First, multiple-choice questions (this big question * * 12 small questions, 3 points for each small question, out of 36 points)

1. In the numbers given below, the number opposite to 2 is

A.-2 B. 1 2 C.2 D.- 1 2

2. As shown in the figure, the physical shapes described in the three views are as follows

A. prism B. pyramid C. cylinder D. cone

3. The following calculation is correct

A. 10a6÷5a2=2a4 B.32+23=55

C.2(a2)3=6a6 D.(a-2)2=a2-4

4. On June 9th, 20 1 1, China's second lunar exploration satellite "Chang 'e II" rushed into the deep space1500,000 km away from the Earth. Scientific notation shows that 1500000 is

a . 1.5× 106 b . 0. 15× 107 c . 1.5× 107d . 15× 106

5. In the function, the value range of the independent variable X is

A.x ≠ 2 b.x ≥ 2 c.x ≤ 2 d. All real numbers

6. The result of factorization of polynomial x3-4x is as follows

A.x(x2-4) B.x(x+4)(x-4)

C.x(x+2)(x-2) D.(x+2)(x-2)

7. The image of function y = 2 | x | is

8. The curve of a highway is an arc AB⌒, and point O is the center of the arc and point C..

Is the midpoint of AB⌒, OC and AB intersect at point D. Known AB = 120m, CD = 20m,

So the radius of this bend is

In 2003

C.100m D.1003m

9. As shown in the figure, there is a cat at the vertex P of the conical straw pile, and it sees a mouse at point A on the circumference of the bottom surface. The cat walked down the bus to catch mice. When the cat reaches point A, the mouse has escaped along the circumference of the bottom, and the cat is chasing after it along the same route. After catching the mouse at point B on the circumference, return to vertex P along the bus BP. In this process, it is assumed that the speed of the cat is uniform, and the distance from the cat to point P after starting is S.

10. In the grid composed of small squares with side length of 1, there are two points, A and B, as shown in the figure. The probability that the area of △ABC is 1 by arbitrarily placing point C in the grid is

A. 1 5 D. 6 25

1 1. As shown in the figure, four small circles with a radius of 1 are all around the center of the great circle and inscribed with the great circle.

The shaded part is

A.B- 4

C.2 D. 2+ 1

12. As shown, in △ABC, ∠ ACB = 90? ，∠A= 15？ ，AB=8，

Then AC? The value of BC is

a . 14 b . 163 c . 4 15d . 16

II. Fill in the blanks (6 small questions in this big question, 3 points for each small question, full mark 18)

13. If 5m in the east is marked as +5m and 3m in the west is marked as m. 。

14. As shown in the figure, it is the residual part of a trapezoidal iron sheet. Measure ∠ A = 100? The trapezoid is incomplete.

The degree of the base angle is.

15. In the plane rectangular coordinate system, point A (- 1, 3) is symmetrical about the origin of point AO.

The coordinates are.

16. The mode of a set of data is -2, 0, -3, -2, -3, 1, and x is -3, so the median of this set of data is.

17. Simplification: x2-1x2+2x+1+2x+1=.

18. As shown, in △ABC, ∠ ACB = 90? ，∠A=30？ ，BC = 1。 Intersection c is cC 1 ⊥ ab in C 1, intersection c1is C2, intersection C2 is C2C3⊥AB, ... in C3, and so on.

Three. (This topic is entitled ***2 small questions, with 6 points for each small question, with a full score of 12).

19. calculation:-12+6Sin60? - 12+20 1 10.

20. Solve the fractional equation: 2x- 1 = 4x2- 1.

Four. (This topic is entitled ***2 small questions, with 8 points for each small question, with a full score of 16).

2 1. As shown in the figure, each small square in the grid paper is a square with a side length of 1 unit, and the vertices of △ABC are all on the grid points, thus establishing a plane rectangular coordinate system.

(1) The coordinates of point A and point C are respectively.

(2) Translate △ABC to the left by 7 units. Please draw the translated △ A 1b 1c 1. If m is a point in △ABC and its coordinate is (a, b), then the coordinate of the translation point m corresponding to the point M 1 is.

(3) Take the origin O as the similarity center, and reduce △ABC, so that the ratio of corresponding edges after △A2B2C2 and △ABC transformation is 1: 2. Please draw △A2B2C2 in the grid and write down the coordinates of point A2.

22. A seventh-grade school in Nanning implements group cooperative learning. In order to understand the students' speeches in class, some students of this grade are randomly selected and their speeches in class every day are investigated and counted. The statistical table is as follows, and two incomplete statistical charts are drawn. It is known that the histogram height ratio of the number of speakers in group A and group B is 1 ∶ 5.

Please use the relevant data in the picture to answer the following questions:

(1) What is the number of people in Group A? What is the sample size of this survey?

(2) Find the number of people in Group C and complete the histogram.

There are 250 students in grade seven in this school. Please estimate that there are no fewer than 15 students who speak in class every day.

Verb (abbreviation for verb) (the full mark for this big question is 8)

23. As shown in the figure, points B, F, C and E are on the same straight line, BF = Ce, ∠ B = ∠ C.

(1) Please add only one condition (no auxiliary line) to make △ ABC △ def.

The condition you added is:.

(2) After adding conditions, it is proved that △ ABC △ def.

Six, (full score for this big question 10)

24. A 24,000-meter-long new road is about to be laid in wuxiang new district, Nanning.

(1) Write the functional relationship between paving time t (days) and paving speed v (meters/days).

(2) The existing paving machine of the engineering company responsible for paving roads can pave 400 meters every day. How many days is the fastest to complete the paving task?

(3) In order to speed up the project progress, the company decided to invest no more than 4 million yuan to buy 65,438+00 more advanced pavers. There are two kinds of machines to choose from. The price and daily paving capacity of each machine are shown in the following table. After the original paving machine was paved for 40 days, the newly purchased 10 machine was added to pave the road, and the company was at least 65438+ earlier than originally expected. Please explain which scheme costs the least by calculation.

Jiayi

Price (ten thousand yuan/set) 45 25

Daily paving capacity (m) 50 30

Seven, (this big question full score 10)

25. As shown in the figure, it is known that CD has a diameter of ⊙O, AC⊥CD, a vertical foot of C, a chord of de∨OA, and a straight line AE intersects with CD at point B. 。

(1) Prove that straight line AB is tangent to ⊙ O 。

(2) when AC = 1 and BE = 2, find the value of tan∠OAC.

Eight, (the full score of this big question is 10)

26. As shown in the figure, in the plane rectangular coordinate system, the parabola y = x2+mx+n passes through points A (3 3,0) and B (0 0,3), point P is the moving point on the straight line AB, the perpendicular line with point P as the X axis intersects with the parabola at point M, and the abscissa of point P is t. 。

(1) The analytical expressions of straight line AB and this parabola are obtained respectively.

(2) If point P is in the fourth quadrant, connect AM and BM. When the line segment PM is the longest, find the area of △ABM.

(3) Is there such a point P, and the quadrilateral with points P, M, B and O as its vertices is a parallelogram? If it exists, please write the abscissa of point P directly; If it does not exist, please explain why.