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江苏省泰兴市第一高级中学2015届高三下学期学情监测数学试题 Word版含答案

江苏省泰兴市第一高级中学2015届高三下学期学情监测数学试题 Word版含答案
江苏省泰兴市第一高级中学2015届高三下学期学情监测数学试题 Word版含答案

2014-2015学年高三学情监测

数 学 试 卷

一、填空题:(本大题共14小题,每小题5分,共70分.请将答案填入答题纸填空题的相

应答题线上.)

1. 已知集合{}lg M x y x ==,{N x y ==,则M∩N = ▲ .

2. 已知复数()2i+1(1i)z =-为虚数单位),则z = ▲ .

3. 某校从高一年级学生中随机抽取部分学生,将他们的模块测试成绩分成6组:加以统

计,得到如图所示的频率分布直方图已知高一年级共有学生600名,据此估计,该模块测试成绩不少于60分的学生人数为 ▲ .

4. 阅读下面的流程图,若输入a =10,b =6,则输出的结果

是 ▲ .

5. 盒中装有形状、大小完全相同的5个球,其中红色球3个,黄色球2个.若从中随机取

出2个球,则所取出的2个球颜色不同的概率等于 ▲ .

6. 函数a x f x +-=1

31)( ()0≠x ,则“1)1(=f ”是“函数)(x f 为奇函数”的 ▲ 条件(用“充分不必要”,“必要不充分”“充要”“既非充分又非必要”)

7. 在平面直角坐标系xOy 中,双曲线22

221(0,0)x y a b a b

-=>>的两条渐近线与抛物线y 2

=4x 的准线相交于A ,B 两点.若△AOB 的面积为2,则双曲线的离心率为 ▲ .

8. 过点(2,0)引直线l 与曲线21x y -=相交于A ,B 两点,O 为坐标原点,当△AOB

的面积取最大值时,直线l 的斜率等于 ▲ .

9. 已知ABC ?中,cos tan tan 2A B C =

?=,且B C <,则B = ▲ . 10.在ABC ?中,90,1A AB AC ∠===,点P 在边BC 上,则2PB PC +的最大值为 ▲ .

11. 若关于

x 的方程323

2ln 21x m x x =++在区间)2,1(上有解,则实数m 的取值范围是 ▲ .

12.在正三棱锥S ABC -中,1,30SA ASB =∠=?,过A 作三棱锥的截面AMN ,则截面三

角形AMN 的周长的最小值为 ▲ .

13.已知实数a x f x x x ax x x f a 232167)(1

,log 1;2)(,0=???>≤+-=>,若方程,有且仅有两个不等实根,且较大的实根大于3,则实数a 的取值范围 ▲ .

14.若等差数列{}n a 满足2212015110

a a +≤,则2015201620174029S a a a a =++++L 的最大值为 ▲ .

二、解答题:(本大题共6小题,共90分.解答应写出文字说明,证明过程或演算步骤.)

15.(本题满分14分)

已知向量()sin 2,1m x =-,向量()3cos 2,0.5n x =

-,函数m n m x f ?+=)()(. ⑴求)(x f 的最小正周期T ;

⑵已知c b a ,,分别为ABC ?内角C B A ,,的对边,A 为锐角,13,2a c ==,且()f A 恰是()f x 在0,4π??????

上的最大值,求A 和b .

16.(本题满分14分)

如图,在四棱锥P ﹣ABCD 中,侧棱P A 丄底面ABCD 底面ABCD 为矩形,E 为PD 上一点,AD =2AB =2AP =2,PE =2DE .

⑴若F 为PE 的中点,求证BF ∥平面ACE ;

⑵求三棱锥P ﹣ACE 的体积.

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