数学-广东省揭阳市普通高中2017-2018学年下学期高二3月月考试题08
广东省揭阳市普通高中2017-2018学年高二第二学期3月月考英语试卷07
下学期高二英语3月月考试题07第I卷（共105分）I. Listening Comprehension（30%）Section ADirections: In section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. In a library B. Under a big chair C. In his officeD. Under a big tree2. A. 8:05 a.m. B. 9:30 a.m. C. 7:30 a.m. D. 11:30 a.m.3. A. Boss and secretary B. ClassmatesC. Husband and wifeD. Teacher and student4. A. She wants to get some sleep. B. She has had too much coffee.C. She needs time to write a paper.D. She has a literature class to attend.5. A. See a doctor B. Stay in bed for a few days.C. Get treatment in a better hospital.D. Make a phone call.6. A. To paint it grey and draw a duck on it.B. To paint it white and write something on it.C. To paint is white and put up some drawings.D. To pain it grey and do some drawings on it.7. A. Have a rest B. Take two weeks offC. Continue his work outdoors.D. Go to the park with the woman.8. A. She also has a dictionary of this kind.B. She didn’t know the man was good at writing.C. She isn’t surprised at the man getting the prize.D. The dictionary is so marvelous that she want to have it.9. A. The 2:30 train has a dining car.B. The man prefers to take the 2:30 train.C. The 2:00 train will reach Washington earlier.D. They are going to have some fast food on the train.10. A. He was seriously injured in a car accident.B. He was absent all week because of sickness.C. He called to say that his wife had been injured.D. He has to be away from school to look after his wife..Section BDirections: In section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. By getting organized. B. By finding a hobby.C. By setting clear goals.D. By making new friends.12. A. Saving money. B. Joining clubs more easily.C. Fighting against boredom.D. Achieving clubs more easily.13. A. Employees. B. Parents. C. Students. D. Teachers. Questions 14 through 16 are based on the following passage.14. A. They strongly follow family rules.B. They are very likely to succeed in life.C. They are in the habit of obeying their parents.D. They tend to take responsibility for themselves.15. A. They grow up to be funny and charming.B.They tend to be smart and strong-willed.C.They often have a poor sense of direction.D.They get less attention from their parents.16. A. They usually don’t follow family orders.B.They are less likely to be successful in life.C.They tend to believe in their parents’ ideas.D.They don’t like to take chances in their lives.Section CDirections: In section C, you will hear two longer conversations. Each conversation will be read twice. After you hear the conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Complete the form. Write ONE WORD OR NUMBER for each answer.。
广东省揭阳市普通高中2017-2018学年高二数学1月月考试
上学期高二数学1月月考试题02一、选择题(每小题5分，共50分)1．设m ＞0，则直线2(x ＋y )＋1＋m ＝0与圆x 2＋y 2＝m 的位置关系为( )． A ．相切 B ．相交 C ．相切或相离 D ．相交或相切2．若直线2ax －by ＋2＝0(a ＞0，b ＞0)被圆x 2＋y 2＋2x －4y ＋1＝0截得的弦长为4，则1a ＋1b的最小值是( )． A ．4 B ．2 C . 12 D . 14 3. 若集合A={1,sin θ}，B={122,}，则“56πθ=”是“AB ={12}”的( )A.充要条件B.必要不充分条件C.充分不必要条件D.既不充分也不必要条件4. 命题p ：∅={∅}；命题q ：若A={1,2}, B={x |x A ⊆}，则A B ∈. 下列关于p 、q 的真假性判断正确的是 ( )A . p 假q 假B . p 真q 假C . p 假q 真D . p 真q 真 5．如图中，x 1，x 2，x 3为某次考试三个评阅人对同一道题的独立评分，p 为该题的最终得分．当x 1＝6, x 2＝9，p ＝8.5时，3x 等于( )．A ．11B ．10C ．8D ．76. 已知函数f (x )=2020x x x x +,≤,⎧⎨-+,>,⎩ 则不等式2()f x x ≥的解集为( )A . [11]-,B . [22]-,C . [21]-,D . [12]-,7．在正方体ABCD —A 1B 1C 1D 1中，M 、N 分别为棱AA 1和BB 1的中点，则1sin ,CM D N <>的值为( )．A . 19B . 49 5C . 29 5D . 238. 设,m n 是平面α内的两条不同直线；12l l ,是平面β内的两条相交 直线. 则αβ的一个充分而不必要条件是( ) A . m ∥β且1l ∥α B . m ∥1l 且n ∥2l C . m ∥β且n ∥βD . m ∥β且n ∥2l9. 已知f (x )是定义在R 上的函数，且满足()()11f x f x +=-，则“f (x )为偶函数”是“2为函数f (x )的一个周期”的( )A . 充分不必要条件B . 必要不充分条件C . 充要条件D . 既不充分也不必要条件10. 如图，样本A 和B 分别取自两个不同的总体，它们的样本平均数分别为A x 和B x ，样本标准差分别为A s 和B s ，则（ ） A . A B x x >,A B S S > B . A x <B x ,A B S S > C . A x >B x ,A B S S < D . A x <B x ,A B S S <二、填空题(每小题5分，共25分)11．已知A ，B 是圆O ：x 2＋y 2＝16上的两点，且|AB |＝6，若以AB 的长为直径的圆M 恰好经过点C (1，－1)，则圆心M 的轨迹方程是________．12. 若0,0,2a b a b >>+=，则下列不等式对一切满足条件的,a b 恒成立的是 (写出所有正确命题的编号).①1ab ≤； ≤ ③222a b +≥； ④3a +33b ≥； ⑤112a b+≥.13. 在第3、6、16路公共汽车的一个停靠站(假定这个车站只能停靠一辆公共汽车)，有一位乘客需在5分钟之内乘上公共汽车赶到厂里，他可乘3路或6路公共汽车到厂里，已知3路车、6路车在5分钟之内到此车站的概率分别为0.20和0.60，则该乘客在5分钟内能乘上所需要的车的概率为14. 连掷两次骰子得到的点数分别为m 和n ,记向量(),a m n =与向量()1,1b =-的夹角为θ,则(0]2πθ∈,的概率是15. 对于空间三条直线,有下列四个条件：①三条直线两两相交且不共点； ②三条直线两两平行；③三条直线共点； ④有两条直线平行,第三条直线和这两条直线都相交. 其中，使三条直线共面的充分条件有 .(把符合要求的条件序号都填上) 三、解答题(共25分)16．某花店每天以每枝5元的价格从农场购进若干枝玫瑰花，然后以每枝10元的价格出售．如果当天卖不完，剩下的玫瑰花作垃圾处理． (1) 若花店一天购进17枝玫瑰花，求当天的利润y (单位：元)关于当天需求量n (单位：枝，n ∈N )的函数解析式；(2) 花店记录了100天玫瑰花的日需求量(单位：枝)，整理得下表：单位：元)的平 均数；②若花店一天购进17枝玫瑰花，以100天记录的各需求量的频率作为各需求量发生的概率，求当天的利润不少于75元的概率．17. (本小题13分)如图，四棱锥P ABCD -中，P A ⊥底面ABCD . 四边形ABCD 中，AB ⊥AD ， AB ＋AD ＝4，CD ＝2，∠CDA ＝45°. (1) 求证：平面P AB ⊥平面P AD ；(2) 设AB ＝AP . 若直线PB 与平面PCD 所成的角为30°，求线段AB 的长.参考答案一、选择题(每小题5分，共50分)1、解析：圆心到直线l 的距离为d ＝1＋m2，圆半径为m . 因为d －r ＝1＋m 2－m ＝12(m －2m ＋1)＝12(m －1)2≥0，所以直线与圆的位置关系是相切或相离，故选C . 答案：C 2、解析 圆(x ＋1)2＋(y －2)2＝4，∵弦长为4，故为直径，即直线过圆心(－1,2)，∴a ＋b ＝1， ∴1a ＋1b ＝⎝⎛⎭⎫1a ＋1b (a ＋b )＝2＋b a ＋a b ≥2＋21＝4，当且仅当a ＝b ＝12时，取等号，∴1a ＋1b 的最小值为4. 选A 3、答案：C 解析：56AB πθ=⇒={12}，但A B ={12}不能推出5,6πθ=故选C .4、答案：C解析：命题p 显然为假；由命题q 可得B={∅,{1},{2},{1,2}}，∴A B ∈,即q 为真.5、解析：本题代入数据验证较为合理，显然满足p ＝8.5的可能为6＋112＝8.5或9＋82＝8.5；显然若x 3＝11，不满足|x 3－x 1|<|x 3－x 2|，则x 1＝11，计算p ＝11＋92＝10，不满足题意；而若x 3＝8，不满足|x 3－x 1|<|x 3－x 2|，则x 1＝8，计算p ＝8＋92＝8.5，满足题意．答案 C 6、答案：A解析：当0x ≤时，不等式2()f x x ≥化为22x x +≥,即220x x x ⎧+≥,⎨≤,⎩所以10x -≤≤；当x >0时，不等式2()f x x ≥化为22x x -+≥,即220x x x ⎧-+≥,⎨>,⎩所以01x <≤.综上可得不等式的解集为[11]-,.7、解析 设正方体的棱长为2，以D 为坐标原点， DA 为x 轴，DC 为y 轴，DD 1为z 轴建立空间直角 坐标系(如图)，可知()2,2,1CM =-，()12,2,1D N =-11cos ,9CM D N <>=-，1sin ,9CM D N <>=答案 B8、答案：B解析：对于B ，∵m ∥1l ,且n ∥2l ,又1l 与2l 是平面β内的两条相交直线, ∴α∥β,而当α∥β时不一定推出m ∥1l 且n ∥2l ,也可能异面. 故选B. 9、答案：C解析：由f (1+x )=f (1-x )得f (x +2)=f [1+(1+x )]=f [1-(1+x )]=f (-x ). 若f (x )为偶函数，则f (x +2)=f (x )，即2为函数f (x )的一个周期. 若2为函数f (x )的一个周期,则f (x +2)=f (x ).又由()()11f x f x +=-，得()()2f x f x +=-，所以()()f x f x -=，即()f x 为偶函数. 10、答案：B解析：由图可知A 组的6个数为2.5，10，5，7.5，2.5，10； B 组的6个数为15，10，12.5，10，12.5，10. 所以 2.51057.5 2.5106.256A x +++++==，151012.51012.51011.676B x +++++=≈，显然A B x x <，又由图形可知，B 组的数据分布比A 均匀，变化幅度不大，故B 组的数据比较稳定，方差较小，从而标准差较小，所以A B S S >二、填空题(每小题5分，共25分)11．解析 设圆心坐标为M (x ，y )，则(x －1)2＋(y ＋1)2＝⎝⎛⎭⎫|AB |22，即为(x －1)2＋(y ＋1)2＝9. 答案 (x －1)2＋(y ＋1)2＝9 12. 答案：①③⑤解析：两个正数,和定积有最大值， 即2()1a b ab +≤=, 当且仅当a b =时取等号，故①正确；224a b =+++,当且仅当a b =2≤,故②错误；由于222()124a b a b ++≥=,故222a b +≥成立， 故③正确； 332222()()2()a b a b a b ab a b ab +=++-=+-, ∵1ab ≤,∴1ab -≥-. 又222a b +≥,∴221a b ab +-≥. ∴332a b +≥,故④错误：1111()11222a b a b a b a b b a ++=+=++≥+当且仅当a b =时取等号,故⑤成立.13.答案：0.80解析：令“能上车”记为事件A ，则3路或6路车有一辆路过即事件A 发生， 故()0.200.600.80P A =+=. 14.答案：712解析：∵0,0m n >>,∴(),a m n =与()1,1b =-不可能同向.∴夹角0θ≠. ∵(0]2πθ∈,⇔0a b ⋅≥，∴0m n -≥,即m n ≥.当m=6时,n=6,5,4,3,2,1; 当m=5时,n=5,4,3,2,1; 当m=4时,n=4,3,2,1; 当m=3时,n=3,2,1; 当m=2时,n=2,1; 当m=1时,n=1.∴所求的概率是：65432176612P +++++==⨯15. 答案：①④解析：①中两直线相交确定平面,由于第三条直线不过前两条直线的交点且又分别与它们都相交,所以第三条直线也在这个平面内. ②中可能有直线和平面平行. ③中直线最多可确定3个平面.④中两条平行线确定一个平面,第三条直线与它们都相交, 所以第三条直线也在这个平面内.三、解答题(共25分)16．解：(1)当日需求量n ≥17时，利润y ＝85. 当日需求量n <17时，利润y ＝10n －85.所以y 关于n 的函数解析式为 y ＝⎩⎨⎧10n －85，n <17，85，n ≥17(n ∈N )．(2)①这100天中有10天的日利润为55元，20天的日利润为65元，16天的日利润为75元，54天的日利润为85元，所以这100天的日利润的平均数为 1100(55×10＋65×20＋75×16＋85×54)＝76.4. ②利润不低于75元当且仅当日需求量不少于16枝．故当天的利润不少于75元的概率为 p ＝0.16＋0.16＋0.15＋0.13＋0.1＝0.7.17. (1)【证明】因为P A ⊥平面ABCD ，AB ⊂平面ABCD ， 所以P A ⊥AB .又AB ⊥AD ，P A ∩AD ＝A ， 所以AB ⊥平面P AD .又AB ⊂平面PAB ，所以平面PAB ⊥平面PAD .(4分) (2)【解】：以A 为坐标原点，建立空间直角坐标系Axyz (如图)． 在平面ABCD 内，作CE ∥AB 交AD 于点E ， 则CE ⊥AD .在Rt △CDE 中，DE ＝CD ·cos 45°＝1，CE ＝CD ·sin 45°＝1. 设AB ＝AP ＝t ，则B (t,0,0)，P (0,0，t )，由AB ＋AD ＝4得AD ＝4－t .所以E (0,3－t,0)，C (1,3－t,0)，D (0,4－t,0)，()1,1,0CD =-，()0,4,PD t t =--．设平面PCD 的法向量为n ＝(x ，y ，z )，由n ⊥CD ，n ⊥PD ， 得⎩⎨⎧－x ＋y ＝0，(4－t )y －tz ＝0.取x ＝t ，得平面PCD 的一个法向量n ＝(t ，t,4－t )．又PB ＝(t,0，－t )，故由直线PB 与平面PCD 所成的角为30°得sin30cos ,n PB n PB n PB⋅=<>=⋅， 即|2t 2－4t |t 2＋t 2＋(4－t )2·2t2＝12，解得t ＝45或t ＝4(舍去，因为AD ＝4－t ＞0)，所以 AB ＝45.。
广东省揭阳市普通高中18学年高二数学下学期3月月考试题08
下学期高二数学3月月考试题08满分150分．时间120分钟． 第Ⅰ卷(选择题 共60分)一、选择题 (本大题共12个小题，每小题5分，共60分，在每小题给出的四个选项中，只有一项是符合题目要求的)1．若函数32121212()1,()[()()]0f x x x mx x x R x x f x f x =+++∈-->对任意满足，则实数m 的取值范围是( )A B C D 【答案】D2．已知定义在R 上的函数2()sin x f x e x x x =+-+，则曲线()y f x =在点(0,(0))f 处的切线方程是( ) A ．1y x =+ B ．32y x =- C ． 21y x =- D ．23y x =-+【答案】A3( )A ．0B ．1C ．2D ．2-【答案】D4．下列命题为真命题的是( )A ．)(x f 在0x x =处存在极限，则)(x f 在0x x =连续B ．)(x f 在0x x =处无定义，则)(x f 在0x x =无极限C ．)(x f 在0x x =处连续，则)(x f 在0x x =存在极限D ．)(x f 在0x x =处连续，则)(x f 在0x x =可导 【答案】C 5，其在点(,())M t f t 处的切线为l ，l y 与轴和直线1y =分别交于点,P Q ，又点()0,1N ，若PQN 的面积为b 时的点M 恰好有两个，则b 的取值范围为( )A B C D 【答案】A6．给出以下命题: ⑴若()0b af x dx >⎰,则f(x)> 0；⑶f(x)的原函数为F(x),x R ∈,且F(x)是以T 为周期的函数,则()()a a T Tf x dx f x dx +=⎰⎰；其中正确命题的个数为( )A ．1B ．2C ．3D ．0 【答案】B7．设a 为实数，函数f(x)=x 3+ax 2+(a-2)x 的导数是)('x f ，且)('x f 是偶函数，则曲线y=f(x)在原点处的切线方程为( ) A ．y=-2x B ．y=3x C ．y=-3x D ．y=4x 【答案】A8．．两曲线22y x x =-+，224y x x =-所围成图形的面积S 等于( ) A ．4- B ．0C ．2D ．4【答案】D9．函数y ＝()f x 的图象如左下图所示，则导函数'()y f x =的图象可能是( )【答案】D10．当x ∈R 时，f （x ）＋x '()f x < 0成立（其中'()f x 是f （x ）的导函数），若a ＝ (30.3) ·f(30.3)，b ＝(log 3)(log 3)f ππ，c 31)(log )9f ，则a ，b ，c 的大小关系是( ) A ． a ＞b ＞c B ． c ＞a ＞b C ． c ＞b ＞a D ． a ＞c ＞b 【答案】C11．函数f(x)的定义域为开区间(a ，b)，其导函数f ’(x)在(a ，b)内的图像如右图所示，则函数f(x)在开区间(a ，b)内极小值点的个数有( )A ．1个B ．2个C ．3个D ．4个【答案】A12．（t 表示时间，单位：秒；s 表示位移，单位：米），则瞬时速度为0米/每秒的时刻是( ) A ．0秒、2秒或4秒 B ．0秒、2秒或16秒 C ．2秒、8秒或16秒 D ．0秒、4秒或8秒 【答案】D第Ⅱ卷(非选择题 共90分)二、填空题 (本大题共4个小题，每小题5分，共20分，把正确答案填在题中横线上) 13．定积分dx x ⎰π20sin =____________【答案】014．（3，2）处的切线与直线10ax y ++=垂直，则a =____________。
广东省揭阳市普通高中2017_2018学年高二数学1月月考试题07201803191253
高二数学 1月月考试题 07一：选择题（每题 4分，共 48分）4. 设 A,B 是任意事件，下列哪一个关系式正确的（ ）___A.A+B=AB.AB AC.A+AB=AD. A BA13．把 38化成二进制数为（ ）A.100110 2B.101010 2C.110110 2D.110010 2(2)已知 a b ,c d ,则下列不等式中恒成立的是（ ）1.a d b c B.ac bdC. a bD.d a cb c d4.函数xf (x )的最大值为（）x 1A.2 5B .1 2C . 22D.15.阅读下图所示的程序框图，运行相应的程序，输出的 i 值等于( )A ．2B ．3C ．4D ．56.采用系统抽样方法从 960人中抽取 32人做问卷调查，为此将他们随机编号为 1,2，…，960，分组后在第一组采用简单随机抽样的方法抽到的号码为 9.抽到的 32人中，编号落入区间1, 450 的人做问卷 A ，编号落入间451, 750 的人做问卷 B ，其余的人做问卷C .则抽到的人中，做问卷 B 的人数为( )A.7B. 9C.10D.157.已知点P(x,y)在圆x2 (y 1)2 1上运动，则y1x2的最大值与最小值为（）A．33，3B．3, 3C．33 3D．,221,2128．一个样本a,3,5,7的平均数是b，且a、b是方程x2－5x＋4＝0的两根，则这个样本的方差是()A．3B．4 C．5 D．69．已知集合A＝{(x，y)|y－3x≤0}，集合B＝{(x，y)|x2＋(y－a)2≤1}，若A∩B＝B，则a的取值范围是( )A．[2，＋∞) B．(－∞，－2] C．[－2,2] D．(－∞，－2]∪[2，＋∞)10.已知函数f(x) |lg x|，若0 a b，且f(a) f(b)，则a 2b的取值范围是( ) A． 22， B． 22， C．(3， )D． 3，11.设两圆C1、C2都和两坐标轴相切，且都过点(4,1)，则两圆心的距离|C1C2|=()A．4 B．4 2 C．8 D．8 212.已知等腰三角形腰上的中线长为3,则该三角形的面积的最大值为()A. 3B.2C.23D.3二：填空题（每题3分，共12分）13.点（2a,a 1）在圆x2 y2 2y 4 0的内部，则a的取值范围是14.若设变量x，y满足约束条件 1x yx y4，则目标函数z 2x 4y的最大值y2为．15.若圆x2 y2 2x 4y 1 0上有且只有两个不同点到直线l：x y b 0的距离为1，则b的取值范围是_________．16.为调查南山学子喜欢数学课的人数比例,采用如下调查方法:(1)随机抽取100名学生,并编号为1,2,3, ,100;(2)在箱内放置两个白球和三个红球,让这100名学生分别从箱中随机摸出一球,记住其颜色并放回;(3)请下列两类学生举手:①摸到白球且号数为偶数的学生;②摸到红球且不喜欢数学课的学生.如果总共有32名学生举手,那么用统计的知识估计,本校学生中喜欢数学课的人数比例大约是__________.(用百分比表示)三：解答题（每题10分，共40分）17.驾驶员血液酒精浓度在20～80 m g/100 m L(不含80)之间，属酒后驾车，血液酒精浓度在80 mg/100 mL(含80)以上时，属醉酒驾车．市交警一队对过往的车辆进行抽查共查出喝过酒的驾车者60名，下图是这60名驾车者血液中酒精浓度的频率分布直方图．(1) 求这60名驾车者中属醉酒驾车的人数；(图中每组包括左端点，不包括右端点)(2) 求这60名驾车者血液的酒精浓度的平均值；(3) 将频率分布直方图中的七组从左到右依次命名为第一组，第二组，…，第七组，在第五组和第七组的所有人中抽出两人，记他们的血液酒精浓度分别为x，y(单位：mg/100 ml)，则事件|x－y|≤10的概率是多少？18.在线段AD上取两点B、C，在B、C处折断而得三个线段，求“这三个线段能构成三角形”的概率。
广东省揭阳市普通高中2017-2018学年高二数学1月月考试题04
高二数学1月月考试题04第Ⅰ卷(选择题，共60分)一、选择题(本大题共12小题，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的)1． 已知数列{}n a 中，12211,2,n n n a a a a a ++===+，则5a 等于( ) A.13 B.8 C.5 D.92．在△ABC 中，,,A B C ∠∠∠所对的边分别为,,a b c ，若2220a b c +-<，则△ABC 是 1.锐角三角形B.直角三角形C.等腰三角形D. 钝角三角形3．关于直线a ,b,c 以及平面M ，N ，给出下面命题：①若a //M ，b//M, 则a //b ②若a //M, b ⊥M ，则b ⊥a ③若a ⊂M ，b ⊂M,且c ⊥a ，c ⊥b,则c ⊥M ④若a ⊥M, a //N ，则M ⊥N ，其中正确命题的个数为 （ ） A ．0个 B ．1个 C ．2个 D ．3个 4．如图1，直三棱柱111ABC A B C -侧面11AA B B 是边长为5的正方形，AB BC ⊥，AC 与1BC 成60角，则AC 长 （ ）A ．13B ．10C．D．5．已知点P 在抛物线24y x =上，则点P 到直线1:4360l x y -+=的距离和到直线2:1l x =- 的距离之和的最小值为（ ）A.3716B.115C.2D.36．若△ABC 的三边长为a ，b ，c ，它的面积为a2＋b2－c24，那么内角C 等于( )A ．30°B ．45°C ．60°D ．90°7．若011<<b a ，则下列不等式：①ab b a <+；②22a b >；③b a <；④2>+b a a b 中正确的不等式是 ( c )A.①②B. ②③ C ．①④ D ．③④ 8．等比数列的前n 项，前2n 项，前3n 项的和分别为A,B,C,则( )A. A+B=CB. B2=ACC. (A+B)-C=B2D. A2+B2=A(B+C)9．设0,0a b >>3a 与3b的等比中项，则11a b +的最小值为( ) A. 8 B. 4 C. 1 D.1410.设双曲线)0,0(12222>>=-b a by a x 的右顶点为A ，P 为双曲线上的一个动点（不是顶点），从点A 引双曲线的两条渐近线的平行线，与直线OP 分别交于,Q R 两点，其中O 为坐标原点，则2||OP 与||||OQ OR ⋅的大小关系为（ ）111 1A ．2||||||OP OQ OR <⋅B ．2||||||OP OQ OR >⋅ C ．2||||||OP OQ OR =⋅ D ．不确定11.在正四棱柱1111ABCD A B C D -中，顶点1B 到对角线1BD 和到平面11A BCD 的距离分别为h 和d ，则下列命题中正确的是（ ）A ．若侧棱的长小于底面的边长，则hd的取值范围为(0,1)B ．若侧棱的长小于底面的边长，则hd的取值范围为C ．若侧棱的长大于底面的边长，则hd的取值范围为D ．若侧棱的长大于底面的边长，则hd的取值范围为()3+∞ 12 ．正方形ABCD 的边长为1,点E 在边AB 上,点F 在边BC 上,37AE BF ==,动点P 从E 出发沿直线向F 运动,每当碰到正方形的边时反弹,反弹时反射角等于入射角.当点P 第一次碰到E 时,P 与正方形的边碰撞的次数为（ ）A ．16B ．14C ．12D ．10二、填空题(本大题共4小题，每小题5分，共20分，请把正确答案填在题中横线上) 13．已知三角形的两边长分别为4和5，其夹角的余弦是方程22320x x +-=的根，则第三边是14．已知递增的等差数列{}n a 满足，则n a = ．15．若关于x 的一元二次方程21321,4a a a ==-2(1)0x m x m -+-=有两个不相等的实数根,则m 的取值范围是 .16．给出下列四个条件:①0b a >>;②0a b >>;③0a b >>;④0a b >>.其中能推出11a b<成立的是 三、解答题（本大题共6小题，共70分，解答应写出文字说明，证明过程或推演步骤） 17. (10分) 若不等式kx2-2x+6k<0(k ≠0). (1)若不等式解集是{x|x<-3或x>-2}，求k 的值； (2)若不等式解集是R ，求k 的取值。
广东省珠海市普通高中2017-2018学年下学期高二数学3月月考试题 08 含答案 精品
下学期高二数学3月月考试题08一、选择题（本大题共10小题，每小题4分，共40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．设集合错误！未找到引用源。
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C ．a ＞b 2D ．a2＞2b5．在△ABC 中，若B a b sin 2=，则A 等于（ ）A. 06030或 B. 06045或 C. 060120或 D. 015030或 6. 将函数错误！未找到引用源。
的图象先向左平行移动6π个单位长度，再向上平行移动1个单位长度，得到的函数解析式是（ ） A. 错误！未找到引用源。
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8．公差不为0的等差数列｛a n ｝中，a 2、a 3、a 6依次成等比数列，则公比等于( ) A. 错误！未找到引用源。
广东省揭阳市普通高中2017_2018学年高二英语下学期3月月考试题07201804211113
下学期高二英语3月月考试题07第I卷（共105分）I. Listening Comprehension（30%）Section ADirections: In section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. In a library B. Under a big chair C. In his office D. Under a big tree2. A. 8:05 a.m. B. 9:30 a.m. C. 7:30 a.m. D. 11:30 a.m.3. A. Boss and secretary B. ClassmatesC. Husband and wifeD. Teacher and student4. A. She wants to get some sleep. B. She has had too much coffee.C. She needs time to write a paper.D. She has a literature class to attend.5. A. See a doctor B. Stay in bed for a few days.C. Get treatment in a better hospital.D. Make a phone call.6. A. To paint it grey and draw a duck on it.B. To paint it white and write something on it.C. To paint is white and put up some drawings.D. To pain it grey and do some drawings on it.7. A. Have a rest B. Take two weeks offC. Continue his work outdoors.D. Go to the park with the woman.8. A. She also has a dictionary of this kind.B. She didn’t know the man was good at writing.C. She isn’t surprised at the man getting the prize.D. The dictionary is so marvelous that she want to have it.9. A. The 2:30 train has a dining car.B. The man prefers to take the 2:30 train.C. The 2:00 train will reach Washington earlier.D. They are going to have some fast food on the train.10. A. He was seriously injured in a car accident.B. He was absent all week because of sickness.C. He called to say that his wife had been injured.D. He has to be away from school to look after his wife..Section BDirections:In section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. By getting organized. B. By finding a hobby.C. By setting clear goals.D. By making new friends.12. A. Saving money. B. Joining clubs more easily.C. Fighting against boredom.D. Achieving clubs more easily.13. A. Employees. B. Parents. C. Students. D. Teachers. Questions 14 through 16 are based on the following passage.14. A. They strongly follow family rules.B. They are very likely to succeed in life.C. They are in the habit of obeying their parents.D. They tend to take responsibility for themselves.15. A. They grow up to be funny and charming.B.They tend to be smart and strong-willed.C.They often have a poor sense of direction.D.They get less attention from their parents.16. A. They usually don’t follow family orders.B.They are less likely to be successful in life.C.They tend to believe in their parents’ ideas.D.They don’t like to take chances in their lives.Section CDirections: In section C, you will hear two longer conversations. Each conversation will be read twice. After you hear the conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Complete the form. Write ONE WORD OR NUMBER for each answer.II. Grammar and Vocabulary （ 25%）Section ADirections: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.25. The last time we had a family reunion was ________ my brother’s wedding ceremon y four years ago.A. overB. atC. onD. in26. — Do you often talk with your friends on the telephone or mobile phone?— __________ . I like using QQ.A. NoneB. EitherC. AnyD. Neither27. ---This is the first time that I have seen you in this neighbourhood!--- I ________ here only last week.A. movedB. moveC. had movedD. am moving28. China won 100 medals in the Beijing Olympic Games, which are almost ______ thoseof the Sydney Olympic Games.A. twice as many asB. as many as twiceC. as much as twiceD. twice as much as29. ---Look! The girl passing by must be a newcomer!---No, she _______ be a newcomer. I’m sure it is at least one year since she came to live here.A. shouldn’tB. can’tC. mustn’tD. oughtn’t30. His ability has never been in doubt----the question is ___________ or not he isprepared to work hard.A. thatB. ifC. whereD. whether31. Standing on the top of the Oriental Pearl TV Tower, ______ a good bird’s–eyeview of Shanghai city.A. it will beB. you will getC. there will beD. it will have32. I’m only brave when I have to be. __________ d oesn’t mean you go looking fortrouble.A. To have been braveB. Having been braveC. Being braveD. Be brave33. Considering that she did her work ______ her manager had instructed, it was notproper to criticize her.A. asB. untilC. when D .though34. The Spring Festival is our traditional festival, __________ people usually visittheir friends and relatives.A. for whichB. to whichC. during whichD. about which35. __________ in the fields on a March afternoon, he could feel the warmth of spring.A. To walkB. WalkingC. WalkedD. Having walked36. During the 1960s, songs about winter ___________ by many famous rock groups werepopular among people of different ages.A. releasedB. being releasedC. releasingD. having been released37. Passengers on board aren’t allowed _____ calls during take-off.A. making or receivingB. having made or receivedC. to have made or receivedD. to make or receive38. Do you know ______________ had reported the accident to the police?A. who it was thatB. who was it thatC. it was who thatD. that it was who39. More and more Chinese people follow the practice ______ they will travel to variousscenic spots to enjoy the scenery in their leisure time.A. whetherB. whichC. whereD. that40. ______________ that my dearest friend would play a trick on me in front of allmy students.A. Never I thoughtB. Never did I thinkC. I thought neverD. Never thought ISection BDirections: Complete the following passage by using the words in the box. Each wordcan only be used once. Note that there is one word more than you need.Life on land probably began about 430 million years ago, though it has existedin the water for perhaps as much as 3,000 million years. When we think of the first 41 on land, we 42 think of strange animals coming out of the oceans, but,in fact, no animals could have been living if plants had not been on land first. Plantshad to be on land before animals arrived. They 43 the first land animals withthe 44 and food necessary, since they ---the plants are the only form of lifethat is able to get and store 45 .The first plants to exist out of the water were probably certain kinds of algae （藻类）which were followed by other plants that grew close to the ground and needed water in which to 46 . Once the move to land has been made, however, evolution took place quickly. By the end of 100 million years, plants had developed their 47 , and some have got tree-like forms since height was very important in 48 sunlight. About 300 million years ago, much of the world was 49 with forestsof huge trees. In most ways they were like modern trees. They had roots, leaves, wood,but mostly they had not developed seeds.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.When I was a college student, I did a lot of travelling abroad. That was because a professor 50 me to do so. She said,“Now is the time for you to travel around the world, 51 your knowledge through actual experiences and have fun!” I agreed with her.Since I started to work for a 52 company, however, I have done most of my travellling through the Internet. By using the Internet, I have seen the sights of many cities on my computer screen. And I have really made business 53 , too. With the help of the Internet, I have also got 54 about food in different countries.Therefore, I was beginning to feel that actual trips were 55 necessary when I happened to read a famous chef’s comment on the Internet. He said,“It is very difficult to have real Italian food in a foreign country, because we enjoy food and the atmosphere around us at the same time. So why don’t you fly over to Italy and enjoy real Italian 56 ?” Those words reminded me of my 57 advice. As information technology 58 ,you might be able to do without making some real trips. But this also means that you will miss the various 59 you can get from travelling.Today there are people who 60 direct communication with others and spend much of their time on the Internet. It is not surprising to see a group of people 61 not with each other but into their micro phones. It seems as if such people are 62 by an invisible wall. They seem to be losing out on a good chance to 63 and talk with other people. I do not think that they are taking good advantage of information technology. We should use information technology as a tool to make our daily communication more fruitful. However, we should never let it 64 our time for face-to-face communication. Let’s make use of information technology more wisely, and have great fun in experiencing the actual world.50. A. promised B. allowed C. hurried D. encouraged51. A. build up B. use C. practice D. exchange52. A. computer B. food C. clothing D. machine53. A. plans B. bargain C. progress D. trips54. A. information B. taste C. cooks D. feelings55. A. even more B. no longer C. much D. actually56. A. shoes B. dishes C. customers D. situations57. A. friend’s B. parents’ C. professor’s D. boss’58. A. produces B. advertises C. forms D. advances59. A. news B. pleasures C. troubles D. places60. A. avoid B. keep C. lose D. enjoy61. A. meeting B. talking C. communicating D. travelling62. A. stopped B. met C. surrounded D. hurt63. A. look at B. employ C. travel D. meet64. A. spare B. increase C. reduce D. make use of Section BDirections: Read the following four passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.ALast week my youngest son and I visited my father at his new home in Tucson, Arizona. He moved there a few years ago, and I was eager to see his new place and meet his friends. My earliest memories of my father are a tall, handsome, successful man devoted to his work and his family, but uncomfortable with his children. As a child I loved him. He seemed unhappy with me unless I got straight A’s and unhappy with my boyfriends if their fathers were not as “successful” as he was. Whenever I we nt out with him on weekends, I used to struggle to think up things to say, feeling on guard.On the first day of my visit, we went out with one of my father’s friends for lunch at an outdoor café. We talked along that afternoon, did some shopping, ate on the street table, and laughed over my son’s funny facial expressions. Gone w as my father’s critical (挑剔的) air and strict rules. Who was this person I knew as my father, who seemed so friendly and interesting to be around? What had held him back before?The next day dad pulled out his childhood pictures and told me quite a few stories about his own childhood. Although our times together became easier over the years, I never felt closer to him at that moment. After so many years, I’m at last seeing another side of my father. And in so doing, I’m delighted with my new friend. My dad, in his new home in Arizona, is back to me from where he was.65. Why did the author feel bitter about her father as a young adult?A. He was silent most of the time.B. He was too proud of himself.C. He did not love his children.D. He expected too much of her.66. When the author went out with her father on weekend, she would feel .A. nervousB. sorryC. tiredD. safe67. What does the author think of her father after her visit to Tucson?A. More critical.B. More talkativeC. Gentle and friendly.D. Strict and hard-working.68. The underlined words “my new friend” in the last paragraph refer to .A. the author’s sonB. the author’s fatherC. the friend of the author’s fatherD. the café ow nerBAttractions in WisconsinWisconsin Historical Museum30 N. Carroll Street on Madison’s Capital SquareDiscover Wisconsin’s history and culture on four floors of exhibits. Open for public program.Admission is free.Open Tuesday through Saturday, 9:00am---4:00pm.( 608 ) 264-6555 /museumSwiss Historical Village612 Seventh Ave., New GlaresThe Swiss Historical Village offers a delightful look at pioneer life in America’s heartland.14 buildings in the village give a full picture of every day life in the nineteenth-century Midwest.Tue.---Fri., May 1st ---October 31st , 10:00am---4:00pm. Admission is $20( 608 ) 527-2317 Artisan Gallery & Creamery Cafe`6858 Paoli Rd., Paoli WIOne of the largest collections of fine arts and crafts in Wisconsin. Over 5000 sq. ft. of exhibition space in a historical creamery. While visiting enjoy a wonderful prepared lunch at our cafe` overlooking the Sugar River. Just minutes from Madison!Gallery open Tue.—Sun.,10:00am—5:00 pmCafe` open Wed.—Sat, 11:00 am—3:00 pmSun. brunch with wine, 10:00---3:00 pm( 608 ) 845-6600 Christopher Columbus Museum239 Whitney St., ColumbusWorld-class exhibit ---2000 quality souvenirs marking Chicago’s 1893 World Columbus Exhibition. Tour buses are always welcome.Open daily, 8:15 am—4:00 pm( 608 ) 623-1992( )69. Where can you go for a visit on Monday?A. Wisconsin Historical MuseumB. Swiss Historical VillageC. Artisan Gallery & Creamery Cafe`D. Christopher Columbus Museum( )70. Where can visitors have lunch?A. At Wisconsin Historical MuseumB. At Swiss Historical VillageC. At Artisan Gallery & Creamery Cafe`D. At Christopher Columbus Museum ( )75. We can learn from the text that_________.A.Swiss Historical Village is open for half a year.B.Christopher Columbus Museum overlooks a river.C.Tickets are needed for Wisconsin Historical MuseumD.Artisan Gallery & Creamery Cafe are open daily for 4 hours.CSomeday a stranger will read your e-mail without your permission or scan the website you’ve visited or perhaps someone will casually glance through your credit card purchases or cell phone bills to find out your shopping calling habits In fact, it’s likely that some of these things have already happened to you. Who would watch you without your permission? It might be a spouse, a girlfriend, a marketing company, a boss, a cop or a criminal. Whoever it is, they will see you in a way you never intended to be seen.Psychologists tell us boundaries are healthy, that it’s impor tant to revealyourself partly to friends, family and lovers at appropriate times. But few boundaries remain. The digital bread crumbs you leave everywhere make it easy for strangers to know who you are, where you are and what you like. In some cases, a simple Google search can reveal what you think. Like it or not, increasingly we live in a world where you simply cannot keep a secret.The key question is: Does that matter?For many Americans, the answer apparently is “no”.When opinion polls ask Americans about privacy, most say they are concerned about losing it. 60 percent of respondents say they feel their privacy is “slipping away, and that bothers me”.But people say one thing and do another. Only a small number of Americans change any behavior in an effort to preserve their privacy. Few people turn down a discount at tollbooths to avoid using the EZ-Pass system that can track automobile movements. Privacy economist Acquisti has run a series of tests that reveal people will give up personal information like social security numbers just to get their hands on a 50-cents-off coupon. But privacy does matter－at least sometimes. It’s like health: when you have it, you don’t notice it. Only when it’s gone do you wish you’d done more to protect it.72. What would psychologists advise on the relationships between friends?A. Friends should open their hearts to each other.B. Friends should always be faithful to each other.C. There should be a distance even between friends.D. There should be fewer arguments between friends.73. Why does the author say “we live in a world where you simply cannot keep a secret”?A. Modern society has finally developed into an open society.B. People leave traces around when using modern technology.C. There are always people who are curious about others’ affairs.D. Many search engines profit by revealing people’s identities.74. According to the passage, privacy is like health in that _____.A. people will make every effort to keep itB. its importance is hardly understoodC. It is something that can easily be lostD. people don’t value it until they lose it75. What would be the best title for the passage?A. Value your health.B. Treasure your privacy.C. Boundaries are important between friends.D. The information age has its own shortcomings.Section CDirections:Read the following text and choose the most suitable heading from the listA - F for each paragraph. There is one extra heading which you do not need.an important part of your life. Relationships help you meet your social and emotional needs. They help you feel accepted and liked by others. The feelings you have about yourself and others depend on how well these needs are met.One of the most important things in life is to be loved and accepted by others. This gives you a feeling of security. You feel secure when you know you can count on family and friends to love and to accept you the way you are. You add to your feeling of security by making others feel loved. Helping people you care about makes you feelThink about how good you feel when someone compliments or thanks you. “What a good job” or “I appreciate your help” are comments that you like to hear about yourself. Such comments make you feel worthwhile. Naturally you feel happy when you receive a compliment. Likewise, you can compliment your family members or friends onthoughts clearly and listen to what others say. Talk things over with your family and friends. Share your hopes and dreams. Express your joys and frustrations. When family members and friends are talking, take time to listen to what they are saying. Give them clues that show you are listening, such as a nod of approval or a smile.Another relationship skill that helps people get along with one another is trust. To earn trust you need to show parents, adults, and friends that you can handle new experiences and responsibilities. Being honest and truthful with people can also help you.Section DDirections: Read the following passage carefully. Then answer the questions or complete the statements in the fewest possible words.The library is one of the most popular places at a Western university. Students turn to it for research, conversations about class, and many other services.Compared with Chinese libraries, college libraries in the US and UK tend to offer more resources. A graduate student at Yale University can borrow as many as 225 books at a time.In addition to borrowing books, there are online and electronic resources. These include a database(数据库) search of popular and academic material, such as LexisNexis Academic, which offers items from newspapers and magazines.Although books and articles are the items that students ask for most frequently, some libraries provide video recordings. At some schools, teachers and tutors put electronic copies of their teaching PPTs on the library Web to give easier access for students.Another useful service in Western college libraries is the Interlibrary Loan. This allows a student at one school to borrow books from another school. The loan request is made through the student’s college library, which gets the book, gives it to the user, and arranges for its return.Technology has made libraries more attractive. Some universities have services for students to send messages through the computer.Earlier this year, Harvard University introduced a new Scan and Deliver service, allowing students to make requests for parts of books and articles. Requests made through the system are handled by library staff. The student receives an e-mail with an Internet link to the scanned pages. The service is free and all material comes within four days.It used to be that libraries didn’t allow food or drinks. But that rule is changing and many of them now contain a café so students can spend as much time as they want in the library.Additionally, some US university libraries are now all-night affairs, or have at least one study room open all night.(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)81. In comparison with Chinese libraries, college libraries in the US and UK notonly_________________.82. According to Paragraph 4 and 5, what are the two useful services for students inWestern College libraries?83. The purpose of Harvard University’s introducing a new Scan and Deliver serviceis to let __________________.84. What have some US university libraries done for a change?第II卷（共45分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 志愿者经历让我受益匪浅。
广东省揭阳市普通高中2017-2018学年高二数学下学期3月月考试题03
下学期高二数学3月月考试题03一、填空题：本大题共10小题，每小题5分，共50分。
在每小题列出的四个选项中，选出符合题目要求的一项。
1.命题“若p 则q ”的逆命题是 （ ） A.若q 则p B.若p ⌝则q ⌝ C.若q ⌝则p ⌝ D.若p 则q ⌝2.命题“存在R x ∈0，020≤x ”的否定是 ( )A.不存在R x ∈0,02>x B.存在R x ∈0, 020≥xC.对任意的R x ∈, 02≤xD.对任意的R x ∈, 02>x3.设R x ∈，则“21≥x ”是“0122≥-+x x ”的 （ ） A.充分而不必要条件 B.必要而不充分条件 C.充分必要条件 D.既不充分也不必要条件4.椭圆63222=+y x 的焦距是 ( ) A. )23(2-B. 2C.52D.)23(2+5.已知直线l 过抛物线C 的焦点,且与C 的对称轴垂直, l 与C 交于A 、B 两点且12=AB ,若P 为C 的准线上一点,则ABP ∆的面积为 ( ) A.18 B.24 C.36 D.486.椭圆的长轴长为20，短轴长为16，则椭圆上的点到椭圆中心距离的范围是（ )A.[]10,6B.[]8,6C.[]10,8D.[]20,167.若椭圆)0(122>>=+n m n y m x 和双曲线)0,0(122>>=-b a by a x 有相同的焦点 1F 、2F ，点P 是两条曲线的一个交点，则21PF PF ⋅的值为 （ ）A.a m -B.)(21a m - C.22a m - D.a m - 8.已知双曲线22221(0,0)x y ab a b-=>>的左顶点与抛物线22(0)y px p =>的焦点的距离为4,且双曲线的一条渐近线与抛物线的准线的交点坐标为)1,2(--,则双曲线的焦距为 ( )A.32B.52C.34D.549.已知F 是抛物线x y =2的焦点，A 、B 是该抛物线上的两点,3=+BF AF ,则线段AB 的中点到y 轴的距离为 ( )A.43B.23C.45D.47 10.已知双曲线)0,0(12222>>=-b a by a x 的左、右焦点分别为1F 、2F ,点P 在双曲线的右支上且214PF PF =,则此双曲线的离心率e 的最大值为 （ ）A.34B.35C.2D.37二、填空题：本大题共5小题，每小题5分，共25分，把答案填在题中横线上。
广东省揭阳市月城中学2018年高二数学理月考试卷含解析
广东省揭阳市月城中学2018年高二数学理月考试卷含解析一、选择题：本大题共10小题，每小题5分，共50分。
在每小题给出的四个选项中，只有是一个符合题目要求的1. 已知点分别是双曲线的左右焦点，过且垂直于轴的直线与双曲线交于两点，若是锐角三角形，则该双曲线的离心率的取值范围是( )A． B． C． D．参考答案：C略2. 从2008名学生中选取50名学生参加某项活动，若采用下面的方法选取：先用简单随机抽样从2008人中剔除8人，剩下的2000人再按系统抽样的方法抽取50人，则在2008人中，每人入选的概率（）A．不全相等 B．均不相等C．都相等，且为 D．都相等，且为参考答案：C略3. 已知，设函数若关于x的不等式在R上恒成立，则a的取值范围为（）A. [0,1]B. [0,2]C. [0,e]D. [1,e]参考答案：C【分析】先判断时，在上恒成立；若在上恒成立，转化为在上恒成立。
【详解】∵，即，（1）当时，，当时，，故当时，在上恒成立；若在上恒成立，即在上恒成立，令，则，当函数单增，当函数单减，故，所以。
当时，在上恒成立；综上可知，的取值范围是，故选C。
【点睛】本题考查分段函数的最值问题，关键利用求导的方法研究函数的单调性，进行综合分析。
4. 观察下面频率等高条形图，其中两个分类变量x，y之间关系最强的是（）A. B.C. D.参考答案：D【分析】在频率等高条形图中，与相差很大时，我们认为两个分类变量有关系，即可得出结论．【详解】在频率等高条形图中，与相差很大时，我们认为两个分类变量有关系，四个选项中，即等高的条形图中x1，x2所占比例相差越大，则分类变量x，y关系越强，故选：D．【点睛】本题考查独立性检验内容，使用频率等高条形图，可以粗略的判断两个分类变量是否有关系，是基础题5. 命题p: x0∈R，+10＜0，则p:（）A. x0∈R，+10＞0B. x0∈R，+10≥0C. x∈R，+10＞0D. x∈R，+10≥0参考答案：D6. 已知命题：，．则是（）A. ，B. ，C. ，D. ，参考答案：A7. 把十进制数15化为二进制数为（ C ）A． 1011 B．1001 (2） C． 1111D．1111（2）参考答案：C8. 曲线y=e x在点A（0，1）处的切线斜率为（）A．1 B．2 C．e D．参考答案：A【考点】直线的斜率；导数的几何意义．【分析】由曲线的解析式，求出导函数，然后把切点的横坐标x=0代入，求出对应的导函数的函数值即为切线方程的斜率．【解答】解：由y=e x，得到y′=e x，把x=0代入得：y′（0）=e0=1，则曲线y=e x在点A（0，1）处的切线斜率为1．故选A．9. 方程的实根个数是（）A.3B.2C.1D.0参考答案：C略10. 已知两圆，动圆C与圆C1外切，且和圆C2内切，则动圆C的圆心C的轨迹方程为（）A. B.C. D.参考答案：D二、填空题:本大题共7小题,每小题4分,共28分11. △ABC中，,b,c分别为∠A、∠B、∠C的对边.如果,b,c成等差数列,∠B=30°,△ABC的面积为，那么b=参考答案：12. 在平行四边形ABCD中，AD=1，AB=2，，E是CD的中点，则.参考答案：13. 已知函数（），对于，总有成立，则实数a的值为．参考答案：414. .能说明“若，则是函数极值点”为假命题的一个函数是______________．参考答案：或等，答案不唯一【分析】根据极值点的定义求解.【详解】极值点的导数必需为零，且极值点左右两侧的函数单调性相反.函数，当时，，但是在上单调递增，所以不是函数的极值点.【点睛】本题考查极值点的定义，考查命题真假的判断，属于基础题15. 空间四个点P、A、B、C在同一球面上，PA、PB、PC两两垂直，且PA=PB=PC=a，那么这个球面的面积是________．参考答案：略16. 直线l经过点P(3,2)且与x轴、y轴的正半轴分别交于A、B两点，△OAB的面积为12，则直线l的方程为__________________.参考答案：2x＋3y－12＝0设直线方程为，当时，；当时，，所以，解得，所以，即。
广东省揭阳市普通高中18学年高二数学下学期3月月考试题07
下学期高二数学3月月考试题07（时间120分钟．满分150分）一、选择题：本大题共8小题，每小题5分，满分40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．设i 为虚数单位，复数i a z 31-=，bi z +=22，其中12,z z 互为共轭复数，则a b +=（ ）A ．1-B ．5C ．6-D ．62. 已知全集{2,1,0,1,2,3,4}U =--，集合M ={大于2-且小于3的正整数}，则=M C U （ ）A ．∅B ．{234}-，，C ．{4}D ．{2,1,0,3,4}-- 3.已知23)(23++=x ax x f ，若4)1(/=-f ，则a 的值为（ ）A 、310 B 、313 C 、316 D 、3194. 下列函数为偶函数的是（ ）A y=sinxB y=3xC |1|x y e -=5. 曲线2y x =与直线2y x =所围成图形的面积为 （ ）A ．163 B ．83 C ．43 D ．236. 一空间几何体的三视图如图所示，则该几何体的体积为（ ）A．2π+ B．2πC．6π+．62π+7. 若函数()f x 在0x 处可导,且/0()f x m =, 则000()()limx f x x f x x x→--+= （ ）A ．mB ．m -C ．2mD ． 2m -8.设)(21312111)(+∈+++++++=N n n n n n n f ，则=-+)()1(n f n f （ ） A 、121+n B 、221121+-+n n C 、221121+++n n D 、221+n俯视侧视第６题图二、填空题：本大题共6小题，每小题5分，满分30分. 9. 函数22--=x x y 的定义域为10.⎰=+-12)123(dx x x11．已知等差数列{n a }，满足758a a +=，则此数列的前11项的和11S = 12. 已知变量x,y 满足约束条件 ， 则z=x+2y 的最大值为 13.设△ABC 的内角A BC 、、 的对边分别为a b c 、、,且1cos 4a b C ==1，=2，,则sin B =__ __14. 对实数,a b a b n n⊗=定义一种运算：（为常数），具有性质(1)1a b n +⊗=+，(1)2a b n ⊗+=-. 若112⊗=，则20112011⊗=____________三、解答题：本大题共6小题，满分80分. 解答须写出文字说明、证明过程和演算步骤 15、（本小题满分12分）已知函数1)(23+++=bx ax x x f 在1-=x 与2=x 处有极值. （1）求函数)(x f 的解析式； （2）求)(x f 在]3,2[-上的最值.16、（本小题满分12分）已知函数()tan 34f x x π⎛⎫=+⎪⎝⎭． （1）求9f π⎛⎫⎪⎝⎭的值； （2）设3,2απ⎛⎫∈π ⎪⎝⎭，若234f απ⎛⎫+= ⎪⎝⎭，求cos 4απ⎛⎫- ⎪⎝⎭的值．1110x y x y x +≤⎧⎪-≤⎨⎪+≥⎩17、（本小题满分14分）如图,已知四棱锥P ABCD -，底面ABCD 是正方形，⊥PA 面ABCD ， 点M 是CD 的中点，点N 是PB 的中点,连接AM ,AN MN ,. (1) 求证：MN //面PAD ；（2）若5MN =,3AD =，求二面角N AM B --的余弦值.18、（本小题满分14分）在数列{}n a 中，已知111,().12nn na a a n N a ++==∈+（1）求234,,a a a ，并由此猜想数列{}n a 的通项公式n a 的表达式； （2）用数学归纳法证明你的猜想.19、（本小题满分14分）已知二次函数2()3f x ax bx =+-在1x =处取得极值，且在(0,3)-点处的切线与直线20x y +=平行． (1）求()f x 的解析式；(2）求函数()()4g x xf x x =+的单调递增区间及极值。
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广东省揭阳市普通高中2017-2018学年下学期
高二3月月考试题08
满分150分．时间120分钟．
第Ⅰ卷(选择题共60分)
一、选择题(本大题共12个小题，每小题5分，共60分，在每小题给出的四个选项中，只有一项是符合题目要求的)
1．若函数，则实数m的取值范围是( )
A．B．C．D．
2．已知定义在上的函数，则曲线在点处的切线方程是( )
A．B．C．D．
3．等于( )
A．B．C．D．
4．下列命题为真命题的是( )
A．在处存在极限，则在连续
B．在处无定义，则在无极限
C．在处连续，则在存在极限
D．在处连续，则在可导
5．函数，其在点处的切线为，轴和直线分别交于点，又点，若的面积为时的点恰好有两个，则的取值范围为( )
A．B．C．D．
6．给出以下命题:
⑴若,则f(x)> 0；
⑵;
⑶f(x)的原函数为F(x),,且F(x)是以T为周期的函数,则；其中正确命题的个数为( )
A．1 B．2 C．3 D．0
7．设a为实数，函数f(x)=x3+ax2+(a-2)x的导数是，且是偶函数，则曲线y=f(x)在原点处的切线方程为( )
A．y=-2x
B．y=3x
C．y=-3x
D．y=4x
8．．两曲线，所围成图形的面积等于( ) A．B．C．D．
9．函数y＝的图象如左下图所示，则导函数的图象可能是( )
10．当x R 时，f（x）＋x< 0成立（其中是f（x）的导函数），若a ＝(30.3) ·f(30.3)，b＝，c＝，则a，b，c的大小关系是( )
A．a＞b＞c B．c＞a＞b C．c＞b＞a D．a＞c＞b
11．函数f(x)的定义域为开区间(a，b)，其导函数f’(x)在(a，b)内的图像如右图所示，则函数f(x)在开区间(a，b)内极小值点的个数有( )
A．1个B．2个C．3个D．4个
12．已知物体的运动方程是（表示时间，单位：秒；表示位移，单位：米），则瞬时速度为0米/每秒的时刻是( )
A．0秒、2秒或4秒B．0秒、2秒或16秒
C．2秒、8秒或16秒D．0秒、4秒或8秒
第Ⅱ卷(非选择题共90分)
二、填空题(本大题共4个小题，每小题5分，共20分，把正确答案填在题中横线上)
____________
13．定积分
=
14．设曲线在点（3，2）处的切线与直线垂直，则____________。
15．对于三次函数（），定义：设是函数y＝f(x)的导数y＝的导数，若方程＝0有实数解x0，则称点(x0，f(x0))为函数y＝f(x)的“拐点”．有同学发现“任何一个三次函数都有‘拐点’；任何一个三次函数都有对称中心；
且‘拐点’就是对称中心．”
请你将这一发现为条件，函数，则它的对称中心为；计算= .
16．曲线在处的切线方程为．
三、解答题(本大题共6个小题，共70分，解答应写出文字说明，证明过程或演算步骤) 17．设函数在点处可导，试求下列各极限的值．
(1)；
(2)
18．已知，，.
(1）当时，求的单调区间；
(2）求在点处的切线与直线及曲线所围成的封闭图形的面积；
(3）是否存在实数，使的极大值为3？若存在，求出的值；若不存在，请说明理由.
19．统计表明，某种型号的汽车在匀速行驶中每小时的耗油量（升）关于行驶速度（千
米/小时）的函数解析式可以表示为：已知甲、乙两地相距100千米。
(I）当汽车以40千米/小时的速度匀速行驶时，从甲地到乙地要耗油多少升？
(II）当汽车以多大的速度匀速行驶时，从甲地到乙地耗油最少？最少为多少升？
20．某商场销售某种商品的经验表明，该商品每日的销售量(单位：千克)与销售价格(单位：元/千克)满足关系式，其中，为常数，已知销售价格为5元/千克时，每日可售出该商品11千克．
(Ⅰ) 求的值；
(Ⅱ) 若该商品的成本为3元/千克, 试确定销售价格的值,使商场每日销售该商品所获得的利润最大．
21．一出租车每小时耗油的费用与其车速的立方成正比，当车速为时，该车耗油的费用为/h,其他费用为12元/h.；甲乙两地的公路里程为160km，在不考虑其他因素的前提下，为了使该车开往乙地的总费用最低，该车的车速应当确定为多少公里/小时？
22．已知函数处的切线方程为
(I）求的解析式；
(II）设函数恒成立。
参考答案
满分150分．时间120分钟．
第Ⅰ卷(选择题共60分)
一、选择题(本大题共12个小题，每小题5分，共60分，在每小题给出的四个选项中，只有一项是符合题目要求的)
1．【答案】D
2．【答案】A
3．【答案】D
4．【答案】C
5．【答案】A
6．【答案】B
7．【答案】A
8．【答案】D
9．【答案】D
10．【答案】C
11．【答案】A
12．【答案】D
第Ⅱ卷(非选择题共90分)
二、填空题(本大题共4个小题，每小题5分，共20分，把正确答案填在题中横线上) 13．【答案】0
14．【答案】-2
15．【答案】; 2012
16．【答案】
三、解答题(本大题共6个小题，共70分，解答应写出文字说明，证明过程或演算步骤) 17．【答案】(1)原式＝
(2)原式＝
18．【答案】（1）当.
∴的单调递增区间为（0，1），单调递减区间为：，
(2）切线的斜率为，∴切线方程为.
所求封闭图形面积为
.
(3），
令.
列表如下：
由表可知，.
设，
∴上是增函数，
∴，即，
∴不存在实数，使极大值为3.
19．【答案】（I）当时，汽车从甲地到乙地行驶了小时，
要耗没（升）。
答：当汽车以40千米/小时的速度匀速行驶时，从甲地到乙地耗油17.5升。
(II）当速度为千米/小时时，汽车从甲地到乙地行驶了小时，设耗油量为升，依题意得
令得
当时，是减函数；
当时，是增函数。
当时，取到极小值
因为在上只有一个极值，所以它是最小值。
答：当汽车以80千米/小时的速度匀速行驶时，从甲地到乙地耗油最少，最少为11.25升20．【答案】(Ⅰ)因为时，所以；
(Ⅱ)由(Ⅰ)知该商品每日的销售量，所以商场每日销售该商品所获得的利润：
；
，令得
函数在上递增，在上递减，所以当时函数取得最大值
答：当销售价格时,商场每日销售该商品所获得的利润最大，最大值为42
21．【答案】设这辆出租车得车速为，耗油的费用为A元/h
由甲地开往乙地需要得时间为th,总费用为B元
依题意，得时，
由此可得
即
令即
得
答：为了使这辆出租车由甲地开往乙地得总费用最低，
该车得速度应确定为
22．【答案】（Ⅰ）将代入切线方程得，
又，化简得．
.
．
解得：；所以.
(Ⅱ）证明：要证在上恒成立，
即证在上恒成立，
即证在上恒成立．
设，. ∵，∴，即．
∴在上单调递增，
∴在上恒成立．
11。