1、高考模拟考试数学理2019-2020年高考模拟考试（数学理）本试卷共4页，21题，满分150分，测试用时120分钟参考公式：锥体的体积公式，其中是锥体的底面积，是锥体的高一、选择题：本大题共8小题，每小题5分，满分40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已知集合，若，则A B C D若四边形满足，则该四边形一定是A直角梯形 B菱形 C矩形 D正方形某社区现有个住户，其中中等收入家庭200户、低收入家庭160户，其他为高收入家庭。在建设幸福广东的某次分层抽样调查中，高收入家庭被抽取了6户，则该社区本次被抽取的总户数为A B C D直线，都是函数的对称轴，且函数在区间上单调递减，则
2、A， B，C， D，一个底部水平放置的几何体，下半部分是圆柱，则这个几何体的体积A BC D、，“、成等差数列”是“、成等比数列”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在平面直角坐标系中，与所表示的曲线如图2所示，则常数、之间的关系可能是A且 B且C且 DA或C已知平面区域，（是常数），记为事件，则使的常数有A个 B个 C个 D个以上二、填空题：本大题共7小题，考生作答6小题，每小题5分，满分30分 (一)必做题（913题）已知，某次全市xx0人参加的考试，数学成绩大致服从正态分布，则本次考试120分以上的学生约有 人图3是讨论三角函数某个性质的程序框图，若输入
3、，则输出 设抛物线：的准线与对称轴相交于点，过点作抛物线的切线，切线方程是 在平面直角坐标系中，四边形在映射：作用下的象集为四边形，若的面积，则的面积 以下命题中，真命题的序号是 （请填写所有真命题的序号）回归方程表示变量增加一个单位时，平均增加个单位已知平面、和直线，若且，则“若，则”的逆否命题是“若或，则”若函数与函数的图象关于直线对称，若，则(二)选做题（14、15题，考生只能从中选做一题）（坐标系与参数方程选做题）若直线（为参数）与圆（，为参数，为常数且）相切，则 （几何证明选讲选做题）如图4，是圆外一点，直线与圆相交于、，、是圆的切线，切点为、。若，则四边形的面积 三、解答题：本大题
4、共6小题，满分80分解答须写出文字说明、证明过程和演算步骤（本小题满分14分）如图5，一架飞机原计划从空中处直飞相距的空中处，为避开直飞途中的雷雨云层，飞机在处沿与原飞行方向成角的方向飞行，在中途处转向与原方向线成角的方向直飞到达处已知在飞行路径中，求；求新的飞行路程比原路程多多少（参考数据：，）（本小题满分12分）某校举行环保知识大奖赛，比赛分初赛和决赛两部分，初赛采用选手选一题答一题的方式进行，每位选手最多有次选题答题的机会，选手累计答对题或答错题即终止其初赛的比赛：答对题者直接进入决赛，答错题者则被淘汰已知选手甲答对每个问题的概率相同，并且相互之间没有影响，答题连续两次答错的概率为求选手
5、甲可进入决赛的概率；设选手甲在初赛中答题的个数为，试求的分布列，并求的数学期望（本小题满分14分）如图6，是棱长为的正方体，、分别是棱、上的动点，且求证：；当、共面时，求：到直线的距离； 面与面所成二面角的余弦值（本小题满分14分）已知圆锥曲线上任意一点到两定点、的距离之和为常数，曲线的离心率求圆锥曲线的方程；设经过点的任意一条直线与圆锥曲线相交于、，试证明在轴上存在一个定点，使的值是常数（本小题满分12分）已知数列，求数列的通项；设数列的前项和为，试用数学归纳法证明（本小题满分14分）设是定义在区间（）上的函数，若对、，都有，则称是区间上的平缓函数试证明对，都不是区间上的平缓函数；若是定义在
6、实数集上的、周期为的平缓函数，试证明对、，理科数学评分参考一、选择题 CBBA DDAC二、填空题 （对一个3分，全对5分） （正确选项一个3分，全对5分；错误选项一个扣3分，2个扣5分，扣完为止） （答给3分，其他0分） 三、解答题，是锐角，所以1分，2分，4分，5分7分，由正弦定理9分，得11分，13分，新的飞行路程比原路程多14分设选手甲任答一题，正确的概率为，依题意1分，2分，甲选答3道题目后进入决赛的概率为3分，甲选答4道、5道题目后进入决赛的概率分别为、5分，所以，选手甲可进入决赛的概率6分可取3，4，57分，依题意8分，9分，10分，（或10分）所以，的分布列为： 11分12分以
7、为原点，、所在直线分别为轴、轴、轴建立空间直角坐标系1分，则、，设，则，2分，从而、3分，直接计算知，所以5分当、共面时，因为底面，所以6分，所以，从而、分别是、的中点7分，设到直线的距离为，在中，解得9分由得，、 ，设平面的一个法向量为，依题意10分，所以11分，同理平面的一个法向量为13分，由图知，面与面所成二面角的余弦值（即）14分依题意，设曲线的方程为（）1分，2分，3分，所求方程为4分当直线不与轴垂直时，设其方程为5分，由6分，得7分，从而，8分，设，则10分，当，时11分，对，12分；当轴时，直线的方程为，13分，对，即存在轴上的点，使的值为常数14分（方法一）由得，2分，所以3分
8、，4分，5分（方法二）由得，1分，3分，累加得5分时，左边，右边，左边=右边，命题成立7分；设时，命题成立，即8分，则9分，从而时，命题成立11分综上所述，数列的前项和12分21.、，1分。若，则当、时，2分，从而3分；若，则当、时，4分，从而，所以对任意常数，都不是区间上的平缓函数5分若、，当时，6分；当时，不妨设，根据的周期性，7分，9分，11分，所以对、，都有12分对、，根据的周期性（且），存在、，使、，从而14分2019-2020年高考模拟试卷（附答案）I. ListeningPart A Short Conversations1.A. She is happy B. She is j
9、oking. C. She is certain. D. She is busy2.A. She agrees that they met before.B. She met Professor Wang at the mans office.C. She denies the fact that they met before.D. She wants to meet the man at Professor Wangs office.3.A. She is sorry that the man asked her. B. She is going to ask a new number.C
10、. She lost her phone number.D. she doesnt have a phone number at this time.4.A. It was very cold just before Christmas.B. It wasnt very cold, and it snowed a little in December.C. There wasnt much snow, but the weather was bad.D. The temperature dropped below freezing after Christmas.5. A. Ask direc
11、tions B. Walk to the shopping center. C. Take a taxi. D. Wait for the bus.6. A. Its band new. B. She just repaired it. C. someone painted it. D. Its just been sold.7. A. The graduation list has an error on it. B. The man had already graduated. C. The mans name is the same as that of another student.
12、 D. The graduation will not be until next spring.8. A. Go on a diet. B. Talk to her sister. C. Look at a map. D. Try to win first prize.9. A. The weather was colder last year. B. The weather was rainier last year. C. The weather was warmer last year. D. The weather was drier last year.10. A. Tomorro
13、w morning. B. At 10:00 C. At 11:00 D. At 11:30Part B PassagesQuestions 11 through 13 are based on the following passage.11. A. It gets its water from the ocean. B. It is a little saltier than the ocean. C. It is far from the ocean. D. It is larger than any state.12. A. The lake is too deep. B. The s
14、peaker was too heavy. C. The water held up ;the speaker. D. The speakers eyes hurt.13. A Interesting. B. Painful C. Useful. D. Surprising.Questions 14 through 16 are based on the following passage.14. A. Her mother doesnt love her as much as her grandfather did. B. Her mother was the subject of talk
15、s with her grandfather. C. Her mother will misunderstand her problems. D. She missed her grandfather.15. A. Co-workers cannot be your close friends. B. People will be pleased if you call them at 2:00 AM C. You cant discuss your problems with a distant family. D. The one you can call at 2:00 AM is so
16、meone close to you in spirit.16. A. Parents should understand their kids. B. The earth is an inhabited garden if you have close friends. C. There are many ways to make friends. D. There is a difference between a lonely desert and an inhabited garden.Part C Longer Conversations.Questions 17 through 2
17、0 are based on the following conversation.plete the following table using NO MORE THAN THREE WORDS for each question.Places mentioned in the dialogueProblems for studyingHer dormCant concentrate because room-mate has _(17)_._(18)_Some club is _(19)_. The city library Has to walk _(20)_.Questions 21
18、through 24 are based on the following conversation.plete the following table using NO MORE THAN THREE WORDS for each question.Lucys original planTo go to _(21)_. Her final decisionTo go to _(22)_.WhyThe original plan wasnt _(23)_. What Lucy and Richard decide to do Keep _(24)_. .Grammar and Grammar（
19、20%）Directions: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best pletes the sentence.25. The cakes are delicious. Hed like to have _third one because_ second one is rather too small.A. a a B. Thethe C. a the D. The a 26. When _, the
20、 museum will be open to the public next year.A. pleted B. pletingC. being pleted D. to be pleted27. Rain forests _ and burned at such a speed that they will disappear from the earth in the near future.A. cut B. are cut C. are being cut D. had been cut28. _does something good will be praised by the t
21、eacher. A. Anyone B. No matter who C. Those who D. Whoever29. _ fashion differs from country to country may reflect the cultural differences from one aspect.A. What B. That C. This D. Which30. The famous scientist grew up _ he was born and in 1930 he came to Shanghai.A. when B. whenever C. where D.
22、wherever31. Is this the reason _ at the meeting for his carelessness in his work? A. he explained B. what he explainedC. how he explained D. why he explained32. With many difficult problems _, the president is having a hard time.A. settled B. settling C. to settle D. being settled33. When you answer
23、 questions in a job interview, please remember the golden rule: Always give the monkey exactly _ he wants.A. what B. which C. when D. that34. Americans eat _ vegetables per person today as they did in 1910.A. more than twice B. as twice as manyC. twice as many as D. more than twice as many35. Not on
24、ly_ interested in football but _ beginning to show an interest in it.A. the teacher himself is all his students areB. the teacher himself is are all his studentsC. is the teacher himself are all his studentsD. is the teacher himself all the students are 36. He _ a restless person. He kept moving fro
25、m country to country. A. must be B. must have been C. should be D. could have been37. Im looking for a present for my mothers birthday, _ she can use and at a reasonable price. A. that B. one C. what D. which38. His spoken English has e to the point, _ many people think hes a native speaker. A. that
26、 B. which C. where D. when39. In China more and more people are _ interested in after-work activities _ from rugby to rowing. A. growingranging B. beingranged C. showingranging D. takingranged40. Please follow your supervisors instructions, or youll _him.A. discourage B. offend C. disturb D. bother4
27、1. I saw Bob play the piano at Johns party and on that _he was simply brilliant.A. scene B. circumstance C. occasion D. situation42. Although he has taken a lot of medicine, his health _poor.A. proves B. remains C. maintains D. continues 43. Its _ practice in western countries that people fry eggs i
28、n animal fat. A. ordinary B. mon C. normal D. usual44. The beauty of Beijing, which fascinates all the visitors, _the style of its ancientbuildings.A. consists in B. results in C. rests on D. depends on III. Cloze （20%）Directions: For each blank in the following passages there are four words or phra
29、ses marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.(A)It is very important to have healthy teeth. Good teeth help us to chew our food. They also help us to look nice.How does a tooth go bad? The 45 begins in a little crack in the enamel (珐琅) covering of the tooth. This happens after germs and bits of food have 46 there. Then
