2017年福州一中面向福州七县、平潭综合实验区乡镇和农村地区（“追梦计划”）招生考试数学与逻辑参考答案一、选择题（本大题共10小题，每小题4分，共40分）题号12345678910答案CBDCBACCAB二、填空题（本大题共5小题，每小题4分，共20分）5x2y1011．12．x52x5y813．132333435363212114．44315．0n3三、解答题（本大题共7小题，满分90分）16.本小题主要考查实数的运算、代数式的化简等基础知识，考查代数运算能力、化简能力，分类与整合思想等．满分12分．3解：（Ⅰ）原式=13316+8„„„„„„„„5分2=8„„„„„„„„„„„„„„6分x22x4x2（Ⅱ）原式„„„„„„„„„„„„„„8分x2xx1x22xx1„„„„„„„„„„9分x2x2x2x1=.„„„„„„„„„„„„„„11分x212当x时，原式„„„„„„„„„„„12分23.17.本小题主要考查圆的几何性质、等腰三角形的判定及性质等基础知识，考查分析问题、解决问题的能力，考查演绎论证及度量计算的逻辑思想等．满分12分．追梦计划数学与逻辑答案证明：（Ⅰ）∵四边形ABED为⊙O的圆内接四边形BADE180„„„„„„„„„„„„„„2分又∵CDEADE180BCDE„„„„„„„„„„„„„„3分∵ABACBC„„„„„„„„„„„„„„4分CCDE„„„„„„„„„„„„„„5分CDE为等腰三角形„„„„„„„„„„„„„„6分（Ⅱ）法一：连接AE，∵⊙O的直径为ABAEB90AEBC...............................7分∵ABAC1CEBC4.........................................8分2由(Ⅰ)知BCEDC，CCABC∽EDCBCAC...........................................10分DCECBCCE32AC.................................11分DC3∵ABAC16∴⊙O的半径为.„„„„„„„„„„„„„„12分3法二：连接AE，过点E作EFCD，垂足为FCDECD由（Ⅰ）知是以为底边的等腰三角形13CFCD„„„„„„7分22∵⊙O的直径为ABAEB90„„„„„„„„8分∵ABACBECE4„„„„„„„9分∵BC，AEBEFC∴EFC∽AEB，„„„„„„„„„„„10分FCCE∴„„„„„„„„„„„„„„11分BEAB追梦计划数学与逻辑答案CEBE4432∴ABFC33216∴⊙O的半径为.„„„„„„„„„„„„„„12分318.本题考察反比例函数图像及性质、一次函数解析式求解问题,及求平面四边形面积问题,涉及对称与割补思想方法.满分12分．解：（Ⅰ）过点C分别作CEAO于点E，C(m,n)tanCOA2n2m,设点，∵..................................1分∵CB//OAyn,Bn∵D为AE的中点，y,..............................................2分D2C,D又在反比例函数图象上，mnxyk,x2m,..............................................4分DDD∵x2,m1,n2,.............................................5分Bkmn2.2所以，反比例函数的解析式为y............................................6分x（Ⅱ）由（Ⅰ）得C(1,2),D(2,1)，SSS法一：......................9分四边形OCDAAOCACD1152211..............12分222法二：SSS四边形OCDA四边形OABCBCDSSS...............9分COE矩形ABCEB