In 2009, the mathematics examination paper of the unified entrance examination for senior high schools in Dazhou City, Sichuan Province was divided into two parts: Volume I (multiple-choice questions) and Volume II (non-multiple-choice questions). The first volume has 1 to 2 pages, and the second volume has 3 to 10 pages. Examination time 100 minutes. The perfect score is 100. The first volume (multiple choice questions ***24 points) 1. Before answering the first volume, candidates must fill in their names, admission ticket numbers and exam subjects on the answer sheet as required. 2. After choosing the answer to each small question, black the answer label corresponding to the question number on the answer sheet with a pencil, and there can be no answer on the test paper. Return this test paper with the answer sheet. 1. Multiple choice questions: only one of the four options given in each question meets the requirements of this question (8 questions in this question, 3 points for each question, ***24 points) 1. Among the following figures, the smallest one is a.-1b. -2c.0d. 12。 The following calculation is correct: a.a+2a = 3ab.3a-2a = a.c.aa = a.6a÷2a = 3a3. In an environmental knowledge quiz, the scores of a group of students are as follows: the score is 5060708090 100, ABCD the number of students is 149 15 165. The median score of this group of students is A.70B.75C.80d.854 Diagonal line-16. In the plane rectangular coordinate system, if the distance from point P to origin O is, and the angle between OP and the positive direction of X axis is, the polar coordinates of point P are used. Obviously, there is a one-to-one correspondence between the polar coordinates of point P and its coordinates. For example, the polar coordinate of point p, its polar coordinate is. If the polar coordinate of point Q is, the coordinate of point Q is A.B.C. (2 2,2 2) D. (2 2,2) 7. Figure 3 is a beautiful Pythagorean tree, in which all quadrangles are squares and all triangles are right triangles. If the side lengths of squares A, B, C and D are 3, 5, 2 and D respectively, then the area of the largest square E is A, 13 B, 26 C, 47 D and 94 8. Cut out the five-pointed star like me: as shown in Figure 4, first fold a rectangular piece of paper in half according to the dotted line of Figure 1 to get Figure 2, then fold Figure 2 in half along the dotted line to get Figure 3, and then cut out and expand Figure 3 along the dotted line △ABC to get the five-pointed star. If you want to take the regular five-pointed star, that is, the degree of ∠ABC is a, 126 B, 108 C, 90 D, 72. Mathematical considerations for the unified entrance examination for senior high schools in Dazhou in 2009: 1. Answer directly on the test paper with a blue-black pen or ballpoint pen. 2. Before answering the question, fill in all the items in the sealing line clearly. The total score of the 23rd question is (1), (2), (3) and (4). The score is given by the rater's paper 2 (non-multiple choice questions * * 76 points). Fill in the blanks: fill in the final answer directly on the horizontal line of the question (7 questions in this question, 3 points in △ABC question, ***2 1 point). 9. Decomposition factor: Mn-M = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .65433. ∠ b = _ _ _ _ _ _ _ _ _。 1 1, if A-B = 1 and ab=-2, then (A+ 1) (B- 1) has at least _ _ _ _ _ _ _ _ _ _. This solution of four line segments with lengths of 2㎝, 3㎝, 4㎝ and 5㎝ If a train travels from Dazhou to Chengdu at an average speed of 170km/h, the functional relationship between the distance y (km) from Chengdu and the travel time (hours) of ABCD is _ _ _ Third, the solution: when solving the problem, you should write the necessary text description, proof process or calculation steps (55 points) Score checker (1) (2 small questions in this question, *** 13 points) 16. (8 points) (1)(4 points) Calculation: (-1)+(2009-)-(2) (4 points) Solve the inequality group, and the solution set is expressed on the number axis. The solution set of the inequality group is expressed on the number axis as follows: 17. (6 points) During the implementation of "comprehensive management of urban and rural environment" in our city, a school organized students to carry out public welfare activities of "going out of school and serving the society". Wang Hao, Class 1, Grade 8, made the following statistics according to the students' participation in this activity: the frequency of students' participation in various services, the frequency of service categories, civilized propagandists 40.08 civilized persuaders 10 voluntary small traffic police 80. 16 small environmental guards 0.32 small living Lei Feng 120.24 Please answer the following questions according to the above statistics: (/kloc-0. (3) If 900 students in Grade 8 * * * sign up for this charity activity, try to estimate the number of students who participate in civilized persuasion. Grader (2) (this title is 2 small questions, * *11point) 18. (5 points) As shown in Figure 7, in △ABC, AB. Connect DE and rotate △ADE around point E 180 to get △CFE. Try to judge the shape of quadrilateral BCFD and explain the reasons. 19.(6 points) As shown in Figure 8, the images of the straight line and the inverse proportional function (< 0) intersect at point A and point B, and intersect with the X axis at point C, where the coordinate of point A is (-2). (2) Find the area of△ △AOC. Scoring assessor (3) (this title is 2 small questions, *** 13 points) 20. (6 points) On a sunny day, students from the math interest group went to the playground to measure the height of the flagpole. They brought the following measuring tools: leather goods, triangular rulers, benchmarks, flat mirrors, etc. First of all, Xiao Ming said, "We use a tape measure and a triangular ruler (including 30 angles) to measure." So everyone started to work together. The distance AC from Xiaoming to the flagpole is 15㎝, and the distance from Xiaoming's eyes to the ground is 1.6㎝, as shown in Figure 9 (A). Then, Hong Xiao and Xiao Qiang put forward their own ideas. According to the above situation, answer the following questions: (1) Use Figure 9 (A), please help Xiao Ming find the height of flagpole AB (the result is an integer. Reference data:,,; (2) Do you think the scheme proposed by Xiaohong and Xiao Qiang is feasible? If it is feasible, please choose the first scheme and draw the measurement schematic diagram in Figure 9 (b) to briefly describe the measurement steps. 2 1, (7 points) A student canteen stores 45 tons of coal. After five days of use, due to the improvement of equipment, the average daily coal consumption is reduced to half of the original, and the combustion is 10 day. (1) for improvement. (2) Try to adapt the content of this question to problems related to our daily life and study, so that the listed equations are the same or similar (no need to solve). Grading the reviewers (4) (2 small questions in this question, *** 17 points) 22. (8 points) As shown in figure 10, the chord AD passing through the tangent ⊙O of point D intersects with the extension line of BC at point E, AC∑de intersects with BD at point H, and DO intersects with AC and BC at points G and F respectively. (1) Prove: DF bisects AC vertically; (2) Verification: fc = ce(3) If the chord AD = 5 ㎝ and AC = 8 ㎝, find the radius ⊙ O. 23, (9 points) as shown in figure 1 1, and the parabola intersects the axis at two points A and B (point A is at B). ② Is there such a point m on the parabola that △CMP is similar to △APN? If it exists, please directly write the coordinates of all points M that meet the conditions (the solution process need not be written); If it does not exist, please explain why. In 2009, Dazhou senior secondary school unified entrance examination mathematics test questions reference answer 1. Multiple choice questions (8 questions in this question, 3 points for each question, ***24 points) 1. B 2。 B 3。 C 4 explosive D 5。 B 6。 A seven. C 8。 A 2。 Fill in the blanks (7 small questions in this question) ***2 1) 9. m(n+ 1)(n- 1) 10.40 1 1。 -412.1013.3414. y = 350-170x (the range of independent variables can be omitted) * * */kloc-0.50001.00000000015 (1) calculation: (-1) 3+(2009-2) 0-12 =-1+123 points =-/kloc-. 23-point complete frequency distribution histogram 4 points (3) 180 people 6 points mathematical answer page 2 (***4 pages) (2) (this title is 2 small questions, * *1minute) 18. Answer: The quadrilateral BCFD is a diamond. The reasons are as follows: ∫ Point D and point E are the midpoint of AB and AC respectively ∴de∨= 12b c 1 and cfe are obtained by rotating △ ade ∴de = ef∴df∨= BC∫. BCFD is a diamond, with 5 points (note: only the reason is not given 1) 19. Solution: (1)∫ Point A (-2,4) on the inverse proportional function image ∴ 4 = k ′-2 ∴ k ′ =-. 4), point B (-4,2) is on the straight line y=kx+b ∴ 4=-2k+b2=-4k+b, and k= 1b=6∴ The straight line AB is the coordinate of the intersection of point y=x+64 and the X axis C (-6,0 *** 13 points) 20. Solution: (1) The intersection point D is DE⊥AB of point E, 1 point of Rt△BDE, DE=AC= 15m, ∠ BDE = 30.5× 0? 58=8? 70 (m) 2 points ∴AB=BE+AE=8? 70m+ 1？ 6m= 10？ 3m ≈ 65438+300m3。 (2) Both Xiaohong's and Xiao Qiang's schemes are feasible. Xiaohong's plan: measure the shadow length of flagpole Ag with a tape measure and a benchmark: (1); (2) measuring the length of the rEFerence ef; (3) Measure the shadow length of reference FH6 at the same time. Xiao Qiang's plan: Put a small plane mirror in a proper position (as shown in point P). Let Xiao Qiang see the top of flagpole AB in the mirror: (1) Measure the length of AP (2) Measure the length of NP (3) Measure the height of Xiao Qiang's eyes from the ground (MN6: 2 1). Solution: (1) After setting up the improved equipment, the average daily coal consumption is x tons, which is 452x+65433 according to the meaning of the question. 53 points, x= 1? Answer: After improving the equipment, the average daily coal consumption 1? 5 tons, 4 points (2) omitted (as long as the equation of the application problem is the same as or similar to the original question, it can be scored), 7 points (4 points) (this topic is a small question, *** 17 points), 22. It is proved that: (1)∵DE is the tangent of ÷o, and DF passes through the center O∴DF⊥DE and ∴ AC ∥ de ∴ df ∴ AC ∴ df vertical branch ac2) from (/kloc- ∵AG=GC, AC=8cm, ∴ag=4cm△AGD in Rt, GD=AD2-AG2=52-42=3cm6 are obtained by Pythagorean theorem. If the radius of the circle is r, then AO=r and OG=r-3 are at Rt△AOG. According to Pythagorean Theorem, AO2=OG2+AG2 is: r2=(r-3)2+42, r=2568 minutes ∴⊙ The radius of O is 256cm.23 Solution: (1) is 6 = a (-2+3) (- 0), a (1, 0) Let the straight line AC be y=kx+b, then there is 0=k+b6=-2k+b to get k=-2b=2∴ The straight line AC is y=-2x+23 minutes (2)① Let the abscissa of p be a (-2 ≤ -2a2-4a+6)4 points ∴ PM =-2a2-4a+6-(-2a+2) =-2a2-2a+4 =-2a2+a+14+92 =-2a+122+.