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今年新课程卷的高考试题,考生普遍反映选择题较难,用时较多,影响了后面答题时间.事实上,今年的选择题仍以能力立意为目标,以增大思维量为特色.下面介绍其速解策略. (以下是按试卷题序,题目参照高考数学(9)代点相减法:设双曲线方程为x2/a2-y2/b2=1,M(x1,y1)N(x2,y2),中点为(x0,y0),将M、N坐标代入方程相减得,y0/x0×kAB=b2/a2.而x0=-2/3(?)y0=-2/3-1=-5/3,故5/2×1=b2/a2.又a2+b2=7,可解得a2=2,b2=5.故选(D).(10)排除法:结合图形知当tanθ=1/2时.易知P4一定是AB中点,即x4=1,故tanθ=1/2不合要求.观察排除(A)、(B)、(D),故选(C). (11)直接法: 原式= 选(B). (12)构造法:正四面体的6条棱可看作一正方体的6条面对角线,而球的直径就是正方体的体对角线.设正方体棱长为a,则故所以选(A).
In this year’s new test papers, students’ test questions generally show that multiple choice questions are more difficult and time-consuming, affecting the time for subsequent questions. In fact, this year’s multiple-choice questions are still based on competency, and they are characterized by increased thinking. The quick solution strategy. (The following is the order of questions according to the test paper, the title refers to the college entrance examination mathematics (9) Substitution subtraction method: set the hyperbolic equation to x2/a2-y2/b2=1, M(x1,y1)N(x2, Y2), the midpoint is (x0, y0). Substitute the M and N coordinates into the equation, y0/x0×kAB=b2/a2. And x0=-2/3(?)y0=-2/3- 1=-5/3, so 5/2×1=b2/a2. and a2+b2=7, solvable a2=2, b2=5. Therefore, (D). (10) Exclusion method: Combine graphics When tan θ = 1/2, it is easy to know that P4 must be the midpoint of AB, that is, x4 = 1, so tan θ = 1/2 is not satisfactory. Observe the exclusion (A), (B), (D), so choose (C (11) Direct method: Original = Selection (B). (12) Construction method: The six edges of a regular tetrahedron can be seen as a facet of six cubes, and the diameter of the ball is the cube body. Diagonal. Set the cube to a, so choose (A).