The quadrilateral ABCD ABCD and BEFC are both squares, and the point P is the moving point on the side of AB (not coincident with the points A and B). When the vertical line of DP passing through the point P intersects the diagonal BF at the point Q (1), as shown in Figure ①, when the point P is the midpoint of AB: ① DP=PQ can be known through measurement, please prove that ② if m is the midpoint of AD, MP = can be known. When the point P is at any position on the AB side, other conditions remain unchanged. Is the quantitative relationship between two line segments in (1) valid? If yes, please prove it; If it doesn't hold, try to explain reason 2: AB=c,BC=a,CA=b,AD⊥BC in △abc, and prove c2=a2+b2-2abcosc 3: As shown in the figure, BD is the bisector of ∠ABC, DE⊥AB is at point E, and DF ⊥.4 Verification: DB=2CE 5: In triangle ABC, AB=3, AC=4, BC=5, triangle, triangle ABD, triangle ACE, triangle BCF. Si= 1, the number of adoptees. Is to find the area, not to prove the parallelogram 6: in the acute triangle ABC, if ∠ a >; ∠B& gt； ∠C, verification: ∠ a > 60，∠B& gt； ∠ C7: Prove that the distance from a vertex of a triangle to the vertical center is equal to twice the distance from the outer center to the opposite side of this vertex. The general idea is as follows: in △ ADE, ∠DAE=Rt, AC is high, B is on the extension line of DE, ∠ BAE = ∠ D, and it is proved that: Be 2/EC 2 = BD/DC9:.1cubic +2 cubic ... +N cubic = 6 10: It is proved that the difference between any two sides of a triangle is smaller than the third side 1 1: In quadrilateral ABCD, the two diagonals are equal, and the acute angle between them is 60 degrees. Excuse me, what is the relationship between the sum of the lengths of two sides facing a 60-degree angle and one of the diagonals? Please prove your conclusion in detail! ! 12: point p is the intersection of bisectors of angles ∠ABC and ∠ACB. It is proved that ∠ P = 90+2 ∠ A 13: As shown in the figure, triangles ABC, DBF and EFC are equilateral triangles. Please prove it. Let f (a 1) = f (A2) = f (A3) =1,and let b be any integer not equal to a1,a2, a3. Try to prove that f(b) is not = 1? 15: arbitrary triangle abc, where three bisectors of internal angles AD, BE and CF intersect at point h, and point h is taken as the vertical line of ac, and the vertical foot is g, which proves whether the angles of ahe and chg are equal. Why 16: The triangle is inscribed with a circle O, AE is the diameter of the circle O, and AD is the height of the BC side in the triangle. It is proved that AC times BE=AE. 17: Known: in triangle ABC, AC = BC, angle ACB = 90 degrees, D is the midpoint of AC, point F is on AB, and angle FDA= = angle BDC .. Prove: CF is perpendicular to BD. 18: Known proposition: If quadratic function y=ax2 (where 2 represents square), Then y = a (x-x 1) (x-x2) judges whether this proposition holds, and explains the reason 19: It is known that A and B are real numbers, and AB=0 is satisfied, which proves that at least one of A and B is 0. 20: any triangle ABC D is the midpoint of BC side, which connects the bisectors of AD and ∠ADB, AB and E, and the bisectors of ∠ADC, AC and F. EF Proof: Be+FC > EF Share with friends: Everyone Sina Weibo Xin Kai MSN QQ space is helpful to me. 9 Answer time: 20 10-4- 10. 38+0 | Let me comment | Report to TA for help Respondent: Zhao Shuai 3046663 | Second-class pass rate: 10% Expertise: Audio/song sharing activities on the geographical history of basketball crossing the line of fire: activities that I have not participated in for the time being: the questioner's evaluation of the answer: regardless of the relevant content. Let's do a junior high school math problem in February 2009-13! ! Try to prove that the sum of squares of four consecutive natural numbers is not a square number! ! ! Sum of 6 2010-12-31q1+1/3+1/4+...... ! ! ! 2 2010-12-21Three unequal numbers A, B and C satisfy A+1/B = B+1/A, and the verification is made. Check the same question: Junior high school math proof is waiting for you to answer 1 Answer 5 Why not use tombstone devourer to dispose of these cemeteries in survival mode? 0 Answer for a beautiful woman wearing underwear, sexy figure, 0 Answer for documents: Jinan City, Jiangsu Province, 2009-20 10 Senior One Mathematics Final Paper 0 Answer How Hamlet Typed 0 Answer for the name of a European and American movie. When the heroine reached middle age, her marriage was in crisis, and she decided to end this relationship ... 1 Answer Swallow the starry sky Chapter VII Chapter XXVII Chapter XXIX txt Download 1 Answer Seeing the vivid pictures of the beautiful women, she was a little tempted. 0 Answer Learning Guidance Efficient Classroom Answer There are more questions for you to answer in Grade Three Mathematics >> There are two answers, 1. Known: As shown in the figure, BC, point E is the midpoint of DC, and AE divides ∠BAD equally. Proof: divided equally ∠ ABC.2. Known: As shown in the figure, in △ABC, CD is the angular bisector of △ABC. BC=AC+AD。 It is proved that ∠A=2∠B intersects with point E, and EF intersects with AB at f∫ad‖ef ∴∠dae=∠aef∫AE is equally divided ∠DAF (known) ∴. ) ∴∠DEC=∠B ∴∠A=2∠DEC=2∠B Interviewee: Apple _ pxy | Level 2 | 2010-4-919. Report the seventh grade math test paper sampled in the second semester of the 2007-2008 school year in Xicheng District, Beijing, with a perfect score of 100. 1. Choose carefully (a total of 10 small questions, 30 points for each question). Of the four alternative answers to the following questions, only one is correct. Please write the correct conclusion code in parentheses after the question. 1. The result of calculation is (). A.b.c.d.2 The solution set of inequality is correct on the number axis (). 3. It is known that the lengths of two sides of a triangle are 2cm and 7cm, respectively. If the length of the third side is, the value range of is (). A.b.c.d.4 If yes, the following inequality is wrong (). A.b.c.d.5 As shown in the figure, draw a parallel line of a straight line at a point outside the known straight line with a ruler and a triangular ruler. This drawing method is based on (). A the congruence angle is equal and the two straight lines are parallel. B. Two straight lines are parallel and have the same complementary angle. C. The internal dislocation angles are equal, two straight lines are parallel, and the internal dislocation angles are equal. 6. The following four regular polygon tiles, can use the same tile mosaic into a plane pattern is (). On May 4th, 2008, the torch relay of Beijing Olympic Games was passed to Sanya, Hainan Province, which was the first stop of the "Xiangyun" torch relay in China. The relay route is Sanya-Wuzhishan-Wanning-Haikou. As shown in the figure, Xiaohong, a student of a school, uses (-2,-1) to indicate the starting point of the torch relay and (-65438) to indicate Sanya in the map of Hainan Province. Then the location of Haikou, the destination of the torch relay, can be expressed as (). A. (3，4) B. (4，5) C. (4，2) D. (2，4) 8。 The following statistics reflect that all students in Class A and Class B like four kinds of ball games respectively. According to statistics, the following judgment about the percentage of people who like table tennis in the total number of students in the class is correct (). A. class a is big and class b is small. Class a is small and class b is big. Class C is as big as Class B, so it is impossible to determine which class is bigger. As shown in figure 1, a quadrilateral paper ABCD, ∠ A = 50, ∠ C = 150. If it is folded as shown in Figure ②, and it happens to be, then the degree of ∠D is (). A.70 B.75 C.80 D.85 10。 As shown in the figure, square ABCD and square EFGH. Then the area of △BDE is (). A.B.C.D 2. Fill in carefully (8 questions in total, 3 points for each question, 24 points in total) 1 1. Rewrite the proposition "diagonal equality" into the form "If the sum of ... is 12". And 3 is a negative number, which means _ _ _ _ _ _ _ _ _ _ _. 13. As shown in the figure, points AD‖BC and E are on the extension line of BD. If ∠ ADE = 130, the degree of ∠DBC is _ _ _ _ _. 14. The sum of the internal angles of a polygon is 900, and this polygon is _ _ _ _ _ _ _. 15. If the point p (,) is known to be on the axis, the distance from the point p to the origin is _ _ _ _ _ _ _. 16. As shown in the figure, the side length of each small square is 1cm, and the shortest distance for ants to climb from point A to point B is _ _ _ cm along the grid line of the square. 17. When Wang Qiang solved the equations, he found that the solution of the equations was due to carelessness, and some ink was dropped in the exercise book, which just covered the digits, so the digits represented by the digits should be _ _ _ _ _ _ _ _ _. On 18. △ ABC, ∠ B = 20, and AD is the height on the side of BC. If ∠ DAC = 30, the degree of ∠BAC is _ _ _ _ _ _. Third, do it seriously (5 small questions in total, 6 points for each small question, 30 points in total) 19. Simplify first, then evaluate. 20. Solve the equation: 2 1. Solving inequality: 22. As shown in the figure, in a quadrilateral ABCD, AB‖CD, points E and F are on the sides of AD and BC respectively, connecting AC to EF and ∠ 1=∠BAC. (1) verification: ef ‖ CD; (2) If ∠ CAF = 15, ∠ 2 = 45 and ∠ 3 = 20, find the degrees of ∠B and ∠ACD. 23. Students in a school should know about the weekend physical exercise of seventh-grade students in the school. When determining the investigation method, classmate A said, "I went to Class 2, Grade 7 to investigate all my classmates"; Student B said, "I went to the seventh grade and randomly investigated a certain number of students in each class"; Student C said, "I went to the city youth sports center to investigate the students who participated in physical exercise." (1) Please point out which of the above three survey methods is the most reasonable? (2) Students in this school collect data by the most reasonable investigation method, and draw an incomplete frequency distribution table and a frequency distribution square diagram. Please write the values of,, and complete the frequency distribution histogram according to the information provided by the chart; (3) If there are 300 students in the seventh grade of this school, please estimate the number of students who spend less than 1 hour in physical exercise on weekends, and make suggestions to the students according to the investigation. Fourth, solve the problem (a total of 2 small questions, each with 6 points, a total of 12 points). As shown in the figure, move △ABC to the right by 3 units, and then move it up. (1) Draw the translated delta(2) Write the coordinates of the three vertices of the delta; (3) Knowing that point P is on the X axis, that is, the area of a triangle with vertex 0 and p 4, find the coordinates of point P ... 25. A residential area will hold a "Welcome to the Olympics" knowledge contest. When buying prizes, the property staff learned the following information: (1) How much is a box of Fuwa plus a badge? (2) The property management company announced the following prize distribution schemes for this event: first prize, second prize, third prize, 1 box fuwa and 1 box fuwa, 1 badge. If this activity is held, the total cost of purchasing prizes is not less than 1500 yuan, but not more than 1600 yuan. Set up one. V. Answering questions (4 points for this question) 26. △ ABC, AB=2, BC=4, CD⊥AB in D. (1) as shown in Figure ①, AE⊥BC in E, verification: cd = 2ae；; (2) As shown in Figure 2, P is any point on AC (P does not coincide with A and C). If P is used as PE⊥BC in E and PF⊥AB in F, the verification is: 2pe+pf = CD；; (3) In (2), if P is any point on the AC extension line, and other conditions remain unchanged, please draw a diagram in the standby diagram to explore the quantitative relationship between line segments PE, PF and CD. The full mark of volume B is 20 points. 6. Induction and conjecture (6 points in this question) 27. Observe the graph given below and explore the changing law of the number of points in the graph. And fill in the table: the number of the 1, the 2nd, 3rd, 4th, 5th … nth points of the graph is 1.59 … VII. Problem solving (7 points for this question) 28. In the plane rectangular coordinate system, it is known that two points on the axis are on both sides of the origin, and the distance between two points A and B is less than 7 unit lengths. The value range is (1); (2)C is the midpoint of AB, which is the whole point (the point whose abscissa and ordinate are integers is called the whole point). If d is the whole point, when △BCD is an isosceles right triangle, the coordinates of point D can be obtained. Eight, answer (this question 7 points) 29. △ ABC，∠BAC=∠ACB。 (1) As shown in the figure, e is a point on the extension line of AB, the bisector connecting CE and ∠BEC intersects BC at point D, and intersects AC at point P. Verify: (2) If E is a point on the ray BA (E does not coincide with A and B), then the straight line connecting the bisector of CE and ∠BEC intersects with BC at point D, and the straight line intersecting with CA intersects with point P ... What is the relationship between ∠CPD and ∠BCE? Please draw a picture, give your conclusion and explain the reasons. In the second semester of the 2007-2008 school year in Xicheng District, Beijing, the reference answers and grading standards of the seventh grade mathematics test paper were sampled and tested. Volume A (standard volume) 100. First, choose carefully (total 10 questions, 3 points for each question, 30 points in total) 1, A 2, C 3, C 4, D 5, A 6, B 7, D 8, B 9, C 10, D 2. Fill in (8 questions, 3 points for each question, 24 points) 1 1 carefully. 12.； 13.50; 14.7; 15.7; 16.8; 17. 10,2; (the first blank is 1 and the second blank is 2) 18.40 or 100 (only one result is 1). Third, do it seriously (5 small questions in total, 6 points for each small question, 30 points in total) 19. Simplify first. Solution: Step 1: Step 2: Solve the problem ... 6 minutes and 20 seconds. Solve the equation: Solution: From ①, You get .................................................................................................................................................. … ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… ................................................................................................................... ................. 2 points ∵ AB ‖. .............. scored 3 points (2)∫ab‖ef, ∴∠ B+(∠ 2+∠ 3) = 180. ∠∠2 = 45, ∠3=20, ∴∠ B =115 .................. 4 points ∠/= ∠ caf+∠ 3, and ∠. ∴∠acd=∠ 1 =35 ef ab Company .......................................................................................................................................................................... ……………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………………………………………. Fourth, solve the problem (a total of 2 small questions, each with 6 points, a total of 12 points) 24. Solution: (1) As shown in Figure 3: Figure 3 Answer: Second prize 10, 8 third prizes. …………………………………………………………………………………………………………………………………………………………………………………………………………………………………….∵, ∴ .................................................................................................................................................................. Volume B (promotion volume) This volume is full of 20 points. 6. Induction and conjecture (6 points in this question) 27. The number of points in the picture (No.65438 +0, No.2, No.3, No.4, No.5 … Points (No. N) Yes 13, 17 ... Note: 1, 1; 2 points for the second empty deduction; The third one is empty, 3 points. Seven, answer (this question 7 points) 28. Solution: (1) Because A (0), B (4 4,0), A and B are located on both sides of the origin, so. ............. 1 minute because,, so. By (1), and so on. Therefore, when △BCD is an isosceles right triangle, there are four whole points D, namely: (1, 3), (4,3), (1, 3), (4,3). △ace，∠ a+∠ ace+∠ AEC = 180。 ∠∠ace =∠ACB+∠BCE, while ∠CAB=∠ACB, ∴ 2 ∠ A+2 ∠ BEP+∠ BCE = 180. ∴∠CPE =∠a+∠BEP，∴.............................................................................................................................∠BCE=。 There are two situations: I) If point E is on BA (E does not coincide with A and B, as shown in figure 9, ∫∠ace =∠AC b-∠BCE, ∴∠ ACE =. ∵∠.∴∠CPD =∠ced-∠ace，∴∠ CPD = ∴∴....................................................................................................∠∠cab =∠CEA+∠ace， ∴ ∴ ∠CPD=∠ACE+∠CEP, ∴∠ CPD = ∴∠. To sum up, it shows that students' other correct answers are given points according to the grading standard. Analysis of the seventh grade mathematics examination paper in the second semester in 2007-2008. 1. Test paper structure: This exam is divided into two parts: volume A and volume B. Volume A focuses on the implementation of basic knowledge, with a full score of 100, with a total of 26 questions. Volume B pays attention to the expansion of knowledge and the infiltration of mathematical thinking methods, with a full score of 20 and a total of 3 questions, which is somewhat difficult. Second, the content distribution of the test paper: the content of the knowledge learned this semester is relatively basic, which provides an auxiliary role for subsequent study. This test contains all the contents in the seventh grade mathematics textbook. Specifically, the full mark of A+B volume is 120, in which the algebraic part includes: binary linear equations (groups); Inequality (group); Plane rectangular coordinate system; Collection, arrangement and description of data; Multiplication and division of algebraic expressions, etc. It is about 68 points. The geometry part contains relatively few contents, including: parallel lines and intersecting lines; Triangle and polygon, 52 points in total. It can be seen that the knowledge of geometry is less, but it is easier to examine its mathematical skills. Third, the characteristics of the test paper: the test paper covers a wide range of knowledge, and most of the test questions come from the adaptation and expansion of examples and exercises in the textbook, with special emphasis on the examination of basic knowledge, that is, the social knowledge points that should be known, as well as the examination of basic mathematical thinking methods such as the combination of numbers and shapes and classified discussion. The examination of these mathematical thinking methods has improved the level and level of the test paper and also improved the discrimination of the test paper. Judging from the test results, this test paper was completed within 100 minutes, with 87 points for Volume A, 0/3 points for Volume B or about 100 points in total, which shows that this knowledge has been put into practice very well, even excellent. Fourth, test analysis: 1. Investigate the arithmetic of power. 2. Investigate how to express the solution set of inequality intuitively with the number axis. 3. Examine the inequality theorem of three sides of a triangle or the conditions for forming a triangle. 4. Investigate the basic properties of inequality. 5. Examine the application of parallel judgment theorem. 6. Investigate the condition that the plane is inlaid with the same regular polygon, that is, the degree of the internal angle of the regular polygon is a divisor of 360. 7. Investigate the position of points on the plane determined by ordered number pairs or the one-to-one correspondence between points on the plane and ordered number pairs. 8. Investigate the comparison of the corresponding relationship between statistical charts (histogram and fan chart) when describing data. 9. Check that mathematical experiments and operations are based on strict geometric reasoning. 10. It is a comprehensive problem to investigate the area of a graph by using the mixed operation of cut-and-fill method and algebraic expression. 1 1. Examine the structure of the proposition: distinguish the topic from the conclusion. 12. Investigate the inequality relations expressed by mathematical symbols. 13. Study the properties of parallel lines. 14. Examine the four angles and formulas of a polygon. 15. Check the coordinate characteristics of points on the coordinate axis and the distance between these points and the coordinate axis. 16. Check the experiment and operation of graphic translation under given conditions. 17. Check the application of the equation solution. 18. Examine the rigor of mathematical thinking and the application of geometric drawing in the classification discussion of thinking methods. 19. Check multiplication and multiplication formulas of algebraic expressions. 20. Implement basic knowledge and solve equations. 2 1. Implement the basic knowledge and solve the inequality group. 22. Realize basic knowledge, simple geometric reasoning and calculation. 23. Implement the basic knowledge points and investigate the histogram of recognition number distribution and its application in real life. 24. Investigate the area of triangle on the coordinate plane and the known coordinate plane, find the coordinates of related vertices, and pay attention to the rigor of thinking and the infiltration of the thinking method of combining numbers and shapes. 25. The application of equations and inequalities in real life. 26. Gradually investigate the application of area transformation in geometric proof and exploration. The answers to the three questions in this question reflect the gradual expansion and extension of mathematical thinking, and are good questions to test mathematical thinking ability. Volume b: 27. Investigate the basic cognitive methods of mathematics, that is, from special to general, from simple to complex: induction, conjecture and verification. 28. Examine the application of inequality and reading comprehension. Through the combination of numbers and shapes, we can fully understand the mathematical concepts of experimental operation. 29. Investigate the theorem that the sum of the interior angles of a triangle is 180. Used to deal with more complex geometric figures. This topic is divided into two questions, layer by layer exploration, dynamics, conditions, conclusions and guesses. In the process of verification, the position of the moving point has changed, but the methods used in the two problems have changed. This problem is more difficult, so we should learn to explain arguments and geometric propositions by algebraic methods. Summary: This topic has many basic questions, a large amount of calculation and flexible examination of knowledge points. In the exam, generally speaking, 80 points are easy to get, but it is difficult to get more than 1 10. It has good discrimination. For students with relatively weak basic skills, time is tight. This test paper is a good test paper that embodies the concept of the new curriculum standard.