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2018江苏高考数学试题及答案解析【Word真题试卷】

2018-06-10 10:47:13文/李木子

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绝密★启用前

2018年普通高等学校招生全国统一考试(江苏卷)

数学I

注意事项

考生在答题前请认真阅读本注意事项及各题答题要求

1.本试卷共4页,包含非选择题(第1题~第20题,共20题).本卷满分为160分,考试时间为120分钟。考试结束后,请将本试卷和答题卡一并交回。

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?????????????4.作答试题,必须用0.5毫米黑色墨水的签字笔在答题卡上的指定位置作答,在其他位置作答一律无效。

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一、填空题:本大题共14小题,每题5小分,共计70分。请把答案填写在答题卡相应位置上。

1.已知集合www.ziyuanku.com,那么www.ziyuanku.com__________.

2.若复数www.ziyuanku.com满足www.ziyuanku.com,其中www.ziyuanku.com是虚数单位,则zwww.ziyuanku.com的实部为__________.

3.已知5位裁判给某运动员打出的分数的茎叶图如图所示,那么这5位裁判打出的分数的平均数为__________.

www.ziyuanku.com

4.一个算法的伪代码如图所示,执行此算法,最后输出的www.ziyuanku.com的值为__________.

www.ziyuanku.com

5.函数www.ziyuanku.com的定义域为__________.

6.某兴趣小组有2名男生和3名女生,现从中任选2名学生去参加活动,则恰好选中2名女生的概率是__________.

7.已知函数www.ziyuanku.com的图像关于直线www.ziyuanku.com对称,则www.ziyuanku.com的值是__________.

8.在平面直角坐标系www.ziyuanku.com中,若双曲线www.ziyuanku.com的右焦点www.ziyuanku.com到一条渐近线的距离为www.ziyuanku.com,则其离心率的值是__________.

9.函数www.ziyuanku.com满足www.ziyuanku.com,且在区间www.ziyuanku.comwww.ziyuanku.com,则www.ziyuanku.com的值为__________.

10.如图所示,正方体的棱长为2,以其所有面的中心为顶点的多面体的体积为__________.

www.ziyuanku.com

11.若函数www.ziyuanku.comwww.ziyuanku.com内有且只有一个零点,则www.ziyuanku.comwww.ziyuanku.com上的最大值与最小值的和为__________.

12.在平面直角坐标系www.ziyuanku.com中,www.ziyuanku.com为直线www.ziyuanku.com上在第一象限内的点,www.ziyuanku.comwww.ziyuanku.com为直径的圆www.ziyuanku.com与直线www.ziyuanku.com交于另一点www.ziyuanku.com,若www.ziyuanku.com,则点www.ziyuanku.com的横坐标为__________.

13.在www.ziyuanku.com中,角www.ziyuanku.com所对应的边分别为www.ziyuanku.com的平分线交www.ziyuanku.com于点www.ziyuanku.com,且www.ziyuanku.com,则www.ziyuanku.com的最小值为__________.

14.已知集合www.ziyuanku.com,将www.ziyuanku.com的所有元素从小到大依次排列构成一个数列www.ziyuanku.com,记www.ziyuanku.com为数列的前www.ziyuanku.com项和,则使得www.ziyuanku.com成立的www.ziyuanku.com的最小值为__________.

二、解答题

15.在平行四边形www.ziyuanku.com中,www.ziyuanku.com

www.ziyuanku.com

1.求证:www.ziyuanku.com平面www.ziyuanku.com

2.平面www.ziyuanku.com平面www.ziyuanku.com

16.已知www.ziyuanku.com为锐角,www.ziyuanku.com

1.求www.ziyuanku.com的值。

2.求www.ziyuanku.com的值。

17.某农场有一块农田,如图所示,它的边界由圆www.ziyuanku.com的一段圆弧www.ziyuanku.com为此圆弧的中点www.ziyuanku.com和线段www.ziyuanku.com构成,已知圆www.ziyuanku.com的半径为www.ziyuanku.com米,点www.ziyuanku.comwww.ziyuanku.com的距离为www.ziyuanku.com米,先规划在此农田上修建两个温室大棚,大棚Ⅰ内的地块形状为矩形www.ziyuanku.com.大棚Ⅱ内的地块形状为www.ziyuanku.com,要求www.ziyuanku.com均在线段www.ziyuanku.com上,www.ziyuanku.com均在圆弧上,设www.ziyuanku.comwww.ziyuanku.com所成的角为www.ziyuanku.com

www.ziyuanku.com

1.用www.ziyuanku.com分别表示矩形www.ziyuanku.comwww.ziyuanku.com的面积,并确定www.ziyuanku.com的取值范围

2.若大棚Ⅰ内种植甲种蔬菜,大棚Ⅱ内种植乙种蔬菜,且甲、乙两种蔬菜的单位面积年产值之比为www.ziyuanku.com.求当www.ziyuanku.com为何值时,能使甲、乙两种蔬菜的年总产值最大.

18如图,在平面直角坐标系www.ziyuanku.com中,椭圆www.ziyuanku.com过点www.ziyuanku.com,焦点www.ziyuanku.com,圆www.ziyuanku.com的直径为www.ziyuanku.com

www.ziyuanku.com

1.求椭圆www.ziyuanku.com及圆www.ziyuanku.com的方程;

2.设直线www.ziyuanku.com与圆www.ziyuanku.com相切于第一象限内的点www.ziyuanku.com.

①若直线www.ziyuanku.com与椭圆www.ziyuanku.com有且只有一个公共点,求点www.ziyuanku.com的坐标;

②直线www.ziyuanku.com与椭圆www.ziyuanku.com交于www.ziyuanku.com两点.若www.ziyuanku.com的面积为www.ziyuanku.com,求直线www.ziyuanku.com的方程.

19记www.ziyuanku.com分别为函数www.ziyuanku.com的导函数.若存在www.ziyuanku.com,满足www.ziyuanku.comwww.ziyuanku.com,则称www.ziyuanku.com为函数www.ziyuanku.comwww.ziyuanku.com的一个”www.ziyuanku.com点”.

1.证明:函数www.ziyuanku.comwww.ziyuanku.com不存在”www.ziyuanku.com点”.

2.若函数www.ziyuanku.comwww.ziyuanku.com存在”www.ziyuanku.com点”,求实数的值.

3.已知函数www.ziyuanku.com,对任意www.ziyuanku.com,判断是否存在www.ziyuanku.com,使函数www.ziyuanku.comwww.ziyuanku.com在区间www.ziyuanku.com内存在”www.ziyuanku.com点”,并说明理由.

20设www.ziyuanku.com是首项为www.ziyuanku.com,公差为www.ziyuanku.com的等差数列,www.ziyuanku.com是首项www.ziyuanku.com,公比为www.ziyuanku.com的等比数列

1.设www.ziyuanku.com,若www.ziyuanku.comwww.ziyuanku.com均成立,求www.ziyuanku.com的取值范围

2.若www.ziyuanku.com证明:存在www.ziyuanku.com,使得www.ziyuanku.comwww.ziyuanku.com均成立,并求www.ziyuanku.com?的取值范围(用www.ziyuanku.com表示)。


参考答案

一、填空题

1.答案:www.ziyuanku.com

解析:观察两个集合即可求解。

2.答案:2

解析:www.ziyuanku.com,故www.ziyuanku.com

3.答案:90

解析:www.ziyuanku.com

4.答案:8

解析:代入程序前www.ziyuanku.com符合www.ziyuanku.com,

第一次代入后www.ziyuanku.com,符合www.ziyuanku.com,继续代入;

第二次代入后www.ziyuanku.com,符合www.ziyuanku.com,继续代入;

第三次代入后www.ziyuanku.com,不符合www.ziyuanku.com,输出结果www.ziyuanku.com,

故最后输出www.ziyuanku.com的值为www.ziyuanku.com.

www.ziyuanku.com

5.答案:www.ziyuanku.com

解析:www.ziyuanku.com,解之得www.ziyuanku.com,即www.ziyuanku.com.

6.答案:www.ziyuanku.com

解析:假设www.ziyuanku.com名女生为www.ziyuanku.com,男生为www.ziyuanku.com,恰好选中www.ziyuanku.com名女生的情况有:选www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com三种。

总情况有www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.com,www.ziyuanku.comwww.ziyuanku.comwww.ziyuanku.com种,两者相比即为答案www.ziyuanku.com

7.答案:www.ziyuanku.com

解析:函数的对称轴为www.ziyuanku.comwww.ziyuanku.com,

故把www.ziyuanku.com代入得www.ziyuanku.com

因为www.ziyuanku.com,所以www.ziyuanku.com.

8.答案:2

解析:由题意画图可知,渐近线www.ziyuanku.com与坐标轴的夹角为www.ziyuanku.com

www.ziyuanku.com,故www.ziyuanku.com.

9.答案:www.ziyuanku.com

解析:因为www.ziyuanku.com,函数的周期为www.ziyuanku.com,

所以www.ziyuanku.com

www.ziyuanku.com.

10.答案:www.ziyuanku.com

解析:平面www.ziyuanku.com将多面体分成了两个以www.ziyuanku.com为底面边长,高为www.ziyuanku.com的正四棱锥,

所以其体积为www.ziyuanku.com.

www.ziyuanku.com

11.答案:-3

解析:www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com上单调递减,在www.ziyuanku.com上单调递增

∵有唯一零点∴www.ziyuanku.com

求导可知在www.ziyuanku.com上,www.ziyuanku.com

www.ziyuanku.com

12.答案:3

解析:∵www.ziyuanku.com为直径∴www.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com到直线www.ziyuanku.com的距离。

www.ziyuanku.com?

www.ziyuanku.com,又www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com(舍去).

13.答案:9

解析:由面积得:www.ziyuanku.com

化简得www.ziyuanku.com

www.ziyuanku.com

当且仅当www.ziyuanku.com,即www.ziyuanku.com时取等号。

14.答案:27

解析:www.ziyuanku.comwww.ziyuanku.com相比,元素间隔大。所以从www.ziyuanku.com中加了几个www.ziyuanku.com中元素考虑。

www.ziyuanku.com个:www.ziyuanku.com

www.ziyuanku.com个:www.ziyuanku.com

www.ziyuanku.com个:www.ziyuanku.com

www.ziyuanku.com个:www.ziyuanku.com

www.ziyuanku.com个:www.ziyuanku.com

www.ziyuanku.com个:www.ziyuanku.com

发现www.ziyuanku.comwww.ziyuanku.com发生变号,以下用二分法查找:

www.ziyuanku.com,所以所求www.ziyuanku.com应在www.ziyuanku.com之间.

www.ziyuanku.com,所以所求www.ziyuanku.com应在www.ziyuanku.com之间.

www.ziyuanku.com,所以所求www.ziyuanku.com应在www.ziyuanku.com之间.

www.ziyuanku.com

www.ziyuanku.com,而www.ziyuanku.com,所以答案为www.ziyuanku.com.

二、解答题

15.答案:1.∵平行六面体www.ziyuanku.com

∴面www.ziyuanku.comwww.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com

又面www.ziyuanku.comwww.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.comwww.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com
2.由www.ziyuanku.com可知:www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

∵平行六面体www.ziyuanku.com

www.ziyuanku.com

又由www.ziyuanku.comwww.ziyuanku.com

∴四边形www.ziyuanku.com为平行四边形

www.ziyuanku.com

∴平行四边形www.ziyuanku.com为菱形

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com

∴面www.ziyuanku.comwww.ziyuanku.com

解析:

16.答案:1.方法一:

www.ziyuanku.comwww.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

方法二:

www.ziyuanku.com

?
2.方法一:

www.ziyuanku.com为锐角www.ziyuanku.com

www.ziyuanku.com均为锐角,www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

方法二:

www.ziyuanku.com为锐角www.ziyuanku.comwww.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com为锐角∴www.ziyuanku.com又∵www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

解析:

17.答案:1.过www.ziyuanku.comwww.ziyuanku.com垂直于交圆弧www.ziyuanku.com于,设www.ziyuanku.comwww.ziyuanku.comwww.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com?

www.ziyuanku.com点落在劣弧www.ziyuanku.com上时,www.ziyuanku.com,与题意矛盾。

所以点www.ziyuanku.com只能落在劣弧上.

所以www.ziyuanku.com,即www.ziyuanku.com
2.设甲种蔬菜年产值为www.ziyuanku.com,则乙种蔬菜年产值为www.ziyuanku.com,设总年产值为www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com,解得www.ziyuanku.comwww.ziyuanku.com,根据www.ziyuanku.com舍去www.ziyuanku.com,记www.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.comwww.ziyuanku.comwww.ziyuanku.com
www.ziyuanku.comwww.ziyuanku.comwww.ziyuanku.comwww.ziyuanku.com
www.ziyuanku.com单调递增极大值单调递减
www.ziyuanku.com单调递增极大值单调递减

答:当www.ziyuanku.com时,年总产值最大.

解析:

答案:1.www.ziyuanku.com
2.①www.ziyuanku.comwww.ziyuanku.com

解析:1.由题意www.ziyuanku.com

解得www.ziyuanku.com

即椭圆标准方程为www.ziyuanku.com
2.设www.ziyuanku.com,则www.ziyuanku.com

显然www.ziyuanku.com斜率存在,设www.ziyuanku.com,

www.ziyuanku.com,www.ziyuanku.com

www.ziyuanku.com代入,得www.ziyuanku.com

www.ziyuanku.com与椭圆方程联立

www.ziyuanku.com

①与椭圆相切,则www.ziyuanku.com,即www.ziyuanku.com

www.ziyuanku.com代入,解得www.ziyuanku.com(舍去)或www.ziyuanku.com

由于www.ziyuanku.com在第一象限,则www.ziyuanku.com

www.ziyuanku.com

②设www.ziyuanku.com与轴交点为www.ziyuanku.com

www.ziyuanku.com中令www.ziyuanku.com,得www.ziyuanku.com,即www.ziyuanku.com

假设www.ziyuanku.com的纵坐标大于www.ziyuanku.com的纵坐标

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com代入

化简得www.ziyuanku.comwww.ziyuanku.com

解此方程,得www.ziyuanku.com,(由已知条件,www.ziyuanku.com舍)或www.ziyuanku.com

由于www.ziyuanku.com在第一象限,则www.ziyuanku.com

回代入www.ziyuanku.com,得www.ziyuanku.com

答案:1.www.ziyuanku.com

若存在,则有www.ziyuanku.com

根据www.ziyuanku.com得到www.ziyuanku.com代入www.ziyuanku.com不符合,因此不存在
2.www.ziyuanku.com

根据题意有www.ziyuanku.com且有www.ziyuanku.com

根据www.ziyuanku.com得到www.ziyuanku.com代入www.ziyuanku.com得到www.ziyuanku.com

?
3.www.ziyuanku.com

根据题意有www.ziyuanku.com

根据www.ziyuanku.comwww.ziyuanku.com

转化为www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

www.ziyuanku.com

转化为www.ziyuanku.com存在零点www.ziyuanku.com

www.ziyuanku.com

∴恒存在零点大于www.ziyuanku.com小于www.ziyuanku.com

∴对任意均存在www.ziyuanku.com,使得存在"www.ziyuanku.com点".

答案:1.由题意得www.ziyuanku.com对任意www.ziyuanku.com均成立

故当www.ziyuanku.com

可得www.ziyuanku.comwww.ziyuanku.com

所以www.ziyuanku.com
2.因为www.ziyuanku.comwww.ziyuanku.com均能成立

www.ziyuanku.com代入可得www.ziyuanku.com

化简后可得www.ziyuanku.com

因为www.ziyuanku.com,所以www.ziyuanku.com

www.ziyuanku.com

所以存在www.ziyuanku.com,使得www.ziyuanku.comwww.ziyuanku.com均成立

www.ziyuanku.com时,www.ziyuanku.com

www.ziyuanku.com时,设www.ziyuanku.com,则www.ziyuanku.com

www.ziyuanku.com,因为www.ziyuanku.com,所以www.ziyuanku.com单调递增,又因为www.ziyuanku.com

所以www.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com,且设www.ziyuanku.com,那么www.ziyuanku.com

因为www.ziyuanku.com

所以www.ziyuanku.comwww.ziyuanku.com上恒成立,即www.ziyuanku.com单调递增。

所以www.ziyuanku.com的最大值为www.ziyuanku.com,所以www.ziyuanku.com

www.ziyuanku.comwww.ziyuanku.com均满足,所以www.ziyuanku.com单调递减

www.ziyuanku.com

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