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2017 届广东省松昌中学高三下学期开学模拟测试文科数学 试题及答案 松昌中学 13-14 年度高三年级开学统测 数 学(文 科) 2014(2 参考公式: 1Sh 锥体体积公式,其中为锥体的底面积,为锥体的高( VSh,3 一(选择题:本大题共 10 小题,每小题 5 分,满分 50 分( AB:,1(已知函数的定义域,,则 ABxx,,,01yx,ln,, A( B( C( D( 0,,,0,10,10,1,,,,,,,, 2iab,,i2(已知,为虚数单位,若 abi,,,1,则实数 abR,, 1,i 3524A( B( C( D( 3.中央电视台为了调查近三年的春晚节目中各类节目的受欢 迎程度,用分层抽样的方法,从 2011 年至 2013 年春晚的 50 个歌舞类节目,40 个 戏曲类节目,30 个小品类节目中抽取样本进行调查,若样本中的歌舞类和戏曲类 节目共有 27 个,则样本容量为 A.36 B.35 C.32 D.30 ,,,,,,,,,,,, BC,4.若向量,则 BACA,,(1,2),(4,5) 3,3,,5,7A. B. C. D. (5,7)(3,3),,,,,, TAyx,,2sin215(设函数的最小正周期为,最小值为,则 T,2,T,,A,1A,1A(, B. , T,2,T,,A,,3A,,3C(, D(, 1f(x),x,,1(x,0)6(已知函数 f(x),则的 x 第 1 页(共 4 页) A.最小值为 3 B.最大值为 3 C.最小值为 D.,1 最大值为 ,1 N7(执行如图 1 的程序框图,如果输入的的值是 6,那么输出的的值 p 是 A(15 B(105 C(120 D(720 否 输出 p 开始 kN,?结束 N 输入 ppk,,k,1,p,1 是 kk,,2 图 1 8(某几何体的三视图(如图 2 所示)均为边长为 2 的等腰 正视图 侧视图 直角三角形,则该几何体的表面积是 442,42A( B( 42,842,C( D( 图 2 俯视图 32fxxxx()22,,,,9(若函数的一个正数零点附近的函数值用二分法计算, 其参考数据如下: 第 2 页(共 4 页) f (1.25) = , f (1) = ,2 f (1.5) = 0.625 0.984 (1.375) = ,f (1.4375) = f (1.40625) = ,f 0.260 0.162 0.054 32 那么方程 xxx,,,,220 的一个最接近的近似根为 1.21.31.4A( B( C( 1.5D( 223n,2nn10(将 12 个正整数、、、?、()任意排成行列的数表.nn bab,对于某一个数表,计算各行和各列中的任意两个数、()的比 a an,2 值,称这些比值中的最小值为这个数表的“特征值”.当时,数 b 表的所有可能的“特征值”最大值为 3432A( B( C( D( 23 二(填空题: 本大题共 5 小题,考生作答 4 小题,每小题 5 分,满分 20 分( (一)必做题(11,13 题) 2x,0,,f,1,11(设 f(x)为奇函数,当时,,则 *** . f(x),x,x {}aa,a,3aa,12(在等比数列中,若,则 *** ( 231n4 2213(经过点 P(1 , ,1)且与圆相切的直线的方程是 x,(y,2),2 第 3 页(共 4 页) *** ( (二)选做题(14,15 题,考生只能从中选做一题) B14((几何证明选讲选做题) MCAO NACOOBAC,BNAC 如图 3,为?的直径,,弦交于点( M 图 3 OM,1MN 若 OC,3,,则的长为 *** ( 15((坐标系与参数方程选讲选做题) 在极坐标系中,设曲线与的交点分别为 A、C:cos1,,,C:4cos,,,12 B, 则 AB, *** . 三(解答题: 本大题共 6 小题,满分 80 分(解答应写出文字说明、证明过程或 演算步骤( 16((本小题满分 12 分) AC,3ABCCbAB 在?中,角,,所对的边分别为,,,且( accos,23 cosB(1)求的值; a,3b,22(2)若,,求的值( c 17((本小题满分 12 分) 某校高三(1)班全体女生的一次数学测试成绩的茎叶图和频率分布直方图都受 到不同程度的破坏,但可见部分如下,据此解答如下问题: (1)求高三(1)班全体女 生的人数及分数在[80,90)之间的女生人数; 第 4 页(共 4 页) (2)若要从分数在之间的试卷中任取两份分析女学生的失分情[80,100] 况,在抽取的试卷中,求至少有一份分数在之间的概率。 [90,100] 18((本小题满分 14 分) P PAABCD,平面 ABCD 如图所示,是正方形,, F EF、ACPC、是的中点 A D ACDF,(1)求证:; E B C CPED,(2)若,求三棱锥的体积( PAAB,,2,1 19((本小题共 14 分) aaa*3n2,,,,,?2n,Nan,,a 设数列满足,( 1n,21n222 ,,a (1)求数列的通项公式; n an,bbS(2)设,求数列的前 n 项和( ,,nnn11,,aa,,,,,1nn 20((本小题满分 14 分) 第 5 页(共 4 页) 22 在圆上任取一点,设点在轴上的正投影为点(当点 PPDPxx,y,4 C 在圆上运动时,动点满足,动点形成的轨迹为曲线( MMPD,2MD C(1)求曲线的方程; C(2)已知点,若是曲线上的两个动点,且满足,EA,EB,,E1,0A,B 求的取值范围( EA,BA 21((本小题满分 14 分) 2 已知函数 fxxaxax,,,,ln2( ,,,, x,1(1)若在处取得极值,求实数的值; afx() 2(2)求函数在区间上的最大值( fx()[,]aa 第 6 页(共 4 页) 松昌中学 13-14 年度高三年级开学统测数学(文科)

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