mathematics

Tips:

1. Before answering questions, candidates must fill in their county (city, district), school and test number in the designated position of the test paper.

2. After choosing the answer to the multiple-choice question, blacken the letter code of the corresponding question number on the answer sheet with 2B pencil; The answers to multiple-choice questions must be written in the designated position on the answer sheet, and the answers in this volume are invalid.

The full mark of this volume is 120, and the examination time is 90 minutes.

First, choose carefully and trust your own judgment! (This question *** 12 is a small question, with 3 points for each small question and 36 points for each small question. Only one of the four options given in each small topic meets the requirements of the topic. If there is more than one code that is not painted, painted wrongly or painted wrongly, you will get 0 point. )

The reciprocal of 1 Yes ()

A.B. C. D。

2. The total mileage of the torch relay of Beijing Olympic Games with the theme of "harmonious journey" is about137,000 kilometers, which can be expressed as () by scientific notation.

A.km.b.km.

Kilometers are kilometers in diameter.

3. In the formula □, fill in which of the following operations?

Symbol, the calculated value is the smallest ()

A.B. C. D。

4. The three views of a geometric figure are right, and this geometric figure is ()

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

5. The statistics of the highest daily temperature in May in our city are as follows:

Maximum temperature (℃) 28 29 30 3 1

Days 1 1 3 2

Then the mode and median of this set of data (the highest temperature) are () respectively.

A.29，30 B.30，29 C.30，30 D.30，3 1

6. The following operation is correct ()

A.B.

C.D.

7. As shown in the picture, it is a point between two parallel lines.

Then ()

A.B. C. D。

8. In the curve below, the function indicating no is ().

9. In the figure below, the axis symmetry and center symmetry is ().

A. diamond B. trapezoid C. regular triangle D. regular pentagon

10. Translate the parabola to the left by 1 unit, and then translate it up by 3 units, then the analytical formula of the parabola after translation is ().

A.B.

C.D.

1 1. The middle,, and are equal circles.

, circumscribed, the area of the two sectors (i.e. the shaded part) in the figure is one.

Harmony is ()

A.B. C. D。

12. A particle moves in the first quadrant, axis and axis. In the first second, it

Move from the origin to, and then move in the direction shown by the arrow in the figure.

[i.e.] and move by one unit per second,

Then the position coordinate of the particle in the 35th second is ().

A.B. C. D。

Second, fill it out carefully and try your hand! (There are ***6 small questions in this big question, with 3 points for each small question, and *** 18 points. Please fill in the score directly in the corresponding position on the answer sheet).

13. If the image of the inverse proportional function passes the point, then.

14. The math unit of Class 1, Grade 9 in a school is tested by all the students in the class.

Grade frequency distribution histogram as shown in the figure (full mark 100,

Students' grades are rounded off), and the score is 90.5~95.5.

The frequency of this segment is.

15. As shown in the figure,, and perpendicular bisector intersect.

Well, at this point.

16. The solution set of the inequality group is.

17. Define the operation "∞" in the real number range, and its rules are as follows:

Then the solution of the equation is.

18. Four congruent right-angled triangles form a big square, and the vacant part in the middle is

A small square, thus forming a "Zhao Shuangxian diagram" (pictured). If Zheng Xiao.

The square area is 1, the large square area is 25, and the smaller acute angle in the right triangle is,

So ...

Third, do it with your heart and show your ability! (This big question ***7 small questions, out of 66 points, the answer is written on the answer sheet)

19. (The full mark of this question is 6)

Please simplify the formula first, and then select a number from 1, 2,3 as the value of and substitute it for evaluation.

20. (The full mark of this question is 8)

A rectangle with an aspect ratio is called a golden rectangle. Psychological tests show that the golden rectangle is pleasing to the eye, and it gives us a harmonious and symmetrical aesthetic feeling. Now, students can summarize the following drawing steps by folding the golden rectangle in teaching activities (as shown in the figure):

Step 1: Make an arbitrary square;

Step 2: Take the midpoint of and connect them;

Step 3: Draw an arc with the center and length as the radius, and the intersecting extension lines are at;

Step 4: Extend the crosshairs to,

Please follow the above practice to prove that the rectangle is a golden rectangle.

2 1. (The full mark of this question is 10)

The mascots of the 2008 Beijing Olympic Games are Beibei, Jingjing, Huanhuan, Yingying and Nini. Now, put five cards with the names of these five mascots (the cards are the same in shape, size and texture, as shown in the figure) into an opaque box and mix them evenly.

(1) What is the probability that Xiaohong will get happy if he takes any card from the box? (3 points)

(2) Xiaohong randomly takes out a card from the box (without putting it back in the box), and then takes out the second card from the box. Please list all the possible situations in which Xiaohong got the cards twice by list or tree diagram, and find out the probability that the cards she got twice happened to be Beibei and Jingjing (in no particular order). (7 points)

22. (The full mark of this question is 10)

It is known that a quadratic equation with one variable has two real root sums.

(1) Value range of real number; (4 points)

(2) The value of when. (6 points)

Friendly reminder: If there are two quadratic equations in one variable, then there are. )

23. (The full mark of this question is 10)

As shown in the figure, it is diameter, tangency, intersection, intersection.

(1) Verification: Average score; (5 points)

(2) If,, find the radius. (5 points)

24. (The full mark of this question is 10)

According to the actual situation of the company, the joint stock limited company implements the internal medical accumulation fund system for its employees. Company regulations:

(a) each employee is required to pay medical provident fund yuan at the beginning of the year;

(2) The medical expenses of individual employees in the current year shall be treated by stages according to the method in Table 1 at the end of the year:

Table 1

Segmented processing method

Personal burden shall not exceed 150 yuan (including 150 yuan).

More than 150 yuan, not more than 10000 yuan.

(excluding RMB 65,438+050, including RMB 65,438+00,000) shall be borne by some individuals and the rest by the company.

The part exceeding 10000 yuan (excluding 10000 yuan) shall be borne by the company.

Assume that the medical expenses incurred by employees in treating diseases in that year are RMB, and their actual expenses (including personal part of medical expenses and medical accumulation fund paid) are RMB.

(1) According to table 1, when,; So, when,; (in the form of inclusion) (3 points)

(2) The medical expenses and actual expenses of employee Chen Xiaohe Dali in 2007 are shown in Table 2:

Table 2

Medical expenses of employees for treating diseases (yuan)

Actual expenses borne by individuals (yuan)

Xiao Chen

Dali 500 320

Please find the value of according to the information in Table 2, and find the current time about the resolution function; (5 points)

(3) What is the maximum cost actually borne by the employees of this company due to illness in one year? (Write grades directly) (2 points)

25. (The full mark of this question is 12)

In the acute angle, the moving points, and slide on the sides respectively to make a square with the side down, let its side length be, and the area of the square and the common part be.

(1) middle edge height; (2 points)

(2) In time, it just falls on the edge (as shown in figure1); (4 points)

(3) When outside (as shown in Figure 2), find the functional relationship about (indicated value range), and find out why the value is the largest, and what is the maximum value? (6 points)

2008 Xiaogan Junior High School Graduates' Academic Examination

Math exam answers and scoring instructions

First, multiple choice questions

The title is123455678911112.

Answer A C C D C D C B A D A B a b

Second, fill in the blanks

13.14.15.16.17.18. (or 0.6)

Note: No points will be deducted for answering the question 14; 17 Only one correct answer will give 2 points.

Third, answer questions.

19. Solution: 2 points for the original formula.

3 points

4 points

Take the original form. (Take the prototype) 6 points.

20. proof: in the square, take

Yes, the midpoint,

2 points

Yes, four points.

Say it again,

, 6 points

.7 points

So the rectangle is a golden rectangle. Eight points.

2 1. Solution: (1); 3 points

(2) The list is as follows:

Beijing phantom you

Beibei, Jingbei, Huanbei, Yingbei, Ni.

Crystal, shell? -Jing, Huan Jing, Ying Jing, Ni

, North Ring, Jinghuan, Yinghuan, Ni

Ying Ying, Bei Ying, Jing Ying, Ying Ying-Ying Ni

Nini, Bernie, Ginny, Yingying, Yingying-

The tree diagram is as follows:

8 points

As can be seen from the table (figure):. 10.

Note: The above words "Beibei, Jingjing, Welcome and Ni" stand for "Beibei, Jingjing, Huanhuan, Yingying and Nini" respectively. Please use other codes to answer the correct corresponding scores, just list or draw a tree diagram.

22. Solution: (1) There is a meaning in the question, 2 points.

Solve.

That is, the range of real numbers is .4 points.

(2) .5 points.

If, that is, the solution is .7 points.

, irrelevant, give up .8 points

If so, it is known by (1).

So when. 10 o'clock.

23.( 1) proof: connection,

Cut,

. 1 point

Say it again,

3 points

and

.

, which is equal to .5 points.

(2) Solution: If the score exceeds this score, score 6 points.

.

Seven points again.

A quadrilateral is a rectangle. 8 points

Yes,.

The radius is 2. 10 minutes.

24. Solution: (1) 3 points.

(2) According to Table 2, the medical expenses of Xiao Chen and Dali are more than 65,438+050 yuan and less than 65,438+00,000 yuan respectively, so there are:

5 points

Solution: 6 points

.

.8 points

(3) The expenses actually borne by individuals only need 2220 yuan at most. 10.

25. Solution: (1); 2 points

(2) (or); 6 points

(3) If they intersect, a quadrilateral is a rectangle.

Set and pay (as shown in Figure 2)

, .

.

, namely

.8 points

. 10 point

Formula score:. 1 1 min.

When there is a maximum value, the maximum value is 6. 12 points.

Note: 1. Grading according to the grading standards, and the grading points shall not be changed at will; 2./kloc-other solutions to questions 0/9 to 25, as long as the thinking is clear and the solution is correct, you should give the corresponding scores step by step.