Examination questions for the senior high school entrance examination in Binzhou City, Shandong Province

2009 Binzhou Junior High School Academic Level Examination

Math test questions

Tips:

1. This question is ***8 pages, full mark 120, and the examination time 120 minutes.

2. Before answering the questions, candidates must fill in all the items in the sealed line clearly and fill in the seat number in the seat number column in the lower right corner.

3. The vertex coordinates of parabola are.

1. Multiple choice questions: (This big question *** 10, only one of the four options given in each question is correct. Please choose the correct option and fill in the letter label on the answer sheet, and get 3 points for each question. If you choose the wrong answer, don't choose or choose multiple answers, you will get zero points, out of 30 points. )

1. Up to now, the total population of Binzhou City is about 3.73 million, which can be expressed as () by scientific notation.

A.B. C. D。

2. For the formula, there are the following understandings: (1) can represent the opposite number; (2) It can represent the product of and; (3) Representable absolute value; (4) The operation result is equal to 8. The number of comprehension errors is ()

A.0 B. 1 C.2 D.3

3. Choose 1 card from 1 to 10, and the probability that this number is a multiple of 3 is ().

A.B. C. D。

4. Look at the geometric figure shown on the right from above, and the resulting figure is ().

5. Connect the midpoints of the sides of a quadrilateral whose diagonals are perpendicular to each other in turn, and the resulting graph must be ().

A. rectangle B. right-angled trapezoid C. diamond D. square

6. It is known that the radii of two circles are 2 and 3 respectively, and the center distance is 0. If two circles have nothing in common, the following conclusion is correct ().

ABC or d or

7. Xiaoming went out for a walk. After a 20-minute walk from home, he reached the newsstand 900 meters away from home, read the newspaper for 10 minutes, and then returned home in 15 minutes. Then the picture below shows the relationship between the distance and time of Xiao Ming's leaving home ().

8. It is known that the function image is as shown in the figure, so when, the range of independent variables is ().

A.b. or

cash on delivery

9. As shown in the figure, the following conditions are given:

① ; ② ;

③ ; ④ .

Among them, the number that can be determined independently is ()

A. 1

10. Known, and the height of the side.

, the length of the side is ()

A.21B.15c.6d. None of the above answers are correct.

Fill-in-the-blank question: This big question is ***8 small questions, and each small question gets 4 points out of 32 points. Only the final result is needed.

1 1. Simplified:

12. The mode of data 1, 5, 6, 5, 6, 6 is, the median is, and the variance is.

13. The known point A is the point on the inverse proportional function image. If perpendicular to the axis, the vertical feet are, and the area of is.

14. When solving the equation, if set, the equation can be simplified to.

15. As we all know, its meaning on the number axis is the distance between the point representing 5 and the origin (that is, the point representing 0). For another example, its meaning on the number axis is the distance between the point representing 6 and the point representing 3. Similarly, the meaning of the formula on the number axis is.

16. The side view of the stairs is shown in the figure, in which a red carpet is needed for an activity, and the length of the carpet laid on the stairs in section AB is.

17. It is known that the circumference of the isosceles is 10. If the waist length is, the value range of is.

18. In the plane rectangular coordinate system, the coordinates of vertices are. If the similarity ratio of the drawing with the origin o as the similarity center is equal to, the coordinate of the point is.

Third, the answer: this big question ***7 small questions, out of 58 points. Please write the necessary text description and deduction process when answering.

19. (The full score of this question is 5)

Calculation:.

20. (The full mark of this question is 6 points)

In order to promote the development of sunshine sports activities, the third class of grade nine in a school has established four sports groups: football, basketball, table tennis and skipping rope. After investigation, the whole class participated, and the fan chart and bar chart of the number distribution of each activity group are as follows:

(1) Find the number of students in this class;

(2) Please fill in the blank part of the bar chart;

(3) Find the size of the fan-shaped central angle occupied by the number of people skipping rope.

2 1. (The full mark of this question is 7)

As shown in the figure, it is tangent, and A is tangent point. This straight line intersects at two points and is connected. Verification:.

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

Observe the characteristics of the following equations and their solutions:

The solution of (1) is:

The solution of (2) is:

The solution of (3) is:

…… ……

Answer the following questions:

(1) Please guess: the solution of the equation is;

(2) Please guess: the solution of the equation about is;

(3) Take solving the equation as an example to verify the correctness of the conjecture conclusion in (1).

Solution: The original equation can be reduced to.

Please write down the detailed process of solving this equation by matching method. )

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

Answer the following questions according to the meaning of the questions:

(1) As shown in Figure ①, it is known that the straight line intersects the axis and the axis at two points respectively, and the length of the line segment is found;

(2) As shown in Figure ②, compare the solution process of (1). Please draw a right triangle and find the distance between two points.

(3) As shown in Figure ③, and are two points in the plane rectangular coordinate system.

Verification:

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

The purchase price of a commodity is 40 yuan per piece. 60 yuan can sell 300 pieces a week for each piece, and now it's going to be reduced. According to market research, every time the price is reduced by 1 yuan, 20 pieces can be sold every week. On the premise of ensuring profitability, answer the following questions:

(1) Assuming that the price reduction of each commodity and the profit of goods sold every week are RMB, please write the functional relationship with and find out the range of independent variables;

(2) When the price is reduced by several yuan, the weekly profit is the largest? What is the maximum profit?

(3) Please draw a sketch of the above functions.

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

As shown in Figure ①, the cross-sectional figure of product logo consists of isosceles trapezoid and a part of parabola. In the isosceles trapezoid, for the parabolic part, its vertex is the midpoint of two points and passes through two points, and the connecting lines at the open ends are parallel and equal.

(1) As shown in Figure ①, in the coordinate system with a point as the origin and a straight line as the axis, the coordinates of this point are,

Try to find the coordinates of two points;

(2) Find the height of the sign (that is, the distance from the highest point of the sign to the straight line where the trapezoid bottom is located);

(3) According to the actual situation, it is necessary to evenly coat a protective film with a thickness of 3cm on the periphery of the trapezoidal part of the logo cross section, as shown in Figure ②. Please supplement the schematic diagram of the complete coating part in the drawing and find out the outer circumference of the coating.

2009 Binzhou Junior High School Academic Level Examination

Math Test Questions (1) Solution Reference and Scoring Criteria

Tag description:

1. There are only two grading files, full marks and zero marks, and there is no middle mark for each sub-question and each blank in multiple-choice questions.

2. The corresponding score in the answer to each small question refers to the cumulative score that the candidate should get if he answers this step correctly. Only one solution is given for each small question in this answer. For other solutions, please refer to the grading standard.

3. If the candidate makes a calculation error in the middle of the answer, but does not change the substance and difficulty of the test question, he will be given a follow-up part as appropriate, but the follow-up part will not exceed half of the correct answer score at most; If there is a serious logical error, the subsequent part will not be scored.

First, multiple-choice questions (this big question * *10 small questions, 3 points for each small question, out of 30 points)

The title is 1 23455 6789 10.

Answer C A C B A D D B C D

2. Fill in the blanks (this topic is entitled ***8 small questions, with 4 points for each small question, out of 32 points)

1 1. 12.6, 5.5, (score distribution: 1, 1, 2)

13. 14.

15. The distance between the point representing the number and the point represented.

16m (or 5.464m)

17.

18. Or

Third, answer the question (this big question ***7 small questions, out of 58 points)

19. (The full score of this question is 5)

Solution: The original formula has 4 points (four inspection points, 1 correct, get 1).

.5 points

20. (The full mark of this question is 6 points)

Solution: (1) According to the pie chart, the number of table tennis teams accounts for the whole class.

According to the crossing chart, the number of the table tennis team is 12. 1.

Therefore, the class size is 0.2.

(Note: Only the last step can get full marks, but only the result can't be scored. )

(2) According to the pie chart, the number of basketball teams is.

According to the bar chart, the number of football teams is 16.

So the number of skipping groups is .3.

So the histogram of the number of people in each group is as follows

4 points (note: only the right picture is drawn, and the full score is 2 points. )

(3) Because the number of skipping groups accounts for the whole class, 5 points will be deducted.

Therefore, it occupies a fan-shaped central angle of 0.6 points.

2 1. (The full mark of this question is 7)

Prove that the tangent is. 1 point.

Besides, two o'clock.

, 3 points

, 4 points

.5 points

Diameter again, 6 points.

(ASA) .7 points

(Note: Other methods are graded step by step. )

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

Solution: (1),; 1 point

(2) (or); 3 points

(3) Convert the quadratic term into 1 and get 0.4 points.

Formula, score, 5 points

.6 points

Prescription, score .7 points

Solution, .8 points

After investigation, all of them are the solutions of the original equation (whether this link is temporary scoring or deduction)

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

Solution: (1) is derived from, so the coordinate of the point is, so. 1 point.

This is also the case. 2 points

So in the middle, 0.3 points.

(2) Axis, axis and point .4 points.

Then, the point coordinate is .5 points.

So .6 points.

So in the middle, 0.7 points.

(Note: If the conclusion of (3) is directly applied, no score will be scored. )

(3) Axis, axis and intersection.

So, the coordinates of this point are .8 points.

Therefore, (there is no sign of absolute value, so no penalty will be deducted here) 9 points.

So in the middle,. 10 point

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

Solution: (1), 3 points.

That's 0.4 points.

Because the price reduction should ensure profitability, so (or can).

Get (or) .6 points.

(Note: If there is deduction 1 min; Write the correct result directly, without deduction, get 2 points. )

2, 7 points.

There is a maximum value,

That is, when the price of 2.5 yuan is reduced, the profit is the largest, which is 6 125 yuan. Eight points.

(3) The approximate image of the function is (note: the end point on the right should be a circle; If it is drawn as a solid point, deduct 1 minute; The left end point can be in any case. ) 10.

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

Solution: (1) Left and vertical feet are respectively.

The quadrilateral is a rectangle,. 1 point.

Say it again,

(HL), .2 points

Say it again,

.3 points

Again,

The coordinates of the points are 0.4 points respectively.

(2) Let the resolution function of parabola be 0.5.

From a point on its image.

The resolution function of parabola is 0.6 points.