开放教育专科入学水平测试数学考试资料

测试资料开放教育专科入学水平测试数学考试大纲数学科入学测试旨在考查中学数学基础知识、基本技能、基本方法，考查逻辑思维能力、运算能力、空间想象能力，以及运用所学数学知识和方法分析问题和解决问题的能力。复习考试范围包括代数、三角、平面解析几何三部分。 本说明对所列知识提出了三个层次的不同要求，三个层次由低到高顺序排列，且高一级层次要求包含低一级要求。三个层次分别为： 了解：要求考生对所列知识的含义有初步的认识，识记有关内容，并能进行直接运用。 理解、会：要求考生对所列知识的含义有较深的认识，能够解释、举例或变形、推断，并能运用知识解决有关问题。 掌握、熟练掌握：要求考生对所列知识能够综合运用，并能解决较为复杂的数学问题。 要求学生会对问题进行观察、比较、分析、综合、抽象与概括；会用演绎、归纳和类比进行推理；能准确、清晰、有条理地进行表述；会根据法则、公式、概念进行数、式、方程的正确运算和变形；能分析条件，寻求与设计合理、简捷的运算途径；能根据要求对数据进行估计；能根据条件画出图形，根据图形想象出直观形象；能正确地分析出图形中基本元素及其相互关系；能对图形进行分解、组合、变形。 要求学生具有一定的分析问题和解决问题的能力：能阅读理解对问题进行陈述的材料；能综合应用所学数学知识、思想和方法解决问题，包括解决在相关学科、生产、生活中的数学问题，并能用数学语言正确地加以表述。 一、复习考试内容 第一部分 代 数 （一）数、式、方程和方程组 1、理解有理数、实数及数轴、相反数、绝对值、倒数、算术平方根的概念，会进行有关计算。 2、理解有关整式、分式、二次根式的概念，掌握它们的一些性质和运算法则。3、掌握一元一次方程，一元二次方程的解法，能运用一元二次方程根的判别以及根与系数的关系解决有关问题。4、会解有唯一解的二元一次方程组、三元一次方程组；会解由一个二元二次方程和一个二元一次方程组成的方程组；会解简单的由两个二元二次方程组成的方程组（主要指以下几种类型：用加减消元法可消去某个未知数、可消去二次项的，以及至少有一个方程可分解成一次方程的）。（二）集合 了解集合的意义及其表示方法。了解空集、全集、子集、交集、并集、补集的概念及表示方法，并能运用相应符号表示集合、元素与集合的关系。（三）不等式和不等式组 1、理解不等式的性质。会用不等式的性质和基本不等式a2 0 (aR)、 a2+b22ab (a、bR)、a+b2 （a、b0）解决一些简单问题。2、会解一元一次不等式，一元一次不等式组和可化为一元一次不等式组的不等式，会解一元二次不等式，了解区间的概念，会在数轴上表示不等式或不等式组的解集。3、了解绝对值不等式的性质，会解形如 |a+ b|c 和|a+b| c 的绝对值不等式。（四）指数与对数 1、理解零指数、负整数指数、分数指数幂的概念，会用幂的运算法则进行计算。2、理解对数的概念，会用对数的性质、对数恒等式、运算法则和换底公式进行计算。了解常用对数的概念。3、掌握简单的指数方程和对数方程的解法。（五）函数 1、理解函数概念，会求一些常见函数的定义域。2、理解函数的单调性和奇偶性的概念，掌握增函数、减函数及奇函数、偶函数的图像特征。3、理解一次函数、反比例函数的概念，掌握它们的图像和性质，会求它们的解析式。4、理解二次函数的概念，掌握它的图像和性质以及函数y = a2 + b+ c (a0) y = a2 (a0)的图像间的关系；会求二次函数的解析式及最大值或最小值。能灵活运用二次函数的知识解决有关问题。5、了解反函数的意义。会求一些简单函数的反函数。6、理解幂函数、指数函数、对数函数的概念，掌握它们的图像和性质，会用它们解决有关问题。 第二部分 三角 （一）三角函数及其有关概念 1、了解正角、负角、零角的概念，理解象限角和终边相同的角的概念。2、理解弧度的概念，会进行弧度与角度的换算。3、理解任意角三角函数的概念。识记三角函数在各象限的符号和特殊角的三角函数值。（二）三角函数式的变换 1、掌握同角三角函数间的基本关系式，诱导公式，会用它们进行计算、化简和证明。2、掌握两角和、两角差、二倍角的正弦、余弦、正切的公式，会用它们进行计算、化简和证明。（三）三角函数的图像和性质 1、掌握正弦函数，余弦函数的图像和性质，会用这两个函数的性质（定义域、值域、周期性、奇偶性和单调性）解决有关问题。2、了解正切函数的图像和性质。3、了解函数yAsin x , y sin(+) , ysin, yAsin(+) 与ysin 的图像之间的关系，会用“五点法”画出它们的简图，会求函数yAsin(+)的周期、最大值和最小值。（四）反三角函数了解反三角函数的概念、图像和性质，会由已知三角函数值求角，并会用符号 arcsin、 arccos、arctan 表示。第三部分 平面解析几何 （一）平面坐标 掌握平面内两点间的距离公式、有向线段的概念、线段的中点公式和平移公式。（二）直线 1、理解直线的倾斜角和斜率的概念，会求直线的斜率。2、会求直线方程，能灵活运用直线方程解决有关问题。3、掌握两条直线平行与垂直的条件以及点到直线的距离公式，会用它们解决有关问题。了解两直线所成角的公式。（三）圆锥曲线 1、了解曲线和方程的关系，会求两条曲线的交点。2、了解充分条件、必要条件、充分必要条件的概念。3、掌握圆的标准方程和一般方程以及直线与圆的位置关系，能灵活运用它们解决有关问题。4、理解椭圆、双曲线、抛物线的概念，掌握它们的标准方程和性质，能灵活运用他们解决有关问题。5、了解坐标轴的平移公式，会用平移公式化简圆锥曲线方程。6、了解参数方程的概念、理解圆和椭圆的参数方程。二、考试形式及试卷结构 考试采用闭卷形式，全卷包括语文、数学和英语三部分，分数比例考试时间由教务部门决定。试卷内容比例：代数约占50，三角约占25，平面解析几何约占25。题型比例:选择题约占40，填空题约占40，解答题（包括证明题）约占20。入学测试题数学部分参考答案一、 单选题1. C 2. A 3. A 4. B 5. A二、 填空题6. 07. 28. -9. 010.三、 解答题11. 化简 sin2325o + cos2215o + tan2420o =sin235o + cos235o + tan260o = 1 + 3 = 4.12. 用长为l的铝合金材料弯成下部为矩形，上部为半圆形的框架。若矩形底边长为 2x,求此框架围成面积y与x的函数关系式。解：y= - (2+p/2)x2+lx数学模拟试题一得 分评卷人一、选择题（每小题5分，共25分）1. 设集合P = 1,2,3, Q = 3,4,5，则 PQ = ( )。 (A) 1,2; (B) 1,2,4,5; (C) 3; (D) 1,2,3,4,5.2. 函数 y = a x - 1 (a 0且a1)的定义域是( )。 (A) (-, +); (B) (1, +); (C) 1, +); (D) (0, 1)(1, +).3. 设 f (x) = (xR且x-2)，则f -1(2) = ( )。(A) -1; (B) ; (C) 1 ; (D) -.4. 设y = f (x) 在(-, +)上是偶函数，并且在0, +)上是减函数，则( )。(A) f (-3) f (-2) f (1); (B) f (1) f (-2) f (-3); (C) f (-2) f (-3) f (1); (D) f (1) f (-3) f (-2).5. 属于第三象限的角是( )。(A) -460 o; (B) 0.8p; (C) 720 o ; (D) 450 o.得 分评卷人二、填空题（每小题5分，共25分）6. 方程 4x - 2x = 0 的解是_。7. 已知对数函数 y = log a x 经过点(2, 1)，则a = _。8. 已知 sin a =，且a在第二象限，则 cos a = _。9. 如果 cos q = 1，那么 sin 2q = _。10. 直线 y = -x tan+ 2的倾斜角是_。得 分评卷人三、计算解答题（每小题5分，共10分）11. 化简 sin2325o + cos2215o + tan2420o . 12. 用长为l的铝合金材料弯成下部为矩形，上部为半圆形的框架。若矩形底边长为2x,求此框架围成面积y与x的函数关系式。入学测试题数学部分参考答案四、 单选题1. C 2. D 3. D 4. C 5. B五、 填空题a) 4b) 10c)d) 奇函数e)六、 解答题11. 计算 解： 12. 解：圆心O(0,0)到直线的距离为由于圆的半径为1，所以圆上的点到直线的最大距离dmaxd+1 3;最小距离dmind-1 1.数学模拟试题二得 分评卷人一、选择题（每小题5分，共25分）13. 设集合P = 1, 2, x, Q = 3，且P Q = Q则 x = ( )。 (A) 1; (B) 2; (C) 3; (D) 4.14. 函数 的定义域是( )。 (A) (-5, 5); (B) -5, 5; (C) (0, 5); (D) (0, 5.15. 函数y = (0.5) -x + 1的反函数是 ( )。(A) y = logx 2 +1; (B) y = log2 x +1; (C) y = log2 x - 1 ; (D) y = log2 (x 1).16. 函数( )在(0, +)上是减函数。 （A） （B） （C） （D）17. 若，则( )。 （A） （B）（C） （D）得 分评卷人二、填空题（每小题5分，共25分）18. 已知，那么的最大值是 _。19. 中，点A(4, -1)，AB的中点为M(1, -3)，则边AB的长为_。20. 圆半径是，圆心角是（弧度）的扇形面积为_。21. 函数是 _(填奇函数、偶函数或非奇非偶)。22. 方程lg (2-x2) lg (2-3x) - lg2的解是_。得 分评卷人三、计算解答题（每小题5分，共10分）23. 计算 24. 求圆上的点到直线的最大、最小距离。入学测试题数学部分参考答案七、 单选题1. A2. C3. C4. D5. C八、 填空题a) 3b) 10c) 15d)e) 1 / b九、 解答题11. 解：原式=12. 解：设所求坐标为(10, y)，则(104)2 + (y2)2 = 102得(y2)2 = 64y2 = 8所以 y = 10 或 6.故所求坐标为(10, 10) 或 (10,6).数学模拟试题三得 分评卷人一、选择题（每小题5分，共25分）25. a,b互为相反数，c,d互为倒数，m的绝对值为2，那么= ( )。(A) 3; (B) 4; (C) 3 0.5; (D) 4 0.5.26. 已知a + b 0, b b a b; (B) a a b b; (C) a b b a; (D) a b a b.27. 已知y = 1是方程的解，那么关于x的方程 m(x + 4) = m(2x + 4)的解是 ( )。(A) x = 1; (B) x = 1; (C) x = 0 ; (D) 方程无解.28. 下列各函数中，与函数 y = x 相同的是( )。 （A） （B） （C） （D）29. 函数y = ax2 + bx + c的图象如右，则( )。 （A）a 0, b 0, c 0 （B）a 0, b 0, c 0, b 0, c 0, b 0得 分评卷人二、填空题（每小题5分，共25分）30. 已知a2 + |b1| = 0，那么2a + 3b = _。31. =_。32. _。33. sin 70 cos 130- cos 70 sin 130 = _。34. 曲线 b x + a y 1 (b0) 在x轴上的截距是_。得 分评卷人三、计算解答题（每小题5分，共10分）35. 计算 36. 求与y轴及点A(4, 2)的距离都是10的点的坐标。语文一、汉语言文学基础知识（每小题4分，共 20分）1B 2C 3A 4C 5B得 分评卷人一、汉语言文学基础知识题(每小题4分，共 20分) 1.下列各组词语中没有错别字的一组是( ) A.一心一意 千军一发 手足无措 B.百废待兴 晴空万里 面面相觑 C.波谲云诡 不名一文 顾名思意 D.得陇望蜀 春寒料峭 鬼鬼崇崇 2.填入下列空白处最恰当的词语是 （ ）学习中，学生多有一些不良的学习习惯，如不少学生往往只在文章的字义上 ，不愿对文章的内容和思想内涵作细致入微的研读。A.轻描淡写 B.浅尝辄止 C.管窥蠡测 D.浮光掠影3.“问君能有几多愁，恰似一江春水向东流”出自（ ）之口：A.李煜 B.柳永 C.秦观 D.杜牧 4.下列作品与作家对应正确的一项是（ ）汉宫秋 琵琶记 长生殿 桃花扇A.马致远 洪升 高明 孔尚任B.洪升 孔尚任 马致远 高明C.马致远 高明 洪升 孔尚任D.洪升 马致远 孔尚任 高明5.“今天下三分，益州疲弊，此诚危急存亡之秋也”中加点词语指的是（ ）A.秋季 B.时刻 C.年龄 D.年岁得 分评卷人二、作文（每小题40分，共40分）作文题目：家/童年趣事（任选一题）要求：除诗歌外，文体不限；不少于800字。一、汉语言文学基础知识（每小题4分，共 20分）1B 2B 3D 4D 5C得 分评卷人一、汉语言文学基础知识题(每小题4分，共 20分) 1.下列词语中没有错别字的一项是 ( ) A美轮美焕 坚韧不拔 不速之客 B诚惶诚恐 义薄云天 强词夺理 C克勤克捡 守株待兔 装腔作势 D惊慌失措 百密一疏 食不裹腹2. 下列各组词语中，加点字注音全部正确的一组是（ ） A怆然（cng） 陨落（yn） 赊账（sh） B负荷（h） 分泌（m） 裙裾（j） C梦魇（yn） 纤细（qin） 暮霭（i）D连累（li） 渎职（d） 参差（cn）3“劝君更进一杯酒，西出阳关无故人”出自（ ）A王昌龄的芙蓉楼送辛渐B高适的别董大 C李白的送孟浩然之广陵D王维的送元二使安西4下列作品、题材、作家、国别对应正确的一项是（ ）A战争与和平小说歌德德国 B巴黎圣母院戏剧雨果法国 C威尼斯商人诗歌莎士比亚意大利D老人与海小说海明威美国5.下列句子中对加点词解释正确的一项是（ ）A. 后之览者，亦将有感于斯文。（举止文雅） B.焚百家之言，以愚黔首。（工匠）C.不出，火且尽。（将要） D.寿毕，请以舞剑，因击沛公于坐。（击打）得 分评卷人二、作文（每小题40分，共40分）作文题目：谈读书/谈作人/谈工作（任选一题）要求：除诗歌外，文体不限；不少于800字。一、汉语言文学基础知识（每小题4分，共 20分）1B 2C 3A 4D 5A得 分评卷人一、汉语言文学基础知识题(每小题4分，共 20分) 1下列词语中有错别字的一项是 ( ) A请君入瓮 见异思迁 胸有成竹 B天下为公 异彩缤纷 无动于中 C天人合一 衣冠禽兽 平步青云 D越俎代庖 三令五申 顾名思义2.依次填入下列空白处词语使用恰当的一组是 （ ）蛙眼能 地发现具有特定形状的运动目标， 地确定目标的位置、运动方向和速度，并能选择 的攻击时刻。A.敏捷 准确 适当B.迅捷 明确最佳 C.敏捷 准确最佳D.迅捷 明确适当3.“先天下之忧而忧，后天下之乐而乐”出自（ ）之口：A.范仲淹 B.欧阳修 C.王安石 D.苏轼 4下列作品、题材、作家、国别对应正确的一项是（ ）A悲惨世界小说狄更斯法国 B威尼斯商人戏剧泰戈尔印度 C园丁集诗歌拜伦英国D伊豆的舞女小说川端康成日本5.对下句中加点词语解释正确的一项是（ ）余之力尚足以入，火尚足以明也。A. 照明 B.明亮 C.持续 D.明晰得 分评卷人二、作文（每小题40分，共40分）作文题目：互联网/生活（任选一题）要求：除诗歌外，文体不限；不少于800字。开放教育专科入学水平测试英语题型及模拟试题复习提要：高中起点。复习高中课本和有关语法及功能。阅读高中水平的英语文章。答案1. a 2. c 3. a 4. d. 5.c 6. T 7. T 8. T 9.F 10. F11.F 12.F 13.F 14.F 15.F 模拟试题A: Vocabulary and Structure (20%)1. Dearer electricity will mean _ bills for most families.a. expensive b. difficultc. hard d. heavy2. He knew nothing about his journey _ he was likely to be away for three months. a. expect b. except for c. except that d. in addition3. At last he _ finish it in time. a. managed to b. tried to c. succeeded to d. got to4. Mrs. Edward doesnt like to take a bus. We walked there _. a. instead of b. as wellc. as well as d. instead5. 1. That dress is very dear. After buying it, I will be _. a. break b. broken c. broke d. breakedB: Read the passage carefully and then decide whether the statements that follow are True or False. (10%) The pubs, or public houses, are perhaps the most popular places for the British to meet friends and to relax outside the home. Pubs serve alcoholic drinks, but they must obtain special permit from the local council. They are open only during certain hours each day. By law no one under the age of 14 can go to a pub and no one under 18 can be served with alcoholic drinks. Many pubs also serve food in addition to drinks, and some also provide entertainment such as jazz music or folk singing, but no dancing is permitted. Admission to the pub is free: you only pay for your drinks and food. In most pubs, there are at least two bars: the public bar which is decorated and furnished quite simply; and the saloon and lounge bar which often has small tables and chairs, a more comfortable and relaxing atmosphere, but charges slightly higher prices. In both bars customers buy their drinks from the bar itself. There is no waiter service. 1. The pub is probably the most popular place for the British to meet friends.2. People can enjoy jazz music in some pubs.3. People buy their drinks from a bar itself in public bars.4. Pubs can serve alcoholic drinks without special permit.5. The pub is open 24 hours a day.6. No one under the age of 18 can go into a pub according to the law.7. People can dance in pubs.8. Drinks and food are free in most pubs.9. Public bars usually have small tables and chairs, providing a more comfortable atmosphere.10. There is waiter service in saloon and lounge bar.A卷试题答案及评分标准一、Vocabulary and Structure 20%1. b 2. a 3. b 4. c 5. d6. a 7. d 8.a 9. c 10.c 二、Reading: 10%Passage A1. D 2. B 3. B 4. D 5. DPassage B1.B 2. B 3.B 4. C 5. CA卷开放教育专科入学测试（英语部分）模拟试题一、Vocabulary and Structure: Choose the correct words to fill in the blanks: 20%1. There is a _ of two hours in the 7:40 train. a. late b. delay c. later d. decay2. Pay attention _ the details.a. to b. for c. with d. in3. Those who have applied for the post are _ in the office.a. talked b. interviewed c. asked d. questioned4. Will I get an invitation _ the party?a. in b. for c. to d. on5. Whenever we visited them, they _ television.a. have watched b. watch c. watched d. were watching6. I would like to make a request _ a contribution.a. for b. with c. from d. in7. There are several things of the textbook _attention.a. worthwhile b. worth of c. worthy d. worthy of 8. The big tree _ a lot of apples. a. bears b. wears c. grows d. takes9. The _ driver thinks that accidents only happen to other people. a. most b. usual c. average d. general 10. Jack was going out of the shop when he ran _ an old man who was coming in. a. for b. along c. into d. at二、Reading 10%Passage ATo me, music is food and water. I cant live without it. I know this is not true for everybody. Many people dont listen to music and they can get along quite well. But music is everywhere in our life. For example, when you watch films or TV plays, do you find them interesting if there is no music? You would find them boring. And when you are waiting for the train or the plane, you would like music because it makes the time seem shorter.It is true that music is everywhere in our life. Some people like to sit by the sea and listen to the sound of the sea. Some enjoy listening to the singing of birds. Those sounds are some kinds of music. So music has meaning for everyone in some way or other. Of course, it has special meaning for people like me. We spend our lives playing or writing music.Someone said, “Though music a child goes into a world of beauty, learns to take care of others and makes his mind and body strong.” Music is an important part of our lives.1. The passage tells us that the writer _.a. likes to sit by the sea b. is not interested in musicc. likes to travel by plane d. likes music very much2. The word “boring” in the first paragraph means _.a. interesting b. not interestingc. tiring d. foolish3. Music is important to _. a. some people b. everyone c. nobody d. writers only4. Listening to music can _ when you are waiting for the train. a. make time fly quickly b. help you save time c. make time short d. make you feel time passes more quickly5. Which of the following is true? a. The writer likes to write music every day. b. The writer becomes strong through music. c. Most people like to listen to the sound of the sea. d. Music has some kind of meaning to everyone.Passage BIll Show You the Way Mr. Adamson was traveling around the country in his car. One evening he was driving along a road, looking for a small hotel when he saw an old man at the side of the road. He stopped his car and said to the old man, “I want to go to the Sun Hotel. Do you know it?” “Yes,” the old man answered. Ill show you the way.” He got into Mr. Adamsons car, and they drove for about twelve miles. When they came to a small house, the old man said, “Stop here”. Mr. Adamson stopped and looked at the hose. “ But this isnt a hotel,” he said to the old man. “No”, the old man answered, “this is my house. And now Ill show you the way to the Sun Hotel. Turn around and go back nine miles. Then youll see the Sun Hotel on the left.1. Where did Mr. Adamson want to stay that night?a) In the old mans house.b) In a small hotel.c) In his friends housed) In his own house.2. Why did Mr. Adamson stop his car on the road?a. He found something special.b. He wanted to ask the way.c. He saw a hotel.d. He wanted to give the old man a lift.3. Where did the old man take Mr. Adamson to?a. The small hotel b. The old mans housec. The Sun Hoteld. Mr.Adamsons house.4. Why didnt the old man stop Mr.Adamson when they passed the hotel?a. He didnt know the hotel.b. He wanted Mr.Adamson to stay in his house.c. He wanted to get home.d. He didnt see the hotel.5. How far was the Sun Hotel from the place where Mr.Adamson asked the way?a. two miles. b. nine miles c. three miles d. twelve milesB卷试题答案及评分标准一、Vocabulary and Structure（每小题2分，共20分）1. b 2. c 3. b 4. c. 5. c6. d 7. b 8. d 9. c 10. c 二、Reading: （每小题1分，共10分）Passage A1. C 2. C 3. A 4. B 5. CPassage B1. A 2. D 3.A 4.B 5.DB卷（英语部分）模拟试题一、Vocabulary and Structure: Choose the correct words to fill in the blanks: 20%1. A number of students in this class _ to Beijing once or twice.a. were b. have been c. is d. has been2. I find it hard to _ my thanks to you for your kind help.a. speak b. sayc. express d. tell3. The weather is so nice today. Lets go there _. a. by foot b. on foot c. on bus d. by walk4. The nurse is even more tender _ the sick child than his parents. a. at b. by c. to d. with5. He _ talk a lot. But now he is very quiet. a. is used to b. was used to c. used to d. did use to 6. You should fill in this application _ very carefully. a. file b. letter c. visa d. form 7. He _ many beautiful post cards to us. a. takes b. shows c. obtains d. has8. Five miles _ a long distance to an old lady of her age.a. seem to being b. seem to be c. seems to being d. seems to be9. Students are usually introduced to history by a thick book full _ names, dates and data.a. for b. in c. of d. from10. I didnt meet Mary white at the party. She _ by the time I arrived.a. was left b. left c. had left d. was leaving二、Reading: 10%Mr. Jones and Mr. Brown worked in the same office. One day Mr. Jones said to Mr. Brown, “We are going to give a small party at our house next Wednesday evening. Will you and your wife come?”Mr. Brown said, “Thank you very much. Thats very kind of you. We are free t