I can't find the map. Please look at the mathematics examination paper for the senior high school entrance examination in Xining in 2007 (full score 120, examination time 120). 1. Fill in the blanks (this question * *12 is empty 15 is empty, with 2 points each and * * 30 points). 2. The reciprocal of is _ _ _ _ _ _ _ _ _ _ _ _; Decomposition factor: _ _ _ _ _ _ _ _ _ _ _. On the morning of April 6th+May 6th, 2007, BOCOG held a press conference in Beijing on the sale of tickets for the Beijing 2008 Olympic Games, and more than 7 million tickets for the Beijing Olympic Games began to be accepted by the public. This data can be expressed in scientific symbols as _ _ _ _ _ _ _ _ _ _ _. 4. Find the pattern and fill in the numbers: 20 13, 4 102, 30 14, 5 103, 40 15, _ _ _ _ _ _ _ _. Calculation: _ _ _ _ _ _ _ _ _ _. 5. As shown in figure 1, a, c and b are three points on the circle O. If ∠ AOC = 40, the degree of ∠ABC is _ _ _ _ _ _ _ _ _ _ _ _. Figure 1 6. As shown in Figure 2, it is a pattern densely paved by isosceles trapezoid with the same shape and size, so the bottom angle (acute angle) of the isosceles trapezoid in this pattern is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. Figure 2 7. Grade 9 (1) class in a school has a physical education graduation exam. The scores of all the students in this class are as follows: the probability of randomly selecting one person to get exactly 30 points is _ _ _ _ _ _ _ _ _ _ _ _ _ _; The information that can be obtained from the table is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. (Just write one) 8. It is known that in linear functions (A and B are constants), some corresponding values of X and Y are as follows, so the solution of the equation about X is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. 9. As shown in Figure 3, reduce △DEF to half of its initial value. The operation method is as follows: take any point P, connect DP, take the midpoint A of DP, then connect EP and FP, and take their midpoints B and C to get △ABC, then the area ratio of △ABC to △DEF is _ _ _ _ _ _ _ _ _ _ _ _ _. Figure 3 10. As shown in Figure 4, rotate △ ABC 25 counterclockwise around point C to get △DEC. If ∠ AFD = 50 and ∠ ACE = 80, ∠ B = _ _ _ _ _ _ _ _ Figure 4 1 1. As shown in Figure 5, point P is on the image of inverse proportional function, and the area of △OAP is 5, then k = _ _ _ _ _ _ _ _ Figure 5 12. As shown in Figure 6, let two rectangles with a length of 12 and a width of 8 overlap, and if the length of AB is known to be 7, the area of the overlapped shadow of the two rectangles is _ _ _ _ _ _ _ _ _ _ _. Figure 6 2. Multiple-choice questions (this question has 8 small questions, each with 3 points ***24 points. Of the four options given in each question, only one meets the requirements. Please fill in the option number that you think is correct in the brackets of the corresponding question number below. ) 13. The following calculations are correct: () A. B. C. D. 14. A train runs from Xining to Lhasa at a constant speed. In fig. 7, the image that can roughly reflect the relationship between the distance S(km) from Lhasa and the travel time t(h) is () fig. 7 15. In less than a year, in order to hedge the problem of excess economic liquidity in China, the People's Bank of China has raised the deposit reserve ratio five times, and commercial banks have implemented the deposit reserve ratio of 7.5% before July 5, 2006, and in February 2007. The deposit reserve ratio is raised to 10.0%, and the increase range is () A.33.3% B.25.0% C.20.0% D.10.0%16. "In order to treat sewage, our city needs to lay a 960-meter-long pipeline to minimize construction. Assuming that the original plan is to lay the pipeline x meters every day, the equation can be obtained. " According to this scenario, the omission indicated by "◆" in the title should be supplemented as: (a) The paving was 20m less than the original plan, resulting in the completion of the task four days ahead of schedule; b) The paving was 20m more than the original plan, resulting in the completion of the task four days ahead of schedule; c) The paving was 20m more than the original plan, resulting in the completion of the task four days ahead of schedule; d) As a result, it took four days to complete the task 17. According to the information in the grid figure 8, it is estimated that the following values are closest to the values in () a.0.6246b.0.8121C.1.6582d.2.1809 figure 865438. Suitable for general survey is () A. Investigate the air quality in Xining in May 1 day. Investigate the height of all the students in your class. C. Investigate the weekly pocket money of all middle school students in Xining. D. Investigate whether the bacterial content of milk in bags in supermarkets in Xining "Tianlu" exceeds the standard 19. The internal angle of N- polygon, and not more than 2007. Then the maximum number of sides of this N-polygon is () a.11b.12c.13d.1420. As shown in Figure 9, Xiao Ming found that the drawstring of the swing was 2 meters long and the pedal was 0.5 meters off the ground. Then the length of the ABCD swung by the swing is () A.B.C.D Figure 9 III. Solution (3 small questions in this question, 7 points for each small question, ***2 1 point) 2 1. Calculation: 22. Known: quadrilateral is shown in figure 10. Please take f as the endpoint and connect it with a point marked with letters in the figure to form a new line segment. Guess and prove that it is equal to an existing line segment in the graph (just prove that a group of line segments are equal) (1) And connect _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. (3) Proof: Figure 10 23. Enclose an isosceles triangle with a thin iron wire with a length of 16cm. If the base length is ycm, the waist length is xcm. (1) Write the functional relationship between base length y and waist length x; (2) Find the range of independent variable x; (3) Draw the image of this function in the grid diagram 1 1. Figure 1 1 4. (There are 3 small questions in this question, 8 points for each question ***24 points) 24. According to the research of biologists, many characteristics of human body are controlled by genes. Some people have single eyelids, while others have double eyelids, which is controlled by a pair of human genes. The gene f controlling single eyelid is recessive, and the gene f controlling double eyelid is dominant, so a pair of genes controlling eyelid may be ff, Ff or FF. People with ff gene have single eyelids, and people with Ff or FF gene have double eyelids. Genetically, it is also possible for parents to pass on a gene they carry to their children. For example, if both parents have double eyelids and their genes are ff, then their children have only three possibilities: Ff, Ff or FF, which can be expressed in the following table: (1) Can you calculate the probability that their children have double eyelids? (2) If the father's gene is ff and the mother's gene is Ff, please use the tree diagram to find out the probability that their children are double eyelids. 25. as shown in figure 12, in circle o, AB is the diameter, AD is the chord, and the tangent passing through point b intersects with the extension line of AD at point c, and AD=DC, so find the degree of ∠ABD. Figure 12 26. A middle school in Xining decided to recommend one of the three classes of Grade 9 (2), (3) and (6) as the municipal advanced collective candidate class after a preliminary comparison with the graduating classes of junior high school. Now make a comprehensive quality evaluation of these three classes. The following table shows their scores of three quality evaluations (full marks for each item are 10). (1) Please complete the above table; (2) Excuse me, among the three evaluation scores of each class, can the statistics of the average reflect the differences in the evaluation results of the three classes? If possible, please recommend a class as a candidate class for the municipal advanced collective; If not, please set the proportion of each evaluation content according to the importance of the three projects, recalculate the score of each class, and recommend a class with the highest score as the candidate class of the municipal advanced collective. (The proportion you set must meet the following requirements: ① All are integers; ② Total 10). V. (This question * * *, question 27, 9 points, question 28 12 points, * * 2 1 points) 27. In a mathematical inquiry, Xiao Qiang used a straight line to divide the rectangular ABCD into two parts with equal area, as shown in figure 13: figure 65438+. Please boldly try to draw a straight line that conforms to the above segmentation method (note: ① The special points that the drawn straight line passes through must be clearly marked; (2) Draw only one rectangle): Figure 14 (2) According to the division method of you and Xiao Qiang, a rectangle can be divided into two parts with equal area by only one straight line. Do you think there is _ _ _ _ _ _ _ _ _ _? _ _ _ _ _ _ _ _ _ _ _ (3) From the above experimental operation, what regularity do you find in the straight line you drew in the rectangle? ________________________________________________________________________。 (4) Can the irregular figure 15 below be divided into two parts with equal area by a straight line according to the above division method? Figure 15 28. As shown in figure 16, it is known that the image of the quadratic function intersects the X axis at point C and point C, and the vertex is P. (1) Find the analytical expression of this parabola; (2) Find the line segment length PC; (3) Let D be a point on the line segment OC, and ∠DPC=∠BAC, and find the coordinates of point D ... Figure 16 Reference answer and grading opinion answer of mathematics test paper for senior high school entrance examination in Xining in 2007 1. Fill-in-the-blank question (this question * * 12 sub-question 15 is empty, with 2 points each and ***30 points) 1. 2.3.4.6104,15.20 6.607.24 ~ 26 (the answer is not unique) 8.9.1:410.5011. 3 points for each small question, ***24 points) CBAB·CBCD III. (There are ***3 small questions in this question, each with 7 points, * * 2 1 point) 2 1. Solution: The original formula is 3 points, 4 points, 6 points = 0.7 points, 22. (The answer is not unique) Solution: link AF 65438. The intersection BD: quadrilateral ABCD at O 4 is a diamond ∴AC⊥BD at O, and od = ob∶de = BF, ∴OF=OE 5 ∴AC perpendicular bisector EF 6 ∴AF=AE (the distance between the point on perpendicular bisector and both ends of the line segment is equal) 7: 23. Solution: (1) 3 points (2) According to the meaning of the question, the solution is: 5 points (3) (see grid diagram) 7 points and 4 points. ***24 points) 24. Answer: (1)P (their children have double eyelids) = 3 points (2) Look at the tree map 6 points ∴P (their children have double eyelids) 8 points 25. Solution: ∫BC tangent circle O is at point B, and AB is the diameter ∴AB⊥BC 2 minutes ∫ad = DC ∴bd=ad=cd (the midline on the hypotenuse of a right triangle is equal to half of the hypotenuse) 4 minutes ∴∠ABD=∠DAB (. 3 points (the answer is not unique, as long as ① the proportional design meets the requirements, ② the calculation is accurate, and ③ the recommended result is obtained, all points can be scored). Example: Set the score ratio as 4: 5: 1, and get 4 points according to the topic: Grade 9 (2) Class 5: Grade 9 (3). 8 points and 5 points, (this question is ***2 small questions, question 27 is 9 points, question 28 12 points, * * 2 1 point) 27. (1) (The answer is not unique, and the following answers are for reference only) Draw the correct 3 points (2) Countless 5 points (3) Any straight line passing through the symmetrical center of a rectangle can divide the rectangle into two parts with equal areas (4) (The answer is not unique, and the following answers are for reference only) Draw the correct 9 points. 28. Solution: (1)∵ PM⊥xarabolic intersection 2 points ∴ The analytical formula for finding parabola is: 4 points (2) ∴ 5 points when the coordinates of point P are (1, -2)y = 0, ∴. On = 3∫cn = oc+on = 6 9 ∫ An = CN ∴∠ NAC = ∠ NCA = 45 ∴∠ MCP = ∠ NCA = 45 ∠∞.