry axis is on the right side of the Y axis.