1. Fill in the blanks (this big question contains 10 small questions, each with 2 points and * * * 20 points).
Fill in the answer on the horizontal line in the question or answer as required.
1. When x _ _ _ _ _ _ _ _ _ _ the score is meaningful.
2. Decomposition coefficient = _ _ _ _ _ _ _ _ _ _
3. The integer solution of the inequality group is _ _ _ _ _ _ _ _ _ _
4. If known, the value of is equal to _ _ _ _ _ _ _ _ _ _
5. As shown in the figure, at △ABC, DE‖BC, ad: AB = 2: 3, BC=6cm,
The length of DE is _ _ _ _ _ _ \ \.
6. If yes, then = _ _ _ _ _ _ _ _ _ _
7. Two packaging machines, A and B, each containing 500 grams of salt at the same time. 65,438+00 bags were taken out from them and their mass was measured.
The average and variance of 10 bag salt are calculated, and the average is 50 1.5g, and the variances are respectively
= 36.3, = 8.63. In two machines A and B, _ _ _ _ _ _ _ _ _ _ _ _
8. At present, A and B vehicles are used to transport 46 tons of drought-resistant materials to the disaster area, with a load of 5 tons and a load of 4 tons. If a * * * arranges 10 vehicles to transport these materials, then at least _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
9. As shown in the figure, in the square grid of 10×6, the vertex of each small square is called the lattice point.
△ The vertices of △AOB are all on the grid. Please draw a graph similar to △AOB in the grid.
Let two graphs take point O as the similarity center, and the similarity ratio between the drawn graphs and △AOB is 2: 1.
10. As shown in the figure, trapezoidal ABCD, AB‖DC, diagonal intersect at point O, DC=2.
AB = 4。 Then the area ratio of △DOC to △DOA is _ _ _ _ _ _ _.
Second, multiple-choice questions (this question contains 8 small questions, each with 3 points and ***24 points)
Only one of the four options given in the following question meets the requirements. Please fill in the letter code of the correct answer in the corresponding position in the table below.
1 1. Among the following survey methods, the ones suitable for general survey are
A. know the service life of a batch of light bulbs.
B: Know the ratings of Taiyuan TV News Express.
C. Know the height of our school basketball team 12 players.
To understand the satisfaction of foreign tourists with Jinyang Culture and Food Festival.
12. The true proposition in the following propositions is
All rectangles are similar.
All diamonds are similar.
C.all squares are similar
D. All isosceles triangles are similar
13. The following operation results are correct.
A, B, C and D
14. The variance of a set of data 3, 4, 5, 6 and 7 is
A.B.2 C、5 D. 10
15. As shown in the figure, Xiao Ming uses a bamboo pole with a length of 2.4m as a measuring tool to measure the height of the school flagpole, and moves the bamboo pole so that the shadow of the top of the bamboo pole and the flagpole falls on the same point on the ground. At this time, the bamboo pole is 8m away from this point and 22m away from the flagpole, so the height of the flagpole is
A.10m B.9m C.8m D.7m
16. The image of the linear function is shown in the figure. When, the value range of x is
A.x & gt2 B.x & lt2c . x & gt； 0d . x & lt； 0
17. As shown in the figure, 1= 2 is known, so ABC ADE cannot be determined after adding one of the following conditions.
A.AED。
18. As shown in the figure, point P is a point in ABC, with the following conclusions: ① BPC > a； ② BPC must be obtuse;
③ BPC= A+ ABP+ ACP ... Among them, the correct conclusion is * * *.
A.0 B. 1 C.2 D.3
Third, answer the question (this big question contains 8 small questions, ***56 points)
To solve the problem, you should write the necessary words, prove the process or calculation steps.
19. (3 points for each small question, 6 points for * * *)
Decomposition factor: (1); (2) .
20. (The perfect score for this short question is 6)
Solve inequality.
2 1. (Full score for this small question)
Simplify first, then evaluate.
22. (The full score for this short question is 8)
June 5th is World Environmental Protection Day. In order to let students know about environmental protection knowledge, a middle school organized 3000 students from all over the school to participate in the "Environmental Protection Knowledge Competition". In order to understand the distribution of the results of this competition, some students' scores (out of 65,438+000, all scores are positive integers) are selected for statistics, and the following frequency distribution table and frequency distribution histogram are obtained.
Please answer the following questions according to the above statistical chart:
(1) Complete the frequency distribution table and frequency distribution histogram;
(2) The number of selected students whose competition scores fall within the range of _ _ _ _ _ _ _ _ _.
(3) More than 90 points (excluding 90 points) are considered excellent. How many students do well in this school?
23. (The full score for this short question is 8)
Students from Class 8 (1) take a bus to visit a scenic spot on weekends, which is 20 km away from the school1. Some students took the local train first, 1 hour later, and some students took the express train. As a result, they arrived at the same time. It is known that the speed of express train is 0.5 times that of 65438+ local train, so the speed of local train is required.
24. (The full score for this short question is 6)
It is known that AB//CD and E are moving points on a straight line AC (not coincident with point C) and connected to ED.
(1) As shown in figure (1), when point E is on the extension line of line segment AC, it is proved that CED+CDE+A =180;
(2) As shown in Figure (2), is the conclusion in (1) valid when point E is on the line AC? If established. Please prove; If it is not true, please write the equivalent relationship of these three angles directly.
25. (The full score for this short question is 8)
In response to the call of "low-carbon life", an enterprise decided to purchase A and B sewage treatment equipment 10. The price of each equipment and the monthly sewage treatment capacity are shown in the following table. According to the calculation, the fund for purchasing equipment does not exceed/kloc-0.05 million yuan, and the enterprise produces 2040 tons of sewage every month. Please design a scheme for purchasing sewage treatment equipment for this enterprise.
26. (The full score for this short question is 8)
It is known that in ABC, AB=6 and the height on the side of AB is 4.
(1) As shown in Figure (1), the quadrilateral EFGH is a square, with E and F on the AB side, and G and H on the AC and BC sides. Find the side length of a square;
(2) As shown in Figure (2), there are two congruent squares side by side in the triangle, and the vertices D and E of the rectangle DEFG formed by them are in
On the AB side of ABC, G and F are on the AC and BC sides respectively. The side length of a square is _ _ _ _ _ _ _ _ _ _ _;
(3) As shown in Figure (3), there are three congruent squares side by side in the triangle, and the rectangle formed by them has two vertices at ABC.
On the AB side, the other vertices are on the AC side and BC side respectively. The side length of a square is _ _ _ _ _ _ _ _;
(4) As shown in Figure (4), there are congruent squares side by side in the triangle, and the two vertices of the rectangle formed by them are at ABC.
On the AB side, the other vertices are on the AC side and BC side respectively. The side length of a square is expressed by an algebraic expression containing n _ _ _ _ _ _ _ _