四川成都市实验外国语学校2020-2021第一学期高二第二阶段性考试数学(无答案)
2023届四川省成都市实验外国语学校高三模拟考试(二)英语试题
2023届四川省成都市实验外国语学校高三模拟考试(二)英语试题一、听力选择题1. What language does the woman know a little?A．Italian.B．French.C．German.2.A．He is not lazy at all.B．He prefers online shopping.C．He’s on the way to a physical store.D．He considers shopping offline a waste of time.3. When will the game begin?A．At 8: 00.B．At 8: 30.C．At 9: 00.4. What’s John doing now ?A．Playing football.B．Watching TV.C．Studying.5. Why didn’t the woman have breakfast?A．She is busy with her paper.B．She gets used to skipping it.C．She doesn’t think it’s important.二、听力选择题6. 听下面一段较长对话，回答以下小题。
1. What day is it today?A．Wednesday.B．Thursday.C．Friday.2. What has stopped the woman taking the table by the window?A．It’s already been reserved.B．It’s in the smoking area.C．It costs more.3. What does the man suggest the woman do?A．Try another restaurant.B．Choose an outdoor table.C．Make a reservation another day.7. 听下面一段较长对话，回答以下小题。
四川省成都市金牛实验中学外国语学校2021年高二数学文测试题含解析
四川省成都市金牛实验中学外国语学校2021年高二数学文测试题含解析一、选择题：本大题共10小题，每小题5分，共50分。
在每小题给出的四个选项中，只有是一个符合题目要求的1. 设等差数列的前n项和为,若,,则当取最小值时，=（）A.6B.7C.8D.9参考答案：A2. 如图，平面中两条直线和相交于点O，对于平面上任意一点M，若、分别是M到直线和的距离，则称有序非负实数对是点M的“距离坐标”．对于给定的常数，给出下列命题：①若，则“距离坐标”为的点有且仅有1个；②若，且，则“距离坐标”为的点有且仅有2个；③若，则“距离坐标”为的点有且仅有4个．上述命题中，正确命题的个数是A.0B.1C.2D.3参考答案：D略3. 命题“”的否定是（）A. B..C. D.参考答案：A4. 已知圆M：（x﹣1）2+y2=，椭圆C：+y2=1，若直线l与椭圆交于A，B两点，与圆M相切于点P，且P为AB的中点，则这样的直线l有（）A．2条B．3条C．4条D．6条参考答案：C【分析】讨论直线AB的斜率不存在和存在，利用点差法求得直线AB的斜率，根据k MP?k AB=﹣1，求得P点横坐标，确定在椭圆内，即可得到所求直线的条数．【解答】解：当直线AB斜率不存在时且与圆M相切时，P在x轴上，故满足条件的直线有两条；当直线AB斜率存在时，设A（x1，y1），B（x2，y2），P（x0，y0），由+y12=1，+y22=1，两式相减，整理得：=﹣?，则k AB=﹣，k MP=，k MP?k AB=﹣1，则k MP?k AB=﹣?=﹣1，解得：x0=，由＜，可得P在椭圆内部，则这样的P点有两个，即直线AB斜率存在时，也有两条．综上可得，所求直线l有4条．故选：C．5. 设M=, 且a+b+c=1(其中a、b、c∈R+), 则M的取值范围是（）A． B． C． D．参考答案：D6. 在空间中，设是不同的直线，是不同的平面，且，则下列命题正确的是（）A. 若，则B. 若异面，则异面C. 若，则D. 若相交，则相交参考答案：D7. 算法的有穷性是指（）A．算法必须包含输出 B．算法中每个操作步骤都是可执行的C．算法的步骤必须有限 D．以上说法均不正确参考答案：C8. 若方程C：（是常数）则下列结论正确的是（）A．，方程C表示椭圆B．，方程C表示椭圆C．，方程C表示双曲线D．，方程C表示抛物线参考答案：C9. 已知集合,则( )A. [－1,0]B. [1,2]C. [0,1]D.(－∞,1]∪[2,+∞)参考答案：D 10. 如右图，A、B是⊙O上的两点，AC是⊙O的切线，∠B=70°，则∠BAC等于（）A. 70°B. 20°C. 35°D. 10°参考答案：B二、填空题:本大题共7小题,每小题4分,共28分11. 若三角形内切圆的半径为，三边长为,,，则三角形的面积等于根据类比推理的方法，若一个四面体的内切球的半径为，四个面的面积分是,,，则四面体的体积______________.参考答案：略12. 设圆的弦AB的中点P，则直线AB的方程是______________.参考答案：13. 甲袋中放有大小和形状相同的小球若干，其中标号为0的小球为1个，标号为1的小球2个，标号为2的小球2个.从袋中任取两个球，已知其中一个的标号是1，则另一个标号也是1的概率为__________．参考答案：记“一个标号是”为事件,”另一个标号也是”为事件，所以。
四川省成都七中实验学校2020-2021学年高二下学期期中考试数学(理)试题
【全国百强校】四川省成都七中实验学校2020-2021学年高二下学期期中考试数学（理）试题学校:___________姓名：___________班级：___________考号：___________一、单选题1．如图，直三棱柱111ABC A B C -中，若CA a =，CB b =，1CC c =，则1A B 等于（ ）A ．a b c +-B ．a b c -+C ．b a c --D ．b a c -+ 2．函数()sin x f x x e =+，则()'0f的值为( ) A ．1 B ．2 C ．3 D ．03．已知m ，n 表示两条不同直线，α表示平面，下列说法正确的是（ ）A ．若//,//,m n αα则//m nB ．若m α⊥，n α⊂，则m n ⊥C ．若m α⊥，m n ⊥，则//n αD ．若//m α，m n ⊥，则n α⊥ 4．函数()()1ln x f x x x =>的单调递减区间是( ) A ．(1,)+∞ B ．2(1,)e C ．(1,)e D ．(,)e +∞ 5．如图，在棱长为2的正方体1111ABCD A B C D -中，O 是底面ABCD 的中心，E 、F 分别是1CC 、AD 的中点，那么异面直线OE 和2016v v =所成角的余弦值等于A BC ．45D ．236．已知函数()sin f x x x =-,若12,,22x x ππ⎡⎤∈-⎢⎥⎣⎦且()()120f x f x +>,则下列不等式中正确的是( )A ．12x x >B ．12x x <C ．120x x +>D ．120x x +< 7．某几何体的三视图如图所示，且该几何体的体积是32，则正视图中的x 的值是（ ）A ．2B ．92C ．32D ．38．若对任意的0x >，恒有()ln 10x px p ≤->成立，则p 的取值范围是（ ） A ．()0,1 B ．(]0,1 C ．()1,+∞ D ．[)1,+∞ 9．甲、乙两人约定在下午4:305:00~间在某地相见，且他们在4:305:00~之间到达的时刻是等可能的，约好当其中一人先到后一定要等另一人20分钟，若另一人仍不到则可以离去，则这两人能相见的概率是（ ）A ．34B ．89C ．716D ．111210．如图在一个60的二面角的棱上有两个点A 、B ，线段AC 、BD 分别在这个二面角的两个面内，并且都垂直于棱AB ，且1AB AC ==，2BD =，则CD 的长为( )A ．2BCD ．1 11．已知函数()32f x ax bx cx d =+++的图象如图所示，则12b a ++的取值范围是( )A ．21,52⎛⎫- ⎪⎝⎭B ．13,22⎛⎫- ⎪⎝⎭C ．35,22⎛⎫- ⎪⎝⎭D ．31,22⎛⎫- ⎪⎝⎭ 12．已知曲线()21:0,0C y tx y t =>>在点4,2M t ⎛⎫⎪⎝⎭处的切线与曲线12:1x C y e +=-也 相切，则24ln e t t的值为（ ） A ．24eB ．8eC ．8D ．2二、填空题13．120x dx =⎰_______.14．已知椭圆22122:1(0)x y C a b a b+=>>与双曲线222:4C x y -=有相同的右焦点2F ，点P 是椭圆1C 与双曲线2C 在第一象限的公共点，若22PF =，则椭圆1C 的离心率等于_______.15．已知函数()()f x x R ∈的导函数为()f x '，满足()37f =，()2f x '<，则()21f x x <+的解集为_______.16．已知函数()211xme f x x x =-++，若存在唯一的正整数0x ，使得()00f x ≥，则实数m ∈_______.三、解答题17．如图，在直三棱柱111ABC A B C -中，AC BC ⊥，点D 是AB 的中点．求证：（1）1AC BC ⊥；（2）1//AC 平面1B CD ．18．某校举行汉字听写比赛，为了了解本次比赛成绩情况，从得分不低于50分的试卷中随机抽取100名学生的成绩(得分均为整数，满分100分)进行统计，请根据频率分布表中所提供的数据，解答下列问题：（Ⅰ）求a b 、的值；（Ⅱ）若从成绩较好的第3、4、5组中按分层抽样的方法抽取6人参加市汉字听写比赛，并从中选出2人做种子选手，求2人中至少有1人是第4组的概率．19．已知函数()22ln f x x a x =+。
2020-2021成都市实验外国语学校(西区)小学数学小升初第一次模拟试题(附答案)
2020-2021成都市实验外国语学校（西区）小学数学小升初第一次模拟试题(附答案)一、选择题1．如图：r＝3dm，这个扇形的面积是（）dm2．A. 28.26B. 9.42C. 7.065D. 4.71 2．在下面边长是10cm的正方形纸中，剪去一个长6cm、宽4cm的长方形，下列四种方法中，剩下的部分（）的周长最长．A. B. C.D.3．分别用5个大小相同的小正方体搭成下面的三个立体模型，从（）看这三个立体模型的形状是完全一样的。
A. 前面B. 上面C. 左面4．甲、乙两数的比是3：4，那么甲比乙少（）.A. B. C. D.5．如图，阴影部分的面积相当于甲圆面积的，相当于乙圆面积的，那么甲、乙两个圆的面积是（）.A. 6： 1B. 5： 1C. 5： 6D. 6： 5 6．用6个同样大小的正方体拼成一个立体图形，从上面、正面和左面看到的形状完全一样，这个立体图形是（）。
A. B. C.D.7．当a表示所有的自然数0，1，2，3，…时，2a表示（）。
A. 奇数B. 偶数C. 质数D. 合数8．钟面上，时针经过1小时旋转了（）度。
A. 30B. 60C. 180D. 3609．下列描述正确的是（）A. 在图上可以找到-5、20、3.5三个数对应的点。
B. 上图中，直线上的数不是正数就是负数。
C. 在0和3之间的数只有1和2．10．把正方体的表面展开，可能得到的展开图是（）。
A. B. C. D.11．一个零件长4毫米，画在图上长12厘米。
这幅图的比例尺是（）。
A. 1：30B. 1：3C. 30：1D. 3：1 12．在一个圆中剪掉一个圆心角是90°的扇形，其余部分占整个圆面积的（）A. B. C. D.二、填空题13．一个直角三角形两个锐角度数的比是1：4，则这两个锐角分别是________度和________度。
14．如图中∠1是________°，按边分是一个________三角形，它有________条对称轴．15．汽车与轿车的速度之比为5：7，两车同时从甲乙两地出发，相向而行，两车的相遇地点距离中点16km。
四川省成都市成都实验外国语学校2023-2024学年下学期新七年级分班(奖学金)真题数学试题
四川省成都市成都实验外国语学校2023-2024学年下学期新七年级分班（奖学金）真题数学试题一、单选题1．（分数的基本性质）把分数a 的分子扩大到原来的9倍，分母扩大到原来的11倍，得到一个新分数b ；把分数a 的分子扩大到原来的8倍，分母扩大到原来的9倍，得到一个新分数c ．那么b 和c 比较（ ）A ．b c >B ．b c <C ．b c =D ．无法比较 2．（行程问题）从甲地到乙地，小明的平均速度是每分钟120米，已知他往返的平均速度是每分钟90米，那么他返回的平均速度是每分钟（ ）米．A ．60B ．72C ．75D ．1053．（百分数的应用）一件上衣，如果卖84元，可赚12%，如果要赚40%，那么应该卖（ ）元．A ．98B ．100C ．105D ．1144．（等量代换）王老师去买书，买4本故事书和8本漫画书共需136元，买同样的3本故事书和10本漫画书共需150元．8本故事书和4本漫画书共（ ）A ．80B ．50C ．96D ．1285．（分数、百分数的应用）某班的男生比全班人数的59少4人，女生比全班人数的40%多6人，那么这个班男生比女生少（ ）人．A ．5B ．3C ．9D ．10二、填空题6．开始时，王老师的积分券有120张，小明的积分券数量是小李的两倍．后来，王老师给小明和小李发了相同数量的积分券，现在三人的积分券数量之比为2:4:3．现在王老师还剩积分券( )张．7．（发车间隔问题）甲、乙两地是电车发车站，每隔一定时间两地同时发出一辆电车．小王骑自行车每隔12分钟就被一辆后面开来的电车追上，每隔8分钟就与一辆迎面开来的电车相遇．那么相邻两辆电车的发车时间相差分钟．8．（数字问题）小王家的WiFi 密码是一个六位数，其中左边三个数字是由小到大的3个连续自然数，右边三个数字都相同，6个号码的数字之和恰好等于末尾的两位数，这个WiFi密码是．9．（有理数的乘法）算式18152010⨯⨯⨯⋅⋅⋅⨯的乘积末尾有个连续的0．10．（倍数问题）1至40这40个自然数中，最多可以取出个个数，使得其中每两个数的和都不是4的倍数．11．（计数原理）甲、乙、丙、丁四人各有一个作业本混放在一起，4个人看也不看就随便各拿了1本，那么至少有一人拿错的可能有种．12．（行程问题）甲、乙两人进行百米赛跑，当甲到达终点时，乙在甲后面15米，如果甲、乙两人的速度保不变，要使甲、乙两人同时到达终点，甲的起跑线要比原来向后移动米．13．（行程问题）某人从山脚上山平均每小时行35千米，从山顶沿原路下山时平均每小时行40千米，往返一次共用7.5小时，山脚到山顶的距离是千米．14．（工程问题）甲、乙两管同时打开，10分钟就能注满水池．现在先打开甲管，9分钟后再打开乙管，再过4分钟就注满了水池．已知甲管比乙管每分钟多注入0.28立方米的水，那么这个水池的容积是立方米．15．某团体有100名会员，男会员与女会员的人数比是14:11，会员分三组，甲组人数与乙、丙两组人数之和一样多．各组男会员与女会员人数之比是：甲12:13，乙5:3，丙2:1，则丙有名男会员．三、解答题16．计算：(1)5223 522522526527523523÷+÷(2)2349899 1239798 34599100 129697 58112932964599100+++⋅⋅⋅+++++⋅⋅⋅++(3)5291113154143···6720304256420462 -+-+-++-(4)3818326 21334515965997118.513985⎛⎫-÷+⨯⎪⎝⎭⎛⎫-⨯⎪⎝⎭(5)121079289 21201514 x x x x----+=+17．（组合图形求面积）如图，长方形ABCD 的面积为2平方厘米，2EC DE =，F 是DG 的中点，则阴影部分的面积是多少？18．（组合图形求面积）如图ABCD 是平行四边形，8cm AD =，10cm AB =，30DAB ∠=︒，高4cm CH =，弧BE 、DF 分别以AB 、CD 为半径，弧DM 、BN 分别以AD 、CB 为半径，阴影部分的面积为多少？（π取3）19．（工程问题）某车间有28名工人生产某种螺栓和螺母，每人每天能生产螺栓12个或螺母18个，为了合理分配劳动力，使生产的螺栓和螺母配套（一个螺栓套两个螺母），则应分配多少人生产螺栓，多少人生产螺母？20．（百分数的应用）甲、乙、丙三杯糖水的浓度分别为40%,48%,60%，将三杯糖水混合后浓度变为50%，如果乙、丙两杯糖水质量一样，都比甲杯糖水多30克，那么三杯糖水共有多少克？21．某商店面包的成本是定价的80%，可乐的定价是10元，成本是8元．现在商店把2个面包与1杯可乐配套出售，并且按它们的定价之和的90%出售．这样每套可获得利润3元．面包的成本是多少元？22．（盈亏问题）小明从家到学校上课，开始时每分钟走50米，走了2分钟，根据以往经验，按照这个速度走下去，将要迟到2分钟，于是他立即加快速度，每分钟多走10米，结果小明早到了5分钟，小明家到学校的路程有多远？23．（经济问题）春节期间，某商店按下面两种方式促销，第一种方式：减价20元后再打八折；第二种方式：打八折再减20元．刘老师到商店买了两件不同的商品，其中一件按第一种方式促销，另一件按第二种方式促销，共花了252元．已知两件商品的原价都大于100元，而且其中一件商品的原价是另一件的整数倍（倍数大于1)，那么这两件商品的原价分别是多少元？。
四川省成都市实验外国语学校2020—2021学年九年级下学期一诊考试英语试卷(含答案)
成都市实验外国语学校2020—2021年学年度下期一诊考试九年级英语试题考试时间120分钟满分150分A卷（共100分）第一部分听力测试（共35分）Ⅰ.Listen to the sentences carefully and choose the right picture for each sentence.Each sentence will be read only once.(4scores)A. B. C. D.1._________2.__________3.___________4.____________II.Listen to the sentences carefully and choose the correct responses.Each sentence will be read only once.(5scores)5.A.Yes,he is. B.Yes,it is. C.Yes,I am.6.A.My pleasure. B.That’s right. C.Sounds greatl17.A.Yes,that’s true. B.Sorry to hear that. C.How careless you are.8.A.I think so. B.Me too. C.See you9.A Well done. B.Thanks a lot C.Not good enoughIII.Listen to the short dialogues carefully and choose the best answer to each question.Each dialogue will be read twice.(6scores)10.What’s the price of the day flight?A.$360B.$400C.$45011.What is the probable relationship between the speakers?A.Schoolmates.B.Boss and employee.C.Salesman and customer.12.What are the speakers talking about?A.An office.B.A shopping center.C.A house.13.How often does Susan go to the gym?A.Every day.B.Twice a week.C.Four times a week.14.What does the singer’s hair look like?A.Long and dark.B.Short and blondeC.Short and dark15.What will the speakers do first?A.Have brunch.B.Check out.C.Go to the airport.IV.Listen to the long dialogue carefully and judge the following statements true or false.If it’s true,please choose“A”;if it’s false,please choose“B”.The dialogue will be read twice.(5scores)16.The man’s grandson will meet him at the airport.17.The man has been to Berlin,Paris and London.18.The man first went to Europe during World WarⅠ.19.The man will spend two weeks in London with his wife and grandson.20.The conversation probably happens in a restaurant.V.Listen to two short passages carefully and choose the best answer to each question.Each passage will be read twice.(10scores).21.What does Peter probably do?A.A famous painter.B.An art expertC.A museum worker.22.When did Peter find the painting?A.Before the museum was open.B.After the museum was closed.C.During his visit to the museum.23.Why did the director decide to hang the painting up in the museum?A.The painting was beautifully designed by Peter.B.Quite a few experts thought highly of the painting.C.The director thought the painting was of great art value.24.Why did the boy cry in front of the painting?A.Because he found his painting was not good enough.B.Because he wanted to have his painting back.C.Because he was not satisfied with his painting.25.How did the director feel after he heard the truth?A.Mad.B.Proud.C.Shocked.B26.Who designed the White House?A.George Washington.B.John Adams.C.James Hoban.27.Which president first moved into the White House?A.The first.B.The second.C.The third.28.When was the White House rebuilt?A.In1790.B.On Nov.1st1800.C.After the War of1812.29.Which of the following statement is Correct?A.The White House caught fire by accident in1812.B.Visitors aren’t allowed to visit any public places in the White House.C.It was in1792that people began to build the White House.30.What does the speaker mainly talk about?A.The history of the White HouseB.Some American presidents.C.The rebuilding of the White House.VI.Listen to the passage carefully and complete the chart with no more than THREE.words for each blank.The passage will be read three times.(5scores)Teenagers and part-time jobs in the UK31The children find job to make some pocket money.and learn life experience.Advantages Teenagers learn to be independent,32and know how to manage the money.Doing part-time jobs helps with job hunting in the future.Recent situation_______teenagers in the UK take part-time jobs compared with five years ago.Experts’findings Teenagers feel more stressed to study hard.Doing part-time jobs may34.Conclusion It’s necessary to35between study and part-time jobs.第二部分笔试（共65分)I.Choose the best answers to fill in the blanks.(10scores)36.There will be_______exhibition of the landscape paintings next week.A.aB.anC.the37.—Do you want coffee or tea,Madam?—______.I don’t really mind.A.NeitherB.EitherC.None38.—I think everyone should play a part in saving our environment.—I agree.There will be less air pollution_____we drive less.A.ifB.thoughC.unless39.Wolf Warriors is a fantastic movie_______almost every Chinese loves.A.whoB.thatC.what40.—Whose trumpet is this?Is it Sam’s?—It_______be his.Don’t you remember he didn’t come to the studio today?A.can’tB.mightC.mustn’t41.The lady______behind me is my aunt.She’s a college professor.A.sittingB.to sitC.sat42.Anthony________in a big storm when the boat engine suddenly broke down.A.sailedB.was sailingC.has been sailing43.Don’t forget_______the lights when they are not in use!A.to turn offB.turning onC.turning off44.During the Spring Festival,paper cuttings______on doors,windows and walls.A.are putting upB.put upC.are put up45.—Sir,could you please tell me______?—Sure.There is one on Tong Xin Road and it opens for24hours per day.A.where is the nearest caféB.when the nearest caféopensC.if there is a cafénearbyplete the dialogue and fill In the blanks with the sentences given in the box.(5scores) A:Good morning,doctor!B:Good morning,lady!46A:I am not feeling well.I have a sore throat and cough a lot these days.B:47A:Yes,of course.But I don’t have a fever.B:How long have you been like this?A:48B:Don’t worry.Many people have the same situation as you because of the cold weather.A:I see.49B:Drink more water and try to stay in bed for a couple of days,then you’ll get better soon.A:50Thank you.B:You are welcome.A.So what should I do?B.Ever since last Friday.C.OK,I will.D.What’s the matter with you?E.Have you taken your temperature?Ⅲ.Cloze test.Fill in the blanks with the best choices to complete the passages.(20scores)AHaving a positive attitude towards life is extremely important in all aspects,especially in an interview.Most people do poorly at interviews because they don’t have a positive attitude.In other words,they are51and forget all of their strengths and achievements.Don’t be shy!Tell the world about the good things you have done.Here are some things to encourage you and improve your performance in life.Always keep52with people you are talking to.Looking into someone’s eyes is helpful to show your ideas.Besides,your smile will cheer up everyone.Always look on the bright side of life.Point out advantages of everything and everyone. Every person has shining points,find them!Be53to learn something new every day.Be generous to54something interesting with your partner every day.Always say more than“yes or no”55you are asked.As long as you know the above tips,your life will be filled with active responses.51.A.excited B.nervous C.strange52.A.personal distance B.physical signal C.eye contact53.A.glad B.scared C.mad54.A.play B.work C.share55.A.how B.when C.whatBThere are purple clothes,purple handbags,purple bicycles,purple furniture,even purple computers!So purple is one of the most56colors today.But in the past,purple was a very expensive and unusual color.Let’s take a look at the rich history of the color purple.Some scientists believe that the first plants to appear on Earth over500million years ago probably looked purple,not green.Plants today are green because57use green chlorophyll(叶绿素)to produce energy.But these early plants probably used something called retinal,which is a dark purple color.During the time of the Roman Empire(37BC-476AD),it was very58to make purple dye. The dye came from sea snails(海螺).But10,000dead sea snails59you just one gram of purple dye...as well as a very bad smell!This special purple dye was called Tyrian purple,and it was the preferred color of emperors.In16th-century.England,purple was60for the king’s family members.Queen Elizabeth I’s clothes were purple,but ordinary people were not allowed to61the color.In.1856,William Perkin,an18-year-old62student,noticed something strange while doing an experiment.The chemicals he used to clean his instruments63with the:chemicals he used in his experiment and produced a bright purple color.The64led Perkin to start a company using this chemical mixture to make purple dye.The dye was much65than sea snail dye.Thanks to Perkin, now anyone can afford to wear purple clothes.56.A.peaceful B.popular C.exciting57.A.others B.they C.we58.A.dangerous mon C.difficult59.A.got B.wasted C.cost60.A.even B:never C.only61.A.wear B.make C.change62.A.geography B.science C.artpared B.mixed C.connected54.A.experiment B.chemicals C.discovery65.A.darker B.more expensive C:cheapeIV.Reading comprehension.Read the passages and choose the best answers.(30scores)AToothpaste does more than just keep our teeth bright and white.It can be used wisely in many other ways.Here are some useful tips that can save us time and money,and leave a fresh smell——using toothpaste!Clean a Dirty MirrorIf you want to clean a dirty bathroom mirror,try to put a bit of toothpaste on the mirror and wipe it dry.The glass can be cleaned up beautifully.And doing this can also stop the mirror from fogging.Then you can still see yourself in the mirror after taking a shower.Remove the Unpleasant Food SmellHave some bad food smell,like the smell of onions or fish,on your hands?You can remove it by washing your hands with toothpaste,You’ll be fresh-smelling in no time.Make Your Sports Shoes WhiterThis time,clean your sports shoes by yourself,not by your mother.Wipe some toothpaste around your shoes and then clean it with a wet cloth.See?Your shoes are white as new!A little toothpaste also does an amazing job of removing scuffs（磨痕）from leather shoes.Just put a little on the scuffed area and clean with a soft cloth.The leather will look new again.Make the Metal ShiningRings will get not so bright or shiny over time,yet with a little bit of toothpaste and a good washing,they’ll be shining away right away.But do not use this method on pearls(珍珠),as it will hurt the surface.66.The passage is written to introduce________.A.how to use the toothpaste in other waysB.where to buy cheaper toothpasteC.what we need to make the toothpaste67.With the help of the toothpaste,the mirror will be________.A.foggyB.clearC.fresh-smelling68.We can use the toothpaste to deal with_________.A.holes in sports shoesB.scuffs on leather shoesC.the dull pearls69.The underlined word“surface”means________.A.表层B.内部C.质地70.In which column（栏目）of the newspaper can the passage found?A.Entertainment.B.Culture.C.Life.BMaking friends with ducksIn traditional pet stores,you can buy an animal to be your companion at home.But there’s a new kind of“pet store”where you can spend some time with animals and just walk away without taking any of them with you.What really matters is to be there.My colleagues and I visited one of these stores in the Sanlitun neighborhood of Beijing.We were looking for Call ducks(柯尔鸭),a Dutch species of pet ducks.They are famous for their cute looks and their sky—high prices—one of them can easily cost a few thousand yuan.Since we were not planning to spend so much on a duck any time soon,visiting them in one of these places —what I’d call“mini-zoos”—seemed to be the perfect choice.There were five Call ducks at the store and we spent a good three hours with them.We learned a lot about the species.Call ducks are not as obedient enough to follow what they are told to do as dogs,so playing with them takes lot of running from our side and quacking(呱呱叫)from theirs.Also,don’t expect them to be house-trained—one of the ducks actually pooped(排便)sitting on my leg.But none of this took the pleasure out of holding them in my hands and touching their full chests.That’s the magic of animals—you are refreshed again.71.According to the passage,the new kind of pet stores________.A.sell Call ducks at a very high priceB.provide the service of experiencingC.teach rich knowledge about animals72.The underlined word obedient is closest in meaning to__________.A.strongB.gentleC.honest73.It’s clear that Call ducks________.A.are better companions than dogsB.like running after people aroundC.are difficult to be house-trained74.The writer wants to tell us_________.A.the trip to mini-zoos is very refreshingB.spending time with animals is fashionableC.keeping pets at sky-high prices is unnecessary75.What would be another title for this passage?A.To Touch Is MagicB.To Be There Is EnoughC.To Visit Is CheapCThere are quite a few advantages of wearing school uniforms.The idea may seem disagreeable at first,but considering all the positive effects coming from wearing uniforms you would be more likely to enjoy them.Teachers love school uniforms because it helps provide an orderly learning environment. Having students dressed in uniforms may teach them how to present themselves in a neat and professional manner.It gives students the opportunity to learn how to dress like young ladies and gentlemen.And they can focus their attention on studies rather than fashion.Buying school uniforms is easy.No matter what the school rules are,there are only several pieces to the wardrobe that are necessary,so it won’t break the bank.School uniforms can last a long time.Parents could also enjoy an easy morning,as it will take less time to choose a set of clothes for the school day.Students wearing uniforms will feel less pressure about what to wear or not to wear when their classmates are dressed similarly.Getting dressed before school becomes less of a chore whenstudents are limited in their choices,so there shouldn’t be any trouble about choosing an outfit for the day and getting ready quickly.Some students may not like the lack of individuality with uniform,but it doesn’t matter so much.Right?Uniforms today are also becoming more fashionable and can be seen in many areas of pop culture.Celebrities and fashion designers are using uniforms as inspiration for new looks which also attract students.76.What would be the best title for the text?A.How to Dress Properly.B.The History of School Uniforms.C.The Advantages of School Uniforms.77.Teachers think that wearing school uniforms_________.A.is just a tradition that students should followB.helps students put more effort into their studiesC.makes students feel less pressure in study78.The underlined part“It won’t break the bank”in Paragraph3probably means“_________.”A.a school uniform doesn’t cost a lot of moneyB.a school uniform should be worn every dayC.parents who work in a bank can afford the uniform79.We can infer from the text that school uniforms_________.A.are not popular with fashion designersB.were not accepted by parents in the pastC.will be more popular in the future80.The author’s attitude towards school uniforms is__________.A.supportiveB.negativeC.doubtfulB卷（共50分）Ⅰ.Pattern shift.Rewrite the following sentences according to the instructions.(5scores)1.I enjoy reading science fiction.My wife enjoys reading science fiction too.I enjoy reading science fiction.__________________my wife.2.The terrible earthquake has made thousands of people homeless.(Change it into the passive voice.)3.“Don’t leave the office without permission,”the teacher said to the students.(Change it into the indirect speech.)4.The old couple who live next door got married fifty years ago.(Change it into the present perfect tense.)5.Our teachers have given us lots of helpful suggestions in the past three years.(Change it into an exclamatory sentence.)plete the dialogue and fill in each blank with only one word.(10scores)W:Hi,Bezos.Did you have a good time yesterday?M:Hey,Marta.Forget about it.W:What was the matter?You didn’t enjoy the film?M:Oh,the movie was fine.I just got6by the couple sitting beside me.W:What happened?M:Well,first they came in7.They spent a while getting into the8.All this was happening during an exciting part of the film.And then they started talking.W:Oh,I hate it.M:The man had seen the.film before.He was telling the woman the9story.W:What?Unbelievable!M:Yeah,the beginning,development even the ending and you won’t believe what happened10!A young man asked them to be quiet.11,of course.W:Wow,he still has very good manners in such a situation.So they12in reply.Right?M:No way.You can’t imagine the three got into an13several minutes later!Their voices were so loud that everyone around them started14.W:Well,what finally happened?M:The manager of the cinema had to be called in.Everyone quieted down eventually,but it was too late.They damaged my mood for the movie.W:What a pity!The couple must be15of their behavior.III.Choose10from the12words in the box to complete the passage with their proper forms.Each word can be used only once.(10scores)accept bad comfortable frightening fast imagine loud I not pass place strongAs a child,I was really afraid of the dark and of getting lost.These fears were very real and caused me some16moments.Maybe.it was the.strange way things looked and sounded in my own room at night that17 me so much.There was never complete darkness,but always a streetlight or18car lights,which made clothes on the back of a chair take on the shape of a wild animal.Out of the corner of.my eye,I saw the curtains seem to move when there was19wind.A very low sound in the floor would seem a hundred times20than in the day.My21would run wild,and my heart would beat 22.I would lie very still so that the“enemy”would not discover me.Another of my childhood fears was that I would get lost,especially on the way home from school.Every morning I got on the school bus right near my home.That was no problem.After school,though,when all the buses were lined up along the street,I was afraid that I would get in the wrong one and be taken to some other strange23.On school or family trips to a park or a museum,I wouldn’t let the leaders out of my sight.Perhaps one of24fears of all I had as child was that of not25or liked by others.One of the processes growing up is being able to realize and overcome our fears. Understanding the things that scared us as children helps us achieve greater success later in life. plete the passage and fill in the blanks with the sentences given in the box.Each can be used only once.(5scores)Taking exercise regularly can improve your health.It leads to much better use of vitamins, minerals as well as oxygen in your body.26,you may miss some periods of exercise in the end.If exercise is so good for your health,what happens when you miss a few parts?You should balance the amount of exercise and the amount of time allowed for recovery from exercise.Quality must always come before quantity(量).Shortly after you stop normal exercise, obvious changes begin to happen in your body based upon your level of fitness.27.Once you stop exercising,the amount of oxygen you breathe into your body is influenced.28.And there is a decrease in your strength.Other important factors of physical fitness are also influenced.So what can you do with these changes?29.If you are injured or sick,talk with your doctor to find out what kind of exercise you can safely perform.30,it is high time you started your practice of exercising regularly.There are many choices of exercise for you to choose from.Just choose one that matches your personal interest.Great interest can help you stick to your exercise schedule.A.Since regular exercise is good for your healthB.This change will do harm to the balance in your bodyC.Sometimes,although you’ve made efforts to exerciseD.You should get back to your regular exercise scheduleE.Even though you’ve kept the same level of physical activityF.The lack of exercise influences how you look,feel and represent yourselfV.Task-based reading.Finish each task according to the requirement.(5scores) Have you ever heard someone use the phrase“once in a blue moon”?People use this expression to describe something that they do not do very often.For example,someone might say that he tries to avoid eating sweets because they are unhealthy,but will eat chocolate“once in a blue moon”.Or someone who does not usually like to go to the beach might say“I visit the shore once in a blue moon”.While many people use this phrase,not everyone knows the meaning behind it.The first thing to know is that the moon itself is never really blue.This is just an expression. In fact,the phrase“blue moon”has to do with the_______,not the________.As the moon travels around the earth,it appears to change shape.We connect certain names with certain shapes of the moon.For example,when we can see a small part of the moon it is called a crescent moon.A crescent is a shape that looks like the tip of fingernail.When we cannot see the moon at all,it is called a new moon.When we can see the whole moon,it is called a full ually,there is only one full moon every month.However,sometimes there will be two full moons in one month.When this happens,the second full moon is called“a blue moon”.Over the next20years,there will only be15blue moons.As you can see,a blue moon is a very rare event.This fact has led people to use the expression“once in a blue moon”to describe other very rare events in their lives.31.The phrase“once in a blue moon”is used to describe something that________happens.(only one word)32.A blue moon happens in nature when_______________________.(no more than8words)33.Find out a letter in the alphabet which has a crescent shape.9plete the sentence in the second paragraph.35.The underlined part“This fact”in the last paragraph refers to_____________________.(no more than8words)position.(15scores)The Chengdu2021World University Games Summer will be put off to2022because of the global COVID-19situation.We have more time to prepare for it.It is reported that more than 10,000athletes from about170countries and regions will battle it out.Please write an article with the theme---Love Chengdu.Welcome the Universiade2022.The following points should be included.(Write90—120words)1.A short introduction of Chengdu.(location,speciality...)2.The advantage the event brings to our city.3.What can the citizens do to welcome the big event?(At least2points)4.Would you like to do some volunteer work?And the reasons.成都市实验外国语学校2020—2021年学年度下期一诊考试参考答案A卷I.1-4DACBII.5-9BCABBIII.10-15BBCBBAIV.16-20ABBBBV.21-25CBCBC26-30CBCCAⅥ.31.Parent’s expectations32.work with adults33.fewer34.influence teenagers’study35.keep balance笔试I.36-45BBABA ABACCII.46-50DEBACIII.51-55BCACB56-65BBCAC ABBCC IV.66-70ABBAC71-75BBCAB 76-80CBACAB卷I.te8.seats9.hole10.then11.politely12.stopped13.argumentplaining15.ashamedIII.16.uncountable17.frightened18.passing19.no20.louder 21.imagination22.fast23.places24.the worst25.been acceptedIV.26-30CFBDA20V.31.hardly32.there are two full moon in one month33.C34.shape color35.a blue moon is very rare event.。
四川省成都市外国语学校2022-2023学年九年级上学期期中数学考试
成都外国语学校2022-2023学年度上期期中考试初三数学试卷A卷一．选择题（本大题共8个小题，每小题4分，共32分）1．如图所示的几何体的左视图是（）2．下列说法正确的是（）A．对角线互相垂直的四边形是菱形B．矩形的对角线互相垂直C．对角线相等的菱形是正方形D．一组对边平行的四边形是平行四边形3．已知两个相似三角形的相似比为1：4，则它们的对应高的比为（）A．1：2B．1：4C．1：8D．1：164．要估计鱼塘中的鱼数，养鱼者首先从鱼塘中打捞了50条鱼，在每条鱼身上做好记号后把这些鱼放归鱼塘，再从鱼塘中打捞出200条鱼，发现只有两条鱼是刚才做了记号的鱼，假设鱼在鱼塘内均匀分布，那么估计这个鱼塘的鱼数约为（）A．1750条B．1250条C．5000条D．2500条5．关于x的一元二次方程kx2+2x﹣1＝0有两个不相等的实数根，则k的取值范围是（）A．k＞﹣1B．k＞﹣1且k≠0C．k＜1D．k＜1且k≠06．对于函数y＝，下列说法错误的是（）A．点（，6）在这个函数图象上B．这个函数的图象位于第一、三象限C．这个函数的图象既是轴对称轴图形又是中心对称图形D．当x＞0时，y随x的增大而增大7．有一根1m长的铁丝，怎样用它围成一个面积为0.06m2的长方形？设长方形的长为xm，依题意，下列方程正确的是（）A．x（1﹣x）＝0.06B．x（1﹣2x）＝0.06C ．x （0.5﹣x ）＝0.06D ．2x （1﹣2x ）＝0.06 8．已知菱形的周长为4，两条对角线的和为6，则菱形的面积为（ ） A ．2 B ． C ．3 D ．4二．填空题本（大题共5个小题，每小题4分，共20分）9．已知函数y ＝（m +3）x |m |﹣4是反比例函数，则m ＝ ．10．如图，在Rt △ABC 中，CD 是斜边AB 上的中线，∠A ＝20度，则∠BCD ＝ 度．11．如果a +b +c ＝0，那么一元二次方程ax 2+bx +c ＝0必有一个根是 ．12．把12cm 长的线段进行黄金分割后得两条线段，其中较长的线段的长为 cm ．13．如图，小明在B 时测得直立于地面的某树的影长为12米，A 时又测得该树的影长为3米，若两次日照的光线互相垂直，则树的高度为 米．三．解答题（本大题共5个小题，共48分）14．（12分）（1）计算：01-23-2821-2）（）（）（++ （2）计算：5422-=-x x x15．（8分）为了丰富校园文化生活，提高学生的综合素质，促进中学生全面发展，学校开展了多种社团活动．小明喜欢的社团有：合唱社团、足球社团、书法社团、科技社团（分别用字母A ，B ，C ，D 依次表示这四个社团），并把这四个字母分别写在四张完全相同的不透明的卡片的正面上，然后将这四张卡片背面朝上洗匀后放在桌面上．（1）小明从中随机抽取一张卡片是足球社团B 的概率是多少？（2）小明先从中随机抽取一张卡片，记录下卡片上的字母后不放回，再从剩余的卡片中随机抽取一张卡片，记录下卡片上的字母．请你用列表法或画树状图法求出小明两次抽取的卡片中有一张是科技社团D 的概率．16．（8分）如图，在矩形ABCD 中，AB ＝3，AD ＝6，动点E 在边BC 上，连接DE ，过点A 作AH ⊥DE ，垂足为H，AH交CD于F．（1）求证：△CDE∽△DAF；（2）当FC＝2时，求EC的长．17．（10分）如图，在平面直角坐标系中，把以格点为顶点的三角形称为格点三角形（每个小方格都是边长为1的正方形）．图中△ABC是格点三角形，点A、B、C的坐标分别是（﹣3，﹣1），（﹣2，﹣3），（0，﹣2）．（1）画出△ABC关于x轴对称的△A1B1C1；（2）以O为位似中心，在第一象限内将△ABC放大为原来的2倍，得到△A2B2C2，画出△A2B2C2；（3）△ABC内有一点P（a，b），直接写出经过（2）位似变换后P的对应点P1的坐标．18．（10分）如图，在平面直角坐标系中，一次函数y1＝x﹣2的图象与反比例函数（k≠0）的图象交于A（﹣2，a）、B（m，2）两点，与y轴交于点C，与x轴交于点D，连接OA、OB．（1）求反比例函数（k≠0）的表达式；（2）求△AOB的面积；（3）点N为坐标轴上一点，点M为y2的图象上一点，当以点C、D、M、N为顶点的四边形是平行四边形时，请直接写出所有满足条件的N点的坐标．B卷一、填空题（本大题共5个小题，每小题4分，共20分）19．设m、n分别为方程x2+2x﹣2025＝0的两个实数根，则m2+3m+n＝．20．完全相同的四张卡片上分别印有正三角形、正方形、正五边形和正六边形，现将印有图形的一面朝下，混合均匀后先由甲随机抽取一张，放回后，重新混合均匀再由乙随机抽取一张，则甲乙两人抽到的图形都是中心对称图形的概率为 ．21．若以方程x 2﹣2（k ﹣3）x +k 2﹣4k ﹣1＝0的两个实数根作为横坐标、纵坐标的点恰在反比例函数y ＝的图象上，则满足条件的k 值为 ．22．如图，点P 是等边△ABC 的一边BC 上的任意一点，且BP CP 3 ，连接AP ,作AP 的垂直平分线交AB 、AC 于M 、N 两点，则AN AM :的值为 ．23．如图，在边长为4正方形ABCD 中，以AB 为腰向正方形内部作等腰△ABE ，点G 在CD 上，且CG ＝3DG ．连接BG 并延长，与AE 交于点F ，与AD 延长线交于点H ．连接DE 交BH 于点K ．若AE 2＝BF •BH ，则S △CDE ＝ ．二、解答题（本大题共3个小题，共30分）24．（8分）由于新冠疫情的影响，口罩需求量急剧上升，经过连续两次价格的上调，口罩的价格由每包10元涨到了每包16.9元．（1）求出这两次价格上调的平均增长率；（2）在有关部门大力调控下，口罩价格还是降到了每包10元，而且调查发现，定价为每包10元时，一天可以卖出30包，每降价1元，可以多卖出5包．当销售额为315元时，且让顾客获得更大的优惠，应该降价多少元？25．（10分）问题背景 如图（1），已知△ABC ∽△ADE ，求证：△ABD ∽△ACE ；尝试应用 如图（2），在△ABC 和△ADE 中，∠BAC ＝∠DAE ＝90°，∠ABC ＝∠ADE ＝30°，AC 与DE相交于点F，点D在BC边上，＝，求的值；拓展创新如图（3），D是△ABC内一点，∠BAD＝∠CBD＝30°，∠BDC＝90°，AB＝4，AC＝2，直接写出AD的长．26．（12分）如图1，在平面直角坐标系xOy中，点A（﹣1，0），B（4，0），点C在y轴的负半轴上，连接AC，BC，满足∠ACO＝∠CBO．（1）求直线BC 的解析式；（2）如图2，已知直线l 1：623-=x y 经过点B ． ①若点D 为直线l 1上一点，直线AD 与直线BC 交于点H ，若32=∆∆ABH BDH S S ，求点D 的坐标； ②过点O 作直线l 2∥BC ，若点M 、N 分别是直线l 1和l 2上的点，且满足∠ABC ＝∠MNB ．请问是否存在这样的点M 、N ，使得△ABC 与△MBN 相似？若存在，请直接写出点N 的坐标；若不存在，请说明理由．。
成都实验外国语学校2021~2022学年高一一阶考试数学试题及参考答案
成都市实验外国语2021~2022学年上期第一次阶段性考试高 一 数 学本试卷分为选择题和非选择题两部分。
满分150分，考试时间120分钟。
注意事项：1. 答题前，务必将自己的姓名、考籍号填写在答题卡规定的位置上。
2. 答选择题时，必须使用2B 铅笔将答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦擦干净后，再选涂其它答案标号。
3. 答非选择题时，必须使用0.5毫米黑色签字笔，将答案书写在答题卡规定的位置上4. 所有题目必须在答题卡上作答，在试题卷上答题无效。
5. 考试结束后，只将答题卡交回。
第Ⅰ卷(选择题，共60分)一、选择题(每小题只有一个正确答案，每小题5分，共60分)(2021 成都实外一阶考试 1)已知集合M 中的元素,,a b c 是ABC ∆的三边，则ABC ∆一定不是( )A. 锐角三角形B. 钝角三角形C. 直角三角形D. 等腰三角形 【答案】D(2021 成都实外一阶考试 2)已知集合(){}(){},|2,,|4M x y x y N x y x y =+==-=，那么集合MN 为( )A. 3,1x y ==-B. (){}3,1-C. {}3,1-D. ()3,1-【答案】B(2021 成都实外一阶考试 3)已知{}{}2|1,|1M y y x P y y x ==-==-，则集合M 与P 的关系是( )A. M P =B. P R ∈C. M P ⊂≠D. P M ⊂≠ 【答案】A(2021 成都实外一阶考试 4)已知{}2|24,|11A x Z x B x x ⎧⎫=∈-<<=>⎨⎬-⎩⎭，则()RA B 的元素个数为( )A. 1B. 2C. 3D. 4【答案】D(2021 成都实外一阶考试 5)下列各组函数中，是同一函数的是( )①21,y x y =+=2,1x xy y x x-==-；③22321,312y x x u v v =++=++；④11,111x y y x x x -==++- A. ①②③ B. ①②③ C. ②④ D. ③ 【答案】D(2021 成都实外一阶考试 6)若函数()2212f x x x +=-，则()3f =( )A. 3B. 1-C. 0D. 4 【答案】B(2021 成都实外一阶考试 7)已知函数()f x 的定义域为(),2-∞，则函数()f x 的定义域为( )A. [)1,2-B. []1,1-C. ()2,2-D. [)2,2- 【答案】C(2021 成都实外一阶考试 8)函数42xy x-=+的值域是( ) A. R B. 11,,22⎛⎫⎛⎫-∞--+∞ ⎪ ⎪⎝⎭⎝⎭C. ()(),22,-∞--+∞D. ()(),11,-∞--+∞【答案】D(2021 成都实外一阶考试 9)水滴进玻璃容器，如图所示(设单位时间内进水量相同)，那么水的高度是如何随时间变化的？下列匹配的图像与容器符合实际的有( )A. I----(2)B. II----(4)C. III----(3)D. V----(1) 【答案】A(2021 成都实外一阶考试 10)若函数()f x =在[)2,+∞上是减函数，则实数a的取值范围是( )A. (],4-∞B. (]4,4- C. [)4,4- D. (),4-∞【答案】B(2021 成都实外一阶考试 11)对于任意两个数()*,,x y x y N ∈，定义某种运算“*”如下：①当()*,,x y x y N ∈同为奇数或同为偶数时，*x y x y =+；②当()*,,x y x y N ∈一奇一偶时，*x y xy =，则集合(){},|*10A x y x y ==的子集个数是( )个 A. 142 B. 132 C. 112 D. 72 【答案】B(2021 成都实外一阶考试 12)函数()f x 对任意的实数,x y 都满足()()()222f x y f x f y +=+⎡⎤⎣⎦，()10f ≠，则()2021f 的值为( )A.20212B. 2021C. 12 D. 1【答案】A第II 卷(非选择题，共90分)二.填空题(每小题5分，共20分)(2021 成都实外一阶考试 13)用列举法表示集合{}*|,4________.x x N x ∈<= 【答案】{}1,2,3(2021 成都实外一阶考试 14)设函数()231f x x =-，则()()_______.f a f a --=【答案】0(2021 成都实外一阶考试 15)已知函数()10y a a x x=>+的图像如图所示，则实数a 的取值范围是_________.【答案】()1,+∞(2021 成都实外一阶考试 16)已知函数()()24,11f x x ax g x x x =-++=++-，若不等式()()f x g x ≥的解集包含[]1,1-，则实数a 点的取值范围是_______.x【答案】[]1,1-三.解答题(写出必要的证明、解答过程，共70分) (2021 成都实外一阶考试 17) (1)计算：10.532072720.139125π--⎛⎫⎛⎫+-- ⎪⎪⎝⎭⎝⎭；(2)已知11223a a-+=，求22a a -+的值.【答案】(1)97；(2)47(2021 成都实外一阶考试 18)已知集合{}|37A x x =≤<，{}2|12200B x x x =-+<，{}|c x x a =<(1)(),RAB A B ；(2)若A C ≠∅，求a 的取值范围. 【答案】(1)()2,10AB =，()()[)2,37,10R A B =；(2)()2,+∞(2021 成都实外一阶考试 19)记函数()f x =定义域为集合A ，()g x =定义域为集合B(1)求集合A ；(2)若A B ⊆，求a 的取值范围. 【答案】(1)[)3,4；(2)[)4,+∞(2021 成都实外一阶考试 20)新学期开学季，成都某学校附近又新开了一家奶茶店，其中有一种名为“奶茶三兄弟”的饮品很受学生欢迎，老板费尽心思想在这种饮品上赚得第一桶金，其销售的价格在一学期不同周次有所变化. 设开始时每杯定价10元，从第一次周开始每周涨价2元，5周后开始保持20元的价格平稳销售，10周后，学生的新鲜感已过，平均每周削价2元，直到16周周末，老板为了让学生安心准备期末考试复习而不挂念“三兄弟”，该饮品暂停销售.(1)试求该饮品每杯价格p (元)与周次[](),1,16,t t t N ∈∈之间的函数关系式； (2)若此饮品每杯成本价q (元)与周次t 之间的关系是()[]21812,1,168q t t =--+∈，t N ∈，试问该饮品第几周每杯的销售利润最大，并求出最大值.【答案】(1)102,1520,510202,1016t t p t t t +≤≤⎧⎪=<≤⎨⎪-<≤⎩；(2)第五周，最大利润为73/8(2021 成都实外一阶考试 21)定义在()()1,00,1-上的函数()221f x x x=- (1)判断函数()f x 的奇偶性并证明； (2)解关于x 的不等式()()3151f x f x +>+.【答案】(1)偶函数，证明略；(2)2111,,5334⎛⎫⎛⎫---- ⎪ ⎪⎝⎭⎝⎭【解析】(2)031511x x <+<+<(2021 成都实外一阶考试 22)已知二次函数()f x 满足()()121f x f x x +-=+，()()f x f x -=，()01f =-(1)求()f x 的解析式；(2)求()f x 在[],2a a +上的最小值； (3)若对于任意3,2x ⎡⎫∈+∞⎪⎢⎣⎭，()()()2414x fm f x f x f m m ⎛⎫-≤-+ ⎪⎝⎭恒成立，求实数m 的取值范围.【答案】(1)()21f x x =-；(2)()2min243,21,201,0a a a f x a aa ⎧++≤-⎪=--<<⎨⎪-≥⎩；(3)3,,2⎛⎡⎫-∞-+∞ ⎪⎢ ⎪⎝⎦⎣⎭。
四川省成都市武侯外国语学校2020-2021学年高二英语上学期期末试题含解析
四川省成都市武侯外国语学校2020-2021学年高二英语上学期期末试题含解析一、选择题1. I'm sure you'd rather she returned home, ____?A. wouldn't youB. shouldn't youC. didn't sheD. couldn't you参考答案：A2. --May I pick a flower in the garden?--No, you _________.A. needn’t B mustn’t C. can’t D. won’t参考答案：B3. My MP4 player isn’t in my bag. Where I have put it?A. wouldB. mustC. shouldD. can参考答案：D略4. He has_____great interest in____history, especially______history of_____Tang Dynasty.A. a; 不填; 不填; theB. a; the; the; 不填C. a; 不填; the; theD. 不填; 不填; the; 不填参考答案：D5. --Good afternoon. Can I help you?--My bike is broken. I’d like to have it______, sir.A. repairedB. repairingC. to repairD. to be repaired参考答案：A 略6. ---- How can I find you in the large crowd?---- _______ down the street and you will see me wearing a red shawl.A. If walkingB. To walkC. WalkD. Walking参考答案：C略7. The documentary film “Under the Dome” released by the famous journalist Chai Jing reminds us that it’s high time the Chinese government ______ air pollution in China.A. addressesB. addressedC. will addressD. address参考答案：B考查虚拟语气。
四川省成都市实验外国语学校(西区)2022-2023学年高二上学期10月月考英语试题
四川省成都市实验外国语学校（西区）2022-2023学年高二上学期10月月考英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读理解The best science fiction books of 2021We take a look at the most exciting new science-fiction books of 2021. No matter what kind of science fiction fan you are, we're sure you'll find something to add to your reading list.The Saints of SalvationBy Peter F. HamiltonThe Olyix have laid siege（围攻）to Earth, harvesting people for their god. Cities are ru¬ined by their weapons and millions have either fled to seek refuge in space or are fighting a war that seems unwinnable. As Earth's defeat draws ever closer, a team are sent to enter the Olyix's air-ship secretly. Their plan? This is the final science fiction in Peter F. Hamilton's extremely surprising series The Salvation Sequence.A Desolation Called PeaceBy Arkady MartineThis impressive sequel（续集）to Arkady Martinets Hugo Award-winning science fiction book sees the Teixcalaanli Empire facing an alien threat which could bring about its complete destruction. Fleet captain Nine Hibiscus sends a person to negotiate with the mysterious invaders...Jack FourBy Neal AsherJack Four-one of twenty human clones-has been created to be sold. His purchasers are the aliens and they only want him for their experimentation program. But there is something different about Jack. No clone should possess the knowledge that's been loaded into his mind.RabbitsBy Terry MilesRabbits is a secret, dangerous and sometimes deadly underground game. The rewards for winning are unclear, but there are rumors of money or it might unlock the universe's greatest secrets. Everyone knows that the deeper you get, the more deadly the game becomes-and thebody count is rising. Since the game first started, ten rounds have taken place. The eleventh round is about to begin, and what happens in the game, stays in the game...1．What can we know about The Saints of Salvation?A．It's about the war among people on earth.B．The Olyix are defeated in the end.C．It belongs to The Salvation Sequence.D．It's the last novel of Peter F. Hamilton.2．What does Nine Hibiscus do to save Teixcalaanli Empire?A．He gives the alien a complete destruction.B．He lets someone negotiate with the alien.C．He fights against the alien bravely.D．He makes the alien face a threat.3．Where can the text be found?A．In a book recommendation.B．In an art magazine.C．In a biography.D．In a novelGuy Bryant never intended to be a father figure. But over the past 12 years, he’s housed more than 50 foster kids in his Brooklyn apartment.For decades, Bryant, 61, worked with teens aging out of New York’s child welfare system. His job was to find services that would make the transition (过渡) to living on their own easier. But he felt that what he could accomplish at the New York City Administration for Children’s Services office wasn’t enough. So in 2007, he decided to become a foster parent.In an interview last month, Bryant told Romario Vassell, 21, one of his foster children, that agreeing to care for him was definitely one of the best decisions he made in foster care. Bryant told Vassell that he was nervous when he took in his first foster child. He said, “I lived alone at that point, and he was a kid that nobody wanted to take because of his behaviors. He got in a fight and he appeared at my house.” Bryant said his family thought he was out of his mind for making such a big lifestyle change and wondered how Bryant would adjust.Bryant had been Vassell’s assigned case worker when they met. Bryart suggested that Vassell, then an untidy 18-year-old, consider foster care as an option to get out of the home lead shelter where he was staying.At first, Vassell was hesitant. “I didn’t know how foster care was.” he said.Since living with Bryant, Vassell now feels like he has a support network. “If I feel down and like I’m cornered, I have someone I can reach out to and talk to.” he said. “And that’s what I really love.”Bryant told Vassell, “Whatever you’ve learned from me, I want you to teach it to someone else. Because that’s what’s important to me.”4．What is the second paragraph mainly about ?A．The shift of teens’ life.B．An introduction of Bryant’s task.C．Bryant’s challenge as a foster parent.D．The reason for Bryant’s being a foster parent.5．How did Bryant’s family feel about his decision?A．Disappointed.B．Ashamed.C．Puzzled.D．Embarrassed. 6．What can we know about Vassell from the text?A．He is now living alone.B．He was Bryant’s first foster kid.C．He refused Bryant’s offer at first.D．He was instructed to pay kindness forward.7．What is the author’s purpose in writing the text ?A．To call for social care.B．To praise Bryant’s deeds.C．To tell the story of Vassell.D．To comment on Bryant’s life.Priscilla Ouchida’s “energy efficient” house turned out to be a horrible dream. When she and her engineer husband married a few years ago, they built a $100,000 three-bedroom home in California. Tightly sealed to prevent air leaks, the house was equipped with small double-paned windows and several other energy-saving features. Problems began as soon as the couple moved in, however. Priscilla’s eyes burned. Her throat was constantly dry. She suffered from headaches and could hardly sleep. It was as though she had suddenly developed a strange illness.Experts finally traced the cause of her illness. The level of formaldehyde gas in her kitchen was twice the maximum allowed by federal standards for chemical workers. The source of the gas? Her new kitchen cabinets and wall-to-wall carpeting.The Ouchidas are victims of indoor air pollution, which is not given sufficient attention partly because of the nation’s drive to save energy. The problem itself isn’t new. “The indoor environment was dirty long before energy conservation came along,” says Moschandreas, a pollution scientist at Geomet Technologies in Maryland. “Energy conservation has tended to accentuate the situation in some cases.”The problem appears to be more troublesome in newly constructed homes rather than old ones. Back in the days when energy was cheap, home builders didn’t worry much about unsealed cracks. Because of such leaks, the air in an average home was replaced by fresh outdoor air about once an hour. As a result, the pollutants generated in most households seldom built up to dangerous levels.8．It can be learned from the passage that the Ouchidas’ house ________.A．is well worth the money spent on its constructionB．is almost faultless from the point of energy conservationC．failed to meet energy conservation standardsD．was designed and constructed in a scientific way9．What made the Ouchidas’ new house a horrible dream?A．Poor quality of the air inside.B．Poor quality of the construction. C．Gas leakage in the kitchen.D．The newly painted walls.10．The word “accentuate” (Para. 3) most probably means “________”.A．relieve B．accelerate C．worsen D．improve 11．Why were cracks in old houses not a big concern?A．Because indoor cleanliness was not emphasized.B．Because energy used to be inexpensive.C．Because environmental protection was given top priority.D．Because they were technically unavoidable.12．This passage is most probably taken from an article entitled ________.A．Energy Conservation B．House Building CrisisC．Air Pollution Indoors D．Traps in Building ConstructionThe regular world presented to us by our five senses—you could call it reality 1.0—is not always the most user-friendly of places. We get lost in unfamiliar cities; we meet people whose language we don’t understand. So why not try the improved version: augmentedreality (AR) or reality 2.0? AR technology adds computer-produced images (图像) on the real world via a mobile phone camera or special video glasses.Early forms of AR are already here. With the right downloads, smart phones can deliver information about nearby ATMs and restaurants and other points of interest. But that’s just the beginning. A few years from now the quantity of information available will have increased hugely. You will not only see that there’s a Chinese restaurant on the next block, but you will be able to see the menu and read reviews of it.This is where the next revolution in computing will take place: in the interface (界面) between the real world and the information brought to us via the Internet. Imagine bubbles floating before your eyes, filled with cool information about anything and everything that you see in front of you.Let’s jump ahead to ten years from now. A person trying to fix their car won’t be reading a book with pictures; they will be wearing a device that projects animated 3-D computer graphics onto the equipment under repair, labelling parts and giving step-by-step guidance.The window onto the AR world can be a smart phone or special video glasses. But in ten years’ time these will have been replaced by contact lenses (隐形眼镜) with tiny LEDs, which present something at a readable distance in front of the eye. So a deaf person wearing these lenses will be able to see what people are saying.The question is, while we are all absorbed in our new augmented reality worlds, how will we be communicating with each other?13．What does the text mainly talk about?A．The next information technology revolution.B．Early forms of augmented reality technology.C．The differences between reality 1.0 and reality 2.0.D．The relationship between people living in reality 2.0.14．What does the underlined word “it” refer to in Paragraph 2?A．The menu.B．The block.C．The revolution.D．The restaurant.15．What are tiny LEDs used to do?A．Protect people’s eyes.B．Show text and images.C．Warn users of dangers.D．Replace video glasses.16．What’s the author’s attitude towards AR technology?A．Doubtful.B．Disapproving.C．Favourable.D．Ambiguous.二、七选五Master Your DeadlinesThe struggle begins in high school, sometimes earlier. Deadlines, and lots of them, start to pile up. At college, the pressure sometimes leads to last-minute rush and unsatisfactory work. At work, failing to meet deadlines can easily get you fired. ___17___ Here are a few best practices.▪Assign deadlines to what matters.If the task isn’t of high importance, don’t set a specific deadline. In this way, you are able to keep it on your radar for a while without feeling pressured. ___18___ This will provide just enough pressure to ensure you get it done.▪ ___19___Set a personal deadline for yourself a day or two before the actual deadline. ___20___ If you’re working with a group of people, add in even more time to account for potential follow-ups and the need for approvals.▪ Keep communicating.___21___ This means letting others know when something is taking longer than expected, when a delivery didn’t come in, when a client is not providing the necessary information, etc. Although it may feel embarrassing to admit that something is not on schedule, being honest is much better for relieving your stress.A．Plan for flexible hours.B．Finish your project as early as possible.C．But if an activity is urgent, set a deadline immediately.D．In this way, you’ll never have to stay up late and feel stressed.E．But handled properly, deadlines can actually improve productivity.F．Whenever you feel challenged to finish work on time, communicate.G．So if anything takes longer than expected, you can still wrap it up and submit it on time.三、完形填空I was shopping at the local food store and started chatting with the cashier about my three - year - old daughter’s favorite food. It was applesauce (苹果酱). The cashier warmly ___22___ me some wonderful brands. She smiled and then told me that her son who was one year old also loved ___23___. That got us talking a little about ___24___.I mentioned to her that we need to spend as much ___25___ with them as possible, since the time goes by ___26___. I also have two teenage daughters and had to ___27___ a lot of their younger days because I was busy working outside the home as a nurse. Now, with my three - year - old daughter to look after, I am able to stay at home and really ___28___ each minute.The ___29___ then sadly told me that she didn’t see her son much because she did two ___30___ and that she wanted to be able to give him the best of everything and ____31____ money so that someday her son could go to college and be ____32____ This made me____33____. On one hand, I understood what she meant, but on the other hand, I knew how much more ____34____ time with kids was against jobs and money.I wanted to do something nice for her. I had a little extra money, ____35____ I decided to bless this girl by giving her $ 100 and a ____36____ telling her to take ____37____ one day off and just spend time with her son, doing whatever he wants to do - maybe have lunch out or have some ice cream. In the note, I told her to use the money to ____38____ herself with her son for one day.I then called the store to ____39____ that she was working that day and talked to her briefly. I told her that I was a ____40____she had served a few days before and I wanted to do something nice for her ____41____. I then went to the store and when she had a free moment, I gave her an envelope with the note and money in it.22．A．recommended B．gave C．bought D．borrowed 23．A．shopping B．applesauce C．parents D．food 24．A．cooking B．stores C．kids D．work 25．A．money B．energy C．childhood D．time 26．A．happily B．slowly C．hopelessly D．quickly 27．A．discover B．spare C．afford D．miss 28．A．forget B．treasure C．bear D．ignore29．A．store keeper B．cashier C．child D．daughter 30．A．sports B．wrongs C．jobs D．favors 31．A．contribute B．waste C．save D．collect 32．A．successful B．different C．helpful D．popular 33．A．excited B．shocked C．sad D．angry 34．A．important B．dangerous C．unnecessary D．impossible 35．A．so B．and C．but D．or 36．A．hug B．note C．gift D．warning 37．A．at most B．as usual C．by chance D．at least 38．A．enjoy B．behave C．teach D．prepare 39．A．take notice B．make sure C．give a promise D．put forward 40．A．father B．mother C．customer D．nurse 41．A．at first B．out of pity C．on purpose D．in return四、用单词的适当形式完成句子42．The woman looked at him in _______(confuse) and said something about changing her clothes. (所给词的适当形式填空)43．When________(compare) different cultures, we often pay attention only to the differences without noticing their similarities. （所给词的适当形式填空）44．Our products have good fame at home and abroad, deeply ________(favour) by customers. （所给词的适当形式填空）45．The reference book the teacher _________ (refer) to just now is said to be popular among students. (所给词的适当形式填空)46．The head teacher demanded that the blackboard _________ (clean) before every class. (所给词的适当形式填空)47．The phone boxes are making a comeback to meet the _________ (require) of green economy. (所给词的适当形式填空)48．His first novel ________(receive) good reviews since it came out last month.49．I sincerely hope my _________ (apply) can meet with your approval. (所给词的适当形式填空)50．The road _________ (lead) to the house was muddy and narrow, making it hard to drive.(所给词的适当形式填空)51．Finally getting the answer he wanted, the teacher smiled with _________ (satisfy) (所给词的适当形式填空)五、选用适当的单词或短语补全短文选词填空52．As for the environmental protection, it is not what we say but what we do that_________________.53．_________________ modem science and technology, people lead a more and more comfortable and richer life.54．Tom is always ready to help others, _________________those who are in trouble. 55．_________________, people who don’t smoke are healthier than people who do in contrast.56．You should not _________________ that you can do the work perfectly.57．I feel much affection for my mum, whose words and actions _________________ me. 58．The government calls on people to _________________by using public transport. 59．In the 1940s, electricity _________________people in almost all areas of the United States.60．Later, he worked in Africa, where many people _________________ blindness for lack of proper treatment.61．After Tom retired from office, he _________________painting for a while, but soon lost interest.六、短文改错62．假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下作文。
四川省成都市实验外国语学校2022-2023学年高一下学期第一次周考化学考试
成都市实验外国语学校高2022级高一下化学周考（一）班级姓名相对原子质量:H—1C—12N—14O—16S—32Zn—65Cu—64Ba —137一、单选题（每题3分，共45分）1．下列关于硫及其化合物说法错误的是A ．工业上用98.3%的浓H 2SO 4吸收SO 3，目的是防止形成酸雾，以使SO 3吸收完全B ．葡萄酒中添加适量SO 2可以起到抗氧化的作用C ．硫酸钡可用作消化系统X 射线检查的内服药剂D ．实验室常用98.3%的浓硫酸与Na 2SO 3固体制备SO 22．下列“类比”合理的是A ．Cl 2能够从KI 溶液中置换出I 2，则F 2也能够从KI 溶液中置换出I 2B ．3CaCO 溶解度小于()32Ca HCO ，则23Na CO 溶解度小于3NaHCO C ．NaClO 溶液与2CO 反应生成3NaHCO 和HClO ，则NaClO 溶液与2SO 反应生成3NaHSO 和HClOD ．2Cl 与Fe 反应生成3FeCl ，则2Cl 与Cu 反应生成2CuCl 3．1891年Engel 首次制得S 6分子，1912年Beckmann 获得S 8分子。
下列说法正确的是A ．S 6和S 8互为同位素B ．S 6和S 8分别与铜粉反应，所得产物均为CuSC ．S 6和S 8分别与过量的氧气反应可以得到SO 3D ．等质量的S 6和S 8分别与足量的热KOH 溶液反应，消耗KOH 的物质的量相同4．下列说法正确的是A ．氨水显碱性，是因为氨水是一种弱碱，可以电离出OH -B ．氨气易液化得液氨，液氨是纯净物常作制冷剂C ．氨气遇浓硫酸能产生白烟D ．NO 2能与水反应生成硝酸，所以NO 2是酸性氧化物5．大气中的氮循环(如图所示)可以减少环境的污染。
下列说法正确的是A ．转化过程中-2NO 被+4NH 氧化为2NB ．2N 转化成+4NH 发生了还原反应C ．温度越高，2N 转变成+4NH 的速率越快D ．图中含氮物质中氮元素的化合价共有三种6．将足量的2SO 通入2BaCl 溶液中，无明显现象，当加入(或通入)某试剂(或气体)X 后有沉淀生成。
四川省成都市实验外国语学校2024-2025学年高三上学期10月月考数学试题(含答案)
成都市实验外国语学校高三10月月考数学试题总分：150考试时间：120分钟一、单选题：本题共8小题，每小题5分，共40分。
在每小题给出的选项中，只有一项是符合题目要求的。
1．命题“，使”的否定是（ ）A ．，使B ．不存在，使C ．，D ．，2．已知等差数列的前项和为，若，且，则（ ）A ．60B ．72C ．120D ．1443．若，则（ ）A ．3B ．4C ．9D ．164，侧面展开图的扇形圆心角为的圆锥侧面积为（ ）A ．B ．C ．D ．5．小王每次通过英语听力测试的概率是，且每次通过英语听力测试相互独立，他连续测试3次，那么其中恰有1次通过的概率是（ ）A ．B ．C ．D ．6．已知，是方程的两个根，则（ ）A ．B ．C ．D ．7．当阳光射入海水后，海水中的光照强度随着深度增加而减弱，可用表示其总衰减规律，其中是消光系数，（单位：米）是海水深度，（单位：坎德拉）和（单位：坎德拉）分别表示在深度处和海面的光强．已知某海域5米深处的光强是海面光强的，则该海域消光系数的值约为（参考数据：，）（）A ．0.2B ．0.18C ．0.1D ．0.148．已知函数，方程有四个不同根，，，，且满足，则的取值范围是（ ）x ∃∈R 210x x +-=x ∃∈R 210x x +-≠x ∈R 210x x +-=x ∀∉R 210x x +-≠x ∀∈R 210x x +-≠{}n a n n S 21024a a +=36a =8S =24log log 2m n +=2m n =2π39π6π23292273949tan 23︒tan 37︒2230x mx +-=m =--0eKDD I I -=K D D I 0I D 40%K ln 20.7≈ln 5 1.6≈()22log ,012,04x x f x x x x ⎧>⎪=⎨++≤⎪⎩()f x a =1x 2x 3x 4x 1234x x x x <<<221323432x x x x x x +-A ．B ．C ．D ．二、多选题：本题共3小题，共18分。
四川省成都市实验外国学校(西区)2020-2021学年度上期九年级英语学科期中测试卷(无答案)
成都市实验外国语学校西区2020-2021学年度上期初三年级英语学科期中考试题出题人:李颖琪王康审题人:杨琼考试时间120分钟，满分150分Listening Part (35 scores)Ⅰ．Listen to the sentences and choose the right pictures．Each sentence will be read only once．(4 scores)A．B．C．D．1．_________________ 2．_________________ 3．_________________4．_________________Ⅱ．Listen to the sentences and choose the correct responses．Each sentence will be read only once．(5scores) 5．A．Yes, please．B．I'd like to．C．That’s OK．6．A．Bad luck．B．That's awful．C．I'm sorry to hear that．7．A．For two hours．B．In two hours．C．Two hours' drive．8．A．It's OK．B．Yes, I do．I'll turn it off．C．Of course not．I'll turn it off．9．A．Congratulations!B．Good luck．C．It's good for you．Ⅲ．Listen to the short dialogues and choose the best answer to the question．Each dialogue will be read twice．(6 scores)10．What does the girl think of the cake?A．Spicy．B．Cold．C．Sweet．11．Where is Longjing tea from?A．Fujian．B．Zhejiang．C．Yunnan．12．Where is the post office?A．Opposite the bank．B．Next to the Library．C．Between the supermarket and the bank．13．When will Candy leave the party?A．At 8:20 p．m．B．At 8:40 p．m．C．At 9:00 p．m．14．What does the girl want to be?A．An inventor．B．A pianist．C．A doctor．15．Why does the boy want to do a part-time job?A．To make money．B．To keep healthy．C．To improve himself．Ⅳ．Listen to the long dialogue and judge the sentences true or false．If it is true, please choose A．If it is false, please choose B．The dialogue will be read twice．(5 scores)16．Miss Johnson fell on the snow from the 18th floor．17．When Miss Johnson was found, she was frozen．18．Doctors said Miss Johnson couldn't be better．19．Miss Johnson now can't live without others' help．20．Miss Johnson uses her Weibo to help the ones who are also in trouble．Ⅴ．Listen to the two passages carefully and choose the best answer to each question．Each passage will be read twice．(10 scores)Passage A21．How many steps are there when we do online shopping?A．2B．3C．422．Why do people like online shopping?A．Because you can shop at anytime．B．Because you can always buy the products at the lowest price．C．Because it always takes you less time than shopping in the stores．23．Why do people like going out to shop in the stores?A．They can try the clothes on．B．Going out to shop is a kind of exercise．C．They can have delicious food in the stores．24．What's the writer's opinion of online shopping?A．The products you buy are usually cheaper．B．People can't buy things from very faraway places．C．There will be no shops in the streets any more．25．From the passage, what problem does online shopping have right now?A．People have less communication．B．It's hard for old people to do it．C．Paying online isn't always safe．Passage B26．In what aspect can volunteering help you?A．Make a decision．B．See the world clearly．C．Make people's life better．27．How often is National V olunteer Week held?A．Every week．B．Every month．C．Every year．28．Why do people hold the National V olunteer Week?A．To raise money for people in need．B．To show thanks to the volunteers for their work．C．To create a chance for volunteers to make friends with each other．29．What may be the reason stopping people taking the first step to become a volunteer?A．They don't have enough time．B．Their families don't let them do it．C．They fear that their abilities are shared．30．How many tips are mentioned in this passage?A．3B．4C．5Ⅵ．Listen to the passage and complete the chart with no more than three words．The passage will be read three times．(5 scores)笔试部分Paper A（共45分)Ⅰ．Multiple choices．(10 scores)36．It will be difficult for you to pass the test, ____________ you work hard every day．A．if B．unless C．as soon as37．Two small power stations ____________by the local government since the scheme was started last year．A．have closed B．were closed．C．have been closed38．I wonder if failing the oral test is ____________experience in his life．He looks so worried．A．a sad B．the sad C．the saddest39．It was in the 1960s ____________the first cassette recorders became popular．A．when B．that C．where40．The shop assistant advises me ____________the milk in the fridge, or it can go ____________easily．A．putting, badly B．to put, worse C．to put, bad41．____________catching the virus, we'd better wear masks when going out．A．To avoid B．Avoiding C．Avoid42．Zhong Nanshan with his workmates ____________all the efforts to help the sick since last January．A．have made B．has made C．made43．It is said the sea levels will ____________by 13 to 22cm in 30 years because of climate changes?A．rise B．raises C．be risen44．——Steve, will you go to the Strawberry Music Festival this weekend?——It depends on you．If you don't go, ____________．A．so will I B．neither do I C．neither will I45．——I haven't seen Lucy for a long time．Where is she?——She ____________Britain to have a ____________education．A．has gone to; further B．has been to; furtherC．Will go to; furtherⅡ．Cloze test．(15 scores)A thousand years ago, Hong Kong was covered by a thick forest．As more and more people came to ___46___in Hong Kong, these trees were cut down and burnt．Now there is___47___ forest left, though there are still some small areas covered with trees．We call these woods．Elephants, tigers and many___48___ animals were living in the thick forest．When people came to live in Hong Kong, they grew rice andy___49___ pigs and chickens in the valleys．They cut down the trees and burnt them．They needed fire to keep themselves warm in winter, to cook their food and to keep away the dangerous animals．Elephants quickly disappeared because there was not enough food for them．___50___ did most of the wolves and tigers．Monkeys and the other animals soon___51___ in the same way．You might think that there are no longer any animals in Hong Kong___52___ in the zoos．There are still about 36 different animals,___53___there．One of the most interesting animals in Hong Kong is the barking deer．These are beautiful little animals___54___ a rich brown coat and a white patch(补丁)under the tail．They look like deer but they are much like a dog barking．In HongKong the barking deer has only a real enemy-___55___ People hunt these little animals though it is illegal．There aren't many barking deer left in Hong Kong now．46．A．work B．study C．live47．A．many B．a few C．no48．A．other B．others C．the other49．A．rose B．raised C．raising50．A．So B．Such C．Nor51．A．lived B．died C．came52．A．A besides B．except C．and53．A．live B．to live C．living54．A．have B．without C．with55．A．wolves B．humans C．tigersⅢ．Reading comprehension．Read the passages and choose the best answers．(20 scores)Passage AA couple of weeks ago, I went on a camping trip at Pitt Lake, I spent three days and two nights there．It was a new experience for me, so I felt both nervous and excited at first．Fortunately, the weather was beautiful, so we got off to a good Start．There were so many people to take part in, including both instructors and students-we had one big canoe and one smaller canoe．I chose to be in the smaller canoe with my friend Mitra but ye soon found that this was not a wise choice．In order to keep up with the bigger canoe, both of us had to paddle (划桨) hard．My arms quickly became sore and my hands had no feelings．To take off our minds of the pain, Mitra and I played “20questions” while paddling, In this game, one person thinks of an object and the other person asks 20 questions to try and figure out what the object is．We had a good laugh before we finally arrived at the campsite．We started a campfire soon after we arrived．At night, we stayed together around the fire, listening to scary stories．Some of the other campers put their wet shoes and socks beside the fire to dry．However, because of the wind, one pair of socks almost caught on fire．Everyone panicked(惊慌)．One person got so scared that he fell out of his folding chair．Everyone thought it was pretty funny! The time flew quickly．Soon, it was time to go back．We didn't want to leave and agreed that we would hang out together again sometime soon．56．The writer realized that the smaller canoe was a bad choice because__________．A．they couldn't move at all in the smaller canoeB．it was difficult to control the direction of the canoeC．they had to paddle much harder than in the bigger one57．Mitra and the writer played “20 questions” game in order to__________．A．forget their pain B．build up their brainsC．keep their minds active58．What didn't the writer do at the campsite?A．Gathering around the fire．B．Listening to scary storiesC．Putting the wet shoes and socks beside the fire to make them dry．59．They panicked（惊慌) at the campsite because____________．A．they were scared by a scary story B．one student fell out of his folding chairC．the wind almost set someone's socks on fire60．How did the writer feel at the end of the trip?A．Sad to leave．B．Excited to go home．C．Nervous and excited．Passage BHow has technology made your life easier? When you go to a shopping mall, you can enjoy free Wi-Fi there．When you want to take a taxi, you can book one with your phone．In fact, all of these things can be seen as the first building blocks of a mart city The idea of a smart city was first suggested by tech company IBM in 2010．Generally, a smart city is a city that uses digital (数字的）technology, such as 5G networks and the “internet of things”, to improve city planning, save money and resources, and make our lives more convenient．Cities like Boston, Amsterdam and Copenhagen are already using smart technology to improve public services．In the US cities of Boston and Baltimore, smart trash bins can tell how full they are and tell workers when they need to be cleaned．In Amsterdam, traffic is monitored and adjusted (调整) according to real-time facts and figures with the help of digital cameras around the city．There is less traffic jam．Smart cities will allow us to save resources．Byusing special equipment and 5G networks to check the use of water, gas and electricity, city governors can find out how to use these resources more efficiently．For example, water and gas pipes could remind repair workers when there is something wrong．Air pollution could be more closely monitored, too．Of course, it will take time to build the smart cities of the future．But since we've already seen successful examples, it won't be long until more cities join in．Tech Republic predicts that by 2050, about 60 percent of people worldwide will live in smart cities．61．A smart city is a city___________．A．that is full of smart people B．that uses digital technologyC．which has a lot of building blocks62．From the examples given of smart cities, we know that___________．A．there will be no traffic jams in the futureB．smart cities can make our lives more convenientC．people can make a lot of resources in smart cities63．Smart trash bins in Boston and Baltimore___________．A．cost the local government much moneyB．can tell the cleaners when to clean them in any languageC．can tell how full they are and tell workers to clean them in time64．The underlined word monitored means___________．A．developed B．improved C．watched65．What can we infer(推断) from the passage?A．There are few advantages to live in smart cities．B．It won't be long before more cities become smart cities．C．60percent of cities will be turned into smart cities by 2050．笔试部分Paper B（共70分)Ⅰ．Complete the sentences with the right forms of the given words．(10 scores)1．As we all know, Steve Jobs was one of the most famous ___________in the computer market．(innovate) 2．What made the boy upset was that his father was too angry to listen to his ___________．(explain)3．The Comic Relief charity ___________many activities to raise money in the past few years．(organiser) 4．Tour ___________job is to organize different kinds of holidays for people with different needs．(operate) 5．The doctor dealt with his head injury ___________, which made the situation from bad to worse．(patience) 6．The TV producers make the series as ___________as possible to attract the viewers' attention．(drama)7．The ___________one uses a language the easier it is to express one's thoughts in it．(frequent)8．The waste paper and plastic ___________by citizens can be easily made into something new．(recycle) 9．Some students find giving a speech in public ___________, so they aren't willing to do it．(embarrass) 10．The COVID-19 pandemic ___________China seriously last winter, but we're now nearly back to normal．(hit)Ⅱ．Pattern shift．(5 scores)11．No other student in my class can sneak English more fluently than him．(Same meaning) =He can speak English________ ________ ________ ________ ________students in my class．12．Miss Williams gave us the speech instead of her colleague．(Same meaning)=Miss Williams________ ________ ________ ________ ________ ________to give us the speech．13．Kevin killed time by watching TV while waiting for his friends．(Same meaning)=Kevin killed time by watching TV while________ ________ ________ for his friends．14．I noticed Tina practice oral English with her classmate in the classroom．(Passive voice) ________________________________________________________________________________________ 15．The cottage caught fire two minutes ago．(Rewrite the sentence with “for two minutes”．) ________________________________________________________________________________________Ⅲ．Complete the dialogues with only one word．(10 scores)A:Guess what? I've got a new pet-a pet spider!B:I don't believe you．____16____ me for saying so but I do remember you used to be really afraid of spiders．A:That's true．I didn't just cry ‘Uurgghh’ but suddenly, 1 froze(惊呆) ____17____--I can't move at all．B:Once you shouted so loudly that your neighbors would worry about you and think about calling the police．A:To avoid such a bad_____18_____on others, I decided to make a change．So I went to a doctor who can deal with my problem in a more scientific way．It's called the “behavioral method”(行头治疗法)．B:What's that?A:It's like this…For the first time, the doctor took out a small plastic spider from his drawer．However, I shouted loudly even though it wasn't real．A:What's more, my doctor told me to touch the plastic spider．I tried my best but I could_____19_____touch it for more than two seconds．B:Wow, sounds like a good_____20_____．Once you take the first step, you will get better and better．A:That's not all．I went back the next day, and this time the plastic spider was already on the_____21_____desk and I was asked to hold it for five minutes．Then; for the third day, the spider was already on my chair!B:I got to know the behavioral method．It seemed to_____22_____well on you．A:It still takes time．The spider needed putting away so I could sit down．The following days I held the spider while I sat in my chair．The_____23_____day, the doctor told me to take it home and put it in the place where spiders usually_____24_____in my house—then everywhere! That’s all for my treatment．B:It is really a long process_____25_____you can face the spiders bravely．A:Yeah, now I only feel a little bit afraid so that I can keep the real one as my pet!Ⅳ．Complete the texts with the correct words according to the first letters．(10 scores)1．Some people believe that talent is the only f_____26_____that can help make i_____27_____possible．But in fact, this idea is not right．Besides the u_____28_____ability to do well in musical composition, Mozart practiced hard every day as well．In Edison's opinion, it was diligence as well as i_____29_____that made an inventor Successful．In addition, age is not a big problem to create something new．Never think you are too young to create it．Louise Braille invented a s_____30_____of reading and writing for the blind at the age of 15．And George Nissen got an idea to invent trampoline by watching the artists' performance in the circus when he was young．2．It is said that although the bicycle scheme won't solve all the traffic problems, it can help to r_____31_____pollution levels in the air．The d_____32_____of rainforests together with the pollution, has caused global warming and climate changes, Besides, the traffic problems in cities are also serious．With the help of bikes, people might lead a h_____33_____life than before．However, the answers to traffic problems are not s_____34_____．If we do nothing, the e_____35_____will get worse because of the heavy traffic and high temperature?Ⅴ．Choose ten words from the twelve words and fill in the blanks with the correct forms of the words．(10 scores)Do you like shopping? For shopping-lovers in the UK, the place that they used to go was the “high street”．This location refers to the streets in the ___36___of a town where businesses and popular stores could be found．It was also the place where you could find familiar fashion brands and necessary everyday___37___．But the British high street is suffering because of changes in our shopping habits．News about shops losing money and shutting down is now___38____．You may read and watch it every day on TV or in newspapers．A large number ofdepartment stores kept___39___for a year．Even long-established stores such as Marks & Spencer have reported a drop in profits．As the BBC's journalist Emma Simpson writes, things ___40___ much harder for traditional stores already．They have faced___41___costs from rents, wages and business rates than before．But the biggest problem has come from online shopping．Some shoppers would like___42___things online for less money．___43___, what we know now is that, for cheaper price and more convenience of online shopping, shoppers are making fewer visits to high streets．Therefore, town centers could become places ____44____ghost towns．If people aren't out or going shopping, they won't go to other businesses, like cafes, restaurants and cinemas, either．It will also result in job losses．The British Retail Consortium(英国零售商协会) has already warned that at least 900,000 people in UK___45___their jobs connected with shopping in 2025．Ⅵ．Read the following passage and complete it with the right sentences in the box．(5 scores) The earth is our home．We must take care of it．This means keeping the land, air and water clean．Pollution is a dirty word．To pollute means to make things unfit or unclean to use．Pollution comes in many ways．___46___Pollution is beginning to threaten(威胁）our health, our happiness and our life．Man has been polluting the earth from the time he first made fire, washed his clothes in the river and threw his waste on the ground．When land was used up or water became dirty, men moved on to another place．___47___．There weren’t so many people then and their wants were fewer．All the dirty things could be absorbed(吸收) by nature and soon covered over．But this is no longer true．___48___Man is slowly poisoning(毒害) his environment．Through the use of poison, man has polluted the land, killing the animals．___49___Obriously, our increasing population is part of the problem．More people, more waste．Where is this all to end? Are we turning the world into a big rubbish dump, or is there any hope that we can get rid of the pollution? ___50___Large numbers of people are now working hard to bring pollution under control．Ⅶ．Task-based reading．Finish each task according to the requirement．(5 scores)As the global pandemic(流行病）speeds up, many are wondering about the effectiveness of masks and whenit's proper to wear them．Most people from the East believe that wearing a mask is important to control the spread of the COVID-19．But people in the West generally would argue that, unless one is already ill, wearing a mask is unnecessary．In Eastern countries like China, mask-wearing has a long history in their cultures．In fact, people in the East wear masks not just to protect themselves from illness but also for a variety of other reasons．In many Asian countries, masks are worn in many situations in daily life, such as doing housework or ____________in the hospital．They can give people the comfort of being protected．In recent years, they are worn simply for beauty．Young people in Japan, for example, wear masks as a fashion statement, expressing their personal style through unique designs and patterns．In Asia, wearing a face mask is also an expression of group-oriented values（集体主义)．Wearing a mask, one becomes part of a giant group．People show their responsibilities to the social group of which they were members．In Western countries, however, individual values are the most important．As a citizen, it is one's duty to prevent the spread of illness in following ways, such as washing one's hands and limiting one's contact with others．A face mask is kept only for those showing symptoms of illness．Whether from the East or the West, social culture has played an important role in one's decision about whether or not to wear a mask．That's because human beings are social creatures who consider much about what other members of society think of us．The most important thing is to respect others' opinions, no matter how different they are．51．List two reasons for people in Asian countries wearing masks．(each reason with no more than 5 words) 52．Complete the sentence in paragraph 3 with only two words．53．What stops people in Western countries wearing the masks?54．The writer disagrees with the idea western people have for masks, does he?55．What do the East and the West have in common on wearing a mask?Ⅷ．Composition．(15 scores)During the pandemic of COVID-19, students study at home all day．As a result, their eyesight gets poorer and poorer．Now write a short report about 100 words according to the two charts below to analyze the major reasons and give some proper suggestions to this problem．The following aspects must be included:1．The report must cover all the information in the two charts．2．Give at least two suggestions to the problem．3．Give a proper title to your report．。
2023年四川省成都外国语学校初升高直升考试数学试卷(含详细答案)
2023年四川省成都外国语学校直升数学试卷A 卷一、选择题（本大题共8个小题，每小题4分，共32分，每小题均有四个选项，其中只有一项符合题目要求）1．（4分）的相反数是（ ）A ．B．C ．D ．2．（4分）如图所示的几何体是由5个大小相同的小立方块搭成，它的俯视图是（ ）A ．B ．C ．D ．3．（4分）俄罗斯驻华大使伊戈尔•莫尔古洛夫在接受卫星通讯社采访时表示，俄中两国2023年的贸易额将大幅突破2000亿美元大关．将数据2000亿用科学记数法表示为（ ）A ．2×1011B ．2×1010C ．2×109D ．2×10124．（4分）如图，已知∠DAC ＝∠DBC ，添加下列条件不能判定△ACD ≌△BDC 的是（ ）A ．∠ACD ＝∠BDCB ．∠ADC ＝∠BCD C ．AB ∥CD D ．AC ＝BD5．（4分）下列运算正确的是（ ）A ．3x +2y ＝6xyB ．2x ×3y ＝6x +yC ．（x ﹣y ）2＝x 2+y 2﹣xyD ．（x +3）（x ﹣3）＝x 2﹣96．（4分）某校六个年级举行的“爱成都迎大运”知识比赛中，各年级得分（单位：分）如下：98，94，133-133-133313313-98，97，94，96，则各年级得分的中位数是（ ）A．96分B．97分C．96.5分D．98分7．（4分）我国古代数学著作《张丘建算经》中著名的“百鸡问题”叙述如下：“鸡翁一，值钱五；鸡母一，值钱三；鸡雏三，值钱一；百钱买百鸡，则翁、母、雏各几何？”意思是公鸡五钱一只，母鸡三钱一只，小鸡一钱三只，要用一百钱买一百只鸡，问公鸡、母鸡、小鸡各多少只？若现已知母鸡买4只，设公鸡买x只，小鸡买y只，则可列方程组为（ ）A．B．C．D．8．（4分）对于二次函数y＝﹣x2+2x+3（1≤x≤4）的图象，下列说法正确的有（ ）①开口向上；②函数最小值是﹣5；③与直线有两个交点；④当x＞2时，y随x的增大而减小．A．4B．3C．2D．1二、填空题（本大题共5个小题，每小题4分，共20分）9．（4分）分解因式：＝ ．10．（4分）在平面直角坐标系xOy中，△ABC顶点A的坐标是A（﹣3，﹣1），将△ABC向左平移5个单位长度得到△A′B′C′，则点A′的坐标是 ．11．（4分）如图，圆内接四边形ABCD两组对边的延长线分别交于点E，F，且∠E＝45°，∠F＝35°，则∠A＝ ．12．（4分）从﹣3，0，1，2四个数中随机抽取一个为a的值，则a是方程x2+2x﹣3＝0解的概率是 ．13．（4分）如图，在△ABC中，∠BAC＝60°，∠C＝90°，AB＝m，按以下步骤作图：①分别以点B和C为圆心，以大于的长为半径作弧，两弧相交于点M和N；②作直线MN交AB于D，交BC于E ．则线段DE ＝ ．三、解答题（本大题共5个小题，共48分）14．（12分）（1）计算：；（2）解不等式组：．15．（8分）2023年7月28日至8月8日，成都市将举办第31届世界大学生夏季运动会，成都大运会主场馆包含“一场三馆”．某校从“A ：主体育场、B ：多功能体育馆、C ：小球馆、D ：游泳跳水馆”四个场馆对学生进行了一次抽样调查，要求每个学生从这四个场馆中选出自己最喜欢的场馆，现将调查的结果绘制成如图两幅不完整的统计图，请你根据图中提供的信息，解答下列问题：（1）抽取的总人数是 ，并补全条形统计图；（2）在扇形统计图中，求“小球馆”所对应的扇形的圆心角的度数；（3）我校九年级有3000人，估计有多少同学最喜欢“游泳跳水馆”？16．（8分）某数学兴趣小组决定利用所学知识测量天府艺术公园•蜀园帘月亭的高度．如图，帘月亭的高度为AB ，∠ADB ＝30°，∠ACB ＝20°，DC ＝9米，请你根据以上测量数据，帮助兴趣小组求出帘月亭AB 的高度．（结果保留根号）．（参考数据：sin20°≈0.34，cos20°≈0.94，tan20°≈0.36）7330cos 216)21(3-++---17．（8分）如图，在直角三角形ABC中，AD垂直斜边BC于D，以AD为直径作⊙O交AB于E，交AC 于F，连接BF交⊙O于G，连接EF．（1）证明：∠ABC＝∠AFE；（2）若AD＝2，CD＝1，求BG的长．18．（12分）如图，在平面直角坐标系xOy中，一次函数y＝3x﹣2的图象与反比例函数的图象相交于A（n，﹣6），B两点．（1）求反比例函数的表达式；（2）点C是反比例函数第三象限图象上一点，且在直线AB的上方，若三角形ABC的面积与三角形AOB 面积的相等，求点C的坐标；（3）对平面内任意一点P（a，b），定义K变换：若a≥b，则P变为P′（﹣b，﹣a）；若a＜b，则点P变为P′（a，﹣b），若线段AB经过K变换后的图形与另一个反比例函数的图象没有交点，求m的取值范围．B卷一、填空题（本大题共5个小题，每小题4分，共20分）19．（4分）比较大小： （填“＞”、“＜”或者“＝”）．20．（4分）若a+3b＝4，则a2﹣9b2+24b+5的值是 ．21．（4分）如图，在菱形ABCD中，对角线AC、BD交于点E，AC＝8，BD＝6，以点E为圆心作圆E，圆E与菱形的四条边相切，现随机向菱形ABCD内掷一枚小针，则针尖落在圆E的概率为 ．22．（4分）如图，点B在反比例函数的图象上，点A在x轴上，OB＝AB，过点A作AD∥OB交y轴负半轴于点D，连结BD，当△OCD面积为3时，则k的值为 ．23．（4分）在Rt△ABC中，∠ACB＝90°，AB＝5，AC＝3．点D在BC边上，DE⊥AB，垂足为E，CD ＝DE，如图1，将Rt△BDE绕点B顺时针旋转，连结CE，在CE上方作∠FCE＝∠ABC，∠FCE的边与AB交点为F，连结AD，延长CF交AD于点M，如图2，在Rt△BDE旋转的过程中，线段AM的最小值是 ．二、解答题（本大题共3个小题，共30分）24．（8分）成都市某新能源汽车销售商，购进某种型号的汽车成本价为20万元/台，投入市场销售，其销售单价不低于成本．开展购买新能源汽车补贴活动后，发现每月销售量y（台）与销售单价x（万元/台）之间存在一次函数关系，且已知两月数据为：销售价定20.1万元，每月销售39台；销售价定为20.3万元，每月销售37台．（1）若该店销售这种新能源汽车每月获得30万元的利润，则这种新能源汽车的销售单价定为多少元？（2）设每月的总利润为w万元，当销售单价定为多少时，该店每月的利润最大？最大利润是多少？25．（10分）如图，在平面直角坐标系xOy中，动直线l：y＝kx+1（k≠0）与抛物线相交于A，B 两点（点A在点B的左侧），动直线l分别交y轴、x轴于C、D两点．（1）若点A的横坐标是﹣4，求点B的坐标；（2）若直线l运动过程中，有CD＝2BC，求此时k的值；（3）若线段AC的中点是点E，EF垂直x轴于F，在直线l运动过程中，探究线段CE与CF的数量关系，并证明你的结论．26．（12分）如图，在▱ABCD中，点E在DC边上，连接BE交AC于点F，若DE＝CD，∠BAC＝∠BAD．（1）如图1，求的值；（2）如图2，点M在AD上，作EM∥AC交BC的延长线于点N，若∠MBE＝∠BAD，BC＝4，求BE 的长；（3）如图3，点G在BC上，连接FG，若∠FGC＝∠FEC，，求的值．参考答案一、选择题（本大题共8个小题，每小题4分，共32分，每小题均有四个选项，其中只有一项符合题目要求）1．（4分）的相反数是（ ）A ．B．C ．D ．【解答】解：的相反数是，故选：B ．2．（4分）如图所示的几何体是由5个大小相同的小立方块搭成，它的俯视图是（ ）A ．B ．C ．D ．【解答】解：由题干中的几何体可得其俯视图是，故选：C ．3．（4分）俄罗斯驻华大使伊戈尔•莫尔古洛夫在接受卫星通讯社采访时表示，俄中两国2023年的贸易额将大幅突破2000亿美元大关．将数据2000亿用科学记数法表示为（ ）A ．2×1011B ．2×1010C ．2×109D ．2×1012【解答】解：2000亿＝200000000000＝2×1011．故选：A ．4．（4分）如图，已知∠DAC ＝∠DBC ，添加下列条件不能判定△ACD ≌△BDC 的是（ ）133-133-133313313-133-133A．∠ACD＝∠BDC B．∠ADC＝∠BCD C．AB∥CD D．AC＝BD 【解答】解：由图可得，DC＝CD，∵∠DAC＝∠DBC，∴添加∠ACD＝∠BDC时，△ACD≌△BDC（AAS），故选项A不符合题意；添加∠ADC＝∠BCD时，△ACD≌△BDC（ASA），故选项B不符合题意；添加AB∥CD时，不能证明△ACD≌△BDC，故选项C符合题意；添加AC＝BD时，作CH⊥AD，DG⊥BC，根据AAS得出△AHC≌△BGD，则CH＝DG，根据HL可得：△CDH≌△DCG，可得：∠CDH＝∠DCG，根据AAS可得△ACD≌△BDC（AAS），故选项D不符合题意；故选：C．5．（4分）下列运算正确的是（ ）A．3x+2y＝6xy B．2x×3y＝6x+yC．（x﹣y）2＝x2+y2﹣xy D．（x+3）（x﹣3）＝x2﹣9【解答】解：A、3x与2y不是同类项，不能合并，故此选项不符合题意；B、2x×3y≠6x+y，故此选项不符合题意；C、（x﹣y）2＝x2﹣2xy+y2，故此选项不符合题意；D、（x+3）（x﹣3）＝x2﹣9，故此选项符合题意；故选：D．6．（4分）某校六个年级举行的“爱成都迎大运”知识比赛中，各年级得分（单位：分）如下：98，94，98，97，94，96，则各年级得分的中位数是（ ）A．96分B．97分C．96.5分D．98分【解答】解：各年级得分排序如下：94，94，96，97，98，98，∴中位数为：＝96.5（分）．故选：C．7．（4分）我国古代数学著作《张丘建算经》中著名的“百鸡问题”叙述如下：“鸡翁一，值钱五；鸡母一，值钱三；鸡雏三，值钱一；百钱买百鸡，则翁、母、雏各几何？”意思是公鸡五钱一只，母鸡三钱一只，小鸡一钱三只，要用一百钱买一百只鸡，问公鸡、母鸡、小鸡各多少只？若现已知母鸡买4只，设公鸡买x只，小鸡买y只，则可列方程组为（ ）A．B．C．D．【解答】解：∵共买了100只鸡，∴x+y+4＝100；∵公鸡五钱一只，母鸡三钱一只，小鸡一钱三只，且共花费100钱，∴5x+4×3+y＝100．∴根据题意得可列方程组．故选：A．8．（4分）对于二次函数y＝﹣x2+2x+3（1≤x≤4）的图象，下列说法正确的有（ ）①开口向上；②函数最小值是﹣5；③与直线有两个交点；④当x＞2时，y随x的增大而减小．A．4B．3C．2D．1【解答】解：∵a＝﹣1＜0，抛物线开口向下；故①错误；∵y＝﹣x2+2x+3＝﹣（x﹣1）2+4，∴x＝4时，y＝﹣5，∴函数最小值是﹣5，故②正确；∵y＝﹣x2+2x+3＝﹣（x﹣1）2+4，∴顶点为（1，4），∴与直线有两个交点，故③正确；∵抛物线开口向下，对称轴为直线x＝1，∴当x＞2时，y随x的增大而减小，故④正确．故选：B．二、填空题（本大题共5个小题，每小题4分，共20分）9．（4分）分解因式：＝ ．【解答】解：＝＝，故答案为：．10．（4分）在平面直角坐标系xOy中，△ABC顶点A的坐标是A（﹣3，﹣1），将△ABC向左平移5个单位长度得到△A′B′C′，则点A′的坐标是 （﹣8，﹣1） ．【解答】解：∵A的坐标是（﹣3，﹣1），现将△ABC向左平移5个单位，∴点A′的坐标为（﹣8，﹣1），故答案为：（﹣8，﹣1）．11．（4分）如图，圆内接四边形ABCD两组对边的延长线分别交于点E，F，且∠E＝45°，∠F＝35°，则∠A＝ 50° ．【解答】解：∵四边形ABCD是圆内接四边形，∴∠BCD＝180°﹣∠A，∵∠CBF＝∠A+∠E，∠DCB＝∠CBF+∠F，∴180°﹣∠A＝∠A+∠E+∠F，即180°﹣∠A＝∠A+45°+35°，解得∠A＝50°．故答案为：50°．12．（4分）从﹣3，0，1，2四个数中随机抽取一个为a的值，则a是方程x2+2x﹣3＝0解的概率是 ．【解答】解：∵x2+2x﹣3＝0，∴（x﹣1）（x+3）＝0，解得：x1＝1，x2＝﹣3，∵a是方程x2+2x﹣3＝0的解，∴a＝1或﹣3，∴从﹣3，0，1，2四个数中随机抽取一个为a的值，则a是方程x2+2x﹣3＝0解的概率是＝．故答案为：．13．（4分）如图，在△ABC中，∠BAC＝60°，∠C＝90°，AB＝m，按以下步骤作图：①分别以点B和C为圆心，以大于的长为半径作弧，两弧相交于点M和N；②作直线MN交AB于D，交BC 于E．则线段DE＝ m ．【解答】解：作图如下，由作图可得，DE为△ABC的中位线，∴DE＝AC，在△ABC中，∠BAC＝60°，∠C＝90°，AB＝m，∴∠ABC ＝30°，∴AC ＝m ，∴DE ＝m ，故答案为：m ．三、解答题（本大题共5个小题，共48分）14．（12分）（1）计算：；（2）解不等式组：．【解答】解：（1）原式＝＝﹣8﹣4+＝﹣5．（2），解不等式①得，x ≥﹣4，解不等式②得，x ＜8，所以不等式组的解集为：﹣4≤x ＜8．15．（8分）2023年7月28日至8月8日，成都市将举办第31届世界大学生夏季运动会，成都大运会主场馆包含“一场三馆”．某校从“A ：主体育场、B ：多功能体育馆、C ：小球馆、D ：游泳跳水馆”四个场馆对学生进行了一次抽样调查，要求每个学生从这四个场馆中选出自己最喜欢的场馆，现将调查的结果绘制成如图两幅不完整的统计图，请你根据图中提供的信息，解答下列问题：（1）抽取的总人数是 100 ，并补全条形统计图；（2）在扇形统计图中，求“小球馆”所对应的扇形的圆心角的度数；（3）我校九年级有3000人，估计有多少同学最喜欢“游泳跳水馆”？7330cos 216)21(3-++---【解答】解：（1）抽取的总人数是：40÷40%＝100；最喜欢B场馆的人数为：100﹣40﹣15﹣35＝10，补全条形统计图如下：故答案为：100；（2）“小球馆”所对应的扇形的圆心角的度数为：360°×＝54°；（3）3000×＝1050（名），答：我校九年级有3000人，估计有1050名同学最喜欢“游泳跳水馆”．16．（8分）某数学兴趣小组决定利用所学知识测量天府艺术公园•蜀园帘月亭的高度．如图，帘月亭的高度为AB，∠ADB＝30°，∠ACB＝20°，DC＝9米，请你根据以上测量数据，帮助兴趣小组求出帘月亭AB的高度．（结果保留根号）．（参考数据：sin20°≈0.34，cos20°≈0.94，tan20°≈0.36）【解答】解：∵∠B＝90°，∠ADB＝30°，∴BD＝＝AB，∵∠B＝90°，∠ACB＝20°，∴BC＝＝，∵DC＝9米，∴BC﹣BD＝﹣AB﹣＝9，解得AB＝，答：帘月亭AB的高度为（米）．17．（8分）如图，在直角三角形ABC中，AD垂直斜边BC于D，以AD为直径作⊙O交AB于E，交AC 于F，连接BF交⊙O于G，连接EF．（1）证明：∠ABC＝∠AFE；（2）若AD＝2，CD＝1，求BG的长．【解答】（1）证明：∵∠BAC＝90°，∴∠AFE+∠AEF＝90°，EF是⊙O的直径，∵AD⊥BC，∴∠ADB＝90°，∴∠ABC+∠BAD＝90°，∵OE＝OA，∴∠AEO＝∠EAO，即∠AEF＝∠BAD，∴∠ABC＝∠AFE；（2）解：如图，连接AG，DF，DG，∵∠ADC＝90°，AD＝2，CD＝1，∴AC＝＝，∵∠BAC＝∠ADC＝90°，∠C＝∠C，∴△ACD∽△BCA，∴，∴＝，∴BC＝5，∴BD＝4，AB＝＝＝2，∵AD是⊙O的直径，∴∠AFD＝90°，∵AC•DF＝AD•CD，∴DF＝＝＝，在Rt△ADF中，AF＝＝，∴BF＝＝，∵＝，∴∠DAG＝∠BFD，∵AD是⊙O的直径，∴∠DAG+∠ADG＝90°，∵AD⊥BC，∴∠BDG+∠ADG＝90°，∴∠BDG＝∠DAG＝∠BFD，又∵∠DBG＝∠FBD，∴△BDG∽△BFD，∴＝，∴BG＝＝＝．18．（12分）如图，在平面直角坐标系xOy中，一次函数y＝3x﹣2的图象与反比例函数的图象相交于A（n，﹣6），B两点．（1）求反比例函数的表达式；（2）点C是反比例函数第三象限图象上一点，且在直线AB的上方，若三角形ABC的面积与三角形AOB 面积的相等，求点C的坐标；（3）对平面内任意一点P（a，b），定义K变换：若a≥b，则P变为P′（﹣b，﹣a）；若a＜b，则点P变为P′（a，﹣b），若线段AB经过K变换后的图形与另一个反比例函数的图象没有交点，求m的取值范围．【解答】解：（1）由题意，将A（n，﹣6）代入y＝3x﹣2中，∴3n﹣2＝﹣6．∴n＝﹣．∴A（﹣，﹣6）．又∵点A在反比例函数y＝上，∴k＝（﹣）×（﹣6）＝8，∴反比例函数的解析式为y＝；（2）如图所示，联立y＝3x﹣2，y＝得：3x2﹣2x﹣8＝0，∴x＝﹣或2，∴B（2，4）．∵三角形ABC的面积与三角形AOB面积的相等，∴直线OC∥直线AB，∴直线OC解析式为y＝3x．联立y＝和y＝3x得：3x2＝8，∴x＝±，∴C（﹣，﹣2）．（3）∵A（﹣，﹣6）中﹣＞﹣6，∴A'（6，）．∵B（2，4）中2＜4，∴B'（2，﹣4）．设直线A'B'解析式为y＝kx+b，∴＝6k+b，﹣4＝2k+b，∴k＝，b＝﹣，∴直线A'B'解析式为y＝x﹣，设直线A'B'与y＝相切，∴x﹣＝，∴4x2﹣20x﹣3m＝0，∴Δ＝400+48m＝0，∴m＝，∵直线A'B'与y＝没有交点，∴m＜．一、填空题（本大题共5个小题，每小题4分，共20分）19．（4分）比较大小： ＞ （填“＞”、“＜”或者“＝”）．【解答】解：﹣＝＝，∵（5）2＝150，112＝121，∴150＞121，∴5＞11，∴5﹣11＞0，∴＞0，∴＞，故答案为：＞．20．（4分）若a+3b＝4，则a2﹣9b2+24b+5的值是 21 ．【解答】解：∵a+3b＝4，∴代入可得：a2﹣9b2+24b+5＝（a+3b）（a﹣3b）+24b+5＝4（a﹣3b）+24b+5＝4a﹣12b+24b+5＝4a+12b+5＝4（a+3b）+5＝4×4+5＝21．故答案为：21．21．（4分）如图，在菱形ABCD中，对角线AC、BD交于点E，AC＝8，BD＝6，以点E为圆心作圆E，圆E与菱形的四条边相切，现随机向菱形ABCD内掷一枚小针，则针尖落在圆E的概率为 ．【解答】解：如图，设圆E与AB相切于F点，连接EF，则EF⊥AB，∵菱形ABCD，AC＝8，BD＝6，∴AE＝AC＝4，BE＝BD＝3，AE⊥BE，∴，，∴，∵，∴，∴＝，∴随机向菱形ABCD投一根针，针尖落在圆E的概率为．故答案为：．22．（4分）如图，点B在反比例函数的图象上，点A在x轴上，OB＝AB，过点A作AD∥OB交y轴负半轴于点D，连结BD，当△OCD面积为3时，则k的值为 ．【解答】解：如图，过点B作BE⊥OA于点E，作BF⊥y轴于点F，∵OB＝AB，∴OE＝AE，∵S△OBE＝k，∴S△ABE＝S△OBE＝k，∴S△ABO＝k，∵AD∥OB，∴S△OBD＝S△ABO＝k，∵S△OCD＝3，∴S△BOC＝k﹣3，∵＝，∴＝，设B（b，），则BF＝b，BE＝，∴OD•BF＝OA•BE，∴OD＝＝＝＝2BE，∴＝，∵BE∥OD，∴△BCE∽△DCO，∴＝，∴＝，解得：k＝．故答案为：．23．（4分）在Rt△ABC中，∠ACB＝90°，AB＝5，AC＝3．点D在BC边上，DE⊥AB，垂足为E，CD ＝DE，如图1，将Rt△BDE绕点B顺时针旋转，连结CE，在CE上方作∠FCE＝∠ABC，∠FCE的边与AB交点为F，连结AD，延长CF交AD于点M，如图2，在Rt△BDE旋转的过程中，线段AM的最小值是 ．【解答】解：∵∠ACB＝90°，AB＝5，AC＝3，∴BC＝＝＝4，如图1，∵DE⊥AB于点E，CD＝DE，∴∠DEB＝∠ACB＝90°，DB＝4﹣CD＝4﹣DE，∵∠B＝∠B，∴△DBE∽△ABC，∴＝＝，∴DE＝，∴BE＝×4＝2，DB＝4﹣＝，如图2，作EG⊥CE交CM的延长线于点G，连接并延长GD交CE于点H，交BC于点L，连接AG、CD，∵∠GEC＝∠DEB＝90°，∠FCE＝∠ABC＝∠DBE，∴△GCE∽△DBE，∴＝，∴＝，∵∠DEG＝∠BEC＝90°﹣∠CED，∴△DEG∽△BEC，∴＝，∠DGE＝∠BCE，∴DG＝＝＝3，∵∠CHL＝∠GHE，∴∠GLB＝∠CHL+∠BCE＝∠GHE+∠DGE＝90°，∴∠GLB＝∠ACB，∴DG∥AC，且DG＝AC，∴四边形ACDG是平行四边形，∴AM＝DM，∴AD＝2AM，∴AD+DB≥AB，∴2AM+≥5，∴AM≥，∴线段AM的最小值是，故答案为：．二、解答题（本大题共3个小题，共30分）24．（8分）成都市某新能源汽车销售商，购进某种型号的汽车成本价为20万元/台，投入市场销售，其销售单价不低于成本．开展购买新能源汽车补贴活动后，发现每月销售量y（台）与销售单价x（万元/台）之间存在一次函数关系，且已知两月数据为：销售价定20.1万元，每月销售39台；销售价定为20.3万元，每月销售37台．（1）若该店销售这种新能源汽车每月获得30万元的利润，则这种新能源汽车的销售单价定为多少元？（2）设每月的总利润为w万元，当销售单价定为多少时，该店每月的利润最大？最大利润是多少？【解答】解：（1）设y与x之间的函数关系式为y＝kx+b（k≠0），则解得∴y与x之间的函数关系式为y＝﹣10x+240（x≥20）．依题意得（x﹣20）（﹣10x+240）＝30，解得x1＝21，x2＝23，答：这种新能源汽车的销售单价定为21万元或23万元．（2）由题意得w＝（x﹣20）（﹣10x+240）＝﹣10x2+440x﹣4800＝﹣10（x﹣22）2+40．∵﹣10＜0，∴当x＝22时，w取得最大值40．答：当销售单价定为22万元时，该店每月的利润最大，最大利润是40万元．25．（10分）如图，在平面直角坐标系xOy中，动直线l：y＝kx+1（k≠0）与抛物线相交于A，B两点（点A在点B的左侧），动直线l分别交y轴、x轴于C、D两点．（1）若点A的横坐标是﹣4，求点B的坐标；（2）若直线l运动过程中，有CD＝2BC，求此时k的值；（3）若线段AC的中点是点E，EF垂直x轴于F，在直线l运动过程中，探究线段CE与CF的数量关系，并证明你的结论．【解答】解：（1）当x＝﹣4时，y＝，∴A（﹣4，4），∴﹣4k+1＝4，∴k＝﹣，∴y＝﹣，由得，x＝﹣4或x＝1，当x＝1时，y＝，∴B（1，）；（2）如图1，当k＞0时，作BM⊥x轴于M，∴OC∥BM，∴△DOC∽△DMB，∴，∵OC＝1，CD＝2BC，∴BM＝，由得，∴x1＝，x2＝﹣（舍去），∴B（），∴，∴k＝，如图2，当k＜0时，作BN⊥OD，∴BN∥OC，∴，∴OD＝2OF，∴BN＝OC＝，由得，x1＝，x2＝﹣（舍去），∴B（），∴，∴k＝﹣，综上所述：k＝或﹣；（3）2CE＝CF2，理由如下：设A（m，），∵E是AC的中点，∴E（），∵EF⊥x轴，∴F（），∴＝，∴CE＝m2+，∵CF2＝（m）2+1＝m2+1＝2CE，∴2CE＝CF2．26．（12分）如图，在▱ABCD中，点E在DC边上，连接BE交AC于点F，若DE＝CD，∠BAC＝∠BAD．（1）如图1，求的值；（2）如图2，点M在AD上，作EM∥AC交BC的延长线于点N，若∠MBE＝∠BAD，BC＝4，求BE 的长；（3）如图3，点G在BC上，连接FG，若∠FGC＝∠FEC，，求的值．【解答】解：（1）∵四边形ABCD是平行四边形，∴AB＝CD，AB∥CD，∴∠BAF＝∠ECF，∵∠AFB＝∠CFE，∴△ABF∽△CEF，∴，∵，∴，∴，∴，∴；（2）∵四边形ABCD是平行四边形，∴AD//BC，AD＝BC＝4，∴，设ME＝3m，则MN＝4m，∵∠BAC＝∠BAD，∴∠DAC＝∠BAD，又∵∠MBE＝∠BAD，∴∠MBE＝∠DAC，∵AD∥BC，MN∥AC，∴∠DME＝∠DAC，∠MNB＝∠DME，四边形AMNC是平行四边形，∵DE＝CD，∴，∵MN∥AC，∴，∴DM＝3，MA＝1，∴NC＝MA＝1，∴BN＝5，∴∠MNB＝∠DAC，∴∠MBE＝∠MNB，又∵∠EMB＝∠BMN，∴△MBE∽△MNB，∴，∵ME＝3m，MN＝4m，∴，∴MB＝m，∴，∴BE＝．（3）如图，作AN平分∠DAC交CD于N，过点F作FM∥AN交CD于M，∵∠BAD＝3∠BAC，∴∠DAC＝2∠BAC，∵AN平分∠DAC，∴∠DAN＝∠NAC＝∠BAC，∵AB∥CD，∴∠BAC＝∠ACD，∴∠DAN＝∠NAC＝∠ACD，∴AN＝CN，∵，设BC＝4a，则AC＝5a，∴AD＝4a，由（1）知，AF：FC＝4：1，∴AF＝4a，FC＝a，过N作NQ⊥AD于Q，NP⊥AC于P，∴NP＝NQ，∴，又∵，∴，设DN＝4b，则NC＝5b，∴CD＝9b，∴DE＝×9b＝b，CE＝b，∵∠DAN＝∠ACD，∠D＝∠D，∴△ADN∽△CDA，∴，∴16a2＝4b×9b，即16a2＝36b2，∴b＝a，∴DE＝×a＝a，CE＝a，∴AN＝CN＝5×a＝a，∵FM∥AN，∴△CFM∽△CAN，∴，∴FM＝CM＝×a＝a，∴EM＝CE﹣CM＝，∵AD∥BC，∴∠DAC＝∠ACB＝2∠ACD，∵∠FME＝∠MEC+∠MCE＝2∠ACD，∴∠FME＝∠FCG，又∵∠FEM＝∠FGC，∴△FGC∽△FEM，∴，∴，∴CG＝a，∵CD＝AB＝9b＝6a，∴．。
四川省成都市实验外国语学校2024-2025学年高三上学期11月期中考试数学试题
四川省成都市实验外国语学校2024-2025学年高三上学期11月期中考试数学试题一、单选题1．若命题p ：20430x x x ∃>-+>，，则命题p ⌝为（）A ．20430，∃>-+≥x x xB ．20430，∃≤-+≤x x xC ．20430，∀>-+≤x x xD ．20430，∀≤-+≤x x x 2．在ABC V 中，“π6A >”是“1sin 2A >”的（）A ．充分不必要条件B ．必要不充分条件C ．充要条件D ．既不充分也不必要条件3．已知向量,a b 的夹角为2π3，且5,4a b == ，则a在b 方向上的投影向量为（）A ．38b -B ．58b -C ．58bD ．78b- 4．已知等差数列{}n a 和{}n b 的前n 项和分别为n S 、n T ，若342n n S n T n +=+，则62102a b b +（）A ．11113B ．3713C ．11126D ．37265．遗忘曲线由德国心理学家艾宾浩斯研究发现，描述了人类大脑对新事物遗忘的规律，某同学利用信息技术拟合了“艾宾浩斯遗忘曲线”，得到记忆率y 与初次记忆经过的时间x （小时）的大致关系：0.0610.6y x =-，则记忆率为20%时经过的时间约为（）（参考数据：lg 20.30≈，lg 30.48≈）A ．80小时B ．90小时C ．100小时D ．120小时6．已知圆锥的侧面展开图是一个半径为43，面积为4π3的扇形，则该圆锥的外接球的表面积为（）A ．256π63B ．4πC ．9π2D ．9π7．若()*n n ∈N 次多项式()()1212100n n n n n n P t a t a t a t a t a a --=++⋅⋅⋅+++≠满足()cos cos n P x nx =，则称这些多项式()n P t 为切比雪夫多项式．如，由2cos 22cos 1θθ=-可得切比雪夫多项式()2221P x x =-，同理可得()3343P x x x =-．利用上述信息计算sin 54︒=（）A B C ．48D ．488．函数()2e 12e 21x x xh x -=++，不等式()()2222h ax h ax -+≤对x ∀∈R 恒成立，则实数a 的取值范围是（）A ．()2,-+∞B ．(),2-∞C ．()0,2D ．[]2,0-二、多选题9．设1z ，2z 为复数，且120z z ≠，则下列结论正确的是（）A ．1212z z z z =B ．1212z z z z +=+C ．若12=z z ，则2212z z =D ．1212z z z z ⋅=⋅10．下列关于概率统计的知识，其中说法正确的是（）A ．数据1-，0，2，4，5，6，8，9的第25百分位数是1B ．已知随机变量(),X B n p ，若()40E X =，()30D X =，则160n =C ．若事件M ，N 的概率满足()()0,1P M ∈，()()0,1P N ∈且()()1P N M P N +=，则M 与N 相互独立D ．若一组样本数据(),i i x y （1i =，2，…，n ）的对应样本点都在直线132y x =-+上，则这组样本数据的相关系数为12-11．“曼哈顿距离”是十九世纪的赫尔曼•闵可夫斯省所创词汇，用以标明两个点在标准坐标系上的绝对轴距总和，其定义如下：在直角坐标平面上任意两点()()1122,,,A x y B x y 的曼哈顿距离()1212,d A B x x y y =-+-，则下列结论正确的是（）A ．若点()()1,3,2,4P Q ，则(),2d P Q =B ．若对于三点,,A B C ，则“()()(),,,d A B d A C d B C +=”当且仅当“点A 在线段BC 上”C ．若点M 在圆224x y +=上，点P 在直线280x y -+=上，则(),d P M 2-D ．若点M 在圆224x y +=上，点P 在直线280x y -+=上，则(),d P M 的最小值是4三、填空题12．6(12)(13)x x -+的展开式中，含2x 的项的系数为．（用数字作答）13．已知椭圆2222:1(0)x y C a b a b +=>>的右焦点和上顶点分别为F 和A ，连接AF 并延长交椭圆C 于B ，若32AOB AOF S S = ，则椭圆C 的离心率为．14．设数列{}n a 的前n 项和为21212,1,1,23n nn n a a S a a a +++===．对任意()()*22221N ,21log log n n n n S a a λ+∈++>恒成立，则λ的取值范围为.四、解答题15．锐角ABC V 的内角,,A B C 所对的边分别为,,a b c ，若2cos 2b a B c +=，且a =3b =.(1)求边c 的值；(2)求内角A 的角平分线AD 的长．16．如图，在四棱锥P ABCD -中，2PD =，1AD =，PD DA ⊥，PD DC ⊥，底面ABCD 为正方形，M ，N 分别为AD ，PD 的中点.(1)求点B 到平面MNC 的距离；(2)求直线MB 与平面BNC 所成角的余弦值.17．某工厂生产某款电池，在满电状态下能够持续放电时间不低于10小时的为合格品，工程师选择某台生产电池的机器进行参数调试，在调试前后，分别在其产品中随机抽取样本数据进行统计，制作了如下的22⨯列联表：产品合格不合格合计调试前451560调试后35540合计8020100(1)根据表中数据，依据0.01α=的独立性检验，能否认为参数调试与产品质量有关联；(2)现从调试前的样本中按合格和不合格，用分层随机抽样法抽取8件产品重新做参数调试，再从这8件产品中随机抽取3件做对比分析，记抽取的3件中合格的件数为X ，求X 的分布列和数学期望；(3)用样本分布的频率估计总体分布的概率，若现在随机抽取调试后的产品1000件，记其中合格的件数为Y ，求使事件“Y k =”的概率最大时k 的取值.参考公式及数据：()()()()22()n ad bc a b c d a c b d χ-=++++，其中n a b c d =+++.α0.0250.010.0050.001x α5.0246.6357.87910.82818．已知双曲线()2222:10,0x y C a b a b-=>>的实轴长为4，渐近线方程为12y x =±.(1)求双曲线C 的标准方程；(2)双曲线的左､右顶点分别为12A A ､，过点()3,0B 作与x 轴不重合的直线l 与C 交于P Q ､两点，直线1A P 与2A Q 交于点S ，直线1AQ 与2A P 交于点T .（i ）设直线1A P 的斜率为1k ，直线2A Q 的斜率为2k ，若12k k λ=，求λ的值；（ii ）求2A ST 的面积的取值范围.19．已知定义：函数()f x 的导函数为()f x '，我们称函数()f x '的导函数()f x ''为函数()f x 的二阶导函数，如果一个连续函数()f x 在区间I 上的二阶导函数()0f x ''≥，则称()f x 为I 上的凹函数;二阶导函数()0f x ''≤，则称()f x 为I 上的凸函数.若()f x 是区间I 上的凹函数，则对任意的12,,x x n x I ∈，有不等式()()()1212n nf x f x f x x x x f n n ++++++⎛⎫≤ ⎪⎝⎭恒成立（当且仅当12n x x x === 时等号成立）.若()f x 是区间I 上的凸函数，则对任意的12,,n x x x I ∈ ，有不等式()()()1212n nf x f x f x x x x f n n ++++++⎛⎫≥⎪⎝⎭恒成立（当且仅当12n x x x === 时等号成立）.已知函数()1f x x x =+，π0,2x ⎛⎤∈ ⎥⎝⎦.(1)试判断()f x 在π0,2⎛⎤⎥⎝⎦为凹函数还是凸函数?(2)设12,x x ，L ，0n x >，2n ≥，且121n x x x +++= ，求1212111n nx x xW x x x =++++++ 的最大值;(3)已知*N a ∈，且当π0,2x ⎛⎤∈ ⎥⎝⎦，都有()()()sin sin 31cos 0x ax x f x x +-+>恒成立，求实数a的所有可能取值.。
四川省成都教科院附属中学2020-2021学年度第一学期半期考试数学试卷(无答案)
成都教科院附中 2020-2021 学年度上期高 2020 级半期考试数学 试卷时间：120 分钟 满分：150 分命题：宋利、王进 审题：杨超本试卷分选择题与非选择题两部分。
第Ⅰ卷(选择题)1 至 2 页，第Ⅱ卷 (非选择题)2 至 6 页。
注意事项：1.答题前，考生务必将自己的姓名、准考证号、条形码粘贴或填写在答题卡规定位置上。
2.回答选择题时，选出每小题答案后，用 2B 铅笔把答题卡上对应题目的答案标号涂黑。
如需改动，用橡皮擦干净后，再选涂其他答案标号，写在本试卷上无效。
3.答非选择题时，必须使用 0.5 毫米黑色签字笔，将答案书写在答题卡规定的位置上。
第Ⅰ卷（选择题，共 60 分）一、选择题：本题共 12 小题，每小题 5 分，共 60 分，在每个小题给出的四个选项中，只 有一项符合题目要求的。
1.集合 A={-2，1，2，3}的真子集．．．个数为()A.16 B.15 C.14 D.134.所有题目必须在答题卡上作答，在试题卷上、错误答题卡区域作答均无2.函数y=f(x)的图象与直线x=2019的交点个数是()A.至多有一个B.至少有一个C.有且仅有一个D.无数个3.若函数，则函数(x)的定义城为() A.(-,2) B.(0,2) C.(0,) D.(0,+) 4.比较大小:( ) A.a＜c＜b B.c＜a <b C.c<b ＜aD.a ＜b ＜c ()()12x -log 1x f 31+=¥21¥21ln 1.03,,2log a ec e b ===5.在下列区间中，函数f(x)=e x +4x-3的零点所在的区间为()6.设集合则() A.A=BB.A BC.B AD.A B=Ø7.计算等于() A. B. C.- D.-8.函数f(x)=的图象是()A. B.9.函数在[-1，2]的最小值是() A.1 B. C. D.310.函数f(x)=ln(x 2-2x-8)的单调递增区间是()A.(-，-2)B.(-，1)C.(1，+)D.(4，+)11.加工爆米花时，爆开且不糊的粒数占加工总粒数的百分比称为“可食用率”，在特定条件下，可食用率P 与加工时间t(单位：分钟)满足函数关系P(t)=at 2+bt+c，(其中a，b，c 为常数).如图记录了三次实验的数据，根据上述函数模型和实验数据，得到最佳加工时间为()÷øöçèæ÷øöçèæ÷øöçèæ÷øöçèæ4321.2141.410.041-.，，，，D C B A {}，＜＜，＜þýüîíì==2221x0lgx x x B A ÍÍÇa 1-a a-a a -a 2x -x e ()121-41x f x x +÷øöçèæ÷øöçèæ=161343¥¥¥¥A.3.50分钟B.3.75分钟C.4.00分钟D.4.25分钟12.已知若方程f(x)-a=0有四个根x 1，x 2，x 3，x 4且 x 1＜x 2＜x 3＜x 4，则x 1+x 2+x 3+x 4的取值范围是()A.(0.1)B.(0，)C.(0，]D.(0，+)第Ⅱ卷(非选择题，共90分) 二、填空题：本题共4小题，每小题5分，共20分.13.已知幂函数f(x)=x a 的图象过点(9，3)，若f(t)=2，则实数t 的值为 .14.已知函数则f[f(9)]的值是. 15.已知函数y=f(x-1)是奇函数，且f(2)=1.则f(-4)= .16.2019年1月1月新修订的个税法正式实施，规定：公民全月工资、薪金所得不超过5000元的部分不必纳税，超过5000元的部分为全月应纳税所得额。
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成都市实验外国语学校2021学年上期第二次阶段考试
高2019级数学学科试题
注意事项：
本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。
考生作答时，须将答案全部作答在答题卡上，在本试卷、草稿纸上答题无效。
第Ⅰ卷（选择题） 一、单选题
1．已知命题p ：0∀>x ，总有()121+>x
x ，则命题p 的否定为（ ）
A ．00∃≤x ，使得()00121+≤x x
B ．00∃>x ，使得()00121+≤x
x
C ．0∀>x ，总有()121+≤x x
D ．0∀≤x ，总有()121+≤x
x
2．某工厂为了对40个零件进行抽样调查，将其编号为00，01，…，38，39．现要从中选出5个，利用下面的随机数表，从第一行第3列开始，由左至右依次读取，则选出来的第3个零件编号是（ ） 0347 4373 3686 9636 6233 6011 1410 2616 6147 4698 6371 8045 9577 7424 6762 4281 1457 2042 5332 3732 2707 3607 5124 5179 A ．11
B ．14
C ．10
D ．33
3．已知在最小二乘法原理下，具有相关关系的变量x ，y 之间的线性回归方程为ˆ0.710.3=-+y
x ，且变量x ，y 之间的相关数据如表所示，则下列说法正确的是（ ）
A ．变量x ，y 之间呈现正相关关系
B ．可以预测，当20=x 时，ˆ 3.7=y
C ．可求得表中 4.7=m
D ．由表格数据知，该回归直线必过点()9,4
4．方程=x ） A ．圆的一部分
B ．椭圆的一部分
C ．双曲线的一部分
D ．直线的一部分
5．若()2,1P 是圆()2
2125-+=x y 的弦AB 的中点，则直线AB 的方程是（ ） A ．30+-=x y B ．10--=x y
C ．30--=x y
D ．10+-=x y
6．已知抛物线2
34
=
y x ，则它的焦点坐标为（ ）
A ．30,
16⎛⎫
⎪⎝⎭
B ．3,016⎛⎫
⎪⎝⎭
C ．1,03⎛⎫ ⎪⎝⎭
D ．10,3⎛⎫ ⎪⎝⎭
7．两圆2
2
230+-+=x y y 与22
20++=x y x 公共弦所在的直线方程是（ ）
A ．2230--=x y
B ．2230-+=x y
C ．2230+-=x y
D ．2230++=x y
8．右图是抛物线形拱桥，当水面在l 时，拱顶离水面2m ，水面宽4m ，若水面下降0.42m 后，则水面宽为（ ）
A ．2.2m
B ．4.4m
C ．2.4m
D ．4m
9．如图所示，1F ，2F 分别为椭圆22
221+=x y a b
的左右焦点，点P 在椭圆上，2OF P △角形，则2b 的值为（ ）
A
B ．
C ．
D ．10．已知1F ，2F 分别为椭圆C ：()22
2210+=>>x y a b a b
的左右焦点，P 是椭圆上一点，若122=PF PF ，
则椭圆离心率的取值范围为（ ） A ．10,2⎛
⎫ ⎪⎝⎭
B ．11,
32⎛⎫
⎪⎝⎭
C ．1,13⎡⎫⎪⎢⎣⎭
D ．
1,12⎡⎫⎪⎢⎣⎭
11．已知圆C ：()2
222-+=x y ，直线l ：2=-y kx ，若直线l 上存在点P ，过点P 引圆的两条切线1l ，
2l ，使得12⊥l l ，则实数k 的取值范围为（ ）
A ．(),0-∞
B ．[)0,+∞
C ．()
0,22⎡⋃+∞⎣
D ．2⎡+⎣
12．已知双曲线C ：()22
2210,0-=>>x y a b a b
右支上的一点P ，经过点P 的直线与双曲线C 的两条渐近
线分别相交于A ，B 两点．若点A ，B 分别位于第一，四象限，O 为坐标原点，当1
2
=AP PB 时，AOB △的面积为2b ，则双曲线C 的实轴长为（ ） A ．
329
B ．
169
C ．
89
D ．
49
第Ⅱ卷（非选择题） 二、填空题
13．设集合{}01=<<A x x ，{}
03=<<B x x ，那么“∈m A ”是“∈m B ”的______条件（填“充分不必要”、“必要不充分”、“充要”或“既不充分又不必要”）．
14．()()2
2
111+--=k x k y 表示焦点在x 轴上的双曲线，则k 的取值范围为______．
15．已知F 是抛物线C ：2
8=y x 的焦点，M 是C 上一点，FM 的延长线交y 轴于点N ．若M 为FN 的中点，则=FN ______．
16．已知直线l ：0++=mx y m 交圆C ：()2
211-+=x y 于()11,A x y ，()22,B x y 两不同点，
则114-+x y 224+-+x y 的取值范围为______．
三．解答题
17．设∈t R ，已知命题p ：函数()2
1=-+f x x tx 有零点：命题q ：[)1,∃∈+∞x ，4
≥+
t x x
．若∧p q 为真命题，求实数t 的取值范围．
18．已知数列{}n a 的各项均为正数，观察程序框图，若1=k ，2=k 时，分别有13=
S 和25
=S ．
（1）试求数列{}n a 的通项公式；
（2）令3=+n
n n b a ，求数列{}n b 的前n 项和n T ．
19．学校为了制定培养学生阅读习惯，指导学生提高阅读能力的方案，需了解全校学生的阅读情况，现随机调查了200名学生每周阅读时间X （单位：小时）并绘制如图所示的频率分布直方图．
（1）为查找影响学生阅读时间的因素，学校团委决定从每周阅读时间为[)6.5,7.5，[)7.5,8.5的学生中抽取6名参加座谈会，你认为6个名额应该怎么分配？
（2）利用样本估计总体的方法，估计全校每周阅读时间的中位数a （a 的值精确到0.01）． 20．已知抛物线()2
20=>x py p 的焦点为F ，抛物线上的点A 到x 轴的距离为1-AF ．
（1）求p 的值：
（2）已知点()2,0M ，若直线AF 交抛物线于另一个点B ，且⊥AM BM ，求直线AF 的方程． 21．平面内动点M 到点()2,0F 的距离与M 到直线92=x 的距离之比为2
3
． （1）求动点M 的轨迹C 的方程：
（2）过点F 的直线l 交轨迹C 于不同两点A 、B ，交y 轴于点N ，已知1=NA AF λ，2=NB BF λ，试问12+λλ是否等于定值，并说明理由．
22．已知椭圆C ：()22
2210+=>>x y a b a b
的长轴长为6，C 上一点M 关于原点O 的对称点为N ，若
⊥MF NF ，设∠=MNF α，且π3sin 44⎛
⎫+= ⎪⎝
⎭α．
（1）求椭圆C 的标准方程：
（2）经过圆O ：2
2
10+=x y 上一动点P 作椭圆C 的两条切线，切点分别记为A 、B ，求AOB △面积的取值范围．。