2018年普通高等学校招生全国统一考试模拟(五)(衡水金卷调研卷)文数试题-附答案精品

【最新整理，下载后即可编辑】2017—2018学年度上学期高三年级五调考试数学(文科)试卷本试卷分第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．第I 卷(选择题 共60分)一、选择题(本题共12小题，每小题5分，共60分．从每小题所给的四个选项中，选出最佳选项，并在答题纸上将该项涂黑) 1．已知集合{}{}2540,0,1,2,3M x x x N =-+≤=，则集合M N ⋂中元素的个数为A ．4B ．3C ．2D ．1 2．已知,,a b R i ∈是虚数单位，若2a i bi -+与互为共轭复数，则()2a bi += A ．34i - B ．5+4i C ．3+4i D ．5－4i3．如图所示程序框图的算法思路源于我国古代数学名著《九章算术》中的“更相减损术”，执行该程序框图，若输入的,a b 分别为14，18，则输出的a =A ．0B ．14C ．4D ．24．设()1112,1,,,,1,2,3232a f x x α⎧⎫∈---=⎨⎬⎩⎭，则使为奇函数且在区间()0,+∞内单调递减的α值的个数是A ．1B ．2C ．3D ．45．若点()cos ,sin P αα在直线2y x =-上，则cos 22πα⎛⎫+ ⎪⎝⎭的值等于 A ．45-B ．45C.35-D ．356．如图，网格纸上小正方形的边长均为1，粗实线画出的是某几何体的三视图，则该几何体的体积为 A ．803B ．403C ．203D ．1037．已知函数()()cos f x x ωϕ=+的部分图像如图所示，则()f x 单调递减区间为A ．13,,44k k k Z ππ⎛⎫-+∈ ⎪⎝⎭ B ．132,2,44k k k Z ππ⎛⎫-+∈ ⎪⎝⎭ C ．13,,44k k k Z ⎛⎫-+∈ ⎪⎝⎭D ．132,2,44k k k Z ⎛⎫-+∈ ⎪⎝⎭8．已知H 是球O 的直径AB 上一点，AH ：HB=1：3，AB ⊥平面，,H α为垂足，α截球O 所得截面的面积为4π，则球O 的表面积为 A ．163π B ．1633π C ．643π D ．169π9．若在函数()()20,0f x ax bx a b =+>>的图像的点()()1,1f 处的切线斜率为2，则8a bab+的最小值是 A ．10B ．9C ．8D ．3210．若,x y 满足约束条件220,0,4,x y x y x y ⎧+≤⎪-≤⎨⎪+≤⎩则23y z x -=+的最小值为 A ．2- B ．23-C ．125-D ．247- 11．已知动圆M 与圆()221:11C x y ++=，与圆()222125C x y -+=：内切，则动圆圆心M 的轨迹方程是A ．22189x y += B. 22198x y += C ．2219x y += D ．2219y x +=12．已知()f x 是定义在R 上的可导函数，且满足()()()10x f x xf x '++>，则A ．()0f x >B ．()0f x < C. ()f x 为减函数 D ．()f x 为增函数第Ⅱ卷(非选择题 共90分)二、填空题(本题共4小题，每小题5分，共20分) 13．已知函数()()3311log 2log 212xf x f f ⎛⎫=+= ⎪+⎝⎭，则___________．14．已知向量(),a b a b==，则与的夹角的大小为___________．15．等比数列{}n a 中，若1532,4a a a =-=-=，则__________．16，已知平面α过正方体1111ABCD A B C D -的面对角线1AB ，且平面α⊥平面1C BD ，平面α⋂平面111ADD A AS A AS =∠，则的正切值为_________．三、解答题(共70分．解答应写出必要的文字说明、证明过程或演算步骤．第17～21题为必考题，每个试题考生都必须作答．第22、23题为选考题，考生根据要求作答) (一)必考题：共60分． 17．(本小题满分12分)已知{}n a 是公差为3的等差数列，数列{}n b 满足121111,,3n n n n b b a b b nb ++==+=． (1)求数列{}n a 的通项公式； (2)求数列{}n b 的前n 项和．18．(本小题满分12分)在ABC ∆中，角A ，B ，C 的对边分别为,,,32a b c a c =，且tan tan tan tan A B A B +=．(1)求角B 的大小；(2)若2224,a a c b =+<，求BA CB 在方向上的投影．19．(本小题满分12分)如图，四棱柱11111ABCD A B C D A A -⊥中，底面ABCD ，四边形ABCD 为梯形， AD ／／BC ，且AD=2BC ，过1,,A C D 三点的平面记为1,BB α与平面α的交点为Q ． (1)求BQ ：1QB 的值；(2)求此四棱柱被平面α分成上、下两部分的体积之比．20．(本小题满分12分)已知函数()()ln xe f x a x x x=+-(e为自然对数的底数)．(1)当0a >时，求函数()f x 的单调区间； (2)若函数()f x 在区间1,22⎛⎫⎪⎝⎭内有三个不同的极值点，求实数a 的取值范围．21．(本小题满分12分)已知圆()()()2222:222840M x y N x y -+-=+-=，圆：，经过坐标原点的两直线12,l l 满足121l l l ⊥，且交圆M 于不同的两点A ，B ，2l 交圆N 于不同的两点C ，D ，记1l 的斜率为k ． (1)求实数k 的取值范围；(2)若四边形ABCD 为梯形，求k 的值．(二)选考题：共10分．请考生在第22、23题中任选一题作答，如果多做，则按所做的第一题计分．22．(本小题满分10分)选修4—4：坐标系与参数方程 在平面直角坐标系xOy 中，曲线1:4C x y +=；曲线21cos ,:sin x C y θθ=+⎧⎨=⎩(θ为参数)．以坐标原点O 为极点，x 轴的正半轴为极轴建立极坐标系． (1)求曲线C 1，C 2的极坐标方程；(2)若射线():0l θαρ=≥分别交12,C C 于A ，B 两点(B 点不同于坐标原点O)，求OB OA的最大值．23．(本小题满分10分)选修4-5：不等式选讲 已知函数()212f x x x =--+． (1)求不等式()0f x >的解集；(2)若存在0x R ∈，使得()2024f x a a +<，求实数a 的取值范围．。

衡水金卷2018届高三上学期全国大联考数学（文科）本试卷分共4页，23题（含选考题）。

第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

全卷满分150分。

考试时间120分钟。

注意事项：1．答卷前，考生务必将自己的姓名和考生号、试室号、座位号填写在答题卡上，并用铅笔在答题卡上的相应位置填涂考生号。

2．回答第Ⅰ卷时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。

写在本试卷上无效。

3．回答第Ⅱ卷时，将答案写在答题卡上。

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4．考试结束后，将本试卷和答题卡一并交回。

第Ⅰ卷一、选择题：本大题共12个小题,每小题5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{}2540M x x x =-+≤，{}0,1,2,3N =，则集合N M 中元素的个数为（ ）A ．1B ．2C ．3D ．4 2．已知命题p ：x ∀∈R ，()1220x -<，则命题p ⌝为（ ） A ．0x ∃∈R ，()12020x -> B ．x ∀∈R ，()1210x -> C ．x ∀∈R ，()1210x -≥ D ．0x ∃∈R ，()12020x -≥ 3．已知复数5i2i 1z =-（i 为虚数单位），则复数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4．已知双曲线C ：()2221016x y a a -=>的一个焦点为()5,0，则双曲线C 的渐近线方程为（ ） A ．430x y ±= B ．1690x y ±=C．40x = D ．4312x y ±=5．2017年8月1日是中国人民解放军建军90周年，中国人民银行发行了以此 为主题的金银纪念币.如图所示的是一枚8克圆形金质纪念币，直径22毫米， 面额100元.为了测算图中军旗部分的面积，现向硬币内随机投掷100粒芝麻， 已知恰有30粒芝麻落在军旗内，据此可估计军旗的面积大约是（ ）A ．2726mm 5π B ．2363mm 10π C ．2363mm 5π D ．2363mm 20π6．下列函数中，与函数122xx y =-的定义域、单调性与奇偶性均一致的函数是（ ）A ．sin y x =B ．3x y = C ．1y x = D ．()()2200x x y x x ⎧-≥⎪=⎨<⎪⎩7．如图是一个空间几何体的正视图和俯视图，则它的侧视图为（ ）8．设55log 4log 2a =-，2lnln 33b =+，1lg5210c =，则a b c ，，的大小关系为（ ） A ．a b c << B ．b c a << C ．c a b << D ．b a c << 9．执行如图所示的程序框图，则输出的S 值为（ ）A ．1819 B ．1920 C ．2021 D ．12010．将函数()2sin 43f x x ⎛⎫=- ⎪⎝⎭π的图象向左平移6π个单位，再把所有点的横坐标伸长到原来的2倍，得到函数()y g x =的图象，则下列关于函数()y g x =的说法错误．．的是（ ） A ．最小正周期为π B ．图象关于直线12x =π对称C ．图象关于点,012⎛⎫⎪⎝⎭π对称 D ．初相为3π11．抛物线有如下光学性质：由焦点射出的光线经抛物线反射后平行于抛物线的对称轴；反之，平行于抛物线对称轴的入射光线经抛物线发射后必经过抛物线的焦点.已知抛物线24y x =的焦点为F ，一平行于x 轴的光线从点()3,1M 射出，经过抛物线上的点A 反射后，再经抛物线上的另一点B 射出，则直线AB 的斜率为（ ）A ．43 B ．43- C ．43± D ．169- 12．已知ABC ∆的内角A B C ，，的对边分别是a b c ，，，且()()222cos cos a b c a B b A abc +-⋅+=，若2a b +=，则c 的取值范围为（ ）A ．()0,2B ．[)1,2C ．1,22⎡⎫⎪⎢⎣⎭D ．(]1,2第Ⅱ卷（共90分）本卷包括必考题和选考题两部分.第13~21题为必考题，每个试题考生都必须作答.第22~23题为选考题，考生根据要求作答.二、填空题（每题5分，满分20分，将答案填在答题纸上）13．已知向量⎪⎭⎫⎝⎛=6cos ,3sinππa ，)1,(kb =，若b a //，则k = ． 14．已知函数()32f x x x =-，若曲线()f x 在点()()1,1f 处的切线经过圆C ：()222x y a +-=的圆心，则实数a 的值为 ．15．已知实数x y ，满足约束条件3,,60,x y x y +≤⎧⎪⎪≥⎨⎪≥⎪⎩ππ则()sin x y +的取值范围为 （用区间表示）．16．在《九章算术》中，将底面为长方形且有一条侧棱与底面垂直的四棱锥称之为阳马.若四棱锥M ABCD -为阳马，侧棱MA ⊥底面ABCD ，且2MA BC AB ===，则该阳马的外接球与内切球表面积之和为 ．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） 在递增的等比数列{}n a 中，1632a a ⋅=，2518a a ⋅=，其中*n ∈N .（1）求数列{}n a 的通项公式；（2）记21log n n n b a a +=+，求数列{}n b 的前n 项和n T . 18．（本小题满分12分）如图，在三棱柱111ABC A B C -中，1AA ⊥平面ABC ，AC BC ⊥，12AC BC CC ===，点D 为AB 的中点.（1）证明：1AC ∥平面1B CD ； （2）求三棱锥11A CDB -的体积.19．（本小题满分12分）随着资本市场的强势进入，互联网共享单车“忽如一夜春风来”，遍布了一二线城市的大街小巷.为了解共享单车在A 市的使用情况，某调查机构借助网络进行了问卷调查，并从参与调查的网友中抽取了200人进行抽样分析，得到下表（单位：人）：（1）根据以上数据，能否在犯错误的概率不超过0.15的前提下认为A 市使用共享单车情况与年龄有关？（2）现从所抽取的30岁以上的网友中利用分层抽样的方法再抽取5人. （i ）分别求这5人中经常使用、偶尔或不用共享单车的人数；（ii ）从这5人中，再随机选出2人赠送一件礼品，求选出的2人中至少有1人经常使用共享单车的概率.参考公式：()()()()()22n ad bc K a b c d a c b d -=++++，其中n a b c d =+++.参考数据：20．（本小题满分12分）已知椭圆C ：()222210x y a b a b +=>>过点()，离心率为2，直线l ：20kx y -+=与椭圆C 交于A B ，两点. （1）求椭圆C 的标准方程；（2）是否存在实数k-=（其中O 为坐标原点）成立？若存在，求出实数k 的值；若不存在，请说明理由. 21．（本小题满分12分）已知函数()2ln 23f x x x =-+，()()()4ln 0g x f x x a x a '=++≠. （1）求函数()f x 的单调区间；（2）若关于x 的方程()g x a =有实数根，求实数a 的取值范围.请考生在22、23两题中任选一题作答，如果多做，则按所做的第一题记分． 22．（本小题满分10分）选修4-4：坐标系与参数方程已知曲线C 的参数方程为2cos sin x y =⎧⎨=⎩αα（α为参数），以坐标原点为极点，x 轴的正半轴为极轴建立极坐标系，直线lsin 34⎛⎫+= ⎪⎝⎭πθ. （1）求曲线C 的普通方程及直线l 的直角坐标方程； （2）求曲线C 上的点到直线l 的距离的最大值. 23．（本小题满分10分）选修4-5：不等式选讲 已知函数()211f x x x =-++. （1）解不等式()3f x ≤；（2）记函数()()1g x f x x =++的值域为M ，若t M ∈，试证明：223t t -≥.数学（文科）参考答案一、选择题1-5:CDDAB 6-10:DAABC 11、12：BB 二、填空题13．1 14．2- 15．1,12⎡⎤⎢⎥⎣⎦16．36-π 三、解答题17．解：（1）设数列{}n a 的公比为q ，则251632a a a a ⋅=⋅=，又2518a a +=，∴22a =，516a =或216a =，52a =（舍）. （3分） ∴3528a q a ==，即2q =. （4分） 故2122n n n a a q --==（*n ∈N ）. （6分） （2）由（1）得，12n n b n -=+. （8分） ∴12n n T b b b =+++L()()211222123n n -=+++++++++L L()112122n n n +-=+-2212n n n +=-+. （12分）18．解：（1）连接1BC 交1B C 于点O ，连接OD .在三棱柱111ABC A B C -中，四边形11BCC B 是平行四边形. ∴点O 是1BC 的中点. （2分）∵点D 为AB 的中点，∴1OD AC ∥. （4分）又OD ⊂平面1B CD ，1AC ⊄平面1B CD ，∴1AC ∥平面1B CD . （6分） （2）∵AC BC =，AD BD =，∴CD AB ⊥.在三棱柱111ABC A B C -中，由1AA ⊥平面ABC ，得平面11ABB A ⊥平面ABC . 又平面11ABB A I 平面ABC AB =.∴CD ⊥平面11ABB A .∴点C 到平面11A DB 的距离为CD ，且sin 4CD AC ==π（9分）∴11111113A CDB C A DB A DB V V S CD --∆==⨯1111132A B AA CD =⨯⨯⨯⨯=14263⨯=. （12分）19．解：（1）由列联表可知，()2220070406030 2.19813070100100K ⨯⨯-⨯=≈⨯⨯⨯.因为2.198 2.072>，所以能在犯错误的概率不超过0.15的前提下认为A 市使用共享单车情况与年龄有关. （4分）（2）（i ）依题意可知，所抽取的5名30岁以上的网友中，经常使用共享单车的有6053100⨯=（人）， 偶尔或不用共享单车的有4052100⨯=（人）. （6分） （ii ）设这5人中，经常使用共享单车的3人分别为a b c ，，；偶尔或不用共享单车的2人分别为d e ，.则从5人中选出2人的所有可能结果为(),a b ，(),a c ，(),a d ，(),a e ，(),b c ，(),b d ，(),b e ，(),c d ，(),c e ，(),d e ，共10种.其中没有1人经常使用共享单车的可能结果为(),d e ，共1种. 故选出的2人中至少有1人经常使用共享单车的概率1911010P =-=. （12分）20．解：（1）依题意，得22222211,,a b c aa b c ⎧+=⎪⎪⎪=⎨⎪⎪=+⎪⎩解得24a =，22b =，22c =， 故椭圆C 的标准方程为22142x y +=. （4分） （2）假设存在符合条件的实数k .依题意，联立方程222,24,y kx x y =+⎧⎨+=⎩消去y 并整理，得()2212840k x kx +++=.则()226416120k k ∆=-+>，即k >或k <.设()11,A x y ，()22,B x y ， 则122812k x x k +=-+，122412x x k =+. （6分）=+，得0=⋅. （7分） ∴12120x x y y +=. ∴()()1212220x x kx kx +++=.即()()212121240kx xk x x ++++=. ∴()22224116401212k k k k +-+=++.即2012k=+. 即22k =，即k =故存在实数k =-=+成立. （12分）21．解：（1）依题意，得()21144x f x x x x -'=-=()()1212x x x+-=，()0,x ∈+∞. 令()0f x '>，即120x ->. 解得102x <<； 令()0f x '<，即120x -<. 解得12x >. 故函数()f x 的单调递增区间为10,2⎛⎫ ⎪⎝⎭，单调递减区间为1,2⎛⎫+∞ ⎪⎝⎭.（4分） （2）由题得，()()4ln g x f x x a x '=++=1ln a x x+. 依题意，方程1ln 0a x a x +-=有实数根，即函数()1ln h x a x a x =+-存在零点. 又()2211a ax h x x x x -'=-+=.令()0h x '=，得1x a=. 当0a <时，()0h x '<.即函数()h x 在区间()0,+∞上单调递减，而()110h a =->，111111e 1aah a a a e --⎛⎫⎛⎫=+-- ⎪ ⎪⎝⎭⎝⎭1111110e e a-=-<-<. 所以函数()h x 存在零点； （8分） 当0a >时，()h x '，()h x 随x 的变化情况如下表：所以11ln ln h a a a a a a a ⎛⎫=+-=-⎪⎝⎭为函数()h x 的极小值，也是最小值. 当10h a ⎛⎫>⎪⎝⎭，即01a <<时，函数()h x 没有零点；当0h a ≤⎪⎝⎭，即1a ≥时，注意到()110h a =-≤， ()11e 0e eh a a =+-=>，所以函数()h x 存在零点.综上所述，当()[),01,a ∈-∞+∞U 时，方程()g x a =有实数根. （12分）22．解：（1）由曲线C 的参数方程2cos sin x y =⎧⎨=⎩αα（α为参数），得曲线C 的普通方程为2214x y +=. （3分）sin 34⎛⎫+= ⎪⎝⎭πθ，得()sin cos 3+=ρθθ，即3x y +=.∴直线l 的普通方程为30x y +-=. （6分）（2）设曲线C 上的一点为()2cos ,sin αα， 则该点到直线l的距离d ==（其中tan 2=ϕ）.当()sin 1+=-αϕ时，max 2d ==. 即曲线C 上的点到直线l.（10分）23．解：（1）依题意，得()3,1,12,1,213,.2x x f x x x x x ⎧⎪-≤-⎪⎪=--<<⎨⎪⎪≥⎪⎩则不等式()3f x ≤即为1,33x x ≤-⎧⎨-≤⎩或11,223x x ⎧-<<⎪⎨⎪-≤⎩或1,23 3.x x ⎧≥⎪⎨⎪≤⎩解得11x -≤≤.故原不等式的解集为{}11x x -≤≤. （5分） （2）由题得，()()121g x f x x x =++=-+2221223x x x +≥---=，当且仅当()()21220x x -+≤.即112x -≤≤时取等号.∴[)3,M =+∞.（8分） ∴()()22331t t t t --=-+. ∵t M ∈， ∴30t -≥，10t +>. ∴()()310t t -+≥.∴223t t -≥. （10分）。

2018年普通高等学校招生全国统一考试模拟试题（衡水金卷调研卷）五数学（文）注意事项：1．答题前，先将自己的姓名、准考证号填写在试题卷和答题卡上，并将准考证号条形码粘贴在答题卡上的指定位置。

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第I 卷（选择题）一、单选题1．设全集R U =，集合{}|10 A x x =+≥， 1|0 1x B x x +⎧⎫=<⎨⎬-⎩⎭，则图中阴影部分所表示集合为（ ）A. {}| 1 x x ≥-B. {}| 1 x x <-C. {}|1 1 x x -≤≤-D. ﹛| 1 x x <-或1x ≥﹜2．已知复数123z i =+， 2z a i =+（a R ∈， i 为虚数单位），若1218z z i =+，则a 的值为（ ） A. 12 B. 1 C. 2 D. 43．已知函数()fx 的图象关于原点对称，且在区间[]5,2--上单调递减，最小值为5，则()f x 在区间[]2,5上（ ）A. 单调递增，最大值为5B. 单调递减，最小值为5-C. 单调递减，最大值为5-D. 单调递减，最小值为54．已知直线231x y +=与x ， y 轴的正半轴分别交于点A ， B ，与直线0x y +=交于点C ，若OC OA OB λμ=+（O 为坐标原点），则λ， μ的值分别为（ ）A. 2λ=， 1μ=-B. 4λ=， 3μ=-C. 2λ=-， 3μ=D. 1λ=-， 2μ= 5．已知122log 3a =， 22log 3b =， 1232c ⎛⎫= ⎪⎝⎭， 32d e =，则（ ） A. d c a b >>> B. d b c a >>> C. c d a b >>> D. a c b d >>> 6．已知 ，则点 在直线 的右下方是是双曲线 的离心率 的取值范围为 的( ) A. 充要条件 B. 充分不必要条件 C. 必要不充分条件 D. 既不充分也不必要条件 7．已知α、β是两个不同的平面，给出下列四个条件：①存在一条直线a ， a α⊥， a β⊥；②存在一个平面γ， γα⊥， γβ⊥；③存在两条平行直线a 、b ， a α⊂， b β⊂， //a β， //b α；④存在两条异面直线a 、b ， a α⊂， b β⊂， //a β， //b α，可以推出//αβ的是( ) A. ①③ B. ②④ C. ①④ D. ②③ 8．已知直线2y =与函数()()tan 0,2f x x πωϕωϕ⎛⎫=+>< ⎪⎝⎭图象的相邻两个交点间的距离为6，点(P 在函数()f x 的图像上，则函数()()12log g x f x =的单调递减区间为（ ） A. ()()6,26k k k Z ππππ-+∈ B. (),63k k k Z ππππ⎛⎫-+∈ ⎪⎝⎭ C. ()11,63k k k Z ⎛⎫-+∈ ⎪⎝⎭ D. ()()61,26k k k Z -+∈ 9．在如图所求的程序框图中，若输出n 的值为4，则输入的x 的取值范围为（ ） A. 13,84⎡⎤⎢⎥⎣⎦ B. []3,13 C. [)9,33 D. 913,84⎡⎫⎪⎢⎣⎭ 10．已知某几何体的三视图如图所求，则该几何体的表面积为（ ）此卷只装订不密封班级姓名准考证号考场号座位号A. 2914a π⎫-⎪⎪⎝⎭B.2914a π⎫+-⎪⎪⎝⎭C. 2944a π⎛⎫ ⎪ ⎪⎝⎭D.29144a π⎛⎫-- ⎪ ⎪⎝⎭11．甲、乙两人各自在400米长的直线形跑道上跑步，则在任一时刻两人在跑道上相距不超过50米的概率是（ ） A. 18 B. 1136 C. 1564 D. 1412．已知定义在R 上的可导函数()f x 的导函数为()f x '，满足()()f x f x '<，且()102f =，则不等式()102x f x e -<的解集为（ ） A. 1,2⎛⎫-∞ ⎪⎝⎭ B. ()0,+∞ C. 1,2⎛⎫+∞ ⎪⎝⎭ D. (),0-∞第II 卷（非选择题）二、填空题13．已知函数()2log ,2,{ 2,2,x x f x x x ≥=+<则()()()3f f f -的值为__________．14．已知命题:P x R ∀∈， ()22log 0x x a ++>恒成立，命题[]0:2,2Q x ∃∈-，使得022x a ≤，若命题P Q ∧为真命题，则实数a 的取值范围为__________．15．已知()222210x y a b a b +≤>>表示的区域为1D ，不等式组0,0,{ 0,0bx cy bc bx cy bc bx cy bc bx cy bc -+≥--≤+-≤++≥表示的区域为2D ，其中()2220a b c c =+>，记1D 与2D 的公共区域为D ，且D 的面积S为2234x y +=内切于区域D 的边界，则椭圆()2222:10xy C a b a b +=>>的离心率为__________．16．我国南宋著名数学家秦九韶在他的著作《数书九章》卷五“田域类”里有一个题目：“问有沙田一段，有三斜，其小斜一十三里，中斜一十四里，大斜一十五里.里法三百步.欲知为田几何.”这道题讲的是有一个三角形沙田，三边分别为13里， 14里， 15里，假设1里按500米计算，则该三角形沙田外接圆的半径为___________米.三、解答题17．已知数列{}n a 满足11a =， 134n n a a +=+， *n N ∈.（1）证明：数列{}2n a +是等比数列，并求数列{}n a 的通项公式；（2）设()3log 22n n n a b a +=+，求数列{}n b 的前n 项和n T . 18．现从某医院中随机抽取了七位医护人员的关爱患者考核分数（患者考核： 10分制），用相关的特征量y 表示；医护专业知识考核分数（试卷考试： 100分制），用相关的特征量x 表示，数据如（1）求y 关于x 的线性回归方程（计算结果精确到0.01）； （2）利用（1）中的线性回归方程，分析医护专业考核分数的变化对关爱患者考核分数的影响，并估计某医护人员的医护专业知识考核分数为95分时，他的关爱患者考核分数（精确到0.1）； （3）现要从医护专业知识考核分数95分以下的医护人员中选派2人参加组建的“九寨沟灾后医护小分队”培训，求这两人中至少有一人考核分数在90分以下的概率. 附：回归方程ˆˆˆy bx a =+中斜率和截距的最小二乘法估计公式分别为()()()121ˆn i i i n i i x x y y b x x ==--=-∑∑， ˆˆˆa y bx =-. 19．如图，在四棱锥P ABCD -中，底面ABCD 是边长为a 的菱形， PD ⊥平面ABCD ， 60BAD ∠=， 2PD a =， O 为AC 与BD 的交点， E 为棱PB 上一点. （1）证明：平面EAC ⊥平面PBD ； （2）若//PD 平面EAC ，三棱锥P EAD -的体积为a 的值. 20．已知动圆C 恒过点1,02⎛⎫ ⎪⎝⎭，且与直线12x =-相切. （1）求圆心C 的轨迹方程； （2）若过点()3,0P 的直线交轨迹C 于A ， B 两点，直线OA ， OB （O 为坐标原点）分别交直线3x =-于点M ， N ，证明：以MN 为直径的圆被x 轴截得的弦长为定值. 21．已知函数()()322316f x x a x ax =-++， a R ∈.（1）若对于任意的()0,x ∈+∞， ()()6ln f x f x x +-≥恒成立，求实数a 的取值范围；（2）若1a >，设函数()f x 在区间[]1,2上的最大值、最小值分别为()M a 、()m a ，记()()()h a M a m a =-，求()h a 的最小值. 22．选修4-4：坐标系与参数方程在平面直角坐标系xOy中，已知直线11,2:{ 2x t l y =--=（t 为参数），曲线12,:{ 22x cos C y sin ϕϕ=+=-（ϕ为参数），以原点O 为极点， x 轴的正半轴为极轴建立坐标系.（1）写出直线l 的普通方程与曲线C 的极坐标方程；（2）设直线l 与曲线C 交于A ， B 两点，求ABC ∆的面积.23．选修4-5：不等式选讲已知函数()21f x x x =+--.（1）求不等式()2f x ≥的解集；（2）记()f x 的最大值为k ，证明：对任意的正数a ， b ，c ，当a b c k ++=时，有k ≤成立.2018年普通高等学校招生全国统一考试模拟试题（衡水金卷调研卷）五数学（文）答 案1．B 【解析】集合}}{ 10{ 1A x x x x =+≥=≥-，()()}}1|0 {|11 0{|11 1x B x x x x x x x +⎧⎫=<=+-<=-<<⎨⎬-⎩⎭，所以}{|1 A B x x ⋃=≥-，阴影部分表示的是()}{|1 U A B x x ⋃=<-ð，选B.2．C【解析】()()()12232323z z i a i a a i =++=-++，由已知有1218z z i =+，所以231{ 238a a -=+=，解出2a =，选C.3．C【解析】由已知有函数()f x 是奇函数，且在区间[]5,2--上为减函数，且最小值为()25f -=，根据函数()f x 图象的对称性知，函数()f x 在区间[]2,5上为减函数，且最小值为()()555f f =--=-，选C.点睛：本题主要考查函数的奇偶性、单调性和最值等基本性质，奇函数在关于原点对称的区间上的单调性等，属于基础题。

2019年普通高等学校招生全国统一考试高考模拟调研卷英语（五）1～5ABBCB 6～10ABCAB 11～15ACCAC 16～20ABABC21～25BCBAB 26～30DACBD 31～35CCDAD 36～40GEACB41～45 DBACB 46～50 CADAB 51～55 CDCAB 56～60 DBDAC61．spoke 62．largest 63．a 64．equality 65．known66．for 67．as 68．is aimed 69．leaders 70．to discuss短文改错：I’ve been in Britain for two years．My friends in China sometime write to me, asked me how long I’llsometimes askingstay here, and when I’m thinking of returning home．The answer to their question is simple: I do not knowquestionshow to return home．At the moment, I have no reason to return∧China．I like living in Britain: I enjoywhen tomeeting British people and travel around the country．I am expected to have more chances to eat the Britishtravel(l)ing expectingfood．My study is very interesting, and there are so many things I didn’t know about Britain that I hope todon’tdiscover it in the future．them书面表达：Dear Sir/Madam,I think Picture No. 18 is the best choice for this year’s World Animal Day．In the picture we can see a bear and a hunter are on the seesaw．The hunter is aiming at the fearful bear．He is ready to shoot．Actually, if the hunter really shoots, both the bear and the hunter will fall down, destroying themselves．From the picture we can clearly see that both animals and human beings are in the same boat．If animals are destroyed, so are the human beings．On the contrary, if human beings and animals can live harmoniously, we will enjoy a peaceful world．The picture is very simple, but the story is shocking．The message is instructive．Once seen, it can never be easily forgotten．It can arouse the public’s awareness of animal protection．Thank you for your patience to read my letter．Hoping you can choose the picture for this year’s World Animal Day．Yours sincerely,Li Hua第 1 页。

（衡水金卷）2018年普通高等学校招生全国统一考试模拟英语试题五本试题卷共8页。

全卷满分120分，考试用时100分钟。

第一部分阅读理解（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下面短文，从每题所给的A、B、C和D四个选项中，选出最佳选项。

AHave you ever been to France before? It is not only a country of great food, fashion and art. It’s also home to t he most influential painters in the world.Edouard ManetHe was one of the first artists to paint modern life. He began to paint in his own style, but still used some of Couture’s techniques like thick lines and dark colors. He was greatly influenced by Claude Monet and Berthe Morisot, which can be seen in his use of light shades. Most of his paintings had scenes of daily life on the streets of Paris. His works include Olympia and The Absinthe Drinker.Camille PissarroIn his early years, Pissarro painted scenes of a river or a path from memory. After meeting Claude Monet and Paul Cezanne, who painted in a more realistic style, he changed his course to Impressionism. During his career, he experimented with various styles, and finally formed his own one. His works include Old Market at Rouen and Sunset at St. Charles.Vincent van GoghHe had a huge influence on art in the 20th century. His early works were most painted in somber tones. However, influenced by Monet, Pissarro, and Bernard, he adopted brighter colors in his works, and started creating his own techniques. Although he had produced more than 2,000 works of art, the artist sold only one painting during his lifetime —Red Vineyard at Arles. His works include The Potato Eaters, Starry Night and Bedroom in Arles.Claude MonetHe was the founder of the Impressionist movement and completely changed the French painting in the 19th century. Although he first started by selling charcoal caricatures（木炭讽刺画）in Paris, he soon started painting with oil after meeting Eugene Boudin, who taught him to use oil paints and also encouraged him to paint outdoors. And then he painted with his own style. His works include Impression, Sunrise and The Water Liles.1. What can we learn about Edouard Manet’s paintings?A. They reflected the changes of life.B. They were mainly about daily life.C. They were all painted in bright colors.D. They were painted in Morisot’s style.2. Which painting was sold by Vincent van Gogh in person?A. The Potato Eaters.B. Bedroom in Arles.C. Red Vineyard at Arles.D. Starry Night.3. What’s the common point of the four painters from the text?A. All of them were given many awards in their life.B. All of them were taught by some famous painters.C. All of them had a good taste in delicious food.D. All of them had their unique styles in painting.BFinding true love can be pretty tough for a lot of people, but a lady from a fairly well-known San Francisco advertising agency seems to think money helps. She is offering $10,000 to any of her friends who can introduce her to her Mr. Right. She wants to find her future husband through this way.The unnamed husband seeker who sent out the email had just finished reading the best-selling book named Lean In. It was 11 p. m. on a Sunday night and she realized this was the second self-help book she had read in the month. She was still single. Things were not looking fine, but there was hope for her still. If the book had taughther anything, it was that she needed to take a more positive role in finding love. After all, if she wanted to get a better job, she wouldn’t just sit outside an employer’s building and wait for someone to offer it to her, so why should finding a husband be any different? But instead of going out and meeting new people she decided to write an email to all her friends, offering to give them $10,000 on her wedding day if any of them managed to introduce her to her future husband.“I am writing you today because I’ve decided to make an aggressive action plan on finding the man that I get to hang out with forever,” the woman writes in her email. “Introducing me to my husband is just not high on your to-do list. But I think I have an idea that might change that…” You guessed it, and this is where she offers to reward her “closest friends” wi th cold hard cash.“I will personally give ten thousand dollars to the friend who introduces me to my husband.Here is how the program works:Step 1: You set me up on a date with a man.Step 2: I marry that man.Step 3: I give you $10,000 on my wedding day.I know you’re thinking that this is nuts. Just plain crazy. ‘You can find a husband without giving $10,000.’ Well for starters, thank you! I’m happy.”4. What does the lady offer $10,000 to any of her friends for?A. Celebrating the fact that she has made a decision to find a husband.B. Checking the power of money among her circle of friends.C. Encouraging her friends to help find her Mr. Right.D. Sharing her happiness of having found true love.5. What does the underlined word “nuts” mean in the last paragraph?A. deliciousB. sensibleC. angryD. foolish6. What’s the purpose of the author’s mentioning getting a better job in Paragraph 2?A. To stress the importance of finding a good job.B. To stress the importance of taking a positive attitude.C. To show that waiting patiently is necessary to get a job.D. To state that we need to be patient before a job is offered.7. What kind of person do you think the lady is?A. Adventurous.B. Imaginative.C. Considerate.D. Polite.CTaxi-booking app Uber agreed to sell its business in China to Didi Chuxing. The two firms had been fierce competitors, but Didi Chuxing had controlled the Chinese market with an 87% share.Uber China launched in 2014, but it had failed to make any profit for a long time. Cheng Wei, founder and chief executive of Didi Chuxing, said the two companies had learned a great deal from each other over the past two years in China. He added that the deal would set the mobile transportation industry on a healthier path of growth at a higher level. As part of the deal, Mr. Cheng would join the board of Uber, while Uber chief executive Travis Kalanick would also join Didi’s board.Uber’s China business would own its separate branding while US-based Uber Technologies would hold about 17.5% in the combined company. Didi Chuxing is backed by Chinese Internet giants Tencent and Alibaba.Uber had been struggling to break into the Chinese market despite having Chinese search engine Baidu as an investor. Last February, the company admitted it was losing more than $1 billion a year in China. “Funding their Chinese dreams was becoming too expensive for Uber,” Duncan Clark, chairman of Beijing-based consultancy BDA, told the BBC. Travis Kalanick said, “As a businessman, I’ve learned th at being successful is about listening to your head as well as following your heart.”The fierce competition had led both companies to spend much more on their journeys. The combination is likely to see fewer such subsidies（补贴）. “One thing to watch carefully is how quickly consumers feel the impact as subsidies are withdrawn.” Mr. Clark added.The deal with Didi Chuxing came just days after China had agreed to provide alegal framework for taxi-ordering apps. Both Uber and Didi welcomed the decision. The new rules took effect last November and could, among other things, forbid such platforms to operate below cost.8. According the second paragraph, what can we know?A. Being successful is about listening to your head and following your heart.B. The deal would make the mobile transportation industry grow much faster.C. Didi Chuxing had learnt more in China than Uber over the past two years.D. Mr. Cheng would be working as a member of the board of Uber as planned.9. What is the best title of the passage?A. Uber sold Chinese business to Didi ChuxingB. Using Didi Chuxing brings more subsidiesC. Listen to your head and follow your heartD. The new rules look effect last November10. What is the impact of the fierce competition between Uber and Didi?A. Uber dominated the Chinese market with an 87% share.B. China provided a legal framework for taxi-ordering apps.C. Funding their Chinese dreams became expensive for Uber.D. Chinese search engine Baidu became an investor of Uber’s.11. The passage is probably taken from a website about ________.A. appsB. politicsC. economyD. technologyDYou get anxious if there’s no wi-fi in the hotel or mobile phone signal up the mountain. You feel upset if your phone is getting low on power, and you secretly worry things will go wrong at work if you’re not there. All these can be called “always on” stress caused by smart phone addiction.For some people, smart phones have liberated them from the nine-to-five work. Flexible working has given them more autonomy（自主权）in their working lives and enabled them to spend more time with their friends and families. For many others though, smart phones have become tyrants（暴君）in their pockets, never allowing them to turn them off, relax and recharge their batteries.Pittsburgh-based developer Kevin Holesh was worried about how much he was ignoring his family and friends in favour of his iPhone. So he developed an app —Moment —to monitor his usage. The app enables users to see how much time they’re spending on the device and set up warnings if the usage limits are breached（突破）. “Moment’s goal is to promote balance in your life,” his website explains. “Some time on your phone, some time off it enjoying your loving family and friends around you.”Dr. Christine Grant, an occupational（职业的）psychologist at Coventry University, said, “The effects of this ‘always on’ culture are that your mind is never resting, and you’re not giving your body time to recover, so you’re always stressed. And the more tired and stressed we get, the more mistakes we make. Physical and mental health can suffer.”And as the number of connected smart phones is increasing, so is the amount of data. This is leading to a sort of decision paralysis（瘫痪）and is creating more stress in the workplace because people have to receive a broader range of data and communications which are often difficult to manage. “It actually makes it more difficult to make decisions and many do less because they’re controlled by it all and fell they can never escape the office,” said Dr. Chris tine Grant.12. What’s the first paragraph mainly about?A. The popularity of smart phones.B. The progress of modern technology.C. The signs of “always on” stress.D. The cause of smart phone addiction.13. Kevin Holesh developed “Moment” to ________.A. research how people use their mobile phonesB. help people control their use of mobile phonesC. make people love parents and friends aroundD. increase the fun of using mobile phones14. What’s Dr. Christine Grant’s attitude towards “always on” cul ture?A. Confused.B. Positive.C. Doubtful.D. Critical.15. According to the last paragraph, a greater amount of data means ________.A. we will become less productiveB. we can make a decision more quicklyC. we will be equipped with more knowledgeD. we can work more effectively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。

2018年普通高学招生全国统一考试高考英语五模试卷（衡水金卷调研卷）第一部分阅读理解（共两节）第一节（满分30分）阅读下面短文，从每题所给的A、B、C和D四个选项中，选出最佳选项．1. Have you ever been to France before? It is not only a country of great food, fashionand art．It’s also home to the most influential painters in the world．Edouard ManetHe was one of the first artists to paint modern life． He began to paint in his ownstyle, but still used some of Couture’s techniques like thick lines and dark colors． He was greatly influenced by Claude Monet and Berthe Morisot, which can be seen in his use oflight shades． Most of his paintings had scenes of daily life on the streets of Paris． His works include Olympia and The Absinthe Drinker．Camille PissarroIn his early years, Pissarro painted scenes of a river or a path from memory． After meeting Claude Monet and Paul Cezanne, who painted in a more realistic style, he changed his course to Impressionism． During his career, he experimented with various styles, and finally formed his own one． His works include Old Market at Rouen and Sunset atSt． Charles．Vincent van GoghHe had a huge influence on art in the 20th century． His early works were most painted in somber tones． However, influenced by Monet, Pissarro, and Bernard, he adopted brighter colors in his works, and started creating his own techniques． Although he had produced more than 2, 000 works of art, the artist sold only one painting during his lifetime﹣ Red Vineyard at Arles． His works include The Potato Eaters, Starry Night and Bedroomin Arles．Claude MonetHe was the founder of the Impressionist movement and completely changed the French painting in the 19th century． Although he first started by selling charcoal caricatures（木炭讽刺画）in Paris, he soon started painting with oil after meeting Eugene Boudin, who taught him to use oil paints and also encouraged him to paint outdoors． And then he painted with his own style． His works include Impression, Sunrise and The Water Liles．（1）What can we learn about Edouard Manet’s paintings？________A.They reflected the changes of life．B.They were mainly about daily life．C.They were all painted in bright colors．D.They were painted in Morisot’s style．（2）Which painting was sold by Vincent van Gogh in person？________A.The Potato Eaters．B.Bedroom in Arles．C.Red Vineyard at Arles．D.Starry Night．（3）What’s the common point of the four painters from the text？________A.All of them were given many awards in their life．B.All of them were taught by some famous painters．C.All of them had a good taste in delicious food．D.All of them had their unique styles in painting．【答案】BCD【考点】完形综合阅读理解综合【解析】本文章主要讲述了法国的几个有名的画家，并对他们的画作作品进行了简单的介绍和描述．【解答】（1）B．细节题，根据文章内容，Edouard Manet．． Most of his paintings had scenes of daily life on the streets of Paris．由此可知，马内的作品大部分是关于巴黎街头的人们的日常生活．结合选项，故选B．（2）C．细节题．根据文章内容， Although he had produced more than 2，000 works of art， the artist sold only one painting during his lifetime ﹣ Red Vineyard at Arles．由此可知，由梵高本人亲自售出的画只有一副，它就是﹣﹣Red Vineyard at Arles．结合选项，故选C．（3）D．推理题，根据文章内容，Edouard Manet，He began to paint in his own style，but still used some of Couture’s techniques like thick lines and dark colors；Camille Pissarro．．During his career， he experimented with various styles， and finally formed his own one；Vincent van Gogh．． His early works were most painted in sombertones． However， influenced by Monet， Pissarro， and Bernard， he adopted brighter colors in his works， and started creating his own techniques；Claude Monet．．And then he painted with his own style．由此可知，这4个作家在创造作品的时候都有自己的特色．结合选项，故选D．2. Finding true love can be pretty tough for a lot of people, but a lady from a fairly well﹣known San Francisco advertising agency seems to think money helps． She is offering﹩10, 000 to any of her friends who can introduce her to her Mr． Right． She wants to find her future husband through this way．The unnamed husband seeker who sent out the email had just finished reading the best﹣selling book named Lean In． It was 11 p． m． on a Sunday night and she realized this was the second self﹣help book she had read in the month． She was still single． Things were not looking fine, but there was hope for her still． If the book had taught her anything, it was that she needed to take a more positive role in finding love． After all, if she wanted to get a better job, she wouldn’t just sit outside an employer’s building and wait for someone to offer it to her, so why should finding a husband be any different? But instead of going out and meeting new people she decided to write an email to all her friends, offering to give them﹩10, 000 on her wedding day if any of them managed to introduce her to her future husband．“I am writing you today because I’ve decided to make an aggressive action plan on finding the man that I get to hang out with forever, ” the woman writes in her email．“Introducing me to my husband is just not high on your to﹣do list． But I think I have an idea that might change that…” You guessed it,and this is where she offers to reward her “closest friends” with cold hard cash．"I will personally give ten thousand dollars to the friend who introduces me to my husband． Here is how the program works:Step 1: You set me up on a date with a man．Step 2: I marry that man．Step 3: I give you﹩10, 000 on my wedding day．I know you’re thinking that this is ________． Just plain crazy．‘You can find a husband without giving﹩10, 000．’ Well for starters,thank you! I’m happy．"（1）What does the lady offer ﹩10，000 to any of her friends for？________A.Celebrating the fact that she has made a decision to find a husband．B.Checking the power of money among her circle of friends．C.Encouraging her friends to help find her Mr．D.Sharing her happiness of having found true love．（2）What does the underlined word “nuts” mean in the last paragraph？________A.delicious ．B.sensible．C.angry ．D.foolish．（3）What’s the purpose of the author’s mentioning getting a better job in Paragraph 2？________A.To stress the importance of finding a good job．B.To stress the importance of taking a positive attitude．C.To show that waiting patiently is necessary to get a job．D.To state that we need to be patient before a job is offered．（4）What kind of person do you think the lady is？________A.Adventurous．B.Imaginative．C.Considerate．D.Polite．【答案】CDBA【考点】完形综合阅读理解综合【解析】本文章主要讲述了一位女士向朋友提供1万美元的酬谢，让朋友们帮忙给她寻找心上人的故事．【解答】（1）C．细节题．根据文章内容， She is offering﹩10，000 to any of her friends who canintroduce her to her Mr． Right． She wants to find her future husband through this way．由此可知，这个女士将会为能够为她找到心上人的她的任何朋友提供1万美金．结合选项，故选C．（2）D．词义猜测题．根据文章内容，根据最后一段的I know you’re thinking that this is nuts． Just plain crazy可知她给她朋友的信中指出，在她的朋友看了信之后可能会认为她疯了，非常得愚蠢．结合选项，故选D．（3）B．细节题．根据文章内容， If the book had taught her anything， it was that she needed to take a more positive role in finding love． After all， if she wanted to get a better job，she wouldn’t just sit outside an employer’s building and wait for someone to offer it to her由此可知，文中提到得到更好的工作是为了强调做任何事都应该要有以及积极主动的态度，结合选项，故选B．（4）A．推理题．根据全文内容可知，旧金山一家广告公司的一位很有名的女士给她的朋友们写信让朋友们帮助寻找她的白马王子，并在举行婚礼这一天给予成功者一万美金，由此说明她是一个很大胆的敢于冒险的女性．结合选项，故选A．3. Taxi﹣booking app Uber agreed to sell its business in China to Didi Chuxing． The two firms had been fierce competitors, but Didi Chuxing had controlled the Chinese market with an 87% share．Uber China launched in 2014, but it had failed to make any profit for a long time． Cheng Wei, founder and chief executive of Didi Chuxing, said the two companies had learned a great deal from each other over the past two years in China． He added that the deal would set the mobile transportation industry on a healthier path of growth at a higher level． As part of the deal, Mr． Cheng would join the board of Uber, while Uber chief executive Travis Kalanick would also join Didi’s board．Uber’s China business would own its separate branding while US﹣based Uber Technologies would hold about 17.5% in the combined company． Didi Chuxing is backed by Chinese Internet giants Tencent and Alibaba．Uber had been struggling to break into the Chinese market despite having Chinese search engine Baidu as an investor． Last February, the company admitted it was losing more than $1 billion a year in China．“Funding their Chinese dreams was becoming too expensive for Uber, ” Duncan Clark, chairman of Beijing﹣based consultancy BDA, told the BBC． Travis Kalanick said, “As a businessman,I’ve learned that being successful is about listening to your head as well as following your heart．”The fierce competition had led both companies to spend much more on their journeys． The combination is likely to see fewer such subsidies（补贴）．“One th ing to watch carefully is how quickly consumers feel the impact as subsidies are withdrawn．” Mr． Clark added．The deal with Didi Chuxing came just days after China had agreed to provide a legal framework for taxi﹣ordering apps． Both Uber and Didi welcomed the decision． The new rules took effect last November and could, among other things, forbid such platforms to operate below cost．（1）According the second paragraph， what can we know？________A.Being successful is about listening to your head and following your heart．B.The deal would make the mobile transportation industry grow much faster．C.Didi Chuxing had learnt more in China than Uber over the past two years．D.Mr．（2）What is the best title of the passage？________A.Uber sold Chinese business to Didi Chuxing．ing Didi Chuxing brings more subsidies．C.Listen to your head and follow your heart．D.The new rules look effect last November．（3）What is the impact of the fierce competition between Uber and Didi？________A.Uber dominated the Chinese market with an 87% share．B.China provided a legal framework for taxi﹣ordering apps．C.Funding their Chinese dreams became expensive for Uber．D.Chinese search engine Baidu became an investor of Uber’s．（4）The passage is probably taken from a website about________．A.apps．B.politics．C.economy．D.technology．【答案】DACC【考点】阅读理解综合【解析】本文讲述了优步在与滴滴竞争的几年中没有任何盈利，最终被占有市场份额87%的滴滴公司收购合并．【解答】（1）D．细节理解题．由第二段Mr． Cheng would join the board of Uber，．郑志刚将加入优步董事会，可知选D．（2）A．主旨归纳题．本文讲述了优步在与滴滴竞争的几年中没有任何盈利，最终被占有市场份额87%的滴滴公司收购合并，故A，优步将中国业务出售给滴滴出行符合，选A．（3）C．细节理解题．由第四段Last February， the company admitted it was losingmore than $1 billion a year in China．“Funding their Chinese dreams was becoming too expensive for Uber，” 去年2月，优步公司承认在中国每年亏损超过10亿美元．“为他们的中国梦提供资金对优步来说太贵了．”，可知选C．（4）C．出处推断题．本文讲述了优步被占有市场份额87%的滴滴公司收购合并，涉及到的是经济领域，故可能来源于经济类网站，故选C．4. You get anxious if there’s no wi﹣fi in the hotel or mobile phone signal up the mountain． You feel upset if your phone is getting low on power, and you secretly worry things will go wrong at work if you’re not there．All these can be called “always on” stress caused by smart phone addiction．For some people, smart phones have liberated them from the nine﹣to﹣fivework． Flexible working has given them more autonomy（自主权）in their working lives and enabled them to spend more time with their friends and families． For many others though, smart phones have become tyrants（暴君）in their pockets, never allowing themto turn them off, relax and recharge their batteries．Pittsburgh﹣based developer Kevin Holesh was worried about how much he was ignoringhis family and friends in favour of his iPhone． So he developed an app ﹣ Moment ﹣ to monitor his usage． The app enables users to see how much time they’re spending on the device and set up warnings if the usage limits are breached（突破）．“Moment’s goal is to promote balance in your life, ” his website explains．“Some time on your phone, some time off it enjoying your loving family and friends around you．”Dr． Christine Grant, an occupational（职业的）psychologist at Coventry University, said, “The effects of this ‘always on’ culture are that your mind is never resting, and you’re not giving your body time to recover,so you’re always stressed． And the more tired and stressed we get, the more mistakes we make． Physical and mental health can suffer．”And as the number of connected smart phones is increasing, so is the amount of data． This is leading to a sort of decision paralysis（瘫痪）and is creating more stress in the workplace because people have to receive a broader range of data and communications which are often difficult to manage．“It actually makes it more difficult to make decisions and many do less because they’re controlled by it a ll and fell they can never escape the office, ” said Dr． Christine Grant．（1）What’s the first paragraph mainly about？________A.The popularity of smart phones．B.The progress of modern technology．C.The signs of “always on” stress．D.The cause of smart phone addiction．（2）Kevin Holesh developed “Moment” to________．A.research how people use their mobile phones．B.help people control their use of mobile phones．C.make people love parents and friends around．D.increase the fun of using mobile phones．（3）What’s Dr．Christine Grant’s attitude towards “always on” culture？________A.Confused．B.Positive．C.Doubtful．D.Critical．（4）According to the last paragraph， a greater amount of data means________．A.we will become less productive．B.we can make a decision more quickly．C.we will be equipped with more knowledge．D.we can work more effectively．【答案】CBDA【考点】阅读理解综合完形综合【解析】本文描述了手机上瘾的症状，为了控制人们使用手机，平衡生活，Kevin Holesh开发了一个app来控制人们使用手机的时间．【解答】（1）C．主旨大意题．文章中的第一段最后一句“All these can be called ”always on" stress caused by smart phone addiction．“是对前面举例的总结，表达了社会上出现的由于手机上瘾而造成的”在线"压力现象．故选C．（2）B．细节理解题．根据文章第三段前两句话“Pittsburgh﹣based developer Kevin Holesh was worried about how much he was ignoring his family and friends in favor of his iPhone． So he developed an app ﹣ Moment ﹣ to monitor his usage．” 可知Kevin Holesh 发明了“Moment”是为了帮助人们控制使用手机．故选B．（3）D．态度观点题．根据文章第四段可知Dr． Christine Grant说的话：这种总是在线文化使你的大脑得不到休息，不能给你的身体时间去回复，所以你总是处于紧张状态．这样有损你的身心健康．可知他抱有批判的态度．故选D．（4）A．推理判断题．根据文章最后一段This is leading to a sort of decision paralysis（瘫痪） and is creating more stress in the workplace because people have to receive a broader range of data and communications which are often difficult to manage．可推断出，大量数据表明我们的生产率更低．故A正确．第二节（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．Nobody likes to think they are “that guy” at work．（1）_______． So， what are someof the rudest things that people do at work ﹣and why shouldn’t you do them？• Behaving in an unacceptable wayThe most common form of this is eating smelly foods at lunchtime． Other things alike include body smell and its opposite， the wearing of strong perfume， messy desks， orbad breath．（2）_______．• Checking email on your phone when you’re talking to other peopleA recent survey shows that 49 percent of people said their bosses checked their phoneswhile talking with them．（3）_______．If you’ve ever wondered why your team members are unmotivated， this may be why． In fact，when you’re talking to someone at work， you should reject any non﹣important calls．• （4）_______Do you like the sound of your own voice？ Great．Perhaps it’s time you learned to like the sound of other people’s voices too． If you interrupt others when they speak，they’ll dislike you and discount whatever you’re saying． And if you routinely take up three quarters of the meeting with your monologues（独角戏）， people will turn off and， quite rightly， start checking email on their phones． However， if you listen to what others say and show interest by asking intelligent questions，they’ll l ove you and be likely to give you their support when you speak．• ● Showing off how much you earn（5）_______． If you show off your income to someone and then discover you get less than them，you’ll look like a fool． If you earn more，they’ll feel tired of you． So keep them guessing and hide your earning power in quiet ways ﹣ like always paying for the team coffees．A． Talking all the timeB． Being a good listenerC． Team﹣working can never be ignoredD． All these things will become part of your personal brandE．It’s better to be modest when you talk about your incomesF． Bad behavior at work is common ﹣ and often we do it without thinkingG． An interesting email is more valuable than the person you are actually talking to【答案】F,D,G,A,E【考点】七选五阅读【解析】本文是一篇选句填空，文章主要介绍了没有人喜欢在工作中认为自己是“那家伙”，工作上的不良行为是常见的﹣﹣而且我们常常不加思索地去做．那么，人们在工作中做的最糟糕的事情是什么？为什么你不应该这样做呢？【解答】1﹣5 FDGAE（1）F．细节理解题．根据“So， what are some of the rudest things that people do at work ﹣and why shouldn’t you do them？那么，人们在工作中做的最糟糕的事情是什么？为什么你不应该这样做呢？’可知此处应填”工作上的不良行为是常见的﹣﹣而且我们常常不加思索地去做‘故选F．（2）D．细节理解题．根据“Other things alike include body smell and its opposite， the wearing of strong perfume， messy desks， or bad breath．其他类似的东西包括身体的气味和它的反面，浓烈的香水，凌乱的桌子，或者口臭．’可知此处应填”所有这些都将成为你个人品牌的一部分‘故选D．（3）G．细节理解题．根据“A recent s urvey shows that 49 percent of people said their bosses checked their phones while talking with them．最近的一项调查显示，49%的人说他们的老板在和他们谈话时检查了他们的手机．可知此处应填”一封有趣的电子邮件比你实际交谈的人更有价值．‘故选G．（4）A．推理判断题．根据“Do you like the sound of your own voice？你喜欢你自己的声音吗？’可知此处应填”所有的时间都在说‘故选A．（5）E．推理判断题．根据“If you show off your income to someone and then discoveryou get less than them，you’ll look like a fool如果你向某人炫耀你的收入，然后发现你的收入比他们少，你就会看起来像个傻瓜．’可知此处应填”谈论你的收入时最好谦虚一点‘故选E．第二部分英语知识运用（共两节）第一节完形填空（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A、B、C和D四个选项中，选出可以填入空白处的最佳选项．A few years ago, I took a sightseeing trip to Washington, DC．I saw many of our nation’s treasures, and I also saw a lot of our fellow citizens on the street ﹣（1）_______ones, like beggars（乞丐）and homeless folks．Standing outside the Ronald Reagan Center, I heard a voice saying: “Can you help me?” When I （2）_______, I saw an elderly blind woman with her hand （3）_______． In a natural reaction, I （4）_______ into my pocket, pulled out all of my loose change and placed it in her hand without even looking at her． I was （5）_______at being botheredby a beggar．But the blind woman smiled and said: "I don’t want your money． I just need help findingthe （6）_______．"In an instant, I realized what I had done． I had acted with prejudice（偏见）﹣I’d （7）_______another person （8）_______ for what I believed she had to be．I hated what I saw in myself． This incident brought back my basic belief． It （9）_______ me that I believed in being modest even though I’d lost that （10）_______ for a moment．The thing I had forgotten about myself is that I am a （n）（11）_______． I left Honduras and arrived in the U． S． at the age of 15． I started my new life with two suitcases, my brother and sister, and a strong mother． Through the （12）_______, I have been a dish washer, roofer, mechanic, cashier and pizza delivery driver （13）_______many other humble hobs, and （14）_______ I became a network engineer．In my own life, I have （15）_______ many acts of prejudice． I remember a time, atthe age of 17 ﹣ when I was a busboy, I heard a father tell his little boy that if he did not do well on school, he would （16）_______ like me． I have also seen the same treatment of family and friends, so I know what it’s like, and I should have known （17）_______．But now, living my American middle class lifestyle, it is too easy to forget my past, to forget who I am and where I have been, and to lost sight of where I want to go． That blind woman cured me of my（18）_______． She reminded me of my belief in beinghumble, and to always keep my eyes and heart open．（19）_______, I helped that woman to the post office． And in writing this essay, I hope to thank her for the （20）_______ lesson she gave me．（1）A.unfortunateB.charmlessC.greedyD.good﹣for﹣mothing（2）A.turned overB.turned backC.turned aboutD.turned away（3）A.extendedB.expandedC.spreadD.lengthened（4）A.searchedB.reachedC.stuckD.went（5）A.amazedB.astonishedC.amusedD.annoyed（6）A.shopping centerB.police stationC.post officeD.bus station（7）A.judgedB.estimatedC.treatedD.believed（8）A.practicallyB.probablyC.recommendedD.simply（9）A.indictedB.remindedC.recommendedD.warned（10）A.causeB.ideaC.dreamD.belief（11）A.AmericanB.immigrantC.beggarD.engineer（12）A.yearsB.monthsC.momentsD.days（13）A.aboveB.belowC.amongD.beyond（14）A.deliberatelyB.urgentlyC.immediatelyD.eventually（15）A.witnessedB.experiencedC.learnedD.heard（16）A.keep upB.stay upC.turn upD.end up（17）A.betterB.worseC.moreD.less（18）A.ignoranceB.povertyC.blindnessD.fear（19）A.In shortB.By the wayC.On a wholeD.In an instant（20）A.valuelessB.worthlessC.pricelesseless 【答案】ACABDCADBDBACDBDACBC【考点】阅读理解综合完形综合【解析】本文主要讲了“我”在路上遇到一个盲人老太太向“我”请求帮助，于是“我”掏钱给她，但她只是想让“我”给她指路，“我”为自己以貌取人感到惭愧，想起了自己以前被生活所迫工作时因为外表也被人当作反面教材来教育孩子，于是感觉到盲人老太太指引了迷失的我．【解答】（1）A．考查形容词及语境理解．由下文“like beggars and homeless folks”可推断，作者也在街上看见了不少的像乞丐和流浪汉这样的不幸的人，故答案为A．（2）C．考查动词短语及语境理解．A． turned over打翻； B． turned back背对着；C． turned about转身； D． turned away 转身离开；根据下文I saw an elderly blind woman 可知当作者转身，看到一位盲人老太太，故答案为C．（3）A．考查动词及语境理解．根据下文"I into my pocket， pulled out all of my and placed it in her hand without even looking at her．"可推断，作者看见一个年长的盲人女士伸着手（向作者乞讨），故答案为A．（4）B．考查动词及语境理解．根据下文pulled out all of my loose change 可推断，作者将手伸进自己的口袋里，故答案为B．（5）D．考查形容词及语境理解．根据下文“being bothered by a beggar”可推断，被一个乞丐打扰使得作者很恼怒，故答案为D．（6）C．考查名词及语境理解．根据下文“By the way， I helped that lady to the post office．”可知，盲人女士想要找邮局，故答案为C．（7）A．考查动词及语境理解．根据前文In an instant， I realized what I had done． I had acted with prejudice（偏见）﹣可知此处为判断，故答案为A．（8）D．考查副词及语境理解．根据another person （8）for what I believed she had to be可知作者只是简单地设想她应该是干那一行的，故答案为D．（9）B．考查动词及语境理解．根据It （9）me that I believed in being modest可知这件事情再次让作者想起了自己信奉谦逊，故答案为B．（10）D．考查名词及语境理解．根据前文This incident brought back my basic belief可知即使我有一段时间丢失了它，但是它仍旧提醒我相信谦逊，故答案为D．（11）B．考查名词及语境理解．根据下文“I left Honduras and arrived in the U S at theroofer， mechanic， cashier and pizza delivery driver 可知这么多年以来，作者干过很多事情，故答案为A．（13）C．考查介词及语境理解．根据下文many other humble hobs可知，经过这么多年，作者做过洗碗工，修房顶的人，送货工等多个卑微的工作，故答案为C．（14）D．考查副词及语境理解．A． deliberately故意地； B． urgently紧急地；C． immediately立即； D． eventually 最后；根据and （14）I became a network engineer可知最终作者成了网络工程师，故答案为D．（15）B．考查动词及语境理解．根据In my own life， I have （15）many acts of prejudice可知作者经历过很多偏见的做法，故答案为B．（16）D．考查动词及语境理解．A． keep up坚持； B． stay up熬夜； C． turn up出现，露面； D． end up 结束；根据前文 I remember a time， at the age of 17 ﹣ when I was a busboy， I heard a father tell his little boy that if he did not do well on school可知那位父亲说自己的孩子如果不努力学习，他们最终会以作者的下场而结束，故答案为D．（17）A．考查形容词及语境理解．根据前文so I know what it’s like可知作者对这种情况非常了解，故答案为A．（18）C．考查名词及语境理解．根据前文That blind woman cured me of my可知这位盲人女士治愈了我的无知，故答案为C．（19）B．考查固定搭配及语境理解．A． In short总之； B． By the way 顺便说一下；C． On a whole总的来说； D． In an instant立即；根据（19）， I helped that woman to the post office可知顺便说一下，作者帮助老人去了邮局，故答案为B．（20）C．考查形容词及语境理解．根据 And in writing this essay， I hope to thank herfor the （20）lesson she gave me可知我也想谢谢她教了我一节宝贵的课，故答案为C．第二节（每小题1.5分，满分15分）阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式．阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

2018年普通高等学校招生全国统一考试模拟试题理数(五)第Ⅰ卷一、选择题：本大题共12个小题,每小题5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. 已知全集，集合，集合，则（）A. B. C. D.【答案】A【解析】由题可知，，，，故选A.2. 已知，则（）A. B. C. D.【答案】D【解析】，即，则，故选D.3. 设为虚数单位，现有下列四个命题：：若复数满足，则；：复数的共轭复数为：已知复数，设，那么；：若表示复数的共轭复数，表示复数的模，则.其中的真命题为（）A. B. C. D.【答案】B【解析】：若复数满足，，故正确；：，其共轭复数是，故错误；：由题意，可得，则，故错误；：设，则，故，所以正确，故选B.4. 在中心为的正六边形的电子游戏盘中(如图)，按下开关键后，电子弹从点射出后最后落入正六边形的六个角孔内，且每次只能射出一个，现视，，，，，对应的角孔的分数依次记为1,2,3,4,5,6,若连续按下两次开关，记事件为“两次落入角孔的分数之和为偶数”,事件为“两次落入角孔的分数都为偶数”,则（）A. B. C. D.【答案】D【解析】事件包括：共种，而事件包括，共种，由题可得，，故选D.5. 某几何体的正视图与俯视图如图，则其侧视图可以为（）A. B. C. D.【答案】B【解析】由俯视图与正视图可知该几何体可以是一个三棱柱挖去一个圆柱，因此其侧视图为矩形内有一条虚线，虚线靠近矩形的左边部分，只有选项符合题意，故选B.【方法点睛】本题利用空间几何体的三视图重点考查学生的空间想象能力和抽象思维能力，属于难题.三视图问题是考查学生空间想象能力最常见题型，也是高考热点.观察三视图并将其“翻译”成直观图是解题的关键，不但要注意三视图的三要素“高平齐，长对正，宽相等”，还要特别注意实线与虚线以及相同图形的不同位置对几何体直观图的影响.6. 河南洛阳的龙门石窟是中国石刻艺术宝库之一，现为世界文化遗产，龙门石窟与莫高窟、云冈石窟、麦积山石窟并称中国四大石窟.现有一石窟的某处“浮雕像”共7层，每上层的数量是下层的2倍，总共有1016个“浮雕像”，这些“浮雕像”构成一幅优美的图案，若从最下层往上“浮雕像”的数量构成一个数列，则的值为（）A. 8B. 10C. 12D. 16【答案】C【解析】最下层的“浮雕像”的数量为，依题有：公比，解得，则，，从而，故选C.7. 下列函数在其定义域内既是增函数又是奇函数的是（）A. B. C. D.【答案】C【解析】选项中，函数为奇函数，但由，得该函数有无穷多个零点，故不单调；选项中，函数满足，故既不是奇函数又不是增函数；选项中，函数定义域是，并且，函数是奇函数，设，那么当时，，函数是增函数，由复合函数单调性知，函数是增函数；选项中，函数是奇函数且是减函数，故选C.8. 下面推理过程中使用了类比推理方法，其中推理正确的个数是①“数轴上两点间距离公式为，平面上两点间距离公式为”，类比推出“空间内两点间的距离公式为“；AB|=√(x2-x1)2+(y2-y1)2+(z2-z1)②“代数运算中的完全平方公式”类比推出“向量中的运算仍成立“；③“平面内两不重合的直线不平行就相交”类比到空间“空间内两不重合的直线不平行就相交“也成立；④“圆上点处的切线方程为”，类比推出“椭圆上点处的切线方程为”.A. 1B. 2C. 3D. 4【答案】C【解析】对于①，根据空间内两点间距离公式可知，类比正确；对于②，，类比正确；对于③，在空间不平行的两直线，有相交和异面情况两种情况，类比错误；对于④，椭圆上点处的切线方程为为真命题，综合上述，可知正确个数为个，故选C...................9. 已知直线与正切函数相邻两支曲线的交点的横坐标分别为，，且有，假设函数的两个不同的零点分别为，，若在区间内存在两个不同的实数，，与，调整顺序后，构成等差数列，则的值为（）A. B. C. 或或不存在 D. 或【答案】C【解析】由题意及，可知，又，得到，因此，令，，假设存在两个不同的实数，若使调整顺序后能组合成等差数列，设公差为，则有下列情况：①若与相邻，则，，不能相邻，否则，将超出范围. ②若与之间间隔一个数，设这个数为，则，经分析，数列为时，不成立，不妨设数列为，此时，当时，，不存在，当时，，也不存在. ③若与之间间隔两个数，即组成一个等差数列，，，，此时，构成等差数列，当时，，当时，，故选C.10. 已知抛物线的焦点为,双曲线的右焦点为，过点的直线与抛物线在第一象限的交点为，且抛物线在点处的切线与直线垂直，则的最大值为（ ）A.B. C.D. 2【答案】B【解析】由题可知抛物线的焦点为，过的直线方程为，联立方程组 ，，由题可知， ，（舍去），又由，因此，又由题可知，即得，又，当且仅当时，取等号，即，故选B.【易错点晴】本题主要考查抛物线、双曲线的方程与性质、导数的几何意义以及利用基本不等式求最值，属于难题.利用基本不等式求最值时，一定要正确理解和掌握“一正，二定，三相等”的内涵：一正是，首先要判断参数是否为正；二定是，其次要看和或积是否为定值（和定积最大，积定和最小）；三相等是，最后一定要验证等号能否成立（主要注意两点，一是相等时参数否在定义域内，二是多次用或时等号能否同时成立）.11. 已知函数的导函数(其中为自然对数的底数)，且，为方程的两根，则函数，的值域为（ ）A.B.C.D.【答案】C【解析】由题意，可设，则，，为方程的两根，，即得，即得，因此，从而，故，当时，，，，从而得到，即函数在区间上单调递增，，，故选C.12. 底面为菱形且侧棱垂直于底面的四棱柱中，，分别是，的中点,过点，，，的平面截直四棱柱，得到平面四边形，为的中点，且，当截面的面积取最大值时，的值为（）A. B. C. D.【答案】C【解析】由平面与平面平行，得与平行，同理可得与平行，截面四边形是平行四边形，又，可知截面四边形是菱形，因此，设，则，，由余弦定理得，可得，，又，当且仅当，即时，最大，此时也最大，并求得，，因此，故选C.【方法点晴】本题主要考查待直棱柱的性质与截面性质以及最值问题，属于难题.解决高中数学中的最值问题一般有两种方法：一是几何意义，特别是用圆锥曲线的定义和平面几何的有关结论来解决，非常巧妙；二是将最值问题转化为函数问题，然后根据函数的特征选用参数法、配方法、判别式法、三角函数有界法、函数单调性法以及均值不等式法，本题就是用的这种思路，利用配方法求截面积最值的.第Ⅱ卷本卷包括必考题和选考题两部分.第13∽21题为必考题，每个试题考生都必须作答.第22∽23题为选考题，考生根据要求作答.二、填空题：本题共4小题，每小题5分.13. 已知函数,为的导函数，则的展开式中项的系数是__________．【答案】-540【解析】，其展开式中项的系数为，故答案为.【方法点晴】本题主要考查导数的求导法则以及二项展开式定理的通项与系数，属于简单题. 二项展开式定理的问题也是高考命题热点之一，关于二项式定理的命题方向比较明确，主要从以下几个方面命题：（1）考查二项展开式的通项公式；（可以考查某一项，也可考查某一项的系数）（2）考查各项系数和和各项的二项式系数和；（3）二项展开式定理的应用.14. 已知向量，，向量，的夹角为，设，若，则的值为__________．【答案】【解析】由，有，即得，也就是，又，因此，从而得到，故答案为.15. 已知函数，，，，则关于的不等式的解集为__________．【答案】【解析】由，得，，，因此函数在区间上单调递增，，从而，令，故不等式的解集为，故答案为.16. 已知数列的通项公式为，数列为公比小于1的等比数列，且满足，，设，在数列中，若，则实数的取值范围为__________．【答案】【解析】在等比数列中，由，又，且公比小于，，因此，由，得到是取中最大值，是数列中的最小项，又单调递减，单调递增，当时，，即是数列中的最小项，则必须满足，即得，当时，，即，是数列中的最小项，则必须满足，即得，综上所述，实数的取值范围是，故答案为.三、解答题：解答应写出文字说明、证明过程或演算步骤.17. 已知函数在半个周期内的图象的如图所示，为图象的最高点，，是图象与直线的交点，且.（1）求的值及函数的值域；（2）若，且，求的值.【答案】(1).（2）.【解析】试题分析：（1）利用辅助角公式化简函数解析式为.由，，可得，是等腰直角三角形.由点到直线的距离为，得函数的周期为，从而可得解析式，，进而可得函数的值域；（2）由，且，可求出的正弦值和余弦值，，利用两角和的正弦公式可得结果.试题解析：（1）函数化简得.因为，所以，所以，所以，所以是等腰直角三角形.又因为点到直线的距离为4，所以，所以函数的周期为16.所以，函数的值域是.（2）由（1），知因为，所以因为，所以，所以，所以.18. 如图所示的四棱锥中，底面为矩形，，的中点为,，异面直线与所成的角为，平面.（1）证明：平面；（2）求二面角的余弦值的大小.【答案】（1）见解析.（2）.【解析】试题分析：（1）由已为矩形，可得为的中点.结合为的中点，根据三角形中位线定理可得，，由线面平行的判定定理可得结果；（2）由（1）可知，所以或，先证明，可得，因为，，两两垂直，分别以，，所在直线为轴，轴，轴建立空间直角坐标系，平面的一个法向量为，再求出平面的一个法向量，利用空间向量夹角余弦公式可得结果.试题解析：（1）由已知为矩形，且，所以为的中点.又因为为的中点，所以在中，，又因为平面，平面，因此平面.（2）由（1）可知，所以异面直线与所成的角即为 (或的补角).所以或.设，在中，，，又由平面可知，且为中点，因此，此时，所以，所以为等边三角形，所以，即，因为，，两两垂直，分别以，，所在直线为轴，轴，轴建立空间直角坐标系，如图所示，则，，，，所以，.由，，，可得平面，可取平面的一个法向量为.设平面的一个法向量为，由令，所以.因此，又二面角为锐角，故二面角的余弦值为.【方法点晴】本题主要考查线面平行的判定定理、利用空间向量求二面角，属于难题.空间向量解答立体几何问题的一般步骤是：（1）观察图形，建立恰当的空间直角坐标系；（2）写出相应点的坐标，求出相应直线的方向向量；（3）设出相应平面的法向量，利用两直线垂直数量积为零列出方程组求出法向量；（4）将空间位置关系转化为向量关系；（5）根据定理结论求出相应的角和距离.19. 207年8月8日晚我国四川九赛沟县发生了7.0级地震，为了解与掌握一些基本的地震安全防护知识，某小学在9月份开学初对全校学生进行了为期一周的知识讲座，事后并进行了测试（满分100分），根据测试成绩评定为“合格”（60分以上包含60分）、“不合格”两个等级，同时对相应等级进行量化：“合格”定为10分，“不合格”定为5分.现随机抽取部分学生的答卷，统计结果及对应的频率分布直方图如图所示：（1）求的值；（2）用分层抽样的方法，从评定等级为“合格”和“不合格”的学生中抽取10人进行座谈，现再从这10人中任选4人，记所选4人的量化总分为，求的分布列及数学期望；（3）设函数（其中表示的方差）是评估安全教育方案成效的一种模拟函数.当时，认定教育方案是有效的；否则认定教育方案应需调整，试以此函数为参考依据.在（2）的条件下，判断该校是否应调整安全教育方案？【答案】（1）见解析.（2）见解析.（3）见解析.【解析】试题分析：（1）由频率分布直方图可求出，得分在的频率从而可得学生答卷数以及分在的频率，于是可得的值，又，进而可得的值；（2）抽取的人中“合格”有人，“不合格”有人，可取，，，，，根据组合知识，利用古典概型概率公式求出随机变量对应的概率，即可得分布列，利用期望公式可得结果；（3）利用（2）的结论，由方差公式求出，从而得，故需要调整安全教育方案.试题解析：（1）由频率分布直方图可知，得分在的频率为，故抽取的学生答卷数为，又由频率分布直方图可知，得分在的频率为0.2，所以.又，得，所以..（2）“合格”与“不合格”的人数比例为，因此抽取的10人中“合格”有6人，“不合格”有4人，所以有40，35，30，25，20共5种可能的取值.，，，，.的分布列为所以.（3）由（2）可得，所以.故可以认为该校的安全教育方案是无效的,需要调整安全教育方案.20. 如图所示，在平面直角坐标系中，椭圆的中心在原点，点在椭圆上，且离心率为.（1）求椭圆的标准方程；（2）动直线交椭圆于，两点，是椭圆上一点，直线的斜率为，且，是线段上一点，圆的半径为，且，求【答案】（1）；（2）.【解析】试题分析：（1）根据点在椭圆上，且离心率为，结合性质，列出关于、、的方程组，求出、，即可得椭圆的标准方程；（2），联立方程，由韦达定理、弦长公式可得的值，从而可得，再利用两点间距离公式可得，于是，进而可得结果.试题解析：（1）因为在椭圆上，所以.又，联立方程组,故椭圆的标准方程为（2）设，，联立方程.由，得，且，，所以.由题意可知圆的半径.由题设知，因此直线的方程为.联立方程因此.所以.因为，所以，从而有，即得.因此的取值范围为.21. 已知函数，，其中为常数.（1）当，且时，求函数的单调区间及极值；（2）已知，，若函数有2个零点，有6个零点，试确定的值.【答案】（1）见解析.（2）.【解析】试题分析：（1）求出，在定义域内，分别令求得的范围，可得函数增区间，求得的范围，可得函数的减区间，根据函数的单调性可得的极值；（2）若函数存在2个零点，则方程有2个不同的实根，设，利用导数研究函数的单调性，结合函数图象可得，而有6个零点，故方程与都有三个不同的解，可得,结合可得结果.试题解析：（1）因为，所以，令或（舍）.当时，，函数单调递减；时，，函数单调递增.因此的极小值为，无极大值.（2）若函数存在2个零点，则方程有2个不同的实根，设，则.令，得；令，得，或，所以在区间，内单调递减，在区间内单调递增，且当时，令，可得，所以，；，，因此函数的草图如图所示，所以的极小值为.由的图象可知.因为，所以令，得或，即或，而有6个零点，故方程与都有三个不同的解，所以，且，所以.又因为，，所以.请考生在22、23两题中任选一题作答，如果多做，则按所做的第一题记分.22. 选修4-4：坐标系与参数方程在平面直角坐标系中，曲线的参数方程为(为参数)以坐标原点为极点，轴正半轴为极轴建立极坐标系.（1）求曲线的普通方程和极坐标方程；（2）直线的极坐标方程为，若与的公共点为，且是曲线的中心，求的面积.【答案】（1），.（2）.【解析】试题分析：曲线的参数方程利用平方法消去参数，得其普通方程，将，代入普通方程并化简，可得其极坐标方程；（2）将代入极坐标方程可得，根据极径的几何意义利用韦达定理可得，再根据点到直线距离公式及三角形面积公式可得结果.试题解析：（1）由曲线的参数方程消去参数，得其普通方程为.将，代入上式并化简，得其极坐标方程为.（2）将代入得.得.设，，则，，所以.又由（1），知，且由（2）知直线的直角坐标方程为，所以到的距离是，所以的面积.【名师点晴】参数方程主要通过代入法或者已知恒等式（如等三角恒等式）消去参数化为普通方程，通过选取相应的参数可以把普通方程化为参数方程，利用关系式，等可以把极坐标方程与直角坐标方程互化，本题这类问题一般我们可以先把曲线方程化为直角坐标方程，用直角坐标方程解决相应问题．23. 选修4-5：不等式选讲已知函数，.（1）求不等式的解集；（2）求函数的单调区间与最值.【答案】（1）；（2）见解析.【解析】试题分析：（1）原不等式化为为，当时，对上式两边平方，利用一元二次不等式的解法求解，当时，原不等式的解集为空集，综合两种情况可得结果；（2）将函数化为分段函数形式由此可得函数的递减区间为，递增区间为，并且最小值为，无最大值.试题解析：（1）由于，即为，当时，对上式两边平方，得，即得，当时，原不等式的解集为空集，因此的解集为，（2）由题可知作图如下，由.由图易知函数的递减区间为，递增区间为，并且最小值为，无最大值.。

本试题卷共8页。

全卷满分150分，考试用时120分钟。

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。

1. What are the speakers talking about?A. Staying online.B. Getting good grades.C. Making friends.2. What does the woman want the man to do?A. Help with housework.B. Do his homework.C. Have some rest.3. Where does the conversation take place?A. In a police station.B. In the car.C. At a driving class.4. Why does the man like the restaurant?A. It gives healthy food.B. Its food is cheap.C. It offers free bread.5. What does the man say about his mum?A. She has good smell.B. She’s a good cook.C. She has good hearing.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。

2017—2018学年度上学期高三年级五调考试数学(文科)试卷本试卷分第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．第I 卷(选择题 共60分)一、选择题(本题共12小题，每小题5分，共60分．从每小题所给的四个选项中，选出最佳选项，并在答题纸上将该项涂黑)1．已知集合{}{}2540,0,1,2,3M x x x N =-+≤=，则集合M N ⋂中元素的个数为 A ．4B ．3C ．2D ．12．已知,,a b R i ∈是虚数单位，若2a i bi -+与互为共轭复数，则()2a bi +=A ．34i -B ．5+4iC ．3+4iD ．5－4i3．如图所示程序框图的算法思路源于我国古代数学名著《九章算术》中的“更相减损术”，执行该程序框图，若输入的,a b 分别为14，18，则输出的a = A ．0B ．14C ．4D ．24．设()1112,1,,,,1,2,3232a f x x α⎧⎫∈---=⎨⎬⎩⎭，则使为奇函数且在区间()0,+∞内单调递减的α值的个数是 A ．1 B ．2C ．3D ．45．若点()cos ,sin P αα在直线2y x =-上，则cos 22πα⎛⎫+ ⎪⎝⎭的值等于 A ．45-B ．45C. 35-D ．356．如图，网格纸上小正方形的边长均为1，粗实线画出的是某几何体的三视图，则该几何体的体积为 A ．803B ．403C ．203D ．1037．已知函数()()cos f x x ωϕ=+的部分图像如图所示，则()f x 单调递减区间为 A ．13,,44k k k Z ππ⎛⎫-+∈ ⎪⎝⎭ B ．132,2,44k k k Z ππ⎛⎫-+∈ ⎪⎝⎭C ．13,,44k k k Z ⎛⎫-+∈ ⎪⎝⎭ D ．132,2,44k k k Z ⎛⎫-+∈ ⎪⎝⎭8．已知H 是球O 的直径AB 上一点，AH ：HB=1：3，AB ⊥平面，,H α为垂足，α截球O 所得截面的面积为4π，则球O 的表面积为 A ．163πB．3C ．643πD ．169π9．若在函数()()20,0f x ax bx a b =+>>的图像的点()()1,1f 处的切线斜率为2，则8a bab+的最小值是 A ．10B ．9C ．8D．10．若,x y 满足约束条件220,0,4,x y x y x y ⎧+≤⎪-≤⎨⎪+≤⎩则23y z x -=+的最小值为A ．2-B ．23-C ．125-D．4711．已知动圆M 与圆()221:11C x y ++=，与圆()222125C x y -+=：内切，则动圆圆心M 的轨迹方程是A ．22189x y += B.22198x y += C ．2219x y += D ．2219y x += 12．已知()f x 是定义在R 上的可导函数，且满足()()()10x f x xf x '++>，则 A ．()0f x >B ．()0f x <C.()f x 为减函数 D ．()f x 为增函数第Ⅱ卷(非选择题 共90分)二、填空题(本题共4小题，每小题5分，共20分) 13．已知函数()()3311log 2log 212xf x f f ⎛⎫=+= ⎪+⎝⎭，则___________．14．已知向量(),a b a b ==，则与的夹角的大小为___________．15．等比数列{}n a 中，若1532,4a a a =-=-=，则__________．16，已知平面α过正方体1111ABCD A B C D -的面对角线1AB ，且平面α⊥平面1C BD ，平面α⋂平面111ADD A AS A AS =∠，则的正切值为_________．三、解答题(共70分．解答应写出必要的文字说明、证明过程或演算步骤．第17～21题为必考题，每个试题考生都必须作答．第22、23题为选考题，考生根据要求作答) (一)必考题：共60分．17．(本小题满分12分)已知{}n a 是公差为3的等差数列，数列{}n b 满足(2)若射线():0l θαρ=≥分别交12,C C 于A ，B 两点(B 点不同于坐标原点O)，求OB OA的最大值．23．(本小题满分10分)选修4-5：不等式选讲 已知函数()212f x x x =--+． (1)求不等式()0f x >的解集；(2)若存在0x R ∈，使得()2024f x a a +<，求实数a 的取值范围．。

(衡水金卷）2018年普通高等学校招生全国统一考试模拟数学试题五 理第Ⅰ卷一、选择题：本大题共12个小题，每小题5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.已知全集U R =，集合{}223,A y y x x x R ==++∈，集合1,(1,3)B y y x x x ⎧⎫==-∈⎨⎬⎩⎭，则()U C A B =（ ）A ．(0,2)B ．80,3⎛⎫ ⎪⎝⎭C ．82,3⎛⎫⎪⎝⎭D ．(,2)-∞2. 已知3sin(3)2sin 2a a ππ⎛⎫+=+ ⎪⎝⎭,则sin()4sin 25sin(2)2cos(2)a a a a ππππ⎛⎫--+ ⎪⎝⎭=++-（ )A ．12B ．13C ．16D ．16-3。

设i 为虚数单位，现有下列四个命题：1p ：若复数z 满足()()5z i i --=,则6z i =； 2p ：复数22z i=-+的共轭复数为1+i 3p :已知复数1z i =+,设1(,)ia bi ab R z-+=∈，那么2a b +=-；4p ：若z 表示复数z 的共轭复数，z 表示复数z 的模,则2zz z =。

其中的真命题为（ ）A ．13,p pB ．14,p pC ．23,p pD ． 24,p p4.在中心为O 的正六边形ABCDEF 的电子游戏盘中(如图），按下开关键后,电子弹从O 点射出后最后落入正六边形的六个角孔内，且每次只能射出一个,现视A ，B ，C ，D ,E ，F 对应的角孔的分数依次记为1，2,3,4,5,6，若连续按下两次开关,记事件M 为“两次落入角孔的分数之和为偶数”，事件N 为“两次落入角孔的分数都为偶数”，则(|)P N M =( ）A ．23B ．14 C. 13 D ．125。

某几何体的正视图与俯视图如图，则其侧视图可以为（ ）A ．B ． C. D ．6. 河南洛阳的龙门石窟是中国石刻艺术宝库之一，现为世界文化遗产，龙门石窟与莫高窟、云冈石窟、麦积山石窟并称中国四大石窟。

2018年普通高等学校招生全国统一考试高考模拟调研卷英语（五）word版含答案2018年普通高等学校招生全国统一考试高考模拟调研卷英语（五）本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

考试结束后，将本试卷和答题卡一并交回。

第Ⅰ卷第一部分听力（共两节，满分30分）做题时，请先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

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．￡9.15．C．￡9.18．答案是B。

1．What does the woman mean?A．She lacks experience．B．She missed the i nterview．C．She isn’t interested in the job．2．Why can’t the lecture be held tomorrow?A．The lecture hall isn’t big enough．B．The CEO wo n’t be available then．C．The equipment in the lecture hall doesn’t work．3．How are the prices in the restaurant?A．Reasonable．B．High．C．Low．4．What is the man’s problem?A．He has no patience to wait for his wife．B．He can’t see the parking sign clearly．C．He’s parked his car in the wrong place．5．What does the man say about Kate?A．She is popular with children．B．She has always been popular．C．She was surprised at the party．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。