Attention of candidates in the 2009 Loudi Junior High School Graduation Examination in Mathematics: 1. There are five major questions in the examination paper of this subject, with full score 120 and time 120 minutes. Please write the answer on the answer sheet, which is invalid. 1. Choose carefully, and I'm sure you can choose the right one. Out of 30) 1 reciprocal. (-3) 2 is () A.6 B.-6 C.9 D.-9 2. The following calculation is correct (). (A-B) 2 = A 2-B2B。 A 2 A 3 = A5C。 2A+3B = 5AB D.3-2 = 1 3。 As shown in figure 1, AC∑ED, ∠ C = 26, ∞. Then the degree of the bed is () a.63b.83c.73d.534. Which of the following sets of inequalities is represented on the number axis, as shown in Figure 2 (). a x≥2x- 1cx > 2x ≤- 1dx < 2x ≥- 1 5。 According to the statistical bulletin issued by the Municipal Bureau of Statistics, from 2004 to 2008, the GDP growth rate of our city was 9.6%, 10.2%, 10.4%, 10.6% and 10.3% respectively. Economists commented that the annual growth rate of GDP in these five years was quite stable. From a statistical point of view, "the growth rate is quite stable" means that this set of data is relatively small. A. Median B. Average C. Mode D. Variance 6. The following proposition is true. If | A | = | B|, then a=b B The diagonals of the isosceles trapezoid are perpendicular to each other. C. The quadrilateral obtained by connecting the midpoints of the sides of the quadrilateral in turn is a parallelogram. D. arcs with equal circumferential angles are equal. 7. Students in an extracurricular interest group in a primary school in the city make a rectangular learning tool of 200cm 2 for display. Let the width of the rectangle be xcm and the length be ycm. Then the image of the functional relationship between the length y(cm) and the width x(cm) of a rectangle made by these students is roughly () 8. As shown in Figure 3, AB is the chord of ⊙O, and OD⊥AB passes through ⊙O in E, so the following statement is wrong: () A. AD = BDB. ∠ ACB = When aiming at the target point B with a gun, the eye O, the sight A and the target B should be on the same straight line, as shown in Figure 4. When shooting, Xiao Ming swayed slightly, causing the line of sight A to deviate to A'. If OA = 0.2m, OB = 40m, AA'=0.00 15+05m, then the length bB' of the point b' deviated from the target point b' of Xiaoming's shooting is a.3m B.0.3 C.0.03 D.0.2 10. Images of linear function y=kx+b and inverse proportional function y=kx are shown in fig. 5. Then the following statement is correct: a. Their function value y increases with the increase of X. B. Their function value y decreases with the increase of X. C. K < 0 d. Their independent variable X takes the values of all real numbers. 2. Fill it in carefully, and you will be able to fill it correctly (this big question is ***6 small questions, with 3 points for each small question, with full marks 18) 1 1. Calculation: 2- 1+-COS60 =. 12. There are five cards, A, B, C, D and E, which have the same texture and the same size and shape, and their expressions are facing down. The probability of correct operation on the card is .2× (-5) =-10a (3a-1) = 3a2-ab (a2) 3 = a5c =1dx3x-4 = xe13. As shown in fig. 6. PB=4cm，BC = . 14。 In order to cope with the financial crisis and stimulate domestic demand, the Hunan Provincial People's Government has designated this year as "Hunan Tourism Year". At the end of March, the price of tours organized by youth travel agencies to Fenghuang Ancient City and Zhangjiajie Scenic Area was 1000 yuan per person. In order to attract more people to travel to Phoenix and Zhangjiajie, the price was reduced twice in late April and May. The price after two price reductions is 8 10 yuan per person, so the average price reduction rate of these two price reductions is. 15. As shown in Figure 7, the radius ⊙O is 2, C 1 is the image of function y = x 2, and c 2 is the image of function y =-x 2, so the area of the shaded part is .65438+. According to this rule, the pattern in the shape of the nth Chinese character needs a matchstick. Third, do a careful calculation and don't make mistakes (there are three minor problems in this big question, with a full score of 22 points) 17. (This little question has 7 points) Simplify first, then evaluate:+,where x =. 17. City Road and Bridge Company won the bid to contract a section of subgrade engineering. After entering the construction site, the functional relationship between excavation subgrade length y(m) and excavation time x (days) is as shown in the figure. Please answer the following questions according to the information provided: (1) Please make it clear: ① The functional relationship between y and x in the time period of 0 ≤ x < 2; (2) the functional relationship between y and x in the time period of x≥2. (2) How many days will it take to complete 1620 m subgrade construction with analytical function? 19. (8 points in this small question) In the activity of studying and practicing Scientific Outlook on Development, a 30-meter-long publicity banner AE was hung on the wall facing the street of the office building, as shown in Figure 8. Standing on the ground of office building C, Zhang Ming measured that the elevation of a at the top of the banner was 50, and that of e at the bottom of the banner was 30. How far is Zhang Ming measured from the horizontal distance of the office building of this unit? (accurate to the whole meter) (reference data: sin50 ≈0.77, cos50 ≈0.64, TAN 50 ≈ 1.20, sin30 =0.50, cos30 ≈0.87, tan30 ≈ 0.58) IV. About. Operation and application (Benda) Each small square is a square with a side length of 1, and a plane rectangular coordinate system is established with O point as the coordinate origin. (1) Draw a quadrilateral OA 1 B 1 C 1, which is symmetrical about the Y axis of quadrilateral OABC. And write the coordinates of point b 1 as. (2) Draw the quadrilateral OA 2 B 2 C 2 obtained by rotating the quadrilateral OABC 90 clockwise around the O point, and find the length of the rotation path from the C point to the C 2 point. 2 1. (This small question is 8 points) As shown in figure 10, in △ABC, AB=AC, D is the midpoint of BC, connecting AD, and taking a little E on the extension line of AD, connecting BE and CE. (1) Prove: △ Abe △ ace (2) When AE and AD satisfy what quantitative relationship, the quadrilateral ABEC is a diamond? And explain why. 22. (8 points in this small question) In order to speed up the construction of a new socialist countryside and let farmers enjoy the achievements made in the 30 years of reform and opening up, the CPC Central Committee and the State Council have decided that farmers who buy household appliances and motorcycles will be subsidized by the government at 13% (if they buy from the township finance office with the purchase invoice, they will be subsidized at 13%). Li Bobo's family in Xingxing Village spent 6,000 yuan on a color TV and a motorcycle this year. The unit price of a motorcycle is more than twice that of a color TV. (65,438+.(2) What is the unit price of the motorcycle and color TV that Uncle Li bought? 23. (8 points in this small question) "Diligence" is the traditional virtue of the Chinese nation. The school requires students to help their parents do housework as much as possible at home. At the beginning of this semester, Wang Gang made a sample survey on the time of some students doing housework at home during the winter vacation (the time is an integer hour). The statistics of the obtained data are as follows: time grouping 0.5 ~ 20.5 20.5 ~ 40.5 ~ 60.5 60.5 ~ 80.5 80.5 ~100.5 frequency 20 25 301510 (1) sampling capacity. (4) If there are 1260 students in this school, how many students spend 40.5~ 100.5 hours doing housework in winter vacation? V. Synthesis and inquiry (this big topic is ***2 small topics, with full marks of 20) 24. When the quadratic function y = x 2-(2m- 1) x+m 2+3m+4. (1) is known about x, which is the number of intersections between the image of the quadratic function y and the x axis. B(x 2) Let the intersection of the image of the quadratic function Y and the X axis be A (X 1 0) and B (X2, 0), and +=5, the intersection with the Y axis be C, and its vertex be M, and find the analytical formula of the straight line CM. (This little problem is 65438+. ∠ C = 90, BC = 8°, AC = 6°, the bottom DE(HF∨DE, ∠ HDE = 90) of another right-angled trapezoid DEFH falls on CB, and the waist DH falls on CA, with DE=4, ∠DEF=∠CBA. Move the right-angled trapezoid DEFH to the right along the CB direction at the speed of 1 unit per second until the point D coincides with the point B. Let the moving time be t seconds and the right-angled trapezoid after moving be DEFH' (as shown in figure 12). Exploring 1: Can quadrilateral CDH'H be a square in motion? If yes, request the value of t at this time; If not, please explain why. Question 2: The area of the overlapping part of △ABC and right-angled trapezoid DEFH' in the exercise is Y, so find the functional relationship between Y and T.. If there are no pictures in the above documents, please add me QQ: 5450207 12. I hope it helps you. Thank you.

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