【名校复习专用】黑龙江省齐齐哈尔市2020届高考数学一轮复习第13讲变化率与导数学案(无答案)文

综合检测二(标准卷)考生注意：1．本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分，共4页．2．答卷前，考生务必用蓝、黑色字迹的钢笔或圆珠笔将自己的姓名、班级、学号填写在相应位置上．3．本次考试时间120分钟，满分150分．4．请在密封线内作答，保持试卷清洁完整．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．在每小题给出的四个选项中，只有一项是符合题目要求的)1．设全集为R ，集合A ＝⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫x ⎪⎪⎪ 2－x x >0，B ＝{x |x ≥1}，则A ∩B 等于( ) A ．{x |0<x ≤1}B ．{x |0<x <1}C ．{x |1≤x <2}D ．{x |0<x <2} 答案 C解析 由集合A ＝⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫x ⎪⎪⎪ 2－x x >0，可知0<x <2； 因为B ＝{x |x ≥1}，所以A ∩B ＝{}x |1≤x <2，故选C.2．若复数z 满足(1＋2i)z ＝1－i ，则复数z 为( )A.15＋35i B ．－15＋35i C.15－35i D ．－15－35i 答案 D解析 ∵(1＋2i)z ＝1－i ，∴z ＝1－i 1＋2i ＝(1－i )(1－2i )(1＋2i )(1－2i )＝－1－3i 5＝－15－35i ，故选D. 3．设变量x ，y 满足约束条件⎩⎪⎨⎪⎧ y ≥0，x －y ＋1≥0，x ＋y －3≤0，，则z ＝2x －y 的最小值为( )A ．－3B ．－2C ．－1D ．2答案 B 解析 绘制不等式组表示的可行域(阴影部分包含边界)，结合目标函数可得，目标函数在点A (－1,0) 处取得最小值z ＝2x －y ＝－2.4.如图，在△OAB 中，P 为线段AB 上的一点，OP →＝xOA →＋yOB →，且BP →＝2PA →，则( )A ．x ＝23，y ＝13B ．x ＝13，y ＝23C ．x ＝14，y ＝34D ．x ＝34，y ＝14 答案 A解析 由题可知OP →＝OB →＋BP →，又BP →＝2PA →，所以OP →＝OB →＋23B A →＝OB →＋23(OA →－OB →)＝23O A →＋13OB →，所以x ＝23，y ＝13，故选A. 5．(2x ＋x )4的展开式中x 3的系数是( )A ．6B ．12C ．24D ．48答案 C解析 (2x ＋x )4的展开式的通项公式为T k ＋1＝C k 4(2x )4－k (x )k ＝C k 424－k 42k x －，令4－k 2＝3解得k ＝2，故x 3的系数为C 2422＝24，故选C.6．阅读如图所示的程序框图，运行相应的程序，则输出的S 值为( )A ．15B ．37C ．83D ．177答案 B解析 执行程序，可得S ＝0，i ＝1，不符合，返回循环；。

2024-2025学年黑龙江省齐齐哈尔市克东县克东一中、克山一中等五校联考高三毕业班质检物理试题理试题注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置．3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B 铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效．5．如需作图，须用2B 铅笔绘、写清楚，线条、符号等须加黑、加粗．一、单项选择题：本题共6小题，每小题4分，共24分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1、如图甲所示，直径为0.4m 、电阻为0.1Ω的闭合铜环静止在粗糙斜面上，CD 为铜环的对称轴，CD 以下部分的铜环处于磁感应强度B 方向垂直斜面且磁感线均匀分布的磁场中，若取向上为磁场的正方向，B 随时间t 变化的图像如图乙所示，铜环始终保持静止，取π3=，则（ ）A ．2s t =时铜环中没有感应电流B ． 1.5s t =时铜环中有沿逆时针方向的感应电流（从上向下看）C ． 3.5s t =时铜环将受到大小为34.810N -⨯、沿斜面向下的安培力D ．1~3s 内铜环受到的摩擦力先逐渐增大后逐渐减小2、2019年1月3日，“嫦娥四号”探测器成功实现在月球背面软着陆。

探测器在距离月球表面附近高为h 处处于悬停状态，之后关闭推进器，经过时间t 自由下落到达月球表面。

已知月球半径为R ，探测器质量为m ，万有引力常量为G ，不计月球自转。

下列说法正确的是（ ）A ．下落过程探测器内部的物体处于超重状态B ．“嫦娥四号”探测器落到月球表面时的动能为222mh tC ．月球的平均密度为232h RGt π D ．“嫦娥四号”22Rh t 3、如图所示，两个完全相同的小球A 、B ，在同一高度处以相同大小的初速度v 分别水平抛出和竖直向上抛出，下列说法正确的是（）A．两小球落地时的速度相同B．两小球落地时，重力的瞬时功率相同C．从开始运动至落地，重力对两小球做功相同D．从开始运动至落地，重力对两小球做功的平均功率相同4、如图所示，固定在竖直平面内的大圆环的半径为R。

进阶练13 词汇易错易混点辨析50题（原卷版）一、单项选择1．France’s president, Emmanuel Macron, won the 2022 run off election (选举) at last. He will ________ many challenges in his next term.A．take up B．take on C．take off D．take out2．A colorful balcony decorated with fresh vegetables and fruits may be ________ a common sight this year. A．turning into B．breaking into C．falling into D．looking into3．Mom always tells me that I can’t ________ today’s work till tomorrow.A．put off B．put out C．put up D．put away4．The lunar exploration program of our country is ________ 3 parts, including orbiting, landing and sample returning.A．turned into B．broken into C．divided into D．got into5．—Why are you taking the desks away?—Because they ________ too much room.A．stand up B．take up C．pick up D．listen to6．We are sorry to tell you that the plane won’t be able to ________ on time.A．take off B．get off C．turn off D．cut off7．— Hey, Jack! Do you know the meaning of “yyds”?— Sure. It’s an online slang word which ________ “deep admiration for someone”.A．cares for B．looks for C．stands for D．pushes for8．Scientists all over the world are ________ new medicine to fight COVID-19.A．trying on B．trying out C．taking up D．looking up9．— Could you please _________ some ideas for dealing with students’ stress?— Yes, less homework and more outdoor activities may be good ways.A．cut out B．come up with C．care for D．catch up with10．— Do you plan to have a driving tour on the coming May Day?— I’m afraid there is a lot of traffic, so I’d rather ________ the train than ________ a car.A．takes; to drive B．take; drive C．taking; driving D．to take; to drive11．A lot of man-made satellites have been ________ into space so far.A．sent away B．sent off C．sent for D．sent up12．The fire was completely ________ shortly afterwards with the help of the firemen.A．cut down B．putout C．given out D．put away13．The road conditions there ________ to be very good, which was better than we had expected.A．turned out B．worked out C．picked out D．made out14．Please remember ________ tomorrow morning.A．to wake up me B．waking up me C．to wake me up D．waking me up15．After being punished by his mother, the boy sat ________ without a word.A．in danger B．in person C．in silence D．in trouble16．Perhaps we will live on the food ________ the form of pills in the future.A．on B．in C．at D．by17．—________ the way, do you think this job has become easier than it used to be?—To be honest, it has turned out to be more difficult ________ some ways.A．In; on B．By; on C．By; in D．In; by18．The book you want is sold out _________. You can come to our bookstore next week.A．in time B．at all C．for sure D．at present19．Eddie can’t get ________ his food ________ his helmet.A．to; because B．/; because C．to; because of D．/; for20．Maybe in the future, people will be able to travel ________ and live on other planets.A．in space B．in a space C．in the space D．in spaces21．________, what he said in the meeting was true except that a few numbers were still not proved.A．In general B．In all C．In this way D．As a result22．He began taking his ________ lessons________ the age of 15.A．flight; at B．flying; at C．fly; on D．flight; in23．The visitors were stopped from going travelling ________ heavy snow.A．because B．because of C．as D．for24．Don’t be so sad. It isn’t your fault _________.A．in all B．first of all C．above all D．after all25．The old scientist is strict ________ himself and strict ________ his work.A．in; with B．with; in C．in; in D．with; with26．Lucy is ________ sleepy now, because she had ________ sleep last night.A．a bit; little B．a little; a little C．a bit of; little D．a bit of; a little bit 27．Director Huang has made ________ TV plays and films.A．the number of B．number of C．large numbersD．a number of28．The flat is ________ expensive. The Greens don’t have ________ money to afford it.A．too much; too much B．much too; too muchC．much too; too many D．too much; too many29．The basket was ________ vegetables and the bottle was ________ orange juice.A．full with; fill with B．filled of; full into C．full of; filled with D．fill with; full of30．My robot often goes wrong and causes ________ trouble.A．too much B．much too C．too many D．many too31．Many animals ________ the ability to swim, but humans must practice how to swim.A．part with B．are good with C．are born with D．are known as32．—China is ________ the one that it was 73 years ago.—Of course. Our country is developing so rapidly that it has become a focus（焦点）of the whole world. A．interested in B．famous for C．different from D．similar to33．Luke’s mother will be ________ him if he wins the reading competition.A．bored with B．proud of C．strict with D．worried about34．The long journey by air was boring ________ uncomfortable. Many students felt sick all the way.A．so good as B．as good as C．so well as D．as well as35．I know he hasn’t finished yet. ________, he is busy. I can understand.A．After all B．Above all C．First of all D．In all36．He learnt the rules of the game ________.A．one by one B．step by step C．side by side D．shoulder to shoulder 37．These days, many people spend plenty of time playing with the mobile phones. That’s ________ bad for the health.A．too much B．much too C．too many D．many too38．We will do better in English with the help of Mr. Lee. ________, we work harder than before.A．After all B．Best of all C．As a result D．First of all39．The medical team ____ ten doctors.A．makes up B．makes up of C．is made up D．is made up of40．— The words on the blackboard are _______ for me to see.— Yes. I think so. You can take a seat next to the blackboard.A．too large B．large enough C．too tiny D．tiny enough41．When I think back to those days, I regret__________ to my mother.A．to talk back B．talking back C．talked back D．talk back 42．Have you ________ Marie Curie who is regarded as one of the greatest persons in the world? A．heard B．heard from C．heard of D．listened to 43．He has fallen asleep after taking the medicine because his head ________. Don’t ________. A．hurt; wake up him B．hurts; wake him upC．is hurted; wake him up D．hurts; wake up him44．—Which country would you like to ________ after you visit Singapore?—Thailand.A．arrive B．get C．leave for D．arrive at 45．The ugly table ________ too much room of the kitchen.A．takes up B．takes off C．makes up D．makes up of 46．—Smoking is bad for your health.—You’re right. I decide to ________.A．take it down B．give up it C．turn it off D．give it up 47．Susan ________ for Shanghai to attend an international meeting yesterday.A．put off B．fell off C．set off D．kept off48．The smile on my father’s face showed that he ________ me.A．pleased with B．agreed with C．angry with D．is happy with 49．China promises to _______ Paris Agreement on climate change.A．stick into B．stick ontoC．stick to D．stick in50．—When did the singer Cyndi Wang become famous?—She first _________ in the entertainment industry with a lead role in Westside Story(2003). A．broke out B．broke down C．broke into D．broke away进阶练13 词汇易错易混点辨析50题（解析版）一、单项选择1．France’s president, Emmanuel Macron, won the 2022 run off election (选举) at last. He will ________ many challenges in his next term.A．take up B．take on C．take off D．take out【答案】B【详解】句意：法国总统埃马纽埃尔·马克龙最终赢得了2022年的第二轮大选。

【一轮复习讲义】2024年高考数学高频考点题型归纳与方法总结（新高考通用）第53讲事件的独立性、条件概率和全概率公式（精讲）题型目录一览①事件的相互独立性②条件概率③全概率公式④贝叶斯公式一、条件概率1.定义：一般地，设A ，B 为两个事件，且()0P A >，称()()()|P AB P B A P A =为在事件A 发生的条件下，事件B 发生的条件概率．注：（1）条件概率|()P B A 中“|”后面就是条件；（2）若()0P A =，表示条件A 不可能发生，此时用条件概率公式计算|()P B A 就没有意义了，所以条件概率计算必须在()0P A >的情况下进行．2.性质（1）条件概率具有概率的性质，任何事件的条件概率都在0和1之间，即1|0()P B A ≤≤．（2）必然事件的条件概率为1，不可能事件的条件概率为0．（3）如果B 与C 互斥，则(||()(|))P B C A P B A P C A =+ ．注：已知A 发生，在此条件下B 发生，相当于AB 发生，要求|()P B A ，相当于把A 看作新的基本事件空间计算AB 发生的概率，即()()()()()()()()|()n AB n AB n P AB P B A n A n A P A n Ω===Ω．二、相互独立与条件概率的关系1.相互独立事件的概念及性质（1）相互独立事件的概念对于两个事件A ，B ，如果)(|)(P B A P B =，则意味着事件A 的发生不影响事件B 发生的概率．设()0P A >，一、知识点梳理根据条件概率的计算公式，()()()()|P AB P B P B A P A ==，从而()()()P AB P A P B =．由此我们可得：设A ，B 为两个事件，若()()()P AB P A P B =，则称事件A 与事件B 相互独立．（2）概率的乘法公式由条件概率的定义，对于任意两个事件A 与B ，若()0P A >，则()|)()(P AB P A P B A =．我们称上式为概率的乘法公式．（3）相互独立事件的性质如果事件A ，B 互相独立，那么A 与B ，A 与B ，A 与B 也都相互独立．（4）两个事件的相互独立性的推广两个事件的相互独立性可以推广到(2)n n n >∈*N ，个事件的相互独立性，即若事件1A ，2A ，…，n A 相互独立，则这n 个事件同时发生的概率1212()()()()n n P A A A P A A P A = ．2.事件的独立性（1）事件A 与B 相互独立的充要条件是()()()P AB P A P B =⋅．（2）当()0P B >时，A 与B 独立的充要条件是()()|P A B P A =．（3）如果()0P A >，A 与B 独立，则()()()()()()()|P AB P A P B P B A P B P A P A ⋅===成立．三、全概率公式1.全概率公式（1）|()()()()(|)P B P A P B A P A P B A =+；（2）定理1若样本空间Ω中的事件1A ，2A ，…，n A 满足：①任意两个事件均互斥，即i j A A =∅，12i j n = ，，，，，i j ≠；②12n A A A +++=Ω ；③()0i P A >，12i n = ，，，．则对Ω中的任意事件B ，都有12n B BA BA BA =+++ ，且11()()()()|nni i i i i P B P BA P A P B A ====∑∑．2.贝叶斯公式（1）一般地，当0()1P A <<且()0P B >时，有()()()()()()()()()()||||P A P B A P A P B A P A B P B P A P B A P A P B A ==+（2）定理2若样本空间Ω中的事件12n A A A ，，，满足：①任意两个事件均互斥，即i j A A =∅，12i j n = ，，，，，i j ≠；②12n A A A +++=Ω ；③()01i P A <<，12i n = ，，，．则对Ω中的任意概率非零的事件B ，都有12n B BA BA BA =+++ ，且1()()()()()()()()|||j j j j j niii P A P B A P A P B A P A B P B P A P B A ===∑注：贝叶斯公式体现了|()P A B ，()P A ，()P B ，|()P B A ，|()P B A ，()P AB 之间的关系，即()()()|P AB P A B P B =，()()()()()||P AB P A B P B P B A P A ==，|()()()()(|)P B P A P B A P A P B A =+.题型一事件的相互独立性1.判断事件是否相互独立的方法（1）定义法：事件（2）由事件本身的性质直接判定两个事件发生是否相互影响．二、题型分类精讲A．332B．【答案】D【题型训练】一、单选题，从乙口袋内摸出一个白球的概率是6【分析】根据题意，求得事件甲、乙、丙、丁的概率，结合相互独立事件的概念及判定方法，逐项判定，不相互独立，所以本序号说法不正确；二、多选题不能同时发生，但能同时不发生，所以不是对立事件，所以三、填空题四、解答题．一题多解是由多种途径获得同一数学问题的最终结论，一题多解不但达到了解题的目标要求，而且让情．某市举行了一场射击表演赛，规定如下：表演赛由甲、乙两位选手进行，每次只能有一位选手射击，题型二条件概率1.判断所求概率为条件概率的主要依据是题目中的知事件的发生影响了所求事件的概率，也认为是条件概率问题．运用条件概率的关键是求出【题型训练】一、单选题1．核酸检测是目前确认新型冠状病毒感染最可靠的依据．经大量病例调查发现，试剂盒的质量、抽取标本的部位和取得的标本数量，对检测结果的准确性有一定影响．已知国外某地新冠病毒感染率为d二、多选题、表示事件错误；三、填空题个红球，从中任意取出一球，已知它不是白题型三全概率公式全概率公式复杂的概率计算分解为一些较为容易的情况分别进行考虑．【题型训练】一、单选题小时的学生中任意调查一名学生，则（二、多选题，所以表示买到的口罩分别为甲品牌、乙品牌、其他品牌，，对；三、填空题记任选一人去桂林旅游的事件为B ，则123()0.4,()()0.3P A P A P A ===，123(|)0.1,(|)0.2,(|)0.15P B A P B A P B A ===,由全概率公式得112233()(|)()(|)()(5|)30.15014P P A P B A P A P B A P A P B B A =⨯⨯++==++⨯.故答案为：0.145四、解答题附：()2P K k≥0.150.100.05k 2.072 2.706 3.841 (2)将甲乙生产的产品各自进行包装，每来自甲生产的概率为3，来自乙生产的概率为(1)假设四人实力旗鼓相当，即各比赛每人的胜率均为①A获得季军的概率；②D成为亚军的概率；，其余三人实力旗鼓相当，求题型四贝叶斯公式1.利用贝叶斯公式求概率的步骤第一步：利用全概率公式计算【题型训练】一、单选题。