天津市耀华嘉诚国际中学2019-2020学年度第二学期线上学习阶段性评估检测八年级数学试卷

耀华中学高二年级语文学科居家学习网上测试试卷（共100分）一、基础选择题：（每题3分，共45分）阅读下列文字，完成下面小题。

热力学第二定律说，一切孤立系统都朝着熵增的方向，这是大前提。

但生命的神奇就在于，生命通过同环境交换物质与能量，为自己制造“负熵”，并向环境释放“正熵”，以秩序．．。

同样，由个人有机组成的共同体，也必须持续制造或有效输入“负．．来对抗无序与混乱熵流”、有力“正熵流” 的生成，并令“负熵”足以抵消“正熵”而有余，才能健壮强轫．．的共同体。

她需要每一个你付出，需要．．、维持向上的活力。

这个国度就是你我所依恃每一个你贡献无数涓滴．．．．的容颜与活力。

．．“负熵”，才能永保青春目光锁定那更美好的未来，你一直在努力，我们一直在呐喊。

唯有每一个普通人的行动与努力带来的每一个涓滴改进，汇入历史的江河，才是最强大的“熵减”力量。

“天下之至柔，驰骋．．天下之至坚”，这就是柔韧的力量。

每一个涓滴改进，每一处“熵减”，都不应是，而应是义之所在;都不应是高不可攀．．．．可以触及。

小人物从来不．．．．，而应是踮起脚尖是大时代的被动接受者，每一个小人物的参与．．和行动，汇成大时代的洪流；每一个小人物的祈望．．成长。

．．与呐喊，汇成大时代的最强音；每一个小人物的涓滴“熵减”，汇成大时代的茁壮1. 文中加点的字音和字形，全都正确的一组是（）A. 秩序混乱(hǔn) 强轫B. 依恃(shì) 涓滴(juān) 永保青春C. 驰骋高不可攀踮起脚尖(diǎn)D. 参与(yù) 祈望(qǐ) 茁壮2. 依次填入文中横线处的词语，最恰当的一组是（）A. 演化控制强人所难B. 演变抑制勉为其难C. 演化抑制强人所难D. 演变控制勉为其难【答案】1. C 2. C【1题详解】本题主要考查识记并辨析现代汉语中常见汉字的读音和字形的能力。

解答本题时，要结合平时积累的字音、字形知识技巧进行辨析，平时要关注同义词、近义词、形近字、音同音近字的积累。

天津市耀华嘉诚国际中学2019-2020学年第二学期线上学习阶段性评估检测高二年级语文试卷第Ⅰ卷一、基础知识。

（16分，每题2分）1、下列各组中加点词语的读音无误的一组是（）A．曲肱．（gōng）社稷．（jì）稽．首（jī）鲜．克有终（xiǎn）B．踰矩．（jǔ）弑．君（shì）信禀．（bǐng）什伯．之器（bǎi）C．远徙．（xǐ）戚戚．．（qī）忿懥．（zhì）观其徼（jiǎo）D．孝悌．（tì）舟舆．（yú）布橐．（tuó）靡．不有初（mǐ）2、下列各项中没有错别字的一项是（）A.驰骋正言若反憔悴气如悬丝B.敖惰无为而治典籍灯火澜珊C.褒贬格物致知哀矜血气方钢D.梵语克己复理信禀矫柔妆束3、下列加点词的解释，不正确的一项是（）A．中庸其．至矣乎其，表揣测语气B．敏于事而慎于言，就．有道而正焉就：就是C．甘其食，美．其服。

美：使……觉得美D．率．性之谓道率，遵循，按照。

4、下列各句句式不相同的一项（）Ａ.彼且奚适也？Ｂ.天下未之有也。

Ｃ.柔之胜刚，天下莫不知。

Ｄ.何以利吾家？5、读下文，选出画线文句翻译正确的一项()大学之道（1），在明明德（2），在亲民（3），在止于至善。

知止（4）而后有定，定而后能静，静而后能安，安而后能虑，虑而后能得（5）。

物有本末，事有终始。

知所先后，则近道矣。

A.大学的根本宗旨在于弘扬光明正大的品德；在于使人亲近；在于使人停止“至善”。

B.大学的根本宗旨在于弘扬光明正大的品德；在于使人弃旧图新、去恶从善；在于使人知道要达到的最高境界“至善”。

C.大学的根本宗旨在于明白德育；在于使人弃旧图新、去恶从善；在于使人知道要达到的最高境界“至善”。

D.大学的根本宗旨在于弘扬光明正大的品德；在于使人弃旧图新、去恶从善；在于到达善良之地。

6、“在中国传统教育里，最重要的是‘四书’，”一句中“四书”指的是（）A．《诗经》《尚书》《礼记》《易经》B．《大学》《中庸》《论语》《孟子》C．《春秋》《论语》《孟子》《礼记》D．《韩非子》《列子》《孟子》《庄子》7、下列各项表述不正确的一项是（）A.《论语》所体现的孔子儒家思想的核心是“仁”。

天津市耀华嘉诚国际中学2019-2020学年八年级下学期线上学习阶段性评估检测语文试题（PDF版）天津市耀华嘉诚国际中学2019—2020学年度第二学期线上学习阶段性评估检测八年级语文试卷第Ⅰ卷（50分）一、选择题（每小题2分，共50分）1.下列加点字注音正确的一项是A. 凫．水（fú）枸杞．(jǐ) 连翘．（qiào）戛．然而止(jiá)B. 糜．子（mí）锵．然(qiāng) 山麓．（lù）恣．意妄为(zì)C. 狩．猎（shǒu）两栖．（qī）窈．窕（yǎo）如法炮．制(páo)D. 褶．皱（zhě）幽悄．（qiǎo）俶．尔（chù）追本溯．源（sù）2. 下列词语中书写有误的一项是A. 燎原雾霭人情世故B. 躁热元霄翠羽流苏C. 辐射晦暗富贵荣华D. 严峻褪色叹为观止3.依次填入下列句中空缺处的词语恰当的一项是①加快实施教育扶贫工程，让贫困家庭子女都能接受公平有质量的教育，贫困代际传递。

②在实现中华民族伟大复兴的新征程上，应对重大挑战、重大风险、解决重大矛盾，迫切需要迎难而上、挺身而出的担当精神。

③当的现代社会与传统文化有了一次次美丽的“邂逅”，中华文化基因逐渐苏醒，这危机中的微熹，弥足珍贵。

A．阻挠抵制喧嚷 B．阻挠抵御喧嚣C．阻断抵御喧嚣 D．阻断抵制喧嚷4.下列语句中没有语病的一项是A.《舌尖上的中国》这部风靡海内外的纪录片，用镜头展示烹饪技术，用美味包裹乡愁，给观众带来了心灵的震撼。

B.川航机组突遇险情，成功备降，强烈地震撼着网友的心，纷纷为他们的专业素养点赞。

C.为了提高优秀传统文化特色，学校举办了“寻找家乡名人名画”的活动。

D.性格懦弱的李娟的母亲，面对突如其来的家庭变故，表现出了异常的坚韧。

5.下列句子中的标点符号使用有误的一项是A.姑苏城与金鸡湖，是苏州的双面绣：一面是古老的斑斓，一面是现代的辉煌！B.第四届世界互联网大会12月3日至5日举行，主题为《发展数字经济促进开放共享——携手共建网络空间命运共同体》。

2019-2020学年天津市耀华中学高一下学期期中数学试卷一、单选题（本大题共12小题，共60.0分）1. 下列各组向量中，能作为平面内一组基底的是( )A. e 1⃗⃗⃗ =(0,2)，e 2⃗⃗⃗ =(0,−1)B. e 1⃗⃗⃗ =(2,1)，e 2⃗⃗⃗ =(0,0)C. e 1⃗⃗⃗ =(3,1)，e 2⃗⃗⃗ =(5,53) D. e 1⃗⃗⃗ =(−2,1)，e 2⃗⃗⃗ =(4,2)2. 化简：AB ⃗⃗⃗⃗⃗ −CB ⃗⃗⃗⃗⃗ +CD ⃗⃗⃗⃗⃗ −ED ⃗⃗⃗⃗⃗ −AE ⃗⃗⃗⃗⃗ =( )A. 0⃗B. AB ⃗⃗⃗⃗⃗C. BA ⃗⃗⃗⃗⃗D. CA ⃗⃗⃗⃗⃗ 3. 以下给出了5个命题(1)两个长度相等的向量一定相等；(2)相等的向量起点必相同；(3)若a ⃗ ⋅b ⃗ =a ⃗ ⋅c ⃗ ，且a ⃗ ≠0⃗ ，则b ⃗ =c ⃗ ；(4)若向量a ⃗ 的模小于b ⃗ 的模，则a ⃗ <b⃗ ． (5)若b ⃗ =c ⃗ ，且a ⃗ ≠0⃗ ，则a ⃗ ⋅b ⃗ =a ⃗ ⋅c ⃗(6)与a ⃗ 同方向的单位向量为a⃗ |a ⃗ |其中正确命题的个数共有( ) A. 3 个 B. 2 个 C. 1 个 D. 0个4. 以下数据为参加数学竞赛决赛的15人的成绩：(单位：分)78，70，72，86，88，79，80，81，94，84，56，98，83，90，91.则这15人成绩的第80百分位数是( )A. 90B. 91.5C. 91D. 90.5 5. 已知a ，b ∈R ，i 是虚数单位，若(1+i)(1−bi)=a ，则a b 的值为( )A. 2B. 3C. 4D. 56. 已知向量a ⃗ =(1,1),2a ⃗ +b ⃗ =(4,3),c ⃗ =(x,−2)，若b ⃗ //c ⃗ ，则x 的值为( )A. 4B. 2C. −4D. −27. 已知向量a ⃗ =(1,−3)，b ⃗ =(3,m)，若a ⃗ ⊥b ⃗ ，则|2a ⃗ +b⃗ |等于( ) A. 10 B. 16 C. 5√2 D. 4√108. 若|m ⃗⃗⃗ |=2，m ⃗⃗⃗ ·n ⃗ =8，m ⃗⃗⃗ ，n ⃗ 的夹角为60°，则|n ⃗ |的值为( )A. 5B. 6C. 7D. 89. 若z 是复数，且(3+z)i =1(i 为虚数单位)，则z 为( )A. −3+iB. 3+iC. −3−ID. 3−i10. 在平面四边形ABCD 中，AC =2，BD =1，则(AB ⃗⃗⃗⃗⃗ +DC ⃗⃗⃗⃗⃗ )⋅(CA ⃗⃗⃗⃗⃗ +DB⃗⃗⃗⃗⃗⃗ )=( ) A. 5B. −5C. −3D. 3 11. 1−2sin 2π8的值等于( ) A. 0 B. 12 C. √22 D. √3212. 已知向量m⃗⃗⃗ =(−1,2)，n ⃗ =(1,λ)，若m ⃗⃗⃗ ⊥n ⃗ ，则m ⃗⃗⃗ +2n ⃗ 与m ⃗⃗⃗ 的夹角为( ) A. 2π3 B. 3π4 C. π3 D. π4 二、单空题（本大题共6小题，共30.0分）13. 某校高一、高二和高三年级学生的人数比为2：2：1，用分层抽样的方法从全体学生中抽取1个容量为45的样本，则高一年级抽取的学生数为______ 人．14. 某校从高一年级学生中随机抽取100名学生，将他们期中考试的数学成绩(均为整数)分成六段：[40,50)，[50,60)，…，[90,100]后得到频率分布直方图(如下图所示)，则这100名学生的平均成绩为__________．15. 计算：(1+i)(1−i)+(1+2i)2=_______________．16. 在△ABC 中，a =3，b =2，A =30°，则cosB = ______ ．17. 在△ABC 中，AB =AC ，BC =4，则BA ⃗⃗⃗⃗⃗ ⋅BC ⃗⃗⃗⃗⃗ =________．18. 在△ABC 中，若BC ⃗⃗⃗⃗⃗ ·BA ⃗⃗⃗⃗⃗ +2AC ⃗⃗⃗⃗⃗ ·AB ⃗⃗⃗⃗⃗ =CA ⃗⃗⃗⃗⃗ ·CB ⃗⃗⃗⃗⃗ ，则sinA sinC的值为______ ． 三、解答题（本大题共1小题，共10.0分）19. 在△ABC 中，内角A ，B ，C 所对的边分别为a ，b ，c ，sinB(acosB +bcosA)=√3ccosB ．(1)求B ；(2)若b =2√3，△ABC 的面积为2√3，求△ABC 的周长．【答案与解析】1.答案：D解析：本题主要考查平面向量基本定理，基底的定义，属于基础题．判定两个向量是否不共线即可．解：A 中，e 1⃗⃗⃗ =−2e 2⃗⃗⃗ ，所以向量e 1⃗⃗⃗ 与e 2⃗⃗⃗ 共线，不能作为一组基底;B 中，e 2⃗⃗⃗ 为零向量，所以e 1⃗⃗⃗ 与e 2⃗⃗⃗ 共线，不能作为一组基底;C 中，e 1⃗⃗⃗ =35e 2⃗⃗⃗ ，所以向量e 1⃗⃗⃗ 与e 2⃗⃗⃗ 共线，不能作为一组基底;D 中，向量e 1⃗⃗⃗ 与e 2⃗⃗⃗ 不共线，可以作为一组基底．故选D ．2.答案：A解析：本题主要考查了向量的加减运算，属于基础题．根据向量的加减运算法则计算可得．解：AB ⃗⃗⃗⃗⃗ −CB⃗⃗⃗⃗⃗ +CD ⃗⃗⃗⃗⃗ −ED ⃗⃗⃗⃗⃗ −AE ⃗⃗⃗⃗⃗ =AB ⃗⃗⃗⃗⃗ +BC ⃗⃗⃗⃗⃗ +CD ⃗⃗⃗⃗⃗ +DE ⃗⃗⃗⃗⃗⃗ +EA ⃗⃗⃗⃗⃗ =0⃗ ． 故选A ．3.答案：B解析：解：两个向量相等的充要条件是大小相等且方向相同，所以两个长度相等的向量不一定相等，故(1)错误；两个向量只要大小相等且方向相同，就是相等向量，所以相等的向量起点可以不相同，故(2)错误；若a ⃗ ⋅b ⃗ =a ⃗ ⋅c ⃗ ，且a ⃗ ≠0⃗ ，则b ⃗ =c ⃗ 或a ⃗ ⊥b ⃗ 且a⃗ ⊥c ⃗ ，故(3)错误； (4)∵两个向量不能比较大小，∴a ⃗ <b ⃗ 不正确，故(4)错误；(5)由(3)可以得到(5)正确；(6)根据单位向量的定义可以(6)正确．故正确命题的个数为2个，故选：B．根据向量的物理背景与概念、数量积的概念逐个分析．本题考查向量的概念，两个向量的数量积的定义和性质，注意向量的数量积与实数的乘积的区别，正确理解向量相等的含义．4.答案：D解析：本题考查了一组数据的百分位数问题，是基础题．把该组数据从小到大排列，计算15×80%=12，即可求解．解：该组数据从小到大排列为：56，70，72，78，79，80，81，83，84，86，88，90，91，94，98.且15×80%=12，=90.5.所以这15人成绩的第80百分位数是90+912故选D．5.答案：A解析：本题考查复数的运算和复数相等的充要条件，属基础题，解：(1+i)(1−bi)=1−bi+i−bi2=1+b+(1−b)i，∵(1+i)(1−bi)=a，∴1+b+(1−b)i=a，即1+b−a+(1−b)i=0，∴{1+b−a=01−b=0，解得a=2，b=1，=2，∴ab故选A．6.答案：C可求出b⃗ =(2,1)，从而根据b⃗ //c⃗得出x+4=0，解出x=−4．考查向量坐标的减法和数乘运算，平行向量的坐标关系．解：b⃗ =2a⃗+b⃗ −2a⃗=(2,1)；∵b⃗ //c⃗；∴x+4=0；∴x=−4．故选C．7.答案：C解析：解：∵a⃗⊥b⃗ ，∴a⃗⋅b⃗ =3−3m=0，解得m=1．∴2a⃗+b⃗ =(5,−5)，则|2a⃗+b⃗ |=√25+25=5√2．故选：C．通过斜率的数量积求出m，利用斜率的模转化求解即可．本题考查斜率的数量积的应用，斜率的模的求法，是基本知识的考查、8.答案：D解析：本题考查向量数量积的运算，属于基础题.代入向量的数量积公式求解即可．解：因为，所以．故选D．9.答案：C解析：本题主要考查复数代数形式的混合运算，属于基础题．解：∵(3+z)i=1，∴z=1−3=−3−i，i10.答案：C解析：本题主要考查平面向量基本定理的应用，数量积，属于基础题．将所有向量全部用CA ⃗⃗⃗⃗⃗ ,DB⃗⃗⃗⃗⃗⃗ 表示即可求解． 解：(AB ⃗⃗⃗⃗⃗ +DC ⃗⃗⃗⃗⃗ )⋅(CA ⃗⃗⃗⃗⃗ +DB⃗⃗⃗⃗⃗⃗ ) =2AB ⃗⃗⃗⃗⃗ ⋅(CA ⃗⃗⃗⃗⃗ +DB⃗⃗⃗⃗⃗⃗ ) =2(12DB ⃗⃗⃗⃗⃗⃗ −12CA ⃗⃗⃗⃗⃗ )⋅(CA ⃗⃗⃗⃗⃗ +DB ⃗⃗⃗⃗⃗⃗ ) =|DB⃗⃗⃗⃗⃗⃗ |2−|CA ⃗⃗⃗⃗⃗ |2=−3故选C ． 11.答案：C解析：解：1−2sin 2π8=cos(2×π8)=cos π4=√22． 故选：C ．直接利用二倍角的余弦公式，特殊角的三角函数值即可化简得答案．本题考查二倍角的余弦，考查了特殊角的三角函数值，是基础题． 12.答案：D解析：本题考查了平面向量的数量积与夹角的计算问题，属于基础题．根据m⃗⃗⃗ ⊥n ⃗ 得m ⃗⃗⃗ ⋅n ⃗ =0，解得λ的值，再求m ⃗⃗⃗ +2n ⃗ 与m ⃗⃗⃗ 的夹角的余弦值，从而求出夹角大小． 解：∵m⃗⃗⃗ =(−1,2)，n ⃗ =(1,λ)，m ⃗⃗⃗ ⊥n ⃗ ， ∴m ⃗⃗⃗ ⋅n ⃗ =−1×1+2λ=0，解得λ=12，∴m ⃗⃗⃗ +2n ⃗ =(1,3)，∴(m ⃗⃗⃗ +2n ⃗ )⋅m ⃗⃗⃗ =1×(−1)+3×2=5，|m ⃗⃗⃗ +2n ⃗ |=√12+32=√10，|m⃗⃗⃗ |=√(−1)2+22=√5．设m⃗⃗⃗ +2n⃗与m⃗⃗⃗ 的夹角为θ，则cosθ=(m⃗⃗⃗ +2n⃗⃗ )⋅m⃗⃗⃗|m⃗⃗⃗ +2n⃗⃗ |×|m⃗⃗⃗ |=√10×√5=√22，，∴m⃗⃗⃗ +2n⃗与m⃗⃗⃗ 的夹角为π4．故选：D．13.答案：18解析：由某校高一、高二和高三年级学生的人数比为2：2：1，用分层抽样的方法从全体学生中抽取1个容量为45的样本，能求出高一年级抽取的学生数．本题考查分层抽样的应用，解题时要认真审题，是基础题．解：∵某校高一、高二和高三年级学生的人数比为2：2：1，用分层抽样的方法从全体学生中抽取1个容量为45的样本，∴高一年级抽取的学生数为：45×22+2+1=18(人)．故答案为：18．14.答案：71解析：本题考查利用频率分布直方图求平均数，属于中档题．首先求出a的值，然后计算平均数．解：由题意可知：a=1÷10−0.01−0.015−0.015−0.025−0.005=0.03，x=45×0.01×10+55×0.015×10+65×0.015×10+75×0.03×10+85×0.025×10+95×0.005×10=71故答案为71．15.答案：−1+4i解析：本题主要考查复数的运算，属于基础题．按照复数运算直接计算即可．解：(1+i)(1−i)+(1+2i)2=2+1+4i −4=−1+4i ．故答案为−1+4i ．16.答案：2√23．解析：解：由正弦定理可得：sinB =bsinA a =2×sin30°3=13， ∵a =3>b =2，∴由三角形中大边对大角可得∠B <∠A ，即∠B 为锐角．∴cosB =√1−sin 2B =2√23． 故答案为：2√23． 正弦定理可求sin B ，由三角形中大边对大角可得∠B <∠A ，即∠B 为锐角，由同角三角函数关系式即可求cos B ．本题主要考查了正弦定理的应用，考查了三角形中大边对大角的应用，属于基本知识的考查． 17.答案：8解析：本题考查平面向量数量积的求法，向量的数量积及其运算，属于基础题．首先可以建系，转化为坐标运算，也可以利用运算的几何意义解答．解：解法一：取BC 的中点O 为坐标原点，建立平面直角坐标系，因为BC =4，则B(−2,0)，C(2,0)，设A(0,a)，所以BA ⃗⃗⃗⃗⃗ =(2,a)，BC ⃗⃗⃗⃗⃗ =(4,0)，所以BA ⃗⃗⃗⃗⃗ ⋅BC ⃗⃗⃗⃗⃗ =8．解法二：因为AB =AC ，则BA ⃗⃗⃗⃗⃗ 向量在BC ⃗⃗⃗⃗⃗ 上的投影为BO ，则BA ⃗⃗⃗⃗⃗ ⋅BC ⃗⃗⃗⃗⃗ =BO ×|BC ⃗⃗⃗⃗⃗ |=2×4=8．故答案为8．18.答案：√2解析：本题考查平面向量的数量积以及余弦定理和正弦定理的应用，属于中档题． 根据题意，利用平面向量的数量积，结合余弦定理和正弦定理，即可求出sinA sinC 的值． 解：在△ABC 中，设三条边分别为a 、b ，c ，三角分别为A 、B 、C ，由BC ⃗⃗⃗⃗⃗ ·BA ⃗⃗⃗⃗⃗ +2AC ⃗⃗⃗⃗⃗ ·AB ⃗⃗⃗⃗⃗ =CA ⃗⃗⃗⃗⃗ ·CB⃗⃗⃗⃗⃗ ， 得ac ·cosB +2bc ·cosA =ba ·cosC ，由余弦定理得：12(a 2+c 2−b 2)+(b 2+c 2−a 2)=12(b 2+a 2−c 2)， 化简得a 2c 2=2， ∴a c =√2，由正弦定理得sinA sinC =a c =√2．故答案为：√2． 19.答案：解：(1)根据正弦定理得：sinB(sinAcosB +sinBcosA)=√3sinCcosB ， ∴sinBsin(A +B)=√3sinCcosB ，∴sinBsinC =√3sinCcosB ，∵C ∈(0,π)，∴sinC >0，∴sinB =√3cosB ，即tanB =√3，∵B ∈(0,π)，∴B =π3，(2)∵S △ABC =12acsinB =√34ac =2√3， ∴ac =8，根据余弦定理得：b2=a2+c2−2accosB，∴12=a2+c2−8，即a2+c2=20，∴a+c=√(a+c)2=√a2+2ac+c2=6，∴△ABC的周长为：6+2√3．解析：(1)根据正弦定理，两角和的正弦函数公式化简已知等式可得sinBsinC=√3sinCcosB，结合sinC>0，可求tanB=√3，结合范围B∈(0,π)，由特殊角的三角函数值可求B的值．(2)利用已知及三角形面积公式可求ac=8，进而利用余弦定理可求a+c=6，从而可求三角形的周长．本题主要考查了正弦定理，两角和的正弦函数公式，特殊角的三角函数值，三角形面积公式，余弦定理在解三角形中的应用，考查了转化思想，属于基础题．。

2019-2020学年天津市耀华中学高三英语二模试卷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ABest of British：Outdoor CinemasLuna Beach Cinema, BrightonOn the beaches of Brighton this summer, you can enjoy the lapping of waves as you take inFinding Dory, Moana and Sharknadoover a month-long residency. This spot boasts the highest definition outdoor LED screen in the country. stretching to an impressive 33 feet!Moonlight Flicks, ChesterThe biggest outdoor cinema in the North West of England, Moonlight Flicks will be showing some serious blockbusters（大片）this summer, including A Star Is Born and singalong crowd-pleaser, The Greatest Showman. Cinephiles can gather on the lawn and plug into wireless headphones to ensure perfect sound quality.Rooftop Film Club, LondonEnjoy cult classics and family favorites while looking out on a view of London's skyline with the city's unique Rooftop Film Club. The current programme only runs until June 30 and our top picks include The Breakfast Club, Fargo and a special 65th anniversary showing of Rear Window.Chirk Castle, Wrexham, North WalesThe 11th-century Chirk Castle was first built under the reign o£ Edward I, but now it's the destination for Silly Walk superfans, as they put on screenings of the cult classic, Monty Python and the Holy Grail. Has there ever been a more perfect surrounding to enjoy the comedy capers of King Arthur and his dozy squire?1. What can you enjoy in the biggest outdoor cinema in the North West of England?A.Finding DoryB.A Star Is BornC.The Breakfast ClubD.Monty Python and the Holy Grail.2. Where can you enjoy a special anniversary show?A. Luna Beach Cinema, Brighton.B. Moonlight Flicks, Chester.C. Rooftop Film Club, London.D. Chirk Castle, Wrexham, North Wales3. What's the purpose of writing the text?A. To encourage summer activities.B. To advertise several cult classics.C. To recommend some blockbusters.D. To introduce outdoor cinemas.BAbout a month after I joined Facebook, I got a call from Lori Goler, a highly regarded senior director of marketing at eBay. She made it clear this was a business call. “I want to apply to work with you at Facebook,” she said. “Instead of recommending myself, I want to ask you: What is your biggest problem, and how can I solve it?”My jaw hit the floor. I had hired thousands of people over the previous decade and no one had ever said anything remotely like that. People usually focus on finding the right role for themselves, with the implication that their skills will help the company. Lori put Facebook’s needs front and center. It was a killer approach. I responded, “Recruiting is my biggest problem. And, yes, you can solve it.”Lori never dreamed she would work in recruiting, but she jumped in. She even agreed to trade earnings for acquiring new skills in a new field. Lori did a great job running recruiting and within months was promoted to her current job, leading People@Facebook.The most common metaphor for careers is a ladder, but this concept no longer applies to most workers. As of 2010, the average American had eleven jobs from the ages of eighteen to forty-six alone. Lori often quotes Pattie Sellers, who came up with a much better metaphor: “Careers are a jungle gym, not a ladder.”As Lori describes it, there’s only one way to get to the top of a ladder, but there are many ways to get to the top of a jungle gym. The jungle gym model benefits everyone, but especially women who might be starting careers, switching careers, getting blocked by external barriers, or reentering the workforce after taking time off. The ability to create a unique path with occasional dips, detours (弯路), and even dead ends presents great views of many people, not just those at the top. On a ladder, most climbers are stuck staring at the butt of the person above.4. Why did Lori make the call?A. She helped Facebook to solve the biggest problem.B. She wanted to make a business deal with Facebook.C. She tried to ask for a pay rise in Facebook.D. She wanted to become an employee in Facebook.5. What impressed “I” by Lori?A. Lori was good at running recruiting.B. Lori attached great importance to Facebook’s needs.C. Lori jumped in Facebook with no adequate experience.D. Lori was skilled in marketing at eBay.6. What can we infer from the passage?A. Now all people don’t tend to climb the ladder.B. None on the ladder can enjoy the great views.C. Jungle gyms offer limited exploration for employees.D. A pregnant woman, jobless, benefits little from the jungle gyms.7. What is the best title of the passage?A. It’s a Jungle Gym, Not a Ladder.B. Facebook’s Biggest Problem.C. Applying for a Job in Facebook.D. A Jungle Gym is Better than a Ladder.CGuangzhououtbreak linked to strains inIndiaThe gene sequencing of the COVID-19 outbreak inGuangzhou.Guangdongprovince, indicates it is very similar in structure to the mutatedstrains detected inIndia, a senior health official from the city said on Sunday.“And it has the characteristic of quick spread.” Chen Bin, deputy director of the city's health commission, said at a news conference inGuangzhouon Sunday.She urged relevant departments and medical staff to act quickly to block the chain of infection and control the spread of the coronavirus in the southern metropolis.Zhang Zhoubin, deputy director of theGuangzhoucenter for disease control and prevention, said the strain of coronavirus spreads easily.“The virus can be spread through a meal or through a short period of indirect contact,” he said.The city reported five confirmed eases and 21 asymptomatic carriers as of 2 pm Sunday after the first con finned case was detected in the city's Liwan district on May 21, Chen said.To prevent the virus from spreading, the city government tightened its disease control and prevention measures over the weekend. Six communities and housing estates previously designated as low-risk areas were raised to medium-risk ones, Chen said.In addition to asking local residents to get vaccinated, the city has organized nucleic acid testing in Haizhu and Yuexiu districts starting from Sunday. Residents in specific areas of Tianhe, Baiyun and Panyu districts have also been required to take nucleic acid tests to expand the screening of suspected patients and asymptomatic carriers.Liwan previously required all its residents to take nucleic acid tests.As of Saturday, more than 2-25 million residents of the city have had samples collected for nucleic acid tests, Chen said. More than 10,000 medical workers from the entire city have been sent to Liwan to help vaccinate locals against COVID-19 and collect samples for nucleic acid testing.Deng Wenjun, director of circulation section with Guangzhou Supply and Marketing Cooperative, said there are sufficient supplies of food and daily necessities in the medium-risk areas.8. What is the characteristic of the COVID-19 which broke out inGuangzhou?A. It disappears quickly.B. It spreads fast.C. It has a lot to do with temperature.D. It has the same nature as the seasonal flu.9. Which district have residents who have not been required to take nucleic acid tests?A. Tianhe.B. Haizhu.C. Panyu.D. Zengcheng.10. Which of the following statements is TRUE?A. The virus can hardly be spread through a short period of indirect contact.B. There are 21 symptomatic carriers in the Liwan district as of 2 pm Sunday.C. All the people living in Liwan district arc previously asked to take nucleic acid tests.D. Supplies of food and daily necessities in the medium-risk areas arc still not enough.11. Where can you probably find this article?A. On a news website.B. In a fashion magazine.C. In a history book.D. In a travel journal.DLas 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 theprogram. 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 lose more 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。

高二年级B7M1M2测验试卷2I. 单项填空（共30小题；每小题1分，满分30 分）1. ________ i s no doubt that he will pass the exam.A. find 13. --- How about eighto A. needs'clock outtelcinema? B. meets 14. It 'a pity that so many ________ historical records were destroyed.A. meanin glessB. powerlessC. valuelessD. priceless15. It worried her a lot ______ she could not afford ______ she liked.16. Danby left word with my secretary _____ he would call aga in in the after noon.A. whoB. thatC. as 17. Could I speak to ______ is in charge of International Sales, please?A. anyoneB. some oneC. whoever 18. ---Could you please tell me more about the city?---Sorry, I ' m a newcomer. I k no twing else ________ you know now.A. except forB. but thatC. except whatD. but for 19. The problem _______ h im.A. upsettedB. upsetC. was upsetD. upsets to 20. With only five minutes ________ before the teacher collected our exam papers, I felt uneasy as I had not yetA. ThereB. ItC. ThisD. That2. I wish he ______ present at the meeting, but he has jus ______ to Beijing. A. could; bee n B. were; gone C. was; bee n3. Usually children are allowed to ______ when they are six years old.A. jo in schoolB. atte nd the schoolC. atte nd school 4. --- ________ I went to see the doctor, I had to wait about 50 minutes. ---So you must make an appo in tme nt in adva nee. A. Every time B. Since C. While 5. To our great _______ , his parents were ________ at his mark.D. would; goneD. jo in the school D. Even if A. surprises; surprised B. surprises; surpris ing C. surprise; surprised 6. I have no dreams ____ t o have a happy life. A. rather tha n B. more tha n C. other tha nD. surprise; surpris ing D. less tha n 7. He had a lot of friends, none of _____ c ould lend him any money. A. whom B. them C. which D. who8. Why do you stand and watch the milk _______ ? A. boili ngB. boiledC. from boil ingD. havi ng bee n 9. You can find whatever you need at the shopping center, ________ is always busy at the weekend.A. thatB. whereC. whatD. which 10. You should un dersta nd the traffic rule by now. You ' vead it _______ ofte n eno ugh.A. explai ningB. to expla inC. expla in 11. Sometimes we are asked _______ the likely result of an action will be. A. that we thi nk B. what we thi nk C. what do we thinkD. expla ined D. that what we thi nk 12. ---How did you _______the movie last night? ---Oh , both in teresti ng and instructive. B. con siderC. thi nkD. feel ---That _______ m e fine.C. satisfiesD. suits A. whe n; which B. that; whatever C. whether; what D. as; everyth ingD. which D. no matter whochecked the an swers.A. to goB. goingC. goneD. to be gone 21. He said, “ They are repeat and ____________ every respect from us all. ”A. deserveB. receiveC. preserveD. perceive 22. We don ' doubt ______ the people in Beichuan County will recover from the disaster soon and rebuild theirhomes better tha n before.23. I think he is ______ to win, but rm not sure.A. possibleB. likelyC. impossibleD. certa in 24. For breakfast he only drinks juice from fresh fruit _______ on his own farm. A. grow nB. being grow nC. to be grow nD. to grow 25. To every on e's joy, the famous film star was _______ mayor of the city. A . adopted B . appo in ted C . n amed after D . in the n ame of26. His remarks _______ me in my opinion that he was a very con siderate boy. A . concerned B . con tacted C . con firmed D . con sidered27. Teaching is not just a simple piece of work; it's an art _________ a scienee. A . is based onB . based withC . based on 28 . One of the rooms was ________ for a yoga class. A . left beh indB . set asideC . put back 29 . Do you want that cake ? _______ , I'll have it. A . If soB . If possibleC . If n ecessary30 . She _______ herself successfully in court and the judge declared her innocent. A . expressed B . described C . replaced II.完形填空（共20小题；每小题1.5分，满分30分）In our discussion with people on how education can help them succeed in life, a woman remembered the first meeti ng of an in troductory Lcourse about 20 years ago.The professor 2 the lecture hall, placed upon his desk a large jar filled with dried beans （ 豆 ）,and invited the students to 3 how many beans the jar contained. After 4 shouts of wildly wrong guesses the professor smiled a thin, dry smile, announced the 5 answer, and went on saying, “ You have just 6 an importantless on about scie nee. That is: NeverT. your own sen ses ” Twenty years later, the 8 could guess what the professor had in mind. He 9 himself, perhaps, as in vit ing his students to start an exciting _AQ into all unknown world invisible （ 无 形 的 ）to the 11 , which can be discovered only through scientific 12 . But the seventeen-year-old girl could not accept or even 13 the in vitati on. She was just 14 to un dersta nd the world. And she 15 that her firstha nd experie nee couldbe the 16 .The professor, however, said that it was 17 . He was taking away her only _____ 18 for knowing and was providing her with no substitute （ 替代）. re l ember feeling small and_19 , "thewoman says, andI did the only thing I could do. I 20_ the course that after noon, and I have n' t gorsenn e ar Science 1. A. artB. historyC. scie neeD. math 2. A. searched forB. looked atC. got throughD. marched into 3. A. cou ntB.guessC. reportD. watch 4. A. warni ngB. givi ngC. tur ning awayD. liste ning to 5. A. readyB. possibleC. correctD. difficult 6. A. learnedB. preparedC. taughtD. take n 7. A. loseB. trustC.sharpenD.show 8. A. 1ecturer B. scie ntist C. speakerD. woma nA. thatB. ifC. whatD. whether D . depended on D . moved aside D . If not D . defe nded9. A. described B. respected C. saw D. served10. A. voyage B. moveme nt C. change D. rush11. A. professor B. eye C. kno wledge D. light12. A. model B. senses C. spirit D. methods13. A. hear B. make C. prese nt D. refuse14. A. suggest ing B. begi nning C. prete nding D. waiti ng15. A. believed B. doubted C. proved D. expla ined16 . A. growth B. stre ngth C. faith D. truth17. A. firm B. in terest ing C. wrong D. acceptable18. A. task B. tool C. success D. conn ection19. A. cruel B. proud C. frighte ned D. brave20. A. dropped B. started C. passed D. missedIII.阅读理解（共20小题；每小题2分，满分30分）ADo you forget to turn off the lights and heaters whe n you go out of a room? In 2040 it will n ot matter. They will turn themselves off and on again when you return. Y ou will choose the temperature for each room, the lighting and the humidity( 湿度).A sensor will detect the presenee of a human (and, with luck, ignore the dog!) and turn the systems on, and whe n the huma ns leave it will tur n them off aga in.The sensors will work through the central home computer, and they will do much more than just turn the fires and lights on and off for you. They will detect faulty electrical applia nces, plugs or switches, isolate them so that they cannot harm anyone, and the n warn you that they n eed repair. They will detect fire and if you are out of the house, the computer will call the fire brigade. It will also call the police if the sensors detect an intruder. This will not be too difficult because the locks on the outside doors will be electr on ic. You will ope n them using your pers onal card —the one you use for shopp ing —may be using a nu mber known only to you.It will be impossible to lose the key, and a house-breaker will have to tamper with the lock or with a win dow.It is not very difficult to make such tampering send a signal to the computer.The computer will be an entertainer, and most of your entertainment will come right into your home. It does now, of course, but by 2040 “ en terta inment ” will mean much more. For one thi ng, you will be able to take part actively, rather tha n just watchi ng.I. __________________________________________ The author intends to tell us that in 2040A. we will live without lights and heatersB.we will use more lights and heatersC. there will be no switches of lights and heatersD. lights and heaters will be on and off automatically2. Which of the following statements is NOT true?A .The sen sor is multi-fu nction al.B. Without a computer, the sensor cannot do much.C. The sensor will detect fire and make an emergency call.D. You can be taken for an intruder if you tamper with the lock or with a window.3. Accord ing to the author, i n 2040, new tech no logy willA.free us from the keys we use todayC. make the locks out of date4. Tha nks to computers, in 2040 people willA. have no en terta inment outsideC. be con trolled by computers B. turn everyth ing into sen sorsD. get rid of all crimesB. replace TV with computersD. have more fun at homeB. Life at Home in the Y ear 2040D. Lights and Heaters in the Year 20405. ______________________________________ The best title for the passage might beA. Sen sors and ComputersC. The developme nt of scie nee and Tech no logyThe Great Fire of London started in the very early hours of September 2, 1666. In four days it destroyed morethan three-quarters of the old city, where most of the houses were woode n and close together. One hun dred thousa nd people became homeless, but only a few lost their lives.The first started on Sun day morning in the houses of the King ' baker in Puddi ng Lane. The baker, with his wifeand family, was able to get out through a window in the roof. A strong wind blew the fire from the bakery into a small hotel n ext door. Then it spread quickly into Thames Street. That was the begi nning.By eight o ' clock three hun dred houses were on fire. On Mon day n early a kilometer of the city was bur ningalong the River Thames. Tuesday was the worst day. The fire destroyed many well- known build in gs, old St. Paul ' s and the Guildhall among them.Samuel Pepys, the famous writer, wrote about the fire. People threw their things into the river. Many poorpeople stayed in their houses un til the last mome nt. Birds fell out of the air because of the heat.The fire stopped only whe n the King fin ally ordered people to destroy hun dreds of build in gs in the path of thefire. With no thi ng left to burn, the fire became weak and fin ally died out.After the fire, Christopher Wten, the architect, wan ted a city with wider streets and fine new houses of stone.In fact, the streets are still n arrow, but he did build more tha n fifty churches, among them is the new St. Paul The fire caused great pain and loss, but after it London was a better place: a city for the future and not just of thepast.6. The fire began in ____ .A. a hotelB. the palaceC. Puddi ng LaneD. Thames Street7. The underlined word “ family ” in thpasagcaph mean ____ .A. homeB. childre nC. wife and husba ndD. wife and childre n8. It seems that the writer of the text was most sorry for the fact that _____ .A. some people lost their livesB. the birds in the sky were killed by the fireC. many famous buildings were destroyedD. the King ' s bakery was budowln9. Why did the writer cite（弓I用）Samuel Pepys?A. Because Pepys was among those putt ing out the fire.B. Because Pepys also wrote about the fire.C. To show that poor people suffered most.D. To give the reader a clearer picture of the fire.10. How was the fire put out according to the text?A. The King and his soldiers came to help.B. All the wooden houses in the city were destroyed.C. People man aged to get eno ugh water from the river.D. Houses sta nding in the direct ion of the fire were pulled dow n.Have you ever found yourself in this situati on: You hear a song you used to sing whe n you were a child —a bit of nostalgia （怀旧）or “ blast from the past, ” as we say. But it is not a distant childhood memory. The words come back to you as clearly as whe n you sang them all those years ago.Researchers at the Uni versity of Edin burgh studied the relati on ship betwee n music and rememberi ng a foreig n Ian guage. They found that rememberi ng words in a song was the best way to remember eve n one of the most difficult Ian guages.Here is what they did. Researchers took 60 adults and randomly divided them into three groups of 20. Then they gave the groups three differe nt types of -an d-repeatis” nlearning con diti ons. Researchers had one group sirtypspeak the words. They had the sec ond group speak the words to a rhythm, or beat. And they asked the third group to sing the words.All three groups studied words from the Hungarian Ianguage for 15 minutes. Then they took part in a series of Ian guage tests to see what they remembered.Why Hun garia n, you ask? Researchers said they chose Hun garia n because not many people know the Ian guage. It does not share any roots with Germanic or Romance Ianguages, such as Italian or Spanish. After the tests were over, the sin gers came out on top. The people who learned these new Hun garia n words by singing them showed a higher overall performa nce. They did the best in four out of five of the tests. They also performed two times better than those who simply lear ned the words by speak ing them.Dr. Katie Overy says singing could lead to new ways to learn a foreign Ianguage. The brain likes to rememberthings whe n they are contained in a catchy or memorable tune.Dr. Ludke said the findings could help those who struggle to learn foreign Ianguages. On the University of Edin burgh ' s website Ludke writes, “ This study provides the first experime ntal evide nce thaste n-an d-repeat singing method can support foreig n Ian guage lear ning, and ope ns the door for future research in this area. ”11. The “ song ” mentioned in the first paragraphnitended to ________ .A. recall the pastB. amuse the readersC. in troduce the topicD. compare the past with the prese nt12. According to the passage which Ianguage doesn ' t share the sGmuerarafevoiitlRomance Ianguages?A. Hun garia nB. SpanishC. Italia nD. En glish13. From the last two paragraphs, we can conclude that _______ .A. singing is the best way to learn a foreign IanguageB. brain probably works best when foreign Ianguage learners sing the wordsC. a listen-repeat method is very effective for any Ianguage learnerD. Dr. Katie Overy and Dr. Ludke disagree with each other14. What' s correct about the study undertaken by the researchers at the University oEdinburgh?A. Altogether twenty adults were tested in the study.B. People in the 3rd group performed as well as the other 2 groups.C. People in the 2nd group were asked to speak the words to a beat.D. In the study 60 adults were divided into 3 groups according to abilities.15. In which situation can the finding of the research be applied?A. A mother is going to teach her baby how to speak.B. A child is going to have his first music less on.C. A student is going to learn a new English song.D. An American is going to learn some Chinese.V.阅读表达（每小题2分；满分10分）I stood at the edge of the cliff. The wind stung my eyes, cutt ing into my skin. Dark-feathered birds circled the air, swooping （俯冲）low over the ocean every now and then to catch their dinner. Hundreds of feet below, the deep ocean beat against the rough sandy shore. I took a deep breath, filling my lungs with excitement ——and at the same time, fear.Behind me, I heard the rest of the crew start to mutter. I was here for the shooting of a movieas I was one of the lead actors in the film Dangerous Things , and this scene was right in the middle of the climax (故事的高潮).苴was vital that this went right.The director had talked to me about getting a stunt double ( 替身演员),but I ' d persuadedhim that I could handle the dive. I ' d taken a diving course a few years ago, and I ' d beswim ming less ons since I was five years old. I had bee n pretty con fide nt that I could do this —— up till now.Some one called out, “ Ceria, you don ' t have to do this! Are you sure you want to dive?was one of the producers, C allie Evans. I knew I couldn ' t turn back now. I couldn ' t bear to see the disappo in ted look on the director ' s face whe n he was told that I could n ' t do it.At that moment, all my fears and worries broke free. The expectation of adventure andvictory seemed to move all the hesitation. I swooped downwards. The air on either side of me cutinto my extended arms. I knew that this wonderful feeling of flight would only last a fewsec on ds, yet time seemed to slow dow n so I could hear the thrilled whoops of my crew and around of applause that seemed to echo in my pounding ears.1. At the begi nning, how did the author feel about what she was going to do? (No more tha n 3words)2. What does the underlined sentence in Paragraph 2 mean in English? (No more than 15 words)3. Why was the author that con fide nt in divi ng? (No more tha n 10 words)4. What was the crew ' s reaction while the authordiving down? (No more than 10 words)5. How do you like the author? Please explain why. (No more than 25 words)答案：单选：1-5ABCAC 6-10CAADD 11-15BADDB 16-20BCCBA 21. AABAB 26. CCBDD完型：36-40: CDBDC 41-45: ABDCA 46-50: BDABA 51-55 DCBCA阅读理解：DCADB CBCDD CABCD阅读表达1. She felt excited and frightened / fearful.2. It was important that the scene was properly shot.Or: (Because it was the climax of the movie), the dive must perform successfully / well.3. Because she had taken diving and swimming courses.4. The crew cheered loudly for her.5. I think the author was brave and con fide nt, because she could overcome the fear to challe ngeherself and enjoy success.Or: I think she was brave because she didn ' t chicken out when facing challenges.。

2019-2020学年天津市耀华中学高二（下）4月月考数学试卷一、单选题（本大题共10小题，共50.0分）1.函数f(x)=(x−3)e x的单调递减区间是()A. (−∞,2)B. (0,3)C. (1,4)D. (2,+∞)2.若函数f(x)=kx−lnx在区间(1,+∞)上单调递增，则k的取值范围是()A. (−∞,−2]B. (−∞,−1]C. [1,+∞)D. [1,+∞)3.已知i是虚数单位，a，，得“a=b=1”是“”的()A. 充分不必要条件B. 必要不充分条件C. 充分必要条件D. 既不充分也不必要条件4.已知i为虚数单位，则i1+i的实部与虚部之积等于()A. 14B. −14C. 14i D. −14i5.若复数z满足(1+2i)z=(1−i)，则|z|=()A. 25B. 35C. √105D. √106.下列求导运算正确的是()A. (cosx)′=sinxB.C. (lgx)′=1xln10D.7.点P是曲线y=x2−lnx上任意一点，则点P到直线y=x−2的距离的最小值是()A. 1B. √2C. 2D. 2√28.某同学回答“用数学归纳法的证明√n(n+1)<n+1(n∈N∗)”的过程如下：证明：①当n=1时，显然命题是正确的．②假设当n=k(k≥1,k∈N∗)时，有√k(k+1)<k+1，那么当n=k+1时，√(k+1)2+(k+1)=√k2+3k+2<√k2+4k+4=(k+1)+1，所以当n=k+1时命题是正确的，由①②可知对于n∈N∗，命题都是正确的，以上证法是错误的，错误在于()A. 从k到k+1的推理过程没有使用归纳假设B. 假设的写法不正确C. 从k到k+1的推理不严密D. 当n=1时，验证过程不具体9.已知函数f(x)=13x3−12mx2+4x−3在区间[1,2]上是增函数，则实数m的取值范围为()A. 4≤m≤5B. 2≤m≤4C. m≤2D. m≤410.定义在R上的偶函数f(x)，其导函数f′(x)，当x≥0时，恒有x2f′(x)+f(−x)<0，若g(x)=x2f(x)，则不等式g(x)<g(1−2x)的解集为()A. (13,1) B. (−∞,13)∪(1,+∞)C. (13,+∞) D. (−∞,13)二、单空题（本大题共4小题，共24.0分）11.曲线y=e x(x2+2)在点(0,2)处的切线斜率为______．12.函数f(x)=12x2−9lnx的单调减区间为______．13.若函数f(x)=x2+x−lnx+1在其定义域的一个子区间(2k−1,k+2)内不是单调函数，则实数k的取值范围是______．14.若直线y=kx+b是曲线y=lnx+2的切线，也是曲线y=ln(x+1)的切线，则b=______．三、解答题（本大题共2小题，共26.0分）15.已知函数f(x)=x2+2x+alnx，a∈R．(Ⅰ)若a=−4，求曲线y=f(x)在点A(1,f(1))处的切线方程；(Ⅱ)若函数f(x)在[1,+∞)上单调递增，求实数a的取值范围．16.求函数f(x)=e x(e x−a)−a2x(a∈R)的单调区间．答案和解析1.【答案】A【解析】解：∵数f(x)=(x−3)e x∴f′(x)=(x−2)e x，根据单调性与不等式的关系可得：(x−2)e x<0，即x<2所以函数f(x)=(x−3)e x的单调递减区间是(−∞,2)故选：A．要求函数f(x)=(x−3)e x的单调递减区间，求出导函数，解不等式本题考查了导数在判断单调性中的应用，难度不大，属于常规题．2.【答案】C【解析】【分析】本题考查了利用导数研究函数的单调性、恒成立问题的等价转化方法，属于中档题．求出导函数f′(x)，由于函数f(x)=kx−lnx在区间(1,+∞)单调递增，可得f′(x)≥0在区间(1,+∞)上恒成立，解出即可．【解答】解：f′(x)=k−1，x∵函数f(x)=kx−lnx在区间(1,+∞)单调递增，∴f′(x)≥0在区间(1,+∞)上恒成立．∴k≥1，x在区间(1,+∞)上单调递减，而y=1x∴k≥1．∴k的取值范围是：[1,+∞)．故选：C．3.【答案】A【解析】【分析】本题考查的知识点是充分、必要条件的判断，复数的相等，复数的运算，属于简单题．利用复数的运算性质，分别判断“a=b=1”⇒“(a+bi)2=2i”与“(a+bi)2=2i”⇒“a=b=1”的真假，进而根据充分条件和必要条件的判断得到结论．【解答】解：当a=b=1时，(a+bi)2=(1+i)2=2i成立，故“a=b=1”是“(a+bi)2=2i”的充分条件；当(a+bi)2=a2−b2+2abi=2i时，a=b=1或a=b=−1，故“a=b=1”不是“(a+bi)2=2i”的必要条件；综上所述，“a=b=1”是“(a+bi)2=2i”的充分不必要条件．故选A．4.【答案】A【解析】解：∵i1+i =i(1−i)(1+i)(1−i)=12+12i，∴所求的实部与虚部之积是14．故选A．先对所给的复数分子分母同乘以1−i，再进行化简整理出实部和虚部，即求出它们的乘积，本题考查两个复数代数形式的乘除法，以及虚数单位i的幂运算性质，两个复数相除时，需要分子和分母同时乘以分母的共轭复数进行化简．5.【答案】C【解析】【分析】本题考查了复数代数形式的乘除运算，考查了复数模的求法，属于基础题．由(1+2i)z=(1−i)，得z=1−i1+2i，然后利用复数代数形式的乘除运算化简，再根据复数求模公式可求答案．【解答】解：由(1+2i)z=(1−i)，得z =1−i 1+2i =(1−i)(1−2i)(1+2i)(1−2i)=−1−3i 5=−15−35i ，则|z|=√(−15)2+(−35)2=√105．故选C ．6.【答案】C【解析】 【分析】本题主要考查函数的导数的求解，运用函数的导数运算法则是解决本题的关键，属于基础题．根据函数的导数公式进行判断即可． 【解答】 解：，故A 不正确； ，故B 不正确； ，故C 正确；，故D 不正确．故选C ．7.【答案】B【解析】 【分析】本题考查了导数的几何意义以及点到直线的距离，属于中档题．对y 求导，当点P 是曲线的切线中与直线y =x −2平行的直线的切点时，点P 到直线y =x −2的距离的最小，解答即可． 【解答】解：由题意y′=2x −1x=2x 2−1x，x >0，当点P 是曲线的切线中与直线y =x −2平行的直线的切点时，点P 到直线y =x −2的距离最小，令y′=2x −1x =1，解得x =1，所以点P的坐标为(1,1)，故点P到直线y=x−2的最小值为√1+1=√2，故选：B．8.【答案】A【解析】解：用数学归纳法应这样证明：①当n=1时，显然命题是正确的；②假设当n=k(k≥2,k∈N∗)时，有√k(k+1)=√k2+k<k+1，即k2+k<(k+1)2；则当n=k+1时，√(k+1)2+(k+1)=√k2+k+2k+2<√(k+1)2+2k+2<√k2+4k+4=(k+1)+1，所以当n=k+1时命题是正确的，由①②可知对于n∈N∗，命题都是正确的．原题目中的证法是错误的，错误在于从k到k+1的推理过程没有使用归纳假设；只是用了放缩法和不等式的性质，不符合数学归纳法的要求．故选：A．此证明中，从推出P(k+1)成立中，没有用到假设P(k)成立的形式，不是数学归纳法．本题考查了数学归纳法证明命题的应用问题，正确理解数学归纳法证明命题的要求是解题的关键．9.【答案】D【解析】【分析】本题考查了利用导数研究函数的单调性，不等式的恒成立问题，利用基本不等式求最值，转化思想的应用，属于一般题．先求导f′(x)=x2−mx+4，得到函数在区间[1,2]上是增函数，转化为x2−mx+4≥0在区间[1,2]上恒成立，分离参数利用基本不等式求出最小值即可得结果．【解答】解：已知函数f(x)=13x3−12mx2+4x−3，则f′(x)=x2−mx+4，因为函数f(x)=13x3−12mx2+4x−3在区间[1,2]上是增函数，即x2−mx+4≥0在区间[1,2]上恒成立，则m≤x+4x在区间[1,2]上恒成立，因为x+4x ≥2√x·4x=4，当且仅当x=2时取等号，所以m≤4．故选D．10.【答案】A【解析】解：g(x)=x2f(x)，当x≥0时，g′(x)=2x[x2f′(x)+f(−x)]≤0，∴函数g(x)在[0,+∞)上单调递减．∵函数f(x)是定义在R上的偶函数，∴函数g(x)是定义在R上的偶函数，则不等式g(x)<g(1−2x)即g(|x|)<g(|1−2x|)，∴|x|>|1−2x|，解得：13<x<1．∴不等式g(x)<g(1−2x)的解集为(13,1)．故选：A．g(x)=x2f(x)，当x≥0时，g′(x)=2x[x2f′(x)+f(−x)]≤0，可得函数g(x)在[0,+∞)上单调递减．根据函数f(x)是定义在R上的偶函数，可得函数g(x)是定义在R上的偶函数，不等式g(x)<g(1−2x)即g(|x|)<g(|1−2x|)，转化即可得出不等式的解集．本题考查了利用导数研究函数的单调性、函数的奇偶性、单调性，考查了推理能力与计算能力，属于中档题．11.【答案】2【解析】解：由已知得：y′=e x(x2+2x+2)，∴y′|x=0=2．故答案为：2．先求出函数的导数，然后将x=0代入即可．本题考查导数的几何意义以及切线的斜率，属于基础题．12.【答案】(0,3]【解析】【分析】本题主要考查了利用导数研究函数的单调区间，属于基础试题．先对函数求导，然后结合导数与单调性的关系即可求解．【解答】解：定义域(0,+∞)，f′(x)=x−9x =x2−9x，易得当0<x≤3时，f′(x)≤0，函数单调递减，故函数的单调递减区间(0,3]，故答案为：(0,3]13.【答案】[12,3 4 )【解析】解：函数f(x)=x2+x−lnx+1的定义域为(0,+∞)．由区间(2k−1,k+2)，可得：0≤2k−1<k+2，解得12≤k<3．f′(x)=2x+1−1x =(2x−1)(x+1)x，令f′(x)=0，解得x=12．∵函数f(x)=x2+x−lnx+1在其定义域的一个子区间(2k−1,k+2)内不是单调函数，∴2k−1<12<k+2，解得：−32<k<34．与12≤k<3联立解得：12≤k<34．故答案为：[12,3 4 ).函数f(x)=x2+x−lnx+1的定义域为(0,+∞).由区间(2k−1,k+2)，可得：0≤2k−1<k+2，解得k范围．f′(x)=2x+1−1x =(2x−1)(x+1)x，令f′(x)=0，解得x=12.由函数f(x)=x2+x−lnx+1在其定义域的一个子区间(2k−1,k+2)内不是单调函数，可得2k−1<12<k+2，进而解得k的范围．本题考查了利用导数研究函数的单调性、方程与不等式的解法、等价转化方法，考查了推理能力与计算能力，属于中档题．14.【答案】1−ln2【解析】【分析】本题考查了导数的几何意义，属于中档题．设切线与两曲线的切点的横坐标分别为x1，x2，根据导数的几何意义得到k与切点横坐标的关系，由切点在切线上，又在曲线上，列方程组，解之即可得到答案．【解答】解：设直线y=kx+b与曲线y=lnx+2和y=ln(x+1)的切点横坐标分别为x1，x2，对函数y=lnx+2求导，得y′=1x ；对函数y=ln(x+1)求导，得y′=1x+1．由导数的几何意义可得k=1x1=1x2+1①，∴x1=x2+1②，再由切点既在切线上也在各自的曲线上，可得{kx1+b=lnx1+2③kx2+b=ln(x2+1)④,②代入③得，k(x2+1)+b=ln(x2+1)+2⑤，⑤−④得k=2，代入①得x1=12，将k=2，x1=12代入③，得b=1−ln2．故答案为1−ln2．15.【答案】解：(I)f(x)=x2+2x+alnx，a∈R．f′(x)=2x−2x2+ax，a=−4时，f(x)=x2+2x−4lnx，f(1)=1+2−0=3．f′(x)=2x−2x2−4x，f′(1)=2−2−4=−4．∴曲线y=f(x)在点A(1,f(1))处的切线方程为：y−3=−4(x−1)，化为：4x+y−7= 0．(Ⅱ)∵函数f(x)在[1,+∞)上单调递增，∴f′(x)=2x−2x2+ax≥0，化为：a≥2x−2x2．令g(x)=2x−2x2.x∈[1,+∞)．由于函数g(x)在x∈[1,+∞)上单调递减．∴x=1时，函数g(x)取得最大值，g(1)=0．∴a≥0．【解析】(I)f(x)=x2+2x +alnx，a∈R.f′(x)=2x−2x2+ax，a=−4时，f(x)=x2+2x−4lnx，可得：f(1)，f′(1).即可得出曲线y=f(x)在点A(1,f(1))处的切线方程．(Ⅱ)由函数f(x)在[1,+∞)上单调递增，可得f′(x)=2x−2x2+ax≥0，化为：a≥2x−2x2.令g(x)=2x−2x2.x∈[1,+∞).利用函数g(x)在x∈[1,+∞)上单调递减．即可得出结论．本题考查了利用导数研究函数的单调性、切线方程、方程与不等式的解法、等价转化方法，考查了推理能力与计算能力，属于中档题．16.【答案】解：f′(x)=e x(e x−a)+e x⋅e x−a2=2(e x+a2)(e x−a)．下面对a分类讨论：a=0时，f(x)=e2x在R上单调递增．a>0时，令f′(x)=0，解得x=lna.可得：函数f(x)在(−∞,lna)上单调递减，在(lna,+∞)上单调递增．a<0时，令f′(x)=0，解得x=ln(−a2).可得：函数f(x)在(−∞,ln(−a2))上单调递减，在(ln(−a2),+∞)上单调递增．综上可得：a=0时，f(x)在R上单调递增．a>0时，函数f(x)在(−∞,lna)上单调递减，在(lna,+∞)上单调递增．a<0时，函数f(x)在(−∞,ln(−a2))上单调递减，在(ln(−a2),+∞)上单调递增．【解析】f′(x)=e x(e x−a)+e x⋅e x−a2=2(e x+a2)(e x−a).下面对a分类讨论，利用导数研究函数的单调性即可得出．本题考查了利用导数研究函数的单调性、分类讨论方法，考查了推理能力与计算能力，属于中档题．第11页，共11页。

天津市耀华嘉诚国际中学2019—2020 学年度第二学期线上学习阶段性评估检测七年级英语试卷第Ⅰ卷（客观题，请将答案填涂在答题卡上）一、选择题（每小题1 分，共20 分）1.—What do you usually have for breakfast? —A piece of bread and egg.A.a; anB. 不填; theC. a; theD. 不填; an2.Jenny can play piano, but she can’t play table tennis.A.the; theB. the; 不填C. 不填; theD. 不填; 不填3.I’m going to send it to Lily post.A.onB. inC. byD. with4.There’s a bridge the river.A.onB. acrossC. overD. through5.—Can a plane fly the Atlantic Ocean? —Yes, but it needs to go the clouds for hours.A.across; throughB. through; acrossC. through; throughD. across; across6.Turn left the second street the left.A.on; atB. at; onC. in; atD. to; on7.Please choose me your partner.A.withB. asC. toD. from8.There are many trees on sides of the river.A.eachB. everyC. bothD. all9. —is it from the ground to the top of the building? —About two hundred meters.A. How farB. How longC. How highD. How tall10. —is it from our school to the airport? —About half an hour’s walk.A. How longB. How farC. How much timeD. How soon11.The boy was taller than Tina. He was sitting Tina. So Tina see the blackboard at all.A.behind; couldn’tB. behind; couldC. in front of; couldn'tD. in the front of; could12.Tony’ s parents a film tomorrow evening.A.are seeingB. are going to seeC. seeD. is going to see13.I’m going to there.A.flyingB. fly toC. take a planeD. walk to14.The journey will me about two weeks and it will me plenty of money as well.A.spend; takeB. take; costC. pay; takeD. cost; take15.You’d better not the bus at next stop.A.get offB. to get offC. get outD. to get out16.There are three fans at the airport. They are waiting for the famous actor.A.thousandB. thousandsC. thousands ofD. thousand of17.The presents make him excited.A.to feelB. feelC. feelsD. feeling18.The factory makes noise. It is noisy.A.too much; too muchB. too much; much tooC. too many; much tooD. much too; much too19.It took me two weeks the novels written by Mark Twain.A.finish to readB. finishes readingC. to finish readingD. finishing to read20.Which of the following is not in London?A.River ThamesB. Tower BridgeC. River NileD. Big Ben二﹑完形填空（每小题1 分，共10 分）A science teacher wants to show some idea to his students. He takes a large-mouth bottle and 21 several large stones in it. He then asks the class, "Is the bottle full now?" They all reply, "Yes!"The teacher then takes some small rocks and puts them into the 22 .The small rocks go into the 23 between the big rocks. He then asks, "Is it full?" This time some students give no answer, but most reply, "Yes!"The teacher then starts to drop some sand into the bottle. The sand 24 the spacesbetween the small rocks. For the 25 time, the teacher asks, "Is it full?" Now most are doubting, but still, some reply, "Yes!"Then the teacher brings out a cup of water into the bottle. "What's the 26 of this show?" asks the teacher. One 27 student answers, "No matter how 28 you are, you can always find time to do some more things.""No," says the teacher, "the point is that 29 you don't place the big rocks first, you'll never get them in. The big rocks are the 30 things in your life. If you fill your life with small things —as shown by the small rocks, the sand and the water —you'll never have the time for the important things."21. A. touches B. places C. pushes D. hits22. A. mouth B. cup C. bottle D. bowl23. A. spaces B. rooms C. fields D. edges24. A. puts up B. turns up C. sets up D. fills up25. A. first B. second C. third D. fourth26. A. point B. method C. progress D. rule27. A. angry B. funny C. clever D. crazy28. A. busy B. rich C. great D. popular29.A. when30.A. pleasant B. untilB. importantC. unlessC. friendlyD. ifD. interesting三﹑阅读理解（每小题2 分，共30 分）读故事，判断正（A）误（B）(A)A man saw a boy standing beside a lake with a mirror. “Excuse me,” he said, “but could you tell me what you’re doing?”“I’m fishing.”“With a mirror? Could you tell me how it works? ” the man asked.“OK, but I want five dollars.”The man wanted to know the secret very much, so he handed the boy the money. “Now show me how it works,”he said. “Well,”the boy began, “you hold the mirror towards the water, and then a fish goes by, the sunlight in the mirror gives him a surprise. He stops and doesn’t know what to do, and then you catch him at once.”The man was surprised, “Can you really catch fish with the mirror? How many did you catch? ”“You are the fifth today!” replied that boy.31.The man wanted to look at the boy’s mirror.32.The man gave the boy five dollars.33.The boy caught five fish that day.34.The boy got at least twenty-five dollars that day.35.When the man heard the boy’s words, he would be very happy.(B)Mr Zhang 正在国外旅游, 这是他所入住宾馆的房卡。

2019-2020学年天津市耀华中学高三英语二模试卷及答案解析第一部分阅读（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APlan Your Visit to the British MuseumWe've made a few changes to ensure you can safely enjoy your visit:How to book tickets·Tickets for the permanent collection can only be hooked online in advance.·To book tickets for exhibitions, visit our exhibition pages. If you want to guarantee your visit to the permanent collection as well as the exhibition on your visit, you will need to book a separate ticket.·We are limiting numbers of people in the museum to ensure there is room for you to safely enjoy your visit. Everyone, including members and volunteers, will therefore need to book a free, timed ticket in advance.Important information about your ticket booking·You can book up to six tickets for people who live in the same family.·We will email yourticket to you, and you will need to show it either printed out or on your device (设备) when you arrive.·Please arrive at the time stated on your ticket-we cannot guarantee admission before or after it.Following the routeWe have created a new one-way route through the museum which will allow you to safely explore world cultures from the Mediterranean to the Middle East and from the Americas to Africa.·View a map of the route (Open in a new window).·Our audio guides (音频指南) are not available. However, youcan pay to download the audio introductions from iTunes (Open in a new window) or Google Play (Open in a new window) to each of the galleries and listen on your own device. Please remember to bring along your own headphones.1.Why does the museum offer timed tickets?A.To earn more money.B.To hire more volunteers.C.To save room for collections.D.To control the number of visitors.2.How can a visitor learn about the new route in advance?A.View an online map.B.Buy a new headphone.C.Buy audio guides from the museum.D.Download video introductions from iTunes.3.Where can you probably find the text?A.In a newspaper.B.In a magazine.C.On a website.D.In a report.BThe man who invented the World Wide Web a few decades ago is calling for major changes to make it better for humans. In an open letter published on Tuesday, Berners-Lee said that the web was used by half the world's population.Berners-Lee said the web had clearly created great opportunities for humans to progress and had made life easier for millions of people. Actually, it also has offered opportunities to groups traditionally not heard a new voice in society. However, he added that the web had also provided new ways for cheats to commit crimes (犯罪).“Against the background of news stories about how the web is misused, it's understandable that many people feel afraid and unsure if the web is really a force for good,” he wrote.Berners-Lee created a group called the World Wide Web Foundation. He islooking for help from governments, companies and people to become more involved in shaping the web to do more good for humans. His actual plan is called the “Contract (合同) for the Web”.Under this contract, governments are called on to take steps to makesure all people can connect to the Internet and that personal privacy is respected. Businesses are asked to keep the Internet prices low so more people can use the web. In addition, companies should respect privacy and develop technologies that aim to put people first.The plan also calls on people to create materials for the web and work with others to make sure that is rich, quality information for everyone. Besides, people should seek to “build strong communities that respect personal speech and human equality.” “The path to make the Internet better is the responsibility of everyone who uses it,” Bermers-Lee added, “Making big changes will not be easy, but will be very well worth it in the end.”4. What does Berners-Lee think of the World Wide Web?A. It is his greatest regret.B. It stops the progress of humans.C. It needs improving.D. It does more harm than good.5. What's wrong with the web according to Berners-Lee?A. It is misused for bad purposes.B. It is misunderstood by all people.C. It blocks out a new voice in society.D. It is expensive for half the world’s population.6. What are governments called on to do under the “Contract for the Web”?A. Put technology first.B. Create materials for the web.C. Popularize the Internet.D. Make the Internet free of charge.7. What should people do with the Internet in Berners-Lee's opinion?A. Be responsible for it.B. Absolutely reject it.C. Completely rely on it.D. Be unconcerned about it.CItaly's fashion capital is gray — not only because of the blocks of stone buildings，but also due to its often-gray sky, which traps pollution. ButMilannow wants to change it.The city has an ambitious plan to plant 3 million new trees by 2030 - a move that experts say could offer relief from the city's hot weather. Some projects have already contributed to environmental improvements. Architect Stefano Boeri’s Vertical Forest residential (居民的) tower, completed in 2014, aims to improve not only air quality but the quality of life for Milan residents. Boeri created a smallisland of greenery in the heart ofMilan, filling every balcony with plants that absorb carbon dioxide.“I think forestation is one of the best chances that we have today. It is one of the most effective ways we have to fight climate change, because everyone can plant trees, Boeri said.Damiano Di Simine, a member of the environmental group Legambiente , said the greenMilanproject will lower temperatures in a city where the nighttime temperature can be 6 degrees Celsius higher than in the surrounding area. City show thatMilanexperiences 35 hot nights a year. Because the city lies close to theAlps, Milin gets very little wind to lower the city's temperatures. "Planting trees will help this," Di said.TheVerticalForesthas attracted more than 20 species of birds. And the shade provided by the 800 trees and 15,000 plants means that residents rarely have to put on air conditioning, even in hot summers. TheVerticalForest's total greenery- can absorb 30 metric tons of carbon dioxide every year. The presence of green trees has a very important effect on people's health and psychological state, as has already been proved.8. What change doesMilanplan to make?A. Planting more trees.B. Creating a new fashion style.C. Pulling down more gray stone buildings.D. Doing more surveys to study global wanning.9. What's Boeri's opinion on the city's plan?A. It costs a lot.B. It is unpractical.C. It fails to attract people's attention.D. It is helpful to fight against climate change.10. What is Di Simine's attitude toward the city's plan?A. Doubtful.B. Supportive.C. Disappointed.D. Unconcerned.11. What does the last paragraph focus on?A. Specifics of the city's plan.B. Challenges faced by the city.C. The aim of theVerticalForestproject.D. The positive effect of theVerticalForestproject.DIf you think you’d like to live on Mars, you may have that possibility by 2023. A Dutch company called Mars One will soon advertise for people interested in colonizing (开拓) Mars. Ifyou have all the necessary skills, you could be one of the first colonists. Are you ready for the challenge?You won’t have to pay for the mission to Mars. Mars One has already received money from some donors and is hoping to get more from TV viewers who will become interested in the show where all applicants have a debate for the rare chances.The main responsibility of the first colonists is to create an artificial environment on Mars where there is no air to breathe and no land to farm. Scientists know it’s quite possible because something similar has already been done inAntarctica.Another problem is that space travel to Mars takes nearly a year to get to Mars and the colonists will live the rest of their lives there. When a human lives in an environment without gravity or with low gravity for a long time, the systems in the body weaken. Luckily, spinning (旋转) the spaceship can create artificial gravity, and artificial gravity can ease these problems. It will also be difficult for Mars colonists to be far from home, living in small spaces, and seeing the same people over and over. Colonists with depression could put the mission in danger. Fortunately, a few years ago, a joint Russian and European project called the Mars500 Mission studied people’s reactions in a Mars-like environment. It is viewed as a great success because scientists were able to see how people handle emotional and physical stresses.Recent studies show that seven percent of people would want to go on such an adventure.Mars One will soon start accepting its first colonists. Are you interested?12. What do we know about the applicants to Mars from the first two paragraphs?A. They will land on Mars in 2023.B. They can get money from donors.C. They will compete in a TV show.D. They do not need special skills.13. What will the first colonists do to solve the basic living problems on Mars?A. Create earth-like conditions.B. Build labs inAntarctica.C. Spin the spaceship.D. Start the Mars500Mission.14. What can the life of the first colonists be like according to the passage?A. Difficult and dangerous.B. Different but adaptable.C. Challenging and unbearable .D. Acceptable but depressing.15. What’s the best title for the text?A. Mars: our final destination?B. Ready to be Mars’ colonists?C. Space travel: a thrilling adventure?D. Are you a qualified Mars astronaut?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。

天津市耀华嘉诚国际中学2020~2021学年度第二学期期末模拟卷（一）一、选择题1．函数()3ln 2x f x =+的导数为（ ） A ．3ln 3x B ．13ln 32x+C ．132x+D ．3x【答案】A2．已知某种商品的广告费支出x （单位：万元）与销售额y （单位：万元）之间有如下对应数据：根据上表可得回归方程ˆˆˆy bx a =+，计算得7b =，则当投入10万元广告费时，销售额的预报值为 A ．75万元 B ．85万元 C ．99万元 D ．105万元【答案】B3．曲线1x y xe =+在点()0,1处的切线方程是( ) A ．10x y -+= B ．210x y -+= C ．10x y --= D ．220x y -+= 【答案】A4．用数字0,1,2,3,4,5组成没有重复数字的五位数，其中比40000大的偶数共有 A ．144个 B ．120个C ．96个D ．72个【答案】B5．若22)nx 展开式中只有第6项的二项式系数最大，则展开式的常数项是（ ） A ．360 B ．180C ．90D ．45【答案】B6．将三颗骰子各掷一次，记事件A =“三个点数都不同”，B =“至少出先一个6点”，则条件概率()P A B ，()P B A 分别等于 A ．6091，12B ．12，6091C ．2091，12D ．12，2091【答案】A7．若函数()2()e xf x x ax a =-+在区间(1,0)-内单调递减，则实数a 的取值范围是（ ）A ．(,3]-∞B ．[3,)+∞C ．[1,)+∞D ．(,1]-∞【答案】D8．《红海行动》是一部现代海军题材影片，该片讲述了中国海军“蛟龙突击队”奉命执行撤侨任务的故事．撤侨过程中，海军舰长要求队员们依次完成六项任务，并对任务的顺序提出了如下要求：重点任务A 必须排在前三位，且任务E 、F 必须排在一起，则这六项任务的不同安排方案共有 A ．240种 B ．188种C ．156种D ．120种【答案】D 9．函数f (x )=2sin cos x xx x ++在[—π，π]的图像大致为A ．B ．C ．D ．【答案】D 二、填空题1．若π1sin 63α⎛⎫-= ⎪⎝⎭，则2πcos 23α⎛⎫+= ⎪⎝⎭______．【答案】79-2．设随机变量(2,)B p ξ，(4,)B p η，若2()3E ξ=，则(3)P η≥=______. 【答案】193．函数()sin()(0,0,)2f x A x A πωφωφ=+>><的部分图象如图所示，则将()f x 的图象向右平移6π个单位后，得到的图象对应的函数解析式为________.【答案】sin(2)6y x π=-4.已知随机变量X 服从正态分布()2,1N ，若()()223P X a P X a ≤-=≥+，则a =__________． 【答案】15．若8280128(2)(1)(1)(1)x a a x a x a x -=+-+-+⋯+-，则0128a a a a +++⋯+=______．【答案】06．现有16张不同的卡片，其中红色、黄色、蓝色、绿色卡片各4张．从中任取3张，要求这3张卡片不能是同一种颜色，且红色卡片至多1张．不同取法的种数为 ． 【答案】472 三、解答题1.已知,αβ为锐角，3cos ,tan()25ααβ=+=-（1）求tan 2α的值 （2）求sin()αβ-的值（1）247-（2）25- （1）由α为锐角，3cos 5α=，得24sin 1cos 5αα. 所以4tan 3α=所以22tan 24tan 21tan 7ααα==-- （2）42tan()tan 3tan tan()241tan()tan 123αβαβαβααβα--+-=+-=-=++-⨯由题意及同三角函数的基本关系可得sin ββ==所以43sin()sin cos cos sin 55αβαβαβ-=-=-=. 【点评】本题主要考查了三角函数同角的基本关系，以及两角差的正弦和正切公式，以及正切的二倍角公式，属于基础题.2．一盒子中有8个大小完全相同的小球，其中3个红球，2个白球，3个黑球.（Ⅰ）若不放回地从盒中连续取两次球，每次取一个，求在第一次取到红球的条件下，第二次也取到红球的概率；（Ⅱ）若从盒中任取3个球，求取出的3个球中红球个数X 的分布列和数学期望.（Ⅰ）6()6256(|)21()21756P A B P B A P A ⋂∴==== （Ⅱ）∴X 的分布列为X 的数学期望为：【解析】解:（Ⅰ）设事件A=“第一次取到红球”，事件B=“第二次取到红球”由于是不放回地从盒中连续取两次球，每次取一个，所以第一次取球有8种方法，第二次取球是7种方法，一共的基本事件数是56，由于第一次取到红球有3种方法，第二次取球是7种方法，3721()5656P A ⨯∴==… 2分又第一次取到红球有3种方法，由于采取不放回取球，所以第二次取到红球有2种方法，6()56P A B ∴⋂=6()6256(|)21()21756P A B P B A P A ⋂∴====……4分 （Ⅱ）从盒中任取3个球，取出的3个球中红球个数X 的可能值为0,1,2,3…… 5分且有3538105(0)5628C P X C ====,1235383015(1)5628C C P X C ==== 21353815(2)56C C P X C ===,…… 9分X 的分布列为…… 10分X 的数学期望为：……12分3．已知函数()()4242x x f x sin sin x πππ⎛⎫⎛⎫=+--+ ⎪ ⎪⎝⎭⎝⎭．（1）求函数f （x ）的单调递增区间； （2）将函数f （x ）的图象向右平移2π个单位，再将所得图象的横坐标缩短到原来的一半，纵坐标不变，得到新的函数y ＝g （x ），当5012x π⎡⎤∈⎢⎥⎣⎦，时，求g （x ）的值域． （1）[66522k k ππππ-++，]（k ∈Z ）．（2）[1-，2]． 【分析】（1）化简()f x 可得：()32f x sin x π⎛⎫=+ ⎪⎝⎭，利用复合函数的单调性及三角函数性质计算即可．（2）由函数f （x ）的图象平移、伸缩可得新的函数：g （x ）622sin x π⎛⎫=-⎪⎝⎭，由5012x π⎡⎤∈⎢⎥⎣⎦，可得：62632x πππ-≤-≤，利用三角函数性质可得：12126sin x π⎛⎫-≤-≤ ⎪⎝⎭，问题得解． 【详解】解：（1）函数()()4242x x f x sin sin x πππ⎛⎫⎛⎫=+--+ ⎪ ⎪⎝⎭⎝⎭．2x sinx π⎛⎫=++ ⎪⎝⎭，sinx =+．32sin x π⎛⎫=+ ⎪⎝⎭．令：32222k x k πππππ-+≤+≤+（k ∈Z ），解得：52266k x k ππππ-+≤≤+（k ∈Z ）， 所以函数的单调递增区间为：[66522k k ππππ-++，]（k ∈Z ）． （2）将函数f （x ）的图象向右平移2π个单位， 再将所得图象的横坐标缩短到原来的一半，纵坐标不变， 得到：g （x ）622sin x π⎛⎫=-⎪⎝⎭的图象， 由于：5012x π⎡⎤∈⎢⎥⎣⎦，， 所以：62632x πππ-≤-≤， 所以：12126sin x π⎛⎫-≤-≤ ⎪⎝⎭， 故：()12gx -≤≤．故函数g （x ）的值域为：[1-，2]． 【点睛】本题主要考查了诱导公式及二倍角的正弦公式，还考查了两角和的正弦公式，还考查了三角函数性质及转化能力、计算能力，属于中档题．4．（2018年新课标I 卷文）已知函数()e 1xf x a lnx =--．（1）设2x =是()f x 的极值点．求a ，并求()f x 的单调区间； （2）证明：当1ea ≥时，()0f x ≥． (1) a =212e ；f （x ）在（0，2）单调递减，在（2，+∞）单调递增．(2)证明见解析. 【详解】分析：(1)先确定函数的定义域，对函数求导，利用f ′（2）=0，求得a =212e，从而确定出函数的解析式，之后观察导函数的解析式，结合极值点的位置，从而得到函数的增区间和减区间；(2)结合指数函数的值域，可以确定当a ≥1e 时，f （x ）≥e ln 1exx --，之后构造新函数g（x ）=e ln 1exx --，利用导数研究函数的单调性，从而求得g （x ）≥g （1）=0，利用不等式的传递性，证得结果.详解：（1）f （x ）的定义域为()0+∞，，f ′（x ）=a e x –1x． 由题设知，f ′（2）=0，所以a =212e． 从而f （x ）=21e ln 12e x x --，f ′（x ）=211e 2e x x-． 当0<x <2时，f ′（x ）<0；当x >2时，f ′（x ）>0． 所以f （x ）在（0，2）单调递减，在（2，+∞）单调递增．（2）当a ≥1e 时，f （x ）≥e ln 1exx --．设g （x ）=e ln 1ex x --，则()e 1'e x g x x =-．当0<x <1时，g ′（x ）<0；当x >1时，g ′（x ）>0．所以x =1是g （x ）的最小值点．故当x >0时，g （x ）≥g （1）=0． 因此，当1a e≥时，()0f x ≥． 点睛：该题考查的是有关导数的应用问题，涉及到的知识点有导数与极值、导数与最值、导数与函数的单调性的关系以及证明不等式问题，在解题的过程中，首先要保证函数的生存权，先确定函数的定义域，之后根据导数与极值的关系求得参数值，之后利用极值的特点，确定出函数的单调区间，第二问在求解的时候构造新函数，应用不等式的传递性证得结果.5．已知函数2()(2)(1)x f x x e a x =-+-. （Ⅰ）讨论()f x 的单调性；（Ⅱ）若()f x 有两个零点，求a 的取值范围. （Ⅰ）见解析；（Ⅱ）()0,+∞. 【解析】试题分析：（Ⅰ）先求得()()()'12.x f x x e a =-+再根据1,0,2a 的大小进行分类确定()f x 的单调性；（Ⅱ）借助第（Ⅰ）问的结论,通过分类讨论函数的单调性,确定零点个数,从而可得a 的取值范围为()0,+∞.试题解析：（Ⅰ）()()()()()'12112.x x f x x e a x x e a =-+-=-+（Ⅰ）设0a ≥，则当(),1x ∈-∞时，()'0f x <；当()1,x ∈+∞时，()'0f x >. 所以f （x ）在(),1-∞单调递减，在()1,+∞单调递增. （Ⅱ）设0a <，由()'0f x =得x=1或x=ln （-2a ）.①若2e a =-，则()()()'1xf x x e e =--，所以()f x 在(),-∞+∞单调递增. ②若2ea >-，则ln （-2a ）＜1,故当()()(),ln 21,x a ∈-∞-⋃+∞时，()'0f x >；当()()ln 2,1x a ∈-时，()'0f x <，所以()f x 在()()(),ln 2,1,a -∞-+∞单调递增，在()()ln 2,1a -单调递减.③若2ea <-，则()21ln a ->，故当()()(),1ln 2,x a ∈-∞⋃-+∞时，()'0f x >，当()()1,ln 2x a ∈-时，()'0f x <，所以()f x 在()()(),1,ln 2,a -∞-+∞单调递增，在()()1,ln 2a -单调递减.（Ⅱ）（Ⅰ）设0a >，则由（Ⅰ）知，()f x 在(),1-∞单调递减，在()1,+∞单调递增. 又()()12f e f a =-=，，取b 满足b ＜0且ln 2ab <， 则()()()22321022a f b b a b a b b ⎛⎫>-+-=->⎪⎝⎭，所以()f x 有两个零点. （Ⅱ）设a=0，则()()2xf x x e =-，所以()f x 只有一个零点.（iii ）设a ＜0，若2ea ≥-，则由（Ⅰ）知，()f x 在()1,+∞单调递增. 又当1x ≤时，()f x ＜0，故()f x 不存在两个零点；若2ea <-，则由（Ⅰ）知，()f x 在()()1,ln 2a -单调递减，在()()ln 2,a -+∞单调递增.又当1x ≤时()f x ＜0，故()f x 不存在两个零点.综上，a 的取值范围为()0,+∞. 【考点】函数单调性，导数应用【名师点睛】本题第（Ⅰ）问是用导数研究函数单调性,对含有参数的函数单调性的确定,通常要根据参数进行分类讨论,要注意分类讨论的原则：互斥、无漏、最简；第（Ⅱ）问是求参数取值范围,由于这类问题常涉及导数、函数、不等式等知识,越来越受到高考命题者的青睐,解决此类问题的思路是构造适当的函数,利用导数研究函数的单调性或极值破解.。