高二数学国际班试卷1

高一年级 数学 第 1 页 共 4 页 20132013 20142014 学年第一学期期末考试试卷学年第一学期期末考试试卷 高二国际班高二国际班 数学数学 命题人 王瑞命题人 王瑞 1 Given three points find the equation 2 1 A 4 3 B 6 3 C of the perpendicular bisector of a AB b BC Hence find the coordinates of the point equidistant from A B and C 10 2 Given that 2 2 1 4 A find the inverse matrix of A and then use your answer to solve the simultaneous equations 10 11 2 22 11 44 yx yx 3 The line intersects the curve at point 42 xy4 2 xy and Find AB a the coordinates of and 4 AB b the length of AB 4 4 a Express in partial fractions 6 2 72 4 2 x xx b Factorise the cubic polynomial 472 23 xxxxf Hence solve the equation 8 0 xf 学校 班级 姓名 学号 A 密 封 线 内 请 不 要 答 题 高一年级 数学 第 2 页 共 4 页 5 The coefficient of in the expansion of is 70 3 x 56 2 axx a Find the value of the positive constant 8 a b Hence calculate the coefficient of in the expansion of 2 x 6 56 2 axx 6 The function are constants baxxxf 3 bandawhere is exactly divisible by Given that leaves a 3 x xf remainder of 56 when divided by 4 x a find the value of and of 7 ab b determine showing all necessary working the number of real roots of the equation 8 0 xf 7 a Calculate the range of values of for which x 4 xxx4535 2 b Calculate the range of values of for which c for all real values of 7 463 2 cxx x c Find the values of the equationfor which p has 10 ppxx 8 2 1 coincident roots 2 distinct real roots 3 one positive root and one negative root 高一年级 数学 第 3 页 共 4 页 8 a Two variables are related by the equation yx and Draw the graph of 6 yxxy52 2 x y yagainst 2 b Two variables are related by the equation yx and 2 3 5xy Show that 6 5lglg 2 3 lg xy 9 a Given that and that yx 41282 2ln240ln 4ln yx calculate the value of x and of y 6 b Solve the equations 10 1 2 52lg 1lg 21lg 2 xxx yy 53 2 c If find 6 310log6log2log 222 kk d Solve the simultaneous equations 8 8133 248 12 xy xy 学校 班级 姓名 学号 A 密 封 线 内 请 不 要 答 题 高一年级 数学 第 4 页 共 4 页 10 The diagram below shows lines intersecting at 21 and LL Line has equation and has equationA 1 L484 xy 2 L The point is the midpoint of The line 4043 xyMOA intersects the y axis at and the line intersects 1 LB 2 L the x a