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20 13 suihua senior high school entrance examination mathematics examination questions
Suihua junior high school graduation exam in 2009

Mathematics Test

Note to candidates:

Length test time 120 minutes.

2. There are three major questions in the whole volume, with a total score of 120.

Fill in the blanks (3 points for each question, out of 33 points)

1. In the function y=, the value range of the independent variable x is.

2. The report issued by the United Nations Environment Programme said: Although the global investment market was generally weak in 2008, driven by developing countries such as China, the global sustainable investment reached a record high, reaching $654.38+05.5 billion, which can be expressed by the following scientific notation.

Dollars.

3. In the English sentence "I wish you success!" Wish you success! ), the probability that this letter is "s" is

4. Calculation: =.

5. The images of inverse proportional function y= (m≠0) and linear function y=kx+b(k≠O) are shown in the figure. Please write the correct conclusion:

.

6. As shown in the figure, the side length of the square ABCD is 3, and the perimeter of the front view of the obtained geometry is.

7. When x=, the quadratic function y=x2+2x-2 has a minimum value.

8. Assuming that the radii of two circles are 5cm and 4cm, respectively, and the distance between the centers is 6cm, the positional relationship between the two circles is.

10. Form a convex quadrilateral with two right triangles with right sides of 3 and 4 respectively, and the perimeter of the quadrilateral is.

1 1. As shown in the figure, in the rhombic ABCD with the side length of 1, ∠DAB=600, connect diagonal AC, and make the second rhombic ACCl Dl take AC as the side, so ∠ d1AC = 600; Connect AC 1, and then make a third diamond AClC2D2 with AC 1 as the edge, so that ∠ d2ac1= 600; ....., according to this rule, the side length of the nth diamond is.

Second, multiple-choice questions (3 points for each question, out of 27 points)

13. As shown in the figure, parallel lines A and B are cut by straight line C, and ∠ 1=42038', then the degree of ∠2 is ().

a . 137062’b . 137022’c . 47062’d . 47022’

14. The following operation is correct ()

A.a3? a2 = a6 b .(π-3. 14)0 = l c .()- 1 =-2d . = 3

15. The median and mode of a set of data 4, 5, 6, 7, 7 and 8 are () respectively.

A.7,7 B.7,6.5 C. 5.5,7 D. 6.5,7

16. A pool is connected with three water pipes, A, B and C. First, open A, and then open B after a while. After the pool is filled with water, close A and open C until the water in the pool is empty. The functional relationship between the water volume v(m3) in the pool and the time t(h) is as shown in the figure, so the following judgment about the hourly water flow of three water pipes is correct ().

a . b >; ABC >; A C.A. >; BC > Second

18. A hotel has three rooms for tourists to rent: two, three and four rooms. A tour group of 20 people is going to rent seven of the three rooms at the same time, and each room is full. The lease scheme is ().

A.4 species B.3 species C.2 species D. 1 species.

19. In trapezoidal ABCD, if AD‖BC, AD= 1, BC=4, ∠C=700, ∠B=400, the length of AB is ().

A.2 B.3 C.4 D.5

Three, solve the problem (out of 60 points)

2 1. (Full score for this small question)

23. (The full score for this short question is 6)

Make an isosceles triangle in a rectangle with sides 4 and 6, so that one side of the isosceles triangle is the length or width of the rectangle, and the third vertex is on the side of the rectangle. Find the area of a triangle.

(Note: triangles with the same shape are counted as one. )

24. (The full score for this short question is 7)

In order to know how much 300,000 TV viewers like news, animation and entertainment programs in a certain area, a certain number of viewers are randomly selected according to the actual population ratio of 3: 5: 2 for the elderly, adults and teenagers of all ages, and the following statistical chart is obtained.

(1) The above survey methods are (fill in "comprehensive survey" or "sampling survey");

(2) Write the values represented by A and B in the statistical chart of dotted line;

A:: B::

(3) Find out the number of adults who like entertainment programs in this area.

25. (The full score for this short question is 8)

Xiao Wang, the postman, set out from the county seat and rode his bike to deliver goods to village A. On the way, I met Li Ming, a middle school student in the county, and walked back to school from Village A. After completing the delivery work in Village A, Xiao Wang met Li Ming on the way back to the county, so he rode his bike and took Li Ming to the county. As a result, Xiao Wang arrived 1 minute later than expected. Their distance to the county seat is between S (kilometers) and the time when Xiao Wang left the county seat.

(1) How many kilometers was it from the county seat when Xiao Wang and Li Ming first met? Write the answer directly.

(2) Find the time it takes Xiao Wang to return from the county seat.

(3) How long does it take Li Ming to get from Village A to the county seat?

26. (The full score for this short question is 8)

As shown in Figure L, in the quadrilateral A8CD, AB=CD, E and F are the midpoint of BC and AD respectively. Connect EF and extend it, and intersect with the extension lines of BA and CD at points M and N respectively, then ∠BME=∠CNE (without proof).

(Tips: In figure 1, connect BD, take the midpoint H of BD, and connect he and HF. According to the triangle median theorem, it can be proved that HE=HF, thus ∠HFE=∠HEF, and then ∠ BME = ∠ CNE. )

Question 1: As shown in Figure 2, in the quadrilateral ADBC, AB and CD intersect at point O, AB=CD, E and F are the midpoints of BC and AD respectively, and connecting EF, DC and AB intersect at points M and N respectively to judge the shape of △OMN. Please write the conclusion directly.

Question 2: As shown in Figure 3, at △ABC, points AB and D of AC> are on AC, AB=CD, E and F are the midpoint of BC and AD respectively, which connect EF and extend, and intersect with the extension line of BA at point G. If ∠EFC=600, connect GD, and judge and prove the shape of △AGD.

27. (The full mark of this little question is lO)

A computer company sells Type A computers. Due to the economic crisis, the price of computers continues to fall. In March this year, the price of computers was 1000 yuan lower than that of the same period last year. If you sell the same number of computers, last year's sales volume was 1 10,000 yuan, and this year's sales volume is only 80,000 yuan.

(1) What was the price of a computer in March this year?

(2) In order to increase income, the computer company decided to resell the second model computer. It is known that the computer purchase price is 3500 yuan, and the computer purchase price is 3000 yuan. The company expects that the funds for purchasing these two computers will not exceed 50,000 yuan and not be less than 48,000 yuan. * * 65,438+05 units. How many purchase plans are there?

(3) If the price of the second computer is 3,800 yuan per computer, in order to open the market for the second computer, the company decides to return one yuan in cash to the customer for every computer sold, so that all the schemes in (2) have the same profit. What should be the value of a? At this time, which scheme is more beneficial to the company?

28. (The full mark of this little question is lO)

Suihua junior high school graduation exam in 2009

Reference answers and grading standards of mathematics test papers

1. Fill in the blanks (3 points for all correct answers, otherwise no points)

∴ △AGF is an equilateral triangle .............................................. 1 min.

∴ AF=FD。

∴ GF=FD。

∴ ∠FGI=∠FDG=300

∴ ∠AGD=900

That is, △AGD is a right triangle ....................................... 1 min.