A卷

专业课原理概述部分一、选择题（每题1分，共5分）1. 微分学的中心概念是（）A. 极限B. 导数C. 微分D. 积分2. 函数f(x)在x=a处可导，那么f'(a)等于（）A. f(a)的值B. f(x)在x=a处的斜率C. f(a)的极限D. f(a)的平均变化率3.下列函数中，奇函数是（）A. f(x) = x²B. f(x) = x³C. f(x) = cos(x)D. f(x) = e^x4. 不定积分∫(1/x)dx的结果是（）A. ln|x| + CB. x + CC. 1/x + CD. e^x + C5. 多元函数f(x, y)的偏导数f_x表示（）A. 仅对x求导B. 对x和y同时求导C. x和y的乘积求导D. f对x的积分二、判断题（每题1分，共5分）1. 极限存在的充分必要条件是左极限和右极限相等。

（）2. 一切初等函数在其定义域内都可导。

（）3. 若函数f(x)在区间[a, b]上单调增加，则f'(x)≥0。

（）4. 二重积分可以转化为累次积分。

（）5. 泰勒公式是麦克劳林公式的推广。

（）三、填空题（每题1分，共5分）1. 函数f(x)在点x=a处的极限为______，记作______。

2. 若f(x) = 3x² 5x + 2，则f'(x) =______。

3. 不定积分∫sin(x)dx的结果是______。

4. 二重积分∬D dA表示______的面积。

5. 泰勒公式中，f(n)(a)表示______。

四、简答题（每题2分，共10分）1. 简述导数的定义。

2. 解释什么是函数的极值。

3. 简述定积分的基本思想。

4. 举例说明如何应用微分方程解决实际问题。

5. 简述多元函数求导的基本法则。

五、应用题（每题2分，共10分）1. 求函数f(x) = x²e^x的导数。

2. 计算定积分∫(从0到π) sin(x)dx。

福建农林大学考试试卷 高等数学(A)卷参考答案一。

填空题（每小题3分，本题共15分） 1、6e 2、k =1 ． 3、xx+1 4、1=y 5、x x f 2cos 2)(= 二．单项选择题（每小题3分，本题共15分） 1、D 2、B 3、C 4、B 5、A 三．计算题（本题共56分，每小题7分） 1.解：x x x 2sin 24lim-+→81)24(2sin 2lim 21)24(2sin lim 00=++=++=→→x x x x x x x x 7分 2.解 ：21lim 11lim )1(1lim )111(lim 0000=++=+--=---=--→→→→x x x x x x x x x x x x x x xe e e e xe e e e x x e e x 7分 3、解： 2c o s12limx dt e x tx ⎰-→exxe xx 212sin lim 2cos0-=-=-→ 7分 4、解： )111(1122xx x y ++++='……………………… …...4分211x+=……………………………………… …...7分5、解：t t t t dx dy 21121122=++= （4分） 222232112()241d y t d dydxt dtt dt dx dxt t-+===-+ （7分） 6、解：C xd x dx x x ++=++-=+⎰⎰)32cos(21)332()32sin(21)32sin(12 （7分）7、 解：⎰⎰=xx e x x x e d c o s d c o s⎰+=sinxdx e cos x x e x …………………… …….2分 ⎰+=x de sin cos x x e x ..………………… ……….3分 dx cos sin cos x e x e x e x x x ⎰-+= ……… ……5分C x x e x ++=)cos (sin ……………… ……… …7分8、解：⎰⎰⎰⎰--+==-0111120d )(d )(d )(d )1(x x f x x f x x f x x f … …2分⎰⎰+++=-10011d 1d x x e x x ……… ………3分 1001)1ln(d )11(x x ee x x +++-=⎰-…… ……5分 2ln )1ln(101++-=-xe ……………… …6分)1ln()1ln(11e e +=++=-………… ……7分四．应用题（本题7分）解：曲线2x y =与2y x =的交点为（1，1）， 1分 于是曲线2x y =与2y x =所围成图形的面积A 为31]3132[)(10210232=-=-=⎰x x dx x x A 4分A 绕y 轴旋转所产生的旋转体的体积为：()πππ10352)(1052142=⎥⎦⎤⎢⎣⎡-=-=⎰y y dy y y V 7分 五、证明题（本题7分）证明： 设x x f x F -=)()(， ……………………….……… ……2分显然)(x F 在]1,21[上连续，在)1,21(内可导， 且 021)21(>=F ，01)1(<-=F .由零点定理知存在]1,21[1∈x ，使0)(1=x F . …….… …………4分 由0)0(=F ，在],0[1x 上应用罗尔定理知，至少存在一点)1,0(),0(1⊂∈x ξ，使01)()(=-'='ξξf F ，即1)(='ξf … …7分。

第1页/（共4页） 第2页/（共4页）技工学校2021-2022学年度第一学期《城市轨道交通运营管理》考试试卷A 卷一.填空题 (每空2分，共20分)1. 城市轨道交通运营管理的内容包括行车管理、站务管理、票务管理、车站设备管理等。

2. 列车运行图是利用坐标原理对列车运行时间、空间关系（列车运行情况）的图解表示，横坐标是时间轴，纵坐标是车站轴，运行线代表列车的运行轨迹。

3.轨道交通安全管理制度中上级部门领导不定期进行突击检查，检查各班组的“两纪一化”即 劳动纪律、作业纪律及标准化作业。

4.屏蔽门系统设置在车站每侧站台边缘，由滑动门、固定门、应急门和端门组成。

5.报表填写要求真实、准确、完整、及时，并遵守相关的规章制度。

6.在地面或者高架线路两侧各 100 米范围内禁止升放风筝、气球等低空漂浮物体和无人机等低空飞行。

二.选择题 (每题2分，共20分)1.现代城市轨道交通基本上都采用基于无线通信的移动闭塞，其英文缩写为 A 。

A CBTC B AFC C FAS D BAS2. B 用于乘客自助式购票。

其能识别指定的硬币和纸币并退伪币，可以找零；票盒无票或钱箱已满时能提示相关信息，能将设备的状态信息和运营数据自动传输给车站计算机。

A 自动检票机 B 自动售票机 C 自动验票机 D 半自动售票机3. C 系统是安装在城市轨道交通沿线车站站台边缘，用以提高运营安全系数、改善乘客候车环境、节约成本的一套机电一体化的机电设备系统。

A 防火门B 人防门C 屏蔽门D 防淹门 4. A 是指在一定时期（日、月、年）内运送的全部乘客人数。

A 客运量 B 运营量 C 周转量 D 客流量 5.列车在中间站或终点站利用站前渡线进行折返作业的方式称为 D 方式。

A 站中折返 B 站中折返 C 站后折返 D 站前折返6.当基本闭塞无法使用或联锁故障失效的情况下应采用电话闭塞法组织行车，其行车凭证为 A 。

A 路票B 地面信号C 车载信号D 路签 7.城市轨道交通列车车次由服务号、交路号（目的地代码） B 组成。

重庆市2024年初中学业水平暨高中招生考试数学试题（A 卷）（全卷共三个大题，满分150分，考试时间120分钟）注意事项：1.试题的答案书写在答题卡上，不得在试题卷上直接作答；2.作答前认真阅读答题卡上的注意事项；3.作图（包括作辅助线）请一律用黑色2B 铅笔完成；4.考试结束，由监考人员将试题卷和答题卡一并收回．参考公式：抛物线()20y ax bx c a =++≠的顶点坐标为24,24b ac b a a ⎛⎫-- ⎪⎝⎭，对称轴为2bx a =-．一、选择题：（本大题10个小题，每小题4分，共40分）在每个小题的下面，都给出代号为A 、B 、C 、D 的四个答案，其中只有一个是正确的，请将答题卡上题号右侧确答案所对应的方框涂黑．1. 下列四个数中，最小的数是（ ）A 2- B. 0 C. 3D. 12-2. 下列四种化学仪器示意图中，是轴对称图形的是（ ）A. B.C. D.3. 已知点()3,2-在反比例函数()0ky k x=≠的图象上，则k 的值为（ ）A. 3- B. 3C. 6- D. 64. 如图，AB CD ∥，165∠=︒，则2∠的度数是（ ）.的A. 105︒B. 115︒C. 125︒D. 135︒5. 若两个相似三角形的相似比是1:3，则这两个相似三角形的面积比是（ ）A. 1:3B. 1:4C. 1:6D. 1:96. 烷烃是一类由碳、氢元素组成的有机化合物质，下图是这类物质前四种化合物的分子结构模型图，其中灰球代表碳原子，白球代表氢原子．第1种如图①有4个氢原子，第2种如图②有6个氢原子，第3种如图③有8个氢原子，……按照这一规律，第10种化合物的分子结构模型中氢原子的个数是（ ）A. 20B. 22C. 24D. 267. 已知m =，则实数m 的范围是（ ）A. 23m << B. 34m << C. 45m << D. 56m <<8. 如图，在矩形ABCD 中，分别以点A 和C 为圆心，AD 长为半径画弧，两弧有且仅有一个公共点．若4=AD ，则图中阴影部分的面积为（ ）A. 328π-B. 4π-C. 324π- D. 8π-9. 如图，在正方形ABCD 的边CD 上有一点E ，连接AE ，把AE 绕点E 逆时针旋转90︒，得到FE ，连接CF 并延长与AB 的延长线交于点G ．则FGC E的值为（ ）A.B.C.D.10. 已知整式1110:nn n n M a x a xa x a --++++ ，其中10,,,n n a a - 为自然数，n a 为正整数，且1105n n n a a a a -+++++= ．下列说法：①满足条件的整式M 中有5个单项式；②不存在任何一个n ，使得满足条件的整式M 有且只有3个；③满足条件的整式M 共有16个．其中正确的个数是（ ）A. 0B. 1C. 2D. 3二、填空题：（本大题8个小题，每小题4分，共32分）请将每小题的答案直接填在答题卡中对应的横线上．11. 计算：011(3)()2π--+＝_____．12. 如果一个多边形的每一个外角都是40︒，那么这个多边形的边数为______．13. 重庆是一座魔幻都市，有着丰富的旅游资源．甲、乙两人相约来到重庆旅游，两人分别从A 、B 、C 三个景点中随机选择一个景点游览，甲、乙两人同时选择景点B 的概率为_____．14. 随着经济复苏，某公司近两年的总收入逐年递增．该公司2021年缴税40万元，2023年缴税48.4万元，该公司这两年缴税的年平均增长率是______．15. 如图，在ABC 中，延长AC 至点D ，使CD CA =，过点D 作DE CB ∥，且DE DC =，连接AE 交BC 于点F ．若CAB CFA ∠=∠，1CF =，则BF =______．16. 若关于x 的不等式组()411321x x x x a -⎧<+⎪⎨⎪+≥-+⎩至少有2个整数解，且关于y 的分式方程13211a y y-=---的解为非负整数，则所有满足条件的整数a 的值之和为______．17. 如图，以AB 为直径的O 与AC 相切于点A ，以AC 为边作平行四边形ACDE ，点D 、E 均在O 上，DE 与AB 交于点F ，连接CE ，与O 交于点G ，连接DG ．若10,8AB DE ==，则AF =______．DG =______．18. 我们规定：若一个正整数A 能写成2m n -，其中m 与n 都是两位数，且m 与n 的十位数字相同，个位数字之和为8，则称A 为“方减数”，并把A 分解成2m n -的过程，称为“方减分解”．例如：因为26022523=-，25与23的十位数字相同，个位数字5与3的和为8，所以602是“方减数”，602分解成26022523=-的过程就是“方减分解”．按照这个规定，最小的“方减数”是______．把一个“方减数”A 进行“方减分解”，即2A m n =-，将m 放在n 的左边组成一个新的四位数B ，若B 除以19余数为1，且22m n k +=（k 为整数），则满足条件的正整数A 为______．三、解答题：（本大题8个小题，第19题8分，其余每小题10分，共78分）解答时每小题必须给出必要的演算过程或推理步骤，画出必要的图形（包括辅助线），请将解答过程书写在答题卡中对应的位置上．19. 计算：（1）()()22x x y x y -++；（2）22111a a a a-⎛⎫+÷ ⎪+⎝⎭．20.为了解学生的安全知识掌握情况，某校举办了安全知识竞赛．现从七、八年级的学生中各随机抽取20名学生的竞赛成绩（百分制）进行收集、整理、描述、分析．所有学生的成绩均高于60分（成绩得分用x 表示，共分成四组：A ．6070x <≤；B ．7080x <≤；C ．8090x <≤；D ．90100x <≤），下面给出了部分信息：七年级20名学生的竞赛成绩为：66，67，68，68，75，83，84，86，86，86，86，87，87，89，95，95，96，98，98，100.八年级20名学生的竞赛成绩在C 组的数据是：81，82，84，87，88，89．七、八年级所抽学生的竞赛成绩统计表年级七年级八年级平均数8585中位数86b众数a 79根据以上信息，解答下列问题：（1）上述图表中=a ______，b =______，m =______；（2）根据以上数据分析，你认为该校七、八年级中哪个年级学生的安全知识竞赛成绩较好？请说明理由（写出一条理由即可）；（3）该校七年级有400名学生，八年级有500名学生参加了此次安全知识竞赛，估计该校七、八年级参加此次安全知识竞赛成绩优秀()90x >的学生人数是多少？21. 在学习了矩形与菱形的相关知识后，小明同学进行了更深入的研究，他发现，过矩形的一条对角线的中点作这条对角线的垂线，与矩形两边相交的两点和这条对角线的两个端点构成的四边形是菱形，可利用证明三角形全等得到此结论．根据他的想法与思路，完成以下作图与填空：（1）如图，在矩形ABCD 中，点O 是对角线AC 中点．用尺规过点O 作AC 的垂线，分别交AB ，CD 于点E ，F ，连接AF ，CE ．（不写作法，保留作图痕迹）（2）已知：矩形ABCD ，点E ，F 分别在AB ，CD 上，EF 经过对角线AC 的中点O ，且EF AC ⊥．求证：四边形AECF 是菱形．证明：∵四边形ABCD 是矩形，∴AB CD ．∴①，OCF OAE ∠=∠．∵点O 是AC 的中点，∴②．∴CFO AEO ≅△△（AAS ）．∴③．又∵OA OC =，∴四边形AECF 是平行四边形．∵EFAC ⊥，∴四边形AECF 是菱形．进一步思考，如果四边形ABCD 是平行四边形呢？请你模仿题中表述，写出你猜想结论：④．22. 为促进新质生产力的发展，某企业决定投入一笔资金对现有甲、乙两类共30条生产线的设备进行更新换代．（1）为鼓励企业进行生产线的设备更新，某市出台了相应的补贴政策．根据相关政策，更新1条甲类生产线的设备可获得3万元的补贴，更新1条乙类生产线的设备可获得2万元的补贴．这样更新完这30条生产线的设备，该企业可获得70万元的补贴．该企业甲、乙两类生产线各有多少条？（2）经测算，购买更新1条甲类生产线的设备比购买更新1条乙类生产线的设备需多投入5万元，用200万元购买更新甲类生产线的设备数量和用180万元购买更新乙类生产线的设备数量相同，那的的么该企业在获得70万元的补贴后，还需投入多少资金更新生产线的设备？23. 如图，在ABC 中，6AB =，8BC =，点P 为AB 上一点，过点P 作PQ BC ∥交AC 于点Q ．设AP 的长度为x ，点P ，Q 的距离为1y ，ABC 的周长与APQ △的周长之比为2y ．（1）请直接写出1y ，2y 分别关于x 的函数表达式，并注明自变量x 的取值范围；（2）在给定的平面直角坐标系中画出函数1y ，2y 的图象；请分别写出函数1y ，2y 的一条性质；（3）结合函数图象，直接写出12y y >时x 的取值范围．（近似值保留一位小数，误差不超过0.2）24. 如图，甲、乙两艘货轮同时从A 港出发，分别向B ，D 两港运送物资，最后到达A 港正东方向的C 港装运新的物资．甲货轮沿A 港的东南方向航行40海里后到达B 港，再沿北偏东60︒方向航行一定距离到达C 港．乙货轮沿A 港的北偏东60︒方向航行一定距离到达D 港，再沿南偏东30︒方向航行一定距离到达C 港．1.41≈1.73≈2.45≈）（1）求A ，C 两港之间距离（结果保留小数点后一位）；（2）若甲、乙两艘货轮的速度相同（停靠B 、D 两港的时间相同），哪艘货轮先到达C 港？请通过计算说明．25. 如图，在平面直角坐标系中，抛物线()240y ax bx a =++≠经过点()1,6-，与y 轴交于点C ，与x 轴交于A B ，两点（A 在B 的左侧），连接tan 4AC BC CBA ∠=，，．的（1）求抛物线的表达式；（2）点P 是射线CA 上方抛物线上的一动点，过点P 作PE x ⊥轴，垂足为E ，交AC 于点D ．点M 是线段DE 上一动点，MN y ⊥轴，垂足为N ，点F 为线段BC 的中点，连接AM NF ，．当线段PD 长度取得最大值时，求AM MN NF ++的最小值；（3）将该抛物线沿射线CA 方向平移，使得新抛物线经过（2）中线段PD 长度取得最大值时的点D ，且与直线AC 相交于另一点K ．点Q 为新抛物线上的一个动点，当QDK ACB ∠∠=时，直接写出所有符合条件的点Q 的坐标．26. 在ABC 中，AB AC =，点D 是BC 边上一点（点D 不与端点重合）．点D 关于直线AB 的对称点为点E ，连接,AD DE ．在直线AD 上取一点F ，使EFD BAC ∠∠=，直线EF 与直线AC 交于点G ．（1）如图1，若60,,BAC BD CD BAD α∠=︒<∠=，求AGE ∠的度数（用含α的代数式表示）；（2）如图1，若60,BAC BD CD ∠=︒<，用等式表示线段CG 与DE 之间的数量关系，并证明；（3）如图2，若90BAC ∠=︒，点D 从点B 移动到点C 的过程中，连接AE ，当AEG △为等腰三角形时，请直接写出此时CGAG的值．重庆市2024年初中学业水平暨高中招生考试数学试题（A 卷）（全卷共三个大题，满分150分，考试时间120分钟）注意事项：1.试题的答案书写在答题卡上，不得在试题卷上直接作答；2.作答前认真阅读答题卡上的注意事项；3.作图（包括作辅助线）请一律用黑色2B 铅笔完成；4.考试结束，由监考人员将试题卷和答题卡一并收回．参考公式：抛物线()20y ax bx c a =++≠的顶点坐标为24,24b ac b a a ⎛⎫-- ⎪⎝⎭，对称轴为2bx a =-．一、选择题：（本大题10个小题，每小题4分，共40分）在每个小题的下面，都给出代号为A 、B 、C 、D 的四个答案，其中只有一个是正确的，请将答题卡上题号右侧确答案所对应的方框涂黑．1. 下列四个数中，最小的数是（ ）A. 2- B. 0C. 3D. 12-【答案】A 【解析】【分析】本题考查了有理数比较大小，解题的关键是掌握比较大小的法则．根据正数大于0，0大于负数，两个负数比较大小，绝对值大的反而小，即可得到答案．【详解】解：∵13022>>->-，∴最小的数是2-；故选：A ．2. 下列四种化学仪器的示意图中，是轴对称图形的是（ ）A. B.C. D.【答案】C 【解析】【分析】此题考查了轴对称图形的概念，根据概念逐一判断即可，如果一个图形沿一条直线折叠，直线两旁的部分能够互相重合，这个图形叫做轴对称图形，这条直线叫做对称轴，这时，我们也可以说这个图形关于这条直线(成轴）对称，熟练掌握知识点是解题的关键．【详解】A 、不是轴对称图形，故本选项不符合题意；B 、不是轴对称图形，故本选项不符合题意；C 、是轴对称图形，故本选项符合题意；D 、不是轴对称图形，故本选项不符合题意；故选：C ．3. 已知点()3,2-在反比例函数()0ky k x=≠的图象上，则k 的值为（ ）A. 3- B. 3C. 6- D. 6【答案】C 【解析】【分析】本题考查了待定系数法求反比例解析式，把()3,2-代入()0ky k x=≠求解即可．【详解】解：把()3,2-代入()0ky k x=≠，得326k =-⨯=-．故选C ．4. 如图，AB CD ∥，165∠=︒，则2∠的度数是（ ）A. 105︒B. 115︒C. 125︒D. 135︒【答案】B【解析】∠=∠=︒，由邻补角性质得【分析】本题主要考查了平行线的性质，根据平行线的性质得3165∠+∠=︒，然后求解即可，熟练掌握两直线平行，同位角相等是解题的关键．23180【详解】解：如图，∥，∵AB CD∠=∠=︒，∴3165∠+∠=︒，∵23180∠=︒，∴2115故选：B．5. 若两个相似三角形的相似比是1:3，则这两个相似三角形的面积比是（）A. 1:3B. 1:4C. 1:6D. 1:9【答案】D【解析】【分析】此题考查了相似三角形的性质，根据“相似三角形的面积比等于相似比的平方”解答即可．【详解】解：两个相似三角形的相似比是1:3，则这两个相似三角形的面积比是1:9，故选：D．6. 烷烃是一类由碳、氢元素组成的有机化合物质，下图是这类物质前四种化合物的分子结构模型图，其中灰球代表碳原子，白球代表氢原子．第1种如图①有4个氢原子，第2种如图②有6个氢原子，第3种如图③有8个氢原子，……按照这一规律，第10种化合物的分子结构模型中氢原子的个数是（ ）A. 20B. 22C. 24D. 26【答案】B【解析】【分析】本题考查数字的变化类，根据图形，可归纳出规律表达式的特点，再解答即可．【详解】解：由图可得，第1种如图①有4个氢原子，即2214+⨯=第2种如图②有6个氢原子，即2226+⨯=第3种如图③有8个氢原子，即2238+⨯=⋯，∴第10种化合物的分子结构模型中氢原子的个数是：221022+⨯=；故选：B ．7. 已知m =，则实数m 的范围是（ ）A. 23m << B. 34m << C. 45m << D. 56m <<【答案】B【解析】【分析】此题考查的是求无理数的取值范围，二次根式的加减运算，掌握求算术平方根的取值范围的方法是解决此题的关键．先求出m ==，即可求出m 的范围．【详解】解：∵m =-=-==，∵34<<，∴34m <<，故选：B ．8. 如图，在矩形ABCD 中，分别以点A 和C 为圆心，AD 长为半径画弧，两弧有且仅有一个公共点．若4=AD ，则图中阴影部分的面积为（ ）A. 328π- B. 4π-C. 324π- D. 8π-【答案】D【解析】【分析】本题考查扇形面积的计算，勾股定理等知识．根据题意可得28AC AD ==，由勾股定理得出AB =，用矩形的面积减去2个扇形的面积即可得到结论．【详解】解：连接AC ，根据题意可得28AC AD ==，∵矩形ABCD ，∴4AD BC ==，90ABC ∠=︒，在Rt ABC △中，AB ==，∴图中阴影部分的面积2904428360ππ⨯=⨯-⨯=．故选：D ．9. 如图，在正方形ABCD 的边CD 上有一点E ，连接AE ，把AE 绕点E 逆时针旋转90︒，得到FE ，连接CF 并延长与AB 的延长线交于点G ．则FG C E的值为（ ）A.B. C. D.【答案】A【解析】【分析】过点F 作DC 延长线的垂线，垂足为点H ，则90H ∠=︒，证明ADE EHF ≌，则1AD EH ==，设DE HF x ==，得到HF CH x ==，则45HCF ∠=︒，故CF =，同理可求CG ==)1FG CG CF x =-=-，因此FGCE ==．【详解】解：过点F 作DC 延长线的垂线，垂足为点H ，则90H ∠=︒，由旋转得,90EA EF AEF =∠=︒，∵四边形ABCD 是正方形，∴90D Ð=°，DC AB ∥，DA DC BC ==，设1DA DC BC ===，∴D H ∠=∠，∵12AEH AEF D ∠=∠+∠=∠+∠，∴12∠=∠，∴ADE EHF ≌，∴DE HF =，1AD EH ==，设DE HF x ==，则1CE DC DE x =-=-，∴()11CH EH EC x x =-=--=，∴HF CH x ==，而90H ∠=︒，∴45HCF ∠=︒，∴sin 45HFCF ==︒，∵DC AB ∥，∴45HCF G ∠=∠=︒，同理可求CG ==∴)1FG CG CF x =-==-，∴FG CE ==，故选：A ．【点睛】本题考查了正方形的性质，全等三角形的判定与性质，解直角三角形，旋转的性质，正确添加辅助线，构造“一线三等角全等”是解题的关键．10. 已知整式1110:n n n n M a x a x a x a --++++ ，其中10,,,n n a a - 为自然数，n a 为正整数，且1105n n n a a a a -+++++= ．下列说法：①满足条件的整式M 中有5个单项式；②不存在任何一个n ，使得满足条件的整式M 有且只有3个；③满足条件的整式M 共有16个．其中正确的个数是（ ）A. 0B. 1C. 2D. 3【答案】D【解析】【分析】本题考查的是整式的规律探究，分类讨论思想的应用，由条件可得04n ≤≤，再分类讨论得到答案即可．【详解】解：∵10,,,n n a a - 为自然数，n a 为正整数，且1105n n n a a a a -+++++= ，∴04n ≤≤，当4n =时，则2104345a a a a a +++++=，∴41a =，23100a a a a ====，满足条件的整式有4x ，当3n =时，则210335a a a a ++++=，∴()()3210,,,2,0,0,0a a a a =，()1,1,0,0，()1,0,1,0，()1,0,0,1，满足条件的整式有：32x ，32x x +，3x x +，31x +，当2n =时，则21025a a a +++=，∴()()210,,3,0,0a a a =，()2,1,0，()2,0,1，()1,2,0，()1,0,2，()1,1,1，满足条件的整式有：23x ，22x x +，221x +，22x x +，22x +，21x x ++；当1n =时，则1015a a ++=，∴()()10,4,0a a =，()3,1，()1,3，()2,2，满足条件的整式有：4x ，31x +，3x +，22x +；当0n =时，005a +=，满足条件的整式有：5；∴满足条件的单项式有：4x ，32x ，23x ，4x ，5，故①符合题意；不存在任何一个n ，使得满足条件的整式M 有且只有3个；故②符合题意；满足条件的整式M 共有1464116++++=个．故③符合题意；故选D二、填空题：（本大题8个小题，每小题4分，共32分）请将每小题的答案直接填在答题卡中对应的横线上．11. 计算：011(3)()2π--+＝_____．【答案】3【解析】【分析】根据零指数幂和负指数幂的意义计算．【详解】解：011(3)(1232π--+=+=，故答案为：3．【点睛】本题考查了整数指数幂的运算，熟练掌握零指数幂和负指数幂的意义是解题关键．12. 如果一个多边形的每一个外角都是40︒，那么这个多边形的边数为______．【答案】9【解析】【分析】本题考查了多边形的外角和定理，用外角和360︒除以40︒即可求解，掌握多边形的外角和等于360︒是解题的关键．【详解】解：360409︒÷︒=，∴这个多边形的边数是9，故答案为：9．13. 重庆是一座魔幻都市，有着丰富的旅游资源．甲、乙两人相约来到重庆旅游，两人分别从A 、B 、C 三个景点中随机选择一个景点游览，甲、乙两人同时选择景点B 的概率为_____．【答案】19【解析】【分析】本题考查了画树状图法或列表法求概率，根据画树状图法求概率即可，熟练掌握画树状图法或列表法求概率是解题的关键．【详解】解：画树状图如下：由图可知，共有9种等可能的情况，其中甲、乙两人同时选择景点B 的情况有1种，∴甲、乙两人同时选择景点B 的的概率为19，故答案为：19．14. 随着经济复苏，某公司近两年的总收入逐年递增．该公司2021年缴税40万元，2023年缴税48.4万元，该公司这两年缴税的年平均增长率是______．【答案】10%【解析】【分析】本题主要考查一元二次方程的应用．设平均增长率为x ，然后根据题意可列方程进行求解．【详解】解：设平均增长率为x ，由题意得：()240148.4x +=，解得：10.110%x ==，2 2.1x =-（不符合题意，舍去）；故答案为：10%．15. 如图，在ABC 中，延长AC 至点D ，使CD CA =，过点D 作DE CB ∥，且DE DC =，连接AE 交BC 于点F ．若CAB CFA ∠=∠，1CF =，则BF =______．【答案】3【解析】【分析】先根据平行线分线段成比例证AF EF =，进而得22DE CD AC CF ====，4AD =，再证明CAB DEA ≌，得4BC AD ==，从而即可得解．【详解】解：∵CD CA =，过点D 作DE CB ∥，CD CA =，DE DC =，∴1FA CA FE CD==，CD CA DE ==，∴AF EF =，∴22DE CD AC CF ====，∴4AD AC CD =+=，∵DE CB ∥，∴CFA E ∠∠=，ACB D ∠∠=，∵CAB CFA ∠=∠，∴CAB E ∠∠=，∵CD CA =，DE CD =，∴CA DE =，∴CAB DEA ≌，∴4BC AD ==，∴3BF BC CF =-=，故答案为：3，【点睛】本题主要考查了平行线的性质，三角形的中位线定理，平行线分线段成比例以及全等三角形的判定及性质，熟练掌握三角形的中位线定理，平行线分线段成比例以及全等三角形的判定及性质是解题的关键．16. 若关于x 的不等式组()411321x x x x a -⎧<+⎪⎨⎪+≥-+⎩至少有2个整数解，且关于y 的分式方程13211a y y-=---的解为非负整数，则所有满足条件的整数a 的值之和为______．【答案】16【解析】【分析】本题考查了分式方程的解，以及解一元一次不等式组．先解不等式组，根据关于x 的一元一次不等式组至少有两个整数解，确定a 的取值范围8a ≤，再把分式方程去分母转化为整式方程，解得22a y -=，由分式方程的解为非负整数，确定a 的取值范围2a ≥且4a ≠，进而得到28a ≤≤且4a ≠，根据范围确定出a 的取值，相加即可得到答案．【详解】解：()411321x x x x a -⎧<+⎪⎨⎪+≥-+⎩①②，解①得：4x <，解②得：23a x -≥， 关于x 的一元一次不等式组至少有两个整数解，∴223a -≤，解得8a ≤，解方程13211a y y -=---，得22a y -=， 关于y 的分式方程的解为非负整数，∴202a -≥且212a -≠，2a -是偶数，解得2a ≥且4a ≠，a 是偶数，∴28a ≤≤且4a ≠，a 是偶数，则所有满足条件的整数a 的值之和是26816++=，故答案为：16．17. 如图，以AB 为直径的O 与AC 相切于点A ，以AC 为边作平行四边形ACDE ，点D 、E 均在O 上，DE 与AB 交于点F ，连接CE ，与O 交于点G ，连接DG ．若10,8AB DE ==，则AF =______．DG =______．【答案】①. 8 ②. 【解析】【分析】连接DO 并延长，交O 于点H ，连接GH ，设CE 、AB 交于点M ，根据四边形ACDE 为平行四边形，得出∥D E A C ，8AC DE ==，证明AB DE ⊥，根据垂径定理得出142DF EF DE ===，根据勾股定理得出3OF ==，求出538AF OA OF =+=+=；证明EFM CAM ∽，得出EF FM AC AM =，求出83FM =，根据勾股定理得出EM ===，证明EFM HGD ∽，得出FM EM DG DH =，求出DG =．【详解】解：连接DO 并延长，交O 于点H ，连接GH ，设CE 、AB 交于点M ，如图所示：∵以AB 为直径的O 与AC 相切于点A ，∴AB AC ⊥，∴90CAB ∠=︒，∵四边形ACDE 为平行四边形，∴∥D E A C ，8AC DE ==，∴90BFD CAB ==︒∠∠，∴AB DE ⊥，∴142DF EF DE ===，∵10AB =，∴152DO BO AO AB ====，∴3OF ==，∴538AF OA OF =+=+=；∵∥D E A C ，∴EFM CAM ∽，∴EF FMAC AM =，∴48FMAF FM =-，即488FMFM =-，解得：83FM =，∴EM ===∵DH 为直径，∴90DGH ∠=︒，∴DGH EFM ∠=∠，∵ DG DG =，∴DEG DHG =∠∠，∴EFM HGD ∽，∴FMEMDG DH =，即83310DG =，解得：DG =．故答案为：8【点睛】本题主要考查了平行四边形的性质，垂径定理，圆周角定理，切线的性质，勾股定理，三角形相似的判定和性质，解题的关键是作出辅助线，熟练掌握三角形相似的判定方法．18. 我们规定：若一个正整数A 能写成2m n -，其中m 与n 都是两位数，且m 与n 的十位数字相同，个位数字之和为8，则称A 为“方减数”，并把A 分解成2m n -的过程，称为“方减分解”．例如：因为26022523=-，25与23的十位数字相同，个位数字5与3的和为8，所以602是“方减数”，602分解成26022523=-的过程就是“方减分解”．按照这个规定，最小的“方减数”是______．把一个“方减数”A 进行“方减分解”，即2A m n =-，将m 放在n 的左边组成一个新的四位数B ，若B 除以19余数为1，且22m n k +=（k 为整数），则满足条件的正整数A 为______．【答案】①. 82 ②. 4564【解析】【分析】本题考查了新定义，设10m a b =+，则108n a b =+-（19a ≤≤，08b ≤≤）根据最小的“方减数”可得10,18m n ==，代入，即可求解；根据B 除以19余数为1，且22m n k +=（k 为整数），得出34719a b ++为整数，308a b ++是完全平方数，在19a ≤≤，08b ≤≤，逐个检验计算，即可求解．【详解】①设10m a b =+，则108n a b =+-（19a ≤≤，08b ≤≤）由题意得：()()2210108m n a b a b -=+-+-，∵19a ≤≤，“方减数”最小，∴1a =，则10m b =+，18n b =-，∴()()2222101810020188221m n b b b b b b b -=+--=++-+=++，则当0b =时，2m n -最小，为82，故答案为：82；②设10m a b =+，则108n a b =+-（19a ≤≤，08b ≤≤）∴10001001081010998B a b a b a b =+++-=++∵B 除以19余数为1，∴1010997a b ++能被19整除∴134********B a b a b -++=++为整数，又22m n k +=（k 为整数）∴()210108308a b a b a b +++-=++是完全平方数，∵19a ≤≤，08b ≤≤∴308a b ++最小为49，最大为256即716k ≤≤设34719a b t ++=，t 为正整数，则13t ≤≤当1t =时，3412a b +=，则334b a =-，则330830384a b a a ++=+-+是完全平方数，又19a ≤≤，08b ≤≤，无整数解，当2t =时，3431a b +=，则3134a b -=,则3133083084a a b a -++=++是完全平方数，又19a ≤≤，08b ≤≤，无整数解，当3t =时，3450a b +=，则5034a b -=，则5033083084a ab a -++=++是完全平方数，经检验，当6,8a b ==时，3473648757193a b ++=⨯+⨯+==⨯，23068819614⨯++==，3,14t k ==，∴68,60m n ==，∴268604564A =-=故答案为：82，4564．三、解答题：（本大题8个小题，第19题8分，其余每小题10分，共78分）解答时每小题必须给出必要的演算过程或推理步骤，画出必要的图形（包括辅助线），请将解答过程书写在答题卡中对应的位置上．19 计算：（1）()()22x x y x y -++；（2）22111a a a a -⎛⎫+÷ ⎪+⎝⎭．【答案】（1）222x y +；（2）11a a +-．【解析】【分析】（1）根据单项式乘以多项式和完全平方公式法则分别计算，然后合并同类项即可；（2）先将括号里的异分母分式相减化为同分母分式相减，再算分式的除法运算得以化简；本题考查了单项式乘以多项式，完全平方公式和分式的化简，熟练掌握运算法则是解题的关键．【小问1详解】解：原式22222x xy x xy y =-+++，222x y =+；【小问2详解】解：原式()()()1111a a a a a a +-+=÷+，()()()11·11a a a a a a ++=+-，11a a +=-．20. 为了解学生的安全知识掌握情况，某校举办了安全知识竞赛．现从七、八年级的学生中各随机抽取20名学生的竞赛成绩（百分制）进行收集、整理、描述、分析．所有学生的成绩均高于60分（成绩得分用x 表示，共分成四组：A ．6070x <≤；B ．7080x <≤；C ．8090x <≤；D ．90100x <≤），下面给出了部分信息：七年级20名学生的竞赛成绩为：.66，67，68，68，75，83，84，86，86，86，86，87，87，89，95，95，96，98，98，100.八年级20名学生的竞赛成绩在C 组的数据是：81，82，84，87，88，89．七、八年级所抽学生的竞赛成绩统计表年级七年级八年级平均数8585中位数86b 众数a 79根据以上信息，解答下列问题：（1）上述图表中=a ______，b =______，m =______；（2）根据以上数据分析，你认为该校七、八年级中哪个年级学生的安全知识竞赛成绩较好？请说明理由（写出一条理由即可）；（3）该校七年级有400名学生，八年级有500名学生参加了此次安全知识竞赛，估计该校七、八年级参加此次安全知识竞赛成绩优秀()90x >的学生人数是多少？【答案】（1）86，87.5，40；（2）八年级学生竞赛成绩较好，理由见解析；（3）该校七、八年级参加此次安全知识竞赛成绩优秀的学生人数是320人．【解析】【分析】（1）根据表格及题意可直接进行求解；（2）根据平均分、中位数及众数分析即可得出结果；（3）由题意可得出参加此次竞赛活动成绩优秀的百分比，然后可进行求解；本题主要考查扇形统计图及中位数、众数、平均数，熟练掌握扇形统计图及中位数、众数、平均数是解题的关键．【小问1详解】根据七年级学生竞赛成绩可知：86出现次数最多，则众数为86，八年级竞赛成绩中A 组：2010%2⨯=（人），B 组：2020%4⨯=（人），C 组：6人，所占百分比为6100%30%20⨯=D 组：202468---=（人）所占百分比为%110%20%30%40%m =---=，则40m =，∴八年级的中位数为第1011、个同学竞赛成绩的平均数，即C 组第45、个同学竞赛成绩的平均数878887.52b +==，故答案为：86，87.5，40；【小问2详解】八年级学生竞赛成绩较好，理由：七、八年级的平均分均为85分，八年级的中位数高于七年级的中位数，整体上看八年级学生竞赛成绩较好；【小问3详解】640040%50032020⨯+⨯=（人），答：该校七、八年级参加此次安全知识竞赛成绩优秀的学生人数是320人．21. 在学习了矩形与菱形的相关知识后，小明同学进行了更深入的研究，他发现，过矩形的一条对角线的中点作这条对角线的垂线，与矩形两边相交的两点和这条对角线的两个端点构成的四边形是菱形，可利用证明三角形全等得到此结论．根据他的想法与思路，完成以下作图与填空：（1）如图，在矩形ABCD 中，点O 是对角线AC 的中点．用尺规过点O 作AC 的垂线，分别交AB ，CD 于点E ，F ，连接AF ，CE ．（不写作法，保留作图痕迹）（2）已知：矩形ABCD ，点E ，F 分别在AB ，CD 上，EF 经过对角线AC 的中点O ，且EF AC ⊥．求证：四边形AECF 是菱形．证明：∵四边形ABCD 是矩形，∴AB CD ．∴①，OCF OAE ∠=∠．∵点O 是AC 的中点，∴②．∴CFO AEO ≅△△（AAS ）．∴③．又∵OA OC =，∴四边形AECF 是平行四边形．∵EF AC ⊥，∴四边形AECF 是菱形．进一步思考，如果四边形ABCD 是平行四边形呢？请你模仿题中表述，写出你猜想的结论：④．【答案】（1）见解析（2）①OFC OEA ∠=∠；②OA OC =；③OF OE =；④四边形AECF 是菱形【解析】【分析】本题主要考查了矩形的性质，平行四边形的性质与判定，菱形的判定，垂线的尺规作图：（1）根据垂线的尺规作图方法作图即可；（2）根据矩形或平行四边形的对边平行得到OFC OEA ∠=∠，OCF OAE ∠=∠，进而证明()AAS CFO AEO ≌，得到OF OE =，即可证明四边形AECF 是平行四边形．再由EF AC ⊥，即可证明四边形AECF 是菱形．【小问1详解】解：如图所示，即为所求；【小问2详解】证明：∵四边形ABCD 是矩形，∴AB CD ．∴OFC OEA ∠=∠，OCF OAE ∠=∠．∵点O 是AC 的中点，∴OA OC =．∴()AAS CFO AEO ≌．∴OF OE =．又∵OA OC =，∴四边形AECF 平行四边形．∵EF AC ⊥，∴四边形AECF 是菱形．猜想：过平行四边形的一条对角线的中点作这条对角线的垂线，与平行四边形两边相交的两点和这条对角线的两个端点构成的四边形是菱形；证明：∵四边形ABCD 是平行四边形，∴AB CD ．∴OFC OEA ∠=∠，OCF OAE ∠=∠．∵点O 是AC 的中点，∴OA OC =．∴()AAS CFO AEO ≌．∴OF OE =．又∵OA OC =，∴四边形AECF 是平行四边形．∵EF AC ⊥，∴四边形AECF 是菱形．故答案为：①OFC OEA ∠=∠；②OA OC =；③OF OE =；④四边形AECF 是菱形．22. 为促进新质生产力的发展，某企业决定投入一笔资金对现有甲、乙两类共30条生产线的设备进行更新换代．（1）为鼓励企业进行生产线的设备更新，某市出台了相应的补贴政策．根据相关政策，更新1条是。

专业课原理概述部分一、选择题（每题1分，共5分）1. 微分学的中心概念是（）。

A. 极限B. 导数C. 微分D. 积分A. f(x) = |x|B. f(x) = x^2 + 1C. f(x) = 1/xD. f(x) =√x3. 不定积分∫(1/x)dx的结果是（）。

A. ln|x| + CB. x + CC. x^2/2 + CD. e^x + C4. 多元函数f(x, y) = x^2 + y^2在点(1, 1)处的偏导数f_x'是（）。

A. 0B. 1C. 2D. 35. 线性方程组Ax=b有唯一解的条件是（）。

A. A为满秩矩阵B. A为方阵C. A为可逆矩阵D. A为零矩阵二、判断题（每题1分，共5分）1. 极限存在的充分必要条件是左极限等于右极限。

（）2. 任何连续函数都一定可导。

（）3. 二重积分可以转换为累次积分。

（）4. 拉格朗日中值定理是罗尔定理的推广。

（）5. 两个矩阵的乘积一定是方阵。

（）三、填空题（每题1分，共5分）1. 函数f(x) = e^x在x=0处的导数f'(0)等于______。

2. 若函数f(x)在区间[a, b]上连续，则该函数在该区间上______。

3. 微分方程y'' y = 0的通解是______。

4. 矩阵A的行列式记作______。

5. 向量组线性相关的充分必要条件是______。

四、简答题（每题2分，共10分）1. 请简要说明罗尔定理的内容。

2. 什么是函数的极值？如何求函数的极值？3. 简述泰勒公式的意义。

4. 什么是特征值和特征向量？5. 简述空间解析几何中直线的方程。

五、应用题（每题2分，共10分）1. 计算极限lim(x→0) (sin x)/x。

2. 求函数f(x) = x^3 3x的导数。

3. 计算不定积分∫(cos x)dx。

4. 求解微分方程y' = 2x。

5. 计算二重积分∬D (x^2 + y^2) dxdy，其中D是由x轴，y轴和直线x+y=1围成的区域。

大学英语（四）课程考试A 卷 适用于；考试日期：； 试卷所需时间：120分钟 闭卷；试卷A 总分：100分。

Part I Listening Comprehension (30 points) Section A Short Conversations ( 10 points) Directions: In this section, you will hear 10 short conversations. At the end of each conversation, one question will be asked about what was said. Both the conversation and the question will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A), B), C) and D), and decide which is the best answer. Then mark the corresponding letter on the Answer Sheet with a single line through the centre. 1. A. 3 blocks ahead. B. On the 3rd Street. C. At the 3rd Avenue. D. On the 5th Street. 2. A. To punish him. B. To pick him up. C. To reward him. D. To ignore him. 3. A. Theater. B. Restaurant. C. Airport. D. Train station. 4. A. She doesn ’t like either of them. B. John copied it from Jim. C. Jim copied it from John. D. One is the copy from the other. 5. A. Peter is going to fly to New York. B. Peter is going to fly to London next week. C. Peter went to London last week. D. Peter will stay in New York. 6. A. He feels Mike did a good thing. B. He doesn ’t think Mike should move. C. H e thinks it’s better to invest later. D. He doesn ’t think Mike should invest money on stocks. 7. A. Go to a movie. B. Go to her classes. C. Shop for some clothes. D. Buy some new glasses. 8. A. Because he doesn ’t have a TV . B. Because he hates to be bothered. C. B ecause he isn’t watching TV . D. Because he doesn ’t like any of the programs. 9. A. $ 100. B. $ 150. C. $ 200. D. $ 250. 10. A. She likes classical music. B. She needs 100 records. C. She prefers to have the same house I have. D. She is a jazz fan. Section B Long Conversation ( 5 points) Directions: In this section, you will hear one long conversation. At the end of the conversation, some questions will be asked about what was said. Both the conversation and the questions will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A), B), C) and D), and decide which is the best answer. Then mark the corresponding letter on the Answer Sheet with a single line through the centre. 11. A. It ’s expensive. B. They are celebrating a birthday. C. It was recommended by a friend. D. They had dinner here before. 12. A. She wants to check the price. B. She wants to see if the menu is in French. C. She is in a hurry to eat. D. She spends a long time choosing her food. 13. A. A year. B. Only a minute. C. A month. D. A long time. 14. A. Snails are not on the menu. B. The restaurant doesn ’t have any left. C. They want shrimp cocktail instead. D. They are afraid of getting sick. 15. A. French cheese and white wine. B. Seafood. C. Duck. D. Salad and French cheese. Section C Passage ( 5 points) Directions: In this section, you will hear one short passage. At the end of the passage, you will hear some questions. Both the passage and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked A) B) C) and D). Then mark the corresponding letter on Answer sheet with a single line through the centre. 16. A. On TV . B. On the radio C. In the newspaper. D. In a magazine 17. A. A scientific research. B. An invention. C. A visit to a scientist. D. A prize for some scientific discovery.18. A. Unpleasant. B. Cooperative. C. Sympathetic. D. Doubtful. 19. A. He refuted him. B. He went to the library. C. He went to the TV station D. He changed his major 20. A. After the age of 50. B. After the age of 30. C. Between the ages of 25 and 30. D. Between the ages of 30 and 50. Section D ( 10 points) Directions: In this section, you will hear a VOA Special English Report three times, and then fill in the blanks with the exact words you hear from the recording. We answered a question last week about how American college students findjobs after they (21)_________________. Now, we discuss foreign graduates. The院系： 班级： 姓名：学号：考场地点装订线(22)________________ for employing foreign workers in the United States is long. It involves different government agencies. It also involves (23)_____________________________________. For example, the American Recovery and Reinvestment Act that President Obama signed into law in February dealt with this issue. It included conditions against foreign workers displacing qualified Americans at companies that (24)________________________________. Job (25)______________ have slowed in some industries. But the economic downturn has cost millions of jobs and recovery will take some time. Foreign graduates need a job (26)________________ to get an H-1B visa. This is a (27)_________________ visa for work in the person’s area of specialty. The employer is the one who (28)_______________ for it. The visa is good for 3 years and may be extended for another 3 years. Cheryl Gilman directs visa services at the University of Southern California in Los Angeles. She noted that H-1B visas were still (29)_________________ for next year. This tells her that the recession is preventing employers from (30)_________________ as many foreign nationals as they have in the past. Part II Reading Comprehension (30 points) Section A Directions: There are two passages in this part. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A) , B) , C) and D). You should decide on the best choice and mark the corresponding letter on the Answer Sheet with a single line through the center. Passage One As people generally use the word “honor ” they do not do so in the context of thinking about moral virtue. As a result they often confuse honor with fame. A virtuous person is an honorable person, a person who ought to be honored by the community in which he or she lives. But the virtuous person does not seek honor, being secure in his or her own self-respect. Lack of honor does not detract from the efficacy of moral virtue as an operative factor in the pursuit of happiness —as a means to leading a good human life. Virtuous persons may be considered fortunate if their virtue is recognized and publicly applauded. Persons lacking moral virtue can achieve fame as readily as, or perhaps more easily than, those who have a high degree of moral virtue. Fame belongs to the great, the outstanding, and the exceptional, without regard to their virtue or lack of it. Infamy is fame, no less than popularity. The great scoundrel can be as famous as the great hero. There can be famous villains as well as famous saints. Existing in the reputation a person has, regardless of his or her accomplishments, fame does not tarnish as honor does when it is unmerited. We normally desire the esteem of our fellow human beings, but is not this wish for the esteem of others a desire for fame rather than for honor? A virtuous person will not seek fame or be unhappy for lack of it. For fame can be enjoyed by bad men and women, as well as good. When it is enjoyed by virtuous persons without being sought by them, it is not distinguishable from honor, for then it is deserved. 31. What does this passage mainly talk about? A. A virtuous person achieves both honor and fame. B. A virtuous person does not seek honor or fame. C. Honor and fame are different concepts. D. Honor and fame are not distinguishable. 32. A virtuous person leads a good human life by means of _________. A. presuming happiness B. achieving moral virtue C. seeking honor D. seeking fame 33. What tends to tarnish with time? A. The reputation a person has. B. A high degree of moral virtue. C. A person ’s accomplishments. D. Honor that is undeserved. 34. Fame differs from honor in that _______. A. bad men and women can enjoy fame B. the great people can enjoy fame C. fame can fade in color D. virtuous persons will not seek fame 35. Which of the following statements is TURE? A. A virtuous person deserves honor. B. A famous person deserves honor. C. A virtuous person is publicly identified. D. A famous person has great accomplishments. Passage Two If you want to teach your children how to say sorry, you must be good at saying it yourself, especially to your own children. But how you say it can be quite tricky. If you s ay to your children “I’m sorry I got angry with you, but …”, what follows that “but” can render the apology ineffective: “I had a bad day” or “your noise was giving me a headache ” leaves the person who has been injured feeling that he should be apologizing for his bad behavior in expecting an apology. Another method by which people appear to apologize without actually doing so is to say “I’m sorry you’re upset”; this suggests that you are somehow at fault for allowing yourself to get upset by what the other person has done.院系：班级： 姓名：学号：考场地点装订线Then there is the general, all covering apology, which avoids the necessity of identifying a specific act that was particularly hurtful or insulting, and which the person who is apologizing should promise never to do again. Saying “I’m useless as a parent” does not commit a person to any specific improvement. These pseudo-apologies are used by people who believe saying sorry shows weakness. Parents who wish to teach their children to apologize should see it as a sign of strength, and therefore not resort to these pseudo-apologies. But even when presented with examples of genuine contrition, children still need help to become aware of the complexities of saying sorry. A three-year-old might need help in understanding that other children feel pain just as he does, and that hitting a playmate over the head with a heavy toy requires an apology. A six-year-old might need reminding that spoiling other children’s expectations can require an apology. A 12-year-old might need to be shown that raiding the biscuit tin without asking permission is acceptable, but that borrowing a parent’s clothes without permission is not. 36. If a mother adds “but” to an apology, _______. A. she doesn’t feel that she should have apologized B. she does not realize that the child has been hurt C. the child may find the apology easier to accept D. the child may feel that he owes her an apology 37. According to the author, saying “I’m sorry you’re upset” most probably means “_______”. A. You have good reason to get upset B. I’m aware you’re upset, but I’m not to blame C. I apologize for hurting your feelings D. I’m at fault for making you upset 38. It is not advisable to use the general, all-covering apology because _______. A. it gets one into the habit of making empty promises B. it may make the other person feel guilty C. it is vague and ineffective D. it is hurtful and insulting 39. We learn from the last paragraph that in teaching children to say sorry _______. A. the complexities involved should be ignored B. their ages should be taken into account C. parents need to set them a good example D. parents should be patient and tolerant 40. It can be inferred from the passage that apologizing properly is _______. A. a social issue calling for immediate attention B. not necessary among family membersC. a sign of social progressD. not as simple as it seems Section B: Directions: In this section, there is a passage with ten blanks. You are required to select one word for each blank from a list of choices given in a word bank following the passage. Read the passage through carefully before making your choices. Each choice in the blank is identified by a letter. You may not use any of the words in the bank more than once. Blanks 41 to 50 are based on the following passage. There are two factors which determine an individual ’s intelligence. The first is the sort of brain he is born with. Human brains differ 41 , some being more capable than others. But no matter how good a brain he has to begin with, a (an)42 will have a low intelligence unless he has opportunities to learn. So the second factor in what happens to the individual is the sort of environment in which he is 43 . If an individual is handicapped environmentally, it is likely that his brain will fail to develop. And he will never 44 the level of intelligence of which he is capable. The importance of environment in determining an individual ’s intelligence can be 45 by the case history of the identical twins, Peter and Mark. Being identical, the twins had identical brain at birth, and their growth processes were the same. When the twins were three months old, their parents died, and they were placed in 46 foster homes. Peter was reared by parents of low intelligence in an isolated community with poor 47 opportunities. Mark was reared in the home of well-to-do parents who had been to college. He was read to as a child, sent to good schools, and given every opportunity to be 48 intellectually. This environmental difference continued until the twins were in their late teens, when they were given tests to 49 their intelligence. Mark ’s I.Q. was 125, twenty-five points higher than the 50 , and fully forty points higher than his identical brother. Given equal opportunities, the twins, having identical brains, would have scored at roughly the same level.院系： 班级： 姓名：学号：考场地点装订线Part III Vocabulary and Structure (10 points) Directions: There are 20 incomplete sentences in this part. For each sentence there are four choices marked A, B, C and D. Choose the One answer that best completes the sentence. 51. The boy wanted to ride his bicycle in the street, but his mother told him ____. A. not to B. not to do C. not do it D. do not to 52. Would you like a cup of coffee ____shall we get down to business right away? A. and B. then C. or D. otherwise 53. Not until all the fish died in the river ____how serious the pollution was. A. did the villagers realize B. the villagers realized C. the villagers did realize D. didn't the villagers realize 54. I ____that we would be able to leave tomorrow, but it's beginning to look difficult. A. hoped B. was hoping C. had hoped D. am hoping 55. A study shows that students living in non-smoking dorms are less likely to ____the habit of smoking. A. make up B. turn up C. draw up D. pick up 56. Many personnel managers say it is getting harder and harder to____honest applicants from the growing number of dishonest ones. A. distinguish B. disguise C. dissolve D. discount 57. According to the key witnesses, a peculiarly big nose is the criminal's most memorable facial____. A. feature B. hint C. spot D. signature 58. It's good to know that quite a few popular English expressions actually ____from the Bible. A. acquire B. obtain C. derive D. result 59. After working all day, he was so tired that he was in no____ to go to the party with us. A. taste B. mood C. sense D. emotion 60. There is already clear ____to show that plants and animals are being affected by climate change. A. witness B. certification C. identity D. evidence 61. Last year the advertising rate ____ by 20 percent. A. raised B. aroused C. arose D. rose 62. The student was just about to ______ the question, when suddenly he found the answer. A. arrive at B. submit to C. give in D. work out 63. Suddenly she grabbed her stomach and ______. A. threw away B. threw in C. threw up D. threw off 64. They have brought her out of the operating room, but she ’s not fully ____ yet. A. cautious B. conscience C. conscious D. confused 65. He _____ the job because it involved too much traveling. A. turns in B. turns out C. turns over D. turns down 66.To some _______, Mary still does not understand this unit. But she herself does not believe so. A. extend B. part C. extent D. content 67. He checked carefully to _______ the possible errors in his design. A. eliminate B. exceed C. enlarge D. vibrate 68. What we need to learn is how to put theory into _______ when we begin our fieldwork here. A. appearance B. application C. accomplish D. achievement 69. Jack is _______ of stealing the books from the library. A. accused B. witnessed C. strained D. found 70. The Foreign Minister made an excellent _______ on the current international situation. A. committee B. command C. comment D. commission Part IV Translation (15 points) Translate the following sentences into English. 71. 我从未受过正式培训,我只是边干边学. 72. 随着年龄越来越大,你应该考虑未来的计划。

XXXXXXXXXXX学院2011—2012学年第一学期经济与管理系旅游专业《旅游英语》期中（末）考试试题A卷考试说明：本课程为闭卷考试，可携带文具（或课程为开卷考试可携带文具和资料）Ⅰ、Match the words given under A with the meanings given under B. List B has extra items.（10 points）A B1）tour guide a）workplace where clothes are washed and ironed 2）reservation b）A very tall building3） laundry c）a document attesting to the truth of certainstated facts4）lobby d)A photographic image transferred to paper or asimilar surface, usually from a negative.5） skyscraper e）a district that is reserved for particularpurpose6）vegetarian f) large and often sumptuous tent7）pavilion g) a guide who leads others on a tour8）print h）a large entrance or reception room or area 9）calligraphy i）eater of fruits and grains and nuts; someone whoeats no meat or fish or (often)10）certificate j) beautiful handwriting1) 2) 3) 4) 5)6) 7) 8) 9) 10)Ⅱ、Choose one answer that best completes the sentences.（20 points）1._______who would like to go on the trip should put their names on the list.A. ThoseB. TheseC. SomebodyD. The ones2.The only thing _______ is that you consult your lawyer abort it.A. which I can suggestB. which can suggestC. that I can suggestD. that can suggest3.She must know what’s happening _____ a complete idiot.A. so is sheB. or she isC. and she is D .nor is she4.For ten years he did not see Sophia _______to her.A. or to telephoneB. nor telephoningC. or telephoneD. nor telephone 5.The children were eventually found ______in an old mine shaft.A. to hideB. hidingC. hide D hid6.After two hours’ waiting, her patience was beginning to .A. break upB. pass byC. run outD. give away7.One of the of foreign travel is learning how to cope with the unexpected.A. benefitsB. interestsC. profitsD. services8.So much for a brief _____ to this university.A．talk B．summary C．information D．introduction9. Some people have birthday cakes ________noodles.A. InsteadB. instead forC. instead toD. instead of10.A hotel's____ comes from payments made for the use of its rooms and other facilitiesA reservations B. File C. income D. responsibility11.All of the following are located in Xi'an except____ .A.The Bell TowerB. Tang ParadiseC. Fubo HillD. The Big Wild Goose Pagoda12.____ examine the travel and identification documents of all people entering a country.A. Customs officialsB. First officersC. Customs inspectorsD. Immigration officers13.Is there anyone allergic ______ the monosodium glutamate?A. ofB. toC. inD. With14.Which of the folloing is NOT included in the fabled Five Mountains in China?A. HuashanB. LushanC. SongshanD. Taishan15. The department manager ________ a new plan to promote sales at the meeting.A. took awayB.put forwardC. looked afterD. got on16. Location is the first thing customers consider when ________ to buy a house.A. planningB. plannedC. to planD. having planned17. Car was put into production in 2007, ________ helped to provide another 1400 jobs.A. thatB. whenC.whatD. which18. I don’t regret ________ her what I thought about her proposal, even if it upset her.A. tellB. to tellC. toldD. Telling19. They will not start the project until the board chairman ________ back from South Africa.A. will comeB.is comingC. camees20. To obtain a visa to enter that country for the first time, you need to apply ________.A.in partB.in personC. in turnD. in placeⅢ、Reading Comprehension（20 points）Directions: Read the following two passages and then choose the best answer to each question.(1)F alls are the number one cause of death to old people at home. Most old people can live safely at home if they make a few changes. Falls are common as people are getting older. Up to half of home accidents could be prevented simple changes. Here are a few suggestions:Mark trouble spots with bright tapes. The first and last steps on stairs are usually high-risk accident areas. Applying bright tapes and using bright light in these areas would make these spots easier to see.Put grab bars (扶手) in the bathroom. A large number of falls occur in the bathroom. This is unfortunate (不幸的) because it’s easy to make the area safe from accidents. Putting grab bars in the bathroom gives people something to hang on to.Invest in a personal alarm. A personal alarm can be started if a person falls or otherwise gets in trouble. With the push of a button, the alarm automatically sends a signal, which gets someone to call and see if the person needs help.1. By making some very simple changes at home, old people ________.A) are free from home accidentsB) can improve their healthC) are likely to live longerD) can live more safely2. Last steps on stairs may become a high-risk accident area if they are ________.A) not painted in a different colorB) not marked with bright tapesC) fixed with grab barsD) very brightly lit3 Falls in the bathroom are considered to be unfortunate because ________.A) they can easily be avoidedB) old people seldom fall in bathroomsC) grab bars do not help to prevent fallsD) bathroom accidents are difficult to prevent4 A personal alarm is designed for old people to ________.A) detect safety conditions at homeB) avoid falls in the bathroomC) send out signals for helpD) make phone calls easily5The purpose of this passage is to tell people that ________.A) most old people die from accidents at homeB) up to half of home accidents could be preventedC) falls at home can be avoided by taking some simple measuresD) protection be the first concern for the public(2)In recent years, we have seen great progress in houses building. The type of houses found in a certain part of the world depends to a certain extent on the building materials available there. Countries where stone is abundant tend to have more stone houses than a place where there is plenty of timber for example. However, climatic conditions affect the houses built to a greater extent.In equatorial countries like Singapore and Malaysia, two main factors are responsible for the type of houses built: the heat of the sun and the fierceness of rainstorms. Our houses are light and airy but have steep roofs. In some places, houses are built on stilts because they may be in lowlying areas which get flooded easily.In a hot and dry country such as Arabia, the houses are often box-shaped. They have thick stone walls which are painted white. White surfaces radiate heat while dark surfaces absorb it. The houses have no windows, only gaps with shutters over them. Even the door openings are very small and narrow. It is cool inside such houses. The roofs are also flat, so that when the sun goes down, one can sit on the roof and catch any cool breeze that is blowing. Sometimes,a water tank may be placed on the roof to catch the little rain that falls.In cold regions, where there is heavy snow, the roofs,of the houses slope steeply so that the snow can slide off easily. If the roofs were flat, the snow would build up and the roofs might cave in under the weight. The houses also have thick stone walls so that the cold is kept out.Some countries are more likely to be affected by earthquakes. In such places, the houses are made of light building materials. If the houses collapse in an earthquake, few people will get hurt and less damage is caused.In some parts of the world, people take their homes along with them as they travel. These people are called nomads. The Bedouins of Arab lands wander over the desert, setting up tents wherever they stop to rest.6.Houses in equatorial countries _______.A.are light and airyB.have steep roofsC.are always built on stiltsD.are built to shelter from the harsh elements7.Houses in Arabia _______.A.have thin walls painted whiteB.are box-shapedC.have many windowsD.always have water tanks on the roof8.In cold countries roofs slope steeply ______.A.so that people can build caves under itB.so that the roofs won't become so heavyC.because people do not need snow to build the houseD.so that the snow can slide off easily9.In earthquake-affected countries, light building materials are used because _____.A.people there can move more easilyB.the houses won't hurt people in an earthquakeC.less damage will be caused in an earthquakeD.people will not be affected by the earthquake10.Nomads are people who _____.A.live in tentsB.travel over the desertC.wander from place to placeD.set up tents over the desertⅣ、Words and Phrases Translation（15 points）Translate followings into English1.入境签证2.特别服务要求3.路线图4.文化遗迹5.游廊6.办理入住7.讨论日程Translate following into Chinese8.moat9.airport tax10.front office11.sightseeing tour12.green bean cake13.traveling palace14.Chinese Cuisine15.Minority NationalitiesⅤ、Translate the following sentences into English.（20 points）1.我将确保你们有充足的时间轻松。

姓名: 班级: 学号: 重修教师：遵 守 考 试 纪 律 注 意 行 为 大学物理A 试题卷（A 卷）考试形式（开、闭卷）：闭卷 答题时间：120 （分钟） 卷面满分 70 分题号 一1 一2 一3 一4 二 三 平时 成绩 卷 面成 绩总 分分数备用常数：玻耳兹曼常量 k =1.38×10-23 J·K -1，普适气体常量 R = 8.31 J·mol -1·K -1阿伏伽德罗常量 N A =6.02×1023 mol -1，普朗克常量 h = 6.63×10-34 J·s 1atm = 1.013×105 Pa ；海水中声速1.54×103 m/s ；n 水=1.33，1nm=10-9m=10 Å一、计算题（共34分）1) （10分）一横波沿绳子传播，其波的表达式为y =0.005cos (10πt −2πx ) (SI)(1) 求此波的振幅、波速、频率和波长。

(2) 求绳子上各质点的最大振动速度和最大振动加速度。

(3) 求x 1=0.2m 处和x 2=0.7m 处二质点振动的相位差。

2) （8分）理想气体开始处于T 1=300K ，p 1=3.039×105Pa ，V 1=4m 3的平衡态。

该气体等温地膨胀到体积为16m 3，接着经过一等体过程达到某一压强，从这个压强再经一绝热压缩就可使气体回到它的初态。

设全部过程都是可逆的。

已知γ =1.4。

（1） 在p -V 图上画出上述循环过程。

（2） 计算每段过程和循环过程气体所做的功和它的熵的变化。

得分得分p V 03)（8分）在双缝干涉实验中，波长λ=550 nm的单色平行光垂直入射到缝间距a=2×10-4 m的双缝上，屏到双缝的距离D=2 m。

求：(1) 中央明纹两侧的两条第10级明纹中心的间距；(2) 用一厚度为h=6.6×10-5 m、折射率为n＝1.58的玻璃片覆盖一缝后，零级明纹将移到原来的第几级明纹处？4)（8分）一束具有两种波长λ1和λ2的平行光垂直照射到一衍射光栅上，测得波长λ1的第三级主极大衍射角和λ2的第四级主极大衍射角均为30°。

成本会计期末试卷A线订○装○___○__________○____：名姓○__________○__________○：号学____○__________○______：别○班_______○__________○__：室试○《成本会计》试题（A卷）本卷全部填在答题纸上，否则无效。

交卷时只交答题纸，试卷自己带走。

一、单选题（每题1分，共20分）1.基本生产车间一般耗用的材料费用，应借记“（）”账户，贷记“原材料”账户。

A.基本生产成本B.辅助生产成本C.制造费用D.销售费用2.“假退料”是指（）。

A．材料不动，只办理本月退料手续B．材料退回，但不办理退料手续C．材料不动，办理本月退料和下月领料手续D．材料不动，办理本月退料和本月领料手续3.待摊费用的摊销期限（）。

A．没有统一规定B.最长为半年C．最长为一年D.最长为两年4．根据生活福利部门人员工资的14%计提的职工福利费，应借记“（）”账户。

A．应付职工薪酬——职工福利B.应付职工薪酬——工资薪酬C.制造费用D.管理费用5.辅助生产车间完工入库的修理用备件，应借记“（）”账户，贷记“辅助生产成本”账户。

A．周转材料——低值易耗品B.原材料C．库存商品D.自制半成品6.制造费用是企业为生产产品和提供劳务而发生的各项（）。

A.直接费用 B.间接费用C.直接计入费用D.间接计入费用7.下列项目中，属于废品报废损失的是（）。

A.不可修复废品的生产成本B.可修复废品的修复费用C.可修复废品的修复费用扣除残料后的损失D.不可修复废品的实际成本减去回收残料和废料价值后的净损失8.不应计入“废品损失”账户借方的费用是()。

A.不可修复废品的生产成本B.可修复废品返修以前发生的生产费用C.修复废品时发生的工资费用D.可修复废品的全部修复费用9.下列各项中，不应列入在产品的是（）。

A.已验收入库的对外销售的自制半成品B.正在车间加工中的合格产品C.已验收入库的仍需加工的自制半成品D.正在车间加工中的合格产品10.约当产量比例法适用于（）的产品。

诚信应考，考试作弊将带来严重后果！贵州民族大学二0一二———二0一三学年第二学期期末考试试卷（A卷）课程名称：定向运动课程代码：任课教师：宋海滨试卷来源：教师个人出题考试形式：闭卷□√开卷□其它□院（系）：专业：年级：班级：学生姓名：学号：一、名词解释（每题5分，共20分）1、定向运动2、等高线3、比例尺4、山背二、填空题（每题2分，共20分）1、在一条典型的定向越野比赛路线中，三角符号表示（）；单圆圈表示（），它在现地的精确位置是在圆圈的（）；双圆圈表示（）。

2、地图上的每条等高线都是实地等高线的水平投影，它既描绘出地貌的平面轮廓，也表示出地貌的起伏。

在同一幅地图上或同一等高距条件下，等高线多，山就（），等高线少，山就越低，等高线间隔小，实地坡度（越小）；等高线间隔大，实地坡度（）。

3、定向地图上，对于一组属性相近的地物，通常只规定一个基本符号，然后根据这些符号的不同（），分别使用不同的（）。

4、定向运动竞赛地图一般由（ ）、（ ）、（ ）、（ ）、（ ）、五大要素组成。

5、边跑边（ ）是定向运动中重要的技能之一，它能争取节省比赛时间。

6、定向越野是参加人必须借助（ ）和依靠在地图上用许多（ ）表示的比赛路线，自己在野外（ ）、（ ） ，力争用最短的时间完成比赛。

7、在同一幅地图上或同一等高距的条件下，等高线多，山就（ ）；等高线少，山就（ ）；凹地的等高线则表示深浅。

8、定向指北针是用( )制成。

其优点是：灵敏度高；稳定性好；( )，用图速度高。

9、( )年在吉林省吉林市举行了首届全国大学生定向锦标赛。

10、等高线按其作用不同分为( )四种。

1、判定地貌结构，就是综合、完全的了解一定区域内地貌的相互关系和位置。

2、国际定向运动联合会将定向越野项目划分为徒步定向、滑雪定向、山地自行车定向和轮椅定向。

3、运动员打卡，打到非自己路线的检查点，虽已按本组规定的路线和顺序完成竞赛，还是会影响成绩。

4、裁判人员将根据违例的性质和程度，采取从降低成绩直至取消比赛资格的处罚。