Analysis of the difficult problem of addition and subtraction of integral form in volume one of grade seven

Analysis of the difficult problem of addition and subtraction of integral form in volume one of grade seven

Originally, I wrote a lot, but I don't know why I was only allowed to input 100 words
Difficulties:
1. The most error prone part of integral addition and subtraction is when the bracket is removed and the negative factor is in front of the bracket
2. When adding and subtracting integers, you should add brackets when substituting them

Mathematics calculation (give some calculation questions, power operation)

The analysis of mathematics knowledge in the second semester of the seventh grade
Chapter 5 intersecting lines and parallel lines
1、 Knowledge structure diagram intersection line intersection line vertical line isolocation angle, internal stagger angle, internal angle parallel line parallel line and its judgment parallel line property of judgment parallel line property of parallel line Proposition, theorem translation 2. Knowledge definition adjacency complement angle: among the four corners formed by the intersection of two straight lines, the two corners with a common vertex and a common side are adjacency complement angles. Opposite vertex angle: the two sides of one corner are the opposite extension lines of the other. Such two angles are opposite vertex angles to each other. Vertical line: when two straight lines intersect at right angles, they are called mutually perpendicular, One of them is called the vertical line of the other, Two straight lines that do not intersect are called parallel lines. The same angle, internal angle, and internal angle on the same side: the same angle: ∠ 1 and ∠ 5, which have the same positional relationship, is called the same angle. The internal angle: ∠ 2 and ∠ 6, which are like this, is called the internal angle. The internal angle on the same side: ∠ 2 and ∠ 5, which are like this, is called the internal angle on the same side In the plane, a figure is moved along a certain direction for a certain distance. This movement of the figure is called translation transformation, or translation for short. Corresponding point: every point in the new figure obtained after translation is obtained by moving a point in the original figure, Such two points are called corresponding points. 3. Theorem and property. Property of vertex angle: equal to vertex angle. Property of vertical line: Property 1: there is and only one straight line passing through a point which is perpendicular to the known straight line. Property 2: in all line segments connecting a point outside the straight line and each point on the straight line, Parallel axiom: there is and only one straight line passing through a point outside the straight line is parallel to the known straight line. Corollary of parallel axiom: if two straight lines are parallel to the third straight line, then the two lines are parallel to each other. Properties of parallel line: Property 1: two straight lines are parallel, with the same angle. Property 2: two straight lines are parallel, with the same angle. Property 3: two straight lines are parallel, with the same angle, The judgment of parallel lines: judgment 1: the same angle is equal, and two lines are parallel. Judgment 2: the internal stagger angle is equal, and two lines are parallel. Judgment 3: the same angle is equal, and two lines are parallel. 4. Classical example example example example 1 is shown in the figure, where the lines AB, CD and EF intersect at the point O, ∠ AOE = 54 ° and ∠ EOD = 90 ° to find the degree of ∠ EOB and ∠ cob, Then how much is ∠ ACB equal to? Example 3 a triangle's outer angle is equal to 4 times of its adjacent inner angle, and is equal to 2 times of its non adjacent inner angle, then the degree of each angle of the triangle is (). A.450, 450, 900 b.300, 600, 900 c.250, 250, 1300 d.360, 720, 720 example 4 is known as shown in the figure, find the degree of ∠ a ＋ B ＋ C ＋ D ＋ e ＋ F As shown in the figure, ab ∥ CD, EF intersect AB and CD at g and h, Mn ⊥ AB at g, ∠ CHG = 1240, How many degrees is EGM equal to? Chapter 6 plane rectangular coordinate system i. simple application of ordinal number in knowledge structure diagram to plane rectangular coordinate system Second, knowledge defines ordinal number pairs: ordinal number pairs composed of two numbers a and B are called ordinal number pairs, Horizontal axis, vertical axis and origin: the horizontal axis is called X axis or horizontal axis; the vertical axis is called Y axis or vertical axis; the intersection of the two coordinate axes is the origin of the plane rectangular coordinate system. Coordinates: for any point P in the plane, through P, make vertical lines to X axis and Y axis respectively, and the vertical feet are on X axis and Y axis respectively, corresponding to the number a and Y axis, Quadrant: two coordinate axes divide the plane into four parts, the upper right part is called the first quadrant, and the second quadrant, the third quadrant and the fourth quadrant are called counter clockwise. The points on the coordinate axis are not in any quadrant, Then walk 6 meters due north to A2, 9 meters due west to A3, 12 meters due south to A4, and 15 meters due east to A5. If A1 is (3,0), calculate the coordinates of A5. Example 2 is a small flag pattern drawn on checkerboard paper. If (0,0) is used to represent a point and (0,4) is used to represent B point, then the position of C point can be expressed as () a, (0,3) B, (2, 3) C, (3,2) d, (3,0) example 3 is shown in Figure 2. According to the position of the point in the coordinate plane, write the coordinates of the following points: a (), B (), C (). Example 4 is shown in the figure. The △ ABC with an area of 12cm2 is translated to the position of △ def in the positive direction of X axis, and the corresponding coordinates are shown in the figure (a, B are constants), (1) Example 5 through two points a (3,4), B (- 2,4) to make a straight line AB, then the straight line AB () a, through the origin B, parallel to the y-axis C, parallel to the x-axis D, the above statements are not true A triangle is defined by knowledge: a figure composed of three line segments which are not on the same straight line and whose ends are connected in sequence is called a triangle. Trilateral relation: the sum of any two sides of a triangle is greater than the third side, Middle line: in a triangle, the line connecting a vertex and the midpoint of its opposite side is called the middle line of the triangle. Angle bisector: the bisector of an inner angle of a triangle intersects the opposite side of the angle, The line segment between the vertex of the angle and the intersection point is called the angular bisector of the triangle. The stability of the triangle: the shape of the triangle is fixed, and this property of the triangle is called the stability of the triangle, A polygon consists of a number of line segments which are connected in sequence. The inner angle of a polygon: the angle formed by two adjacent sides of a polygon is called its inner angle. The outer angle of a polygon: the angle formed by one side of a polygon and the extension line of its adjacent side is called its outer angle. The opposite corner line of a polygon: the line segment connecting two non adjacent vertices of a polygon, It is called the diagonal of a polygon. Regular polygon: in a plane, all corners are equal, and all sides are equal. Plane mosaic: use some non overlapping polygons to completely cover a part of the plane, It is called covering a plane with a polygon. 3. Formulas and properties the sum of the inner angles of a triangle: the sum of the inner angles of a triangle is 180 ° the sum of the outer angles of a triangle: Property 1: one outer angle of a triangle is equal to the sum of two inner angles not adjacent to it. Property 2: one outer angle of a triangle is greater than any inner angle not adjacent to it. The sum of the inner angles of a polygon: the sum of the inner angles of an n-sided shape is equal to (n-2)· The number of polygonal diagonals: (1) starting from a vertex of an n-polygon, we can introduce (n-3) diagonals and divide the polygon into (n-2) triangles. (2) n-polygons share one diagonal. (4) the classic example 1 is shown in the figure. In △ ABC, AQ = PQ, PR = PS, PR ⊥ AB in R, PS ⊥ AC in S, There are three conclusions: ① as = AR; ② QP ‖ AR; ③ △ BRP ≌ △ CSP, in which () (a) all correct (b) only ① correct (c) only ①, ② correct (d) only ①, ③ correct. Example 2 is shown in the figure. Combined with the figure, the following judgment or reasoning is made: ① as shown in figure a, CD ⊥ AB, D is perpendicular, then the distance from point C to AB is equal to the distance between two points c and D; ② as shown in Figure B, if ab ∥ CD, Then ∠ B = ∠ D; ③ as shown in Figure C, if ∠ ACD = ∠ cab, then ad ‖ BC; ④ as shown in Figure D, if ∠ 1 = ∠ 2, ∠ d = 120 °, then ∠ BCD = 60 °, where the correct number is (). (a) 1 (b) 2 (c) 3 (d) 4 Example 3, in the checkerboard paper as shown in the figure, draw △ def and △ DEG (F and G cannot coincide), Let △ ABC ≌ △ def ≌ deg. can you explain why they are congruent? Example 4 on the measuring tool CDE for measuring the diameter of small glass tube, CD = 10 mm, de = 80 mm. If the small tube diameter AB is facing the 50 mm scale on the measuring tool, what is the length of the small tube diameter AB? Example 5 in the rectangular coordinate system, a (- 4,0), B (1,0), C (0, -2) Three points. Please design two schemes according to the following requirements: make a straight line that does not coincide with the axis and intersects with both sides of △ ABC, so that the triangle cut is similar to △ ABC, and the area is △ AOC area. Draw the design graphics in the following two coordinate systems respectively, and write out the coordinates of the three vertices of the triangle cut. Chapter 8 binary linear equations 1, knowledge structure diagram Let's set the unknowns, Substituting the solution of a series of equations into the system of normal addition and subtraction (elimination) Test two, knowledge definition binary linear equation: contains two unknowns, and the index of the unknowns is 1, such an equation is called binary linear equation, the general form is ax + by = C (a ≠ 0, B ≠ 0). Binary linear equation system: two binary linear equations are combined to form a binary linear equation system, The values of the unknowns that make the values on both sides of the binary linear equation equal are called the solutions of the binary linear equations. In general, the common solutions of the two equations of the binary linear equations are called the binary linear equations. Elimination: the idea of solving the number of unknowns one by one from more to less, It's called elimination thought. Substitution elimination: to express an unknown with an equation containing another unknown, and then substitute it into another equation to realize elimination, so as to obtain the solution of the binary linear equation system. This method is called substitution elimination method, which is called substitution elimination method for short. Addition and subtraction elimination method: when the coefficients of the same unknown in two equations are opposite or equal, The unknown number can be eliminated by adding or subtracting the two sides of two equations respectively. This method is called addition subtraction elimination method, which is called addition subtraction elimination method for short. 3. Classical example example 1 uses addition subtraction elimination method to solve the equations, which is obtained from ① × 2-2. If example 2 is of the same kind, then the values of and are () a, = - 3, = 2 B, = 2, = - 3 C, = - 2, = 3 D. Calculation of example 3: example 4 Uncle Wang contracted 25 mu of land and planted two greenhouse vegetables, eggplant and tomato this spring, which cost 44000 yuan. Among them, 1700 yuan was used for planting eggplant per mu, with a net profit of 2400 yuan; 1800 yuan was used for planting tomato per mu, with a net profit of 2600 yuan