高三第一次周练

高三第一次周练

考试范围：全部考试时间：2020.8.7 命题人：侯竹春满分：100分

一、选择题(每小题7分，

共56分）

1.设，则

A. B. C. D.

2.某地区经过一年的新农村建设，农村的经济收入增加了一倍．实现翻番．为更好地了解该地区农村的经济收入变化情况，统计了该地区新农村建设前后农村的经济收入构成比例．得到如下饼图：

则下面结论中不正确的是

A.新农村建设后，种植收入减少

B.新农村建设后，其他收入增加了一倍以上

C.新农村建设后，养殖收入增加了一倍

D.新农村建设后，养殖收入与第三产业收入的总和超过了经济收入的一半

3.设为等差数列的前项和，若，，则

A. B. C. D.

4. 函数的图像大致为 ( )

A. B. C. D.

5.设函数，若为奇函数，则曲线在点处的切线方程为

A. B. C. D.

6.某圆柱的高为2，底面周长为16，其三视图如图所示，圆柱表面上的点在正视图上的对应点为，圆柱表面上的点在左视图上的对应点为，则在此圆柱侧面上，从到的路径中，最短路径的长度为（）

A. B. C. D.2

7.设抛物线C：y2=4x的焦点为F，过点（–2，0）且斜率为的直线与C交于M，N两点，则=

A.5

B.6

C.7

D.8

8.已知函数．若g（x）存在2个零点，则a的取值

范围是

A.[–1，0）

B.[0，+∞）

C.[–1，+∞）

D.[1，+∞）

二、填空题(每小题7分，

共14分）

9.的展开式中的系数为_________.

10.从2位女生，4位男生中选3人参加科技比赛，且至少有1位女生入选，则不同的选法共有_____________种．（用数字填写答案）

三、解答题(每小题15分，

共30分）

11.在平面四边形中，，，，.

（1）求；

（2）若，求.

12.如图，四边形为正方形，分别为的中点，以为折痕把折起，使点到达点的位置，且.

（1）证明：平面平面；

（2）求与平面所成角的正弦值.

参考答案

一、选择题

1.答案：C

解析：首先根据复数的运算法则，将其化简得到，根据复数模的公式，得到，从而选出正确结果.

解：因为，

所以，故选C.

2.答案：A

解析：首先设出新农村建设前的经济收入为M，根据题意，得到新农村建设后的经济收入为

2M，之后从图中各项收入所占的比例，得到其对应的收入是多少，从而可以比较其大小，并且得到其相应的关系，从而得出正确的选项.

解：设新农村建设前的收入为M，而新农村建设后的收入为2M，

则新农村建设前种植收入为0.6M，而新农村建设后的种植收入为0.74M，所以种植收入增加了，所以A项不正确；

新农村建设前其他收入我0.04M，新农村建设后其他收入为0.1M，故增加了一倍以上，所以B 项正确；

新农村建设前，养殖收入为0.3M，新农村建设后为0.6M，所以增加了一倍，所以C项正确；新农村建设后，养殖收入与第三产业收入的综合占经济收入的，所以超过了经济收入的一半，所以D正确；

故选A.

3.答案：B

解析：首先设出等差数列的公差为，利用等差数列的求和公式，得到公差所满足的等量关系式，从而求得结果，之后应用等差数列的通项公式求得，从而求得正确结果.

解：设该等差数列的公差为，

根据题中的条件可得，

整理解得，所以，故选B.

4.答案：B

解析：通过研究函数奇偶性以及单调性，确定函数图像.

解：为奇函数，舍去A,

舍去D;

，

所以舍去C；因此选B.

5.答案：D解析：利用奇函数偶此项系数为零求得，进而得到的解析式，再对求导得出切线的斜率，进而求得切线方程.

解：因为函数是奇函数，所以，解得，

所以，，

所以，

所以曲线在点处的切线方程为，

化简可得，故选D.

6.答案：B解析：首先根据题中所给的三视图，得到点M和点N在圆柱上所处的位置，点M在上底面上，点N在下底面上，并且将圆柱的侧面展开图平铺，点M、N在其四分之一的矩形的对角线的端点处，根据平面上两点间直线段最短，利用勾股定理，求得结果.

解：根据圆柱的三视图以及其本身的特征，

可以确定点M和点N分别在以圆柱的高为长方形的宽，圆柱底面圆周长的四分之一为长的长方形的对角线的端点处，

所以所求的最短路径的长度为，故选B.

7.答案：D解析：首先根据题中的条件，利用点斜式写出直线的方程，涉及到直线与抛物线相交，联立方程组，消元化简，求得两点，再利用所给的抛物线的方程，写出其焦点坐标，之后应用向量坐标公式，求得，最后应用向量数量积坐标公式求得结果.

解：根据题意，过点（–2，0）且斜率为的直线方程为，

与抛物线方程联立，消元整理得：，

解得，又，

所以，

从而可以求得，故选D.

8.答案：C解析：首先根据g（x）存在2个零点，得到方程有两个解，将其转化为有两个解，即直线与曲线有两个交点，根据题中所给的函数解析式，画出函数的图像（将去掉），再画出直线，并将其上下移动，从图中可以发现，当时，满足与曲线有两个交点，从而求得结果.

解：画出函数的图像，在y轴右侧的去掉，

再画出直线，之后上下移动，

可以发现当直线过点A时，直线与函数图像有两个交点，

并且向下可以无限移动，都可以保证直线与函数的图像有两个交点，

即方程有两个解，

也就是函数有两个零点，

此时满足，即，故选C.

9. 解析：写出，然后可得结果

解：由题可得

令,则

所以

10.答案：16

解析：首先想到所选的人中没有女生，有多少种选法，再者需要确定从6人中任选3人总共有多少种选法，之后应用减法运算，求得结果.

解：根据题意，没有女生入选有种选法，

从6名学生中任意选3人有种选法，

故至少有1位女生入选，则不同的选法共有种，故答案是16.

11.解析：分析：(1)根据正弦定理可以得到，根据题设条件，求得，结合角的范围，利用同角三角函数关系式，求得；

(2)根据题设条件以及第一问的结论可以求得，之后在中，用余弦定理得到所满足的关系，从而求得结果.

解：（1）在中，由正弦定理得.

由题设知，，所以.

由题设知，，所以.

（2）由题设及（1）知，.

在中，由余弦定理得

.所以.

12.答案：(1).由已知可得，BF⊥PF，BF⊥EF，又，所以BF⊥平面PEF.

又平面ABFD，所以平面PEF⊥平面ABFD.(2)..

解析：分析：(1)首先从题的条件中确定相应的垂直关系，即BF⊥PF，BF⊥EF，又因为，利用线面垂直的判定定理可以得出BF⊥平面PEF，又平面ABFD，利用面面垂直的判定定理证得平面PEF⊥平面ABFD.

(2)结合题意，建立相应的空间直角坐标系，正确写出相应的点的坐标，求得平面ABFD的法向量，设DP与平面ABFD所成角为，利用线面角的定义，可以求得，得到结果.

解：（1）由已知可得，BF⊥PF，BF⊥EF，又，所以BF⊥平面PEF.

又平面ABFD，所以平面PEF⊥平面ABFD.

（2）作PH⊥EF，垂足为H.由（1）得，PH⊥平面ABFD.

以H为坐标原点，的方向为y轴正方向，为单位长，建立如图所示的空间直角坐标系H?xyz.

由（1）可得，DE⊥PE.又DP=2，DE=1，所以PE=.又PF=1，EF=2，故PE⊥PF.

可得.

则为平面ABFD的法向量.

设DP与平面ABFD所成角为，则.

所以DP与平面ABFD所成角的正弦值为.

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C.11 am. D.2:30 pm. （2）What can we learn about expert-guided tours? A.People can get in touch with experts ahead of time. B.People have no choice but to go on Tuesday. C.People can be warmly received by the staff. D.People can have a taste of fungi. （3）How much is the guide cost for 5 people? A.￡ 60. B.￡ 120. C.￡ 150. D.￡ 300. 【答案】（1）C （2）B （3）A 【解析】 参加有导游的徒步旅行，更近距离地欣赏英国皇家植物园的奇景。在我们知识渊博的志愿者导游的带领下，这是一种有趣且有益的探索方式。 （1）考查细节理解。根据Free daily walking tours部分中的“Tours leave at 11 am and 1:30 pm from the information desk at Victoria Gate Plaza”可知，这种徒步旅行在上午11点和下午1点半开始，故选C。 （2）考查细节理解。根据Expert-guided tours部分中的“Every Tuesday throughout the year at 11:30 am and 2:30 pm we'll be holding an expert-guided tour”可知，如果你对expert-guided tours感兴趣，你别无选择，只能在星期二参观。故选B。（3）考查推理判断。根据Price部分中的“The cost is ￡ 60 per guide (this does not include your entry to the Gardens). Each guide can take up to 15 people”和“Smaller groups are also accepted but the cost remains ￡ 60”可知，一个导游最多可以带15个人，5个人的导游费用仍然是60英镑，故选A。 【总结】本题考点涉及细节理解和推理判断两个题型的考查，是一篇介绍类阅读，考生需要准确捕捉细节信息，并根据上下文进行逻辑推理，从而选出正确答案。 2.阅读理解

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博爱一中2017级高三周练试卷（五） 英语出题人：仝丽审题人：武玉玲第二部分阅读理解(共两节，满分40分) 第一节(共15小题；每小题2分，满分30分) 阅读下列短文，从每题所给的A、B、C和D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。 A Beautiful Valleys in the World Lauterbrunnen Valley Country: Switzerland This valley in the shadow of the Swiss Alps gets it name “Lauter Brunnen” （“many fountains” in English）from the 72 wonderful waterfalls found here. The green alpine meadows and towering mountains here attract many tourists. Lauterbrunnen is a favorite with adventure sports enthusiasts and skydiving in this valley is a popular activity. Kangaroo Valley Country: Australia The brilliantly sparkling brooks, the jade green rainforests and the abundance of plants and animals are only some of the reasons everyone wants to escape to this valley on the banks of the Kangaroo River in New South Wales. It’s not far from Sydney an d Canberra, which makes it an ideal holiday destination. Surrounded by such natural gift, it is easy to understand why the Australian Aboriginal Wodi Wodi tribe chose the Kangaroo Valley to be their home. Kashmir Valley Country: India Despite being the center of an ongoing border dispute （争端）between India and Pakistan, the beauty and splendor of this Himalayan valley attract thousands of visitors each year. The immense meadows and the numerous flowers, the great lakes and the meandering rivers in summer and snowy skiing tracks in winter are some of Kashmir’s greatest attractions. Yosemite Valley Country: USA Guarded by towering cliffs and carpeted by a thick pine forest, the Yosemite valley is part of the Yosemite National Park, The valley offers hikers some breathtaking views. The Merced River and a number of streams cross the valley and the waterfalls are simply spectacular. Do not miss out the Yosemite Falls — the highest waterfall in the continent. The hiking trails of the valley offer great opportunities to the adventure enthusiasts. 21. Where can you go if you are fond of adventure? A. Lauterbrunnen Valley and Yosemite Valley. B. Lauterbrunnen Valley and Kangaroo Valley. C, Kashmir Valley and Yosemite Valley. D. Kangaroo Valley and Kashmir Valley. 22. Why is Kangaroo Valley an ideal holiday destination? A. It has sparkling brooks. B. Its rainforests are unique.