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2015房山一模 北京市房山区2015届高三第一次模拟考试数学(理)试题

2015房山一模 北京市房山区2015届高三第一次模拟考试数学(理)试题
2015房山一模 北京市房山区2015届高三第一次模拟考试数学(理)试题

房山区2015年高三第一次模拟试题

高三数学(理科) 考 生 须知

1. 本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,共 150分,考试时间为120分钟 。

2. 第Ⅰ卷选择题和第Ⅱ卷非选择题直接写在答题卡上的指定位置,在试卷上作答无效。

3. 考试结束后,将答题卡交回,试卷按学校要求自己保存好。 第I 卷 选择题(共40分)

一、选择题:本大题共8小题,每小题5分,共40分。在每小题列出的四个选项中,选出符合题目要求的一项,直接涂在答题卡上。

1. 已知集合2{|}0M x x x ∈-=R =,{|}21,N x x n n ==∈Z +

,则M N 为( ) A .{}0 B .{}0,1 C .{}1 D .φ

2.双曲线221x my -=的实轴长是虚轴长的2倍,则m =( )

A .4

B .2

C .12

D .14

3. 设变量x 、y 满足约束条件??

???-≥≥+≤632x y y x x y ,则目标函数y x z +=2的最小值为( )

A .2

B .3

C .4

D .9

4.从5名学生中选出4名分别参加数学、物理、化学、英语竞赛,其中学生甲不参加物理、化学竞赛,则不同的参赛方案种数为( )

A .24

B .48

C .72

D . 120

5. 已知二次函数2()f x ax bx =+,则“0

)2(≥f ”是“函数)(x f 在),(∞+1上为增函数”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

6.一个棱长为2的正方体沿其棱的中点截

去部分后所得几何体的三视图如图所示,则该

几何体的体积为( )

A .7

B .223

C .

476 D .233

7.向量(2,0)a =,(,)b x y =,若b 与b a -的夹角等于6

π,则b 的最大值为( ) A .4 B .23 C .2 D .433

8.一个人骑车以6米/秒的速度匀速追赶停在交通信号灯前的汽车,当他离汽车25米时,交通信号灯由红变绿,汽车开始做变速直线行驶(汽车与人的前进方向相同),若汽车在时刻t 的速度()v t t =米/秒,那么此人( )

A .可在7秒内追上汽车

B .不能追上汽车,但其间最近距离为16米

C .不能追上汽车,但其间最近距离为14米

D .不能追上汽车,但其间最近距离为7米

第II 卷 非选择题(共110分)

二、填空题:本大题共6小题,每小题5分,共30分。把答案填在答题卡指定位置。

9.已知复数z 满足(1)1i z i +=-,则复数z =____.

10.执行如下图所示的程序框图,若输入n 的值为8,则输出s 的值为____.

11.如图所示,四个相同的直角三角形与中间的小正方形拼成

一个边长为2的 大正方形,若直角三角形中较小的锐角6πθ=

,现在向该正方形区域内随机地

2015年北京市高考数学试卷(理科)及答案

2015年北京市高考数学试卷(理科) 一、选择题(每小题5分,共40分) 1.(5分)复数i(2﹣i)=() A.1+2i B.1﹣2i C.﹣1+2i D.﹣1﹣2i 2.(5分)若x,y满足,则z=x+2y的最大值为() A.0 B.1 C.D.2 3.(5分)执行如图所示的程序框图输出的结果为() A.(﹣2,2)B.(﹣4,0)C.(﹣4,﹣4)D.(0,﹣8) 4.(5分)设α,β是两个不同的平面,m是直线且m?α,“m∥β“是“α∥β”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 5.(5分)某三棱锥的三视图如图所示,则该三棱锥的表面积是()

A.2+B.4+C.2+2D.5 6.(5分)设{a n}是等差数列,下列结论中正确的是() A.若a1+a2>0,则a2+a3>0 B.若a1+a3<0,则a1+a2<0 C.若0<a 1<a2,则a2D.若a1<0,则(a2﹣a1)(a2﹣a3)>0 7.(5分)如图,函数f(x)的图象为折线ACB,则不等式f(x)≥log2(x+1)的解集是() A.{x|﹣1<x≤0}B.{x|﹣1≤x≤1}C.{x|﹣1<x≤1}D.{x|﹣1<x≤2} 8.(5分)汽车的“燃油效率”是指汽车每消耗1升汽油行驶的里程,如图描述了甲、乙、丙三辆汽车在不同速度下燃油效率情况,下列叙述中正确的是() A.消耗1升汽油,乙车最多可行驶5千米

B.以相同速度行驶相同路程,三辆车中,甲车消耗汽油最多 C.甲车以80千米/小时的速度行驶1小时,消耗10升汽油 D.某城市机动车最高限速80千米/小时,相同条件下,在该市用丙车比用乙车更省油 二、填空题(每小题5分,共30分) 9.(5分)在(2+x)5的展开式中,x3的系数为(用数字作答) 10.(5分)已知双曲线﹣y2=1(a>0)的一条渐近线为x+y=0,则a=.11.(5分)在极坐标系中,点(2,)到直线ρ(cosθ+sinθ)=6的距离为.12.(5分)在△ABC中,a=4,b=5,c=6,则=. 13.(5分)在△ABC中,点M,N满足=2,=,若=x+y,则x=,y=. 14.(5分)设函数f(x)=, ①若a=1,则f(x)的最小值为; ②若f(x)恰有2个零点,则实数a的取值范围是. 三、解答题(共6小题,共80分) 15.(13分)已知函数f(x)=sin cos﹣sin. (Ⅰ)求f(x)的最小正周期; (Ⅱ)求f(x)在区间[﹣π,0]上的最小值. 16.(13分)A,B两组各有7位病人,他们服用某种药物后的康复时间(单位:天)记录如下: A组:10,11,12,13,14,15,16 B组;12,13,15,16,17,14,a 假设所有病人的康复时间相互独立,从A,B两组随机各选1人,A组选出的人记为甲,B组选出的人记为乙.

2015高考数学全国卷1(完美版)

2015高考数学全国卷1(完美版)

2015年普通高等学校招生全国统一考试 理科数学 注意事项: 1.本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分.第Ⅰ卷1至3页,第Ⅱ卷3至5页. 2.答题前,考生务必将自己的姓名、准考证号填写在本试题相应的位置. 3.全部答案在答题卡上完成,答在本试题上无效. 4. 考试结束后,将本试题和答题卡一并交回. 第Ⅰ卷 一、选择题:本大题共12小题,每小题5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.设复数z满足1+z 1-z =i,则|z|= A.1 B.2 C. 3 D.2 2.sin20°cos10°-cos160°sin10°= A.- 3 2B. 3 2C.- 1 2 D.1 2 3.设命题P:?n∈N,n2>2n,则¬P为 A.?n∈N,n2>2n B.?n∈N,n2≤2n C.?n∈N,n2≤2n D.?n∈N,n2=2n

4.投篮测试中,每人投3次,至少投中2次才能通过测 试.已知某同学每次投篮投中的概率为0.6,且各次投篮是否投中相互独立,则该同学通过测试的概率为 A .0.648 B .0.432 C .0.36 D .0.312 5.已知M (x 0,y 0)是双曲线C :x 22 -y 2 =1 上的一点, F 1、F 2是C 上的两个焦点,若 M F 1→· M F 2 →<0 ,则y 0的取值范围是 A .? ???? -33 ,33 B . ? ???? -36 ,36 C .? ????-223,223 D .? ?? ?? -233,233 6.《九章算术》是我国古代内容极为丰富的数学名著, 书中有如下问题:“今有委米依垣内角,下周八尺,高五尺.问:积及为米几何?”其意思为:“在屋内墙角处堆放米(如图,米堆为一个圆锥的四分之一),米堆底部的弧度为8尺,米堆的高为5尺,问米堆的体积和堆放的米各为多少?”已知1斛米的体积约为1.62立方尺,圆周率约为3,估算出堆放斛的米约有

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绝密★启封并使用完毕前 2015年普通高等学校招生全国统一考试 数学(文)(北京卷) 本试卷共5页,150分。考试时长120分钟。考生务必将答案答在答题卡上,在试卷上作答无效。考 试结束后,将本试卷和答题卡一并交回。 第一部分(选择题 共40分) 一、选择题:共8个小题,每小题5分,共40分。在每小题的四个选项中,选出符合题目要求的一项。 (1)若集合{} 52,A x x =-<<{} 33,B x x =-<<则A B =( ) ( A ) {} 32x x -<< ( B ) {}52x x -<< ( C ) {}33x x -<< ( D ) {} 53x x -<< (2)圆心为(1,1)且过原点的圆的方程是( ) (A )()()2 2 111x y -+-= (B )()()2 2 111x y ++-= (C )()()2 2 112x y +++= (D )()()2 2 112x y -+-= (3)下列函数中为偶函数的是( ) (A )2sin y x x = (B )2cos y x x = (C )ln y x = (D )2x y -= (4)某校老年、中年和青年教师的人数见下表,采用分层抽样的方法调查教师的身体状况,在抽取的样本中,青年教师有320人,则该样本的老年人数为( ) (A )90 (B )100 (C )180 (D )300 (5) 执行如图所示的程序框图,输出的k 值为( ) (A )3 (B ) 4 (C) 5 (D) 6 (6)设,a b 是非零向量,“a b a b ?=”是“a //b ”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

2015年北京高考数学(理科)试题及答案

2015年普通高等学校招生全国统一考试 数学(理)(北京卷) 本试卷共5页,150分.考试时长120分钟.考生务必将答案答在答题卡上,在试卷上作答无效.考试结束后,将本试卷和答题卡一并交回. 第一部分(选择题共40分) 一、选择题共8小题,每小题5分,共40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.复数()i 2i -= A .12i + B .12i - C .12i -+ D .12i -- 2.若x ,y 满足010x y x y x -?? +??? ≤,≤,≥,则2z x y =+的最大值为 A .0 B .1 C . 32 D .2 3.执行如图所示的程序框图,输出的结果为 A .()22-, B .()40-, C .()44--, D .()08-,

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2015年高考理科数学试题及答案(新课标全国卷1)

绝密★启封并使用完毕前 试题类型:A 2015年普通高等学校招生全国统一考试 理科数学 注意事项: 1.本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。第Ⅰ卷1至3页,第Ⅱ卷3至5页。 2.答题前,考生务必将自己的姓名、准考证号填写在本试题相应的位置。 3.全部答案在答题卡上完成,答在本试题上无效。 4.考试结束后,将本试题和答题卡一并交回。 第Ⅰ卷 一. 选择题:本大题共12小题,每小题5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) 设复数z 满足1+z 1z -=i ,则|z|= (A )1 (B (C (D )2 (2)sin20°cos10°-con160°sin10°= (A )2-(B )2 (C )12- (D )12 (3)设命题P :?n ∈N ,2n >2n ,则?P 为 (A )?n ∈N, 2n >2n (B )? n ∈N, 2n ≤2n (C )?n ∈N, 2n ≤2n (D )? n ∈N, 2n =2n (4)投篮测试中,每人投3次,至少投中2次才能通过测试。已知某同学每次投篮投中的概率为0.6,且各次投篮是否投中相互独立,则该同学通过测试的概率为 (A )0.648 (B )0.432 (C )0.36 (D )0.312

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