Examination content
Chapter V Intersecting Lines and Parallel Lines Chapter VI Plane Cartesian Coordinate System
Chapter VII Triangle Chapter VIII Binary Linear Equations
Chapter 9 Inequalities and Inequality Groups Chapter 10 Data Collection, Arrangement and Description
Chapter XV Multiplication, Division and Factorization of Algebraic Expressions
Chapter V Intersecting Lines and Parallel Lines
(A) the knowledge structure of this chapter:
(2) Examples and exercises:
1. Vertex angle and adjacent complementary angle: 1. As shown in the figure, ∠ 1 and ∠2 are graphs with vertex angle ().
1。
2. As shown in figure 1- 1, straight lines AB, CD and EF all pass through point O,
There are several pairs of vertex angles in the picture. ( )
3. As shown in figure 1-2, if ∠AOB and ∠BOC are a pair of adjacent complementary angles, OD divides ∠AOB equally.
OE is in ∠BOC, while ∠BOE= ∠COE, ∠ Doe = 72.
Find the degree of ∠COE. ( )
Second, the vertical line:
It is known that there are two villages, A and B, on both sides of a highway.
& lt 1 & gt； Now the township government serves the people, driving buses along the highway, building bus stop P on the roadside, and building roads from station P to villages A and B, and the total number of roads to be built is the shortest. Please design the position of the station, draw the position of point P on the map (keep the traces of drawing), and explain the truth in one sentence on the back horizontal line. ...
& lt2> In order to facilitate motor vehicle travel, Village A plans to build a motor vehicle-only road directly to the village. Can you help Village A save money and design the shortest road? Please draw the shortest road you designed and built in the picture, and explain the truth in one sentence on the back horizontal line.
Third, the judgment of congruent angle, internal dislocation angle and ipsilateral internal angle
1. As shown in Figure 3- 1, according to the position of each corner, the following judgment is wrong ().
(A)∠ 1 and ∠2 are ipsilateral internal angles; (b) < 3 and < 4 are internal angles www.xkb 1.com.
(c) < 5 and < 6 are ipsilateral internal angles; (d) ∠ 5 and ∠ 8 are congruent angles.
2. As shown in Figure 3-2, _ _ forms an internal angle with ∠EFB, and _ _ forms an internal angle with ∠FEB.
Four, the determination and nature of parallel lines:
1. As shown in Figure 4- 1, if ∠3=∠4, then ∨;
If AB∨CD, ∞ =∞.
2. It is known that two sides of two angles are parallel, and one angle is 52.
Then another angle is _ _ _ _ _.
3. When two parallel straight lines are cut by the third straight line, among the eight angles generated,
The two parallel angles of the bisector are ()
A. conformal angle B. ipsilateral internal angle
C. internal dislocation angle D. equidistant angle or internal dislocation angle
4. As shown in Figure 4-2, what conditions are needed to explain AB∑CD?
Try to write down all possible situations and explain why.
5. As shown in Figure 4-3, EF⊥GF, vertical foot is F, ∠ AEF = 150,
∠DGF=60. Try to judge the positional relationship between AB and CD, and explain the reasons.
6. As shown in Figure 4-4, AB∥DE, ∠ ABC = 70, ∠ CDE = 147, find the degree of ∠ C. ()
7. As shown in Figure 4-5, CD∥BE, then ∠2+∠3? What is the degree of ∠ 1? ( )
8. As shown in Figure 4-6: ab∨CD, ∠ABE=∠DCF, and verification: BE ∨ CF.
Verb (abbreviation of verb) the application of parallel lines;
1. If someone starts from point A, walks northeast 10 meter, reaches point B, and then walks southwest from point B 15 meter, and reaches point C, then ∠ABC is equal to ().
105 D. 135
A student practiced driving and found that after turning two corners, the driving direction was the same as the original direction. The turning angle of these two turns may be ().
A First right turn 50, second left turn 130.
B Turn left 50 for the first time and right 50 for the second time.
C first left turn 50, second left turn 130.
D Turn right 50 for the first time and 50 for the second time.
3. As shown in Figure 5-2, after a rectangular piece of paper is folded along EF, the points D and C fall at the positions D ′ and C ′ respectively.
If ∠ EFB = 65, ∠AED is equal to.
4. Calculate the shadow area in Figure 6- 1. (Unit: cm)
5. As shown in (Figure 6-2), it is known that the side length of a large square is 10 cm, and the side length of a small square is 7 cm.
Find the shadow area. (result retention)
6. Find the shaded area in Figure 6-3 (unit: cm).
7. Among the following propositions, the number of true propositions is ().
① The complementary angle of an angle may be an acute angle;
② The distance from any point on two parallel lines to another parallel line is the distance between these two parallel lines;
③ In the plane, there is one and only one straight line perpendicular to the known straight line at one point;
④ In the plane, there is one and only one straight line parallel to the known straight line;
A. 1
8. Known: as shown in Figure 8- 1, AD BC, EF BC, 1= 2.
Proof: ∠ CDG = ∠ B.
9. As shown in Figure 8-2, AB∨CD, 1= 2, ∠ E = 65 20', find the degree of ∠ F.
10. Known: as shown in Figure 8-3, AE ⊥ BC, FG ⊥ BC, ∠ 1 = ∠ 2, ∠ D = ∠ 3+60? ，∠CBD=70？ .
(1) verification: ab ∑ CD; (2) Find the degree of ∠ C ()
1 1. As shown in Figure 8-4, in the rectangular ABCD, ∠ ADB = 20, now fold this rectangular paper along AF. If you succeed,
AB' ∥BD, what is the included angle between crease AF and AB ∠BAF? ( )
12. As shown in Figure 8-5, point B is 30? Direction,
Distance from point a 100 meter, point c 60? ，∠ACB = 40？
(1) Find the distance from point A to line BC; (100 m)
(2) Q: How many degrees is point A southwest of point C?
(Write the calculation and reasoning process) ()
13. As shown in the figure, in the square grid of, the side length of each small square is 1 unit, which will translate down by 4 units, so please draw it (no drawing is needed).
Six, using equal product transformation drawing:
1. As shown in figure △ ABC, the triangle can be divided into two parts with equal area through the center line of point A.. Can you make a straight line EF through a point E on the side of AB, so that it can also divide this triangle into two parts with equal areas?
There is a piece of cultivated land, the shape of which is as shown in the figure. The two brothers want to divide it into two equal parts. Please design a plan and divide it into the required number of parts. If only one straight line is allowed, is it ok?
3. As shown in the figure, if you want to straighten a broken road MPN in the middle of a square cultivated land, but you can't change the size of the cultivated land on both sides of the broken road, how to draw a line?
4. It is known that the pentagon ABCDE is made into a triangle with a triangle ruler and a ruler as shown in the figure, so that the area of the triangle is equal to the area of the given pentagon ABCDE.
Chapter VI Plane Cartesian Coordinate System
(A) the knowledge structure of this chapter:
(2) Examples and exercises:
I. Fill in the blanks:
1. Known point P(3a-8, a- 1).
(1) point p is on the x axis, then the coordinates of point p are:
(2) If point P is in the second quadrant and A is an integer, the coordinates of point P are:
(3) The coordinate of point Q is (3, -6) and the straight line PQ∨x axis, then the coordinate of point P is.
2. As the chessboard shows, if "handsome"
At point (1, -2),
"Phase" is located at point (3, -2),
Then the cannon is located in _ _ _
3. The coordinates of the symmetrical point of the point about the axis are; The coordinates of the symmetrical point of the point about the axis are; The coordinates of the symmetrical point of a point about the origin of coordinates are.
4. It is known that point P is in the fourth quadrant, the distance to the X axis is 0, and the distance to the Y axis is 2, so the coordinate of point P is _ _ _ _ _.
5. Given that the distance from point P to the X axis is 0 and the distance to the Y axis is 2, the coordinates of point P are 0.
6. It is known that,,, then axis, ∑ axis;
7. Translate the point to the right by two units to get a point, and then translate the point up by three units to get a point, and the coordinate is;
8. In right-angle ABCD, a (-4, 1), b (0, 1), c (0 0,3), then the coordinates of point D are;
9. The length of line segment AB is 3, which is parallel to the X axis. If the coordinate of point A is known as (2, -5), the coordinate of point B is _ _ _ _ _.
Second, multiple-choice questions:
The two endpoint coordinates of 10.AB line are A (1 3) and B (2 2,7), and the two endpoint coordinates of CD line are C (2 2,4).
D (3 3,0), then the relationship between AB line and CD line is ()
A. parallel and equal B. parallel but unequal C. nonparallel but equal D. nonparallel and unequal
Third, answer questions:
1. Known: as shown in figure,,, find the area of △.
2. It is known that this point is on the axis.
(1) Find the coordinates of this point;
⑵ If, find the coordinates of this point.
3. It is known that the vertex coordinates of quadrilateral ABCD are A(-4, -2), B(4, -2), C (3, 1) and D (0, 3).
(1) Draw a quadrilateral ABCD in a plane rectangular coordinate system;
(2) Find the area of quadrilateral ABCD.
(3) If you subtract 2 from the abscissa of each vertex of the original quadrilateral ABCD and add 3 to the ordinate, what is the area of the graph?
4. Known:,,.
(1) Find the area of δ;
⑵ Set points on the coordinate axis,
And the areas of delta and delta are equal,
Find the coordinates of a point.
5. As shown in the figure, it is a schematic plan of a wildlife park. Establish an appropriate right angle.
Coordinate system, write down the coordinates of each point, and find the actual distance between goldfish hall and panda hall.
6. As shown in the figure, translate △ABC in the coordinate system to the position of AB translation.
Set, and then translate it to the right by 3 units.
Draw and find the coordinate change from △ABC to.
Chapter VII Triangle
(A) the knowledge structure of this chapter:
(2) Examples and exercises:
1. If one outer angle of a triangle is smaller than its adjacent inner angle, the triangle is ().
A. acute triangle B. right triangle
C. acute triangle or obtuse triangle
2. As shown in the figure, a pair of triangular rulers are spliced into a pattern, so ∠ AEB = _ _ _ _ _ _ _
3. In △ABC, if a = 3 and b = 5, the value range of side C is _ _ _ _ _.
4. If the ratio of three line segments is:
( 1)5:20:30 (2)5: 10: 15 (3)3:4:5
(4)3:3:5 (5)5:5: 10 (6)7:7:2
Then there are () scales that can form a triangle.
A.2 B.3 C.4 D.5
5. If the three sides of a triangle are 3, 8, 1-2x respectively, then the value range of x is ().
A.0 < x < 2 B.-5 < x
6. If the intersection of the heights of two sides of a triangle is outside the triangle, then the triangle is _ _ _ _ _ _ _.
7. Given △ABC, find the midline AD of (1)△ABC; (2) the angular bisector AE of △ ABC;
8. Given △ABC, find the high-speed lines AD and CE of △ABC.
9. In △ABC, two bisectors BD and CE intersect at point O, ∠ BOC = 1 16, then ∠A's degree is _ _ _ _ _ _.
10. BD and CE are known to be the heights of △ABC. If one of the angles formed by the intersection of straight lines BD and CE is 50, ∠BAC is equal to _ _ _ _ _ _ _ _.
1 1. In △ABC, ∠ b-∠ a = 15, ∠ c-∠ b = 60, then the shape of △ABC is _ _ _ _ _ _ _ _.
12. (Beijing, Volume 5, 2008). If the sum of the inner angles of a polygon is equal to, then the number of sides of the polygon is ().
a . 5b . 6c . 7d . 8
13. If every inner angle of a polygon is 144, then its number of sides is _ _ _ _ _ _ _ _ _ _ _.
14. Cut off one corner of the Pentagon, and the sum of its internal angles is () degrees.
A.360b.540c.720d. All the above answers are possible.
15. For a polygon, except one internal angle, the sum of other internal angles is 2750. Find the number of sides of a polygon.
16. The following regular polygons cannot be inlaid into a plane pattern ().
A. regular triangle B. square C. regular pentagon D. regular hexagon
17, drawing questions
When a program crew shoots a program, the lens can only move on track 0A, and the actor performs at a certain point P in the 0B direction. When the lens reaches point C, it is closest to the actor and the shooting effect is the best. Please determine the position p of the actor in the picture. (Keep drawing traces, do not write drawings)
18. Question: There are four handicraft factories, the locations of which are shown in the figure. It is planned to build a public exhibition hall to display the products of four factories. Where should the exhibition hall be built to minimize the sum of the distances between the exhibition halls of four handicraft factories?
19. Fold the △ABC paper along the DE as shown in the figure. When the point a falls within the quadrilateral BCDE,
Then there is a constant quantitative relationship between ∠A and ∠ 1+∠2.
The rule you find is ()
A.∠A =∠ 1+∠2 b . 2∠A =∠ 1+∠2
c . 3∠A = 2∠ 1+∠2d . 3∠A = 2(∠ 1+∠2)
20. (Wuhu, 2008) Choose four puzzles from the picture below to make a rectangle. The correct choice is. (Only fill in the code of the jigsaw puzzle)
2 1. The drawing shows a part, and the drawing requirements are ∠ A = 90, ∠ B = 32, ∠ C = 2 1.
When the inspector measures ∠ BDC = 145, it is determined that the part is unqualified.
Can you tell the truth?
22.( 1) As shown in figure 1, there is a right triangle XYZ placed on △ABC, which is just a triangle.
The two right-angled sides XY and XZ of XYZ pass through point B and point C △ ABC respectively, and △ A = 30.
Then ∠ ABC+∠ ACB = degree, ∠ XBC+∠ XCB = degree;
(2) As shown in Figure 2, if the position of the right-angled triangle XYZ is changed so that the two right-angled sides XY and XZ of the triangle XYZ still pass through the points B and C respectively, will the size of ∠ abx+∠ acx change? If yes, please give examples; If not, request the size of ∠ ABX+∠ ACX.
23. As shown in figure 1, △ABC, D is on the extension line of BC, E is on the extension line of CA, and F is on AB.
Verification: ∠ 2 > ∠ 1.
As shown in figure 2, △ABC, CD is the bisector of its external angle ∠ACE, and it is verified as ∠ 2 >; ∠ 1.
24.( 1) It is known that, as shown in figure 1, in △ABC, d is a point on AB except the vertex. Verification: AB+AC > d b+ DC； (2) As shown in Figure 2, in △ABC, D is a point on the side of AB, which proves that AB+AC ≥ DB+DC;
(3) As shown in Figure 3, point P is any point in △ABC, which proves that: pa+Pb+PC > (a b+ BC+AC)；
(4) As shown in Figure 4, D and E are two points in △ABC, which proves AB+AC > BD+DE+EC。
25. As shown in Figure 1, the five-pointed star ABCDE.
(1) Please guess: How many degrees is ∠A+∠B+∠C+∠D+∠E?
(2) If a vertex B is moving, is the conclusion that the pentagram becomes a B diagram and a C diagram (1) correct? Please provide a justification for the answer.
26.( 1) As shown in figure 1, in △ABC, ∠ C = 80, ∠ B = 40, Ad is perpendicular to BC and D, AE is divided into ∠BAC,
Find the degree of ∠EAD?
(2) if "∠ c = 80, ∠ b = 40" is changed to "∠ c > ∠ b", other conditions remain unchanged, it can be found.
Is there a quantitative relationship between ∠EAD and ∠B and ∠C?
(3) As shown in Figure 2, in △ABC, AE bisects ∠BAC, point F is on AE, and FD is perpendicular to BC and D. What is the relationship between ∠ EFD and ∠B and ∠C? Please state your reasons.
(4) As shown in Figure 3, in △ABC, AE bisects ∠BAC, point F is on the extension line of AE, and FD is perpendicular to BC and D. What is the relationship between ∠ EFD and ∠B and ∠C? Please state your reasons.
27. As shown in the figure, the height of BC side of △ABC is the same as that of △ side.
28. As shown in the figure, a point is the midpoint of three sides. If the area of is 12, the area of is.
The first network of new curriculum standards
Chapter VIII Binary Linear Equations
(A) the knowledge structure of this chapter:
(2) Examples and exercises:
1, and () of the following equations are binary linear equations.
① ② ③
④ ⑤
A.2 B.3 C.4 D.5
2. If the equation is a binary linear equation, the value of k is ().
A.2 B- 2 c. 2 or -2 D. None of the above is correct.
3. If it is the solution of the binary linear equation 3x-2y= 1 1, then y = _ _ _ _ _ _ _
4. The nonnegative integer solution of equation 2x+y=5 is _ _ _ _ _ _ _ _ _ _ _ _.
5. In Equation 2(x+y)-3(y-x)=3, y is represented by an algebraic expression containing x, which is ().
a . y = 5x-3 b . y =-x-3 c . y =-5x-3d . y =-5x+3
6. Knowing the solution of a binary linear equation group, try to write a binary linear equation group that meets the conditions.
_______________ __。
7. Solve the following equation by substitution elimination method:
( 1) (2) (3)
8. Solve the following equation by adding, subtracting and eliminating elements:
( 1) (2)
9. If the solution of the equation is satisfied, then m = _ _ _ _ _ _
10, and solve the following equation:
( 1) (2)
1 1. If the solutions of equations x and y are equal, then k = _ _ _ _ _ _ _
13, in the equation, when x= 1, y =1; When x=2 and y=4, the values of k and b are ().
A B C D
14 is known to be similar, so the values of a and b are ().
A.B. C. D。
15, if the value is ()
A.8 B.2 C.-2 D.-4
Comprehensive application of the equation;
1. It is known that it is the solution of binary linear equations about X and Y. Try to find the value of (m+n)2004.
2. Given the equation and the same solution, find the numerical value.
3. the solution of the equations should be, but because the number m is mispronounced, the solution is to find the values of a, b and m. ..
4. It is known that in the algebraic expression ax +bx+c, when X takes 1, its value is 2; When x takes 3, its value is 0; When x takes -2, its value is 20; Find this algebraic expression.
5. Explore the solution of the equation.
What are the values of (1)m and n? Is there a solution to the equations? No solution? There are countless solutions?
(2) Discuss that the solution of the following equation is known:
① ②
6. Let "○" □ "and △" represent three different objects and weigh them twice with a balance, as shown in the figure. Then, the order of the three objects in descending order of mass is ().
A.□ ○ △ B.△ ○ □
C.□ △ ○ D.△ □ ○
7. As shown in the figure, eight identical rectangular floor tiles are spliced into a rectangle, and the length and width of each rectangular floor tile are respectively
8. It takes 65,438+02 days for team A, 65,438+05 days for team B and 20 days for team C to complete a project. According to the original plan, this request will be completed within 7 days. Now Team A and Team B have been working together for several days. Later, in order to speed up the work, Team C joined in, thus completing the task one day ahead of schedule. Ask how much the two teams have cooperated. How many days did team c do after joining?
9. Master Wang opened a small shop after he was laid off. Last week, he bought 50 A and B goods. The purchase price of a commodity is 35 yuan/piece, and the profit rate is 20%. B The purchase price of goods is 20 yuan/piece, the profit rate is 15%, and the profit is 278 yuan. Do you know how many A goods and B goods Master Wang bought respectively?
10. (Jiangxi 07) Tickets for the 2008 Beijing Olympic Games began to be booked by the public. The following table shows the ticket prices of several ball games published on the official ticketing website of Beijing Olympic Games. A fan is going to use 8000 yuan to book tickets for events below 10.
(1) If all the funds are used to book tickets for men's basketball and table tennis, how many tickets can he book for men's basketball and table tennis?
(2) If he wants to book the following three kinds of tickets within the existing fund of 8,000 yuan, and the total number of tickets for men's basketball is the same as that for football, and the cost of table tennis tickets is not more than that for men's basketball, how many tickets for each of the three kinds of tickets can he book?
Ticket price of competition events (yuan/field)
Men's Basketball Team 1000
Football 800
Table tennis 500
Chapter 9 Inequality and Unequal Groups
(A) One-dimensional linear inequality knowledge network diagram
(B) One-dimensional linear inequality group knowledge network diagram
(3) Examples and exercises:
I. Concept and nature
1, when k _ _ _ _, the inequality is linear;
Where the solution set is all real numbers, it is _ _ _ _ _ _, and where there is no solution, it is _ _ _ _ _ _ _.
3. Statement ① If
The correct one is _ _ _ _
4. The statement ""is obviously incorrect. Try to change it into a correct statement according to the following requirements: ① Add conditions to make the conclusion unchanged; ② Keep the conditions unchanged and change the conclusion.
5. Known a>b and c> answer the following questions:
① Prove A+C > b+d
② Does inequality ac & gtbd hold? Is to explain why.
6. As we all know,
Second, the solutions and solution sets of inequalities and inequality groups
1. Solve the following inequalities
2、
3. Inequality10+4x >; The negative integer solution of 0 is _ _ _ _ _ _ _ _ _
4. Given the solution set of inequality ax≥2 about X, it is shown on the number axis, and the value of A is _ _ _ _ _ _ _.
5. on the inequality A (X- 1) about the solution of X > X-2.
6. The inequality about x is known as (2a-b) x+3a >; The solution set of 0 is the solution set of inequality ax>b.