《最新高考理科数学湖南卷试题与答案word解析版优秀名师资料.doc》由会员分享，可在线阅读，更多相关《最新高考理科数学湖南卷试题与答案word解析版优秀名师资料.doc（31页珍藏版）》请在三一文库上搜索。
1、2013年高考理科数学湖南卷试题与答案word解析版2013年普通高等学校夏季招生全国统一考试数学理工农医类 (湖南卷) 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，只有一项是符合题目要求的( 1(2013湖南，理1)复数z,i?(1，i)(i为虚数单位)在复平面上对应的点位于( )( A(第一象限 B(第二象限 C(第三象限 D(第四象限 2(2013湖南，理2)某学校有男、女学生各500名，为了解男、女学生在学习兴趣与业余爱好方面是否存在显著差异，拟从全体学生中抽取100名学生进行调查，则宜采用的抽样方法是( )( A(抽签法 B(随机数法 C(系统抽样法
2、D(分层抽样法 3(2013湖南，理3)在锐角?ABC中，角A，B所对的边长分别为a，b.若2asin B,b，则角A等于( )( 312643A( B( C( D( yx,2,xy，,1,4(2013湖南，理4)若变量x，y满足约束条件则x，2y的最大值是( )( ,y,1.,555,232A( B(0 C( D( 25(2013湖南，理5)函数f(x),2ln x的图象与函数g(x),x,4x，5的图象的交点个数为( )( A(3 B(2 C(1 D(0 6(2013湖南，理6)已知a，b是单位向量，a?b,0，若向量c满足|c,a,b|,1，则|c|的取值范围是( )( 21,21，21
3、,22，21，22，A(， B(， C(1， D(1， 7(2013湖南，理7)已知棱长为1的正方体的俯视图是一个面积为1的正方形，则该正方体的正视图的面积不可能等于( )( 21,21，222A(1 B( C( D( 8(2013湖南，理8)在等腰直角三角形ABC中，AB,AC,4，点P为边AB上异于A，B的一点，光线从点P出发，经BC，CA反射后又回到点P.若光线QR经过?ABC的重心，则AP等于( )( A(2 B(1 83C( 43D( 二、填空题:本大题共8小题，考生作答7小题，每小题5分，共35分( (一)选做题(请考生在第9,10,11三题中任选两题作答，如果全做，则按前两题记分
4、) xt,9(2013湖南，理9)在平面直角坐标系xOy中，若直线l:(t为参数)过椭圆C:,yta,x,3cos,(为参数)的右顶点，则常数a的值为_( ,y,2sin,10(2013湖南，理10)已知a，b，c?R，a，2b，3c,6，则a2，4b2，9c2的最小值为_( 11(2013湖南，理11)如图，在半径为7的O中，弦AB，CD相交于点P，PA,PB,2，PD,1，则圆心O到弦CD的距离为_( and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management,
5、 marketing management branch within the Departments credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspec
6、tion, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection
7、(a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is compl
8、ete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligen
9、ce evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatibl
10、e with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head (二)必做题(12,16题) T0,12(2013湖南，理12)若x2dx,9，则常数T的值为_( 13(2013湖南，理13)执行如图所示的程序框图，如果输入a,1，b,2，则输出的a的值为_( 22xy,122ab14(2013湖南，理14)设F1，F2是双曲线C:(a,0，b|的最小,0
11、)的两个焦点，P是C上一点(若|PF1|，|PF,6a，且?PFF212内角为30?，则C的离心率为_( 15(2013湖南，理15)设Sn为数列an的前n项和，Sn,(,1)nan1n2,，n?N*，则 (1)a,_; 3(2)S，S，S,_. 1210016(2013湖南，理16)设函数f(x),ax，bx,cx，其中c,a,0，c,b,0. (1)记集合M,(a，b，c)|a，b，c不能构成一个三角形的三条边长，且a,b，则(a，b，c)?M所对应的f(x)的零点的取值集合为_; (2)若a，b，c是?ABC的三条边长，则下列结论正确的是_(写出所有正确结论的序号) ?,x?(,?，1)
12、，f(x),0; xxx?x?R，使a，b，c不能构成一个三角形的三条边长; ，?若?ABC为钝角三角形，则x?(1,2)，使f(x),0. ，三、解答题:本大题共6小题，共75分(解答应写出文字说明、证明过程或演算步骤( x,2sin17(2013湖南，理17)(本小题满分12分)已知函数，(),2. gxfxxx()sincos,，,263,33(1)若是第一象限角，且f(),，求g()的值; 5(2)求使f(x)?g(x)成立的x的取值集合( implementation of double system; (E) other supervision and inspection of
13、the contents. 25th due diligence evaluation offices real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical tive,accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis i
14、s objecand the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are ditd inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of creloan investigation work, and based on th
15、e evaluation results, the implementation of diversity management. 24th the control an-reloan investigation work by way of conducting supervision and inspection, quality evaluation p-site inspection, investigation report, interviews with investigators for pre-site and off-risdiction), risk management
16、, Marketing Management Department through ones (juon assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branchhead office, branch (jurisdiction), risk management, marketing management branch within the Departments credit business persa
17、nd due diligence evaluations article 22nd impartiality and fairness. Article 26th headould be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, mption should be. Investigators shloan investigation supervision and inspection work, eva
18、luate whether investigators due diligence to determine whether the exe-ranches (jurisdiction), risk management, Marketing Management Department agreed to carry out preand b2 18(2013湖南，理18)(本小题满分12分)某人在如图所示的直角边长为4米的三角形地块的每个格点(指纵、横直线的交叉点以及三角形的顶点)处都种了一株相同品种的作物(根据历年的种植经验，一株该种作物的年收获量Y(单位:kg)与它的“相近”作物株数X之
19、间的关系如下表所示: X 1 2 3 4 Y 51 48 45 42 这里，两株作物“相近”是指它们之间的直线距离不超过1米( (1)从三角形地块的内部和边界上分别随机选取一株作物，求它们恰好“相近”的概率; (2)从所种作物中随机选取一株，求它的年收获量的分布列与数学期望( and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch wit2013 湖南理科数学 第3页 hin the Department
20、s credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with invest
21、igators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there
22、 is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators a
23、nalysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction),
24、 risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based o
25、n the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head19(2013湖南，理19)(本小题满分12分)如图，在直棱柱,?，?,90?，ABCDABCD中，ADBCBADAC1111?BD，BC,1，AD,AA,3. 1(1)证明:AC?BD; 1(2)求直线BC与平面ACD所成角的正弦值( 111implementation of double system; (E) other supervision and inspection of the
26、 contents. 25th due diligence evaluation offices real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical tive,accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is o
27、bjecand the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are ditd inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of creloan investigation work, and based on the e
28、valuation results, the implementation of diversity management. 24th the control an-reloan investigation work by way of conducting supervision and inspection, quality evaluation p-site inspection, investigation report, interviews with investigators for pre-site and off-risdiction), risk management, M
29、arketing Management Department through ones (juon assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branchhead office, branch (jurisdiction), risk management, marketing management branch within the Departments credit business persand
30、due diligence evaluations article 22nd impartiality and fairness. Article 26th headould be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, mption should be. Investigators shloan investigation supervision and inspection work, evalua
31、te whether investigators due diligence to determine whether the exe-ranches (jurisdiction), risk management, Marketing Management Department agreed to carry out preand b4 中，将从点出发沿纵、横方向到达点20(2013湖南，理20)(本小题满分13分)在平面直角坐标系xOyMN的任一路径称为M到N的一条“L路径”(如图所示的路径MMMMN与路径MNN都是M到N的“L路径”(某1231地有三个新建的居民区，分别位于平面xOy内三
32、点A(3,20)，B(,10,0)，C(14,0)处(现计划在x轴上方区域(包含x轴)内的某一点P处修建一个文化中心( (1)写出点P到居民区A的“L路径”长度最小值的表达式(不要求证明): (2)若以原点O为圆心，半径为1的圆的内部是保护区，“L路径”不能进入保护区，请确定点P的位置，使其到三个居民区的“L路径”长度之和最小( 221(2013湖南，理21)(本小题满分13分)过抛物线E:x,2py(p,0)的焦点F作斜率分别为k，k的两12条不同直线l，l，且k，k,2，l与E相交于点A，B，l与E相交于点C，D，以AB，CD为直径的圆M，121212圆N(M，N为圆心)的公共弦所在直线记
33、为l. ,2FN(1)若k,0，k,0，证明:?,2p; FM1275(2)若点M到直线l的距离的最小值为，求抛物线E的方程( 5and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch wit2013 湖南理科数学 第5页 hin the Departments credit business person assumed responsibility for the supervision and in
34、spection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision a
35、nd inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the
36、head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and r
37、easonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-
38、loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and
39、 fairness. Article 26th headxa,22(2013湖南，理22)(本小题满分13分)已知a,0，函数f(x),. xa，2(1)记f(x)在区间0,4上的最大值为g(a)，求g(a)的表达式; (2)是否存在a，使函数y,f(x)在区间(0,4)内的图象上存在两点，在该两点处的切线互相垂直,若存在，求a的取值范围;若不存在，请说明理由( implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation
40、offices real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical tive,accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objecand the head office; (B) dual credit
41、rating: timeliness of ratings, whether the provisions of the rating, rating results are ditd inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of creloan investigation work, and based on the evaluation results, the implementation of
42、diversity management. 24th the control an-reloan investigation work by way of conducting supervision and inspection, quality evaluation p-site inspection, investigation report, interviews with investigators for pre-site and off-risdiction), risk management, Marketing Management Department through on
43、es (juon assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branchhead office, branch (jurisdiction), risk management, marketing management branch within the Departments credit business persand due diligence evaluations article 22nd im
44、partiality and fairness. Article 26th headould be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, mption should be. Investigators shloan investigation supervision and inspection work, evaluate whether investigators due diligence to
45、 determine whether the exe-ranches (jurisdiction), risk management, Marketing Management Department agreed to carry out preand b6 2013年普通高等学校夏季招生全国统一考试数学理工农医类 (湖南卷) 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，只有一项是符合题目要求的( 1(答案:B 2解析:z,i，i,1，i，对应点为(,1,1)，故在第二象限，选B( 2(答案:D 解析:看男、女学生在学习兴趣与业余爱好是否存在明显差异，应当分层抽
46、取，故宜采用分层抽样( 3(答案:D 23解析:由2asin B,b得2sin Asin B,sin B，故sin A,，故A,或.又?ABC为锐角33332三角形，故A,. 34(答案:C 解析:约束条件表示的可行域为如图阴影部分( 1dyx,，令x，2y,d，即， 2214512,，,由线性规划知识可得最优点为，所以d,. ,max,33333,5(答案:B 解析:设f(x)与g(x)图象的交点坐标为(x，y)， 222则y,2ln x，y,x,4x，5，联立得2ln x,x,4x，5，令h(x),x,4x，5,2ln x(x,0)， 212，12,由h(x),2x,4,0得x,，x,(舍
47、)( 12x12，当h(x),0时，即x?(0,)时，h(x)单调递减; 12，当h(x),0，即x?(，?)时，h(x)单调递增( 又?h(1),2,0，h(2),1,2ln 2,0，h(4),5,2ln 4,0， ?h(x)与x轴必有两个交点，故答案为B( 6(答案:A 22解析:由题意，不妨令a,(0,1)，b,(1,0)，c,(x，y)，由|c,a,b|,1得(x,1)，(y,1),1，|c|22xy，,可看做(x，y)到原点的距离，而点(x，y)在以(1,1)为圆心，以1为半径的圆上(如图所示，21,21，当点(x，y)在位置P时到原点的距离最近，在位置P时最远，而PO,，PO,，故
48、选A( and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch wit2013 湖南理科数学 第7页 hin the Departments credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan