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1、一道高考试题的多解与评析（Multiple solutions and analysis of a college entrance examination question）This article is contributed by aqqw5284Pdf documents may experience poor browsing on the WAP side. It is recommended that you first select TXT, or download the source file to the local view.VIP information http:/
2、High school mathematics journal (middle) 20 high, 07 years SixthForty-oneOneHow they question in college entrance examination and evaluation for209107 Zeng, Xiaoping, Li QunSchool of mathematics and computer science, Nanjing Normal UniversityAnalytic geometry solution of Jiangsu college entrance exa
3、mination mathematics test in 2007Answer to:=0., obviously A = 0, so that the line A is a parabola tangent. QIdea two: to prove that the line AQ and parabola Y = tangent,As shown in plane Cartesian coordinatesOneYTo be proved on parabolic A point tangent after a point Q is q,Line XY, Y, in the direct
4、 direction, O, over axis point COC, make a straight line, (.)/B.OneThe coordinate satisfies the tangent equation of the A point. The derivative of the 2 parabola Y = Y = 2, while the slope of the tangent from the A point is k = 2, and the cut a is A by the point oblique xThe tangent equation is Y, o
5、ne = 2 (ax, one, Y = 2x). That is, aIntersect with parabola Y = A,Two points, a straight line perpendicular to the axis, respectively, with line segments A and straight BLine Z = = C:) to P,.QPC.When): 2. :. One: wife,. Lets say 2. : Z2L() 1 if?Tangent of object line;= 2, the value of c;AB = C to A
6、a tangent point by point, Q, C. (a).Train of thought three: Q over the tangent line as a parabola, to prove its over A, points() P is a line segment A2, if the midpoint of the B is proved: A to throw Q (), ask () 3, the inverse proposition of test 2 is set up? A clear reasonOr prove that the slope i
7、s equal to the slope of the tangent of the A pointLThe question of the first () ask more basic, easy to answer; 1, the first() the 3 question can be regarded as the inverse process of the first (2) question, and the answer is similar3 set point Q, C line for YC = (a +)Therefore, the main body of thi
8、s question is the first () and the 2 question to illustrate the questionMore targeted, this article on the (2) questions for answer analysis. () ask the starting point low, mouth width, law and more, one can, 2 people isM (testis) line (1) parabolic equation Y = = YFor about a Kc equation I = 0, A =
9、 MT by 0l X,.A good question for evaluating students mathematics studyMethod to solve the questions, the main error on students answer, have certain reference significance of.1 solution and answers first list the kinds of answers are used for the high school mathematics teaching:A linear equation is
10、 Y = AB and Y = Kxc parabola,M = k J4 = K (CM + 4 + / + to C / J.)Thus M = K 1,J + 4 = (B + C)= 2 toThe derivative of the parabola Y = Y = 2, while the slope of the X from the point tangent to A is k = 2.aSo the line AQ is the parabola tangent. Thought four: the straight line, A, Q, and the A point
11、on the parabolaThe intersection point is Aaa) Bbb) (, (), the line and the parabolaThe process obtains a X - KC = 0 at the same time,B = Ka, B = C.Line coincidence, that is, Ko = k cutThe derivative of the sign 4 parabola Y = Y:2, and over x fromThought 1: find the equation of straight line A, strai
12、ght line A and throw Q certificate QObject line Y = tangent, that is to prove the linear equation and parabolic equation at the same time, the A equation of the two equation =The slope of tangent point A is k2. = a by the cut Q (a curse,C, line A) is the slope of Q,1 by Q / C, you know, (a) is linea
13、r A cable QDan: rate of a = 2, line A port is straight Q.Export C AA mouthful of B-. One. A T. One. OnceThus K a = k, AQ is a straight cut tangent.2 answer frequently encountered problemsThe procedure is Y = 2 (mouth, Y = 2x, one mouthful ax 1), i.e. a portMatter line equation Y = = 2x = a = 2x + po
14、rt aThis question out of 5 points, the average sample statistics for the 2. pumping pointsVIP information http:/Forty-twoHigh school mathematics journal (middle) 20 high, 07 years SixthWhat are the major problems encountered? What are the common mistakes? The pen analyzes all kinds of answers, and t
15、he conclusions are as follows: 21 the substitution is simplified and the calculation is complicatedA Yc. / Q equation (a J / = +(1) (wife)Generation of a people. = Y, J (aOneA wife (J).4 wife (11),.J2In fact, the basic data for solving the problem is aan,B =.A (Bbb) port, and + JB = a, his data shou
16、ld try to use the C.C = 0.)For A = (a.J4) + CC=These basic data indicate that at the same time, these basic data should also be flexibly changed. When you do something, you should see the target, every stepThe results are quantified and simplified into basic data. If the new unknown quantity is intr
17、oduced aimlessly, the calculation will not be simplified properlyKk4 a 2 2C / C 4 B.+ 4C, 4C = 0, slightly belowThe result is extremely complex, resulting in a huge amount of computationProof 5 sets the line AB = Y = KC and parabola Y = x +,The above two methods to prove the computation greatly, mos
18、t students must know the mathematical method, calculation error (such as the slope of the line, but the one or two order equation and delta etc.) failed to get the correct results. By 7, CK. : t:L oneThe AY (y) by Q (, the intersection problem (one, 2One C = 0C = one, getFallI one-21 .The C rate of
19、A. = straight line Q) line Q is inclined to , A, J QOneLoss(the same as below 4) 8 is a x K. C = o. =! .Q j j ,For the party, its history) = / = C + (k generation) will be a,L oneYlc.I YtOneC+.O.- -:A Il a(4 under the same card) -,.One2 (A / C.Bu = = poison.The two methods of calculation are smaller
20、 and replaced by simple onesSkills are strong, students who choose this method can generally make a good choiceAnswer.22 logical reasoning errorsHave a parabola Y = aan (), the tangent slope is k = a A Ya2 (a) tangent equation - 2, Y2x = ax, a substitution) a port, a port, a 2x + = 0, a = O and stra
21、ight line is obviously parabola tangent. Note that this card and card, l, is used to prove that the tangent tangent ring, is on the demonstration.= 4 + xx4l +) = O, so the line Ax4l2 - x (L2, Q) isThe tangent parabola card 6 Y = C. Linear and parabolic Y = simultaneousTo c:o and - K, - V: One4C:,23,
22、 vague concepts, know how to reasonMm -(give up).Some students use derivatives to obtain the slope of the tangent of the A pointFor = 2, the slope formula calculates k = denier n with A port. -=Direct Q cable. The rate of A / = = line j QOneLoss= 2, these are related to the tangent, a, but I do not
23、know.j.2COne. A,So straightHow to prove that Q is the tangent of a parabola can not be deep. Some students are also used to write the tangent equation by K, and the diagrams are tested by the discriminant method-OneOneVIP information http:/High school mathematics journal (high school) 20 years, 607t
24、hAt the 43 moment, the question is concise; the dimension is shallow and the problem is solved; the solution is the solutionGet delta = 0 but by calculation or other reasons failed. The reason may be, the tangent slope, the number of students, the concept of the number of guideThe essence of learnin
25、g lacks the real understanding of.3s Enlightenment to mathematics teachingComplexity, for example, involves vectors, derivatives, and analytic geometryThe basic knowledge and methods to function; analysis of the problem of time, if only to pay attention to the tangent and parabola with delta = 0 to
26、prove,The college entrance examination questions play a guiding role in daily teaching and senior high school reviewGive us some meaningful insights,.31 basic knowledge and basic methodsIn the case of 5 and 6, the idea is simple and the amount of calculation is great. If deep thought is taken into a
27、ccount, the parabolic equation can be regarded as a function, and the derivative is tangent to the tangentOff, and verify the tangent point Q in A (such as from 2 on, or)The parabola in the A tangent coincides with the Aq (e.g., 4), the amount of computationIt is obvious that flexible and profound t
28、hinking is very important for quick and accurate answersIn recent years, the national college entrance examination in all provinces and municipalities has many problems, but the general trend is to pay attention to the basic and desalination skillsTo pay attention to the investigation of basic knowl
29、edge and basic methods, such asThe main question is the basic properties of parabola, straight line and parabolaThe relationship of location, the number of vector product, the number of easy use, simple logic guide basic knowledge and basic operation. Answer the college entrance examination need onl
30、y through the law, need wakongxinsi skills. Therefore, no examples and exercises should be used in small difficulty, wide mouth, into the solution of much attention to basic questions,Then, the problem of difficult partial blame. Abandoned 32 focus on the development of thinking ability. Another fea
31、ture of the college entrance examination is to pay attention to the integration and method of knowledge connection, to check the students learning ability and the development potential. Borrow from the point of view of mathematics, problem analysis andBuried in the problem, the key to thinking, to f
32、ind a solution to the problem of thinking,.33 pay attention to the cultivation of computing abilityComputing power is an important mathematical ability, and it is a fundamental condition to solve the problemThe idea of calculating errors can not; sometimes the idea is not very good, as long as the m
33、eterAbility to calculate, can also successfully solve. For example, before the card 5 and card 6 points,The analysis is not deep enough and the calculation is large, but the calculation ability will be favorableIn recent years, many studies have shown that primary and secondary school students consi
34、der meThe apparent decline in computing power, which has to pay attention to computing power, can not be accomplished overnight. It takes a long timeCheng, and also to develop good calculation habits, this is good, and then count, you want to count is accurate.The ability to solve problems mainly li
35、es in the ability of thinking: flexibility and depth of thinkingAnalysis of proposition errors in college entrance examinationHuzhou No.1 Middle School of Zhejiang ProvinceSince 20, the Ministry of education examination center to try to teach the use of multiple sets of papers from 01. 20 to 07 year
36、s, only the physical examination volume reached more than.0 high 2 sets and compilation of college entrance examination questions is the number of tasteOneThree hundred and thirty thousand and one hundredHuangjiaweiMathematics to rigorous and thorough mathematical proposition is known, conditions an
37、d conclusions must be consistent, and many conditions, not harmonious clear, there is no ambiguity. But if the proposition does not fully consider the issue, there will be the following 2007 Zhejiang college entrance examination volume a fill in the blanks (that is, science first, Arts 6First) probl
38、em of 7 cases of 1 known points in 0 - edge - dihedral penetration point, P, LPB = 4. For Lu in 0 and O5. if the concentration of any point Q, LPQ = 4. The two plane angle O5 - 18 grapefruit size is:Hard and meticulous work, even though the proposition is in the branch of the propositionIt has made
39、great efforts in such aspects as learning, rationality and preciseness,However, due to the limitations of the provinces and municipalities in their own research, funding and other factors, missing teachers scatteredThe phenomenon still occur. The definition of proposition errors is a broad concept,
40、including the answer is debatable, the stem itself problems, and biased questions in design of project design technologyQuestions and difficulties, etc., in recent years, this paper attempts to test the local college entrance examinationThe first answer is 9. Later, 0, the answer was changed to: gre
41、ater than or equal to 9. In fact, the former is wrong, O, and the latter is not appropriate in terms of preciseness. The author believes that the accurate answer should be: 9. 10 o,. An angle in the interior! Its narrative 8 andThe way of mistakes, misleading candidates. Note analysis as follows: ex
42、po-plastThe phenomenon of errors in some propositions in the volume is analyzed as an exampleThe attention of the proposition and the teacher avoids or reduces such errors1, in recent years, the college entrance examination proposition error case11, the proposition is not comprehensive. It leads to an open answerOne