Math test
Note: 1. The whole volume is divided into two parts, the first part is multiple-choice questions, the second part is non-multiple-choice questions, ***4 pages. The examination time is 90 minutes, and the full mark is 100.
2. The test questions in this volume must be answered according to the regulations on the answer sheet; Any answer on the test paper or draft paper will be invalid. The answer sheet must be kept clean and cannot be folded.
3. Before answering the question, please write your name, candidate number, examination room number, examination room number and seat number on the answer sheet with the prescribed pen, and stick a barcode on it.
4. The multiple-choice question in this volume is 1- 10. After choosing the answer for each small question, use 2B pencil to black the answer label of the corresponding question in the multiple-choice answer area of the answer sheet. If necessary, clean it with an eraser, and then choose another answer. Non-multiple-choice questions 1 1-23. The answers (including auxiliary lines) must be written in the non-multiple-choice answer area of the answer sheet with the specified pen according to the answer number.
After the exam, please return the test paper and the answer sheet together.
The first part of multiple choice questions
(There are *** 10 questions in this section, with 3 points for each question and 30 points for * * *. Each question is given four options, only one of which is correct. )
The reciprocal of 1 Yes ()
A.B. C. D。
2. This year, the total number of candidates taking the academic examination for junior high school graduates in our city is ().
A.B. C. D。
3. Carefully observe the two objects shown in figure 1, and the top view is ().
4. The following graphics, not axisymmetric graphics is ()
5. It is known that the length of three sides of a triangle is: if the value of is even, the value of is ().
A.B. C. D。
6. If a commodity with a price of RMB is sold at a 20% discount, the actual price of the commodity is ().
Yuan RMB
7. The variance of a set of data,,, is ()
A.B. C. D。
8. If is, the value of is ()
A.B. C. D。
9. As shown in Figure 2, for a straight line, the degree is ().
A.B. C. D。
10. In the same rectangular coordinate system, the image of function sum is roughly ().
Part II Non-multiple choice questions
Fill in the blanks (there are ***5 small questions in this question, each with 3 points, *** 15 points)
1 1. There are four white balls, five red balls and six yellow balls in a pocket. Every ball is the same except the color. After stirring, randomly draw a ball from the bag. The probability that this ball is a white ball is.
12. Decomposition factor:.
13. If the single sum is similar, the value of is.
14. The length of the hypotenuse of a right triangle is, and the area of a circle with the center of the hypotenuse and the center of the hypotenuse as the radius is.
15. Teacher Deng designed a calculation program. Input and output data are as follows:
Input data 1 2 3 4 5 6 …
Output data ...
Then, when the input data is 0, the output data is 0.
Answer (this topic is ***8, in which 16 is 5 points, 17 is 6 points, 18 is 6 points, 19 is 6 points, 20 questions are 7 points, 2 1 8 points, 22 questions and 23 questions.
16. Calculation:
17. Solve the inequality group and express its solution set on the number axis;
18. As shown in Figure 3, in the trapezoid,,, is the last point.
(1) Verification:.
(2) If you ask for a long time.
19.2007 During the international auto show in a city, a company conducted a random questionnaire survey on consumers who visited the auto show, and * * * distributed 1000 copies, all of which were recovered. ① According to the results of the questionnaire survey, sort out the annual income of consumers and make the following table:
Annual income (ten thousand yuan) 4.8 6 7.2 9 10
Number of consumers surveyed (persons)
② After sorting out the situation that consumers intend to buy a car, make a part of the frequency distribution histogram (as shown in Figure 4).
Note: Each group contains the minimum value but not the maximum value, and the car price is rounded. Please answer the following questions based on the above information.
(1) According to the information in ①, the annual income pattern of the consumers surveyed is _ _ _ _ ten thousand yuan.
(2) Please complete the frequency distribution histogram in Figure 4.
(3) The percentage of consumers who intend to buy cars below 10,000 yuan in the number of consumers surveyed is _ _ _ _.
20. As shown in Figure 5, a cargo ship transports a batch of important materials from this place to the place due east at the speed of nautical miles per hour. At this point, an island is measured in the north-east direction. After sailing for 10 minutes, the cargo ship arrived at its destination. At this time, it was measured that the island was in the east-north direction, and it was known that there were reefs in the waters around the island. If we continue sailing eastward, will the cargo ship be in danger of hitting the rocks? Try to explain why.
2 1. The distance between the two places is kilometers, so Engineering Team A will lay a natural gas pipeline between the two places and Engineering Team B will lay an oil pipeline between the two places. It is known that the number of kilometers laid by Team A per week is less than that of Team B, and Team A started work earlier. As a result, both teams completed the task at the same time. How many kilometers of pipelines do teams A and B have to lay each week?
22. As shown in Figure 6, in the plane rectangular coordinate system, the side length of the square is, and the point is on the positive semi-axis of the shaft and intersects with the point.
(1).
(2) Find the coordinates of the point.
(3) Find the analytical formula of parabola passing through three points. (The calculation result requires the denominator to be reasonable. References:
Remove the root sign of the denominator, so that the denominator is rational. For example: ①;
② ; (3) and other operations are denominators.
23. As shown in Figure 7, in the plane rectangular coordinate system, a parabola intersects a straight line at two points.
(1) Find the length of the line segment.
(2) If the perimeter of a sector is equal to the length of the line segment in (1), what is the maximum area of the sector when the radius of the sector is taken?
(3) As shown in Figure 8, the vertical line of the line segment intersects the axis, the axis is at two points, and the vertical foot is at one point. Calculate the length of the line segment respectively and verify the equation.
(4) As shown in Figure 9, in the middle, the vertical foot is, set,, and try to explain.
Mathematics examination paper of Shenzhen junior high school graduates' academic examination in 2007
Reference answer
The first part of the multiple-choice question (this question * * 10 small question, each small question 3 points, ***30 points)
The title is 1 23455 6789 10.
Answer D B A A D B B C C C
Part II Non-multiple choice questions
Fill in the blanks (there are ***5 small questions in this question, each with 3 points, *** 15 points)
The title is112131415.
answer
Answer (this topic is ***7, in which 16 is 5 points, 17 is 6 points, 18 is 6 points, 19 is 6 points, 20 questions are 7 points, 2 1 questions are 8 points, and 22 questions are 9 points.
16.
17. The solution set of the original inequality group is ≤
18.( 1) Proof
(2)∴MC=7
19.( 1) 6 (2) Omit (3)
20. Therefore, the cargo ship will not be in danger of heading due east.
2 1. Construction group A lays pipeline kilometers every week, and construction group B lays pipeline kilometers every week.
According to the meaning of the question, you must
After testing, these solutions are the roots of the original equation.
But it doesn't fit the meaning of the question.
∴
A: Team A lays 2 kilometers of pipelines every week, and Team B lays 3 kilometers of pipelines every week.
22.( 1)∴
∴
(2) The coordinates of point E are,)
(3) The analytical formula of the three-point parabola of B, O and D is
∫B(- 1， 1)，O(0，0)，D(，0)
∴
Solve,
So the analytical formula of parabola is
23.( 1) ∴A(-4,-2),B(6,3)
Points A and B are taken as axes respectively, and the axes and vertical feet are e and f respectively.
∴AB=OA+OB
(2) Let the sector radius be, the arc length be and the sector area be.
rule
∵
When, the function has a maximum value.
(3) Point A is AE⊥ axis, and the vertical foot is point E.
∵CD bisects AB vertically, and point M is vertical foot.
∴
∵
∴△AEO∽△CMO
∴ ∴ ∴
In the same way.
∴
∴
∴
(4) The equation holds for the following reasons:
∵
∴
∴
∴
∴
∴
∴
∴
∴