(Huangshi City, 2009)
The reciprocal of 1 Yes ()
A.B. C. D。
2. The corresponding point of the real number on the number axis is shown in the figure, then,
The size relationship of is ()
A.B.
C.D.
3. Among the following radicals, the one that is not the simplest quadratic radical is ().
A.B. C. D。
4. In the figure below, there are only three symmetry axes ()
A. diamond B. equilateral triangle C. square D. circle
5. The image of a linear function only passes through the first, second and third quadrants, then ()
A.B.
C.D.
6. A geometric figure of three views is as shown in the figure, so this geometric figure is ().
A. cone B. prism C. cylinder D. prism
7. The two sides of a triangle are 3 and 4 respectively, and the length of the third side is the root of the equation, so the perimeter of the triangle is ().
A.14b.12c.12 or 14d. None of the above is correct.
8. In order to prevent and control imported influenza A (H 1N 1), a hospital in a certain city set up a prevention and control team to treat patients with fever and runny nose in isolation, and decided to deploy three of the five key physicians in internal medicine (including A), so the probability that A must be transferred to the prevention and control team is ().
A.B. C. D。
9. As shown in the figure, if it is an inscribed triangle, then the area of the inscribed square is ()
A.2 B.4 C.8 D. 16
10. Given the image of quadratic function as shown in the figure, the following conclusions are drawn:
① ; ② ; ③ ; ④ ;
⑤ The serial number of all correct conclusions is ()
A.①② B. ①③④
C.①②③⑤ D.①②③④⑤
Second, fill in carefully (6 small questions in this question, 3 points for each small question, *** 18 points)
1 1. factorization.
12. As shown in the figure, then.
13. Yes, yes, if, then.
14. During the Wenchuan earthquake, air dropped relief supplies to the designated area (circle A), as shown in the figure. If the probability of air-dropped materials falling in the central area (circle B) is 0, then its ratio to the radius is 0.
15. In the figure below, the images of the proportional function and the inverse proportional function intersect at two points, and two circles tangent to the axis are drawn with these two points as the center. If the coordinate of the point is (2, 1), the sum of the areas of the two shaded parts in the figure is.
16. If the two intersections of parabola sum are symmetrical about the origin, they are respectively.
Three, comprehensive answer (this question has 9 small questions, ***72 points)
The solution should be written in words, proof process or deduction steps. If you think some questions are a little difficult, you can write some answers that you can write.
17. (Full score for this small question)
Evaluation.
18. (The full score for this short question is 7)
As shown in the figure, on the floor,
Verification:
19. (Full score for this small question)
Simplify first, then evaluate
One of them is.
20. (The full mark of this small question is 8) Known function (constant)
(1) If the image of the function has exactly one intersection with the axis, the value of; (4 points)
(2) If the image of the function is a parabola, and the vertex is always above the axis, find the value range. (4 points)
2 1. (Full score for this small question)
Orient Mountain, the first mountain of Sanchu, is a Buddhist holy land in Huangshi area and a national AAA scenic spot. Its main peak is about 600 meters above sea level, and there is a telecom signal transmitter on it. Now the elevation of the peak measured at the foot of the mountain is, the elevation of the top of the transmitter is, and the height of the transmitter is needed here.
22. (The full score for this short question is 8)
The "Plastic Restriction Order" was implemented nationwide for one year on June 1 this year. Three reporters from a newspaper randomly investigated the use of shopping bags by a certain number of customers before and after the implementation of the "plastic restriction order" at the gates of three major commercial groups in Wuhan that day. The following is a statistical chart drawn by these three reporters according to the summarized data.
Please answer the following questions based on the above information.
(1) In the figure 1, the ratio of the height of each rectangle from left to right is 2: 8: 8: 3: 3: 1. Knowing that 24 customers used four and five plastic shopping bags in this survey, I asked three reporters how many people they surveyed. (2 points)
(2) Before the implementation of the "Plastic Restriction Order", if there are about 6,000 people shopping in the three major shopping malls every day, according to the average number of plastic shopping bags used by a certain number of customers, how many plastic shopping bags do the three major commercial groups need to provide customers every day? (3 points)
(3) According to the Wuhan Evening News, from June/kloc-0 to the end of February last year, 65,438+Compared with the same period of last year, the usage of plastic bags in all stores under the three major commercial groups decreased from 1 29.27 million to 33.55 million, with a decrease of (accurate to 1%). This result is compared with the percentage of paid plastic shopping bags in Figure 2.
23. (The full score for this short question is 8)
In order to expand domestic demand, benefit farmers, enrich their spare time life and encourage farmers to send color TVs to the countryside, the state has decided to implement government subsidies for farmers who buy color TVs. It is stipulated that the government will subsidize several yuan for each color TV set. After investigation, the relationship between the number of color TV sets sold in a shopping mall and the subsidy amount (yuan) roughly satisfies the linear function as shown in figure 1. With the increase of subsidy, the sales volume is also increasing, but the income (yuan) of each color TV will increase.
(1) Before the government introduced the subsidy measures, what was the total revenue from selling color TVs in this shopping mall? (2 points)
(2) After the implementation of the government subsidy policy, the functional relationship between the number of color TV sets sold in shopping malls, the income of each household appliance and the amount of government subsidy is obtained respectively; (3 points)
(3) In order to maximize the total revenue (RMB) from selling color TV sets in this shopping mall, what should the government set as the subsidy for each color TV set? And find the maximum of the total income. (3 points)
24. (The full score for this short question is 9)
As shown in the figure, the midpoint is the moving point on the side, passing through a straight line, the intersection bisector is at point, and the intersection bisector is at point.
(1) Explore and prove the quantitative relationship between line segments and; (3 points)
(2) When the point moves on the edge, will the quadrilateral be a diamond? If yes, please prove it, if not, explain the reasons; (3 points)
(3) When the point moves to where and what conditions are met, a quadrilateral is a square? (3 points)
25. (Full score for this small question 10)
The square is in the plane rectangular coordinate system as shown in the figure, on the positive semi-axis of the shaft, on the negative semi-axis of the shaft, the positive semi-axis of the horizontal shaft is on the negative semi-axis of the horizontal shaft, and the parabola passes three points.
(1) Find the analytical formula of parabola; (3 points)
(2) is a point in the middle of a parabola, and the intersection point is crossed by a straight line parallel to the axis, and the straight line at the intersection point is, if so, the shape of a quadrilateral is judged; (3 points)
(3) Whether there is a moving point on the ray and whether there is a moving point on the ray. If so, please strictly prove it. If not, please explain the reason. (4 points)
Academic Examination for Junior High School Graduates in Huangshi City in 2009
Mathematical answers and grading standards
First, multiple-choice questions (3 points for each small question, 30 points for * * *)
The title is 1 23455 6789 10.
Answer D C C B B C B A A C
Fill in the blanks (3 points for each small question, *** 18 points)
1 1. 12.60 13.3∶5 14. 15. 16.
Third, answer questions (9 small questions, ***72 points)
17. Solution: 4 points for the original formula.
3 points
18. Proof:
,
.2 points
Say it again,
, that is. Two points.
Say it again,
.
.3 points
19. Solution: 4 points for the original formula.
.2 points
When, the original formula. 1 point
20. Solution: (1) When the function is, its image is obviously consistent with the axis.
There is only one intersection. Two points.
When the equation has two equal real roots according to the meaning of the question.
, .
When or, the function image and the axis have exactly one intersection point. Two points.
(2) Discuss the solution according to the meaning of the problem.
When or, the vertex of the parabola is always 0.4 minutes above the axis.
2 1. solution: in,
∵ ,
Three points
Yes,
∵ ,
Three points
∴.2 o'clock
A: The height of the launcher is 25 meters. ..
22. Solution: (1) If the number of people shopping in six packages at a time is people, the conditions are as follows.
The reporter surveyed people. 2 points
(2) The average number of shopping bags used by these 65,438+000 customers at one time is
(1)
Answer.
It is estimated that these three commercial groups provide customers with 18000 plastic shopping bags every day. Three points
(3)74%; 25;
Most people have increased awareness of environmental protection (as long as they care about environmental protection and energy conservation). 3 points
23. Solution: (1) The total income from the sale of household appliances in this mall is (RMB) 2 points.
(2) according to the meaning of the question.
,
Yes,
Solve.
So, 0.3 points.
(3)
The government should set the subsidy for each TV set at 100 yuan, with the highest total income.
Its maximum value is 0.3 yuan.
24. Solution: (1).
This is proved as follows:
Yes, the bisector.
∵ ,∴ .
∴ .
∴ .
It can also be proved.
Three points
(2) The quadrilateral can't be a diamond. If it is a diamond, then (1) shows that there can't be two straight lines perpendicular to one straight line when passing through the same point on the plane. Three points
(3) When the point moves to the midpoint,,, then the quadrilateral is, if you want to make a square, you must be.
∵, ∴, ∴ are right triangles with right angles,
When the point is the midpoint and it is a right triangle with right angles,
A quadrilateral is a square. 3 points
25. Solution: (1) Conditionally.
Yuji
Yes.
∴ .
Substitute the coordinates of into the parabolic equation,
Yes
The analytical formula of parabola is 0.3 minutes.
(2) Settings,,.
∴
That is all right
(Give up)
At this point, points coincide with points,,,,
It is an isosceles trapezoid. Three points
(3) There is one point on the ray and one point on the ray.
Make and maintain water, as evidenced by the following:
When the point is in the position shown in Figure ①, it is best to set it as follows: crossing point, and vertical foot.
If. Author:
,
.
and
.2 points
When the pointer is in the position shown in fig. ②,
Do a little work,
The vertical feet are respectively.
It can also be proved.
.
Say it again,
,
. 1 point
When it is in the position shown in Figure ③, the over-point operation, the vertical foot is, the extension line, and the vertical foot is.
It can also be proved.
. 1 point
Note: If the discussion is divided into three situations, and the drawing is correct and one situation is proved to be correct, it can be proved that the other two situations are equally given 4 points; If only one correct proof is given and the other two cases are not explained, you can give 2 points. If you use the four-point knowledge of * * * circle to prove and prove that the process is correct, you can only give 2 points without discussing the three situations.