2016年山东药品食品职业学院单招数学模拟试题(附答案解析)
山东高职单招数学模拟题
2016年山东高职单招数学模拟题（1）第1题：设集合M={－1,0,1}，N={－1,1}，则（）A.M⊆ NB.M⊂NC.M＝ND.N⊂M第3题：函数y=sinx的最大值是（）A．-1 B.0 C.1 D.2第4题：设a＞0，且|a|＜b，则下列命题正确的是（）A.a＋b＜0B.b－a＞0C.a－b＞0D.|b|＜a第5题：一个四面体有棱（）条A．5 B.6 C.8 D.12第6题：“|x-1|<2成立”是“x(x-3)<0成立”的( )A.充分而不必要条件B.必要而不充分条件C.充分必要条件D.既不充分也不必要条件：第9题：在等差数列{an}中，已知a5＋a7＝18，则a3＋a9＝()A．14 B．16 C．18 D．20第10题：将5封信投入3个邮筒，不同的投法共有( ) A.53种B.35种C.3种D.15种第11题：(1+2x)5的展开式中x2的系数是（）A.80B.40C.20D.10第12题：甲乙两人进行一次射击，甲击中目标的概率为0.7，乙击中的概率为0.2，那么甲乙两人都没击中的概率为( )A.0.24B.0.56C.0.06D.0.86第13题：函数y=x2在x=2处的导数是( ) A．1 B.2 C.3 D.4第15题：如果双曲线的焦距为6，两条准线间的距离为4，那么双曲线的离心率为（）第16题：已知集合，M={2,3,4}，N={2,4,6,8},则M∩N＝（）。
A.{2}B..{2,4}C.{2,3,4,6,8}D.{3,6,8}第17题：设原命题“若p则q ”真而逆命题假，则p是q的（）A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分又不必要条件第18题：不等式x＜x²的解集为（）A.{x|x＞1}B.{x|x＜0}C.{x|0＜x＜1}D.{x|x＜0或x＞1}第19题：数列3,a，9为等差数列，则等差中项a等于（）A．-3 B. 3 C.-6 D.6[第20题：函数y=3x+2的导数是（）A．y=3x B.y=2 C.y=3 D.3[第21题：从数字1、2、3中任取两个数字组成无重复数字的两位数的个数是（）A.2个B. 4个C. 6个D. 8个第24题：在同一直角坐标系中，函数y=x+a 与函数y=ax的图像可能是（）第25题：函数y=loga(3x−2)+2的图像必过定点( )语文第1题：在过去的四分之一世纪里，这种力量不仅增大到了令人不安的程度，而且其性质亦发生了变化。
山东单招数学模拟试卷(含答案)
山东单招数学模拟试卷一、判断题（请把“√"或“×"填写在题目前的括号内。
每小题3分，共36分。
）（ ）1。
已知集合1,2,3,4A,2,4,6,8B ,则2,4A B .（ )2。
两个偶函数的和是偶函数，两个奇函数的积也是偶函数。
（ ）3.与等差数列类似，等比数列的各项可以是任意的一个实数。
（ ）4.两个向量的数量积是一个实数,向量的加、减、数乘的结果是向量. （ ）5.如果0cos >θ，0tan <θ，则一定是第二象限的角。
（ ）6。
相等的角终边一定相同，终边相同的角也一定相等。
（ ）7。
第一象限的角不见得都是锐角，第二象限的角也不见得都是钝角. （ )8。
平面内到点1(0,4)F 与2(0,4)F 距离之差等于12的点的轨迹是双曲线. （ ）9。
直线的倾斜角越大，其斜率就越大.椭圆的离心率越大则椭圆越扁. （ )10。
如果两条直线与相互垂直，则它们的斜率之积一定等于。
( ）11。
平面外的一条直线与平面内的无数条直线垂直也不能完全断定平面外的这条直线垂直平面.( ）12. 在空间中任意一个三角形和四边形都可以确定一个平面。
二、单项选择题(请把正确答案的符号填写在括号内.每小题4分，共64分）1.已知集合{}31≤<-=x x A ,57Ux x，则UC （ )、{}7315<<-≤<-x x x 或； 、{}7315<<-<<-x x x 或; 、{}7315≤≤-≤<-x x x 或； 、{}7315<≤-<<-x x x 或。
2.若不等式20axbx c 的解集为(1,3)，则（ ）、0a； 、0a ； 、1a ； 、3a 。
3。
已知函数⎩⎨⎧-+=x x y 515221<≤<≤-x x ,则函数在定义域范围内的最大值为（ ）、； 、； 、; 、.4.计算25lg 50lg 2lg 2lg 2+⋅+的值为（ )、1； 、2； 、3； 、4.5。
山东单招数学试题及答案
山东单招数学试题及答案一、选择题（每题2分，共10分）1. 下列哪个数是无理数？A. 0.33333B. πC. √2D. √4答案：B、C2. 已知函数f(x) = 2x - 1，求f(2)的值。
A. 3B. 4C. 5D. 6答案：A3. 如果一个等差数列的首项是3，公差是2，那么第10项的值是多少？A. 23B. 27C. 29D. 31答案：A4. 一个圆的半径是5，它的面积是多少？A. 25πB. 50πC. 75πD. 100π答案：B5. 下列哪个是二次方程的解？A. x = 2B. x = -2C. x = 3D. x = 1/2答案：A、B二、填空题（每题2分，共10分）6. 一个直角三角形的两条直角边分别为3和4，斜边的长度是________。
答案：57. 一个数的平方根是4，这个数是________。
答案：168. 一个数的立方根是2，这个数是________。
答案：89. 一个圆的周长是2πr，其中r是圆的半径，如果周长为12π，那么半径r是________。
答案：610. 一个等比数列的首项是2，公比是3，那么第5项的值是________。
答案：162三、计算题（每题5分，共15分）11. 计算下列表达式的值：(2 + 3) × (5 - 2)答案：11 × 3 = 3312. 解一元一次方程：3x - 7 = 5x + 1答案：3x - 5x = 1 + 7-2x = 8x = -413. 已知一个直角三角形的两个角分别为30°和60°，斜边长度为2，求另外两边的长度。
答案：根据30°-60°-90°三角形的性质，较短边为斜边的一半，即1。
较长边为较短边的√3倍，即√3。
四、解答题（每题10分，共20分）14. 证明勾股定理。
答案：设直角三角形的直角边分别为a和b，斜边为c。
根据面积的两种表示方法，有：1/2 * a * b = 1/2 * c * h（其中h为斜边上的高）ah = ba^2 + b^2 = c^215. 解不等式组：\[\begin{cases}x + 2 > 4 \\3x - 1 < 8\end{cases}\]答案：由第一个不等式得 x > 2，由第二个不等式得 x < 3。
单招数学模拟试题及答案
单招数学模拟试题及答案一、选择题（本题共10小题，每小题3分，共30分）1. 下列哪个数是最小的正整数？A. 0B. 1C. 2D. 32. 若函数f(x) = x^2 - 4x + 3，求f(5)的值。
A. 8B. 18C. 28D. 383. 已知等差数列的首项a1=3，公差d=2，求第10项的值。
A. 23B. 25C. 27D. 294. 圆的半径为5，求圆的面积。
A. 25πB. 50πC. 75πD. 100π5. 已知三角形ABC，∠A=30°，∠B=45°，求∠C的度数。
A. 75°C. 105°D. 120°6. 一个长方体的长、宽、高分别为2米、3米和4米，求其体积。
A. 24立方米B. 26立方米C. 28立方米D. 30立方米7. 已知方程x^2 - 5x + 6 = 0，求x的值。
A. 2, 3B. 1, 6C. 3, 4D. 2, 48. 一个数的平方根是4，求这个数。
A. 16B. 8C. 12D. 209. 已知正弦函数sin(x) = 1/2，求x的值（x在第一象限）。
A. π/6B. π/4C. π/3D. 5π/610. 一个直角三角形的两条直角边分别为3和4，求斜边的长度。
A. 5B. 6D. 8二、填空题（本题共5小题，每小题4分，共20分）11. 若一个数的平方是25，那么这个数是________。
12. 一个圆的直径为10，那么这个圆的周长是________。
13. 已知三角形的面积是18平方米，高是6米，求底边的长度。
14. 一个等腰三角形的两个底角相等，如果其中一个底角是40°，那么顶角的度数是________。
15. 一个直角三角形的斜边长度是10，一个锐角是30°，求对边的长度。
三、解答题（本题共3小题，每小题10分，共30分）16. 解不等式：3x + 5 > 14 - 2x。
2016年山东药品食品职业学院单招英语模拟试题(含答案解析)
考单招——上高职单招网2016年山东药品食品职业学院单招英语模拟试题（含答案解析）单项选择（20分）16. He bought a knife and fork ________.A. to eat B. to eat with C. for eatingD. to eat by17. The little village which lies ___ the railway for 20 miles is ___the great man was born.A. off; whereB. at; whenC. to; howD. by; why18.The window which hasn’t been cleaned for at least 3 weeks requires ____.Who’d like to take the job?A. to cleanB. cleaningC. cleanedD. being cleaned19. Everyone present at the meeting agreed to stick to the ___ that everyone should be treatedfairly.A. purpose B. ambition C. principle D. level20. After the war, that country ___ their defense works in case of the next unexpectedattack.A. raised B. strengthened C. increased D. powered21. Great efforts have been ____to i mprove people’s living conditions in China in the past twoyears.A. got B. won C. made D. did22. When he came back with plenty of money, his father ____ three d ays before.A. had diedB. was deadC. diedD. had been dead23. The fire was finally ______ after the building had ______ for two hours.A. put off; caught fireB. put away; been on fireC. put out; caught fireD. put out; been on fire24. He did everything he could _______ the old man. A. to save B. saveC. saving D saved25.—Shall I give you a hand with this as you are so busy now?—Thankyou.__________A. Of course you canB. If you likeC. it’s up to youD.It couldn’t be better26. Everyone has periods in their lives _____ everything seems very hard.A. when B. where C. which D. that27. When he heard the news, he hurried home,______ the book ______ on the desk.A.leaving; lying openB.to leave; lying openC.left; lying openD.leaving; lying opened考单招——上高职单招网28. Who do you think he would _____ a letter of congratulation to our monitor?A. have writtenB. have to writeC. have writeD. have been writing29. Taiyuan, _____ in the centre of Shanxi province is a most beautiful city. A. located B. to locate C. locate D. locating30. I was told that there were about 50 foreign students _____Chinese in the school, most____were from Germany.A. study, of whomB. study, of themC. studying, of themD. studying, of whom31. Hurricane brought down a great number of houses, _____ thousands of people ho meless.A. to make B. making C. made D. having made32. We need clean air, but ___, air pollution is generally present, especially in cities.A. fortunately B. strangely C. sadly D. hopefully33. I feel greatly honoured _____ the chance to speak here. I’m feeling very excited.A. to giveB. to be givingC. to have been givenD. to have given34.___ two children attending college, the parents have to work really har dto make the ends meet. A. From B. For C. Of D. With35. — Sorry to have hurt you the other day. — _____, but don’t do it again.A. Forget itB. Don’t mention itC. Don’t worryD. With pleasure完型填空（20分）Perhaps the most interesting person I have ever met is an Italian professor of philosophy who teaches at the University of Pisa. 36 I last met this man eight years ago, I have not forgotten his 37 quali t ies. Firs t of all, I respected his 38 to teaching. Because his lectures were always well-prepared and clearly delivered, students crowded into his classroom. His followers liked thefact that he 39 what he taught Further more, he could be counted on to explain his ideas in a n 40 way, introducing such aids (辅助) to 41 as oil paintings, music, and guest lecture r s. Once he 42 sang a song in class in order to make a point clear. 43 , I admired the fact that h e would talk to students outside the classroom or talk with them 44 the telephone. Drinking coffee in the cafe, he would easily make friends with students. Sometimes he would 45 a student to a game of chess (国际象棋) 46 he would join student groups to discuss a variety of 47 : agriculture, diving and mathematics. Many young people visited him in his office for 48 on their studies; others came to his home for social evenings. Finally,考单招——上高职单招网I was 49 by his lively sense of humor. He believed that no lesson is a success50 , during it, the students and the professor 51 at least one loud 52 .Through his sense of humor, he made learning more 53 and more lasting, If it is 54 that life makes a wise man smile and a foolish man cry, 55 my friend isindeed a wise man.36. A. Although B. When C. Even if D. Now that 37. A. basic B. special C. common D. particular38. A. attention B. introduction C. relation D. Devotion39. A. insisted on B. talked about C. believed in D. agreed with40. A. imaginative B. ordinary C. opposite D. open41. A. listening B. understanding C. information D. discovery42. A. also B. nearly C. even D. only43. A. Later B. Secondly C. However D. Therefore44. A. with B. by C. from D. on45. A. invite B. leadC. preferD. show46. A. As a matter of fact B. Later on C. Other times D. In general47. A. questions B. subjectsC. mattersD. contents48. A. support B. explanation C. experience D. advice49. A. disturbed B. moved C. attracted D. defeated50. A. for B. until C. since D. unless 51. A. hear B. suggest C. shareD. demand52. A. laugh B. cry C. shout D. question53. A. helpful B. enjoyableC. practicalD. useful54. A. natural B. normalC. hopeful D. true55. A. so B. for C. then D. yetIV．阅读理解（30分）A One evening after dinner, Mr. and Mrs. Tisich called a family meeting. “We’ve had to make a difficult decision,” Mr. Tisich announced. “You see, your mother has been offered a post as co-director of a television station in Chicago. Unfortunately,the station is not here. After thinking long and hard a bout it, we’ve concluded thatthe right decision is to move to Chicago.”Marc looked shocked, while his sister Rachel breathlessly started asking when they’d be moving. “It’s surprising, but考单招——上高职单招网exciting!” she said. Marc simply said, “We can’t go—I can’t leave all my friends. I’d rather stay here and live with Tommy Lyon s!”The Tisichs hoped that by the time they moved in August, Marc would grow more accustomed to the idea of leaving. However, he showed no signs of accepting the news, refusing to pack his belongings.When the morning of the move arrived, Marc was nowhere to be found. His parents called Tommy Lyon s’ house, but Mrs. Lyons said she hadn’t seen Marc. Mrs. Tisich became increasingly concerned, while her husband felt angry with their son for behaving so irresponsibly.What they didn’t know was that Marc had started walking over to Tommy’s house, with a faint idea of hiding in Lyons’ attic(阁楼) for a few days. But something happened on the way as Marc walked past all the familiar landscape of the neighborhood: the fence that he and his mother painted, the tree that he and his sister used to climb, the park where he and his father often took evening walks together. How much would these mean without his family, who make them special in the first pla ce? Marc didn’t take the time to answer that question but instead hurried back to his house, wondering if there were any moving cartons(纸板箱)the right size to hold his record collection.56. The conflict in this story was caused by___________.A. Marc and R achel’s different tempersB. a quarrel between Tommy Lyons and MarcC. Marc’s disagreement with his parents about their moveD. Mr. and Mrs. Tisich’s remark of Marc’s irresponsibility57. Marc and Rachel’s reactions to the move were similar in the way t hat bothwere____________A. surprisedB. angry and upsetC. anxious for more detailsD. worried about packing考单招——上高职单招网58. The reason for Marc’s going home was that _________________.A. he did not want to be left behindB. he realized his family was essential to himC. he hoped to reach an agreement with his parentsD. he wished to be a more responsible person59. What would most likely happen next?A. Marc would bring his records over to the Lyons’s house.B. Mr. and Mrs. Tisich would call the police.C. Marc would join his family for house moving.D. Mr. and Mrs. Tisich would start searching for Marc.C Deserts are found where there is little rainfall or where rain for a whole year falls in only a few weeks' time. Ten inches of rain may be enough for many plants to survive if the rain is spread throughout the year, If it falls, within one or two months and the rest of the year is dry, those plants may die and a desert may form.Sand begins as tiny pieces of rock that get smaller and smaller as wind and weather wear them down. Sand dunes are formed as winds move the sand across the desert. Bit by bit, the dunes grow over the years, always moving with the winds and changing the shape. Most of them are only a few feet tall, but they can grow to be several hundred feet high.There is, however, much more to a desert than sand. In the deserts of the southwestern United States, cliffs and deep valleys were formed from thick mud that once lay beneath a sea more than millions of years ago. Over the centuries, the water dried up. Wind, sand, rain, heat and cold all wore away at the remaining rocks. The faces of the desert mountains are always changing—very, very slowly—as these forces of nature continue to work on the rock.Most deserts have a surprising variety of life. There are plants, animals and insects that:have adapted to life in the desert. During the heat of the day, a visitor may see very few signs of living things, but as the air begins to cool in the evening,考单招——上高职单招网the desert comes to life. As the sun begins to rise again in the sky, the desert once again becomes quiet and lonely.60. Many plants may survive in deserts when___________. A. the rain is spread out in a yearB. the rain falls only in a few weeksC. there is little rain in a yearD. it is dry all the year round61. Sand dunes are formed when___________. A. sand piles up graduallyB. there is plenty of rain in a yearC. the sea has dried up over the yearsD. pieces of rock get smaller62. The underlined sentence in the third paragraph probably means that in a desert there is____________.A. too much sandB. more sand than beforeC. nothing except sandD. something else besides sand63 It can be learned from the text that in a desert____________.A. there is no rainfall throughout the yearB. life exists in rough conditionsC. all sand dunes are a few feet highD. rocks are worn away only by wind and heatD When we walk through the city, we all experience a kind of information overload but we pay attention only to those that are important to us. We don’t stop, we keep our faces expressionless and eyes straight ahead, and in doing so, we are not just protecting ourselves but are avoiding overloading other people as well.We make use of stereotypes (刻板的模式) as convenient ways to make quick judgements about situations and people around us. They may not always be accurate, and they can often be dangerously wrong, but they are used regularly.The problem with the stereotypes is that they restrict experience.By using limited clues to provide us with a rapid opinion of other people考单招——上高职单招网or places we may choose to limit our communication. We may decide not to go to certain places because we believe they will not offer something we enjoy.In the city, styles of dress are particularly important with regardto self-presentation. Different groups often use clearly identifiablestyles of clothes so that they can be easily recognized. It is becoming increasingly common for brand names to be placed on the outside of clothes, and this labeling makes it easy to send out information about fashion and price instantly, and lets others tell at a distance whether an individual has similar tastes and is a suitable person to associate with.In England, where social grouping or class continues to make social distinctions（区分）, clothes, hairstyles, people’s pronunciation and the manner of speaking are all clues to our social group. Class distinctions tend tobe relatively fixed, although in the city where greater variety is permitted, they are more likely to be secondary determining factors of friendship and association.67. People walking in cities ignore the surroundings because __________.A.they do not wish to talk to other people B。
单招试题及答案数学山东
单招试题及答案数学山东一、选择题（每题3分，共30分）1. 下列哪个选项是无理数？A. 2.718B. 根号3C. πD. 0.8080080008…（最后一位无限循环）答案：C2. 如果函数f(x) = x^2 + 2x + 1在区间[-3, 1]上是减函数，那么f(x)在该区间的最大值是：A. 0B. 4C. 6D. 10答案：A3. 已知数列1, 3, 5, 7, ... 的第10项是：A. 19B. 21C. 23D. 25答案：B4. 不等式|x+2| + |x-3| < 5的解集是：A. (-2, 3)B. (-∞, -2) ∪ (3, +∞)C. (-7, 8)D. (-∞, -7) ∪ (8, +∞)答案：C5. 已知三角形ABC中，∠BAC = 90°，AB = 3cm，AC = 4cm，那么BC 的长是：A. 5cmB. 6cmC. 7cmD. 8cm答案：A6. 函数y = sin(x)在区间(0, π)上是：A. 增函数B. 减函数C. 先增后减D. 先减后增答案：C7. 已知集合A = {1, 2, 3}，B = {2, 3, 4}，则A∪B等于：A. {1, 2, 3}B. {1, 2, 3, 4}C. {2, 3}D. {1, 4}答案：B8. 以下哪个选项是复数：A. iB. 5C. 根号(-1)D. π答案：A9. 已知等差数列的前三项和为12，且第三项是第一项的3倍，则该数列的首项a1和公差d是：A. a1 = 2, d = 2B. a1 = 3, d = 1C. a1 = 4, d = 2D. a1 = 1, d = 3答案：B10. 以下哪个选项是指数函数：A. y = 2^xB. y = log2(x)C. y = x^2D. y = 1/x答案：A二、填空题（每题4分，共20分）11. 已知f(x) = 2x - 1，若f(x) = 3，则x = ____。
2016年山东商务职业学院单招数学模拟试题(附答案解析)
考单招——上高职单招网2016年山东商务职业学院单招数学模拟试题（附答案解析）一、选择题：本大题共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、A＝{x||x－1|≥1，x∈R}，B＝{x|log2x＞1，x∈R}，则“x∈A”是“x∈B”的()A．充分非必要条件B．必要非充分条件C．充分必要条件D．既非充分也非必要条件1．函数是偶函数，则函数的对称轴是（）A． B． C． D．2．已知，则函数的图象不经过（）A．第一象限 B．第二象限 C．第三象限 D．第四象限3．函数的零点必定位于区间（）A．(1,2) B．(2,3) C．(3,4) D．(4,5)4．给出四个命题：（1）当时，的图象是一条直线；（2）幂函数图象都经过（0，1）、（1，1）两点；（3）幂函数图象不可能出现在第四象限；（4）幂函数在第一象限为减函数，则。
其中正确的命题个数是（）A．1 B．2 C．3 D．4考单招——上高职单招网6．设是奇函数，当时，则当时， ( ) A． B． C． D．7．若方程2（）+4的两根同号，则的取值范围为（）A． B．或C．或 D．或8．已知是周期为2的奇函数，当时，设则（）A． B． C． D．9．已知0，则有（）A． B． C．1< D．10．已知，则（）A． B． C． D．11．设则的定义域为（）A．( B． C．( D．(12．已知是R上的减函数，那么的取值范围是（）A．(0,1) B．(0, C． D．二、填空题：本大题共4小题，每小题4分，共16分。
把答案填在题中横线上。
考单招——上高职单招网13．若函数的定义域是R,则的取值范围是．14.函数y=log a(2－ax)在定义域上单调递增，则y=lo g a(2x－x2+3)的单调递减区间是 .15．光线透过一块玻璃板，其强度要减弱，要使光线的强度减弱到原来的以下，至少有这样的玻璃板块。
2016年高职高考数学答案
2016年高职高考数学答案篇一：2016年高职数学模拟试卷高职高考班《数学》模拟试题班别学号姓名一、选择题：（本大题共15小题，每小题5分，共75分。
请把每题唯一的正确答案填入表格内）1、设集合M?{xx?1?1}，集合N?{1,2,3,4}，则集合M?N?（）A. {1,2} B. {2,3} C. {3,4} D. {2,3,4}2、x?2是x?4的（）A. 充分条件B. 必要非充分条件C. 充要条件D. 既非充分条件又非必要条件3、函数y?x?1在区间(?1,??)上是（）A. 奇函数B. 偶函数C. 增函数D. 减函数4、不等式1?x0的解集为（）1?xA. (??,?1)?[1,??)B. [?1,1]C. (??,?1]?[1,??)D. [?1,1) 5、已知tan?cos??0，且tan?sin??0，则角?是（）A.第一象限角B. 第二象限角C. 第三象限角D. 第四象限角6、函数f(x)?2x?8?x?2x?152的定义域是（）A. (?3,5)B. (??,?3)?(5,??)C. [?3,5]D. (?3,4)?(4,5)2x1,x17、设函数f(x)??2，则f[f（?3）]?（）?x?2,x?1A. ?5 B. 15 C. ?11 D. 7 8、已知向量?(1,2)与向量?(4,y)垂直，则y?（）A. ?8 B. 8C. 2 D. ?2 9、已知两条直线y?ax?2和y?(a?2)x?1互相垂直，则a?（）A. 1 B.2 C. 0D. ?110、函数f(x)??x2?4x?7在区间[?3,4]上的最大值是（）A. ?25B. 19C. 11D. 10111、等比数列{an}中，a1?,a4?3，则该数列的前5项之积为（）9A. ?1B. 3C. 1D. ?312、已知数列{an}中，a1?3，an?an?1?3则a10?（）A. 30B. 27C. 33D. 36x?13、函数f(x)?3sin(?)（x?R）的最小正周期是（）46A. 2?B. 4?C. 8?D. ? 14、中心在原点，焦点在y轴上，离心率为，的椭圆标准方程为（）2x2y2x2x2y2y222y1 C. ?1 ??1 B. ??1 D. x?A.44622615、在10件产品中有4件次品，现从中任取3件产品，至少有一件次品的概率是（） A.2531 B.C.D.5656二、填空题：（每小题5分，共5×5=25分。
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2016年山东药品食品职业学院单招数学模拟试题（附答案解析）一、选择题(本大题共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a<b<0，则下列不等式一定成立的是()A．a2<ab<b2B．b2<ab<a2C．a2<b2<ab D．ab<b2<a2答案B2．关于数列3,9，…，2187，…，以下结论正确的是()A．此数列不是等差数列，也不是等比数列B．此数列可能是等差数列，也可能是等比数列C．此数列可能是等差数列，但不是等比数列D．此数列不是等差数列，但可能是等比数列解析记a1＝3，a2＝9，…，a n＝2187，…若该数列为等差数列，则公差d＝9－3＝6，a n＝3＋(n－1)×6＝2187，∴n＝365.∴{a n}可为等差数列．若{a n}为等比数列，则公比q＝＝3.a n＝3·3n－1＝2187＝37，∴n＝7.∴{a n}也可能为等比数列．答案B3．在△ABC中，若sin2A＋sin2B＝2sin2C，则角C为()A．钝角B．直角C．锐角D．60°解析由sin2A＋sin2B＝2sin2C，得a2＋b2＝2c2.即a2＋b2－c2＝c2>0，cos C>0.答案C4．设{a n}是公比为正数的等比数列，若a1＝1，a5＝16，则数列{a n}的前7项和为()A．63 B．64C．127 D．128解析a5＝a1q4＝q4＝16，∴q＝2.∴S7＝＝128－1＝127.答案 C5．一张报纸，其厚度为a，面积为b，现将此报纸对折7次，这时报纸的厚度和面积分别为()A．8a，B．64a，C．128a，D．256a，答案C6．不等式y≤3x＋b所表示的区域恰好使点(3,4)不在此区域内，而点(4,4)在此区域内，则b的范围是()A．－8≤b≤－5 B．b≤－8或b>－5C．－8≤b<－5 D．b≤－8或b≥－5解析∵4>3×3＋b，且4≤3×4＋b，∴－8≤b<－5.答案C7．已知实数m，n满足不等式组则关于x的方程x2－(3m＋2n)x ＋6mn＝0的两根之和的最大值和最小值分别是()A．7，－4 B．8，－8C．4，－7 D．6，－6考单招——上高职单招网解析两根之和z＝3m＋2n，画出可行域，当m＝1，n＝2时，z max＝7；当m＝0，n＝－2时，z min＝－4.答案A8．已知a，b，c成等比数列，a，x，b成等差数列，b，y，c成等差数列，则＋的值等于()A. B.C．2 D．1解析用特殊值法，令a＝b＝c.答案C9．制作一个面积为1m2，形状为直角三角形的铁架框，有下列四种长度的铁管供选择，较经济的(够用、又耗材最少)是() A．4.6m B．4.8mC．5m D．5.2m解析设三角形两直角边长为a m，b m，则ab＝2，周长C＝a＋b＋≥2＋＝2＋2≈4.828(m)．答案C10．设{a n}是正数等差数列，{b n}是正数等比数列，且a1＝b1，a2n＋1＝b2n＋1, 则()A．a n＋1>b n＋1B．a n＋1≥b n＋1C．a n＋1<b n＋1D．a n＋1＝b n＋1解析a n＋1＝≥＝＝b n＋1.答案B11．下表给出一个“直角三角形数阵”：，，，……满足每一列成等差数列，从第三行起，每一行的数成等比数列，且每一行的公比相等，记第i行第j列的数为a ij(i≥j，i，j∈N*)，则a83等于()A. B.C. D．1解析第1列为，＝，，…，所以第8行第1个数为，又每一行都成等比数列且公比为，所以a83＝××＝.答案C12．已知变量x，y满足约束条件则z＝2x＋y的最大值为()A．4 B．2C．1 D．－4解析先作出约束条件满足的平面区域，如图所示．由图可知，当直线y＋2x＝0，经过点(1,0)时，z有最大值，此时z＝2×1＋0＝2.考单招——上高职单招网答案B二、填空题(本大题共4小题，每小题5分．共20分．把答案填在题中横线上)13.在△ABC中，B＝45°，C＝60°，c＝1，则最短边的边长等于________．解析∵B＝45°，C＝60°，∴A＝180°－B－C＝75°.∴最短边为b.由正弦定理，得b＝＝＝.答案14．锐角△ABC中，若B＝2A，则的取值范围是__________．解析∵△ABC为锐角三角形，∴∴∴A∈(，)．∴＝＝2cos A.∴∈(，)．答案(，)15．数列{a n}满足a1＝3，a n＋1－2a n＝0，数列{b n}的通项公式满足关系式a n·b n＝(－1)n(n∈N*)，则b n＝________.＝2a n，解析∵a1＝3，a n＋1∴数列{a n}为等比数列，且公比q＝2.∴a n＝3·2n－1.又a n·b n＝(－1)n.∴b n＝(－1)n·＝.答案16．不等式ax2＋bx＋c>0的解集为{x|－1<x<2}，那么不等式a(x2＋1)＋b(x－1)＋c>2ax的解集为________．解析由题意，得则所求不等式可化为x2＋1－(x－1)＋(－2)<2x，解得0<x<3.答案{x|0＜x＜3}三、解答题(本大题共6个小题，共70分．解答应写出必要的文字说明、证明过程或演算步骤)17．(10分)已知全集U＝R，A＝，B＝{x|3x2－4x＋1>0}，求∁(A∩B)．U解A＝{x|3x2－4x－4<0}＝，B＝.A∩B＝，∁U(A∩B)＝{x|x≤－，或≤x≤1，或x≥2}．18．(12分)在△ABC中，a，b，c分别是角A，B，C的对边，且8sin2－2cos2A＝7.(1)求角A的大小；(2)若a＝，b＋c＝3，求b和c的值．解(1)在△ABC中，有B＋C＝π－A，由条件可得4[1－cos(B＋C)]－4cos2A＋2＝7，即(2cos A－1)2＝0，∴cos A＝.又0<A<π，∴A＝.(2)由cos A＝，得＝，即(b＋c)2－a2＝3bc，则32－()2＝3bc，即bc＝2.考单招——上高职单招网由解得或19．(12分)递增等比数列{a n}满足a2＋a3＋a4＝28，且a3＋2是a2和a4的等差中项．(1)求数列{a n}的通项公式；(2)若b n＝a n·log12a n，求数列{b n}的前n项和．解(1)设等比数列的公比为q(q>1)，则有解得或(舍去)．所以a n＝2·2n－1＝2n.(2)b n＝a n·log12a n＝－n·2n，S n＝－(1·2＋2·22＋3·23＋…＋n·2n)，2S n＝－(1·22＋2·23＋…＋(n－1)·2n＋n·2n＋1)．两式相减，得S n＝2＋22＋23＋…＋2n－n·2n＋1＝－n·2n＋1＝－(n －1)·2n＋1－2.20．(12分)配制两种药剂，需要甲、乙两种原料．已知配A种药需要甲料3毫克，乙料5毫克；配B种药需要甲料5毫克、乙料4毫克．今有甲料20毫克，乙料25毫克，若A，B两种药至少各配一剂，问A、B两种药最多能各配几剂？解设A、B两种药分别能配x，y剂，x，y∈N*，则作出可行域，图中阴影部分的整点有(1,1)，(1,2)，(1,3)，(2,1)，(2,2)，(3,1)，(3,2)，(4,1)．所以，在保证A，B两种药至少各配一剂的条件下，A种药最多配4剂，B种药最多配3剂．21．(12分)在△ABC中，已知＝，且cos(A－B)＋cos C＝1－cos2C.(1)试确定△ABC的形状；(2)求的范围．解(1)由＝，得＝，即b2－a2＝ab，①又cos(A－B)＋cos C＝1－cos2C，所以cos(A－B)－cos(A＋B)＝2sin2C.sin A·sin B＝sin2C，则ab＝c2. ②由①②知b2－a2＝c2，即b2＝a2＋c2.所以△ABC为直角三角形．(2)在△ABC中，a＋c>b，即>1.又＝≤＝＝，故的取值范围为(1，]．22．(12分)设{a n}是公差不为零的等差数列，S n为其前n项和，满足a＋a＝a＋a，S7＝7.(1)求数列{a n}的通项公式及前n项和S n；(2)试求所有的正整数m，使得为数列{a n}中的项．考单招——上高职单招网解(1)由题意，设等差数列{a n}的通项公式为a n＝a1＋(n－1)d，(d≠0)．由a＋a＝a＋a，知2a1＋5d＝0.①又因为S7＝7，所以a1＋3d＝1.②由①②可得a1＝－5，d＝2.所以数列{a n}的通项公式a n＝2n－7，S n＝＝n2－6n.(2)因为＝＝a m＋2－6＋为数列{a n}中的项，故为整数，又由(1)知a m＋2为奇数，所以a m＋2＝2m－3＝±1，即m＝1,2.当m＝1时，＝＝－15.显然它不是数列{a n}中的项．当m＝2时，＝＝1.它是数列{a n}中的项．因此，符合题意的正整数只有m＝2.。