1. Multiple choice questions: (3 points for each question, * * 36 points, and only one answer for each question)
1. Represents the solution set of inequality groups on the number axis, which should be ().
2. It is known that the following inequality is incorrect ().
A.B. C. D。
3. The image of the function y = kx+b (k, b are constants, k0) is as shown in the figure, so the inequality of x.
The solution set of kx+b type & gt0 is ().
A.x & gt0 B.x & lt0 C.x & lt2d . x & gt； 2
4. In the following deformation from left to right, the factorization is ().
a . a2–4a+5 = a(a–4)+5 b .(x+3)(x+2)= x2+5x+6
c . a2–9 B2 =(a+3b)(a–3b)d .(x+3)(x– 1)+ 1 = x2+2x+2
5. There is no common factor () in the following algebraic expressions.
A.4a2bc and 8ab2b.a3b2+ 1 and a2b3–1
C.b (a–2b) 2 and a (2b–a) 2d.x+1and x2–1.
6. The following factorization is correct ()
A.–4a 2+4b 2 =–4(a2–4b 2)=–4(a+2b)(a–2b)b . 3m 3– 12m = 3m(m2–4)
c . 4x4y– 12x2y 2+7 = 4x2y(x2–3y)+7d . 4–9 m2 =(2+3m)(2–3m)
7. In the following four fractional operations, () is the correct operation result.
①; ②; ③; ④;
A.0 B. 1 C.2 D.3
8. If the values of a and b in the score are expanded to twice the original value, the value of the score will be ().
A. expand to twice the original B. keep the value of the score unchanged C. shrink to the original D. shrink to the original
9. Some students chartered a van to travel, and the rental price of the van was 180 yuan. Later, two students were added to rent a car.
The price remained unchanged, and as a result, each student shared the 3 yuan fare less than before. If there are x students taking part in the tour, then according to the question.
Meaning countable equation ()
A.B.
C.=2 D。
10. The actual distance between the two places is 500 m, and the distance drawn on the map is 25 cm. If you measure the distance between a and b on this map,
40 cm, then the actual distance between A and B is ()
800 megabytes. 8000 meters
C.32250 cmD .3225 meters
1 1. The following two triangles must be similar ().
A. Two isosceles triangles B. Two right triangles
C. two obtuse triangles. Two equilateral triangles
12. It is known that the following proportional formula holds ()
A.b.c.d.
Fill in the blanks: (3 points for each small question, * * * 30 points)
13. Expressed by inequality:
(1) The difference between x and 5 is not less than 2 times of x:
(2) Xiao Ming's height h exceeds 160 cm.
14. The non-negative integer solution of inequality is.
15. After extracting the common factor–x from–x4–3x2+x, the residual factor is.
16. If 4a4–Ka2b+25b2 is completely flat, then k =.
17. If the area of a square is 9m2+24mn+ 16n2, then the side length of the square is.
18. Decomposition factor: _ _ _ _ _ _ _ _ _ _.
19, when =, the value of the score is.
20. It is known that the solution set of the inequality about X (1-a) x > 2 is X.
2 1. If point C is the golden section of line segment ab, AC >: BC, then the relationship among AB, AC and BC can be expressed by a formula.
Stands for _ _ _ _ _ _ _ _ _ _ _.
22. The height of a bamboo pole is 1.5cm, and the shadow length is 2m. At the same time, the shadow length of the tower is 40m, so the height of the tower is _ _ _ _ _ _.
Third, the calculation problem: (5 points for each small question, 20 points * * *)
23. Decomposition coefficient: 24. Solve the equation:
25. Simplify first, then evaluate: Among them
26. Solve the inequality group and express the solution set on the number axis.
4. Answer questions (7 points for each small question, *** 14 points)
28. Given the value of k, the known polynomial (A2+Ka+25)–B2 can be factorized, that is, the first half can be written as a complete square formula. .
(1) Write the possible values of the constant k;
(2) Write the factorization process of one of the given k values.
29. As shown in the figure, AB is a reclining long ladder, with a length of 4.4m, the foot b of the ladder is away from the wall root 1.6m, and the point d on the ladder is away from the wall1.4m..
Given △ADE∽△ABC, what is the length AD from point A to point D?
Verb (abbreviation of verb) Operation and exploration (score 10 for each small question, 20 points * * *)
27. The distance between A and B is 360 kilometers. After the opening of the new expressway, the average speed of long-distance buses between A and B increased by 50%, while the time from A to B was shortened by 2 hours. Try to determine the original average speed.
28. The buyer of a shopping mall predicted that a shirt would sell well in the market this season, so he spent 80 thousand yuan to buy this shirt, which was really in short supply after it was put on the market. The department store bought the second batch of this kind of shirts for 6.5438+0.76 million yuan, which was twice as much as the first batch, but the unit price was higher than that of 4 yuan. When these shirts are sold in department stores, each one is priced at 58 yuan. The last remaining 150 pieces were sold out at a 20% discount. In these two transactions, how much did the commercial building profit?