The rational number (1), the important content of the first volume of seventh grade mathematics.
(1) Definition: 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"
(2) Algebraic expression
(1) Algebraic expression: it is the general name of monomial and polynomial, and it is a part of rational formula. 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.
(3) One-dimensional linear equation
(1) Definition:
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.
(4) Geometry
(1) geometry
All kinds of figures abstracted from objects are collectively called geometric figures. Geometric graphics are divided into three-dimensional graphics and plane graphics.
(2) Three-dimensional graphics
A three-dimensional figure is a geometric figure whose parts are not in the same plane, and it is surrounded by one or more surfaces that can exist in real life. Points become lines, lines become faces, and faces become bodies.
Classification: cylinder, cone, rotating body, sectional body, etc.
(3) Plane graphics
Plane figure is a kind of geometric figure, which means that all points are on the same plane, such as straight line, triangle and parallelogram. Are basic plane figures.
Classification: circle, polygon, bow, multi-arc.
(4) Points, lines, surfaces and bodies
Point: Point is the simplest shape and the most basic component of geometric figure. A point is a figure with only position but no size in space.
Line: A line is a figure composed of countless points.
Face: the trajectory from two points in space to a point with the same distance.
Volume: A polyhedron is a solid surrounded by four or more polygons.
(5) Lines, rays and line segments
Straight line: A straight line consists of countless points. There is no end point, extending to both ends indefinitely, and the length cannot be measured. A straight line is an axisymmetric figure.
Ray: refers to a straight line formed by the infinite extension of one end of a line segment. The light has only one endpoint, so the length cannot be measured.
Line segment: refers to the limited part (including two endpoints) between two points on a straight line, which is different from straight lines and rays.
(6) Angle: In geometry, an angle is a geometric object composed of two rays with a common endpoint. These two rays are called the edges of an angle, and their common endpoint is called the vertex of the angle.
(7) Complementary angle: If the sum of the two angles is 90, the two angles are complementary to each other, and the complementary angles of equal angles are equal.
(8) Complementary angle: If the sum of two angles is 180, then the two angles are complementary angles, and the complementary angles of equal angles are equal.