This paper is divided into two parts: the first volume (multiple choice questions) and the second volume (non-multiple choice questions). Page 1 of volume 1 to page 2, and page 3 to page 10 of volume 2. The full mark of the test paper is 120, and the test time is 100 minutes. After the exam, the test paper and answer sheet should be returned together. Good wishes.

The first volume (multiple choice questions ***30 points)

Precautions:

1. Before answering the first question, candidates must first fill in their names and admission ticket numbers on the "answer sheet" with pen (signature pen) or ballpoint pen in blue and black ink; Black out the information points corresponding to the examination subjects with 2B pencil; Stick the exam bar code in the specified location.

2. The answer on the test paper is invalid. After selecting the answer for each question, use 2B pencil to blacken the information points on the "Answer Sheet" corresponding to the answer label of the question. If necessary, wipe them clean with an eraser, and then select the information points with other answer labels.

1. Multiple-choice question: This topic is entitled *** 10, with 3 points for each question and 30 points for each question. Only one of the four options given in each small question meets the requirements of the topic.

The value of 1.2 sin is equal to ().

BC 1 year

2. In the art word, some letters are centrosymmetric figures, and among the following five letters, () is centrosymmetric figures.

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

3. If it is a real number and, the value of is ().

A. 1 B. C.2 D

4. The inscribed circle radius of a regular hexagon with side length is ()

A.B. C. D。

5. The top right picture is the front view of a steel pipe, so its three views are ().

A.B. C. D。

6. In order to take part in the "Tianjin Junior High School Graduates Entrance Examination" in 2009, Xiao Gang worked hard. When throwing the solid ball, the scores (unit: m) of the five throws are 8, 8.5, 9, 8.5 and 9.2 respectively. The mode and median of this set of data are () in turn.

A.8.5，8.5 B.8.5，9 C.8.5，8.75 D.8.64，9

7. In sum, if the perimeter of is 16 and the area is 12, then the perimeter and area of are () in turn.

A.8，3 B.8，6 C.4，3 D.4，6

8. In the plane rectangular coordinate system, the two endpoints of the known line segment are respectively, and the line segment is obtained after the line segment is translated. If the coordinate of the point is, the coordinate of the point is ().

A.B. C. D。

9. As shown in the picture, it is engraved on,

If is, the size of is ()

A.B. C. D。

10. In the plane rectangular coordinate system, the parabola is axisymmetrical transformed first, and then the obtained parabola is axisymmetrical transformed, so the analytical formula of the new parabola obtained after two transformations is ().

A.B.

C.D.

Examination paper of Tianjin junior high school graduates' academic examination in 2009

mathematics

Volume 2 (non-multiple choice questions ***90 points)

Precautions:

1. Before answering paper 2, candidates must clearly fill in the items in the sealed line and the "seat number" in the upper left corner of page 3 of the test paper.

2. Volume 2 * * * Page 8, use a blue-black ink pen (signature pen) or ballpoint pen to answer directly on the test paper.

Fill in the blanks: this big question is ***8 small questions, each with 3 points and ***24 points. Please fill in the answer directly on the horizontal line in the question.

1 1. Simplified: =.

12. If the value of the score is 0, the value of is equal to.

13. The quadrilateral obtained by connecting the midpoints of any quadrilateral in turn is called the midpoint quadrilateral. If the midpoint of a quadrilateral is a rectangle, the quadrilateral can be.

14. Given that the image of a linear function intersects with the sum of points, the coordinates of the intersection of the image and the axis of the function are _ _ _ _ _ _ _ _ _.

15. Each book is priced in 8 yuan. If the number of books purchased does not exceed 10, the original price shall be paid; If you buy more than 10 at one time, the part that exceeds 10 will be 20% off. If the number of books purchased at one time is RMB, please fill in the following table:

X (Ben) 2 7 10 22

Yuan 16

16. In order to understand the growth of a new cucumber variety, the number of cucumber roots grown on some cucumber plants was randomly selected, and the following histogram was obtained. Observing this chart, we can know that * * * randomly selected _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

17. As shown in the figure, it is a plane figure inlaid by 12 equilateral triangles, so there are _ _ _ _ _ parallelograms in the figure.

18. As shown in the figure, there is a square paper with a side length of 5, and it should be cut into two small squares with a side length of respectively, so that the value of. (1) can be _ _ _ _ _ _ _ (write a group casually); (2) Please design a general cutting method, draw a cutting line in the picture and splice it into two small squares, and explain that this cutting method is universal:

__________________________________________

_________________________________________

_________________________________________

Third, the solution: this big question is ***8 small questions, with ***66 points. The solution should be written in words, calculation steps or proof process.

19. (6 points for this small question)

Solving inequality system

20. (8 points for this short question)

It is known that the curve in the graph is a branch of the inverse proportional function (constant) image.

(i) In which quadrant is the other branch of this inverse proportional function image? What is the value range of the constant?

(2) If the intersection of the image of the function and the image of the proportional function is in the first image, the intersection is perpendicular to the axis and the vertical foot is, when the area is 4, find the coordinates of this point and the analytical expression of the inverse proportional function.

2 1. (8 points for this small question)

There are three identical balls. They are numbered 1, 2 and 3 respectively, put them in a pocket, randomly draw a ball without putting it back, and then randomly draw another ball.

(i) List all possible results of two touches of the ball with a tree diagram (or list method);

(2) Find the probability that the sum of two balls is equal to 5.

22. (8 points for this short question)

As shown in the figure, the diameter is known as the tangent, which is the tangent point.

(i) the scale of the solution;

(ii) If so, the length of the search (the result retains the root symbol).

23. (8 points for this short question)

In an extracurricular exercise, students must measure the distance between two pavilions on both sides of the artificial lake in the park. Now, m, m, please calculate the distance between the two pavilions.

24. (8 points for this short question)

Note: In order to help students solve this problem better, we provide a problem-solving idea. You can fill in the blanks according to this idea and complete the whole process of solving this problem. If you choose other solutions, you don't need to fill in the blanks at this time, just answer according to the general requirements of solving problems.

As shown in figure 1, a rectangular pattern with a width of 20cm and a length of 30cm should be designed, in which there are two horizontal color bars and two vertical color bars, and the width ratio of horizontal color bars to vertical color bars is 2: 3. If the area occupied by all color bars is one third of the original rectangular pattern, how should the width of each color bar be designed?

Analysis: From the width ratio of horizontal and vertical color bars to 2∶3, we can set the width of each horizontal color bar to, and then set the width of each vertical color bar to. In order to better find the equivalent relationship in the topic, the horizontal and vertical color bars are separated and concentrated, and the original problem is transformed into the situation shown in Figure 2, and a rectangle is obtained.

Fill in the blanks with the above analysis, as shown in Figure ②, expressed by algebraic expressions, including:

= _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ cm；

= _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ cm；

The area of a rectangle is _ _ _ _ _ _ _ _ cm;

List the equations and complete the solution.

25. (This little question is 10)

A paper with a right triangle is known. As shown in the figure, the paper is folded in a plane rectangular coordinate system, and the crease intersects the edge at the point and the edge at the point.

(i) If these points coincide with each other after folding, find the coordinates of these points;

(ii) If the point that falls on the edge after folding is, let, try to write the resolution function and determine the value range;

(iii) If the point on the folded edge is and makes, the coordinates of the point are found.

26. (This little question is 10)

It is known that the function is the two roots of the equation, and the points are on the image of the function.

(i) If the analytic formula of the function is found;

(ii) Under the condition of (i), if the two intersections of the function and the image are, and if the area is, the value of;

(iii) If and when, try to determine the relationship between the three and explain the reasons.

Reference answers and grading standards

Rating description:

1. All questions are graded according to the reference answers and grading standards.

2. If the candidate's non-multiple choice answer is not exactly the same as the reference answer, but it is reasonable, it may be graded as appropriate, but it shall not exceed the score assigned to the question.

First, multiple-choice questions: this big question * * 10 small questions, 3 points for each small question, * * 30 points.

1.A 2。 B 3。 B 4。 C 5。 D

6. A seven. An eight. B 9。 D 10。 C

Fill in the blanks: this big question is ***8 small questions, each with 3 points and ***24 points.

1 1.

12.2

13. Square (quadrilaterals with orthogonal diagonals are acceptable)

14.

15.56,80, 156.8

16.60; 13

17.2 1

18.13,4 (hint: the answer is not unique);

② Cutting lines and splicing methods are shown in the figure: The points in the figure can be any point (except points) on a semicircle with a diameter of, and the length of each point is the side length of two small squares.

Third, answer: This big question is ***8 small questions, ***66 points.

19. The full score of this little question is 6.

Solution:

Starting from ①, 2 points.

Starting from ②, 4 points.

The solution set of the original inequality group is 6 points.

20. This little question scored 8 points.

Solution: (i) The other branch of this inverse proportional function image is in the third quadrant. 1.

Because the images of this inverse proportional function are distributed in the first and third quadrants,

So, the solution is 0.3.

(ii) As shown in the figure, starting from the point in the first quadrant on the proportional function image,

If the coordinates of a point are, the coordinates of the point are,

, solution (negative value discarded).

The coordinates of this point are 0.6 points.

And points on the inverse proportional function image,

, that is.

The analytical expression of the inverse proportional function is 0.8 points.

2 1. The full score of this little question is 8.

Solution (1) Method 1: According to the meaning of the question, you can draw the following tree diagram:

As can be seen from the tree diagram, there are six possible results of finding two balls.

Method 2: According to the meaning of the question, the following table can be listed:

As can be seen from the above table, there are six possible results for two balls. Four points.

(Ⅱ) Let the sum of two balls equal to 5 as an event.

There are two results when the sum of two balls is equal to 5. They are:

.8 points

22. The score of this short question is 8.

Solution (i) is the tangent and diameter,

.

.

.2 points

Also, to the point.

.

This is an equilateral triangle.

.5 points

(ii) As shown in the figure, connect,

Then.

In,,

Because because.

Is an equilateral triangle,

.

.8 points

23. The full score of this short question is 8.

Solution: As shown in the figure, the intersection point is an extension line perpendicular to the point. 1

At .2.

Sin. sin.

cos cos = 15。

In the middle again,

.7 points

The distance between the two exhibition halls is 50 meters. Eight minutes.

24. This little question scored 8 points.

Solution (1); 3 points

(2) According to the meaning of the question, get 0.5 points.

Tidy it up and bring it here.

Solve the equation and get (irrelevant, give up).

Then.

Answer: The width of each horizontal and vertical color bar is cm and cm respectively. Eight minutes respectively.

25. The score of this small question is 10.

Solution (1) As shown in Figure ①, the folding point coincides with the point.

Then.

The coordinates of the set point are.

Then.

So ...

In Pythagorean Theorem,

That is, get the solution.

The coordinates of this point are 0.4 points.

(2) As shown in Figure ②, the point that falls on the edge after folding is,

Then.

Set by the topic,

Then,

In, from Pythagorean theorem, we get.

That's six points.

Viewed from the side,

Analytical formula is what you want.

It decreases with the increase of,

The value range of is 0.7 points.

(3) As shown in Figure ③, the point on the folded edge is, and.

Then.

Say it again, yes.

.

Yes, I got 0.9 points.

Yes,

Okay, then.

Judging from the conclusion of (ii),

Solve.

The coordinate of the point is. 10 point.

26. The score of this small question is 10.

Solution (i),

. 1 point

Substitute them separately and get.

Solve.

The analytical expression of the function is .3 points.

(ii) from the known, derived and set high,

, that is.

According to the meaning of the question,

By, by.

When, solution;

We can solve it then.

The value of is 0.6 points.

(3) From the known situation.

.

Simplify it.

, get,.

Yes

Again,,,

When,;

When,;

. 10 o'clock