The first volume of seventh grade mathematics 1 and the number greater than 0 is called a positive number, and the number with the negative sign "-"in front of it is called a negative number. 2. Rational numbers can be divided into integers and fractions, and integers can be divided into positive integers, zero and negative integers; Scores can be divided into positive scores and negative scores. 3. Use points on a straight line to represent numbers. This straight line is called the number axis. 4. Take any point on the straight line to represent the number 0. This point is called the origin. 5. Two numbers with different symbols are called reciprocal. 6. The distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A. 7. 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. 8.( 1) Positive number is greater than 0, 0 is greater than negative number, and positive number is greater than negative number; (2) Two negative numbers, the larger one has the smaller absolute value. 9.( 1) Add two numbers with the same symbol, take the same symbol, and add the absolute values. (2) Add two numbers with different absolute values, take the sign of the addend with larger absolute value, subtract the number with smaller absolute value from the number with larger absolute value, and add the two numbers with opposite numbers to get 0. (3) When a number is added to 0, the number is still obtained. 10, two numbers are added, the position of the addend is exchanged, and the sum is unchanged. 1 1, when three numbers are added, the first two numbers are added first, or the last two numbers are added first, and the sum is unchanged. 12, subtracting a number is equal to adding the reciprocal of this number. 13, two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0. Two numbers whose product is 14 are reciprocal. 15, when two numbers are multiplied, the positions of exchange factors are equal. 16, multiply three numbers, multiply the first two numbers first, or multiply the two numbers first, and the products are equal. 17. Multiplying a number by the sum of two numbers is equivalent to multiplying this number by these two numbers respectively, and then adding the products. 18 divided by a number not equal to 0 equals the reciprocal of this number. 19, two numbers are divided, the same sign is positive, the different sign is negative, and divided by the absolute value, and 0 is divided by any number that is not equal to 0 to get 0. 20. The operation of finding the product of the same factor of n is called the power, and the result of the power is called the power. In, a is called the base and n is called the exponent. 2 1, the odd power of negative number is negative, and the even power of negative number is positive. Any power of a positive number is a positive number, and any power of a positive integer is 0. 22. When doing the mixed operation of rational numbers, we should pay attention to the following operation order: 1, multiply first, then divide, and finally add and subtract; 2. Operation at the same level, from left to right; 3. If there are brackets, do the operation in brackets first, and then follow the brackets, brackets and braces in turn. 23. Numbers greater than 10 are expressed in the form of a× 10n (where a is a number with only one integer and n is a positive integer), and scientific notation is used. 24. From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number. 25. The product of numbers or letters is called a monomial. The numerical factor in a single item is called the coefficient of the item. The sum of the exponents of all letters is called the degree of this monomial. 26. The sum of several monomials is called polynomial. Each monomial is called a polynomial term, and the term without letters is called a constant term. The degree of the term with the highest degree in a polynomial is called the degree of the polynomial. 27, monomials and polynomials are collectively referred to as algebraic expressions. 28. Items with the same letter and the same letter index are called similar items. Several constant terms are similar. 29. Merging similar items in polynomials into one item is called merging similar items. After merging similar items, the coefficient of the obtained item is the sum of the coefficients of similar items before merging, and the letter part remains unchanged. 30. If the factor outside the brackets is positive, the symbols of the items in the original brackets are the same as the original symbols after removing the brackets; If the factor outside the brackets is negative, the symbols of the items in the original brackets are opposite to those after the brackets are removed. 3 1, Algebraic expression addition and subtraction algorithm: add and subtract several algebraic expressions. If there are brackets, remove them first, and then merge similar items. 32. There is only one unknown, and the number of unknown is 1. Such an equation is called a linear equation. 33. Properties of Equation 1: Adding (or subtracting) the same number (or formula) to both sides of the equation will still result in the same result. Property 2 of the equation: Multiply both sides of the equation by the same number, or divide by the same number that is not 0, and the results are still equal. 34. Steps to solve a linear equation: remove denominator, brackets, shift terms, merge similar terms, convert coefficients to 1 35, and all kinds of graphs abstracted from objects are collectively called geometric graphs. All parts of a geometric figure (such as cuboid, cube, cylinder, cone, sphere, etc.). ) is not on a plane, it is a three-dimensional figure. 36. Three-dimensional graphics are surrounded by some plane graphics. If their surfaces are properly cut, they can be unfolded into plane figures. This kind of plane figure is called the expanded figure of the corresponding three-dimensional figure. 37. Cuboid, cube, cylinder, cone, sphere, prism, pyramid, etc. They are all geometric bodies, and geometric bodies are also called volumes. What surrounds the body is the surface. 38. There is a straight line after two o'clock, and there is only one straight line. In short, two points determine a straight line. 39. When two different straight lines have a common point, we say that the two straight lines intersect, and this common point is called their intersection. Between two points, the line segment is the shortest. The length of the line segment connecting two points is called the distance between these two points. 4 1, divide a fillet into 360 equal parts, each part is an angle of 1 degree, and divide the angle of 1 degree into 60 equal parts, each part is an angle of 1 minute, and each part is an angle of 1 second. An angle measuring system in degrees, minutes and seconds is called an angle system. 42. Starting from the vertex of an angle, the ray that divides this angle into two equal angles is called the bisector of this angle. 43. If the sum of two angles equals 900 (right angle), the two angles are said to be complementary. If the sum of two angles is equal to 1800 (flat angle), the two angles are said to be complementary. 44. Equiangular complementary angles are equal. The complementary angles of equal angles are equal. That's all for seventh grade, brother. Good luck. Go to the bookstore and buy some exercises. Hurry up! ! ! Remember the above! ! !