山西省临汾一中、忻州一中、康杰中学等五校2017届高三第五次联考理科综合化学试题
山西省临汾一中、忻州一中、长治二中等五校2017届高三上学期第五次联考文数试题 Word版含答案
2016-2017年度高三第五次联合考试（期末）数学试卷（理科）考生注意：1.本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，共150分，考试时间120分钟．2、请将各题答案填在试卷后面的答题卡上．3、本试卷主要考试内容：必修一、三，必修五第三章不等式（不含线性规划）．第Ⅰ卷（共60分）一、选择题：本大题共12个小题,每小题5分,共60分.在每小题给出的四个选项中，只有一项是符合题目要求的.1.已知集合2{1,0,1,2,3,4},{|16,}A B x x x N =-=<∈，则A B 等于（ ） A ．{1,0,1,2,3}- B ．{0,1,2,3,4} C ．{1,2,3} D ．{0,1,2,3} 2. 复数21ii++的共轭复数z 在复平面内对应的点位于（ ） A ．第一象限 B ．第二象限 C ．第三象限 D ．第四象限 3.变量,x y 之间的一组相关数据如下表所示：若,x y 之间的线性回归方程为ˆˆ12.28ybx =+，则ˆb 值为（ ） A ．0.92- B ．0.94- C ．0.96- D ．0.98-4.在平行四边形ABCD 中，3,4AB AD ==，则AC DB ⋅等于（ ）A ． 7-B ．1C ．7D ．255.在我刚明代数学家吴敬所著的《九章算术比类大全》中，有一道数学命题叫“宝塔装灯”，内容为“远望魏巍塔七层，红灯点点倍加增；共灯三百八十一，请问顶层几盏灯？”（“倍加增”指灯的数量从塔的顶层到底层按公比为2的等比数列递增），根据此诗，可以得出塔的顶层和底层共有（ ）A ．3盏灯B ．192盏灯C ．195盏灯D ．200盏灯6.执行如图所示的程序框图，若输出的8k =，则输入的k 为（ ）A ．0B ．1C ．2D ．37.某几何体的三视图如图所示，则该几何体的表面积为（ ）A ．1)π++B ．1)2π++C ．1)π-D ．1) 8.将函数cos(2)3y x π=+的图象向左平移6π个单位后，得到()f x 的图象，则（ ）A ．()sin 2f x x =-B ．()f x 的图象关于3x π=-对称C ．71()32f π= D ．()f x 的图象关于(,0)12π对称 8.已知奇函数()f x 满足()()2f x f x -=，当01x <<时，()2xf x =，则2(log 9)f 的值为（ ）A ．9B ．19-C ．169-D ．16910.已知(,2)B m b 是双曲线22221(0,0)x y a b a b-=>>的右支上一点，A 为右顶点，O 为坐标原点，若60AOB ∠= ，则该双曲线的渐近线的方程为（ ）A．y = B．y x = C．y x = D．y x = 11. 已知三棱锥A BCD -内接与球O，且BC BD CD ===A BCD -体积的最大值为O 的表面积为（ ） A ．16π B ．25π C ．36π D ．64π12.已知定义在R 上的偶函数()f x 在[0,)+∞上递减，若不等式2(ln 1)(ln 1)f ax x f ax x -+++--()31f ≥对[]1,3x ∈恒成立，则实数a 的取值范围是（ ）A ．[]2,eB ．1[,)e +∞ C ．1[,]e e D ．12ln 3[,]3e +第Ⅱ卷（共90分）二、填空题（每题5分，满分20分，将答案填在答题纸上）13.抛物线210x y =- ．14.若,x y 满足约束条件28390,0x y x y x y +≤⎧⎪+≤⎨⎪≥≥⎩，则4x y +的最大值为 ．15.若(0,)2πα∈，且cos 2)4παα=+，则tan α= ． 16.已知函数()f x 满足2(1)41f x x x +=--+，函数()()4,4,f x x mg x x x m -≤⎧=⎨->⎩有两个零点，则m 的取值范围为 ．三、解答题 （本大题共6小题，共70分.解答应写出文字说明、证明过程或演算步骤.）17. （本小题满分12分）在ABC ∆中，角,,A B C 所对的边分别为,,a b c cos (2)cos A b C =-． （1）求角C ；（2）若,6A ABC π=∆D 为AB 的中点，求sin BCD ∠．18. （本小题满分12分）为调查了解某高等院校毕业生参加工作后，从事对工作与大学所学专业是否专业对口，该校随机调查了80位该校2015年毕业的大学生，得到具体数据如下表：（1）能否在犯错误的概率不超过5%的前提下，认为“毕业生从事的工作与大学所学专业对口与性别有关？”参考公式：22(),()()()()n ad bc K n a b c d a b c d a c b d -==+++++++ 附表：（2）求这80位毕业生从事的工作与大学所学专业对口的概率，并估计该校近3年毕业的2000名大学生总从事的工作与大学所学专业对口的人数；（3）若从工作与所学专业不对口的15人中选出男生甲、乙，女生对丙、丁，让他们两两进行一次10分钟的职业交流，该校宣传部对每次交流都一一进行视频记录，然后随机选取一次交流视频上传到学校的网站，试求选取的视频恰为异性交流视频的概率． 19. （本小题满分12分）已知等差数列{}n a 的公差0d >，且163411,12a a a a ⋅=+=． （1）求数列{}n a 的通项公式；（2）求数列1122n n n a a ++-⎧⎫⎨⎬⎩⎭的前n 项和n T ． 20. （本小题满分12分）在四棱锥P ABCD -中，PA ⊥平面ABCD ，底面ABCD 为矩形，点,,,E F M S 分别为棱,,PB AD,AB CD 的中点，G 为线段EM 的中点，且24,PA AB AD N ===为SM 上一点，且//NG 平面CEF（1）确定N 的位置，并求线段NG 的长；（2）平面CEF 与PA 交于点K ，求三棱锥B CKN -的体积． 21. （本小题满分12分）已知a R ∈，函数()()()32,(3)f x x ax ax a g x f x a x =-++=+-．（1）求证：曲线()y f x =在点(1,(1))f 处的切线过点(2,4)；（2）若()1g 是()g x 在区间(0,3]上的极大值，但不是最大值，求实数a 的取值范围． 22. （本小题满分12分）设点F 为椭圆22:1(0)43x y C m m m+=>的左焦点，直线y x =被椭圆C 截得弦长为． （1）求椭圆C 的方程；（2）圆222:(((0)P x y r r +=>与椭圆C 交于,A B 两点，M 为线段AB 上任意一点，直线FM 交椭圆C 于,P Q 两点AB 为圆P 的直径，且直线FM 的斜率大于1，求PF QF ⋅的取值范围．试卷答案一、选择题1-5:DACAC 6-10:CABCC 11、B 12：D二、填空题13.25 14.16 15. 1316.[2,0)[4,)-+∞ 三、解答题17.解：（1cos (2)cos A b C =-，得2cos cos )b C cdosA a C =+， 由正弦定理可得2sin cos cos sin cos ))B C C A A C A C B =+=+=，因为sin 0B ≠，所以cos C =，因为0C π<<， 所以6C π=． 5分（2）因为6A π=，故ABC ∆为等腰三角形，且顶角23B π=， 6分故21sin 2ABCS a B ∆===， 7分所以2a =，在DBC ∆中，由余弦定理得2222cos 7CD DB BC DB BC B =+-⋅=，所以CD =在DBC ∆中，由正弦定理可得sin sin CD DBB BCD =∠1sin BCD=∠，所以sin BCD ∠=． 12分 18.解：（1）根据列联表中的数据，得到2K 的观测值为2280(3053510)80 2.051 3.8414040651539K ⨯-⨯==≈<⨯⨯⨯，故不能在犯错误的概率不超过5%的前提下，认为“毕业生从事的工作与大学所学专业对口与性别有关”．5分（2）这80为毕业生从事的工作与大学所学专业的概率为65138016=，6分由此估计该校近3年毕业的2000大学生中从事的工作与大学所学专业对口的人数为132000162516⨯=， 7分 （3）两两进行一次10分钟的职业交流的所有结果为（甲，乙），（甲，丙），（甲，丁），（乙，丙），（乙，丁），（丙，丁）共有6个基本事件， 10分其中异性交流的有4个基本事件，故所有概率为4263P ==． 12分 19. 解：（1）因为163412a a a a +=+=， 1分 所以16,a a 是方程212110x x -+=两根，且16a a <， 2分解得161,11a a ==，所以61510a a d -==，即2d =， 5分 所以21n a n =-． 6分（2）（方法一）因为11112222n n n nn n n a a a a ++++-=-， 8分所以3112121213211112112222222222n n n n n n n n a a a a a a a a n T ++++++=-+-+-=-=- ． 12分（方法二）因为112123222n n n n a a n ++--=-⨯， 7分所以23111323()22222n nn T --=-⨯++++ ， 所以23411111323()222222n n n T +--=-⨯++++ ， 8分所以21234111111122223112322()1222222242212n n n n n n n T +++----=-⨯++++-=-+⨯- ， 所以121122n n n T ++=- 12分20.解：（1）设CF 与SM 交于点O ，连接OE ，则N 为OM 的中点， 1分 证明如下：因为//NG 平面CEF ，且平面CEF 平面MOE EO =， 所以//NG OE ，又G 为线段EM 的中点， 则N 为OM 的中点， 3分因为E 为棱PB 的中点，所以//EM PA ，又PA ⊥底面ABCD ， 所以EM ⊥底面ABCD ， 4分则EM OM ⊥，因为12322OM +==，2EM =,所以1524NG OE ===， 6分（2）延长CF 交BA 的延长线于点Q ，由//AF BC ，且2BC AF =，得A 为QB 的中点， 7分连接EQ ，则但K 为PA 与QE 的交点， 8分易得AKQ MKQ ∆∆ ，则42423AK QA EM QM ===+，所以2433AK EM ==，10分因为BCN ∆的面积为12222⨯⨯=， 所以18239B CKN B CKNV V AK --==⨯⨯=. 12分 21.(1)证明：因为()232f x x ax a '=-+，所以()13f a '=-， 1分因为()11f a =+，所以曲线()y f x =在点(1,(1))f 处的切线方程为(1)(3)(1)y a a x -+=--， 2分即(2)42a x x y -=--，令2x =，则4y =，故曲线曲线()y f x =在点(1,(1))f 处的切线过点(2,4)； 4分 （2）解：()()233223(1)[3(23)]g x f x a x ax a x x a ''=+-=-+-=---，令()0g x '=得1x =或233a x -=， 6分 因为()1g 是()g x 在区间(0,3]上的极大值，所以2313a ->，所以3a >，7分令()0g x '>，得1x <或()23,3a x g x ->递增；令()0g x '<，得()231,3a x g x -<<递减，因为()1g 不是()g x 在区间(0,3]上最大值，所以()g x 在区间(0,3]上的最大值为()3182g a =-， 10分 所以()3182(1)22g a g a =->=-，所以5a <，又3a >，所以35a <<． 12分22. 解：（1）由22143y xx ym m=⎧⎪⎨+=⎪⎩，得22127m x y ==，故==，解得1m =，故椭圆C 的方程为22143x y +=． 3分（2）设1122(,),(,)A x y B x y ，则1212x x y y ⎧+=⎪⎪⎨⎪+=⎪⎩又22112222143143x y x y ⎧+=⎪⎪⎨⎪+=⎪⎩， 4分 所以12121212()()()()043x x x x y y y y +-+-+=，则1212()()0x x y y ---=，故12121AB y y k x x -==-，则直线AB的方程为y x =+，即y x =C的方程并整理得270x +=，则120,x x ==，故直线FM的斜率)k ∈+∞， 7分 设:(1)FM y k x =+，由22(1)143y k x x y =+⎧⎪⎨+=⎪⎩，得2222(34)84120k x k x k +++-=，设3344(,),(,)P x y Q x y ，则有223434228412,3434k k x x x x k k --+==++， 8分1+，所以22223434224128(1)()1(1)13434k k PF QF k x x x x k k k-⋅=++++=+-+++ 222991(1)(1)34434k k k=+=+++， 10分因为k ≥299112(1)44345k <+≤+， 即PF QF ⋅的取值范围是912(,]45． 12分11。
山西省临汾一中、忻州一中、长治二中等五校2017届高三上学期第三次五校联考化学试题
可能用到的相对原子质量：H1 Li 7 C 12 N 14 O 16 Mg 24 S 32 Cu 64第I卷(选择题共42分)―、选择题(本题包括14小题,每小题3分，共42分。
每小题只有一个选项符合题意) 1．下列关于化学与环境的叙述中的错误是A．燃煤时鼓入过量的空气可以减少酸雨的产生B．利用汽车尾气催化装置可将尾气中的NO和CO转化为无害气体C．“煤改气”、“煤改电”等工程有利于减少雾霾D．工业废气排放之前必须回收处理以防污染大气【答案】A【考点定位】考查空气污染【名师点晴】本考点考查了空气的污染、危害及其措施，环保问题已经引起了全球的重视，本考点的基础性比较强，主要出现在选择题和填空题中。
空气污染的途径主要有两个：有害气体和粉尘．有害气体主要有一氧化碳、二氧化硫、二氧化氮等气体；粉尘主要指一些固体小颗粒．雾霾是一种大气污染现象，是由固体小颗粒造成的污染。
2. 下列化学用语书写正确的是A．镁离子的结构示意图:B．苯甲酸乙酯的结构简式：C．CO2的电子式：D ．中子数为18的氯原子：Cl 1817 【答案】B 【解析】试题分析：A ．镁离子的结构示意图为，故A 错误；B ．苯甲酸乙酯的结构简式为，故B 正确；C ．CO 2的电子式为，故C 错误；D ．中子数为18的氯原子的质量数为35，故D 错误；故选B 。
【考点定位】考查化学用语的正误判断【名师点晴】解决这类问题过程中需要重点关注的有：①书写电子式时应特别注意如下几个方面：阴离子及多核阳离子均要加“”并注明电荷，书写共价化合物电子式时，不得使用“”，没有成键的价电子也要写出来。
②书写结构式、结构简式时首先要明确原子间结合顺序(如HClO 应是H —O —Cl ，而不是H —Cl —O)，其次是书写结构简式时，碳碳双键、碳碳三键应该写出来。
③比例模型、球棍模型要能体现原子的相对大小及分子的空间结构。
3． 同温同压下，分别用等质量的H 2、CO 、CO 2、NH 3四种气体吹起四个气球，其中由H 2吹起的是【答案】C【考点定位】考查阿伏伽德罗定律及其推论【名师点晴】本题考查了阿伏伽德罗定律及其推论，灵活运用公式是解本题关键。
山西省临汾一中、忻州一中、康杰中学等五校2017届高三第五次联考理综化学试题含答案
7、化学与生活、社会发展息息相关，下列说法正确的是A。
聚乙烯和聚氯乙稀的单体相同B.自来水中加入漂白粉与加入硫酸铝的作用相同C.洗涤剂除油污的原理与热碱液除油污的原理相同D。
食品包装内放置生石灰与放置硅胶的作用相同8、设N A为阿伏加德罗常数的值,下列说法中正确的是A。
由6 g CaCO3和5 g KHCO3组成的混合物中含有的碳原子数为0。
11N AB.42 g C3H6中含有的共用电子对数目为8N AC.1 L0.01 mol • L-1 KAl(SO4)2溶液中含有的阳离子数为0。
02N AD.标准状况下，22.4 L氯气与56 g铁充分反应，转移的电子数为3N A9、下列关于有机物的说法正确的是A。
2—甲基丁烷也称异丁烷B.乙醇、糖类和蛋白质都是人体必需的营养物质C。
能发生加成反应和取代反应D。
合成纤维与光导纤维都属于有机高分子材料10、下列实验操作和现象对应的结论错误的是11、直接尿素电池的结构如图所示，下列说法不正确的是A。
碳电极采用多孔并用触媒层可加快反应速率B.电池工作时,化学能转化为电能C.Y极的电极反应式为H2NCONH2+H2O-6e—=N2↑+CO2+6H+ D。
电池工作时,H+向Y极区迁移，Y极周围溶液的pH减小12、常温下，K a(CH3COOH)=K b（NH3• H2O)=1.75×10-5,下列说法正确的是A.0.2mol·L—1的醋酸与0。
1mol·L-1的氢氧化钠溶液等体积混合，所得溶液中:c(CH3COO—）+c（OH-）= C（CH3COOH）+C(H+) B。
pH=3的盐酸与pH=11的氨水到体积混合，所得溶液中C(NH3·H2O）>C（NH4+）〉C（Cl-）C.用0。
1mol·L—1的盐酸滴定0.1mol·L-1的氨水时，可用酚酞作指示剂D.pH=3的醋酸与pH=11的氨水到体积混合，所得溶液中有水电离出的C（H+）=1×10-7mol·L-113、短周期元素W、X、Y、Z的原子序数依次增大，其中Z的原子序数为W的2倍。
【山西省临汾一中、忻州一中、康杰中学等五校】2017届高三第五次联考文综政治试卷(附答案)
山西省临汾一中、忻州一中、康杰中学等五校2017届高三第五次联考文综政治试卷本卷共35小题，每小题4分，共140分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
12．国务院办公厅2016年11月印发的《关于进一步扩大旅游文化体育健康养老教育培训等领域消费的意见》提出，要加强消费基础设施建设、畅通流通网络、健全标准规范、创新监管体系、强化线上线下消费者权益保护等。
文件所提要求有利于（）①提升居民消费品质②引导居民消费观念③增强居民消费信心④优化居民消费结构A．①③B．①④C．②③D．②④13．在经济生活中，一种经济现象的出现往往会引起另一现象的产生。
不考虑其他因素，下列表述能体现这一关系的是（）①国家下调增值税起征点，导致小微企业成本下降②美国联邦储备委员会加息，导致我国资金更多地流向美国③国有企业加大重组力度，导致资本周转加快④国家积极发展跨境电子商务，推动了企业国际竞争力的提升A．①②B．①③C．②④D．③④14．甲商品和乙商品是互补品，如生产甲商品的社会劳动生产率提高，使乙商品的需求量发生了变化。
假定其他条件不变，下图中（P为价格，Q为需求量）能正确反映乙商品需求量从D1向D2变化的是（）A．①③B．①④C．②③D．②④15．《关于实行以增加知识价值为导向分配政策的若干意见》提出，构建基本工资、绩效工资和科技成果转化性收入的三元薪酬体系，使科研人员的收入与岗位的责任、工作的业绩和实际的贡献紧密联系，在具体的措施上突出了推动形成体现知识价值的收入分配机制。
下列关于该文件的作用传导正确的是（）①实行产权激励——调动科研人员积极性——推动科技成果转化——激发经济发展内生动力②实行股权、期权激励——落实按劳分配政策——调整收入分配格局——实现收入分配公平③实施股权激励——生产要素按贡献参与分配——激发科研人员创造性——提高自主创新能力④实行项目收益分红、岗位分红——完善分配机制——提高科研人员收入——缩小收入分配差距A．①②B．①③C．②④D．③④16．有评论员文章指出，国家凝聚力的核心要素是人民与政府之间公信力与向心力的互动关系，而向心力又体现为人民对国家或政府的信任感、认同感和归属感。
物理卷·2017届山西省临汾一中、忻州一中、康杰中学等五校高三第五次联考
2016-2017年度第五次五校联考理科综合试卷物理部分（长治二中晋城一中康杰中学临汾一中忻州一中）二、选择题：本题共8小题，每小题6分。
在每小题给出的四个选项中，第14～17题只有一项符合题目要求，第18～21题有多项符合题目要求。
全部选对的得6分，选对但不全的得3分，有选错的得0分。
14.下列说法中正确的有（）A. α粒子的散射实验说明原子核具有复杂的结构B. 比结合能越大，原子核中核子结合得越牢固，原子核越稳定C. 只有光子具有波粒二象性，电子、质子等粒子不具有波粒二象性D. 原子核发生衰变时，不遵循能量守恒定律，但遵循动量守恒定律15.如图所示，A、B、C、D四个小物块放置在粗糙水平面上，小物块间由四根完全相同的轻橡皮绳相互连接，正好组成一个菱形，ABC=60°，整个系统保持静止状态。
已知A物块所受的摩擦力大小为30 N，则A物块所受的摩擦力大小为（）16.如图为所示，交流发电机通过理想变压器为负载电阻R供电，发电机线圈的面积为0.5㎡、匝数为100，匀强磁场的磁感应强度为0.2T，变压器原副线圈匝数比为10:1，负载电阻R的阻值为5Ω，其他电阻均忽略不计，若发电机的线圈以20rad/s的角速度匀速转动，则( )A.变压器原线圈两端的电压为200VB. 电阻R的电流为2AC. 线圈在图示位置时原线圈两端的电压为零，穿过线圈的磁通量最大D. 若将R 的阻值变为10Ω，则变压器原线圈中通过的电流减小17.2017年1月18日, 我国发射的世界首颗量子科学实验卫星“墨子号”圆满完成了4个月的在轨测试任务,正式交付用户单位使用,假设“墨子号”绕地球做匀速圆周运动,经过时间t (t 小于“墨子号”的运行周期),“墨子号”运行的弧长为s ,其余地心连线扫过的角度为θ(弧度),引力常量为G ,则 ( )A. “墨子号”的环绕周期为θs2B. “墨子号”的轨道半径为θπ2 C. 地球的质量为22t G s θ D. 地球的密度为2243Gtπθ 18.甲、乙两辆质量相同的汽车从同一点同时出发，沿同一方向行驶，它们的v-t 图象如图所示。
山西省临汾一中、忻州一中、康杰中学等五校高三第五次联考英语试卷有答案
山西省临汾一中、忻州一中、康杰中学等五校2017届高三第五次联考英语试卷第Ⅰ卷第一部分听力（共两节,满分30分）第一节（共5小题;每小题1.5分,满分7.5分）听下面5段对话.每段对话后有一个小题,从题中所给的A．B．C三个选项中选出最佳选项,并标在试卷的相应位置.听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题.每段对话仅读一遍.例:How much is the shirt? ________A．£19．15．B．£9．18．C．£9．15．1．Where does the conversation take place? ________A．In a hotel.B．In a clinic.C．In a library.2．When is the woman able to get her photos? ________A．Half an hour later.B．One hour later.C．Two hours later.3．Why doesn’t the woman buy the necklace? ________A．Because she doesn’t like itB．Because she thinks it is expensive.C．Because she considers it of low quality.4．What is the man probably? ________A．A taxi driver.B．A policeman.C．A train station worker.5．What does the man suggest? ________A．Booking a table.B．Meeting around 6100.C．Meeting inside the restaurant.第二节（共15小题;每小题1.5分,满分22.5分）听下面5段对话或独白.每段对话或独白后有几个小题,从题中所给的A．B．C三个选项中选出最佳选项,并标在试卷的相应位置.听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各小题将给出5秒钟的作答时间.每段对话或独白读两遍.听第6段材料,回答第6．7题.6．What is the man’s major? ________A．Finance.B．Business administration.C．English literature.7．What course did the man like best as a student? ________A．Project management.B．English literature.C．Computer engineering.听第7段材料,回答第8．9题.8．Why didn’t the woman go to school yesterday? ________A．Her throat hurt.B．She caught a cold.C．Her leg was broken.9．What does the man advise the woman to do at first? ________A．Have enough rest.B．Take another day off.C．Drink plenty of water.听第8段材料,回答第10至12题.10．How much does the four-week course cost? ________A．£l,000.B．£1,100.C．£1,200.11．Which course will the man choose? ________A．The one in July.B．The one in August.C．The one in September.12．What does the woman advise the man to do? ________A．Stay with a family.B．Send the college his picture.C．Write to the college with his information.听第9段材料,回答第13至16题.13．How does the woman find Hainan Island? ________A．It deserves visiting.B．It is sunny all year around.C．It is cool all year around.14．What is the Hainan’s average temperature in July? ________A．6℃ to 16℃.B．16℃ to 24℃.C．25℃ to 29℃.15．Which month is among the rainy seasons in Hainan? ________A．June.B．March.C．December.16．Which is famous for history? ________A．Yalong Bay National Holiday Resort.B．The Five Officials Memorial Temple.C．Nanshan Cultural and Tourist Zone.听第10段材料,回答第17至20题.17．When do people celebrate All Saints’ Day every year? ________A．On November 1．B．On October 30.C．On October 31．18．Who may like Halloween best? ________A．Children.B．Women.C．Adults.19．Which vegetable is the mark of Halloween? ________A．Tomato.B．Potato.C．Pumpkin.20．What do the adults give to the children? ________A．Fruit or candy.B．Treat-money or candy.C．Treat-money or vegetables.第二部分阅读理解（共两节,满分40分）第一节（共15小题;每小题2分,满分30分）阅读下列短文,从每题所给的四个选项（A.B.C和D）中,选出最佳选项.AAre you wishing for the days when your feed was filled with posts from friends you care about the most? The good news is that you can fix your Facebook News Feed to show more posts that interest you and fewer that do not. By taking just a few minutes to fix your feed, you may be able to enjoy Facebook again.●No need to unfriend anyone.Just set your feed to see what you want to see and hide what you do not want to see.See important friends firstFacebook lets you choose which friends’ posts show at the top of your News Feed. Maybe you have dear friends who do not post often, but you want to be sure you see their posts first.You can easily choose whose posts you want to see first by changing your News Feed settings.●Procedures: On the Facebook website tap the Down arrow in the upper right corner of the blue bar at the top of the screen. Then, choose “News Feed Preferences.” Then click on “List who to see first.” Choose the names of people whose posts you want to see at the top of your News Feed. The final step is to click “Don e” at the bottom. Block friends’ posts wit hout unfriending anyoneYou may be best friends with someone in real life but have no interest in their Facebook posts. Maybe they post angry messages or childish videos. Facebook lets you secretly block friends’ posts from your feed. No one will know you blocked them unless you tell them.●Procedures: The process is simple. Tap the Down arrow in the upper right comer of the blue bar at the top of the Facebook page. Then, choose “News Feed Preferences.” Next, choose “Unfollow people to hide their posts.” Then, mark the friends you want to unfollow. This will prevent their posts from appearing in your News Feed. When you finish blocking just tap “Done”.21．What does the text guide people to do? ________A．To update information on Facebook.B．To reset Facebook for receiving posts.C．To search for favourite posts on Facebook.D．To download an application for Facebook.22．How many steps docs it take to reset your favorite posts? ________A．3．B．4．C．5．D．6．23．Why do you want to block some of your friends’ posts? ________A．Because their posts may bother you.B．Because you are too busy to read them.C．Because they are not your best friends.D．Because you want to stay away from them.24．What will happen if you mark your friends as “Unfollo w”? ________A．They will not get in touch with you.R．You will make them angry with you.C．They will not see your posts on Facebook.D．Your News Feed will not show their posts.BFreda Bright says, “Only in opera do people die of love.” It’s true. You really can’t love somebody to death. I’ve known people to die from no love, but I’v e never known anyone to be loved to death. We just can’t love one another enough more.A heart-warming story tells of a woman who finally decided to ask her boss for a raise in salary. All day she felt nervous and apprehensive. Later in the afternoon she summoned the courage to approach her employer. To her delight, the boss agreed to a raise. The woman arrived home that evening to a beautiful table set with their best dishes. Candles were softly glowing. Her husband had come home early and prepared a festive meal. She wondered if someone from the office had tipped him off, or did he just somehow know that she would not get turned down? She found him in the kitchen and told him the good news. They embraced and kissed, then sat down to the wonderful meal. Next to her plate the woman found a beautifully lettered note. It read: “Congratulations, darling! I knew you’d get the raise! These things will tell you how much I love you.” Following the supper, her husband went into the kitchen to clean up. She noticed that a second card had fallen from his pocket. Picking it off the floor, she read: “Don’t worry about not getting the raise! You deserve it anyway! These things will tell you how much I love you.”Someone has said that the measure of love is when you love without measure. What this man feels for his wife is total acceptance and love, whether she succeeds or fails. His love celebrates her victories and soothes her wounds. He stands with her, no matter what life throws in their direction.25．When the woman saw all her husband had prepared, what was the first feeling of her? ________ A．Confusion.B．Sweetness.C．Excitement.D．Happiness.26．What is the meaning of the underlined part “tipped him off”? ________A．Scolded him.B．Informed him.C．Threatened him.D．Comforted him.27．What can we know about the author’s husband from the second paragraph? ________A．He likes cooking.B．He often writes to his wife.C．He is a careful and clever man.D．He had already known the result.CMany details in life appear to be neglected by us in a hurry urban life. Some think that our passion has been ironed out by tough life. Some people come to the sensation that they have already been numbed（麻木）by the fast-paced life Maybe all these contribute a little to the present situation, or maybe none. Actually, in the modem city, what we lack more and more desperately is a heart of gratefulness.Once a time, I began to lose my direction and become numb without too much affection in this material-flooding world. I was not sure whether the reason why I locked tightly my heart was to fear loneliness or to protect myself. Less and less emotion and smile, so someone said that I was awfully icy to others. Not until one day when I was stricken by a sense of gratitude did I totally change myself. Gratefulness touches deeply the tenderness of my heart. It is like the soft melody of “kiss the rain”, so tender, so emotional and so fascinating, leaving me out of all the worldly troubles.Yes, life needs gratefulness. Gratefulness is not only confined to love, but also to friend-ship, family bonds, mutual cherishing as well as constant missing each other. A tiny gratefulness can give us a lasting positive mood, which requires our consciousness and gratefulness. Then with a heart of gratefulness, everything turns out to be beautiful.Yes, God is fair to anyone. When he closes one of your doors, he will open another for you. Even though I just have a window, I can still embrace sunshine, fresh air, beautiful landscapes. Though the eyesight might be somewhat narrow, it is my world after all.Every drop in life and every silk of gratefulness direct me to my real heart and mind.28．According to the author in the paragraph 1, the reason why many details are neglected is that ________ A．we live a hurry urban lifeB．we lack a heart of gratefulnessC．our passion has been ironed outD．we have been numbed by the fast-paced life29．What’s the possible reason why the author lost his direction and became numb? ________A．He had no interest in others.B．His life was filled with fears.C．He feared loneliness or needed self-protect ion.D．He had too much affection in this material-flooding world.30．What is it that moved and changed the author? ________A．Smile.B．Melody.C．Friendship.D．Gratefulness.31．What can we learn about gratefulness according to the third paragraph? ________A．It requires consciousness.B．It should be cherished.C．It makes the world full of sunshine.D．It contains love, friendship and family bonds.DAs Canadians approach the ends of their career, they start to wonder how much they need to save to maintain their standard of living in retirement. This is not an easy question as many variables are unknown. The first is life expectancy.Life expectancy is one of the most misunderstood aspects of retirement income planning— yet, it is one of the most important factors. Most people assume that life expectancy is the same as lifespan. This is not correct. Instead t life expectancy is a medium number of years—such that 50 percent of a particular age group will die before this number of years, and the other 50 percent will die after this periodHow you save for retirement is also important. What you care about in retirement is how much income you have after tax and after inflation. You want to know what lifestyle you can maintain in retirement.If you saved for retirement only using registered retirement savings plan（RRSP）, you will need a larger account balance, as every dollar that you redeem from an RRSP is fully taxable while funds withdrawn from a tax-free savings account (TFSA) are free of tax. And if you were lucky enough to save funds outside these structures（non-registered investments, real estate, bank accounts and so on）, only the earnings on these funds are taxable.Government pension rights arc important in retirement income planning. Old Age Security（OAS）offers up to $ 569 a month and the Canada Pension Plan（CPP）gives a maximum of $ 1,065 a month. The average right for new beneficiaries is $640 a month.But let’s look at this from another po int of view. When you retire, one of the greatest risks that you have is running out of money. If you can maintain your lifestyle on your personal investment, then delaying the start of your CPP pension can be viewed as a version of longevity insurance.32．Why is it difficult to solve the question mentioned in paragraph 1? ________A．Because of people’s mind.B．Because of living standard.C．Because of people’s lifestyle.D．Because of changeable factors.33．Which of the following factors is the most important on saving for retirement? ________A．Life expectancy.B．The way to save.C．Personal investment.D．Government pension rights.34．How do people avoid risks after retirement according to the text? ________A．Keeping account balanced.B．Making a spending planning.C．Saving funds outside the mentioned structures.D．Maintaining personal investment and delaying CPP.35．What might be the best title for the passage? ________A．Canadians’ Pension Plan.B．Saving For Retirement.C．Extending Life Expectancy.D．Managing Personal Account.第二节（共5小题;每小题2分,满分10分）根据短文内容,从短文后的选项中选出能填入空白处的最佳选项.选项中有两项为多余选项.Cycling for Weight LossLike many aspects of health and fitness, weight loss is actually a combination of several factors. Any weight loss method really should influence all of these elements. 36Calorie Bum37 Depending on your speed, fitness level, landscape, and type of equipment, a 30- minute ride could bum about 320 calories.When losing weight, if you burn more calories than you eat, weight loss will result. Your body stores any calories you eat that you don’t immediately need as body fat. Generally, one pound of body fat contains about 3,500 calories. 38 To lose weight at a slow, steady pace, you need to bum about 500 more calories than you eat daily.Building MuscleIn truth, however, the real weight loss power of cycling doesn’t come from this initial caloric loss. In fact, compared to the 400-and-something calories that a comparable 30-minute run could burn, cycling leaves quite a bit to be desired. 39Because cycling challenges your muscles to handle a considerable amount of resistance repeatedly-something running does not do—so that ride will help you build more muscle fibers in your legs. 40 Therefore, developing your muscles via cycling will help you lose more weight in the long-term.A．Bicycling can help you burn calories.B．Cycling just happens to meet the factors perfectly.C．What makes cycling such an effective weight loss tool?D．Therefore, to lose one pound, you’re going to need to burn 3,500 calories.E．But cycling has one obvious advantage over running: muscular development.F．Combining bicycling with a calorie-controlled diet can help you reach your goalG．It’s reported that each pound of muscle increases your daily caloric burn by about 6 to 10 calories.第三部分语言知识运用（共两节,满分45分）第一节完形填空(共20小题;每小题1.5分,满分30分）阅读下面短文,从短文后各题所给的四个选项(A.B.C和D)中,选出可以填入空白处的最佳选项.Yesterday after school I took my boys through the drive thru (汽车餐厅)at McDonald’s. It was a 41 day and they wanted a nice cool treat. So I said yes. So off we went 42 I ordered, I remembered a promise I made to myself a year or two ago. The promise is that every 43 I drive through the drive thru I pay for the car behind me. I made this promise because I 44 the drive thru about 4 times a year. So it’s an 45 one to keep. And up until yesterday, I have stuck to 46 promise.However, as I drove around to pay the cashier the $ 6 for our 47 I really did not want to do it this time. I didn’t want to pay or offer to pay for the car 48 behind me. In my head I begun to 49 myself out of it. “It’s OK Nicole; you don’t have to”. “You haven’t much 50 this week”. “And what if it’s a $ 40 order or 51 !”That’s when the other voice stepped in. It’s a voice that is 52 my own, the wise voice, the voice I am 53 to listen out for and follow. It said, “This is 54 the time you need to do it! It isn’t 55 and only given when it suits you!”So I did it. 1 paid for the car behind. I asked the cashier to 56 the order of the car be-hind to my card, which 57 was only $2.95. Can you believe it? $ 2.95!Anyway, that isn’t the 58 The most important of all is that I 59 it. And to think, I almost didn’t. I almost 60 that $ 2.95 to myself!41．A．hot B．cold C．rainy D．pleasant42．A．Although B．Since C．If D．As43．A．time B．day C．month D．step44．A．care about B．dream of C．go through D．deal with 45．A．unnecessary B．easy C．awful D．unusual46．A．another B．his C．that D．each47．A．turn B．order C．preference D．duty48．A．pulling up B．breaking down C．calming down D．carrying on49．A．warn B．get C．force D．talk50．A．energy B．money C．chance D．determination51．A．less B．higher C．bigger D．more52．A．ever B．still C．never D．even53．A．fearing B．learning C．hesitating D．failing54．A．exactly B．merely C．likely D．probably 55．A．impossible B．powerful C．conditional D．shameful56．A．lend B．send C．bring D．add57．A．pitifully B．thankfully C．regretfully D．obviously58．A．reason B．result C．point D．amount59．A．did B．accepted C．refused D．ignored60．A．spent B．lost C．wasted D．kept第Ⅱ卷第三部分英语知识运用（共两节,满分45分）第四部分写作（共两节,满分35分）第一节短文改错（共10小题;每小题1分,满分10分）假定英语课上老师要求同桌之间交换修改作文,请你修改你同桌写的以下作文.文中共有10处语言错误,每句中最多有两处.每处错误仅涉及一个单词的增加、删除或修改.增加;在缺词处加一个漏字符号（∧）,并在其下面写出该加的词.删除:把多余的词用斜线（\）划掉.修改:在错的词下画一横线,并在该词下面写出修改后的词.注意:1．每处错误及其修改均仅限一词;2．只允许修改10处,多者（从第11处起）不计分.When talking about sport, I always feel very exciting, because I like sport so much. I love playing tennis, bat it is my favorite sport. One day that I came home after school, I turned on TV and watch a tennis match. At first, I was attracted by the two beautiful tennis player. When I watched the match for ten minutes I found it wonderful From now on, I star-ted to watch tennis matches. I have learned to play the tennis, and I often invite my friendsplay with me. My love to tennis are more than I could express. I am so luckily to have some friends who share the same interest with me.第二节书面表达（满分25分）假定你是李华,你的英国好友Lucy来信问你计划在大学学什么专业.就此请你用英语写封回信,主要内容包括: 1．你的专业选择;2．你选择该专业的理由;3．为此你打算怎么做.注意:1．词数100左右,2．可以适当增加细节,以使行文连贯;3．开头和结尾已为你写好,不计人总词数.Dear Lucy,I’m writing to tell you about the major I will choose in the university.____________________________________________________________________________________ ____________________________________________________________________________________________ Best wishes. I’m looking forward to your reply.Yours,Li Hua山西省临汾一中、忻州一中、康杰中学等五校2017届高三第五次联考英语试卷答案1~5．BCBAA 6~10．BAACC 11~15．BCACA 16~20．BAACB21~25．BCADA 26~30．BCBCD 31~35．CDADB 36~40．BADEG41~45．ADACB 46~50．CBADB 51~55．DCBAC 56~60．DBCAD 61．what62．certainly63．communication64．tracks65．were66．the67．friendly68．advise69．to do70．in71．exciting改成excited72．but改成and73．that改成when/after74．watch改成watched75．player改成players76．now改成then77．the tennis去掉the78．play前面加to79．are改成is80．luckily改成lucky81．Dear Lucy,I’m writing to tell you about the major I will choose in the university. I have decided to major in computer science. There are some reasons why I made such a decision. Firstly, with the development of society, computers are playing an important role in many aspects of our life Secondly, browsing the Internet is one of my hobbies, so I think I can study computer science well. Last but not least, being good at computer science may help me find a good job after graduating from college.I know there is a long way to go before I enter a college. So now I must devote myself to study and try mybest to get good grades in all subjects. If I can learn computer science as I wish, I will focus on it and study hard to develop some software.Best wishes I’m looking forward to your reply.Yours,Li Hua山西省临汾一中、忻州一中、康杰中学等五校2017届高三第五次联考英语试卷解析听力材料(Text 1)W: What’s the trouble, Mike?M: Well, doctor. It’s my eyes. I can’t see clearly.W: How long have you had the problem?M: Since last week, I think.(Tact 2)W: Could you please have these films developed?M: When would you want them back?W: Two hours later. Is that all right?M: Yes. Sure.(Text 3)W: Can you recommend something for an anniversary present?M: Yes, sure How about this natural pearl necklace?W: It’s too expensive. Do you have a cheaper one?(Text 4)M: Where to, madam?W: Central Station, please.M: OK.W: Sir, I’ve got to catch a train at 10: 30. Do you think I’ll make it?M: Yes. easily. It’s only five to ten.(Text 5)W: Well. a new restaurant has just opened on Silver Street. Would you like to go for a meal?M: I’d love to. Why don’t we book a table for 8 o’clock?W: Great. Let’s meet inside the restaurant around 8:00.M: OK. See you then. Bye.(Text 6)W: What is your major?M: My major is business administration I am especially interested in marketing.W: Have you received any degrees?M: Yes. First, I received my Bachelor’s degree in English literature, and then an MBA degree.W: What course did you like best?M: Project management. I was very interested in this course when I was a students and I think it’s very useful formy present work.W: Do you feel that you have received a good general training?M: Yes, I have studied in an English training program and a computer training program since I graduated from university. I am currently studying finance at a training school.(Text 7)M: What’s wrong with you, Karen? You didn’t come to class yesterday.W: I had a sore throat and it hurt very much.M: Oh, I’m sorry to hear that. How do you fed now?W: I am not feeling well.M: I suggest you drink plenty of water. That would be helpful.W: Yeah, you are right.M: Have you taken anything for it?W: I got some vitamin C from the drugstore, but it hasn’t done much good.M: Then why don’t you see a doctor?W: Yes, I think I wiltM: Don’t worry. I don’t think it s anything serious.W: Thanks. That’s very nice of you.M: I hope you will feel better soon. Let us know if there’s anything we can do.(Text 8)W: Hello. Hove International Institute Can I help you?M: Oh, yes. I would like some information about the college, please.W: Yes, certainly. Do you want to come here to do a course?M: I think so. How much is a course?W: A four-week course is £lt200. That includes accommodation, all meals and the social programmes.M: I’d like to come on a course in the summer. When does the course begin?W: There are courses in July, August and September.M: Oh, good. Maybe I will take the course in August. Now, where can I stay? I’d like to stay with a family. Is that possible?W: Yes, it is. You can stay with a family in Hove or Brighton. Why don’t you write to us with some information about yourself, and we’ll send you all the details about courses and accommodation?(Text 9)W: Edward, it’s your first time to Hainan, isn’t it?M: Yes. What a beautiful island! Look, there’re so many coconut trees, the water’s so clear and the sky’s so blue. W: The beautiful coconut trees and the fine beaches make impressive views all over Hainan Island—it’s the only tropical seaside resort in China. And it s an ideal tourist resort all year round.M: Can tourists swim or dive in winter?W: Certainly. In January and February, the average temperature is 16℃to 24℃, and 25℃to 29℃in July and August. The rainy seasons are from May to October.M: Wonderful! Anything interesting to see?W: Of course You can go to the Five Officials Memorial Temple and Hairui Tomb,which are historical sites Haikou is a modem seaside city with tropical attractions.M: How about the attractions in Sanya City?W: Sanya has international tourist accommodations and facilities along with the clean seawater, fresh air, beauty-ful beaches and bright sunshine. The tourist attractions include Yalong Bay National Holiday Resort, Da-donghai Tourist Zone, Tianyahaijiao, and Nanshan Cultural and Tourist Zone.M: Great! I can’t wait to see them.(Text 10)Halloween is an autumn holiday that Americans celebrate every ye ar. It means “ho l y evening”, and it comes every October 311 the evening before All Saints’ Day. However, it is not really a church holiday, but it is a holiday for children mainly.Every autumn, when the vegetables are ready to eat, children pick large orange pumpkins. Then they cut faces in the pumpkins and put a burning candle inside. It looks as if there were a person looking out of the pumpkin! These lights are called jack-o’-lanterns, which means “Jack of the lantern”.The children also put on strange masks and frightening clothes every Halloween. Some children paint their faces to look like monsters. Then they carry boxes or bags from house to house Every time they come to a new house, they say, “Trick or treat! Money or e at!” The grown-ups put treat-money or candy in their bags. Not only children, but most grown-ups also love Halloween and Halloween parties because on this day, they can dis-guise themselves as ghost as their imaginations will lead them. This brings them the satisfaction of being young.。
山西省临汾一中等五校2017届高三英语上学期第五次联考试题
2016～2017年度高三第五次联合考试（期末）英语试卷第I卷第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
例：How much is the shirt?A.￡19. 15.B.￡9.18.C.￡9.15.1. What has been fixed according to the woman?A. The dates.B. The schedule.C. Optional books.2. How does the woman sound?A. Excited.B. Relaxed.C. Worried.3. How many trips are organized on Wednesday afternoons every month?A．2． B．3． C．5．4. When does the man usually go off work?A. At 4:30 pm.B. At 5:00 pm.C. At 8:00 pm.5. Where is the woman probably?A. In a soap factory.B. In her house.C. At the man's home.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料，回答第6至7题。
6. What did the woman forget to do?A．Turn off the stove．B. Wash the pan after using it.C. Leave some breakfast for the man.7．Who might Maria be?A. The man's girlfriend.B. The speakers' neighbor.C. The woman's roommate.听第7段材料，回答第8至10题。
以数学文化史为背景的专题训练
专题1 以数学文化史为背景的专题训练题型一渗透数学文化的数列题1.【2017届安徽省池州市东至县高三12月联考】《九章算术》是我国古代的数学名著，书中有如下问题：“今有五人分五钱，令上二人所得与下三人等，问各得几何？”其意思为“已知甲、乙、丙、丁、戊五人分五钱，甲、乙两人所得与丙、丁、戊三人所得相同，且甲、乙、丙、丁、戊所得依次成等差数列，问五人各得多少钱？”（“钱”是古代一种重量单位），这个问题中，甲所得为（）钱A. B. C. D.2.【2017届甘肃天水一中高三理12月月考】《张丘建算经》是我国南北朝时期的一部重要数学著作，书中系统的介绍了等差数列，同类结果在三百多年后的印度才首次出现．书中有这样一个问题，大意为：某女子善于织布，后一天比前一天织的快，而且每天增加的数量相同，已知第一天织布5尺，一个月（按30天计算）总共织布390尺，问每天增加的数量为多少尺？该问题的答案为（）A．829尺 B．1629尺 C．3229尺 D．12尺3.【2017届湖南长沙一中高三月考五】“珠算之父”程大位是我国明代伟大是数学家，他的应用数学巨著《算法统综》的问世，标志着我国的算法由筹算到珠算转变的完成.程大位在《算法统综》中常以诗歌的形式呈现数学问题，其中有一首“竹筒容米”问题：“家有九节竹一茎，为因盛米不均平，下头三节三升九，上梢四节贮三升，唯有中间两节竹，要将米数次第盛，若有先生能算法，也教算得到天明.”（［注释］三升九：3.9升.次第盛：盛米容积依次相差同一数量.）用你所学的数学知识求得中间两节的容积为（）A.1.9升 B.2.1升C.2.2升D.2.3升4.【2017届山西省临汾一中、忻州一中、长治二中等五校高三上学期第五次联考】在我刚明代数学家吴敬所著的《九章算术比类大全》中，有一道数学命题叫“宝塔装灯”，内容为“远望魏巍塔七层，红灯点点倍加增；共灯三百八十一，请问顶层几盏灯？”（“倍加增”指灯的数量从塔的顶层到底层按公比为的等比数列递增），根据此诗，可以得出塔的顶层和底层共有（）A. 盏灯B. 盏灯C. 盏灯D. 盏灯5.【2017届湖北孝感市高三上学期第一次统考试】《九章算术》中有一个“两鼠穿墙”问题：“今有垣(墙，读音)厚五尺，两鼠对穿，大鼠日（第一天）一尺，小鼠也日（第一天）一尺.大鼠日自倍（以后每天加倍）,小鼠日自半（以后每天减半）.问何日相逢，各穿几何？”在两鼠“相逢”时，大鼠与小鼠“穿墙”的“进度”之比是： .6.【2017届河南漯河高级中学高三12月月考】“中国剩余定理”又称“孙子定理”．1852年，英国来华传教士伟烈亚力将《孙子算经》中“物不知数”问题的解法传至欧洲．1874年，英国数学家马西森指出此法符合1801年由高斯得到的关于问余式解法的一般性定理，因而西方称之为“中国剩余定理”．“中国剩余定理”讲的是一个关于整除的问题，现有这样一个整除问题：将1到2016这2016个数中，能被3除余1且被5整除余1的数按从小到大的顺序排成一列，构成数列{}n a，则此数列的项数为_____________．7.【2017届湖北省荆、荆、襄、宜四地七校考试联盟高三2月联考】“斐波那契”数列由十三世纪意大利数学家斐波那契发现．数列中的一系列数字常被人们称之为神奇数．具体数列为：，即从该数列的第三项数字开始，每个数字等于前两个相邻数字之和．已知数列为“斐波那契”数列，为数列的前项和，则（Ⅰ）__________；（Ⅱ）若，则__________．（用表示）8.【2017届吉林省吉林市普通中学高三毕业班第二次调研测试】艾萨克·牛顿（1643年1月4日----1727年3月31日）英国皇家学会会长，英国著名物理学家，同时在数学上也有许多杰出贡献，牛顿用“作切线”的方法求函数零点时给出一个数列：满足，我们把该数列称为牛顿数列.如果函数有两个零点1，2，数列为牛顿数列，设，已知，，则的通项公式__________．题型二渗透数学文化的立体几何题9.【2017届福建省漳州市七校高三联考】我国古代数学名著《九章算术》中“开立圆术”曰:置积尺数,以十六乘之,九而一,所得开立方除之,即立圆径. “开立圆术”相当于给出了已知球的体积V,求其直径d的一个近似公式3169d V人们还用过一些类似的近似公式. 根据π =3.14159判断,下列近似公式中最精确的一个是（）A．3169d V B．32d V C．3300157d V≈D．32111d V≈10.【2017届河北唐山市高三理上学期期末】《九章算术》中，将底面是直角三角形的直三棱柱称之为“堑堵”，已知某“堑堵”的三视图如图所示，则该“堑堵”的表面积为（）A.4B.642+C.442+D.211.【2017届湖南郴州市高三理第二次质监】我国古代数学名著《数书九章》中有“天池盆测雨”题：在下雨时，用一个圆台形的天池盆接雨水.天池盆盆口直径为二尺八寸，盆底直径为一尺二寸，盆深一尺八寸.若盆中积水深九寸，则平地降雨量是（注：①平地降雨量等于盆中积水体积除以盆口面积；②一尺等于十寸；③台体的体积公式1()3V S S S S h =++下下上上•）. A ． 2寸 B ．3寸 C. 4寸 D ．5寸12.【2017届湖南长沙雅礼中学高三文月考】“牟合方盖”是我国古代数学家刘徽在研究球的体积的过程中构造的一个和谐优美的几何体. 它由完全相同的四个曲面构成，相对的两个曲面在同一个圆柱的侧面上，好似两个扣和（牟和）在一起的方形伞（方盖）. 其直观图如下左图，图中四边形是为体现其直观性所作的辅助线. 其实际直观图中四边形不存在，当正视图和侧视图完全相同时，它的的正视图和俯视图分别可能是（ ）A ．b a ,B ．c a ,C. b c , D ．d b ,13.【2017届湖南师大附中高三理上学期月考四】《九章算术》是我国古代内容记为丰富的数学名著，书中有如下问题：“今有圆堡壔，周四丈八尺，高一丈一尺，问积几何？答曰：二千一百一十二尺．术曰：周自相乘，以高乘之，十二而一”．这里所说的圆堡壔就是圆柱体，它的体积为“周自相乘，以高乘之，十二而一．”就是说：圆堡壔（圆柱体）的体积112V=⨯（底面的圆周长的平方⨯高），则该问题中圆周率π的取值为．题型三渗透数学文化的程序框图题14.【2017届三省高三上学期百校大联考】下边程序框图的算法思路来源于我国古代数学名著《数书九章》中的“秦九韶算法”求多项式的值.执行程序框图，若输入01a=，11a=，20a=，31a=-，则输出u的值为（）A．2 B．1 C．0 D．-115.【2017届云南大理州高三理上学期统测一】下边程序框图的算法思路源于欧几里得名著《几何原本》中的“辗转相除法”，执行该程序框图，若输入,m n分别为225、135，则输出的m=（）A．5 B．9C．45 D．9016.【2017届云南省师范大学附属中学高三高考适应性月考】秦九韶算法是南宋时期数学家秦九韶提出的一种多项式简化算法，即使在现代，它依然是利用计算机解决多项式问题的最优算法，即使在现代，它依然是利用计算机解决多项式问题的最优算法，其算法的程序框图如图所示，若输入的分别为，若，根据该算法计算当时多项式的值，则输出的结果为（）A. 248B. 258C. 268D. 278题型四 渗透数学文化的函数题17.【2017届甘肃天水一中高三理12月月考】德国著名数学家狄利克雷在数学领域成就显著，以其名命名的函数1,()0,x f x x ⎧=⎨⎩为有理数为无理数称为狄利克雷函数，则关于函数()f x 有以下四个命题：①(())1f f x =；②函数()f x 是偶函数；③任意一个非零有理数T ，()()f x T f x +=对任意x R ∈恒成立；④存在三个点11(,())A x f x ，22(,())B x f x ， 33(,())C x f x ，使得ABC ∆为等边三角形．其中真命题的个数是（ ）A ．4B ．3C ．2D ．1题型五 渗透数学文化的复数题18.【2017届四川双流中学高三文必得分训练8】欧拉公式cos sin ixe x i x =+（i 为虚数单位）是由瑞士著名数学家欧拉发明的，它将指数函数的定义域扩大到复数，建立了三角函数和指数函数的关系，它在复变函数论里非常重要，被誉为“数学中的天桥”，根据欧拉公式可知，2i e 表示的复数在复平面中位于（ ）A ．第一象限B ．第二象限C ．第三象限D ．第四象限 题型六 渗透数学文化的概率题19.【2017届重庆巴蜀中学高三12月月考】“勾股定理”在西方被称为“华达哥拉斯定理”，三国时期吴国的数学家赵爽创制了一幅“勾股圆方图”，用形数结合的方法给出了勾股定理的详细证明.如图所示的“勾股圆方图”中，四个相同的直角三角形与中间的小正方形拼成一个边长为2的大正方形，若直角三角形中较小的锐角6πα=，现在向该正方形区域内随机地投掷一枚飞镖，飞镖落在小正方形内的概率是（ ）A. 31 343- 3 20.【2017届广东潮阳黄图盛中学高三月考】数学与文学有许多奇妙的联系，如诗中有回文诗：“儿忆父兮妻忆夫”，既可以顺读也可以逆读.数学中有回文数，如343、12521等，两位数的回文数有11、22、33、…、99共9个，则三位数的回文数中，偶数的概率是 .题型七 渗透数学文化的推理题21.【2017届四川成都市高三理一诊】我国南北朝时代的数学家祖恒提出体积的计算原理（祖恒原理）：“幂势既同，则积不容异”.“势”即是高，“幂”是面积．意思是：如果两等高的几何体在同高处截得两几何体的截面积恒等，那么这两个几何体的体积相等．类比祖恒原理，如图所示，在平面直角坐标系中，图1是一个形状不规则的封闭图形，图2是一个上底为1的梯形，且当实数t 取[]0,3上的任意值时，直线y t =被图1和图2所截得的两线段长始终相等，则图1的面积为 ____________．22.【2017届湖南省长沙市雅礼中学高三月考】如图所示，将平面直角坐标系的格点（横、纵坐标均为整数的点）按如下规则标上数字标签：原点处标数字0，点()1,0处标数字1，点(1)1-，处标数字2，点(0)1-，处标数字3，点(11)--，处标数字4，点(10)-，处标数字5，点()11-，处标数字6，点(0)1，处标数字7，…以此类推：记格点坐标为()m n ，的点（m n ，均为正整数）处所标的数字为()f m n =，，若n m >，则()f m n =， ．题型七 渗透现代科技或数学时事的创新题23.【2017福建莆田二十四中高三理月考】把11化为二进制数为( ).A.1 011(2)B.11 011(2)C.10 110(2)D.0 110(2)。