But as long as you work hard to solve these difficulties, you will feel extremely relaxed and happy. So I sorted out the knowledge points in the first volume of seventh grade mathematics for everyone to learn.
One: rational number
Knowledge network:
Concept, definition:
1 and 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.
5. Take any point on the straight line to represent the number 0. 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. From the definition of absolute value, we can know that 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 absolute value is big but small.
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. 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
Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value.
Any number multiplied by 0 is 0.
15, and rational numbers: 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 power, and the result of power is called power. In an, a is called basenumber and n is called exponeht.
22. According to the multiplication rule of rational numbers, we can draw a conclusion.
The odd power of a negative number is negative and the even power of a negative number is positive.
Obviously, any degree of a positive number is positive, and any degree of 0 is 0.
23, do rational number mixed operation, should pay attention to the following operation order:
(1) Multiply first, then multiply and divide, and finally add and subtract;
(2) the same layer operation, 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.
24. The number greater than 10 is expressed as a? 10n (where A is a number with only one integer and n is a positive integer) adopts scientific counting method.
25. Close to the actual number, but still different from the actual number. This figure is an approximation.
26. From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number.
Note: Bold type is an important part.
Two: Addition and subtraction of algebraic expressions
Knowledge network:
Concept, definition:
1, which is the product of numbers or letters, is called a monomial, and a single number or letter is also a monomial.
2. The numerical factor in a single item is called the coefficient of the item.
3. In the monomial, the sum of the indices of all letters is called the number of times of the monomial.
The sum of several terms is called polynomial, in which each term is called polynomial term ($ TERM) and the term without letters is called constant term (constancy)
Terminology).
5. The degree of the highest term in a polynomial is called the degree of a polynomial.
6. Merging similar terms in polynomials into one term is called merging similar terms.
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.
7. 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;
8. 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.
9. Generally speaking, several algebraic expressions are added and subtracted. If there are brackets, remove them first, and then merge similar items.
Three: One-dimensional linear equation
Knowledge network:
Concept, definition:
1, when listing equations, you should first set letters to represent unknowns, and then write equations containing unknowns according to the equation relationship in the problem.
2, contains an unknown number (element), and the number of unknowns is 1. Such an equation is called a univariate linear equation.
3. It is a method to solve practical problems by using equivalence relation to analyze the quantitative relation in practical problems and list the equations.
4. Properties of the equation 1: Adding (or subtracting) the same number (or formula) to both sides of the equation will still result in the same result.
5. Properties of Equation 2: The results are still equal when both sides of the equation are multiplied by the same number or divided by a number that is not 0.
6. Moving the symbol on one side of the equation to the other side is called shifting the term.
7. application: travel problem: s=v? T engineering problem: total work = work efficiency? time
Profit and loss problem: Profit = selling price-cost interest rate = profit? Cost? 100%
Price = list price? What is the discount? 10% savings profit problem: interest = principal? Interest rate? time
Sum of principal and interest = principal+interest
Fourth, the preliminary understanding of graphics
Knowledge network:
Concept, definition:
1, we call all kinds of abstract figures in objects geometric figures.
2. Some geometric figures (such as cuboids, cubes, cylinders, cones, spheres, etc.). ) are not on the same plane, they are three-dimensional figures.
3. Some geometric figures (such as line segments, angles, triangles, rectangles, circles, etc.). ) are all in the same plane, which is a plane figure.
4. When the surface of the three-dimensional figure surrounded by the plane figure is properly cut, it can be expanded into a plane figure, which is called the expanded figure (net) of the corresponding three-dimensional figure.
5. Geometry is referred to as three-dimensional.
6. Surrounding the body is a curved surface, which has two kinds: plane and curved surface.
7. The intersection of surfaces forms a line, and the intersection of lines is a point.
8. Points move into faces, faces move into lines, and lines move into bodies.
9. After exploration, we can get a basic fact: there is a straight line after two points, and there is only one straight line.
Simply put, two points determine a straight line (axiom).
10, when two different straight lines have a common point, we call these two straight lines intersection, and this common point is called their intersection.
1 1, the point m divides the line segment AB into two equal line segments AM and MB, and the point m is called the center of the line segment AB.
12. After comparison, we can get a basic fact about the line segment: the line segment is the shortest of all two points. To put it simply: between two points, the line segment is the shortest. (axiom)
13, the length of the line segment connecting two points is called the distance between these two points.
14, angle? (Angle) is also a basic geometry.
15, divide a fillet into 360 equal parts, each part is an angle of 1 degree, and record it as 1? ; Divide an angle of one degree into 60 equal parts, each called an angle of 1 minute, and write it as 1? ; Divide the angle of 1 into 60 equal parts, each part is called the angle of 1 sec, and it is recorded as 1? .
16, starting from the vertex of an angle, the ray that divides this angle into two equal angles is called the angle bisector of this angle.
17, if the sum of two angles equals 90? (right angle), that is to say, these two are called complementary angles.
Angle), that is, each angle is the complementary angle of another angle.
18, if the sum of two angles is equal to 180? (flat angle), that is to say, these two angles are complementary (complementary)
Angle), that is, one of the angles is the complement of the other.
19, the complementary angles of equal angles are equal, and the complementary angles of equal angles are equal.