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.
Seven-grade mathematics knowledge points
Variables in life
I. Variables, Independent Variables and Dependent Variables
(1) two variables x and y, y changes with the change of x, so x is the independent variable (the first variable) and y is the dependent variable (the second variable).
Second, the representation between variables:
① List method
② Relationship method: It can accurately reflect the corresponding relationship between independent variables and dependent variables.
(3) Mirror image method: the independent variable is represented by points on the number axis (horizontal axis) in the horizontal direction, and the dependent variable is represented by the number axis (vertical axis) in the fixed direction.
Chapter V Axisymmetry in Life
Axisymmetric graphics and axisymmetry
(1) A graph is folded in half along a straight line, and the graphs on both sides of the straight line can overlap, which is called an axisymmetric graph. This straight line is called the axis of symmetry.
(2) Two figures are folded along a straight line, which can completely overlap. It is said that these two figures are symmetrical about this straight line. This straight line is called the axis of symmetry.
③ Common axisymmetric figures: line segment (two axes of symmetry), angle, rectangle, square, isosceles triangle, equilateral triangle, isosceles trapezoid, circle and sector.
Second, the nature of the angle bisector: the distance from the point on the angle bisector to both sides of the angle is equal.
∫∠ 1 =∠2 pb⊥ob pa⊥oa
∴ PB=PA
Third, the line segment perpendicular bisector:
① Concept: The straight line perpendicular to and bisecting the line segment is called the median vertical line of the line segment.
② Property: The distance between the point on the vertical line of the line segment and the two endpoints of the line segment is equal.
∫OA = ob cd⊥ab
∴ PA=PB
Properties of isosceles triangle: (A triangle with two equal sides is called an isosceles triangle)
① The isosceles triangle is an axisymmetric figure; (axis of symmetry)
② The median line on the bottom of isosceles triangle and the bisector of height coincide with the vertex on the bottom; (three in one)
③ The two base angles of an isosceles triangle are equal. (Abbreviation: Equiangular)
Review materials of mathematics guidance in the second volume of the seventh grade
1. Geometry: Points, lines, surfaces and bodies can help people effectively describe the complex world. It's all called geometry. All kinds of figures abstracted from objects are collectively called geometric figures. Geometric figures whose parts are not in the same plane are called three-dimensional figures. Some geometric figures are all in the same plane, which is called plane figures. Although solid figure and plane figure are two different geometric figures, they are interrelated.
2. Classification of geometric figures: Geometric figures are generally divided into three-dimensional figures and plane figures.
3. Straight line: The basic concept of geometry is the trajectory of a point in space moving in the same or opposite direction. From the point of view of plane analytic geometry, a straight line on a plane is a graph represented by a binary linear equation in a plane rectangular coordinate system. To require the intersection of two straight lines, we only need to solve these two binary linear equations simultaneously. When simultaneous equations have no solution, two straight lines are parallel. When there are infinite solutions, two straight lines coincide; When there is only one solution, two straight lines intersect at one point. The angle between a straight line and the positive direction of the X axis (called the inclination angle of the straight line) or the tangent of the angle (called the slope of the straight line) is often used to indicate the inclination of the straight line on the plane (for the X axis).
4. Ray: In Euclidean geometry, the figure formed by a point on a straight line and its edge is called a ray or a semi-straight line.
5. Line segment: refers to a continuous or discontinuous figure composed of one or more different line elements, such as a real line segment or a two-point long line segment composed of "long stroke, short interval, point, short interval, point and short interval".
The line segment has the following properties: the line segment between two points is the shortest.
6. Distance between two points: The length of the line segment connecting two points is called the distance between these two points.
7. Endpoint: Two points on a straight line and the part between them are called line segments, and these two points are called the endpoints of line segments.
A line segment is represented by letters or lowercase letters representing its two endpoints. Sometimes these letters also represent the length of a line segment, which is recorded as line segment AB or line segment BA and line segment A .. where AB represents any two points on a straight line.
8. The difference between straight lines, rays and line segments: straight lines have no distance. Ray has no distance. Because a straight line has no end point, a ray has only one end point and can extend indefinitely.
9. Angle: A graph composed of two non-overlapping rays with a common endpoint is called an angle. This common endpoint is called the vertex of the angle, and these two rays are called the two sides of the angle.
The figure formed by the rotation of light from one position to another around its endpoint is called an angle. The endpoint of the rotated ray is called the vertex of the angle, the ray at the starting position is called the starting edge of the angle, and the ray at the ending position is called the ending edge of the angle.
10. Static definition of angle: A graph composed of two non-coincident rays with a common endpoint is called an angle. This common endpoint is called the vertex of the angle, and these two rays are called the two sides of the angle.
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