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高二朱锃桓 专练学生版

高二朱锃桓 专练学生版
高二朱锃桓 专练学生版

高二数学专练

1.对于直角坐标平面内的任意两点()()1122,,,A x y B x y ,定义它们之间的一种“距离”:

给出下列三个命题:

①若点C 在线段AB 上,

②在ABC 中,若90C ∠=,

③在ABC 中, 其中真命题的个数为

A . 0

B . 1

C . 2

D . 3

2120x x +>是()()()()1212f x f x f x f x +>-+-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

3.设命题 :实数 满足 ,其中 ;命题 :实数 满足 .

(1)若 ,且 为真,求实数 的取值范围;

(2)若 是 的充分不必要条件,求实数 的取值范围.

4.如图所示,某镇有一块空地OAB ?,其中3OA km =, 90AOB ∠=。当地镇政府规划将这块空地改造成一个旅游景点,拟在中间挖一个人工湖OMN ?,其中

,M N 都在边AB 上,且30MON ∠=,挖出的泥土堆放在OAM ?地带上形成假山,剩下的OBN ?地带开设儿童游乐场. 为安全起见,需在OAN ?的周围安装防护网.

(1 (2)若要求挖人工湖用地OMN ?的面积是堆假山用地OAM ?的面积的AOM ∠ 的大小;

(3)为节省投入资金,人工湖OMN ?的面积要尽可能小,问如何设计施工方案,可使OMN ? 的面积最小?最小面积是多少?

5如图所示的自动通风设施.该设施的下部ABCD 是等腰梯形,其中AB 为2米,梯形的高为1米, CD 为3米,上部CmD 是个半圆,固定点E 为CD 的中点. MN 是由电脑控制可以上下滑动的伸缩横杆(横杆面积可忽略不计),且滑动过程中始终保持和CD 平行.当MN 位于CD 下方和上方时,通风窗的形状均为矩形MNGH (阴影部分均不通风). (1)设MN 与AB 之间的距离为x (且1x ≠)米,试将通风窗的通风面积S (平方米)表示成关于x 的函数()y S x =;

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