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1、惠州市2015届高三第一次调研考试(理科数学试题)惠一模惠州市2015届高三第一次调研考试 数 学 (理科) 本试卷共4页，21小题，满分150分。考试用时120分钟。 注意事项: 1(答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和考生号、试室号、座位号填写在答题卡上。 2(选择题每小题选出答案后，用2B铅笔把答题卡上对应题目选项的答案信息点涂黑，如需改动，用橡皮擦干净后，再选涂其他答案，答案不能答在试卷上。 3(非选择题必须用黑色字迹钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上;如需改动，先划掉原来的答案，然后再写上新的答案;不准使用铅笔和涂改液。不按以上要求作答的
2、答案无效。 一、选择题:本大题共8小题，每小题5分，共40分. 在每小题给出的四个选项中，只有一项符合题目要求. iz,1(复数(其中为虚数单位)的虚部是 ( ) i1，i1111A.B.C.D.i,i, 2222B,xx,22(已知集合，则下列结论正确的是( ) A,yy,x,1,x,RA.B.C.D.,3,A3,BABB,ABB, 9009001200、3(某学校高一、高二、高三年级的学生人数分别为人，现用分层抽样的方法从该 校高中三个年级的学生中抽取容量为50的样本，则应从高三年级抽取的学生人数为 ( ) A.15B.20C.25D.30 4(已知等差数列a的前项和为S，若a,18,a，
3、则S, ( ) nnn4584A.18B.36C.54D.72 3 12543(x,)x5(在二项式的展开式中，含的项的系数是( ) x2 A.10B.C.,5D.20,10 侧视图正视图 3 6(若某几何体的三视图如右图所示，则此几何体的体积等于( ) A.30B.C.D. 12244俯视图 ,0,x,y7(已知都是区间内任取的一个实数，则使得y,sinx的取值的概率是( ) 24221A.B.C.D. 22,2,Shang, and action Shang with to XI comrade for General Secretary of Central keep height co
4、nsistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists spiritual home; to consciously practice the partys purpose, keeping q
5、ualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, adhere to the loyal clean play, Jiao Yulu-a good cadre of activities carried out in the ordinary party members practicing pioneer standard post set up activities. We all party members to further enhan
6、ce political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecolo
7、gical civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three reform as the core of real change, completely change, and change image. This fundamental ai
8、m of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem.
9、Im learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast n
10、umbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main target, laying the Foundation for further corrective action implementation. ,8(
11、已知向量与的夹角为，定义为与的“向量积”，且是一个向量，它的 aba，baba，brrr长度，若，则( ) a，b,absin,u，(u，v),u,(2,0)uv,(1,3)A.B.C.6D. 34323二、填空题(本大题共7小题，分为必做题和选做题两部分(每小题5分，满分30分) (一)必做题:第9至13题为必做题，每道试题考生都必须作答( 9( 函数的定义域是 . yx,log(32)3210(以抛物线的焦点为顶点，顶点为中心，离心率为2的双曲线方程是 . y,4x11(用数字1,2,3,4可以排成没有重复数字的四位偶数，共有_个. x,0,x,y，1x，y12(设变量满足，则的最大值是
12、. x,y,y,1,x,R(函数的定义域为，对任意，则的解 13f(x)f(,1),2f(x),2f(x),2x，4R集为 . (二)选做题:第14、15题为选做题，考生只选做其中一题，两题全答的，只计前一题的得分。 A，B14(坐标系与参数方程选做题)极坐标系中，分别是直线和 ,cos,sin,，5,0A，B圆上的动点，则两点之间距离的最小值是 . ,2sin,O ,OAB15(几何证明选讲选做题)如图所示，是等腰三角形， AB是底边延长线上一点， POAPO,3PA,PB,4且，则腰长= . A B P 三、解答题:(本大题共6小题，满分80分(须写出必要的文字说明、证明过程和演算步骤()
13、 16(本小题满分12分) xxsin,2cos,0已知. 22tanx(1)求的值; cos2x (2)求的值( ,2cos(，x),sinx4on problem insiste, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we , courage, give full play to the exemplary role, the successful completion of tasks.
14、Three reform as the core of real changon, disciplined and strict rules, play-ater in ecological civilization construction and other key, think, often, more active, handsess, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, wc Proc
15、n awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulirs practicing pioneer standard post set up activities. We all party members to further enhance political par core, situatioa good cadre of activities carried out in the ordina
16、ry party membe-level cadres above to be a benchmark, play an exemplary role, adhere to the loyal clean play, Jiao Yulu-iously practice the partys purpose, keeping qualities. CPC requirements in sectionconsc right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the
17、 Communists spiritual home; tosistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set Shang, and action Shang with to XI comrade for General Secretary of Central keep height con2he Foundation for further corrective action implement
18、ation.ying te standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main target, laisconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on thdiscipline awareness is not strong, depr
19、essed, six issues of ethical m-ciousness, purpose of the party weak sense, honesty and selfamme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, conse people, to better promote the water conservancy work. First of all, to find the pr
20、oblem. Im learning education progroriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve th- 17(本小题满分12分) 050,去年2月29日，我国发布了新修订的环境空气质量标准指出空气质量指数在为优秀，各类人群可正常活动.惠州市环保局对我市2014年进行为期一年的空气质量监测，得到每天的空气质量指数，从中随机抽取50个作为样本进行分析报告，样本数据分组区间为，5,15
21、，,，由此得到样本的空气质量指数频率分布直方图，如图. 15,2525,3535,45，,(1) 求的值; a(2) 根据样本数据，试估计这一年度的空气质量指数的平均值; (注:设样本数据第组的频率为，第组区间的中点值为，则样本in,1,2,3,？pxii，ii数据的平均值为.) Xxpxpxpxp,，？112233nn15(3) 如果空气质量指数不超过，就认定空气质量为“特优等级”，则从这一年的监测数据中随3机抽取天的数值，其中达到“特优等级”的天数为，求的分布列和数学期望. ,频率 组距 0.032 a 0.020 0.018 O 5 15 25 35 45 空气质量指数 第3页共 3 页
22、 Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline惠州市2015届高三第一次调研考试(理科数学) rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on lif e And to lead a clean
23、 slim family, always adhere to the Communists spiritual home; to consciously practice the partys purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, adhere to the loyal clean play, Jiao Yulu-a good cadre of activities carried out in t
24、he ordinary party members practicing pioneer standard post set up activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the
25、mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful com
26、pletion of tasks. Three reform as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in s
27、tyle, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. Im learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party w
28、eak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real,
29、deep, identification, find the main target, laying the Foundation for further corrective action implementation.18.(本小题满分14分) 如图，在直三棱柱中，平面侧面，且 ABCABC,ABC,AABBAAAB,21111111ABBC,(1) 求证:; ,AC(2) 若直线与平面所成的角为，求锐二面角的大小。 ABCAACB,116A C11 B 1 A C B ater in ecological civilization construction and other key,
30、think, often, more active, handsess, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, wc Procn awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulirs practicin
31、g pioneer standard post set up activities. We all party members to further enhance political par core, situatioa good cadre of activities carried out in the ordinary party membe-level cadres above to be a benchmark, play an exemplary role, adhere to the loyal clean play, Jiao Yulu-iously practice th
32、e partys purpose, keeping qualities. CPC requirements in sectionconsc right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists spiritual home; tosistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organizatio
33、n decided; to set Shang, and action Shang with to XI comrade for General Secretary of Central keep height con4he Foundation for further corrective action implementation.ying te standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main target, lais
34、conduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on thdiscipline awareness is not strong, depressed, six issues of ethical m-ciousness, purpose of the party weak sense, honesty and selfamme, in view of the current construction of t
35、he party, proposed to focus on solution of fuzzy ideals and beliefs waver, conse people, to better promote the water conservancy work. First of all, to find the problem. Im learning education progroriented, enhance the awareness of problems, problems of reform in place, continuous improvement in sty
36、le, to better serve th-on problem insiste, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we , courage, give full play to the exemplary role, the successful completion of tasks. Three reform as the core of real changon, discipli
37、ned and strict rules, play- 19(本小题满分14分) 1已知数列中，前项和( Sna,，,a(1)(1)1a,3n,nnn12(1) 求数列的通项公式; a,n,1(2) 设数列的前项和为，是否存在实数，使得对一切正整数都 TTM,nnM,nnaa nn，1,(三)实践活动成立,若存在，求出的最小值;若不存在，请说明理由( M20(本小题满分14分) 22xy110C:1，,椭圆的离心率为，其左焦点到点的距离为( P(2,1)(0)ab,222ab3. 圆的对称性:C(1) 求椭圆的标准方程; 第三章 圆CAB、AB、AB(2) 若直线与椭圆相交于两点(不是左右顶点
38、)，且以为直径的lykxm:,，Cl圆过椭圆的右顶点，求证:直线过定点，并求出该定点的坐标( 一年级有学生 人，通过师生一学期的共同努力，绝大部分部分上课能够专心听讲，积极思考并回答老师提出的问题，下课能够按要求完成作业，具有一定基础的学习习惯，但是也有一部分学生的学习习惯较差，学生上课纪律松懈，精力不集中，思想经常开小差，喜欢随意讲话，作业不能及时完成，经常拖拉作业，以致学习成绩较差，还需要在新学期里多和家长取得联系，共同做好这部分学生行为习惯的培养工作。y l A P x O FFA1 2 2 B tanA没有单位，它表示一个比值，即直角三角形中A的对边与邻边的比；第5页共 5 页 Sha
39、ng, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline惠州市2015届高三第一次调研考试(理科数学) rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on lif e And to lead a clean sli
40、m family, always adhere to the Communists spiritual home; to consciously practice the partys purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, adhere to the loyal clean play, Jiao Yulu-a good cadre of activities carried out in the o
41、rdinary party members practicing pioneer standard post set up activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the moth
42、er River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful complet
43、ion of tasks. Three reform as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style
44、, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. Im learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak
45、sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep
46、, identification, find the main target, laying the Foundation for further corrective action implementation.21(本小题满分14分) 等弧：在同圆或等圆中，能够互相重合的弧叫做等弧。132,已知关于的函数，其导函数为(记函数 在gxfx()(),fxxbxcxbc(),，xfx()3一年级数学下册教材共六个单元和一个总复习，分别从数与代数、空间图形、实践活动等方面对学生进行教育。区间上的最大值为( ,11,M,抛物线的顶点在(0，0)，对称轴是y轴(或称直线x0)。4x,1bc、(1) 如
47、果函数在处有极值,，试确定的值; fx()3(3) 扇形的面积公式:扇形的面积 (R表示圆的半径, n表示弧所对的圆心角的度数)(2) 若，证明对任意的，都有; M,2b,1ckMk,bc、(3) 若对任意的恒成立，试求的最大值( 7、课堂上多设计一些力所能及的问题，让他们回答，并逐步提高要求。ciousness, purpose of the party weak sense, honesty and selfamme, in view of the current construction of the party, proposed to focus on solution of fuz
48、zy ideals and beliefs waver, conse people, to better promote the water conservancy work. First of all, to find the problem. Im learning education progroriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve th-on problem insiste, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we , courage, give full play to the exemplary role, the successful completion of tasks. Three reform as the core of real changon, disc