航空类应用数学复习试卷英文版.doc

航空应用数学期末复习试卷1.Translation into Chinese ()(1) In any triangle, the length of any side is less than the sum of the lengths of the other two sides. (2) In any isosceles triangle, the angles opposite the isometric sides are isometric. (3) In any right triangle, the acute angles are complementary. (4) In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. (5) The segment joining the midpoints of the non-parallel sides of a trapezoid is parallel to the bases and its length is one-half the sum of the lengths of the bases. (6) Three non-collinear points determine one and only one circle. (7) In a circle, the measure of the central angle is equal to the degree measure of its intercepted arc. (8) The diagonals of a parallelogram bisect each other. (9) If two sides and the contained angle of one triangle and the two corresponding sides and contained angle of another triangle are isometric, then the triangles are isometric. (10) If the lengths of two sides of one triangle are proportional to the lengths of two sides of another triangle and the contained angles are isometric, then the triangles are similar. 2.Multiple choice ()(1) In Rectangular Plane Coordinate System and , ，determine the coordinate of the point C.（ ）（A） （B） （C） （D） (2) what is the condition between “” and “” （ ）（A）Unnecessary and sufficient condition（B）Need not sufficient condition（C）Sufficient and Necessary Condition （D）Neither fully nor necessary condition(3) The “” is the sum of the n terms of a sequence, if “”, determine “”（ ）（A） （B） （C） （D）(4) If the asymptote of a hyperbola equal to another asymptote of a hyperbola “”, and they through the point , determine the hyperbolic equation.（ ）（A） （B） （C） （D） or (5) The directrix of papabola is the tangent of the circle . Determine the value of p.（ ）（A） （B） （C） （D）3.Fill in the blank () (1) If vector , and ，determine the value of y (2) If a line through the point and the measure of the angle of inclination is ，determine the line equation (3) If the radius of a circle is ，determine the centre coordinates (4) If elliptic equation is,determine the value of (5) In arithmetic sequence , determine the value of 4.Calculation ()(1) In arithmetic sequence , the common difference , and are the roots of the equation .determine The pattern for the nth term of the sequence (2) Determine the shortest distance from the point of the parabola to the straight line ,and determine the coordinates of this point.(3) If coordinates of the points and ,determine the line equation that through the point A and B. Determine the perpendicular bisector equation of segment AB.4. In trapezoidal ABCD，ABCD，BCD=90,AB=1，BC=2，tanADC=2.(1) Prove DC=BC.(2) If the point E is in the trapezoidal and the point FIs out of it,EDC=FBC，DE=BF，infer the shape of ECF.(3) In condition（2）,if BE：CE=1：2，BEC=135，determine sinBFE.5AB is the diameter of O ，joining AD、BD、OC、OD，OD5（1）If ，determine the length of CD；（2）If ADO：EDO4：1，determine the area of sector OAC.Calculation in English（）1. In the diagram,O is the centre of the circle,and AB and AC are tangent segments.Determine the lengths of AC and AO.2. In the diagram,O is the centre of t