Chapter 1: Operation of rational numbers: This chapter mainly introduces conceptual knowledge, and distinguishes the relationship between scores with graphs or symbols. Defined as follows:
1, the concept of rational number: positive integer, 0, negative integer, positive fraction and negative fraction are collectively called rational numbers; Number axis and origin: Numbers are represented by points on a straight line, which is called number axis. Any point on this line represents 0, which is called the origin. The distance from this point to the left or below the origin is represented by a negative number, and the distance from this point to the right or above the origin is represented by a positive number. The two numbers represented by two points with opposite and equal distances from the origin on the number axis are opposite numbers, and the distance from point A to the origin on the number axis is called the absolute value of this number.
2. Addition and subtraction of rational numbers: two numbers with the same sign are added, the sign is unchanged, and the absolute value is added; Add two numbers with different signs and different absolute values, take the sign of the addend with larger absolute value, subtract the absolute value of the smaller number from the absolute value of the larger number, and add two numbers with opposite numbers to get 0; One rational number MINUS another rational number is equivalent to adding the reciprocal of this number;
3. Multiplication and division of rational numbers: two numbers with the same sign are multiplied, the same sign is positive, and the different sign is negative. The product of multiplication is the product of their absolute values, division is the dividend multiplied by the reciprocal of the divisor, and the divisor cannot be 0; Two numbers whose product is 1 are reciprocal, and 0 has no reciprocal; Multiplication turnover rate and combination rate of integers are also applicable to rational numbers; The operation of finding the product of n identical factors is called power, and the result of power is called power. In the n power of a, a is called the base and n is called the exponent. Write a ∧ n;
4. Mixed operation of rational numbers: multiply first, then multiply and divide, and finally add and subtract; Operation at the same level, from left to right; If there are brackets, do the operation in brackets first, and then follow the brackets, brackets and braces in turn.
5. Scientific notation: A number greater than 10 is expressed as a× 10∧n, where a is greater than or equal to 1 less than 10, and n is a positive integer, which is called scientific notation.
Chapter 2: Algebraic addition and subtraction: Algebraic addition and subtraction is the calculation of merging similar items; In a formula, items with the same letters and the same letter index are called similar items, and several constant items are also similar items; Merging similar terms in polynomials into one term is called merging similar terms. After merging similar items, the coefficients of the obtained items are the sum of the coefficients of similar items before merging, and the letters and their indexes remain unchanged. Generally, several integers are added together. If there are brackets, remove them first, and then merge similar items. If the factor outside the brackets is positive, the symbols of the items in the original brackets are the same as those after the brackets are removed. 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.
Chapter 3: One-dimensional linear equation: An equation contains only one unknown, the degree of the unknown is 1, and both sides of the equal sign are integers. This equation is called one-dimensional linear equation; The addition or subtraction of the same numbers or formulas on both sides of the equation is still equal, and the multiplication or division of the same numbers on both sides of the equation is still equal.
Chapter four: This chapter mainly introduces the understanding of three-dimensional graphics and geometric graphics; Understanding of the relationship between point, line, surface and body; Understanding of straight lines, rays and line segments; Comparison of concepts and sizes from different angles.
1, plane graphics and three-dimensional graphics: geometric graphics with all parts in the same plane are called plane graphics; Some parts of geometric figures are not on the same plane, which are called three-dimensional figures, such as cuboids, cylinders and cones. Some three-dimensional graphics are surrounded by some plane graphics and expanded into plane graphics, and the expanded plane graphics are called the expanded drawings of this three-dimensional graphics;
2. Understanding of points, lines, surfaces and bodies: the geometric body is called the body, the enclosing body is called the surface, the place where the surface intersects with the surface is called the line, and the place where the line intersects with the line is called the point, and the line is composed of countless points;
3. Understanding of straight lines, rays and line segments: Only one straight line passes through two points, and two points determine a straight line. The shortest connecting line between two points is called a line segment, the length of the line segment is called the distance between these two points, and it extends infinitely from the line segment to one end, which is called a ray;
4. Angle: If the sum of two angles is equal to 90, then the two angles are complementary; If the sum of two angles is equal to 180, then the two angles are complementary; Starting from the vertex of an angle. The ray that divides this angle into two equal angles is called the bisector of this angle, and the two rays of these three equal angles are called the bisector of this angle.
Seventh grade mathematics test site induction 1. Numbers greater than 0 are called positive numbers.
2. Numbers with negative sign "-"in front of positive numbers are called negative numbers.
3. Integers and fractions are collectively called rational numbers.
People usually use points on a straight line to represent numbers. This straight line is called the number axis.
Take any point on the straight line to represent the number 0, and this point is called the origin.
6. Usually, 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. According to the definition of absolute value:
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. Positive numbers are greater than 0, 0 is greater than negative numbers, and positive numbers are greater than negative numbers.
9. Two negative numbers, the larger one has the smaller absolute value.
10. rational number addition rule:
(1) Add two numbers with the same sign, take the same sign, and add the absolute values.
(2) Add two numbers with different absolute values, take the negative 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.
1 1. In rational number addition, two numbers are added, the position of the addend is exchanged, and the sum is unchanged.
12. In rational number addition, 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.
13. rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number.
14. rational number multiplication rule: 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.
15. There is also a rational number: two numbers whose product is 1 are reciprocal.
16. In general rational number multiplication, two numbers are multiplied, and the exchange factor and product are in the same position.
17. Multiply three numbers, first multiply the first two numbers, or multiply the last two numbers, and the products are equal.
18. Generally speaking, a number multiplied by the sum of two numbers is equivalent to multiplying this number by these two numbers respectively, and then adding the products.
19. Rational number division rule: dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.
20. Divide two numbers, the same sign is positive, and the different sign is negative, divided by the absolute value. Divide 0 by any number that is not equal to 0 to get 0.
2 1. The operation of finding the product of n identical factors 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.
Knowledge point 1, several important algebraic expressions (m, n stands for integer) in the first volume of junior one mathematics.
(1) The square difference between A and B is: A2-B2; The square of the difference between a and b is: (a-b) 2;
(2) If a, b and c are positive integers, the two-digit integer is 10a+b and the three-digit integer is10a+10b+c;
(3) If both m and n are integers, the quotient m is divided by 5, and the remainder n is 5m+n; Even number is 2n, and odd number is 2n+1; Three consecutive integers are: n- 1, n, n+1;
(4) If b>0, positive number is: a2+b, negative number is: -a2-b, non-negative number is: a2, and non-positive number is: -a2.
2. Several points for attention in column algebra:
Multiply (1) by letters, or multiply letters by letters, or omit;
(2) When the numbers are multiplied, they should still be multiplied by "×", but not by "×", and the multiplication sign cannot be omitted;
(3) When a number is multiplied by a letter, the number is usually written in front of the letter in the result. For example, a×5 should be written as 5a;
(4) When the band fraction is multiplied by letters, the band fraction should be changed to a false fraction, for example, a× should be written as a;
(5) When there is a division operation in the algebraic expression, the division method and the division method are generally connected by a fractional line, such as the form written in 3 A;
(6) The difference between A and B should be written in alphabetical order; If we only talk about the difference between two numbers, when we set two numbers as A and B respectively, we should classify them and write them as a-b and B-A. 。
3, rational number proportion size:
(1) The greater the absolute value of a positive number, the greater the number;
(2) Positive numbers are always greater than 0 and negative numbers are always less than 0;
(3) Positive numbers are greater than all negative numbers;
(4) The absolute values of two negative numbers are larger than the size, but smaller;
(5) Of the two numbers on the number axis, the number on the right is always greater than the number on the left;
(6) large number-decimal number >; 0, decimal-large number < 0.
The above are some knowledge points of seventh grade mathematics, I hope to help you.