Mathematics Test

Precautions:

1. This volume is divided into two parts: Volume I *** 12, with ***36 points, from 1 to page 2; Volume 2 *** 14, with 84 points, pages 3 to 8. The full score of the whole paper is 120, and the examination time is 120 minutes.

2. Candidates must scribble their names, admission ticket numbers and exam subjects in pencil at the corresponding positions on the answer sheet before the answer sheet 1, and please fill in the contents in the sealed line clearly.

3. After choosing the answer for each question in Book 1, black the answer label of the corresponding question on the answer sheet with a pencil. If you need to change, please clean it with an eraser, and then choose another answer. I can't answer it on the test paper. Volume two should be answered directly on the test paper.

4. You can use the scientific calculator with the same model as the textbook. If there is no requirement for accuracy, the result will remain accurate, and the calculation process, reasoning steps or text description should be written to solve the problem.

The first volume (multiple choice questions ***36 points)

1. Multiple-choice question: This big question has *** 12 small questions, each with 3 points and ***36 points. Only one of the four options given in each small question is correct. Please fill in the letters of the correct option in the corresponding position on the answer sheet.

1. The result of calculation is ()

A.B. C. D。

2. The following calculation error is ()

A.B.

C.D.

3. In the following quadratic formula, similar to the quadratic formula is ().

A.B. C. D。

4. In the figure below, the surface expansion diagram that is not a triangular prism is ()

A.B. C. D。

5. In an experiment, four sets of corresponding data between the sum of two variables are measured as follows:

1 2 3 4

0.0 1 2.9 8.03 15. 1

Among the following relationships, the relationship between and is the closest ().

A.B. C. D。

6. The root of the unary quadratic equation is ()

A. There are two unequal positive roots. B. There are two unequal negative roots.

C. there is no real number root. D. there are two equal real number roots.

7. The following table shows the demographic data of districts and counties in Meishan City in 2006:

Dongpo County Renshou County pengshan county Hongya County Qingshen County Dan Ling County

Population (ten thousand people) 83 160 33 34 20 16

The range and median population of each district and county in Meishan City are () respectively.

A. 1.6 million, 335,000 b. 1.4 million, 335,000.

C.1440,340,000 D.1440,330,000.

8. The false proposition in the following proposition is ()

A. A set of parallelograms with equal adjacent sides is a diamond.

B. A set of rectangles with equal adjacent sides is a square.

A set of quadrilaterals with equal sides is a parallelogram.

A set of quadrilaterals with equal opposite sides and a right angle is a rectangle.

9. The charging method for long-distance calls is: RMB yuan for the first minute of connection and RMB yuan for each minute thereafter. If someone is charged 8 yuan money for making long-distance calls, the time for this person to make long-distance calls is ().

A. minutes c minutes d minutes

10. As shown in the figure, sum is an isosceles right triangle and quadrilateral is a parallelogram. The following conclusion is wrong ().

A. Take this point as the center of rotation and rotate counterclockwise to coincide with it.

B take this point as the center of rotation and rotate clockwise to coincide with it.

C. after being folded in a straight line, it coincides with.

D, after folding in a straight line, and.

1 1. As shown in the figure, it is two points on the inverse proportional function image.

Vertical to the axis, vertical feet extend out respectively.

This line intersects this point. If the coordinates are,

The ratio of the area of to the area of is ()

A.B. C. D。

12. In order to ensure information security, information needs to be encrypted and transmitted. The sender encrypts plaintext into ciphertext and transmits it to the receiver. After receiving the ciphertext, the receiver decrypts it and restores it to plaintext. It is known that a certain encryption rule is: the ciphertext corresponding to plaintext is plaintext, for example, and the corresponding ciphertext is. When the receiver receives the ciphertext, the decrypted plaintext is ().

A.、b、c、d、

Volume 2 (non-multiple choice questions ***84 points)

Fill-in-the-blank question: This big question has ***6 small questions, each with 4 points and ***24 points. Fill in the correct answer directly on the line in the question.

13. The heights (unit: cm) of four students in Class 1, Grade 9 in a school are: 170, 170, 166, 174 respectively, so the average height of these four students is cm.

14. In the same circle, if the sum of the central angle and the circumferential angle of an arc, then.

15. The two real roots of the unary quadratic equation are 1 and 2 respectively, then,

.

16. The volume formula of the cone is: the volume of the cone with high bottom area is 7.6cm, and the volume of the cone with a bottom radius of 2.7cm is equal to. (Results: Two significant figures were reserved, and 3. 14 was taken).

17. In,,, and then.

18. As shown in the figure, it is known that the length of the right angle of an isosceles right angle and the length of the square are both 20cm, which are on the same straight line. If the starting point coincides with the point and the point moves to the left at a speed of 2cm per second, the functional relationship between the area (cm) of the overlapping part and the time (sec) will be obtained.

Because.

Three, this big topic ***2 small questions, each small question 5 points, *** 10 points.

19. Calculation: (There should be necessary operation steps)

20. calculation:.

Four, this big topic ***3 small questions, each small question 7 points, ***2 1 point.

2 1. Draw a circle in the square as shown in the figure (the side length of each square is 1), and ask the drawn circle to pass through four grids to find the radius of the drawn circle.

22. As shown in the figure, divide the two turntables that can rotate freely into several sectors with equal areas, and mark the numbers 1, 2, 3, 4 and 5 on the divided sectors respectively. Turn both turntables at the same time.

(1) Use tree diagram or list method to show all possible results of the numbers on the sector pointed by the pointer after the turntable stops (if the pointer is on the dividing line, turn it again);

(2) Party A and Party B respectively rotate two turntables at the same time. After the turntables stop, if the sum of the numbers on the sectors pointed by the hands of the two turntables is even, Party A wins; If the sum of the numbers is odd, B wins. Is this game fair to both parties? Please explain the reason.

23. Golden Week has promoted the development of tourism economy. The following figure shows the changes of tourism revenue in recent years according to the statistics of the National Tourism Administration.

Change chart of tourism income in Golden Week

(1) According to the information provided in the picture, please write two conclusions;

(2) According to the data in the figure, find the average annual growth percentage of national tourism revenue in the Golden Week from 2002 to 2004 (accurate to 0. 1).

Five, this big topic ***2 small questions, 9 points for each small question, *** 18 points.

24. As shown in the figure, make a square and a square () on the same side of the line segment to connect and extend the intersection point, line crossing, vertical foot and intersection point.

(1) Find a pair of congruent triangles in the diagram and prove it (except two triangles obtained by dividing the diagonal of a square into squares);

(2) Let the side length of a square be 1. If the quadrilateral made according to the problem setting method is a diamond, find its length.

25. In response to the call of "building an environment-friendly and energy-saving society", a county decided to subsidize some towns and villages to build a number of biogas digesters, so that farmers can use eco-friendly biogas energy. There are 264 villagers in Happiness Village, and the government subsidizes the village by 340,000 yuan. The insufficient part is raised by the villagers themselves. Type and * * * 20 biogas digesters. The construction cost, available households and construction land of the two biogas digesters are as follows.

Construction cost of biogas digester (10,000 yuan/set) Available households (household/set) Covered area (square meter/set)

type

3 20 48

type

2 3 6

The relevant government departments approved the construction of biogas digesters in this village. It costs 10,000 yuan to build two kinds of biogas digesters.

The functional relationship between (1) and;

(2) There are several construction schemes, which do not exceed the land area granted by the government, and build biogas digesters so that every villager in the village can use biogas;

(3) If every villager raises funds from 700 yuan on average, can the construction scheme with the lowest cost be satisfied?

VI. This big topic * *1small topic, *** 11point.

26. As shown in the figure, rotate counterclockwise around a point to get a rectangle (one side is on the positive semi-axis of the shaft and the other side is on the positive semi-axis of the shaft), and the coordinates of this point are.

(1) If the image of the quadratic function () passes through two points, and the ordinate of the vertex of the image is, find the analytic expression of this quadratic function;

(2) Is there a point on the right branch of the symmetry axis of the quadratic function image found in (1) that makes it a right triangle? If it exists, request the area of the coordinate sum of this point; If it does not exist, please explain the reason;

(3) Find the analytical formula of the straight line where the edge is located.

Meishan 2007 Senior High School Education Entrance Examination

Reference answers and grading opinions of mathematics test papers

Description:

1. If the candidate's solution is different from the reference solution provided below, all the correct ones will get full marks; If there is an error in a step, you can refer to the scoring opinions of the question for scoring.

Second, marking the test paper, don't interrupt the marking of this question because of the wrong answer. When there is an error in one step of the answer, it affects the subsequent part, but the answer after that step does not change the content and difficulty of this question. Before new mistakes appear, the score of the latter part is determined by the degree of visual influence. At this time, in principle, it should not exceed half of the score that should be given to the later part. If there are obvious clerical errors, you can deduct less as appropriate. There are serious conceptual errors, do not score. In the process of solving this problem, the part that made the second mistake will not be scored.

Third, it involves the calculation process, allowing the reasonable omission of non-critical steps.

4. The scores on the right hand side of the answers to the following questions indicate the accumulated scores that candidates should get for correctly completing this step.

I. Multiple-choice questions: This topic is entitled *** 12, with 3 points for each question and 36 points for * * *.

1.A 2。 A 3。 D 4。 D 5。 B 6。 C

7.B 8。 D 9。 C 10。 B 1 1。 D 12。 C

Fill-in-the-blank question: This big question has 6 small questions, each with 4 points and * * * 24 points.

13. 170 14.55 15.-3 2 16.58 17. 18.

Three, this big topic ***2 small questions, each small question 5 points, *** 10 points.

19. Solution: 3 points for the original formula.

4 points

5 points

20. Solution: 4 points for the original formula.

5 points

Four, this big topic ***3 small questions, 7 points for each small question, ***2 1 point.

2 1. solution: the drawings meet the requirements; Five points.

7 points if the calculated radius is correct.

22. Solution: (1)

1 2

3 ( 1,3) (2,3)

4 ( 1,4) (2,4)

5 ( 1,5) (2,5)

4 points

(2) This game is fair to both sides.

The probabilities that the sum of numbers is even and odd are respectively

Fair play 7 points

23. Solution: (1)① The tourism income of the Spring Festival over the years is lower than that of "May Day" and "Eleventh Day".

(2) The tourism income in Golden Week is on the rise, 2 points.

(2) Assume that the average annual growth rate is.

Then 4 points

Get five points.

Do not meet the meaning of the question, give up.

A: The average annual growth rate is 7 points.

Five, this big topic ***2 small questions, 9 points for each small question, *** 18 points.

24. Solution: (1)

Proof is slightly 4 points.

(2) Solution 1: Let the side length of a square be,

This is a diamond.

rule

In, there are

That's seven points.

You get 8 points for solving this equation.

refuse

When the side length of a square is,

A quadrilateral is a diamond with nine points.

Solution 2: Let the side length of a square be

This is a diamond.

auxiliary power unit

7 points

that is

8 points

When the side length of a square is,

A quadrilateral is a diamond with nine points.

25. Solution: (1)

2 points

(2) from the meaning of the question.

4 points

Solve (1)

Solve ②

The solution of inequality is 5 points.

Is a positive integer.

The values of are 12, 13 and 14.

That is, there are three construction schemes: ① 12 type, type 8; ② 13 type, 7 type; ③ 14 type, 7 points for type 6.

In (3), it will increase with the increase of, and if the cost is the least, it will be 8 points.

The minimum cost is (ten thousand yuan)

700 yuan, a villager in each household, and fund-raising funds subsidized by the government.

For the construction scheme that can meet the lowest cost in 700 yuan, each household can get 9 points.

VI. This big topic * *1small topic, *** 11point.

26. Solution: (1) link,

rule

, 1 min

Solve,

The analytic expression of quadratic function is 3 points.

(2) Suppose there is a point that meets the conditions of the topic.

Links,,, Through the Axis

rule

, ,

, namely

On the image of quadratic function

Solve or

On the right branch of the symmetry axis

That is the required 5 points.

The connection is obviously an isosceles right triangle.

Meet the requirements of 6 points.

The point that satisfies the condition is or.

,

Or seven points.

(3) Let the intersection of sum be

obviously

auxiliary power unit

that is

solve

9 points

The analytical formula of the line where the edge is located is

rule

Solve,

The analytical formula of the straight line is 1 1.