2018江苏高考数学试卷及答案

There is no doubt that it is unwise to depend completely on the ratings in consumption.The advantages and disadvantages of ratings are often closely related.It is necessary to hold an objective attitude towards ratings.

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Possible version two:

Nowadays,most commodities or services are rated through certain channels.These ratings,easy to access,are playing an increasingly important role in customers ’purchase decision.However,results are sometimes unsatisfactory.

There is no denying that such ratings might bring convenience to consumers,but they are often misleading and unreliable.As we all know,most of the ratings are based on others ’judgment on the product or service concerned.Every judgment comes from a specific need or a unique psychological state.Apparently,blindly following others ’advice will affect our own judgment.Another fact should not be neglected that some of the ratings are the outcome of a careful manipulation of companies or sellers.It has become a common practice for some to pay for good ratings on their products or services so as to increase their sales.

Therefore,we should give a second thought to these ratings whenever we go shopping.

(150words)

数学Ⅰ试题

参考公式: 锥体的体积V =13Sh ,其中S 是锥体的底面积,h 是锥体的高.一㊁填空题:本大题共14小题,每小题5分,共计70分.请把答案填写在答题卡相应位置上∙∙∙∙∙∙∙∙.(第3题)1.已知集合A =0,1,2,{}8,B =-1,1,6,{}8,那么A ∩B =　▲　.2.若复数z 满足i ㊃z =1+2i,其中i 是虚数单位,则z 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　▲　.　(第4题)4.一个算法的伪代码如图所示,执行此算法,最后输出的S 的值为　▲　.5.函数f (x )=log 2x -1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名女生的概率为　▲　.7.已知函数y =sin(2x +φ)(-π2<φ<π2)的图象关于直线x =π3对称,则φ的值为　▲　.8.在平面直角坐标系xOy 中,若双曲线x 2a 2-y 2b 2=1(a >0,b >0)的右焦点F (c ,0)到一条渐近线的距离为32c ,则其离心率的值为　▲　.9.函数f (x )满足f (x +4)=f (x )(x ∈R ),且在区间(-2,2]上,f (x )=cos πx 2,　0

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个零点,则f (x )在[-1,1]上的最大值与最小值的和为　▲　.12.在平面直角坐标系xOy 中,A 为直线l :y =2x 上在第一象限内的点,B (5,0),以AB 为直径的圆C 与直线l 交于另一点D .若→AB ㊃→CD =0,则点A 的横坐标为　▲　.

13.在△ABC 中,角A ,B ,C 所对的边分别为a ,b ,c ,∠ABC =120°,∠ABC 的平分线交AC 于点D ,且BD =1,则4a +c 的最小值为　▲　.14.已知集合A =x x =2n -1,n ∈N {}*,B =x x =2n ,n ∈N {}*.将A ∪B 的所有

元素从小到大依次排列构成一个数列a {}n .记S n 为数列a {}n 的前n 项和,则使得S n >12a n +1成立的n 的最小值为　▲　.二㊁解答题:本大题共6小题,共计90分.请在答题卡指定区域∙∙∙∙∙∙∙内作答,解答时应写出文字说明㊁证明过程或演算步骤.(第15题)15.(本小题满分14分)在平行六面体ABCD -A 1B 1C 1D 1中,AA 1=AB ,AB 1⊥B 1C 1.求证:(1)AB ∥平面A 1B 1C ;(2)平面ABB 1A 1⊥平面A 1BC.16.(本小题满分14分)已知α,β为锐角,tan α=43,cos(α+β)=-55.(1)求cos 2α的值;(2)求tan(α-β)的值.17.(本小题满分14分)某农场有一块农田,如图所示,它的边界由圆O 的一段圆弧MPN (P 为此圆弧的中点)和线段MN 构成.已知圆O 的半径为40米,点P 到MN 的距离为50米.现规划在此农田上修建(第17题)两个温室大棚,大棚Ⅰ内的地块形状为矩形ABCD ,大棚Ⅱ内的地块形状为△CDP ,要求A ,B 均在线段MN 上,C ,D 均在圆弧上.设OC 与MN 所成的角为θ.(1)用θ分别表示矩形ABCD 和△CDP 的面积,并确定sin θ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㊁乙两种蔬菜的单位面积年产值之比为4∶3.求当θ为何值时,能使甲㊁乙两种蔬菜的年总产值最大.18.(本小题满分16分)(第18题)如图,在平面直角坐标系xOy 中,椭圆C 过点(3,12),焦点为F 1(-3,0),F 2(3,0),圆O 的直径为F 1F 2.(1)求椭圆C 及圆O 的方程;(2)设直线l 与圆O 相切于第一象限内的点P.①若直线l 与椭圆C 有且只有一个公共点,求点P 的坐标;②直线l 与椭圆C 交于A ,B 两点.若△OAB 的面积为267,求直线l 的方程.19.(本小题满分16分)记f ′(x ),g ′(x )分别为函数f (x ),g (x )的导函数.若存在x 0∈R ,满足f (x 0)=g (x 0)且f ′(x 0)=g ′(x 0),则称x 0为函数f (x )与g (x )的一个 S 点”.(1)证明:函数f (x )=x 与g (x )=x 2+2x -2不存在 S 点”;(2)若函数f (x )=ax 2-1与g (x )=ln x 存在 S 点”,求实数a 的值;(3)已知函数f (x )=-x 2+a ,g (x )=b e x x .对任意a >0,判断是否存在b >0,使函数f (x )与g (x )在区间(0,+¥)内存在 S 点”,并说明理由.20.(本小题满分16分)设a {}n 是首项为a 1,公差为d 的等差数列,b {}n 是首项为b 1,公比为q 的等比数列.(1)设a 1=0,b 1=1,q =2,若a n -b n ≤b 1对n =1,2,3,4均成立,求d 的取值范围;(2)若a 1=b 1>0,m ∈N *,q ∈(1,m 2],证明:存在d ∈R ,使得a n -b n ≤b 1对

n =2,3, ,m +1均成立,并求d 的取值范围(用b 1