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1、学校 班级 姓名 学号 A密 封 线 内 请 不 要 答 题20132014学年第一学期期末考试试卷高二国际班 数学 命题人：王瑞1、Given three points , find the equation of the perpendicular bisector of (a) AB , (b) BC. Hence, find the coordinates of the point equidistant from A,B and C. 102、Given that ，find the inverse matrix of A，and then use your answer to so
2、lve the simultaneous equations： 10 3、The line intersects the curve at point and . Find (a) the coordinates of and . 4(b) the length of AB. 44、(a) Express in partial fractions. 6 (b) Factorise the cubic polynomial . Hence solve the equation . 85、The coefficient of in the expansion of is 70, (a) Find
3、the value of the positive constant ， 8 (b) Hence calculate the coefficient of in the expansion of . 66、The function ,are constants,is exactly divisible by . Given that leaves a remainder of 56 when divided by ,(a) find the value of and of , 7(b) determine, showing all necessary working, the number o
4、f real roots of the equation . 87、(a) Calculate the range of values of . 4 (b)Calculate the range of values of for all real values of . 7 (c)Find the values of the equation has: 10 (1) coincident roots. (2) distinct real roots. (3) one positive root and one negative root.学校 班级 姓名 学号 A密 封 线 内 请 不 要 答
5、 题8、(a) Two variables are related by the equation ,Draw the graph of . 6 (b) Two variables are related by the equation . Show that . 69、(a) Given that and that , calculate the value of x and of y. 6(b)Solve the equations: 10 (1) (2) (c)If find 6(d)Solve the simultaneous equations 810、The diagram below shows lines intersecting at .Line has equation and has equation. The point is the midpoint of .The lineintersects the y-axis at and the line intersects the x-axis at .(a) Show that angle is , 8(b) Find the ratio of the area of triangle to the area of triangle . 8
