北京市第五中学 2017 年 12 月月考试题 英语学科
2020届北京市东城区第五中学高三上学期12月月考数学试题(解析版)
2020届北京市东城区第五中学高三上学期12月月考数学试题一、单选题1．已知集合{}20A x x a =-，2{|log (2)1}B x x =-≤，若B A ⊆,则实数a 的取值范围是 A ．(,4]-∞ B ．[4,)+∞C ．(,4)-∞D ．(4,)+∞【答案】A先求出,A B ，再根据包含关系求出a 的取值范围. 【详解】2a A x x ⎧⎫=⎨⎬⎩⎭，{}(]|0222,4B x x =<-≤=，因为B A ⊆，所以22a≤即4a ≤.故选A. 解对数不等式时，需要利用对数的运算性质把常数化成同底的对数，然后利用对数函数的单调性求不等式的解，注意对数的真数总是正数（容易忽视）.利用集合的包含关系求参数的取值范围时，注意端点可取否.2．已知0.6log 1.6a =，0.61.6b =， 1.60.6c =，则实数a ，b ，c 的大小关系是( ) A ．a b c << B ．a c b <<C ．c a b <<D ．b c a <<【答案】B根据对数函数和指数函数的单调性容易得出0.6 1.60.61.60,161,0061log <><<g g ，从而可得出a ，b ，c 的大小关系． 【详解】解：0.60.6log 1.6log 10<=Q ，0.601.6 1.61>=， 1.6000.60.61<<=，a cb ∴<<．故选：B ．本题考查了对数函数、指数函数的单调性，指数函数的值域，考查了计算能力，属于基础题．3．对于非零向量,a b r r ，“230a b +=r r r ”是“//a b r r”成立的（ ）A ．充分而不必要条件B ．必要而不充分条件C ．充要条件D ．既不充分又不必要条件【答案】A利用向量共线定理、简易逻辑的判定方法即可得出． 【详解】解：对于非零向量,a b r r ，由“230a b +=r r r ” ⇒3a b 2=-r r⇒ “//a b r r ”；反之不成立，可能λa b =r r ，32λ≠-．因此“230a b +=r r r ”是“//a b r r”的充分不必要条件． 故选：A ．本题考查了向量共线定理、简易逻辑的判定方法，考查了推理能力与计算能力，属于基础题．4．已知函数()()()f x x a x b =--（其中)a b >的图象如图所示，则函数()xg x a b=+的图象是（ ）A ．B ．C ．D ．【答案】C先由函数()f x 的图象判断a ，b 的范围，再根据指数函数的图象和性质即可得到答案． 【详解】解：由函数的图象可知，10b -<<，1a >，则()xg x a b =+为增函数， (0)10g b =+>，()g x 过定点(0,1)b +，故选：C ．本题考查了指数函数和二次函数的图象和性质，属于基础题．5．如图，点1(A x ，1)y ，2(B x ，2)y 分别是单位圆O 上的点，角α、β的终边分别为射线OA 和射线OB ，则1212x x y y +表示的值为( )A ．sin()αβ+B ．sin()αβ-C ．cos()αβ+D ．cos()αβ-【答案】D先根据三角函数的定义求出对应坐标，结合两角和差的三角公式进行计算即可． 【详解】解：由三角函数的定义知1cos x α=，1sin y α=，2cos x β=，2sin y β=， 则1212cos cos sin sin cos()x x y y αβαβαβ+=+=-， 故选：D ．本题主要考查三角函数的定义的应用，利用两角和差的三角公式以及三角函数的定义是解决本题的关键，属于基础题．6．△ABC 的内角A ，B ，C 的对边分别为a ，b ，c ，已知a sin A －b sin B =4c sin C ，cos A =－14，则bc =A ．6B ．5C ．4D ．3【答案】A利用余弦定理推论得出a ，b ，c 关系，在结合正弦定理边角互换列出方程，解出结果. 【详解】详解：由已知及正弦定理可得2224a b c -=，由余弦定理推论可得22222141313cos ,,,464224242b c a c c c b A bc bc b c +---==∴=-∴=∴=⨯=，故选A ． 本题考查正弦定理及余弦定理推论的应用．7． 已知函数()sin()(,0)2f x x πωϕϕω=+的图像在y 轴右侧的第一个最高点为(,1)6P π，在原点右侧与x 轴的第一个交点为5(,0)12Q π，则()3f π的值为（ ） A ．1 B ．12C ．22D ．3 【答案】B2,,2,,44x x x x T P Q T P Q πππωω=-====分别为点P,Q 的横坐标； 点P 为最高点，代入P 坐标得2,2,326k k k Z πππϕπϕπ+=+=+∈，又||2ϕπ<，则6π=ϕ ()sin 26f x x π⎛⎫=+ ⎪⎝⎭251sin sin 33662f ππππ⎛⎫⎛⎫=+== ⎪ ⎪⎝⎭⎝⎭，选B点睛：已知函数sin()(0,0)y A x B A ωϕω=++>>的图象求解析式(1)max min max min,22y y y y A B -+==. (2)由函数的周期T 求2,.T πωω= (3)利用“五点法”中相对应的特殊点求ϕ.8．在直角坐标系xOy 中,对于点(,)x y ,定义变换σ:将点(,)x y 变换为点(,)a b ,使得tan ,tan ,x a y b =⎧⎨=⎩其中ππ,(,)22a b ∈-.这样变换σ就将坐标系xOy 内的曲线变换为坐标系aOb 内的曲线.则四个函数12(0)y x x =>,22(0)y x x =>,3e (0)x y x =>,4ln (1)y x x =>在坐标系xOy 内的图象,变换为坐标系aOb 内的四条曲线（如图）依次是A ．②,③,①,④B ．③,②,④,①C ．②,③,④,①D ．③,②,①,④【答案】A用x ，y 表示出a ，b ，根据反正切函数的单调性得出各自图象的a ，b 的范围及大小关系，从而得出答案． 【详解】解：由x tanay tanb =⎧⎨=⎩可得a arctanx b arctany =⎧⎨=⎩，对于y 3＝e x （x ＞0），显然y 3＞1，∴b ＝arctan y 34π＞，∴y 3对应的图象为①；对于y 4＝lnx （x ＞1），a ＝arctan x ＞arctan14π=，∴y 4对应的图象为④；对于y 1和y 2，当0＜x ＜2时，2x ＞x 2，∴arctan2x ＞arctan x 2， 即当0＜a ＜arctan2时，∴arctan y 1＞arctan y 2， ∴y 1对应的图象为②，y 2对应的图象为③． 故选：A ．本题考查了反正切函数的性质，基本初等函数的性质，属于中档题．二、填空题9．17sin 6π⎛⎫- ⎪⎝⎭的值为_____．【答案】12-利用诱导公式71sin(4)sin 662πππ-+=-=-，故问题得解． 【详解】解：1771sin sin 4sin 6662ππππ⎛⎫⎛⎫-=-+=-=- ⎪ ⎪⎝⎭⎝⎭， 故答案为：12-本题主要考查诱导公式的运用，属于基础题．10．已知平面向量,a b r r 满足()3a a b ⋅+=r r r 且2a =r ，1b =r ，则向量a r 与b r的夹角为_____． 【答案】23π设向量a r 与b r的夹角为θ，[0θ∈，]π，由()3a a b ⋅+=r r r 可得23a a b +=r r r g ，代入数据可得关于cos θ的方程，解之结合θ的范围可得． 【详解】解：设向量a r 与b r的夹角为θ，[0θ∈，]π由()3a a b ⋅+=r r r 可得23a a b +=r r r g ，代入数据可得2221cos 3θ+⨯⨯=， 解之可得1cos 2θ=-， 故可得23πθ= 故答案为：23π本题考查数量积与两个向量的夹角的关系，属于基础题． 11．已知3(,)22ππα∈ ，3tan()4απ-=-，则sin cos αα+=_____． 【答案】15-由已知求得sin cos αα的值，结合平方关系求解sin α，cos α的值，则答案可求．【详解】解：Q 3tan()4απ-=-，3tan 4α∴=-，又3,22ππα⎛⎫∈⎪⎝⎭，,2παπα⎛⎫∈ ⎪⎝∈⎭∴， 则sin 0α>，cos 0α<，联立221sin 3cos 4sin cos αααα⎧+=⎪⎨=-⎪⎩，解得3sin 54cos 5αα⎧=⎪⎪⎨⎪=-⎪⎩． 1sin cos 5αα∴+=-．故答案为：15-．本题考查三角函数的化简求值，考查诱导公式及同角三角函数基本关系式的应用，属于基础题．12．函数的定义域为实数集，，对于任意都有，若在区间内函数恰有三个不同的零点，则实数的取值范围是__________．【答案】∵ ，是以 为周期的函数，若在区间上函数恰有三个不同的零点，则和在上有3个不同的交点，画出函数函数在上的图象，如图示： ，由，结合图象得：，故答案为：．13．已知函数()sin(),()()69f x x f x f ππω=+≤，对任意x ∈R 恒成立，则ω可以是_____．【答案】183,k k Z +∈，直接利用正弦型函数的性质的应用求出结果． 【详解】解函数()sin()6f x x πω=+，()9f x f π⎛⎫⎪⎝⎭„对任意x ∈R 恒成立，所以19f π⎛⎫= ⎪⎝⎭，即sin 196ππω⎛⎫+= ⎪⎝⎭，当2962k πππωπ+=+时，解得183k ω=+，()k ∈Z .故答案为：183k ω=+，()k ∈Z .，本题考查的知识要点：正弦型函数的性质的应用，主要考查学生的运算能力和转换能力及思维能力，属于基础题．14．函数()y f x =图象上不同两点1(A x ，1)y ，2(B x ，2)y 处的切线的斜率分别是A k ，B k ，规定||(,)||A B k k A B AB ϕ-=叫曲线()y f x =在点A 与点B 之间的“弯曲度”，给出以下命题：（1）函数321y x x =-+图象上两点A 、B 的横坐标分别为1，2，则(,)3A B ϕ> （2）存在这样的函数，图象上任意两点之间的“弯曲度”为常数； （3）设点A 、B 是抛物线，21y x =+上不同的两点，则(,)2A B ϕ„；（4）设曲线xy e =上不同两点1(A x ，1)y ，2(B x ，2)y ，且121x x -=，若(,)1t A B ϕ<g恒成立，则实数t 的取值范围是(,1)-∞； 以上正确命题的序号为__（写出所有正确的） 【答案】（2）（3）由新定义，利用导数逐一求出函数321y x x =-+、21y x =+在点A 与点B 之间的“弯曲度”判断（1）、（3）；举例说明（2）正确；求出曲线xy e =上不同两点1(A x ，1)y ，2(B x ，2)y 之间的“弯曲度”，然后结合(,)1t A B ϕ<g得不等式，举反例说明（4）错误． 【详解】解：对于（1），由321y x x =-+，得232y x x '=-， 则1|1A x k y ='==，2|8B x k y ='==，11y =，25y =，则||AB||(,)||A B k k A B AB ϕ-===<（1）错误；对于（2），常数函数1y =满足图象上任意两点之间的“弯曲度”为常数，（2）正确； 对于（3），设1(A x ，1)y ，2(B x ，2)y ，2y x '=，则1222A B k k x x -=-，||AB12|x x =-()2,21A B ϕ∴===，（3）正确； 对于（4），由xy e =，得x y e '=， ()1212,x x x x A B ϕ=．(,)1t A B ϕ<g恒成立，即12||x x t e e -<1t =时该式成立，∴（4）错误．故答案为：（2）（3）．本题是新定义题，考查了命题的真假判断与应用，考查了利用导数研究过曲线上某点的切线方程，考查了函数恒成立问题，关键是对题意的理解，属于中档题．三、解答题15．已知函数2()cos 2sin 1f x x x x =-+ ． （1）求()12f π的值及函数的最小正周期；（2）求f （x ）在区间[0,]2π上的最大值和最小值．【答案】（1）π（2）最小值为﹣1，最大值为2．（1）由题意利用三角恒等变换化简函数的解析式，从而求得12f π⎛⎫ ⎪⎝⎭的值，再利用正弦函数的周期性，得出结论．（2）由题意利用正弦函数的定义域和值域，求得()f x 在区间0,2π⎡⎤⎢⎥⎣⎦上的最大值和最小值． 【详解】解：（1）Q 函数2()cos 2sin 12cos22sin(2)6f x x x x x x x π=-+=+=+，∴2sin 123f ππ⎛⎫== ⎪⎝⎭，故()f x 的最小正周期为222T πππω===． （2）在区间0,2π⎡⎤⎢⎥⎣⎦上，72,666x πππ⎡⎤+∈⎢⎥⎣⎦， 故当7266x ππ+=时，函数()f x 取得最小值为1-； 当262x ππ+=时，函数()f x 取得最大值2．本题主要考查三角恒等变换，正弦函数的周期性、定义域和值域，属于基础题．16．在ABC A B C ∆中，角、、所对的边分别为,a b c 、、且a b c <<，sin A =（1）求角B 的大小；（2）若2a =，b =，求c 及ABC ∆的面积.【答案】（Ⅰ）3B π=；（Ⅱ）ABC S ∆=（Ⅰ）已知等式变形后，利用正弦定理化简，根据sinA 不为0求出cosB 的值，即可确定出角B 的大小；（Ⅱ）利用余弦定理列出关系式，把a ，b ，cosB 的值代入求出c 的值，利用三角形面积公式求出三角形ABC 面积即可． 【详解】(Ⅰ )sin A =Q ，2sin b A =，2sin sin A B A =，又0A π<<Q ，sin 0A ∴>，sin B ∴=a b c <<Q ，B C ∴<， 所以02B π<<，故3B π=.（Ⅱ）2a =Q ，b =，由余弦定理可得：22212222c c =+-⨯⨯⨯，即2230c c --= 解得3c =或1c =-（舍去），故3c =.所以11sin 2322ABC S ac B ∆==⨯⨯=. 解三角形问题，多为边和角的求值问题，这就需要根据正、余弦定理结合已知条件灵活转化边和角之间的关系，从而达到解决问题的目的.其基本步骤是：第一步：定条件，即确定三角形中的已知和所求，在图形中标出来，然后确定转化的方向.第二步：定工具，即根据条件和所求合理选择转化的工具，实施边角之间的互化. 第三步：求结果.17．空气质量指数PM 2.5（单位：μg /m 3）表示每立方米空气中可入肺颗粒物的含量，这个值越高，就代表空气污染越严重：甲、乙两城市2013年2月份中的15天对空气质量指数PM 2.5进行监测，获得PM 2.5日均浓度指数数据如茎叶图所示：（Ⅰ）根据你所学的统计知识估计甲、乙两城市15天内哪个城市空气质量总体较好？（注：不需说明理由）（Ⅱ）在15天内任取1天，估计甲、乙两城市空气质量类别均为优或良的概率； （Ⅲ）在乙城市15个监测数据中任取2个，设X 为空气质量类别为优或良的天数，求X 的分布列及数学期望．【答案】（Ⅰ）甲城市空气质量总体较好（Ⅱ）29 （Ⅲ）分布列见解析，23EX = （Ⅰ）根据茎叶图所给数据分析可得．（Ⅱ）由（Ⅰ）的分析及相互独立事件的概率计算公式即可得出；（Ⅲ）利用超几何分布即可得到分布列，再利用数学期望的计算公式即可得出． 【详解】解：（Ⅰ）由茎叶图可知：甲城市空气质量一级和二级共有10天，而乙城市空气质量一级和二级只有5天，因此甲城市空气质量总体较好．（Ⅱ）甲城市在15天内空气质量类别为优或良的共有10天，任取1天，空气质量类别为优或良的概率为102153=， 乙城市在15天内空气质量类别为优或良的共有5天，任取1天，空气质量类别为优或良的概率为51153=， 在15天内任取1天，估计甲、乙两城市空气质量类别均为优或良的概率为212339⨯=． （Ⅲ）X 的取值为0，1，2，025102153(0)7C C P X C ===，1151021510(1)21C C P X C ===，205102152(2)21C C P X C ===． X 的分布列为：X0 1 2P37 1021 221数学期望31022012721213EX =⨯+⨯+⨯=． 本题考查茎叶图、相互独立事件的概率计算公式、超几何分布、随机变量的分布列、数学期望的计算公式、排列与组合的计算公式是解题的关键，属于中档题．18．四棱锥P ﹣ABCD 中，底面ABCD 是边长为2的菱形，侧面PAD ⊥底面ABCD ，∠BCD ＝60°，2PA PD ==，E 是BC 中点，点Q 在侧棱PC 上．（Ⅰ）求证：AD ⊥PB ；（Ⅱ）若Q 是PC 中点，求二面角E ﹣DQ ﹣C 的余弦值； （Ⅲ）是否存在Q ，使PA ∥平面DEQ ？若存在，求出PQPC的值；若不存在，说明理由． 【答案】（Ⅰ）证明见解析（Ⅱ）217（Ⅲ）存在，23λ=（Ⅰ）取AD 中点O ，连接OP ，OB ，BD ．推导出PO AD ⊥．，BO AD ⊥．从而AD ⊥平面POB ．由此能证明AD PB ⊥．（Ⅱ）以O 为坐标原点，建立空间直角坐标系O xyz -利用向量法能求出二面角E DQ C --的余弦值．（Ⅲ）设(01)PQ PC λλ=u u u r u u u r剟，(),,Q x y z ，推导出(23,1)Q λλλ--+，利用向量法能求出当23λ=时，//PA 平面DEQ ． 【详解】证明：（Ⅰ）取AD 中点O ，连接OP ，OB ，BD ． 因为PA PD =，所以PO AD ⊥．因为菱形ABCD 中，60BCD ∠=︒，所以AB BD =．所以BO AD ⊥．因为BO PO O =I ，且BO ⊂平面POB ，PO ⊂平面POB ， 所以AD ⊥平面POB ． 因为PB ⊂平面POB 所以AD PB ⊥．解：（Ⅱ）由（Ⅰ）可知，BO AD ⊥，PO AD ⊥，因为侧面PAD ⊥底面ABCD ，且平面PAD I 底面ABCD AD =，PO ⊂面PAD 所以PO ⊥底面ABCD ．以O 为坐标原点，如图建立空间直角坐标系O xyz -． 则(1,0,0),(1,3,0),(0,0,1),(2,3,0)D E P C---， 因为Q 为PC 中点，所以311,,2Q ⎛⎫- ⎪ ⎪⎝⎭． 所以(0,3,0)DE =u u u r ，310,,2DQ ⎛⎫= ⎪ ⎪⎝⎭u u u r ，设平面DEQ 的法向量为()1,,n x y z =u r．1100n DE n DQ ⎧⋅=⎪∴⎨⋅=⎪⎩u v u u u v u v u u u v 即3031022y y z ⎧=⎪⎨+=⎪⎩ 所以平面DEQ 的法向量为1(1,0,0)n =u u r．因为1()2DC DQ=-=u u u r u u u r，设平面DQC的法向量为2111(,,)n x y z=u u r，则22·0·0DC nDQ n⎧=⎪⎨=⎪⎩u u u v u u vu u u v u u v，即1111122xy z⎧-+=+=⎩．令1x=111,y z==2n=u u r．所以121212cos,||||n nn nn n<>==u u r u u ru u r u u r gu u r u u r由图可知，二面角E DQ C--为锐角，所以余弦值为7．（Ⅲ）设(01)PQ PCλλ=u u u r u u u r剟由（Ⅱ）可知(1),(1,0,1)PC PA=--=-u u u r u u u r．设(),,Q x y z，则(,,1)PQ x y z=-u u u r，又因为(2,)PQ PCλλλ==--u u u r u u u r，所以21xyzλλ=-⎧⎪=⎨⎪=-+⎩，即(2,1)Qλλ--+．所以在平面DEQ中，(12,1)DE DQλλ==--u u u r u u u r，所以平面DEQ的法向量为1(1,0,21)nλλ=--u u r，又因为//PA平面DEQ，所以1PA n=u u u r u u rg，即(1)(1)(21)0λλ-+--=，解得23λ=．所以当23λ=时，//PA平面DEQ．本题考查线线垂直的证明，考查二面角的余弦值的求法，考查满足线面平行的实数值的求法，考查空间中线线、线面、面面间的位置关系等基础知识，考查运算求解能力，考查函数与方程思想，属于中档题．19．已知函数32()22f x x ax=-+.（1）讨论()f x的单调性；（2）当0<<3a时，记()f x在区间[]0,1的最大值为M，最小值为m，求M m-的取值范围.【答案】(1)见详解；(2) 8[,2)27. (1)先求()f x 的导数，再根据a 的范围分情况讨论函数单调性；(2) 讨论a 的范围，利用函数单调性进行最大值和最小值的判断，最终求得M m -的取值范围. 【详解】(1)对32()22f x x ax =-+求导得2'()626()3a f x x ax x x =-=-.所以有当0a <时，(,)3a -∞区间上单调递增，(,0)3a 区间上单调递减，(0,)+∞区间上单调递增；当0a =时，(,)-∞+∞区间上单调递增；当0a >时，(,0)-∞区间上单调递增，(0,)3a 区间上单调递减，(,)3a +∞区间上单调递增. (2)若02a <≤，()f x 在区间(0,)3a 单调递减，在区间(,1)3a 单调递增，所以区间[0,1]上最小值为()3a f .而(0)2,(1)22(0)f f a f ==-+≥，故所以区间[0,1]上最大值为(1)f .所以332(1)()(4)[2()()2]233327a a a a M m f f a a a -=-=---+=-+，设函数3()227x g x x =-+，求导2'()19x g x =-当02x <≤时'()0g x <从而()g x 单调递减.而02a <≤，所以38222727a a ≤-+<.即M m -的取值范围是8[,2)27.若23a <<，()f x 在区间(0,)3a单调递减，在区间(,1)3a 单调递增，所以区间[0,1]上最小值为()3a f 而(0)2,(1)22(0)f f a f ==-+≤，故所以区间[0,1]上最大值为(0)f .所以332(0)()2[2()()2]33327a a a a M m f f a -=-=--+=，而23a <<，所以3812727a <<.即M m -的取值范围是8(,1)27.综上得M m -的取值范围是8[,2)27. (1)这是一道常规的函数导数不等式和综合题，题目难度比往年降低了不少.考查的函数单调性，最大值最小值这种基本概念的计算.思考量不大，由计算量补充.20．已知椭圆2222:1(0)x y M a b a b +=>>，焦距为k 的直线l 与椭圆M 有两个不同的交点A 、B ． （1）求椭圆M 的方程；（2）设P （﹣2，0），直线PA 与椭圆M 的另一个交点为C ，直线PB 与椭圆M 的另一个交点为D ，若C 、D 与点71(,)42Q 共线，求斜率k 的值．【答案】（1）2213x y += （2）2（1）根据椭圆的离心率公式即可求得a 的值，即可求得b 的值，求得椭圆方程； （2）求得直线PA 的方程，代入椭圆方程，即可根据韦达定理即可求得C 点坐标，同理求得D 点坐标，即可求得QC uuu r 与QD uuu r共线，根据向量的共线定理，即可求得直线AB 的斜率． 【详解】解：（1）由题意可知：2c =，则c =椭圆的离心率c e a ==，则a = 2221b a c ∴=-=，∴椭圆M 的标准方程为2213x y +=；（2）设1(A x ，1)y ，2(B x ，2)y ， 设直线PA 的斜率112PA y k x =+，直线PA 的方程为11(2)2y y x x =++， 联立221133(2)2x y y y x x ⎧+=⎪⎨=+⎪+⎩，消去y 整理得 2222221111111(443)12(1231212)0x x y x y x y x x +++++---=，由221133x y +=代入上式得，整理得2221111(47)(124)(712)0x x x x x x ++--+=， 2111171247C x x x x x +=-+g ，1171274C x x x +=-+，则111111712227474C y x y y x x x ⎛⎫+=-+= ⎪+++⎝⎭，则1111712,7474x y C x x ⎛⎫+- ⎪++⎝⎭，同理可得：2222712,7474x y D x x ⎛⎫+- ⎪++⎝⎭，由7142Q ⎛⎫- ⎪⎝⎭,，则11112471,4(47)2(74)y x QC x x ⎛⎫--= ⎪++⎝⎭u u u r ，22222471,4(47)2(74)y x QD x x ⎛⎫--= ⎪++⎝⎭u u u r ，由C 、D 与点7142Q ⎛⎫- ⎪⎝⎭,共线可得QC uuu r 与QD uuu r 共线， 则22111221247247114(47)2(74)4(47)2(74)y x y x x x x x ----=++++g g ，整理得12122()y y x x -=-， 则直线AB 的斜率12122y y k x x -==-，k ∴的值为2．本题考查椭圆的标准方程及性质，直线与椭圆的位置关系，考查韦达定理，向量的共线定理，考查转化思想，属于中档题．。
北京市第五中学分校2024-2025学年九年级上学期10月月考数学试卷
北京市第五中学分校2024－2025学年九年级上学期10月月考数学试卷一、单选题1．下列图形中，既是中心对称图形，又是轴对称图形的是（ ）A ．B ．C ．D ．2．抛物线241y x x =-+的顶点坐标是（ ）A ．()2,3B ．()2,3-C ．()2,3--D ．()2,3- 3．下列关于函数21y x =-的结论中，正确的是（ ）A ．y 随x 的增大而减小B ．当0x >时，y 随x 的增大而增大C ．当0x <时，y 随x 的增大而增大D ．当0x >时，y 随x 的增大而减小 4．如图，DE 是ABC V 的中位线，若ADE V 的面积为1，则四边形DBCE 的面积为（ ）A ．4B ．3C ．2D ．15．在平面直角坐标系xOy 中，将抛物线23y x =先向右平移4个单位长度，再向上平移1个单位长度，得到的抛物线是（ ）A ．23(x 4)1y =+-B ．23(4)1y x =++C ．23(4)1y x =--D ．23(4)1y x =-+6．某药品经过两次降价，每瓶零售价由56元降为31.5元，已知两次降价的百分比相同，设为x ，那么根据题意可以列方程为（ ）A ．()56131.5x -=B ．()561231.5x -=C ．256(1)31.5x -=D ．256(12)31.5x -=7．已知：二次函数()20y ax bx c a =++≠的图象上部分对应点坐标如下表，m 的值为（ ）A ．1B ．2C ．5-D ．08．如图，抛物线2y ax bx c =++（0a ≠）经过点()1,0-．下面有四个结论：①0a >；②20a b +<：③420a b c ++>；④关于x 的不等式()20ax b c x +->的解集为1x <-或0x >．其中所有正确结论的序号是（ ）A ．①②B ．②③C ．③④D ．②③④二、填空题9．方程23x x =的解是．10．若关于x 的一元二次方程240x x c -+=有两个相等的实数根，则实数c 的值为． 11．二次函数243y x x =-+的图象与y 轴的交点坐标为．12．在平面直角坐标系xOy 中，若点1(2,)y ，2(4,)y 在抛物线22(3)4y x =--上，则1y 2y （填“>”，“ =”或“<”）．13．如图，一次函数y =kx +b k ≠0 与二次函数()20y ax a =≠的图象分别交于点()2,2A -，()4,8B ．则关于x 的方程2ax kx b =+的解为．14．如图，在Rt ABC △中，90A ∠=︒，AD BC ⊥，3AD =，2BD =，则CD 的长为 ．15．已知：如图，在ABC V 中，120BAC ∠=︒，以BC 为边向形外作等边三角形BCD △，把ABD △绕着点D 按顺时针方向旋转60︒后得到ECD V ，若3AB =，2AC =，AD 的长为．16．已知抛物线()2212y x mx m =--≤≤经过点(,)A p t 和点(2,)B p t +，则t 的最小值是．三、解答题17．解方程：(1)2680x x -+=．(2)(25)410x x x -=-．18．已知实数a 是25170x x --=的根，不解方程，求()()()212111a a a ---++的值． 19．已知二次函数2=23y x x --．(1)将其化为2()y a x h k =-+的形式为_______________；(2)在所给的平面直角坐标系xoy 中，画出它的图象；(3)抛物线与x 轴交点坐标为_______________；(4)22x -≤≤时，y 的取值范围是_______________．20．已知关于x 的一元二次方程()210x m x m -++=．(1)求证：该方程总有两个实数根；(2)若0m <，且该方程的两个实数根的差为3，求m 的值．21．如图，ABC V 绕某点按一定方向旋转一定角度后得到111A B C △，点A ，B ，C 分别对应点1A ，1B ，1C ．(1)在图中画出111A B C △；(2)111A B C △是以点______（填“1O ”，“2O ”或“3O ”）为旋转中心，将ABC V ______时针旋转______度得到的．22．如图，在菱形ABCD 中，AC ，BD 相交于点O ，过B ，C 两点分别作AC ，BD 的平行线，相交于点E ．（1）求证：四边形BOCE 是矩形；（2）连接EO 交BC 于点F ，连接AF ，若∠ABC =60°，AB =2，求AF 的长．23．已知二次函数2(0)y ax bx c a =++≠图象上部分点的横坐标x ，纵坐标y 的对应值如下表所示：(1)求二次函数的解析式及顶点坐标；(2)直接写出当0y >时，x 的取值范围．24．如图，A 是直线MN 上一点，90BAC ∠=︒，过点B 作BD MN ⊥于点D ，过点C 作CE MN ⊥于点E ．(1)求证：ADB V :CEA V ；(2)若AB 2AD AE ==，求CE 的长．25．如图1，灌溉车为公路绿化带草坪浇水，图2是灌溉车浇水操作时的截面图．现将灌溉车喷出水的上、下边缘线近似地看作平面直角坐标系xOy 中两条抛物线的部分图象．已知喷水口H 离地竖直高度OH 为1.2m ，草坪水平宽度3m DE =，竖直高度忽略不计.上边缘抛物线最高点A 离喷水口的水平距离为2m ，高出喷水口0.4m ，下边缘抛物线是由上边缘抛物线向左平移4m 得到的，设灌溉车到草坪的距离OD 为d （单位：m ）．(1)求上边缘抛物线的函数解析式，并求喷出水的最大射程OC 的长；(2)下边缘抛物线落地点B 的坐标为______；(3)要使灌溉车行驶时喷出的水能浇灌到整个草坪，d 的取值范围为______．26．已知二次函数243y ax ax =-+（0a ≠）．(1)求该二次函数的图象与y 轴交点的坐标及对称轴．(2)已知点()14,y ，()20,y ，()32,y -，()43,y -都在该二次函数图象上，①请判断1y 与2y 的大小关系：1y _________2y （用“>”“=”“<”填空）；②若1y ，2y ，3y ，4y 四个函数值中有且只有一个小于零，求a 的取值范围． 27．如图，在ABC V 中，AC BC =，90ACB ∠=︒，45APB ∠=°，连接CP ，将线段CP 绕点C 顺时针旋转90°得到线段CQ ，连接AQ ．(1)依题意，补全图形，并证明：AQ BP =；(2)求QAP ∠的度数；(3)若N 为线段AB 的中点，连接NP ，请用等式表示线段NP 与CP 之间的数量关系，并证明． 28．在平面直角坐标系xOy 中，对于抛物线2:C y x x =+和直线:l y x b =+给出如下定义：过抛物线C 上一点()01,A x y 作垂直于x 轴的直线AB ，交直线l 于点()02,B x y ，若存在实数0y 满足102y y y ≤≤，则称点()00,P x y 是抛物线C 的“如意点”，点P 关于直线l 的对称点Q 为点P 与抛物线C 的“称心点”．(1)若2b =，①在点()10,0P ，()21,2P -，()31,3P ，4P 中，抛物线C 的“如意点”是______； ②若点D 是抛物线C 的“如意点”，点E 是点D 与抛物线C 的“称心点”，直接写出DE 的最大值______；(2)若边长为1234R R R R 边上的点都是抛物线C 的“如意点”或某点与抛物线C 的“称心点”，直接写出b 的最小值______．。
北京四中2017-2018学年高二下学期第一次月考英语试卷
北京四中2017-2018学年下学期高二年级第一次月考 英 语 试 卷 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。
2．选择题的作答：每小题选出答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑，写在试题卷、草稿纸和答题卡上的非答题区域均无效。
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4．考试结束后，请将本试题卷和答题卡一并上交。
第Ⅰ卷 第一部分 听力（共两节，满分 30 分）(略) 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，并在答题卡上将该项涂黑。
A （河南省林州市第一中学2017-2018学年高二12月月考）I set out to change the lives of those who need help by joining my school’s newly formed Free The Children Club. Th rough the determination of friends, the group has grown bigger and stronger each year. Over the past two years my friend, Alex Auclair, and I have become the leaders of the club. Already, after only two years of fundraising, we have accumulated over three thousand dollars and almost two thousand food items through various fundraising efforts. For example, each year a 24-hour famine (饥饿) is planned resulting in absolutely no consumption (消耗) of food. By taking part in these activities, we put ourselves in the shoes of someone living in poverty. No money raised goes to waste. At the end of each school year, the group takes a vote to determine where our funds will be spent and donated. Last year, we bought enough desks, chairs,此卷只装订不密封 班级 姓名 准考证号 考场号 座位号supplies and textbooks for every student in a Kenyan school. This year, we plan to spend our earning helping out families in Sierra Leone.Poverty is a worldwide issue affecting the lives of people in not only developing countries, but also first-world countries such as Canada, the United Kingdom and Japan. Living in poverty can result in hunger, many forms of disease, lack of education, and for millions, death. It does not have to be this way. You too can form a club like the Free The Children Club or you can participate in events outside of school. Get your friends, family, even your community involved in fundraising. Do what you can to change the world.21. An annual 24-hour famine is held to ________A. help understand poor people better.B. draw people’s attention to the club.C. call on people not to waste food.D. save food for hungry people.22. How to spend the raised money is based on the opinion of ________.A. the donatorsB. the fundraisersC. the club leadersD. the majority of the club members23. Why does the author write the text?A. To introduce the Free The Children Club.B. To encourage people to change the world.C. To present the serious outcomes of poverty.D. To show how to help poor people live better.B（河北省邢台市2017-2018学年高二第四次月考）I went through a training program and became a literacy volunteer(扫盲志愿者)last summer. The training I received, though excellent, did not tell me how it was to work with a real student. When I began to discover what other people’s lives were like because they could not read, I realized the true importance of reading.My first student Marie was a 44-year-old single mother of three. In the first lesson, I found out she walked two miles to the nearest supermarket twice a week because she didn't know which bus totake. When I told her I would get her a bus schedule, she told me it would not help because she could not read it. She said she also had difficulty once she got to the supermarket because she couldn't always remember what she needed. Since she did not know words, she could not write out a shopping list. Also, she could only recognize items by sight, so if the product had a different label(标识), she would not recognize it as the product she wanted.As we worked together, learning how to read built Marie's self-confidence, which encouraged her to continue her studies. She began to make rapid progress and was even able to take the bus to the supermarket. After this successful trip, she reported how self-confident she felt. At the end of the program, she began helping her youngest son, Tony, a shy first grader, with his reading. As she described this experience, I was proud of myself as well. I found that helping Marie to build herself-confidence was more rewarding than anything I had ever done before.As a literacy volunteer, I learned a great deal about teaching and helping others. In fact, I may have learned more from the experience than Marie did.24. According to the text, Marie is a woman who ___________.A. has three sonsB. has good memoryC. has difficulty in writingD. has difficulty in walking around25. After getting help from the author, Marie felt ____________.A. shyB. proudC. confidentD. peaceful26. What did the author get through the program?A. Some beautiful presents.B. A sense of achievement.C. More confidence and knowledge.D. More ways to help others.27. What can be the best title for the text?A. A Woman Who Lacked Self-confidenceB. The Literacy V olunteer Changed Our LivesC. A Challenge during My V olunteering WorkD. The V olunteering Work Benefited Both of UsC（安徽省池州市东至二中2017-2018学年高二12月月考试题）Venom(毒液）from a local scorpion(蝎子）in Cuba is being used by Cuban scientists as an effective weapon to fight cancer. The venom, with stopping pain, anti-inflammatory (炎症） and anti-cancer properties, is the active ingredient i n the medicine “Vidatox 30 CH which can be used to treat liver, brain, lung and other cancers. The treatment has been successfully used for more than four years in humans after being first tested in biological models. Labiofam, a Cuban laboratory, has breeding(繁殖)centers for both the Red Scorpion and Blue Scorpion. Each month, some 30,000 scorpions in Las Minas town, 270 km east of Havana are made to give the venom. After two years, the scorpions are released back into their natural habitat.Denyer Sanchez, a biologist from Labiofam, explained that the conditions are adjusted for reproduction, proved by the high number of breeding female scorpions. He said when the offspring(后代）becomes able to live in the environment, we release them because they do not have the necessary size yet to remove their venom, said Sanchez. Sanchez also said that there is still much to research on the exploitation process of scorpions, such as female death rate or the ability to survive of the released scorpions.Cuban research on the sc orpion’s venom began at the end of 1980s in Guantanamo province, the island’s eastern tip, where a group of biologists and doctors became interested in the stories told by the peasants about the venom's benefits. However，the first discovery was made by Cuban biologist Misael Bordier. In 2001, Bordier visited Mexico’s National Autonomous University (UNAM) and presented the research progress in a professional journal. Bordier died in 2005, one year before Cuba's Industrial Property Office gave Labiofam the rights to exploit the patent related to the venom.28. How are the scorpions dealt with after their venom has been taken for two years?A. Their bodies are used to make medicines.B. They are bred in the laboratory for research.C. They are raised to give birth to the offspring.D. They are set free into their natural habitat.29. What can we infer from the passage about the research on scorpions?A. The UN provided fund for the research team.B. There is still much to study in detail.C. The achievements will benefit animals.D. Many scientists doubt about the result of the research.30. What can we learn about Bordier in the last paragraph?A. He was given the rights to exploit the patent.B. He began his research at the beginning of the twenty-first century.C. He put forward the research progress in a professional journal.D. He was a peasant who told the stories about the venom’s benefits.31. What does this passage mainly talk about?A. The various uses of scorpions in Cuba.B. Cuban biologists’ research on strange diseases.C. Suitable conditions for Cuban scorpions to breed.D. Cuban scorpion venom’s effect on fighting cancer.D（河南省南阳一中2017-2018学年高二第三次月考）Do you think you would work out more if you were offered money to do so? Science has shown that money can give people motivation to work out, but perhaps not in the way that you think.According to a study published in the Annals of Internal Medicine Journal, the best strategy isn’t offering money; it’s giving someone money, then threatening to take it away.Researchers gave 281 people the goal of walking 7,000 steps every day over 13 weeks.To motivate the people who took part to reach the goal, researchers divided them into three groups.People in the first group received $1,40(9 yuan) each day as long as they finished 7,000 steps, the second group was only able to collect the $1.40 if they had reached 7,000 steps the day before, and the third group was given $42 at the beginning of each month and $1.40 was taken away every time someone failed to meet the goal.The third group met their daily fitness goals 50 percent more often than the other two groups,showing that people were most motivated to walk by the fear of losing money.“People are more motivated by losses than gains, and they like immediate gratification.” study author Dr Mitesh Patel, an assistant professor at the University of Pennsylvania in the US, told CNN. “They want to be rewarded today, not next year or far into the future.”Our brains tend to avoid wanting to lose things more than they try to get the benefits from gaining them, Patel explained. “It makes people think like the money is theirs to lose from day one.”In addition, in most programs, many participants will drop out quickly and only the motivated will stay involved, Patel said.“In ours, we were pleasantly surprised that 96 percent stayed.” he added.The study provides evidence that what matters is not only the money incentive （激励）, but also how you think about them. This is important to how effective they are. The evidence could have a big effect on health promotion programs in the future, according to the study.“Incentives themselves are not all you need,” Stephanie Pronk, a health and wellness consultant with the Aonplc corporation, told Th e Wall Street Journal. “It’s really important to change up the incentive design and keep people on their toes.”32. Acording to Dr Mitesh Patel, the third group did better than the other two groups mostly because______.A. they were satisfied with being paid immediatelyB. they did not want the money they had gained to be taken awayC. they were able to get more money than the other two groupsD. they were given money at first while the others were not33. By mentioning other similar programs, Dr Mitesh Patel intended to______.A. prove that their program has been more successfulB. show that motivation mattered more in other programsC. stress that they didn’t expert the resultD. make a further comparison between these programs34. What can we infer from S tephanie Pronk’s words?A. Incentives are of little importance in the process of getting fit.B. Incentives and ways in which they are given are key to fitness programs.C. People should keep fit actively instead of being motivated by incentives.D. There are many ways to get people to feel motivated to work out more.35. We can learn from the study that for incentives to work______.A. more benefits than losses should be obvious for participantsB. direct profits should be given rather than long-term onesC. designers need to consider how people think about incentivesD. designers need to work out the right from of motivation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。
北京市昌平区2017_2018学年高一英语12月月考试题20180102017
北京市昌平区2017-2018学年高一英语12月月考试题第一部分听力（共两节，满分30分）第一节（共5小题，每小题1.5分）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 does the woman think of cloning?A.It has no side effect at all.B.It should be strictly forbidden.C.It maycause trouble for humans.2.What’s the possible relationship between the two speakers?A.Friends.B.Husband a nd w ife.C.Teacher a nd s tudent.3.What do they hope to do?A.Stop cigarette production.B.Advise people not to smoke.C.Stop youngpeople smoking.4.What teacher are they talking abo u t?A.Their C hinese teacher.B.Their history teacher.C.Their politicsteacher.5.What does the man think the weather will be like in April?A.Cool.B.Hot.C.Windy.第二节（共15小题，每小题1.5分）听下面5段对话,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。
北京市昌平区2017-2018学年高二英语上学期第一次月考试题
2017-2018学年上学期第一次月考高二英语试卷（满分150分，考试时间120分钟）2017-9-23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。
1.What did Dick’s girlfriend do on the weekend?A. She watched TV.B. She went dancing.C. She went shopping.2.Where does the conversation probably take place?A. On a train.B. In a dining hall.C. At a ticket office.3.When will the man go to the birthday party?A. When he gets back from work.B. When Jane finishes her homework.C. When he receives the invitation.4.What was the man doing just now?A. Operating a printer.B. Teaching the woman English.C. Explaining how to use a printer.5.How did the man’s examination go?A. Fairly well.B. Just so-so.C. Very poorly.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。
2017届高三月考英语试题及答案(K12教育文档)
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2017届高三第七次月考英语试题2016-12—20第Ⅰ 卷 (选择题，共 115 分）第一部分听力(共 20 小题；每小题 1。
5 分，共 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．Where are the two speakers？A．In a bookstore．B．In the library．C．In the post office．2．How will the speakers get to their destination?A．By bus．B．By taxi．C．By subway．3．What was the man’s son doing at the supermarket？A．Working．B．Killing the time．C．Going shopping．4．How much does the man weigh now?A．80 pounds．B．120 pounds．C．160 pounds．5．What caused the car accident？A．Speed driving．B．The bad weather． C．Careless driving．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。
北京市五中2012-2013学年高二10月月考英语试题
第一卷I. 听力理解第一节1.Where is the man?A. In a car.B. In a bar.C. In a park.2. What is the man trying to do?A. Lose 50 pounds.B. Improve health.C. Use diet pills.3. How much money do they have between them?A. $86.B. $56.C. $46.4. How will the man make a phone call?A. By his mobile phone.B. By the public phone.C. By the woman’s mobile phone5. What do we know about the man?A. He is jealous of the woman.B. He is worried about his exam.C. He will have a physics test next week.第二节听第6段材料，回答第6至7题6. Where is the woman going?A. Paris.B. China.C. Malaga.7. What is the most probable relationship between the two speakers?A. Friends.B. Husband and wife.C. Strangers.听第7段材料，回答第8至9题8. What time does the store open on Wednesday?A. 5:30 PMB. 6:00 AMC. 8:00 AM9. How much would you pay for this store’s main product on Saturday if it cost $100 during the restof week?A. $90.B. $80.C. $70.听第8段材料，回答第10至12题10. Why was the man late?A. He forgot to look at his watch.B. The math teacher asked him to stay longer than before.C. The math class lasted longer than it should.11. What do we know about the students?A. They are afraid of the math teacher.B. They don’t want to hurt the math teacher.C. They prefer to learn math rather than go home earlier.12. What is the man most likely to do?A. Talk to the math teacher.B. Be polite like his class matesC. Ask the woman to talk to the math teacher.听9段材料，回答第13至15题I. 单项填空16.---What’s the central idea of the passage, Bob?---Sorry. I can’t make ____ of it. It’s beyond my ability.A. judgmentB. understandingC. ideaD. sense17.Susan is always ready to help me ____ I come to ask her for help.A. by the timeB. every timeC. sometimesD. at times18.Eating too much fat can ____ heart disease and cause high blood pressure.A. relate toB. contribute toC. attend toD. devote to19.____ English, the speaker also has a good command of Russian and French.A. ExceptB. Except forC. BesideD. Apart from20.My sister was against my suggestion while my brother was ____ it.A. in favour ofB. in memory ofC. in honour ofD. in search of21.Mr. Green stood up in defence of the 16-year-old boy, saying that he was not the one ____.A. blamedB. blamingC. to blameD. to be blamed22.Only after my friend came _____.A. did the computer repairB. he repaired the computerC. was the computer repairedD. the computer was repaired23.The shopkeeper did not want to sell for ____ he thought was not enough.A. whereB. howC. whatD. which24.---How do you deal with the disagreement between the company and the customers?---The key ____ the problem is to meet the demand ____ by the customers.A. to solving; makingB. to solving; madeC. to solve; makingD. to solve; made25.Because of the heavy sandstorm, we had to put off the visit until tomorrow to the exhibition ofpainting ____ in the nearby city.A. to holdB. heldC. holdingD. being held26.Do you think you will have the work ____ on time?A. finishedB. finishingC. to finishD. finish27.With a lot of difficult problems ____, the man felt like a cat on hot bricks.A. settlingB. settledC. to settleD. being settled28.The suspect was cunning（狡猾的）. He told a lie to the policeman ____ at the scene.A. when questionedB. while to be questionedC. as questioningD. when questioning29.The policeman said nothing, with his eyes fixed on the person _____ near the window.A. having seatedB. seatingC. to seatD. seated30.We often provide our children with toys, footballs or basketballs, ____ that all children likethese things.A. thinkingB. thinkC. to thinkD. thoughtIII. 完形填空“Now,” Mrs. Virginia DeView said, smiling, “we are going to discover our professions（职业）.” The class seemed to be greatly surprised. Our professions? We were only 13 and 14 years old! The teacher must be 31 . “Yes, you will all be searching f or your future 32 . Each of you will have to 33 someone in your field, plus an oral report.”Each day in her class, Virginia DeView reminded us about this. Finally, I 34 print journalism. This meant I had to go to interview a true-blue newspaper reporter. I was extremely nervous. I sat down in front of him 35 able to speak. He looked at me and said, “Did you bring a pencil or pen?” I shook my head. “How about some 36 ?” I shook my head again.Finally, I thought he realized I was 37 , and I got my first big tip as a 38 . “Never, never go anywhere without a pen or paper. You never know what you’ll 39 into.” After a few days, I gave my oral report totally from memory in class. I got an A on the entire project.Years later, I was in college looking around for a new career, but with no success. Then I 40 Virginia DeView and my desire at 13 to be a journalist. And I called my parents. They didn’t 41 me. They just reminded me how 42__ the field was and how I had run away from competition all my life. This was true. But journalism did something to me; it was in my 43 . And it gave me the freedom to go up to total strangers and ask what was 44 .For the past fifty years, I’ve had the most satisfying reporting career, 45 stories from murders to airplane 46 and finally choosing my strongest area. When I went to pick up my phone one day, an incredible wave of memories 47 me and I realized that had it not been48 Virginia DeView, I would not be sitting at that desk.I get 49 all the time : “How did you pick journalism?”“Well, you see, there was this teacher…” I always start out. I just hope I can have the chance to 50 her. She was a teacher who definitely changed my life.31. A. cautious B. mad C. optimistic D. enthusiastic32. A. universities B. families C. professions D. lives33. A. interview B. describe C. admire D. face34. A. considered B. rejected C. expected D. picked35. A. hardly B. totally C. merely D. completely36. A. preparation B. newspaper C. drink D. paper37. A. reliable B. grateful C. terrified D. amazed38. A. student B. journalist C. stranger D. writer39. A. look B. turn C. break D. run40. A. called B. remembered C. recognized D. evaluated41. A. answer B. urge C. stop D. persuade42. A. funny B. competitive C. ordinary D. mysterious43. A. blood B. body C. life D. opinion44. A. coming in B. coming out C. going up D. going on45. A. creating B. recalling C. covering D. writing46. A. flights B. crashes C. journeys D. schedules47. A. hit B. caught C. impressed D. seized48. A. for B. with C. of D. to49. A. hurt B. realized C. adjusted D. asked50. A. respect B. support C. thank D. envyIV. 阅读理解AYears later, I drove to a meeting in a nearby town in the morning. In late afternoon I returned to my car and found that I'd left the lights on all day, and the battery(电池)was dead. Then I noticed that the Friendly Ford dealership - a shop selling cars - was right next door. I walked over and found two salesmen in the showroom."Just how friendly is Friendly Ford?" I asked and explained my trouble. They quickly drove a pickup truck to my car and started it. They would accept no payment, so when I got home, I wrote them a note to say thanks. I received a letter back from one of the salesmen. No one had ever taken the time to write him and say thank you, and it meant a lot, he said."Thank you" --- two powerful words. They're easy to say and mean so much.51. The author planned to stop at Oklahoma City_________.A. to visit a friendB. to see his parentsC. to pay at the cash registerD. to have more gas for his car52. The words “took off” underlined in Paragraph 2 mean “______”.A. turned offB. moved offC. put upD. set up53. By telling his own experiences, the author tries to show______.A. how to write a thank-you letterB. how to deal with car problemsC. the kind-heartedness of older peopleD. the importance of expressing thanksBCan dogs and cats live in perfect harmony in the same home? People who are thinking about adopting a dog as a friend for their cats are worried that they will fight. A recent research has found a new recipe of success. According to the study, if the cat is adopted before the dog, and if they are introduced when still young (less than 6 months for cats, a year for dogs), it is highly probable that the two pets will get along swimmingly. Two-thirds of the homes interviewed reported a positive relationship between their cat and dog.However, it wasn’t all sweetness and lig ht. There was a reported coldness between the cat and dog in 25% of the homes, while aggression and fighting were observed in 10% of the homes. One reason for this is probably that some of their body signals were just opposite. For example, when a cat turns its head away it signals aggression, while a dog doing the same signals submission.In homes with cats and dogs living peacefully, researchers observed a surprising behavior. They are learning how to talk each other’s language. It is a surprise that cats can learn how to talk ‘Dog’, and dogs can learn how to talk ‘Cat’.What’s interesting is that both cats and dogs have appeared to develop their intelligence. They can learn to read each other’s body signals, suggesting that the two may have more in common than was previously suspected. Once familiar with each other’s presence and body language, cats and dogs can play together, greet each other nose to nose, and enjoy sleeping together on the sofa. They can easily share the same water bowl and in some cases groom (梳理) each other.The significance of this research on cats and dogs may go beyond pets --- to people who don’t get along, including neighbors, colleagues at work, and even world superpowers. If cats and dogs can learn to get along, surely people have a good chance.54. The underlined word “swimmingly” in Paragraph 1 is closest in meaning to ______.A. earlyB. sweetlyC. quicklyD. smoothly55. Some cats and dogs may fight when ______.A. they are cold to each otherB. they look away from each otherC. they misunderstand each other’s signalsD. they are introduced at an early age56. It is suggested in Paragraph 4 that cats and dogs ______.A. have common interestsB. are less different than was thoughtC. have a common body languageD. are less intelligent than was expected57. What can we human beings learn from cats and dogs?A. We should learn to live in harmony.B. We should know more about animals.C. We should live in peace with animals.D. We should learn more body languages.CA year after graduation, I was offered a position teaching a writing class. Teaching was a profession I had never seriously considered, though several of my stories had been published. I accepted the job without hesitation, as it would allow me to wear a tie and go by the name of Mr. Davis. My father went by the same name, and I liked to imagine people getting the two of us confused. “Wait a minute,” someone might say, “Are you talking about M r. Davis the retired man, or Mr. Davis the respectable scholar?”The position was offered at the last minute, and I was given two weeks to prepare, a period I spent searching for briefcase and standing before my full-length mirror, repeating the words, “He llo, class. I’m Mr. Davis.” Sometimes I would give myself an aggressive voice. Sometimes I would sound experienced. But when the day eventually came, my nerves kicked in and the true Mr. Davis was there. I sounded not like a thoughtful professor, but rather a 12-year-old boy.I arrived in the classroom with paper cards designed in the shape of maple leaves. I had cut them myself out of orange construction paper. I saw nine students along a long table. I handed out the cards, and the students wrote down their names and fastened them to their breast pockets as I required.“All right then,” I said. “Okey, here we go.” Then I opened my briefcase and realized that I had never thought beyond this moment. I had been thinking that the students would be the first to talk, offering their thoughts and opinions on the events of the day. I had imagined that I would sit at the edge of the desk, overlooking a forest of hands. Every student would yell. “Calm down, you’ll all get your turn. One at a time, one at a time!”A terrible silence ruled the room, and seeing no other opinions, I inspected the students to pull out their notebooks and write a brief essay related to the theme of deep disappointment.58. The author took the job to teach writing because ______.A. he wanted to be respectedB. he had written some storiesC. he wanted to please his fatherD. he had dreamed of being a teacher59. What can we learn about the author from Paragraph 2?A. He would be aggressive in his first class.B. He was well-prepared for his first class.C. He got nervous upon the arrival of his first class.D. He waited long for the arrival of his first class.60. Before he started his class, the author asked the students to ______.A. write down their suggestions on the paper cardsB. cut maple leaves out of the construction paperC. cut some cards out of the construction paperD. write down their names on the paper cards61. The author chose the composition topic probably because ______.A. he got disappointed with his first classB. he had prepared the topic before classC. he wanted to calm down the studentsD. he thought it was an easy topicDIn a world with limited land, water and other natural resources, the harm from the traditional business model is on the rise. Actually, the past decade has seen more and more forests disappearing and globe becoming increasingly warm. People now realize that this unhealthy situation must be changed, and that we must be able to develop in sustainable (可持续的) ways. That means growth with low carbon or development of sustainable products. In other words, we should keep the earth healthy while using its supply of natural resources.Today, sustainable development is a popular trend in many countries. According to a recent study, the global market for low-carbon energy will become three times bigger over the next decade. China, for example, has set its mind on leading that market, hoping to seize chances in the new round of the global energy revolution. It is now trying hard to make full use of wind and solar energy, and is spending a huge amount of money making electric cars and high-speed trains. In addition, we are also seeing great growth in the global markets for sustainable products such as palm oil (棕榈油), which is produced without cutting down valuable rainforest. In recent years the markets for sustainable products have grown by more than 50%.Governments can fully develop the potential of these new markets. First, they can set high targets for reducing carbon emissions(排放) and targets for saving and reusing energy. Besides, stronger arrangement of public resources like forests can also help to speed up the development. Finally, governments can avoid the huge expenses that are taking us in the wrong direction, and redirecting some of those expenses can accelerate the change from traditional model to a sustainable one.The major challenge of this century is to find ways to meet the needs of a growing population within the limits of this single planet. That is no small task, but it offers abundant new chances for sustainable product industries.62. The traditional business model is harmful because of all the following EXCEPT that ______.A. It makes the world warmerB. it consumes natural resourcesC. it brings severe damage to forestsD. it makes growth hard to continue63. What is the main purpose of the passage?A. To introduce a new business model.B. To advocate sustainable development.C. To predict a change of the global market.D. To compare two business models.64. To fully develop the low-carbon markets, government can ______.A. cut public expensesB. forbid carbon emissionsC. develop public resourcesD. encourage energy preservation65. We can learn from the last paragraph that businesses have many chances to ______.A. develop sustainable productsB. explore new natural resourcesC. make full use of natural resourcesD. deal with the major challenge第二卷I.听力理解第三节（每小题仅填写一个词II. 阅读理解第二节Parents and doctors have the same worry over especially low birth weight newborns. ___66___ A trend has therefore developed to make special formulas（配方）of extra nutrients and protein-rich foods for these tiny babies. Unfortunately, a British study has found that this practice could have negative long-term effects, such as high blood pressure in adulthood.Between 1993 and 1995, Atul Singhal of the Institute of Child Health and his colleagues researched 299 full-term newborns, each of whom weighed very little for their age. The babies’ moms had decided not to breastfeed（用母乳喂养）.___67___ The rest received a formula with more nutrients than the standard formula. The growth of all of these children was compared to that of 175 similarly low birth weight babies whose mothers had chosen to breastfeed their children for their 9 months. ___68___ They found 83 babies from normal-formula group, 70 babies from extra-formula group, and 95 babies from the breastfed group. ___69___ According to the latest data, children who received the extra formula had significantly higher blood pressure than those in the other two groups.Seven human tests have indeed shown that when infants are overfed before being stopped breastfeeding, they have an increased possibility to become fat as youngsters.No matter how big a child is at birth, he or she will probably reach the same adult height no matter how quickly the baby grows. But reaching one’s adult size at a slow-to-moderate speed may have a lot of benefits, as Singhal says. ___70___A. Half of these children were given a normal infant （幼儿）formula for 9 months.B. When they grow up, they might have high blood pressure.C. These babies have very little energy because they are so small.D. Six to eight years later, the researchers gave the children a series of measurements and tests.E. The results were quite surprising.F. Tiny babies will grow much slower if they are not specially fed.G. His advice to parents: Be patient. Don’t rush a child’s growth.III. 单词拼写1. They were d ___________ (下决心) to reach the top of the mountain.2. He was a_____________ in the book, so he didn’t hear the doorbell.3. He finished his work in a____________(积极的) way.4. He became______________(狂热的) about classical music.5. Don't ____________(暴露) your skin to the sun or you will be burned.6. If a doctor or a medical treatment c_____ someone's illness, they make the people well again.7. The common interests u__________ the two countries.8. The class ____________of (组成) 56 members.9. Some parents considered that some of their children's friends to be a bad _______ (影响) totheir children.10. There are plans to c_________ a new road bridge across the river to ease the traffic problems inthis area.IIV. 书面表达假设你是某所中学的学生，3月22日（世界水日）你参加了你班开展的一系列节水宣传活动。
北京市五中11-12学年高二上学期期中考试英语试题
班级________姓名________学号__________成绩_________I. 听力理解（每小题1分，共20分）第一节听下面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. When did the man have breakfast?A. At 7:15B. At 7:30 C At 8:002. Who is the man ?A. A taxi driverB. A hotel receptionistC. A waiter3. What can we learn from the conversation?A. Johnson is out now.B. Johnson is waiting for the call.C. The line to Johnson is busy now.4. What does the man mean ?A. He won’t leave the woman behind.B. The woman can call him if she misses him.C. The woman can go to him if she likes.5. What do we know about White?A. He called the woman last weekend .B. He is the man’s classmate.C. He doesn’t live in the city.第二节，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。
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北京市五高2017 年12 月月考试题英语学科高一命题组高三命题组联合制题第一部分：知识运用（共两节，45分）第一节单项填空（共15小题；每小题1分，共15分）从每题所给的A、B、C、D四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。
1. Frank ______stamps in his spare time. It’s his hobby.A. is collectingB. collectsC. collectedD. was collecting2. You have to explain ______you were absent from school yesterday.A. whatB. whichC. whereD. why3 As soon as I got to the airport, I realized I______ my ID card at home.A. had leftB. has leftC. would leaveD. will leave4. Oxford is not far from Stratford, so you can easily visit ______ in a day.A. oneB. eitherC. bothD. all5. My phone ______ have been stolen while I was taking a bus. I can't find it anywhere.A. canB. mustC. shouldD. would6. We were both travelling across Europe, and that’s ______ we first met.A. whichB. whetherC. whenD. whom7. Before getting off the train, ______ sure you have all your belongings with you.A. makingB. to makeC. madeD. make8. ---Would you like to have some ice-cream? ---I’d like to, but I'm on a diet ______ weight.A. loseB. to loseC. being lostD. lost9. ______ the weather improves, we will have to cancel the game.A. ThoughB. UntilC. UnlessD. Since10. Kate _____ by the teacher for she had made an excellent contribution to group discussion.A. praisedB. was praisedC. has praisedD. has been praised11. ---Do you have any plans for the summer break? ---Not really. I think I am just staying at home, ______ some books.A. readingB. to readC. readD. having read12. I wish I ______ the Great Wall with you tomorrow, but I’m preparing for the coming exam.A. will climbB. had climbedC. climbD. would climb13. This year’s children’s party, ______ some parents were invited to, was a great success.A. whichB. whyC. whoseD. where14. The real friend is the one who comes to the rescue______ your hour of need.A. toB. atC. forD. in15. Life isn’t always beautiful, ______ the struggles make you stronger and the changes make you wiser.A. orB. soC. butD. for第二节完形填空（共20小题；每小题1.5分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
The Broken LanternOn a wild July night, the storm was getting worse and worse. Kate Shelley, who lived between Honey Creek(小溪) and Des Moines River, was __16___ looking out of the window, wondering ___17__ it would wash away the bridges over them, when suddenly came the loud ___18___ of breaking wood, then followed by a great splash(飞溅的水花). She realized the bridge over the creek was ___19___. At that time, the midnight train was almost due. If no one told the engineer to ___20___ the train, it would fall into the creek with a hundred or more ___21___ . The situation was so urgent that Kate ___22___ to go to Moingon Railway Station to get help. Immediately she ___23___ out into the s torm with her father’s railway lantern.Moingon lay on the far side of Des Moines River. The only way to get there was to cross a long wooden railroad bridge. Even in the daytime, it was ___24___ to walk on it because there was no foot walk or railing(栏杆) except only rails and ties. The ties were ___25___ enough apart for the girl to fall through.Kate stopped when she came to the ___26___. She had never seen the river rising so high that she was ___27___ . Her father had been killed in a train accident by that river and her brother had drowned there. But she soon managed to___ 28___ thinking more of the past happenings for she knew that train had to be stopped ___29___ it was too late. She started to step on that dangerous bridge, knowing she might fall into the rush water at any moment. What’s worse, she broke her lantern while making her wa y, exposing herself to the ____30__ . She had to climb on her hands and knees…It seemed like a long time. At last she ___31___ the other side.She stopped just long enough to catch her breath. Then she ran ___32___ to the railway station. When she finally got there, she was out of ___33___, wet all over, her hat blown away, her hands and knees still bleeding and her eyes looking ___34___. She told the station man what had happened to the Honey Creek Bridge before her fainting. Finally, the passengers were saved.The girl’s heroic deed was rewarded. For her ___35___ act, Kate enjoyed a right of getting on or off the train at her door when she wanted.16. A. angrily B. eagerly C. anxiously D. hopefully17. A. whether B. that C. when D. how18. A. crash B. cry C. blow D. voice19. A. removed B. blocked C. completed D. broken20. A. change B. stop C. catch D. leave21. A. conductors B. customers C. passengers D. engineers22.A. decided B. tried C. expected D. agreed23.A. fell B. rushed C. climbed D. rode24. A. harmful B. foolish C. dangerous D. strange25. A. long B. wide C. thick D. far26. A. bridge B. station C. train D. rail27. A. moving B. shaking C. escaping D. running28. A. forget B. admit C. avoid D. risk29. A. though B. because C. unless D. before30. A. darkness B. calmness C. emptiness D. coldness31. A. selected B. reached C. found D. passed32. A. cautiously B. slowly C. disappointedly D. desperately33. A. breath B. mind C. sight D. favour34. A sharp B. watchful C. wild D. bitter35. A. honest B. modest C. generous D. courageous第二部分：阅读理解（共两节，40分）第一节（共16小题；每小题2分，共30分，附加1题可不计入总分）阅读下列短文，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。