The second volume of the first day of junior high school is the key knowledge point of mathematics.
Important proving ground
1, application of multiplication and division formula of algebraic expression (six items) and inverse application (calculation of numbers).
( 1)an am2)(am)n =(3)(ab)n = 4)am \an
(5)a0 (a≠0) (6)a-p= =
2. Multiplication laws of monomials, monomials and polynomials.
3. Multiplication formula of algebraic expression (2).
Square difference formula: (a+b)(a-b)= 1
Complete square formula: (a+b)2 (a-b)2
Commonly used formula: (x+m)(x+n)= 1
5, single item divided by single item, polynomial divided by single item (converting single item divided by single item).
6. Sum of complementary angle and complementary angle
7. Conditions for two straight lines to be parallel: (the relationship lines of angles are parallel) ① Equal, and the two straight lines are parallel;
(2) Equal, two straight lines are parallel;
③ Complement each other, and the two straight lines are parallel.
8. Nature of parallel lines: Two straight lines are parallel. (parallelism of lines
9, can distinguish between independent variables and dependent variables in variables, will list the relationship (dependent variable = the relationship between independent variables and constants).
10, mirror method in variables, note: (1) horizontal and vertical objects. (2) What is the difference between the starting point and the end point?
(3) What is the meaning of image intersection? (4) The average value will be calculated.
1 1, triangle (1) trilateral relationship: angle relationship)
(2) Internal angle relation:
(3) Three important segments of a triangle:
(Emphasis) (4) Discriminating method of triangle congruence: (Note: the public side and the public part of the side are opposite to the public part of the vertex angle, the public angle and the angle)
(5) The nature of congruent triangles:
(key points) (6) isosceles triangle: (1) the method of finding the perimeter by knowing the edges.
(B) methods of understanding and looking for angles
(c) Three lines in one:
(7) equilateral triangle:
12. Will judge the axisymmetric figures and draw symmetrical figures (or draw them in the grid) according to them.
13, the common axisymmetric figures are: 14, (1) isosceles triangle: symmetry axis, properties.
(2) Line segment: symmetry axis, nature
(3) Angle: symmetry axis, natural
15, ruler drawing: (1) Make a known line segment, etc. (2) Make a known angle (3) Make the middle vertical line of a line segment.
(4) The angled bisector (5) is triangular.
16, classification of events:, will find the probability of various events.
(1) touching the ball: p (touching a ball) = 1
(2) Touch cards: P (touch a card) =
(3) Turntable: p (pointing to a certain area) =
(4) Roll the dice: p (throw a certain number of points) = 1
(5) Square (area): p (staying in a certain area) =
17, inevitable event, impossible event, uncertain event
18, method induction: (1) Find the edges to be equal.
(2) It is ok to find the equal angle.
(3) The calculation is simple and can be used.
19, pay attention to review: the rule of merging similar terms, scientific notation, solving a linear equation, absolute value.
Mathematics review materials in the second volume of the seventh grade
Chapter 1: Similarity transformation
1, if two line segments AB are measured with the same length unit, and the length of CD is m and n respectively, then the ratio of these two line segments AB:CD=m:n can be said or written. ※ 。
2. Among the four line segments A, B, C and D, if the ratio of A to B is equal to that of C and D, these four line segments are called proportional line segments for short. ※ 。
※ 3. Precautions:
①a:b=k, which means that A is k times that of B;
(2) Because the lengths of line segments A and B are both positive numbers, k is a positive number;
③ The ratio has nothing to do with the length units of the selected line segments, and the length units of the two line segments should be consistent when solving;
④ Except a=b, a:b≠b:a is reciprocal;
Chapter 2: Translation transformation
(1) The shape and size of the graph have not changed before and after translation, but the position has changed;
(2) After the graphic is translated, the line segments connected by the corresponding points are parallel and equal (or on the same straight line).
(3) Multiple translations are equivalent to one translation.
(4) The figure after multiple symmetry is equal to the figure after translation.
(5) Translation is determined by direction and distance.
(6) After translation, the corresponding line segments are parallel (or * * * lines) and equal, the corresponding angles are equal, and the line segments connected by the corresponding points are parallel and equal.
This kind of movement that moves all the points on the graph in a certain direction by the same distance is called the translation movement of the graph, which is called translation for short.
Article 3: similar triangles
1, among the similar polygons, similar triangles is the simplest one. ※ 。
2. A triangle with equal corresponding angles and proportional corresponding sides is called similar triangles. The ratio of corresponding edges in similar triangles is called similarity ratio. ※ 。
3. congruent triangles is a special case of similar triangles, where the similarity ratio is equal to 1. Note: Just like two congruent triangles, the letters representing the corresponding vertices should be written in the corresponding positions. ※ 。
4. similar triangles corresponds to the height ratio, the ratio corresponding to the center line and the ratio corresponding to the angular bisector are all equal to the similarity ratio. ※ 。
5. The ratio of similar triangles perimeter is equal to similarity ratio. ※ 。
6. The ratio of similar triangles area is equal to the square of similarity ratio. ※ 。
The first volume of seventh grade mathematics knowledge points
rational number
★ Classification of rational numbers
1. If divided by definition, rational numbers can be divided into integers (positive integers; Negative integer; 0) and score (positive score, negative score).
If divided by positive and negative, rational numbers can be divided into positive rational numbers (positive integer; Positive fraction), 0, negative rational number (negative integer; Negative score).
2. All rational numbers can be expressed by fractions, and π is not rational.
number axis
★ 1. Definition of number axis: The straight line defining origin, positive direction and unit length is called number axis.
Corresponding thing
1. Only two numbers with different symbols are called reciprocal. (The reciprocal of 0 is 0)
absolute value
The distance from point A to the origin on the 1. number axis represents the absolute value of a. ..
★2. Nature of absolute value: non-negative.
3. The absolute value of a positive number is itself, the absolute value of a negative number is its reciprocal, and the absolute value of 0 is 0.
Size of rational number
1. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.
2. Two negative numbers, the larger one has the smaller absolute value.
Addition of rational numbers
1. Add two numbers with the same sign, take the same sign, and then add the absolute values.
2. Add the numbers of two different symbols with different absolute values, take the addend symbol with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value; Two opposite numbers add up to 0. Add a number to 0 and you still get the number.
3. In addition to rational numbers,
Addition exchange rate: two numbers are added, and the position of the exchange addend remains unchanged.
Law of addition and association: 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.
Rational number subtraction
Subtracting a number is equal to adding the reciprocal of this number.
★ 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 to get 0.
Reciprocal: Two numbers whose product is 1 are reciprocal.
Multiplication exchange law: Multiplication exchange law multiplies two numbers, and the position of exchange factor and product remains unchanged.
Multiplication and association law: when three numbers are multiplied, the first two numbers are multiplied first, or the last two numbers are multiplied first, and the product is unchanged.
Multiplication and distribution law: a number multiplied by the sum of two numbers is equivalent to this number multiplied by these two numbers respectively, and then
Product addition.
★ Division of rational numbers
Divide by a number that is not zero is equal to multiply and divide by that reciprocal of that number.
The same sign is positive, the different sign is negative, and the absolute value is divided.
0 divided by any number that is not equal to 0 equals 0.
Mixed operation of rational numbers
1. Operation order: calculate the power first, then multiply and divide, and finally add and subtract. If it is the same level operation, it is calculated from left to right. If there are brackets, count the brackets first, then the brackets and finally the braces.
Power of rational number
★ 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. exist
When doing the result of the n power of a, it can also be read as the n power of a.
★2. The odd power of a negative number is negative, and the even power of a negative number is positive.
Any power of a positive number is a positive number, and any positive integer power of 0 is 0.
Scientific notation
1. Scientific notation represents numbers as a× 10 to the n power, where a is a number with only one integer and n is a positive integer. In this case, a is called radix and exponent. When watching
The counting method is called scientific counting method.
The related articles of mathematics knowledge points in Grade One of Hunan Education Edition;
★ Review materials of junior high school mathematics by Hunan Education Press.
★ Hunan Education Press review materials for the seventh grade mathematics midterm.
★ Teaching summary of the second volume of seventh grade mathematics in Hunan Education Press
★ Guidance on learning methods in grade seven
★ Final analysis of junior one mathematics
★ Rational Number Test Questions and Answers of Unit 1 of Junior 1 Mathematics in Hunan Education Edition (2)
★ Analysis of the Final Examination Paper of Junior One Mathematics
★ Teaching plan for seventh grade mathematical data analysis of Hunan Education Press.
★ Hunan Education Press, seventh grade, the second volume of mathematics teaching plan.
★ Knowledge practice of ternary linear equation in junior one mathematics.