河南省开封高中2021届高一下学期第三次质量检测
河南省开封市2021届新高考数学三月模拟试卷含解析

河南省开封市2021届新高考数学三月模拟试卷一、选择题:本题共12小题,每小题5分,共60分。
在每小题给出的四个选项中,只有一项是符合题目要求的。
1.如图,圆O 的半径为1,A ,B 是圆上的定点,OB OA ⊥,P 是圆上的动点, 点P 关于直线OB 的对称点为P ',角x 的始边为射线OA ,终边为射线OP ,将OP OP '-u u u r u u u r表示为x 的函数()f x ,则()y f x =在[]0,π上的图像大致为( )A .B .C .D .【答案】B 【解析】 【分析】根据图象分析变化过程中在关键位置及部分区域,即可排除错误选项,得到函数图象,即可求解. 【详解】由题意,当0x =时,P 与A 重合,则P '与B 重合,所以||2OP OP BA '-==u u u r u u u r u u u r,故排除C,D 选项;当02x π<<时,||2sin()2cos 2OP OP P P x x π''-==-=u u u r u u u r ,由图象可知选B.故选:B 【点睛】本题主要考查三角函数的图像与性质,正确表示函数的表达式是解题的关键,属于中档题.2.如图,双曲线()2222:10,0x y C a b a b-=>>的左,右焦点分别是()()12,0,,0,F c F c -直线2bc y a =与双曲线C 的两条渐近线分别相交于,A B 两点.若12,3BF F π∠=则双曲线C 的离心率为( )A .2B 42C 2D 23【答案】A 【解析】 【分析】 易得(,)22c bc B a -,过B 作x 轴的垂线,垂足为T ,在1FTB ∆中,利用1tan 3BT FT π=即可得到,,a b c 的方程. 【详解】由已知,得(,)22c bc B a -,过B 作x 轴的垂线,垂足为T ,故12cFT =, 又12,3BF F π∠=所以1tan 33BT FT π==,即232bcb ac a == 所以双曲线C 的离心率21()2be a =+.故选:A. 【点睛】本题考查双曲线的离心率问题,在作双曲线离心率问题时,最关键的是找到,,a b c 的方程或不等式,本题属于容易题.3.已知函数()2sin()(0,0)3f x x A ωωπ=->>,将函数()f x 的图象向左平移3π个单位长度,得到函数()g x的图象,若函数()g x 的图象的一条对称轴是6x π=,则ω的最小值为A .16B .23C .53D .56【答案】C 【解析】 【分析】 【详解】将函数()f x 的图象向左平移3π个单位长度,得到函数()2sin()33g x x ωωππ=+-的图象,因为函数()g x 的图象的一条对称轴是6x π=,所以sin()1633ωωπππ+-=±,即,6332k k ωωππππ+-=+π∈Z ,所以52,3k k ω=+∈Z ,又0>ω,所以ω的最小值为53.故选C . 4.设全集U=R ,集合()2log 41{|}A x x =-≤,()()35{|}0B x x x =-->,则()U B A =I ð( )A .[2]5,B .[2]3,C .[)24,D .[)34,【答案】D 【解析】 【分析】求解不等式,得到集合A ,B ,利用交集、补集运算即得解 【详解】由于2log (4)124x x -≤∴≤<故集合[)24A =, ()()350x x -->3x ∴<或5x >故集合()()35B =-∞⋃+∞,, ∴ ()[)|34U B A ⋂=,ð 故选:D 【点睛】本题考查了集合的交集和补集混合运算,考查了学生概念理解,数学运算的能力,属于中档题. 5.已知(0,)απ∈,且tan 2α=,则cos2cos αα+=( )A B .C D 【答案】B 【解析】分析:首先利用同角三角函数关系式,结合题中所给的角的范围,求得cos α的值,之后借助于倍角公式,将待求的式子转化为关于cos α的式子,代入从而求得结果. 详解:根据题中的条件,可得α为锐角,根据tan 2α=,可求得cos α=,而22cos 2cos 2cos cos 115αααα+=+-=+-=,故选B. 点睛:该题考查的是有关同角三角函数关系式以及倍角公式的应用,在解题的过程中,需要对已知真切求余弦的方法要明确,可以应用同角三角函数关系式求解,也可以结合三角函数的定义式求解.6.根据散点图,对两个具有非线性关系的相关变量x ,y 进行回归分析,设u= lny ,v=(x-4)2,利用最小二乘法,得到线性回归方程为ˆu=-0.5v+2,则变量y 的最大值的估计值是( ) A .e B .e 2C .ln2D .2ln2【答案】B 【解析】 【分析】将u= lny ,v=(x-4)2代入线性回归方程ˆu=-0.5v+2,利用指数函数和二次函数的性质可得最大估计值. 【详解】解:将u= lny ,v=(x -4)2代入线性回归方程ˆu=-0.5v+2得: ()2ln 0.542y x =--+,即()20.542x y e --+=,当4x =时,()20.542x --+取到最大值2, 因为xy e =在R 上单调递增,则()20.542x y e --+=取到最大值2e .故选:B. 【点睛】本题考查了非线性相关的二次拟合问题,考查复合型指数函数的最值,是基础题,.7.盒中装有形状、大小完全相同的5张“刮刮卡”,其中只有2张“刮刮卡”有奖,现甲从盒中随机取出2张,则至少有一张有奖的概率为( ) A .12B .35C .710D .45【答案】C 【解析】 【分析】先计算出总的基本事件的个数,再计算出两张都没获奖的个数,根据古典概型的概率,求出两张都没有奖的概率,由对立事件的概率关系,即可求解.【详解】从5张“刮刮卡”中随机取出2张,共有2510C =种情况,2张均没有奖的情况有233C =(种),故所求概率为3711010-=. 故选:C. 【点睛】本题考查古典概型的概率、对立事件的概率关系,意在考查数学建模、数学计算能力,属于基础题. 8.如图,已知直线:l ()()10y k x k =+>与抛物线2:4C y x =相交于A ,B 两点,且A 、B 两点在抛物线准线上的投影分别是M ,N ,若2AM BN =,则k 的值是( )A .13B .2 C .23D .2【答案】C 【解析】 【分析】直线()()10y k x k =+>恒过定点()10P -,,由此推导出12OB AF =,由此能求出点B 的坐标,从而能求出k 的值. 【详解】设抛物线2:4C y x =的准线为:1l x =-,直线()()10y k x k =+>恒过定点()10P -,, 如图过A 、B 分别作AM l ⊥于M ,BN l ⊥于N , 由2AM BN =,则2FA FB =, 点B 为AP 的中点、连接OB ,则12OB AF =, ∴OB BF =,点B 的横坐标为12, ∴点B 的坐标为122B ⎛⎝,把122B ⎛ ⎝代入直线()()10y k x k =+>,解得223k =, 故选:C .【点睛】本题考查直线与圆锥曲线中参数的求法,考查抛物线的性质,是中档题,解题时要注意等价转化思想的合理运用,属于中档题.9.若平面向量,,a b c r r r,满足||2,||4,4,||3a b a b c a b ==⋅=-+=r r r r r r r ,则||c b -r r 的最大值为( )A .523B .523C .2133D .2133【答案】C 【解析】 【分析】可根据题意把要求的向量重新组合成已知向量的表达,利用向量数量积的性质,化简为三角函数最值. 【详解】 由题意可得:()(2)c b c a b a b -=-++-r r r r r r r,2222|2|(2)||4||444164452a b a b a b a b -=-=+⋅-⋅=+⨯-⨯=r r r rr r r r Q |2|213a b ∴-=r r2222||()[()(2)]|()(2)|c b c b c a b a b c a b a b ∴-=-=-++-=-++-r r r r r r r r r r r r r r22|||2|2|||2|cos ,2c a b a b c a b a b c a b a b =-++-+⋅-+⋅-⋅<-++>r r r r r r r r r r r r r r r35223213cos ,2c a b a b =++<-++>r r r r r55439cos ,2c a b a b =+<-++>r r r r r55439+…25543952221333(2133)+=+⨯=Q ,故选:C【点睛】本题主要考查根据已知向量的模求未知向量的模的方法技巧,把要求的向量重新组合成已知向量的表达是本题的关键点.本题属中档题.10. “角谷猜想”的内容是:对于任意一个大于1的整数n ,如果n 为偶数就除以2,如果n 是奇数,就将其乘3再加1,执行如图所示的程序框图,若输入10n =,则输出i 的( )A .6B .7C .8D .9【答案】B 【解析】 【分析】模拟程序运行,观察变量值可得结论. 【详解】循环前1,10i n ==,循环时:5,2n i ==,不满足条件1n =;16,3n i ==,不满足条件1n =;8,4n i ==,不满足条件1n =;4,5n i ==,不满足条件1n =;2,6n i ==,不满足条件1n =;1,7n i ==,满足条件1n =,退出循环,输出7i =. 故选:B . 【点睛】本题考查程序框图,考查循环结构,解题时可模拟程序运行,观察变量值,从而得出结论. 11.设等差数列{}n a 的前n 项和为n S ,若5632a a a +=+,则7S =( ) A .28 B .14C .7D .2【答案】B 【解析】 【分析】根据等差数列的性质6345a a a a +=+并结合已知可求出4a ,再利用等差数列性质可得1774()772a a S a +==,即可求出结果. 【详解】因为6345a a a a +=+,所以5452a a a +=+,所以42a =, 所以17747()7142a a S a +===, 故选:B 【点睛】本题主要考查等差数列的性质及前n 项和公式,属于基础题. 12.函数ln ||()xx x f x e=的大致图象为( ) A . B .C .D .【答案】A 【解析】 【分析】利用特殊点的坐标代入,排除掉C ,D ;再由1()12f -<判断A 选项正确. 【详解】1.11.1ln |1.1|( 1.1)0f e --=<,排除掉C ,D ;1211ln 122()22f e e---==122e <=Q 2e ,1()212f e ∴-=<.本题考查了由函数解析式判断函数的大致图象问题,代入特殊点,采用排除法求解是解决这类问题的一种常用方法,属于中档题.二、填空题:本题共4小题,每小题5分,共20分。
河南省开封市2021届新高考三诊数学试题含解析

河南省开封市2021届新高考三诊数学试题一、选择题:本题共12小题,每小题5分,共60分。
在每小题给出的四个选项中,只有一项是符合题目要求的。
1.已知函数21()(1)()2x f x ax x e a R =--∈若对区间[]01,内的任意实数123x x x 、、,都有123()()()f x f x f x +≥,则实数a 的取值范围是( )A .[]12, B .[]e,4C .[]14, D .[)[]12,4e ⋃, 【答案】C 【解析】分析:先求导,再对a 分类讨论求函数的单调区间,再画图分析转化对区间[]01,内的任意实数123x x x 、、,都有()()()123f x f x f x +≥,得到关于a 的不等式组,再解不等式组得到实数a 的取值范围. 详解:由题得()[(1)]()xxxxf x ax e x e ax xe x a e =-+-=-=-'.当a <1时,()0f x '<,所以函数f (x )在[]01,单调递减, 因为对区间[]01,内的任意实数123x x x 、、,都有()()()123f x f x f x +≥, 所以(1)(1)(0)f f f +≥, 所以111,22a a +≥ 故a≥1,与a <1矛盾,故a <1矛盾.当1≤a<e 时,函数f(x)在[0,lna]单调递增,在(lna,1]单调递减. 所以2max 1()(ln )ln ln ,2f x f a a a a a a ==-+ 因为对区间[]01,内的任意实数123x x x 、、,都有()()()123f x f x f x +≥, 所以(0)(1)(ln )f f f a +≥,所以2111ln ln ,22a a a a a a +≥-+ 即211ln ln 1022a a a a a -+-≤令211()ln ln 1,(1)22g a a a a a a a e =-+-≤<,所以21()(ln 1)0,2g a a =-<'所以函数g(a)在(1,e )上单调递减, 所以max 1()(1)02g a g ==-<, 所以当1≤a<e 时,满足题意.因为对区间[]01,内的任意实数123x x x 、、,都有()()()123f x f x f x +≥, 所以(0)(0)(1)f f f +≥, 故1+112a ≥, 所以 4.a ≤ 故 4.e a ≤≤综上所述,a ∈[]14,. 故选C.点睛:本题的难点在于“对区间[]01,内的任意实数123x x x 、、,都有()()()123f x f x f x +≥”的转化.由于是函数的问题,所以我们要联想到利用函数的性质(单调性、奇偶性、周期性、对称性、最值、极值等)来分析解答问题.本题就是把这个条件和函数的单调性和最值联系起来,完成了数学问题的等价转化,找到了问题的突破口. 2.设22(1)1z i i=+++(i 是虚数单位),则||z =( )A B .1C .2D 【答案】A 【解析】 【分析】先利用复数代数形式的四则运算法则求出z ,即可根据复数的模计算公式求出||z . 【详解】∵22)1121(1z i i i i i=-+=+=+++,∴||z == 故选:A . 【点睛】本题主要考查复数代数形式的四则运算法则的应用,以及复数的模计算公式的应用, 属于容易题.3.某中学有高中生1500人,初中生1000人为了解该校学生自主锻炼的时间,采用分层抽样的方法从高生和初中生中抽取一个容量为n 的样本.若样本中高中生恰有30人,则n 的值为( ) A .20 B .50C .40D .60【答案】B 【解析】 【分析】【详解】由题意,30=150015001000n⨯+,解得50n =.故选:B. 【点睛】本题考查简单随机抽样中的分层抽样,某一层样本数等于某一层的总体个数乘以抽样比,本题是一道基础题.4.定义在R 上的奇函数()f x 满足()()330f x f x --+-=,若()11f =,()22f =-,则()()()()1232020f f f f ++++=L ( )A .1-B .0C .1D .2【答案】C 【解析】 【分析】首先判断出()f x 是周期为6的周期函数,由此求得所求表达式的值. 【详解】由已知()f x 为奇函数,得()()f x f x -=-, 而()()330f x f x --+-=, 所以()()33f x f x -=+, 所以()()6f x f x =+,即()f x 的周期为6.由于()11f =,()22f =-,()00f =, 所以()()()()33330f f f f =-=-⇒=,()()()4222f f f =-=-=, ()()()5111f f f =-=-=-, ()()600f f ==.所以()()()()()()1234560f f f f f f +++++=, 又202063364=⨯+,所以()()()()1232020f f f f ++++=L ()()()()12341f f f f +++=. 故选:C本小题主要考查函数的奇偶性和周期性,属于基础题.5.设m ,n 为直线,α、β为平面,则m α⊥的一个充分条件可以是( ) A .αβ⊥,n αβ=I ,m n ⊥ B .//αβ,m β⊥ C .αβ⊥,//m β D .n ⊂α,m n ⊥【答案】B 【解析】 【分析】根据线面垂直的判断方法对选项逐一分析,由此确定正确选项. 【详解】对于A 选项,当αβ⊥,n αβ=I ,m n ⊥时,由于m 不在平面β内,故无法得出m α⊥. 对于B 选项,由于//αβ,m β⊥,所以m α⊥.故B 选项正确.对于C 选项,当αβ⊥,//m β时,m 可能含于平面α,故无法得出m α⊥. 对于D 选项,当n ⊂α,m n ⊥时,无法得出m α⊥. 综上所述,m α⊥的一个充分条件是“//αβ,m β⊥” 故选:B 【点睛】本小题主要考查线面垂直的判断,考查充分必要条件的理解,属于基础题. 6.若ABC ∆的内角A 满足2sin 23A =-,则sin cos A A -的值为( )A B . C D .5-3【答案】A 【解析】 【分析】由2sin 22sin cos 3A A A ==-,得到1sin cos 03A A =-<,得出(,)2A ππ∈,再结合三角函数的基本关系式,即可求解. 【详解】由题意,角A 满足2sin 22sin cos 3A A A ==-,则1sin cos 03A A =-<, 又由角A 是三角形的内角,所以(,)2A ππ∈,所以sin cos A A >,因为225sin cos 12sin cos 1()A A A A -=-=--=,所以sin cos 3A A -=. 故选:A. 【点睛】本题主要考查了正弦函数的性质,以及三角函数的基本关系式和正弦的倍角公式的化简、求值问题,着重考查了推理与计算能力.7.函数()sin 2sin 3f x x m x x =++在[,]63ππ上单调递减的充要条件是( )A .3m ≤-B .4m ≤-C.m ≤D .4m ≤【答案】C 【解析】 【分析】先求导函数,函数在[,]63ππ上单调递减则()0f x '≤恒成立,对导函数不等式换元成二次函数,结合二次函数的性质和图象,列不等式组求解可得. 【详解】依题意,2()2cos 2cos 34cos cos 1f x x m x x m x '=++=++, 令cos x t =,则1[,22t ∈,故2410t mt ++≤在[1,22上恒成立;结合图象可知,1141042341042m m ⎧⨯+⨯+⎪⎪⎨⎪⨯+⨯+⎪⎩„„,解得43m m -⎧⎪⎨-⎪⎩„„故3m ≤-. 故选:C. 【点睛】本题考查求三角函数单调区间. 求三角函数单调区间的两种方法:(1)代换法:就是将比较复杂的三角函数含自变量的代数式整体当作一个角u (或t ),利用基本三角函数的单调性列不等式求解;(2)图象法:画出三角函数的正、余弦曲线,结合图象求它的单调区间. 8.设(),1,a b ∈+∞,则“a b > ”是“log 1a b <”的( ) A .充分而不必要条件 B .必要而不充分条件【解析】 【分析】根据充分条件和必要条件的定义结合对数的运算进行判断即可. 【详解】∵a ,b ∈(1,+∞), ∴a >b ⇒log a b <1, log a b <1⇒a >b ,∴a >b 是log a b <1的充分必要条件, 故选C . 【点睛】本题主要考查充分条件和必要条件的判断,根据不等式的解法是解决本题的关键. 9.已知函数1()cos 22f x x x π⎛⎫=++ ⎪⎝⎭,,22x ππ⎡⎤∈-⎢⎥⎣⎦,则()f x 的极大值点为( ) A .3π-B .6π-C .6π D .3π 【答案】A 【解析】 【分析】求出函数的导函数,令导数为零,根据函数单调性,求得极大值点即可. 【详解】 因为()11cos 222f x x x x sinx π⎛⎫=++=- ⎪⎝⎭, 故可得()12f x cosx '=-+, 令()0f x '=,因为,22x ππ⎡⎤∈-⎢⎥⎣⎦, 故可得3x π=-或3x π=,则()f x 在区间,23ππ⎛⎫-- ⎪⎝⎭单调递增, 在,33ππ⎛⎫-⎪⎝⎭单调递减,在,32ππ⎛⎫ ⎪⎝⎭单调递增,故()f x 的极大值点为3π-.本题考查利用导数求函数的极值点,属基础题. 10.要得到函数()sin(3)3f x x π=+的导函数()f x '的图像,只需将()f x 的图像( )A .向右平移3π个单位长度,再把各点的纵坐标伸长到原来的3倍 B .向右平移6π个单位长度,再把各点的纵坐标缩短到原来的13倍 C .向左平移3π个单位长度,再把各点的纵坐标缩短到原来的13倍 D .向左平移6π个单位长度,再把各点的纵坐标伸长到原来的3倍 【答案】D 【解析】 【分析】 先求得()'fx ,再根据三角函数图像变换的知识,选出正确选项.【详解】 依题意()'553cos 33cos 33sin 33626fx x x x ππππ⎡⎤⎛⎫⎛⎫⎛⎫=+=+-=+ ⎪ ⎪ ⎪⎢⎥⎝⎭⎝⎭⎝⎭⎣⎦3sin 363x ππ⎡⎤⎛⎫=++ ⎪⎢⎥⎝⎭⎣⎦,所以由()sin(3)3f x x π=+向左平移6π个单位长度,再把各点的纵坐标伸长到原来的3倍得到()'f x 的图像.故选:D 【点睛】本小题主要考查复合函数导数的计算,考查诱导公式,考查三角函数图像变换,属于基础题.11.已知函数log ()a y x c =+(a ,c 是常数,其中0a >且1a ≠)的大致图象如图所示,下列关于a ,c 的表述正确的是( )A .1a >,1c >B .1a >,01c <<C .01a <<,1c >D .01a <<,01c <<【答案】D根据指数函数的图象和特征以及图象的平移可得正确的选项. 【详解】从题设中提供的图像可以看出()01,log 0,log 10a a a c c <<>+>, 故得01,01c a <<<<, 故选:D . 【点睛】本题考查图象的平移以及指数函数的图象和特征,本题属于基础题.12.已知1F ,2F 是椭圆与双曲线的公共焦点,P 是它们的一个公共点,且21PF PF >,椭圆的离心率为1e ,双曲线的离心率为2e ,若112PF F F =,则2133e e +的最小值为( ) A.6+ B.6+C .8D .6【答案】C 【解析】 【分析】由椭圆的定义以及双曲线的定义、离心率公式化简2133e e +,结合基本不等式即可求解.【详解】设椭圆的长半轴长为a ,双曲线的半实轴长为a ',半焦距为c , 则1ce a=,2c e a =',设2PF m =由椭圆的定义以及双曲线的定义可得:1222m PF PF a a c +=⇒=+,2122mPF PF a a c ''-=⇒=- 则2133e e +33322633322m m c c a c c c m m c a c c c c ⎛⎫⎛⎫+- ⎪ ⎪⎝⎭⎝⎭=+=+=++'⎛⎫⎛⎫-- ⎪ ⎪⎝⎭⎝⎭68≥+= 当且仅当73a c =时,取等号.本题主要考查了椭圆的定义以及双曲线的定义、离心率公式,属于中等题. 二、填空题:本题共4小题,每小题5分,共20分。
2024届河南省开封市高三下学期第三次质量检测文综地理试题(解析版)

2024届河南省开封市高三下学期第三次质量检测文综地理试题(解析版)一、选择题:在每小题给出的四个选项中,只有一项是符合题目要求的。
净增人口数是人口自然增长数和人口迁移增长数之和。
下图为2000—2020年河南省与上海市人口变动图。
据此完成下面小题。
1. 与2000—2010年相比,2010—2020年河南省人口()A. 人口数量下降B. 出生率提高C. 人口增幅变大D. 人口净减少2. 2010—2020年上海市人口变动幅度变化的主要原因是()A. 住房困难B. 产业转移C. 交通拥堵D. 经济萎缩【答案】1 C 2. B【解析】【1题详解】由图可知,与2000—2010年相比,2010—2020年河南省人口净变动数明显增加,人口增幅变大,C正确;人口数量增加,A错误;无法从图中直接看出出生率是否提高,B错误;人口净增多,D错误。
故选C。
【2题详解】2010--2020年,上海市人口变动幅度减小主要原因是产业转移,劳动密集型产业向外转移,部分劳动力从上海流出,B正确;住房困难、交通拥堵可能在一定程度上减少人口迁入,但不是主要原因,A错误;上海市经济并未萎缩,D错误。
故选B。
【点睛】影响人口迁移的因素:1、自然环境因素。
如:气候、淡水资源分布、土壤、矿产、自然灾害等,这些是人类赖以生存的自然环境,在很大程度上决定了人类生活、生产的空间格局,从而决定着人类的迁移方向和规模。
2、社会经济因素。
如:经济因素、交通和通信的发展、文化教育事业的发展、婚姻和家庭等,人类为了能有更好的生活水平,满足生活态度和生活期望也会进行迁移。
3、政治因素。
如:有关人口迁移的政策、战争、政治变革等,常常引起人口迁移。
2024年2月在新加坡航展上,我国自主设计研发组装的大飞机C919实现国际航展首秀。
C919核心部件全球招标采购,零部件生产分布在全国各地,总装基地位于上海。
下图为C919飞机部分零部件厂家示意图。
据此完成下面小题。
河南省开封市普通高中2021届高三毕业班下学期第三次高考模拟考试数学(文)试题(解析版)

绝密★启用前河南省开封市普通高中2021届高三毕业班下学期第三次高考模拟考试数学(文)试题(解析版)一、选择题(共12小题,每小题5分,共60分).1.设a,b∈R,A={1,a},B={﹣1,﹣b},若A⊆B,则a﹣b=()A.﹣1 B.﹣2 C.2 D.0解:a,b∈R,A={1,a},B={﹣1,﹣b},A⊆B,考试a=﹣1,b=﹣1,所以a﹣b=0,故选:D.2.设复数z满足|z|=|z﹣i|=1,且z的实部大于虚部,则z=()A.B.C.D.解:设z=a+bi,(a,b∈R),∵复数z满足|z|=|z﹣i|=1,∴=1,=1,即x2+y2=1,x2+y2﹣2y=0,解得y=,x=±,∵z的实部大于虚部,∴x=,∴z=+i,故选:B.3.“方程表示双曲线”的一个必要不充分条件为()A.m∈(﹣∞,﹣1)∪(1,+∞)B.m∈(﹣∞,﹣2)∪(1,+∞)C.m∈(﹣∞,﹣2)D.m∈(1,+∞)解:方程为双曲线时,(m+2)(m﹣1)>0∴m∈(﹣∞,﹣2)∪(1,+∞),∵(﹣∞,﹣2)∪(1,+∞)⊊(﹣∞,﹣1)∪(1,+∞),“方程表示双曲线”的一个必要不充分条件为m∈(﹣∞,﹣1)∪(1,+∞).故选:A.4.2021年开始,我省将试行“3+1+2“的普通高考新模式,即除语文、数学、外语3门必选科目外,考生再从物理、历史中选1门,从化学、生物、地理、政治中选2门作为选考科目.为了帮助学生合理选科,某中学将高一每个学生的六门科目综合成绩按比例均缩放成5分制,绘制成雷达图.甲同学的成绩雷达图如图所示,下面叙述一定不正确的是()A.甲的物理成绩领先年级平均分最多B.甲有2个科目的成绩低于年级平均分C.甲的成绩从高到低的前3个科目依次是地理、化学、历史D.对甲而言,物理、化学、地理是比较理想的一种选科结果解:甲的成绩从高到低的前3个科目依次是地理、化学、生物(物理),。
河南省开封市2021届新高考数学第三次调研试卷含解析

河南省开封市2021届新高考数学第三次调研试卷一、选择题:本题共12小题,每小题5分,共60分。
在每小题给出的四个选项中,只有一项是符合题目要求的。
1.若θ是第二象限角且sinθ =1213,则tan()4πθ+= A .177-B .717- C .177D .717【答案】B 【解析】由θ是第二象限角且sinθ =1213知:25cos 1sin 13θθ=--=-,5t n 1a 2θ-=. 所以tan tan 457tan()41tan tan 4517πθθθ+︒+==--︒.2.已知抛物线24y x =的焦点为F ,P 为抛物线上一点,(1,1)A ,当PAF ∆周长最小时,PF 所在直线的斜率为( ) A .43-B .34-C .34D .43【答案】A 【解析】 【分析】本道题绘图发现三角形周长最小时A,P 位于同一水平线上,计算点P 的坐标,计算斜率,即可. 【详解】结合题意,绘制图像要计算三角形PAF 周长最小值,即计算PA+PF 最小值,结合抛物线性质可知,PF=PN ,所以PF PA PA PN AN AG +=+≥≥,故当点P 运动到M 点处,三角形周长最小,故此时M 的坐标为1,14⎛⎫ ⎪⎝⎭,所以斜率为1041314k -==--,故选A . 【点睛】本道题考查了抛物线的基本性质,难度中等.3.若,x y 满足320020x y x y x y --≤⎧⎪-≥⎨⎪+≥⎩,且目标函数2(0,0)z ax by a b =+>>的最大值为2,则416a b +的最小值为( ) A .8 B .4C .22D .6【答案】A 【解析】 【分析】作出可行域,由2(0,0)z ax by a b =+>>,可得22a z y x b b =-+.当直线22a z y x b b=-+过可行域内的点()1,1B 时,z 最大,可得22a b +=.再由基本不等式可求416a b +的最小值. 【详解】作出可行域,如图所示由2(0,0)z ax by a b =+>>,可得22a zy x b b=-+. 平移直线22a z y x b b =-+,当直线过可行域内的点B 时,2zb最大,即z 最大,最大值为2. 解方程组3200x y x y --=⎧⎨-=⎩,得()1,1,11x B y =⎧∴⎨=⎩. 22(0,0)a b a b ∴+=>>.22224164424424248a b a b a b a b +∴+=+≥⨯===,当且仅当244a b =,即12,1222a a b a b b =⎧=⎧⎪⎨⎨+==⎩⎪⎩时,等号成立.416a b ∴+的最小值为8.故选:A . 【点睛】本题考查简单的线性规划,考查基本不等式,属于中档题. 4.已知函数()()614,7,7x a x x f x ax -⎧-+≤=⎨>⎩是R 上的减函数,当a 最小时,若函数()4y f x kx =--恰有两个零点,则实数k 的取值范围是( ) A .1(,0)2-B .1(2,)2- C .(1,1)- D .1(,1)2【答案】A 【解析】 【分析】首先根据()f x 为R 上的减函数,列出不等式组,求得112a ≤<,所以当a 最小时,12a =,之后将函数零点个数转化为函数图象与直线交点的个数问题,画出图形,数形结合得到结果. 【详解】由于()f x 为R 上的减函数,则有()1001714a a a a ⎧-<⎪<<⎨⎪≤-+⎩,可得112a ≤<, 所以当a 最小时,12a =, 函数()4y f x kx =--恰有两个零点等价于方程()4f x kx =+有两个实根, 等价于函数()y f x =与4y kx =+的图像有两个交点.画出函数()f x 的简图如下,而函数4y kx =+恒过定点()0,4,数形结合可得k 的取值范围为102k -<<.故选:A. 【点睛】该题考查的是有关函数的问题,涉及到的知识点有分段函数在定义域上单调减求参数的取值范围,根据函数零点个数求参数的取值范围,数形结合思想的应用,属于中档题目.5.甲在微信群中发了一个6元“拼手气”红包,被乙、丙、丁三人抢完,若三人均领到整数元,且每人至少领到1元,则乙获得“最佳手气”(即乙领到的钱数多于其他任何人)的概率是( ) A .13B .310C .25D .34【答案】B 【解析】 【分析】将所有可能的情况全部枚举出来,再根据古典概型的方法求解即可. 【详解】设乙,丙,丁分别领到x 元,y 元,z 元,记为(,,)x y z ,则基本事件有(1,1,4),(1,4,1) ,(4,1,1),(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1),(2,2,2),共10个,其中符合乙获得“最佳手气”的有3个,故所求概率为310, 故选:B. 【点睛】本题主要考查了枚举法求古典概型的方法,属于基础题型.6.已知函数()()()2ln 14f x ax x ax =-+-,若0x >时,()0f x ≥恒成立,则实数a 的值为( )A .2eB .4eC .2e - D .4e- 【答案】D 【解析】 【分析】通过分析函数()ln 10y ax x =->与()240y x ax x =+->的图象,得到两函数必须有相同的零点t ,解方程组2ln 1040at a at -=⎧⎨+-=⎩即得解.【详解】如图所示,函数()ln 10y ax x =->与()240y x ax x =+->的图象,因为0x >时,()0f x ≥恒成立, 于是两函数必须有相同的零点t ,所以2ln 1040at a at -=⎧⎨+-=⎩24at t e =-=,解得4a e- 故选:D 【点睛】本题主要考查函数的图象的综合应用和函数的零点问题,考查不等式的恒成立问题,意在考查学生对这些知识的理解掌握水平.7.将函数()2sin(3)(0)f x x ϕϕπ=+<<图象向右平移8π个单位长度后,得到函数的图象关于直线3x π=对称,则函数()f x 在,88ππ⎡⎤-⎢⎥⎣⎦上的值域是( )A .[1,2]-B .[2]C .2⎡⎤-⎢⎥⎣⎦D .[2]【答案】D 【解析】 【分析】由题意利用函数sin()y A x ωϕ=+的图象变换规律,三角函数的图象的对称性,余弦函数的值域,求得结果. 【详解】解:把函数()2sin(3)(0)f x x ϕϕπ=+<<图象向右平移8π个单位长度后, 可得32sin 38y x πϕ⎛⎫=-+⎪⎝⎭的图象; 再根据得到函数的图象关于直线3x π=对称,33382k πππϕπ∴⨯-+=+,k Z ∈, 78πϕ∴=,函数7()2sin 38f x x π⎛⎫=+⎪⎝⎭.在,88ππ⎡⎤-⎢⎥⎣⎦上,753,824x πππ⎡⎤+∈⎢⎥⎣⎦,sin 382x π⎡⎤⎛⎫∴-∈-⎢⎥ ⎪⎝⎭⎣⎦,故()2sin 3[8f x x π⎛⎫=-∈ ⎪⎝⎭,即()f x 的值域是[2],故选:D. 【点睛】本题主要考查函数sin()y A x ωϕ=+的图象变换规律,三角函数的图象的对称性,余弦函数的值域,属于中档题.8.曲线(2)x y ax e =+在点(0,2)处的切线方程为2y x b =-+,则ab =( ) A .4- B .8-C .4D .8【答案】B 【解析】 【分析】求函数导数,利用切线斜率求出a ,根据切线过点(0,2)求出b 即可. 【详解】因为(2)x y ax e =+, 所以(2)xy e ax a '=++, 故0|22x k y a ='==+=-, 解得4a =-, 又切线过点(0,2),所以220b =-⨯+,解得2b =, 所以8ab =-, 故选:B 【点睛】本题主要考查了导数的几何意义,切线方程,属于中档题.9.已知集合A ={y|y =},B ={x|y =lg (x ﹣2x 2)},则∁R (A∩B )=( )A .[0,12) B .(﹣∞,0)∪[12,+∞) C .(0,12)D .(﹣∞,0]∪[12,+∞) 【答案】D 【解析】 【分析】求函数的值域得集合A ,求定义域得集合B ,根据交集和补集的定义写出运算结果. 【详解】集合A ={y|y =}={y|y≥0}=[0,+∞); B ={x|y =lg (x ﹣2x 2)}={x|x ﹣2x 2>0}={x|0<x 12<}=(0,12), ∴A∩B =(0,12), ∴∁R (A∩B )=(﹣∞,0]∪[12,+∞). 故选:D. 【点睛】该题考查的是有关集合的问题,涉及到的知识点有函数的定义域,函数的值域,集合的运算,属于基础题目.10.中,如果,则的形状是( ) A .等边三角形 B .直角三角形C .等腰三角形D .等腰直角三角形【答案】B 【解析】 【分析】 化简得lgcosA =lg=﹣lg2,即,结合, 可求,得代入sinC=sinB ,从而可求C ,B ,进而可判断.【详解】 由,可得lgcosA ==﹣lg2,∴,∵,∴,,∴sinC =sinB ==,∴tanC =,C=,B =.故选:B 【点睛】本题主要考查了对数的运算性质的应用,两角差的正弦公式的应用,解题的关键是灵活利用基本公式,属于基础题.11.已知抛物线24y x =的焦点为F ,准线与x 轴的交点为K ,点P 为抛物线上任意一点KPF ∠的平分线与x 轴交于(,0)m ,则m 的最大值为( ) A .322- B .33C .23D .22-【答案】A 【解析】 【分析】211(1)4mmx x-=+++, 求出等式左边式子的范围,将等式右边代入,从而求解. 【详解】解:由题意可得,焦点F (1,0),准线方程为x =−1, 过点P 作PM 垂直于准线,M 为垂足,由抛物线的定义可得|PF|=|PM|=x+1,记∠KPF的平分线与x轴交于(m,0),(1m1)H-<<根据角平分线定理可得||||||=||||||PF PM FHPK PK KH=,211(1)4mmx x-∴=+++,当0x=时,0m=,当0x≠时,212,142(1)4112x xxx⎡⎫=∈⎪⎢⎪++⎣⎭+++,211032221mmm-∴≤<⇒<≤-+,综上:0322m≤≤-.故选:A.【点睛】本题主要考查抛物线的定义、性质的简单应用,直线的斜率公式、利用数形结合进行转化是解决本题的关键.考查学生的计算能力,属于中档题.12.某市气象部门根据2018年各月的每天最高气温平均数据,绘制如下折线图,那么,下列叙述错误的是( )A.各月最高气温平均值与最低气温平均值总体呈正相关B .全年中,2月份的最高气温平均值与最低气温平均值的差值最大C .全年中各月最低气温平均值不高于10°C 的月份有5个D .从2018年7月至12月该市每天最高气温平均值与最低气温平均值呈下降趋势 【答案】D 【解析】 【分析】根据折线图依次判断每个选项得到答案. 【详解】由绘制出的折线图知:在A 中,各月最高气温平均值与最低气温平均值为正相关,故A 正确;在B 中,全年中,2月的最高气温平均值与最低气温平均值的差值最大,故B 正确;在C 中,全年中各月最低气温平均值不高于10℃的月份有1月,2月,3月,11月,12月,共5个,故C 正确;在D 中,从2018年7月至12月该市每天最高气温平均值与最低气温平均值,先上升后下降,故D 错误. 故选:D. 【点睛】本题考查了折线图,意在考查学生的理解能力. 二、填空题:本题共4小题,每小题5分,共20分。
2021届河南省开封市高考物理三模试卷附答案详解

2021届河南省开封市高考物理三模试卷一、单选题(本大题共5小题,共30.0分)1.在电磁波谱中,频率不同的电磁波具有不同的特征.真空中,红外线、紫外线和X射线的波长由长到短排列顺序正确的是()A. X射线、紫外线、红外线B. X射线、红外线、紫外线C. 红外线、紫外线、X射线D. 紫外线、红外线、X射线2.一辆小汽车以12m/s的速度匀速行驶,当车头距路口停车线18m,时,绿灯还有3s时间将熄灭,司机因经验不足而刹车.在这3s内,汽车运动的v−t图象如图所示,下列说法正确的是()A. 小车在这3s内的平均速度为6m/sB. 小车刹车时的加速度大小为4m/s2C. 在绿灯熄灭时,该车的车头己越过停车线6mD. 至少应提前0.4s刹车才能在绿灯熄灭前不超停车线3.物体静止于光滑水平面上,力F作用于物体上的O点,现要使合力沿着OO′方向,如图所示,则必须同时再加一个力F′,如F和F′均在同一水平面上,则这个力的最小值为()A. FcosθB. FsinθC. FtanθD. Fcotθ4.如图所示,质量为m的竖直光滑圆环A的半径为R,固定在质量为m的木板B上,木板B的左右两侧各有一竖直挡板固定在地面上,B不能左右运动,在环的最低点静止放有一质量为m的小球C,现给小球一水平向右的瞬时速度v,使小球C在圆环内侧做圆周运动,某时刻木板离开水平面。
重力加速度为g,则小球的初速度v应满足()A. v≥√6gRB. v≥√7gRC. v≥√5gRD. v≥√3gR5.在如图所示的U−I图像中,直线a为某电源的路端电压与电流的关系,直线b为某电阻元件的电压与电流的关系。
现用该电源直接与元件连接成闭合电路。
则此时A. 电源将其它能转化为电能的功率为18WB. 该元件的电阻为2ΩC. 该元件发热功率为6WD. 电源外电路与内电路消耗功率之比为2:3二、多选题(本大题共5小题,共27.0分)6.图中虚线是某电场的一组等势面.两个带电粒子从P点沿等势面的切线方向射入电场,粒子仅受电场力作用,运动轨迹如实线所示,a、b是实线与虚线的交点.下列说法正确的是()A. 两粒子的电性相反B. a点的场强小于b点的场强C. a点的电势高于b点的电势D. 与P点相比两个粒子的电势能均减小7.四个质量相同的物体a、b、c、d,a做匀速直线运动、b做匀速圆周运动,c做匀减速直线运动,d做平抛运动,其中()A. 速度保持不变的仅是物体aB. 加速度保持不变的仅是物体bC. 动能保持不变的仅是物体a、bD. 动量保持不变的仅是物体b、c、d8.如图所示,两块相对的平行金属板M、N与电池相连接,N板接地,在距两板等远的一点P固定一个带正电的点电荷,如果将M板向上平移一小段距离,则A. 点电荷受到的电场力减小B. 点电荷受到的电场力增大C. 点电荷的电势能减小D. 点电荷的电势能保持不变9.下列说法正确的是()A. 液体表面层分子间距离大于液体内部分子间距离,故液体表面存在张力B. 悬浮在液体中的固体小颗粒会不停的做无规则的运动,这种运动是分子热运动C. 把很多小的单晶体放在一起,就变成了非晶体D. 恒温时压缩气体,气体分子与单位面积容器壁的碰撞次数变多E. 在绝热条件下压缩气体,气体的内能一定增加10.一列简谐横波沿x轴正方向传播,t=0时刻的波形如图所示。
2021届开封高级中学高三英语三模试题及参考答案

2021届开封高级中学高三英语三模试题及参考答案第一部分阅读(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、D四个选项中选出最佳选项AAmid the coronavirus outbreak, the U. S. Department of Homeland Security recommends having at least a two - week supply of water and food.PotatoesShelf life:2 to 5 weeks if stored in a cool, dry, dark placeYukon Gold, red, and fingerling potatoeswill last from two to three weeks. Larger white potatoes can last for three to five weeks. Sweet potatoes have about the same shelf life. Don't store them next to onions, however. The two might go together well in cooking, but raw, each gives off gases and moisture that might cause the other to spoil faster.Tea※Shelf life:6 to 12 months past "sell - by" dateDried tea leaves, whether loose (in a sealed container) or in teabags (in an unopened box) can easily last a year or more if they' re not subjected to damp or humidity. However, the tea does tend to lose flavor over time.Peanuts● Shelf life:1 to 2 monthsPeanuts in their shell, especially when kept cool and dry, are perfectly happy in the cupboard for as long as two months.Canned fruits and vegetables● Shelf life:1 to 2 years past "sell - by” dateCanning is an extremely efficient means of preserving food. Generally speaking, if canned foods aren't subjected to extreme heat, their contents should stay good for two years or more. Be aware, however, of dented cans or those with swollen tops, which may indicate the presence of bacteria inside.1. Which can go bad faster if stored with onions?A. Potatoes.B. Tea.C. Peanuts.D. Canned fruits and vegetables.2. What is special about tea?A. The flavor of tea can always remain the same.B. Tea leaves are better to be preserved in an open jar.C. Tea leaves should be kept away from the state of being wet.D. The maximum length of time that tea can be stored is 6 months.3. What may shorten the "sell - by” date of canned foods ?A. Shapes of cans.B. Categories of foods.C. Decline of the temperature.D. Exposure to high temperature.BDogs are often referred to as “man's best friend”. But MacKenzie, a four-pound Chihuahua (奇瓦瓦狗), who was named winner of the 2020 American Hero Dog competition, is making the world a better place for humans and animals alike. Often called the “Oscars for dogs”, the award recognizes dogs who make great contributions to society.This year's competition attracted over 400 competitors from across the country. While all were impressive, it was tiny MacKenzie who won the judges' hearts. Born at a rescue shelter in Hilton, New York, in 2013, she had a cleft palate (腭裂) that required her to be tube fed for the first year of her life. A life-saving operation, performed in 2014, gave her the ability to eat and drink independently, enabling the tiny dog to focus on doing what she loved most: taking care of others.The seven-year-old Chihuahua is now gainfully “employed” by the Mid Foundation, a Rochester, New York-based non-profit organization that shelters and cares for animals born with disabilities. MacKenzie's official job is “to provide love and care for baby rescue animals born with birth defects”. The Chihuahua is good at her job and hasnurturedmany different species-from puppies to kittens to turkeys, squirrels, birds and even a goat. She acts as their mother and teaches them how to socialize, play, and have good manners.In addition to her role as an animal caretaker, MacKenzie also has the important job of greeting the foundation's volunteers and friends. The incredible dog, who has lost her ability to bark, also visits area schools to help children understand physical disabilities in both animals and people. Her heart-warming and inspiring story makes MacKenzie worthy of America's top dog honor!4. What made MacKenzie American Hero Dog?A. Being man's best friend.B. Her struggle with disabilities.C. Rescuing animals with disabilities.D. Her contributions to a better world.5. What can we infer about MacKenzie from Paragraph 2?A. Her growth path was not easy.B. She was deserted by her owner.C. She was operated on at two years old.D. She still needs taking care of by others.6. What does the underlined word “nurtured” in Paragraph 3 mean?A. Trained.B. Comforted.C. Tended.D. Abused.7. Which can be a suitable title for the text?A. MacKenzie—The Most Hard-working DogB. MacKenzie—America's “Most Heroic Dog”C. Chihuahua—Inspiration of Positive EnergyD. Chihuahua—Appeal for Animals' ProtectionCParents and math teachers regularly asked by their school-aged charges whether math matters inreal life now have an answer.In a study published by the National Bureau of Economic Research this week, Harvard Kennedy School Policy Professor Joshua Goodman took a look at what happened to students whose high schools were required in the 1980s to increase the minimum level of coursework required to graduate. What he found is that the students were more likely to increase the number of math courses they took as a result of the change in standards and that translated into higher earnings down the line.Put simply: About 15 years after they graduated, the high school graduates who went to school when these changes took effect saw their average earnings increase about 10% for every extra year of math coursework. The findings may add fuel to the steady drum of education experts, policy makers and others calling for an increased focus on science and math education.The increase in required math courses didn’t necessarily produce rocket scientists, Goodman notes, because the extra coursework wasn’t at a particularly high level. But becoming familiar with and practicing ly basic math skills allowed high school graduates to pursue and excel at jobs that required some level of computational knowledge, he said.Goodman acknowledged that the earnings boost for the students connected with the up tick (上升)in math education may be dependent on the state of the economy. When Goodman checked in the late 1990s and early 2000s on the earnings of the students who graduated in the late 1985,he found that their earnings increased significantly if they took more math.8. What does Joshua Goodman’s study find?A. High school graduates earn more.B. High school students prefer math.C. Math matters a lot in one’s income.D. Math is a compulsory course in school.9. Why is increase in required math courses useful?A. It produced rocket scientists.B. It makes high school students smarter.C. It meets the requirements of the government.D. It enables high school graduates to get better jobs.10. What might be the author’s purpose in writing the text?A. To give a warning to policy makers.B. To seek help for high school students’ problems.C. To show the great importance of learning math.D. To tell a struggling history of high school students.11. What could be the best title for the text?A. Efforts matter mostB. Math makes moneyC. Earnings of different graduatesD. Changes of high school coursesDLas Vegascity inNevadais built in a desert. The city may be known to the outside world for its partying. But officials have found that there are 21 square kilometers of useless grass. The grass is never laid on, played on or even stepped on. The grass is only there to look nice.Now, the city is asking theNevadastate legislature to ban useless grass. It is trying to become the first place inAmericato ban that kind of grass often seen between streets, in housing developments and in office parks.It is estimated that useless grass makes up 40% of all the grass inLas Vegasand it needs a lot of water to survive. Grass needs four times more water than dry climate plants like cactus. By tearing out the grass, the city could reduce yearly water usage by 15%.In 2003, the Southern Nevada Water Authority banned developers from planting grass in front of new homes. It also offered homeowners $ 30 for each square meter of grass they tear out. But fewer people are now using the program. Water usage has increased in southernNevadaby 9% since 2019. And last year,Las Vegaswent a record 240 days without major rainfall. The Colorado River provides much ofNevada's drinking water. The river could losemore water as climate change affects it.Water officials in other dry cities said water usage needs to be reduced. But they fear the reaction to reforms like the ones inLas Vegasif their communities do not accept them. Cynthia Campbell is the water resources adviser for the city ofPhoenixinArizona. “There might come a point when city restrictions get too severe for some residents. They'll say that is the point of no return for them,”Campbellsaid. “For some people, it's a pool. For some people, it's grass.”12. Why doesLas Vegascity try to ban useless grass?A. To protect the local people.B. To beautify the city.C. To reduce water usage.D. To reduce waste.13. What program was carried out inLas Vegasin 2003?A. Allowing planting grass before new houses.B. Encouraging the residents to tear out grass.C. Praising those who signed on the program.D. Awarding those who reduced water usage.14. What is implied inCampbell's words in the last paragraph?A. Many residents won't follow the ban.B. Reaction to the reform will vary personally.C. Other measures should be taken to protect wetter.D. Water officials should take many factors into account.15. What is the best title for the text?s VegasPlans to Ban Useless GrassB. A Method Is Adopted to SaveLas VegasC. Choices between Beauty and PracticeD. Grass Is Important but Useless inLas Vegas第二节(共5小题;每小题2分,满分10分)阅读下面短文,从短文后的选项中选出可以填入空白处的最佳选项。
2021年开封高中高三英语三模试卷及答案

2021年开封高中高三英语三模试卷及答案第一部分阅读(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、D四个选项中选出最佳选项AMy Biggest ChallengeAs a writer on an adventure sports magazine, I’dalways fought shy of doing the adventurous stuff myself, preferring instead to observe the experts from a safe distance and relay their experiences to readers in the form of written language. Thus, when I was challenged to take part in a mountain climb in aid of raising money for charity-and to write about it afterwards-I was unwilling, to say the least.I was lucky enough to have a brilliant climbing coach called Keith, who put me through my paces after my daily work. He gave me knowledge about everything from the importance of building muscle groups to how to avoid tiredness through nutrition. It quickly became apparent that the mechanics of climbing were more complex than I had imagined. There was the equipment and techniques I’d never even heard of, all of which would come in handy on the snow-capped peak I’d be climbing.Aware of the challenge, Keith made a detailed action plan and I forced myself to stick to it, doing a daily workout at the gym and going on hikes with a heavy pack. I perfected my technique on the climbing wall and even went to climb the mountains to get vital experience. My self-belief increased alongside my muscle power and I became confident about finishing the climb.All too soon I was on a plane to my destination. On that day, when I looked up at the mountain, I thought of abandoning it. But then I remembered all the hard work I’d done and how disappointed Keith would be if I gave up at the last minute-not to mention letting down the charity and the sense of failure I’d experience myself. With a deep breath I gathered my equipment and headed out into the sunshine to meet the rest of the group.And as I sit here now, tapping away on my laptop, I’m amazed at the details in which I can recall every second of the climb: the burning muscles, the tiredness, the minor problems along the way. Could I have been better prepared? Possibly. Would I be back for another go? Thankfully not. The feeling of being excited when I stood on top of the world is a never-to-be-repeated experience but one I will enjoy forever nevertheless.1. At the beginning of the activity, the author revealed his ______.A. disappointment in the coming adventure.B. expectation of writing about his experience.C. lack of enthusiasm for the challenge he’d been offered.D. curiosity about taking part in the mountain climb for charity.2. What did the author realise during his climb training?A. The knowledge about climbing was really confusing.B. The equipment was the key factor to reach the peak.C. Climbing was much more complicated than expected.D. Hard training was far more important than making plans.3. How did the author feel after he succeeded in climbing the mountain?A. He was relieved that he wouldn’t have to do it again.B. He was well satisfied that he had done his best for it.C. He was surprised that he had managed to complete it.D.He was regretful that it wasn’t as smooth as imagined.BBrian Hamilton's life changed in a prison when he went there with his friend, Reverend Robert J. Harris, who often went to local prisons to do ministry work. During the visit,Hamiltonstarted talking to one of the prisoners and asked what he was going to do when he got out. “He said he was going to get a job,”Hamiltonrecalls. “I thought to myself, wow, that’s going to be difficult with a criminal background.”The conversation madeHamiltonconsider how to help those who came out from prison. Finally in 2008, 16 years after that initial conversation,Hamiltoncreated Inmates to Entrepreneurs, a nonprofit organization that helps people with criminal backgrounds start their own small businesses.At the time,Hamiltonwas building his own company, a software technology company for the banking industry. As his company grew, so didHamilton’s time devoted to giving lessons to prisoners. He averaged three to four courses a month at prisons throughoutNorth Carolina.Eventually,Hamiltondecided to shift his focus to his true passion. In May 2019, he sold his company and focused on helping those who were imprisoned. His online courses will be set next year. “By March 1, 2022, anyone will be able to access the courses, either to become a certificated instructor or to access it for themselves as a prisoner or part of the general population,”Hamiltonexplained. In addition, he visits middle schools and presents the course to at-risk students as a preventative measure against crime.The free course is funded by the recently established Brian Hamilton Foundation, which offers assistance to military members as they return to civilian life and provides loans o small businesses. “Starting up a business isn'tfor everyone, but if we make opportunities available, and let people know that other people care about them, it makes a difference.”Hamiltonsaid.4. Why did Brian Hamilton went to a prison?A. He accompanied his friend.B. He took lessons in the prison.C. He wanted to get a job in the prison.D. He had a friend who was in prison.5. What can be inferred about Inmates to Entrepreneurs?A. It often assists military members.B It provides loans to small businesses.C. Its course has been largely broadened.D. It is an organization intended for business men.6. According to the author, which of the following best describesHamilton?A. He is a man who always changes his mind.B. He has a sense of social responsibility.C. He is good at running a big company.D. He makes money by giving lessons.7. What is the main idea of the text?A. A man made a fruitless visit to the prison.B. A man sold his business to teach prisoners.C. A man realized his dream of being a teacher.D. A man successfully created two organizations.CLike all cultural institutions, galleries and art fairs are adapting to a new reality.Art Basel Hong Kong, Asia's biggest contemporary-art fair, was cancelled because of covid-19, but anyone he who had planned to visit last week could enjoy an experimental alternative:the viewing room. At the click of a keyboard) you could enter an overall view but private visual salon, without having to brave the airless Hong Kong Convention and Exhibition Centre.There, on one webpage, was Jeff Koons riffing(翻唱)on Botticelli's "Primavera" in a tribute to the history of painting at David Zwirner Gallery. Ota Fine Arts offered one collector the chance to acquire an "infinity(无限)room“, one of the most Instagrammed artworks of recent years- the creation of the fantasies,nonagenarian (九十多岁) Japanese artist, Yayoi Kusama. White Cube presented a large collection of international works by Andreas Gursky (German), Theaster Gates (American) and Beatriz Milhazes (Brazilian). But not every artist, gallery and form showed to equal advantage in this alternative fair. Not surprisingly, simple two-dimensional works in brightcolours came across best No sculpture or conceptual art was includedBesides depth and texture, there are aspects of gallery hopping that a website is unlikely to copy. One isserendipity—the sense of wandering between artworks and encountering the unexpected. Another is sociability. Art is a communion between artist and viewer, but galleries and fairs are also places to swap opinions and share enthusiasms.Thereare ways to compensate (or these inevitable(不可避免的)disadvantages. As they shut their physical doors, some of the world's nest galleries and museums are offering advanced interactive visits, 360 degree videos and walk around tours of their collections, allwithout queues and high ticket prices. One of the best is laid on by the Rijksmuseum in Amsterdam;its tour allows visitors to view its Vermeers and Rembrandts, including the magnicent "Night Watch”, far more closely than would normally he possible. Another standout offering is from the Museu de Arte de SPaulo, which has an even broader collection. On its virtual platform, its pain tings, spanning 700 years, appear to be hanging in an open-plan space, seemingly hung on glass panels, or "crystal easels” as the. museum calls them, ideal for close-up inspection,8. From the paragraph 3, we may knowA. "Primavera" was originally painted by JeKoonsB.“innity room” was the most popular artworks of recent years on social mediaC. White Cube displayed a great many works by artists from different nationsD. Various paintings and statues showed on the webpage are well-received9. What does the underlined word "serendipity" in Paragraph 4 probably mean?A. surpriseB. treasureC. expectationD. compromise10. What is the purpose of writing the last paragraph?A.To introduce some popular art show in the world.B. To show that there are some alternative ways to promote the display during covid-19 epidemic.C. To prove that paintings hung on glass panels can be idealfor close-up inspection,D. To release some information about some extraordinary art shows.11. What is the best title?A. Art beyond the internet.B. Fascinating art.C. Art under covid-19.D. gallery hoppingDA crew(全体成员)of six teenage girls completed a nine-day sailing trip in the US recently, after havingseasickness and strong winds.For the past three years, the Sea Cadet teenagers whoset sail were all male. Roger Noakes, who captained(担任队长)the boat, said this was the first time he’d taken out an all-female crew.The girls asked for an all-girls trip in August this year. The crew set sail along with three adults, Noakes and two Sea Cadet representatives. The original plan was for the girls to sail 24 hours a day in rotating shifts(轮流换班)along the coast and then return. Things turned out differently, however. “The first night was difficult because the wind was really hard. The waves were going up and down,” said Abby Fairchild,16. “Everybody got seasick.” Noakes gave the girls the choice of just sailing in the bay and not going into open water. “But they decided they were going.”The teenagers then sailed a long way overnight and slept in shifts. “We’ve learned everything from controlling the boat to putting up the sails while we have rough seas,” said 15-year-old Olivia Wilcox.The teenagers stopped on land in Massachusetts. They didn’t make it to their original destination(目的地)in Maine, where they were supposed to have a celebratory dinner, due to the weather and winds. They said they weren’t disappointed, however, as they’d learned a lot. “They learned about boating, and above all, they built confidence and character,” said Noakes.12. What was special about the Sea Cadet trip this year?A. It was the longest sailing trip ever.B. It was the first all-female-crew sailing trip.C. It was the most dangerous sailing trip ever.D. It was the first sailing trip for teenagers.13. What happened on the crew’s first day of the trip?A. They all felt sick on the boat.B. Some of them were hurt.C. Their boat was out of control.D. They went into open water by mistake.14. Which of the following best describes these young sailors?A. Strong-minded and having a strong sense of teamwork.B. Hard-working and having great leadership skills.C. Understanding and creative.D. Adventurous and skillful.15. According to Noakes, what was the sailors’ greatest benefit from the trip?A. They knew the sea better.B. They made many friends.C. They got excellent sailing skills.D. They developed good personalities.第二节(共5小题;每小题2分,满分10分)阅读下面短文,从短文后的选项中选出可以填入空白处的最佳选项。
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河南省开封高中2021届高一下学期第三次质量检测英语试卷第I卷(选择题)第一部分听力理解(略)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。
AThe Ig Nobel Prizes praise research that makes you laugh and then think.The winners are allowed to make a one-minute speech with time kept by an eight-year-old! Every year,in Harvard's Sanders Theatre,people watch the winners step forward to accept their prizes.These are physically handed out by real Nobel laureates (获得者).Let's have a look at some of them.The Empty Bladder (膀胱) ExperimentFour researchers at Georgia Institute of Technology found that animals above 3 kg empty their bladders in about 21 seconds.What is the purpose of this study? The researchers hope this will help solve urinary (泌尿的) problems in animals.The Science of EggsA team of Australian scientists managed to get hard-boiled egg whites to become raw again.While it sounds silly,this research could have a serious influence on cancer (癌症) research. The Fascination with AnimalsCharles Foster and Thomas Thwaites from the UK shared the 2016 Ig Nobel Prize in Biology.Thomas chose to live like a goat and wrote about his experience in “GoatMan:How I Took a Holiday from Being Human”.Charles,on the other hand,spent some time in the wild,trying out the lives of many animals.He felt it gave him a chance to explore the world around us with more of our senses.Colors & HorsefliesA team from Hungary,Spain,Sweden and Switzerland won the 2016 Ig Nobel Prize in Physics.They studied why horseflies have less interest in white-haired horses.The team used handmade horses covered in glue.They found that dark colors attracted more flies because of how sunlight reflected (反射) off them.To the food searchers,it was a sign of food.This finding could explain the white coats of zebras too.21.Who give the Ig Nobel winners their prizes?A.Eight-year-olds. B.Harvard professors.C.Nobel Prize winners. D.Nobel Prize organizers.22.What did Charles Foster and Thomas Thwaites have in common?A.They shared the Ig Nobel Prize in Physics.B.Both their experiments centered on animals.C.They did their research in the same place.D.Both their experiments explored human senses.23.What does the underlined part “food searchers”refer to?A.Zebras. B.Horseflies.C.Handmade horses. D.White-haired horses.BMy beautiful new watch had run eighteen months without losing or gaining (走得快).But at last, one night, I forgot to wind it up (上发条)and it stopped running. The next day I stepped into the jeweler’s to set it by the exact time, and the head of the shop started to set it for me. Then he said, “She is four minutes slow — regulator (调节器)wants pushing up.” I tried to stop him —tried to make him understand that the watch kept perfect time. But no; he calmly and cruelly did the shameful deed.My watch began to gain. It gained faster and faster day by day. Finally I took it to the watchmaker to be regulated. He forced the watch open, and then said it wanted cleaning and oiling, besides regulating. After this, my watch slowed down to an unbearable degree. I began to miss trains and my dinner.At last, I took this instrument to another watchmaker. He said the kingbolt was broken. To tell the truth, I had no idea what the kingbolt was. He repaired it, but what the watch gained in one way it lost in another. It would run awhile and then stop awhile, and so on.So I went with a heavy heart to one more watchmaker. While I waited and looked on I presently recognized in this watchmaker an old acquaintance (熟人)—a steamboat engineer of older days, and not a good engineer, either.“She makes too much steam and...” he said.I gave him a heavy blow on the head and ran away.My uncle William used to say that a good watch was a good watch until the repairers got a chance to look at it. And he used to wonder what became of all the unsuccessful repairmen, and shoemakers, and engineers, and blacksmiths; but nobody could ever tell him.24.What did the author say about the jeweler?A. He made a mistake.B. He had a quick mind.C. He had a hearing problem.D. He was a quiet repairman.25. After being cleaned, oiled and regulated, the author’s watch.A. kept perfect timeB. gained faster and fasterC. was unbelievably slowD. ran awhile and stopped awhile26. Why did the author hit the watchmaker on the head?A. He was a liar.B. He was talking nonsense.C. He treated the watch cruelly.D. He was an old enemy of the author.27. What did the author learn from his experience?A. Never get a watch repaired.B. He should listen to his uncle.C. Repair work was not an easy job.D. Unsuccessful people exist in all walks of life.CIt's early morning,and Katie Smith hears a rooster crowing (报晓).It's time to get up and start working.She and her husband,Chris Cashen,start the day early.They own and run the Farm at Miller's Crossing,in Hudson,New York.With the help of 10 workers and,sometimes,the Cashen kids—Lael,12,Connelly,10,AnneMae,8,and Christopher John,6 —Smith and Cashen harvest crops during much of the year.They grow vegetables and other plants.They also raise and care for some animals.Because the Farm at Miller's Crossing grows different kinds of crops,Cashen says the biggest challenge (挑战) is timing.Several times a year,workers prepare the soil and plant crops.At other times,they transfer (转移) plants from the greenhouse into the fields.The farmers store the fall vegetables in coolers and sell them throughout the winter.Cashen and Smith grow their crops without the use of chemicals.When crops are ready to be harvested,workers pick them daily,wash them,and put them in boxes.In June,they work up to 70 hours a week.As fall nears,workers try to finish the daily harvesting while there is still daylight.The crops are sold through programs that provide buyers with fresh produce weekly.Living on a farm has its perks.The Cashen kids swim in a river from which the crops get their water.They ride their bikes in wide-open spaces.When harvesting tomatoes,they sometimes have exciting tomato fights.They have a big family with which to share their adventures.Everyone takes part in the business.The kids feed the horses.The boys care for the el says she likes transferring plants and selling produce.“It's fun and really busy,” says Lael,“but it's just a part of life.”28.What can we learn about the Cashen family?A.They look needy.B.They lead a busy life.C.They live on selling animals.D.They do all the work on their own.29.What's the most difficult thing on the Farm?A.Storing the fall vegetables.B.Growing crops as fast as possible.C.Moving plants out of the greenhouse.D.Planning when to plant and harvest.30. What does the underlined word “perks” in Paragraph 5 mean?A.Price. B.Reasons.C.Discomfort. D.Advantages.31. What is Lael's attitude toward her life on the Farm?A.She enjoys it. B.She is proud of it.C.She is uninterested in it. D.She feels unsatisfied with it.DCarmakers now allow drivers to make phone calls, use email, and text, etc. Cars used to have a few buttons(按钮). Some cars now have as many as 50 buttons.“It’s adding complex(复杂的)information at drivers’ fingertips without often considering whether it’s a good idea to put it at their fingertips,’’ University of Utah professor David Strayer said. That complexity increases the time drivers spend trying to use the systems, The car industry says that mobile phones are not allowed while driving and navigation devices (导航设备)were not made to be used while driving. But the systems “are developed to be used in the driving environment and require drivers’ attention that is comparable to turning on the radio, which has always been considered acceptable behavior while driving,” said Wade Newton, a spokesman for the Alliance of Automobile Manufacturers.But Jake Nelson, AAA’s director for traffic safety research, said drivers testing all 30 of the 2017 model year cars took their eyes off the road and hands off the wheel while using the systems. The test drivers touch screens and other technologies to make calls, send texts, turn on the radio, or program navigation all while driving.Researchers said 23 of the 30 cars were considered “very high” or “high” in terms of the attention they required from drivers. It takes drivers about 40 seconds to program navigation systems. Research made before has shown that drivers who took their eyes from the road for just two seconds double their risk of a crash.In 2012, the National Highway Traffic Safety Administration made voluntary safety guidelines to carmakers. The guidelines suggest that automakers lock out the ability to program navigation systems while a car is moving. However, the ability to program navigation while driving was allowed in 12 cars in the study. The guidelines also suggest carmakers prevent drivers from texting while driving, but three-quarters of the cars tested allow drivers to text while te car is moving.32.What was David Strayer’s attitude toward the systems?A. He was interested in them.B. He was hopeful of them.C. He was uncertain about them.D. He was dissatisfied with them.33.What did Wade Newton say about the systems?A. They were good choices for drivers.B. They couldn’t be used while driving,C. They were unacceptable to the public.D. They were mainly used for navigation.34.Which of the following might Jake Nelson agree with about the systems?A. They were risky but worthwhile.B. They were quick and easy to use.C. They saved drivers a lot of money.D. They increased the risk of accidents.35.What can be inferred about voluntary safety guidelines?A. They are quite welcome.B. They are not properly made.C. They are not strictly followed.D. They are very helpful to drivers.第二节(共5小题;每小题2分,满分10分)根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。