《剑桥模拟试题剑桥国际高中入学.pdf》由会员分享，可在线阅读，更多相关《剑桥模拟试题剑桥国际高中入学.pdf（2页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、 M o d e l T e s t f o r C a m b r i d g e I n t e r n a t i o n a l S c h o o l Solve the following questions comprehensively.1.Three unit circles are arranged so that each touches the other two.Find the radii of the two circles which touch all three.2.Find all real numbers x such that x+1=|x+3|-|x
2、-1|.3.(1)Given x=(1+1/n)n,y=(1+1/n)n+1,show that xy=yx.(2)Show that 12-22+32-42+.+(-1)n+1n2=(-1)n+1(1+2+.+n).4.All coefficients of the polynomial p(x)are non-negative and none exceed p(0).If p(x)has degree n,show that the coefficient of xn+1 in p(x)2 is at most p(1)2/2.5.What is the maximum possible
3、 value for the sum of the absolute values of the differences between each pair of n non-negative real numbers which do not exceed 1?6.AB is a diameter of a circle.X is a point on the circle other than the midpoint of the arc AB.BX meets the tangent at A at P,and AX meets the tangent at B at Q.Show t
4、hat the line PQ,the tangent at X and the line AB are concurrent.7.Four points on a circle divide it into four arcs.The four midpoints form a quadrilateral.Show that its diagonals are perpendicular.8.Find the smallest positive integer b for which 7+7b+7b2 is a fourth power.9.Show that there are no positive integers m,n such that 4m(m+1)=n(n+1).10.ABCD is a convex quadrilateral with area 1.The lines AD,BC meet at X.The midpoints of the diagonals AC and BD are Y and Z.Find the area of the triangle XYZ.