2015-2016学年(上)松柏中学九年级第一次月考(Units1-3)
九年级英语全册Units1_3综合水平测试新版人教新目标版(含答案)
九年级英语全册新版人教新目标版：Units 1～3 综合水平测试得分________卷后分________评价________听力部分(20分)一、听句子，选择相符的图片，有一项多余。
(5×1分＝5分)A B CD E F1．__F__ 2.__E__ 3.__D__ 4.__A__ 5.__C__二、听短对话，选择正确的答案。
(5×1分＝5分)(C)6.What does the boy want to buy?A．Some books. B．Some flowers.C．Some stamps.(A)7.Where does the man want to go?A．To a bank. B．To a restaurant.C．To a shopping center.(B)8.What festival might the speakers celebrate that day?A．The Spring Festival.B．The Dragon Boat Festival.C．The MidAutumn Festival.(B)9.Why does Tina not make up conversations?A．Because she wants to stay alone.B．Because she doesn't have a partner.C．Because she has to finish writing first.(A)10.What's the matter with the boy?A．He can't read quickly.B.He can't pronounce the words.C．He can't remember the words.三、听长对话，选择正确的答案。
(5×1分＝5分)听下面一段对话，回答第11、12小题。
2015-2016学年(上)松柏中学九年级第一次月考(Units1-3)
松柏中学2015-2016学年初三（上）第一次月考英语试卷九年级Units 1-3（二）基础知识与运用（每小题1.5分，共30分）V. 选择填空：从A、B、C中，选出一个最佳答案完成句子。
17. —I find that learning a language isn’t easy.—I think so. You should be patient. ________.A. It doesn’t matterB. It serves you rightC. It takes time18. He celebrates two festival with his family every year. One is the Spring Festival, and ________, the Mid-Autumn Festival.A. otherB. othersC. the other19. We should often practice ________ English with each other.A. speakingB. spokeC. speak20. I think this movie is ________ interesting. Why not go to another cinema?A. moreB. lessC. fewer21. —How will you improve your English pronunciation?—________ watching English movie.A. WithB. ByC. Under22. —________ lovely day it is today!—Yes. Let’s go out and enjoy the sunshine!A. How aB. What aC. How23. You can’t improve your spoken English ________ to practice it every day.A. unlessB. butC. since24. —Have you asked the policeman ________?—Yes, he told us to turn left onto Main street. It’s on the right.A. where can we find a bankB. when we can get to the nearest bankC. how to get to the nearest bank25. We live near a big supermarket, so it’s very ________ for us to do some shopping.A. noisyB. boringC. convenient26. Jimmy ________ in Shanghai for seven years. Now he lives abroad with his father.A. studiesB. studiedC. has studied27. —It seems that you are worried.—I am wondering ________ they can be here on time today.A. whenB. whetherC. where28. —Let’s go to Water World for a trip tomorrow, OK?—________. Where did you suggest going?A. Pardon me?B. I don’t knowC. I agree with youⅥ.完形填空:从A、B、C中选择一个最佳答案, 使短文意思完整.The first note I ever wrote for my mother said “Hi, Mom! Have a nice day! Love, Marie!” I was twelve when I wrote it, and I folded the 29 into her change purse (零钱包).My mother worked as a cleaner in a clothing factory. I knew that when she 30 meals in the dining hall, she would have to look for change in her purse. I didn’t know that she would keep that note, and always carry it with her.From the day that I 31 folded the small piece of paper into my mother’s change purse, she and I left each other 32 notes. They would be put in the fridge, under a lamp, or beside the TV set. I even found one hidden in my shoe. Fromthe outside, our notes may have been general records of our days, ideas and wishes. But to my mother and 33 , they were a lifeline — a communication with each other that no one else shared.On October 20, 2009, my mother died after a long illness. I stood near her bed, holding her hand. I didn’t cry the day my mom died, 34 I didn’t cry a week later when I went to collect her things. I was so thankful that she no longer had aches and pains.Recently, I 35 a note that my mom had left me. It had been hidden in the pages of my favorite childhood book for years. It read “Dear Marie, I love you always. Miss you a lot. Don’t forget me. Be 36 ! Love, Mom.” That day, I cried.29. A. note B. book C. diary30. A. prepared B. bought C. cooked31. A. carefully B. wisely C. quickly32. A. funny B. beautiful C. secret33. A. her B. me C. us34. A. and B. but C. because35. A. found B. invented C. looked for36. A. patient B. strict C. happy（三）阅读理解（每小题2分，共50分）VII.阅读以下五篇短文，根据文章内容选择最佳答案作答37-61小题。
福建厦门松柏中学2023-2024学年九年级上学期月考数学试题及参考答案
2023-2024学年松柏中学九年级（上）适应性练习数学（试卷满分：150分 考试时间：120分钟）一、选择题（每小题4分，共40分，每小题都有四个选项，其中有且只有一个选项正确）1. 如图所示，其中是中心对称图形的是（ ）A. B.C. D.2. 关于x 的方程2230ax x −+=是一元二次方程，则（ ）A 0a ≠ B. 0a > C. 1a = D. 0a ≥ 3. 若二次函数22y x =的图象经过点P （1，a ），则a 的值为（ ） A. 12 B. 1 C. 2 D. 44. 把抛物线2y x 向上平移1个单位，所得到抛物线的函数表达式为（ ）A. 21y x =+B. 2(1)y x =+C. 21y x =−D. 2(1)y x =− 5. 点()2,5P −关于原点的对称点的坐标是（ ）A. ()2,5−−B. ()2,5C. ()2,5−D. ()5,2− 6. 关于x 的方程2(1)10ax a x +−−=，下列结论正确的是（ ）A. 当0a =时，方程无实数根B. 当1a =−时，方程只有一个实数根C. 当1a =时，有两个不相等实数根D. 当0a ≠时，方程有两个相等的实数根 7. 如图，正方形ODEF 绕着点O 顺时针旋转50°得到正方形OABC ，连接AF ，则OFA ∠的度数是（）.的A. 30°B. 25°C. 20°D. 15°8. 如图，在同一直角坐标系中，0k ≠，函数2y kx =和7y kx k =−−的图象可能是（ ） A. B.C D.9. 已知二次函数2225y x bx b b −++−（b 为常数）的图象与x 轴有交点，且当 3.5x <时，y 随x 的增大而减小，则b 的取值范围是（ ）A. 5b ≤B. 5b ≥C. 3.55b ≤≤D. 3.55b ≤< 10. 如图①，在菱形ABCD 中，∠A=120°，点E 是边BC 的中点，点F 是对角线BD 上一动点，设FD 的长为x ，EF 与CF 长度的和为y ．图②是y 关于x 的函数图象，点P 为图象上的最低点，则函数图象的右端点Q 的坐标为（ ）.A. (B. (C. ()D. ( 二、填空题（本大题有6小题，每小题4分，共24分）11. 一元二次方程2100x =的解是_________．12. 拋物线29(2)5y x =−+的顶点坐标是_________．13. 在平面直角坐标系中，将点()8,4P 绕原点O 逆时针旋转90°得到点P ′，则点P ′的坐标为_________．14. 要组织一次篮球联赛，赛制为单循环形式（每两队之间都赛一场），计划安排15场比赛，设有x 队参加比赛，根据题意，可列方程为______．15. 已知,a b 是方程2320x x +−=的两个实根，a b +=_________，3232a a b ++=_________． 16. 如图，抛物线2y ax bx c ++交x 轴分别于点()()3,0,1,0A B −，交y 轴正半轴于点D ，拋物线顶点为C ．下列结论：①0abc >；②30a c +=；③当ABC是等边三角形时，a = ④若方程21.5ax bx c ++=有四个根，则这四个根的和为4−； 其中，正确结论的序号为_________． 三、解答题（86分）17. 解不等式组：20,12x x x −≤ −< 18. 解方程：（1）240x x −=（2）223x x =−+19. 某厂一月份的杯子产量为160万只，由于市场需求逐渐减少，三月份的产量减少到90万只．求该厂二、三月份的杯子产量的月平均减少率．20. 二次函数24y x bx c ++图象经过()()1,1,0,0−−两点的（1）求这个二次函数的解析式；（2）若另外三点()()()1212,20,,20,,x x x x n +也在该二次函数图象上，求n 的值；（3）当x _________时，0y >．21. 如图，有长为20米的篱笆，一面利用墙（墙的最大可用长度a 为5米），围成长方形花圃．设花圃的宽AB 为x 米，面积为S 米2，（1）求S 与x 的函数关系式，并写出x 的取值范围；（2）能围成面积为32米2的花圃吗？如果能，请求出AB 的长，如果不能，请说明理由．22. 如图，在正方形ABCD 中，点E 是AB 边上的一点（与,A B 两点不重合），将BCE 绕着点C 顺时针旋转，使CB 与CD 重合，这时点E 落在点F 处，连接EF ．（1）按照题目补全图形；（2）题中的旋转中心为_________，旋转角度可为_________°．（3）若正方形边长为,m BE n =，比较AEF △与CEF △的面积大小，并说明理由．23. 当解某些计算较复杂的一元二次方程时，可考虑用“缩根法”简化运算．“缩根法”是指将一元二次方程先转化成系数比原方程简单的新一元二次方程，然后解新一元二次方程，并将新方程的两根同时缩小若干倍，从而得到原方程的两个根．已知：关于x 的一元二次方程()200ax bx c a ++=≠的两根为12,x x αβ==，求关于x 的一元二次方程()2200p ax pbx c ap ++=≠的两根．解：()22200,()0p ax pbx c ap a px b px c ++=≠∴+⋅+= ，令px t =， 得新方程20at bt c ++=，新方程的解为12,,,t t px px αβαβ==∴==，∴原方程的两根为12,x x p p αβ==．这种解一元二次方程的方法叫做“缩根法”举例：用缩根法解方程24935240x x +−=．解：22497,3557,(7)57240x x ==×∴+×−= ，令7t x =，得新方程25240t t +−=．解新方程得：123,8,73,78t t x x ==−∴==−， ∴原方程的两根为1238,77x x ==−． 请利用上面材料解决下列问题，并写出具体步骤：（1）用缩根法解方程：236610x x −−=；（2）用缩根法解方程：2316016000x x −+=．24. 单板滑雪大跳台是北京冬奥会比赛项目之一，滑雪大跳台在设计时融入了敦煌壁画中“飞天”的元素，故又名“雪飞天”、图1为“雪飞天”滑雪大跳台赛道的横截面示意图，运动员从D 点起跳后到着陆坡AC OC 为x 轴，铅垂线OB 为y 轴，建立平面直角坐标如图2，从起跳到着落的过程中，运动员的铅垂高度()m y 与水平距离()m x 近似满足二次函数的关系．在着陆坡AC 上设置点()32,4K 作为标准点，着陆点在K 点或超过K 点视为成绩达标．（1）某运动员的一次试跳中，测得该运动员的水平距离x 与铅垂高度y 的几组数据如下：水平距离()m x0 2 6 10 14 18 铅垂高度()m y 20.00 21.80 24.20 25.00 24.20 21.80根据上述数据，直接写出y 与x 的函数关系式为_________（不需写出自变量的取值范围）；（2）在此次试跳中，该运动员的成绩是否达标？请说明理由；（3）此次试跳中，该运动员在空中从起跳到达最高点的高度或从最高点到下落的高度()m h 与时间()s t 均满足212h gt =（其中g 为常数，表示重力加速度，取210m/s ），运动员要完成“飞天”动作至少要在空中停留3.1秒，问该运动员从起跳到落地能完成动作吗？25. 若函数G 在()m x n m n ≤≤<上的最大值记为M ，最小值记为N ，且满足2M N −=，则称函数在m x n ≤≤上的“极差函数”．（1）函数①21y x =−；②2y x ，其中函数______是在12x ≤≤上的“极差函数”；（填序号） （2）已知函数G ：()2430y ax ax a a =−+>，①当1a =时，函数G 是在1t x t ≤≤+上“极差函数”，求t 的值；②函数G 是在221m x m +≤≤+（m 为整数）上的“极差函数”，若M N 为整数，求a 的值． 的2023-2024学年松柏中学九年级（上）适应性练习数学（试卷满分：150分 考试时间：120分钟）一、选择题（每小题4分，共40分，每小题都有四个选项，其中有且只有一个选项正确）1. 如图所示，其中是中心对称图形的是（ ）A. B.C. D.【答案】B【解析】【分析】根据中心对称图形的定义：把一个图形绕某一点旋转180°，如果旋转后的图形能够与原来的图形重合，那么这个图形就叫做中心对称图形可得答案．【详解】解：选项A 、C 、D 均不能找到这样的一个点，使图形绕某一点旋转180°后与原来的图形重合，所以不是中心对称图形；选项B 能找到这样的一个点，使图形绕某一点旋转180°后与原来的图形重合，所以是中心对称图形； 故选：B ．【点睛】本题主要考查了中心对称图形，关键是找出对称中心．2. 关于x 的方程2230ax x −+=是一元二次方程，则（ ）A. 0a ≠B. 0a >C. 1a =D. 0a ≥【答案】A【解析】【分析】根据一元二次方程的定义，即可求解．【详解】解：∵关于x 的方程2230ax x −+=是一元二次方程∴0a ≠，故选：A ． 【点睛】本题考查了一元二次方程的定义，熟练掌握一元二次方程的定义是解题的关键．一元二次方程定义，只含有一个未知数，并且未知数项的最高次数是2的整式方程叫做一元二次方程．3. 若二次函数22y x =的图象经过点P （1，a ），则a 的值为（ ） A. 12 B. 1 C. 2 D. 4【答案】C【解析】【详解】把点P （1，a ）代入二次函数22y x =即可解得a=2，故答案选C ．4. 把抛物线2y x =向上平移1个单位，所得到抛物线的函数表达式为（ ）A. 21y x =+B. 2(1)y x =+C. 21y x =−D. 2(1)y x =−【答案】A【解析】【分析】求出函数的顶点坐标为(0，0)，向上平移1个单位后变为(0，1)，求解即可．【详解】解：由抛物线2y x =的图象知其顶点坐标为(0，0)，将它向上平移1个单位后，抛物线的顶点坐标为(0，1)，因此所得抛物线的解析式为21y x =+．故选：A ．5. 点()2,5P −关于原点的对称点的坐标是（ ）A. ()2,5−−B. ()2,5C. ()2,5−D. ()5,2− 【答案】C【解析】【分析】根据关于原点的对称点的坐标特点：横纵坐标互为相反数可得答案．【详解】解：因为点()2,5P −关于原点的对称点的坐标特点：横纵坐标互为相反数，所以对称点的坐标是()2,5−，故选：C ．【点睛】此题主要考查了关于原点的对称点的坐标特点，关键是掌握点的坐标的变化规律．6. 关于x 的方程2(1)10ax a x +−−=，下列结论正确的是（ ）A. 当0a =时，方程无实数根B. 当1a =−时，方程只有一个实数根C. 当1a =时，有两个不相等的实数根D. 当0a ≠时，方程有两个相等的实数根【答案】C【解析】 【分析】根据a 的值确定方程的类型，若为一元一次方程，直接求解；若为一元二次方程，根的个数用判别式进行判断．【详解】A ．当0a =时，原方程可化为：10x −=，解得1x =，有一个实数根，故A 错误； B ．当1a =−时，原方程可化为：2210x x −+=，解得1x =，有两个相等的实数根，故B 错误； C ．当1a =时，原方程可化为：210x -=，解得1x =±，有两个不相等的实数根，故C 正确； D ．当0a ≠时，22(1)4(1)(1)0a a a ∆=−−⋅−=+≥，所以方程有两个相等的实数根或两个不相等的实数根，故D 错误故选：C ．【点睛】本题考查了含有参数的一元一次方程，一元二次方程的解法，熟练掌握方程根的个数的判断方法是解题的关键．7. 如图，正方形ODEF 绕着点O 顺时针旋转50°得到正方形OABC ，连接AF ，则OFA ∠的度数是（ ）A. 30°B. 25°C. 20°D. 15°【答案】C【解析】 【分析】由旋转和正方形性质，可得140AOF ∠=°，由OA OF =，即可得到OFA ∠．【详解】解：根据旋转的定义可知，50AOD ∠=︒，又90DOF ∠=°，5090140AOF ∴∠=°+°=°．OA OF = ，()180140220OFA ∴∠=°−°÷=°．故选C ．【点睛】本题考查了正方形的性质和旋转的性质，解题的关键是根据旋转的性质求出AOF ∠的度数．8. 如图，在同一直角坐标系中，0k ≠，函数2y kx =和7y kx k =−−的图象可能是（ ）A. B.C. D.【答案】A【解析】【分析】根据一次函数、二次函数的图象与性质逐项判断即可求解．【详解】解：∵函数2y kx =和7y kx k =−−， 当0k <时，一次函数经过一、二、三象限，抛物线开口向下，当0k >时，一次函数经过二、三、四象限，抛物线开口向上，故选A【点睛】本题考查了一次函数、二次函数的图象与性质，熟知两种函数的图象与性质是解题关键． 9. 已知二次函数2225y x bx b b −++−（b 为常数）的图象与x 轴有交点，且当 3.5x <时，y 随x 的增大而减小，则b 的取值范围是（ ）A. 5b ≤B. 5b ≥C. 3.55b ≤≤D. 3.55b ≤<【答案】C【解析】【分析】根据图象与x 轴有交点，得出判别式△≥0，解得b ≤5；再求出抛物线的对称轴，结合抛物线开口向上，且当x ＜3.5时，y 随x 的增大而减小，可得b ≥3.5，从而得出答案．【详解】解：∵二次函数y =x 2-2bx +b 2+b -5（b 为常数）的图象与x 轴有交点，∴△=（-2b ）2-4（b 2+b -5）≥0解得：b ≤5； ∵抛物线的对称轴为直线22b x b −=−=，抛物线开口向上，且当x ＜3.5时，y 随x 的增大而减小，∴b ≥3.5，∴实数b 的取值范围是3.5≤b ≤5．故选：C ．【点睛】本题考查了抛物线与x 轴的交点和二次函数的图象与性质，掌握抛物线与x 轴的交点个数与判别式的关系及二次函数的性质是解题的关键．10. 如图①，在菱形ABCD 中，∠A=120°，点E 是边BC 的中点，点F 是对角线BD 上一动点，设FD 的长为x ，EF 与CF 长度的和为y ．图②是y 关于x 的函数图象，点P 为图象上的最低点，则函数图象的右端点Q 的坐标为（ ）A. (B. (C. ()D. ( 【答案】D【解析】 【分析】连接AF ，在菱形ABCD 中点A 与点C 关于BD 对称，推出AF CF =，推出y EF CF EF AF =+=+，当,,A F E 三点在同一直线上时y 取最小值，y 的最小值为线段AE 的长，观察图像可知，14F D =，在Rt △ADF 1中，由三角函数求出AD 的长，由平行得出1ADF ∆∽1EBF ∆，求出BE 和F 1B 的长，当点F 和点B 重合时，此时x 取最大值6，y EF CF EB CB =+=+，即可求出点Q 的坐标．【详解】解：连接AF ，如图，∵在菱形ABCD 中点A 与点C 关于BD 对称，∴AF CF =，∴y EF CF EF AF =+=+，当,,A F E 三点在同一直线上时y 取最小值，y 的最小值为线段AE 的长，由图②知此时4x =，即14F D =，在菱形中点E 是边BC 的中点，易得,AE BC EA AD ⊥⊥，∵120,A AB AD ∠== ，∴30ADB ∠= ，∴1cos BC AD F D ADB ==∠=∵AD //BC ，∴11ADF EBF ∆∆ ， ∴112F DAD F B BE==，∴11112,22F B F D BE BC ====，∴116,BD F B F D =+=，当点F 和点B 重合时，此时x 取最大值6，y EF CF EB CB =+=+=．∴点Q 的坐标为(，故选D ． 【点睛】本题考查动点问题的函数图象菱形的性质和解直角三角形，解答本题的关键是明确题意，找出所求问题需要的条件，利用数形结合的思想解答．二、填空题（本大题有6小题，每小题4分，共24分）11. 一元二次方程2100x =的解是_________．【答案】1210,10x x =−= 【解析】【分析】根据直接开平方法解一元二次方程，即可求解．【详解】解2100x =解得：1210,10x x =−=， 故答案为：1210,10x x =−=． 【点睛】本题考查了解一元二次方程，熟练掌握解一元二次方程的方法是解题的关键．12. 拋物线29(2)5y x =−+的顶点坐标是_________．【答案】()2,5【解析】【分析】根据顶点式2()y a x h k =−+的顶点坐标为(),h k 求解即可．【详解】解：抛物线29(2)5y x =−+的顶点坐标是()2,5，故答案为：()2,5．【点睛】本题考查了二次函数顶点式2()y a x h k =−+的顶点坐标为(),h k ，掌握顶点式求顶点坐标是解题的关键．13. 在平面直角坐标系中，将点()8,4P 绕原点O 逆时针旋转90°得到点P ′，则点P ′的坐标为_________．【答案】()4,8−【解析】【分析】如图，过P 、P ′两点分别作x 轴，y 轴的垂线，垂足为A 、B ，由旋转90°可知，OPA OP B ′ ≌，则4P B PA ′==，8BOOA ==，由此确定点P ′的坐标． 【详解】解：如图，过P 、P ′两点分别作x 轴，y 轴的垂线，垂足为A 、B ，线段OP 绕点O 逆时针旋转90°，PO ∴∠P ′90AOB =∠=°，AOP ∴∠=∠P ′OB ，且OP O =P ′，PAO ∠=∠P ′90BO =°，OAP OBP ∴′ ≌()AAS ，则4P B PA ′==，8BOOA ==， ∴P ′()4,8−．故答案为：()4,8−．【点睛】本题考查了点的坐标与旋转变换的关系．关键是根据旋转的条件，确定全等三角形．14. 要组织一次篮球联赛，赛制为单循环形式（每两队之间都赛一场），计划安排15场比赛，设有x 队参加比赛，根据题意，可列方程为______． 【答案】(1)152x x −= 【解析】【分析】设邀请x 个球队参加比赛，那么第一个球队和其他球队打(1)x −场球，第二个球队和其他球队打(2)x −场，以此类推可以知道共打(1231)x +++…+−场球，然后根据计划安排15场比赛即可列出方程． 【详解】解：设邀请x 个球队参加比赛，依题意得123115x +++…+−=， 即(1)152x x −=， 故答案为：(1)152x x −=． 【点睛】本题考查了由实际问题抽象出一元二次方程，此题和实际生活结合比较紧密，准确找到关键描述语，从而根据等量关系准确地列出方程是解决问题的关键．15. 已知,a b 是方程2320x x +−=的两个实根，a b +=_________，3232a a b ++=_________．【答案】 ①. 3− ②. 6−【解析】【分析】根据一元二次方程根与系数的关系可得3a b +=−，根据一元二次方程根的定义可得2320a a +−=，代入代数式3232a a b ++，即可求解．【详解】解：∵,a b 是方程2320x x +−=的两个实根，∴3a b +=−，2320a a +−=∴232a a +=∴3232a a b ++=()()()232222236a a a b a b a b ++=+=+=×−=− 故答案为：3−，6−．【点睛】本题考查了一元二次方程的解的定义，一元二次方程根与系数的关系：若12,x x 是一元二次方程()200ax bx c a ++=≠的两根，12b x x a +=−，12c x x a=，掌握一元二次方程根与系数的关系是解题的关键． 16. 如图，抛物线2y ax bx c ++交x 轴分别于点()()3,0,1,0A B −，交y 轴正半轴于点D ，拋物线顶点为C ．下列结论：①0abc >；②30a c +=；③当ABC 是等边三角形时，a = ④若方程21.5ax bx c ++=有四个根，则这四个根的和为4−； 其中，正确结论的序号为_________．【答案】①②④【解析】【分析】根据二次函数图象的性质，等边直角三角形的性质，二次函数与一元二次方程的关系一一判断即可．【详解】解：∵抛物线开口向下，则a<0，∵抛物线2y ax bx c ++交x 轴分别于点()()3,0,1,0A B −， ∴对称轴为直线3112x −+==− 即12b x a=−=− ∴2b a =0<，抛物线交y 轴正半轴于点D ，则0c >，∴0abc >，故①正确又0a b c ++=，∴20a a c ++=，即30a c +=，故②正确；如图，设对称轴与x 轴相交于点E ，∵()30A −，，()10B ，， ∴4AB =，∵ABC 是等边三角形，CE AB ⊥，∴4AC AB ==，60CAB ∠=°，122AE AB ==，∴CE =，1OE AO AE =−=，∴(1,C −，设抛物线解析式为()21y a x =++ ∵抛物线经过点()10B ，，∴()2011a =++∴a =， 故③错误； ∵方程21.5ax bx c ++=有四个根，∴方程2 1.5ax bx c ++=有两个根，2 1.5ax bx c ++=−有两个根，设方程2 1.5ax bx c ++=有两个根为12,x x ，2 1.5ax bx c ++=−有两个根为34,x x ， ∴1222b a x x a a+=−=−=−，3422b a x x a a +=−=−=−， ∴12344x x x x +++=−． 故④正确．故答案为：①②④．【点睛】本题考查二次函数的性质，等边三角形的判定等知识，解题的关键是熟练掌握二次函数的性质．三、解答题（86分）17. 解不等式组：20,12x x x −≤ −< 【答案】12x −<≤【解析】【分析】分别求出每一个不等式的解集，根据口诀：同大取大、同小取小、大小小大中间找、大大小小找不到确定不等式组的解集． 【详解】解：2012x x x −≤ −< ①② 解不等式①得：2x ≤，解不等式②得：1x >−，∴不等式组的解集为：12x −<≤．【点睛】本题考查了解一元一次不等式组，正确掌握一元一次不等式解集确定方法是解题的关键． 18. 解方程：（1）240x x −=（2）223x x =−+【答案】（1）120,4x x == （2）123,1x x =−= 【解析】【分析】（1）根据因式分解法解一元二次方程，即可求解；（2）先化为一般形式，然后根据因式分解法解一元二次方程，即可求解．【小问1详解】解：240x x −=，∴()40x x −=， 即0x =或40x −=， 解得：120,4x x ==； 【小问2详解】解：223x x =−+，∴2230x x +−=，∴()()310x x +−=， ∴30x +=或10x −=，解得：123,1x x =−=． 【点睛】本题考查了解一元二次方程，熟练掌握解一元二次方程的方法是解题的关键．19. 某厂一月份的杯子产量为160万只，由于市场需求逐渐减少，三月份的产量减少到90万只．求该厂二、三月份的杯子产量的月平均减少率．【答案】25%【解析】【分析】根据题意和题目中的数据，可以得到方程()2160190x −=，即可解决本题．【详解】解：设月平均减少率为x ，则 ()2160190x −=， 解得：10.2525%x ==，2 1.75x =（舍去）， 答：该厂二、三月份的杯子产量的月平均减少率为25%．【点睛】本题主要考查了由实际问题抽象出一元二次方程，解答本题的关键是明确题意，列出相应的方程．20. 二次函数24y x bx c ++的图象经过()()1,1,0,0−−两点（1）求这个二次函数的解析式；（2）若另外三点()()()1212,20,,20,,x x x x n +也在该二次函数图象上，求n 值；的（3）当x _________时，0y >．【答案】（1）245y x x =+ （2）0（3）54x <−或0x > 【解析】【分析】（1）先设出二次函数的解析式，然后将已知条件代入其中并解答即可；（2）先求出抛物线对称轴，再由抛物线的对称性可得12528x x +=−，从而得到1254x x +=−，然后代入解析式即可求得n 的值；（3）令0y =，解方程，得出抛物线与坐标轴交点，根据抛物线开口向上，即可求解．【小问1详解】解：∵二次函数的图象经过点()()1,1,0,0−−三点， ∴041c b c = −+=− ， 解得50b c = =， 所以这个函数关系式是：245y x x =+；【小问2详解】解：∵二次函数为245y x x =+， ∴对称轴为直线55248x =−=−×， ∵三点()()()1212,20,,20,,x x x x n +也在该二次函数图象上， ∴12528x x +=−， ∴1254x x +=−， ∴25545044n =×−+×−=．【小问3详解】解：当0y =时，2450x x +=， 解得：125,04x x =−=，， 又∵40a =>， ∴当54x <−或0x >时，0y >． 故答案为：54x <−或0x >时． 【点睛】本题主要考查二次函数，掌握二次函数的图象和性质以及待定系数法是解题的关键． 21. 如图，有长为20米的篱笆，一面利用墙（墙的最大可用长度a 为5米），围成长方形花圃．设花圃的宽AB 为x 米，面积为S 米2，（1）求S 与x 的函数关系式，并写出x 的取值范围；（2）能围成面积为32米2花圃吗？如果能，请求出AB 的长，如果不能，请说明理由．【答案】（1）S 与x 的函数关系式为：2220S x x =−+15102x≤<（2）能，AB 的长为8米【解析】【分析】（1）由题可知，花圃的宽AB 为x 米，则BC 为(202)x −米，即可得2(202)220S x x x x =−=−+；根据题意得020210x <−≤，即可得；（2）由题意，得222032x x −+=，解得12x =，28x =，根据510x ≤<得2x =不合题意，舍去，即可得．【小问1详解】解：由题可知，花圃的宽AB 为x 米，则BC 为(202)x −米， 2(202)220S x x x x =−=−+，∵02025x <−≤, ∴15102x ≤<，的∴2220S x x =−+15102x≤<； 【小问2详解】 解：由题意，得222032x x −+=，2220320x x −+−=210160x x −+=(2)(8)0x x −−=解得12x =，28x =， ∵15102x ≤<， ∴2x =不合题意，舍去，∴AB 的长为8米．【点睛】本题考查了二次函数的实际应用，一元二次方程的应用，解题的关键是理解题意，掌握这些知识点． 22. 如图，在正方形ABCD 中，点E 是AB 边上的一点（与,A B 两点不重合），将BCE 绕着点C 顺时针旋转，使CB 与CD 重合，这时点E 落在点F 处，连接EF ．（1）按照题目补全图形；（2）题中的旋转中心为_________，旋转角度可为_________°．（3）若正方形边长为,m BE n =，比较AEF △与CEF △的面积大小，并说明理由．【答案】（1）见解析 （2）C ，90°（3）CEF AEF S S >△△，理由见解析【解析】【分析】（1）按照题目要求根据旋转的性质即可画出图形；（2）根据旋转的性质即可求解．（3）首先求出AEF S ，然后证明2AECF ABCDS S m ==四边形四边形，根据CEF AEF AECF S S S =−四边形 求出CEF S △，即可比较AEF △与CEF △的面积大小．【小问1详解】解：如图所示；【小问2详解】根据旋转性质可知：旋转中心为点C ，旋转角度为90BCD ∠=°，故答案为：C ，90．【小问3详解】CEF AEF S S >△△；理由：根据旋转性质可知：DF BE n ==，∵正方形的边长为m ，∴AF AD DF m n =+=+，AE AB BE m n =−=−， ∴()()2211112222AEF S AE AF m n m n m n =⋅=+−=− ， ∵CBE CDF S S =△△，∴2AECF ABCDS S m ==四边形四边形， ∴CEF AEF AECF S S S =−四边形 2221122m m n =−− 221122m n + ∵0n >， ∴222211112222m n m n +>−， ∴CEF AEF S S >△△．【点睛】本题考查了作图—旋转变换，旋转的性质，整式混合运算的实际应用，解决本题的关键是掌握旋转的性质，正确求出AEF S 和CEF S △．23. 当解某些计算较复杂的一元二次方程时，可考虑用“缩根法”简化运算．“缩根法”是指将一元二次方的的程先转化成系数比原方程简单的新一元二次方程，然后解新一元二次方程，并将新方程的两根同时缩小若干倍，从而得到原方程的两个根．已知：关于x 的一元二次方程()200ax bx c a ++=≠的两根为12,x x αβ==，求关于x 的一元二次方程()2200p ax pbx c ap ++=≠的两根．解：()22200,()0p ax pbx c ap a px b px c ++=≠∴+⋅+= ，令px t =， 得新方程20at bt c ++=，新方程的解为12,,,t t px px αβαβ==∴==，∴原方程的两根为12,x x p p αβ==．这种解一元二次方程的方法叫做“缩根法”举例：用缩根法解方程24935240x x +−=．解：22497,3557,(7)57240x x ==×∴+×−= ，令7t x =，得新方程25240t t +−=．解新方程得：123,8,73,78t t x x ==−∴==−，∴原方程的两根为123,7x x == 请利用上面材料解决下列问题，并写出具体步骤：（1）用缩根法解方程：236610x x −−=；（2）用缩根法解方程：2316016000x x −+=．【答案】23. 1x =，=2x 24. =1403x ，240x = 【解析】 【分析】（1）设=6x t ，得到新方程210t t −−=，再求出新方程的解，即可得出原方程的解； （2）将方程两边都乘以3，得−+=2948048000x x ，设=3x t ，得到新方程−+=216048000t t ，再求出新方程的解，即可得出原方程的解．【小问1详解】解：设=6x t ，得到新方程210t t −−=，解得1t =，2t =即6x =或=6x ， 所以原方程两个根是1x==2x ； 【小问2详解】 解：原方程整理为−+=2948048000x x ，设=3x t ，得到新方程−+=216048000t t ，解得140t =，=2120t ， 所以原方程的解是=1403x ，240x =． 【点睛】本题主要考查了“缩根法”解一元二次方程即换元法解一元二次方程，掌握解一元二次方程的方法是解题的关键．24. 单板滑雪大跳台是北京冬奥会比赛项目之一，滑雪大跳台在设计时融入了敦煌壁画中“飞天”的元素，故又名“雪飞天”、图1为“雪飞天”滑雪大跳台赛道的横截面示意图，运动员从D 点起跳后到着陆坡AC 着落时的飞行路线可以看作是抛物线的一部分，取水平线OC 为x 轴，铅垂线OB 为y 轴，建立平面直角坐标如图2，从起跳到着落的过程中，运动员的铅垂高度()m y 与水平距离()m x 近似满足二次函数的关系．在着陆坡AC 上设置点()32,4K 作为标准点，着陆点在K 点或超过K 点视为成绩达标．的（1）某运动员的一次试跳中，测得该运动员的水平距离x 与铅垂高度y 的几组数据如下： 水平距离()m x0 2 6 10 14 18 铅垂高度()m y 20.00 21.80 24.20 25.00 24.20 21.80根据上述数据，直接写出y 与x 的函数关系式为_________（不需写出自变量的取值范围）；（2）在此次试跳中，该运动员的成绩是否达标？请说明理由；（3）此次试跳中，该运动员在空中从起跳到达最高点的高度或从最高点到下落的高度()m h 与时间()s t 均满足212h gt =（其中g 为常数，表示重力加速度，取210m/s ），运动员要完成“飞天”动作至少要在空中停留3.1秒，问该运动员从起跳到落地能完成动作吗？【答案】（1）()21102520y x =−−+ （2）不达标，理由见解析（3）不能【解析】 【分析】（1）根据题意可得抛物线的顶点坐标为()1025.00，，从而得到抛物线的解析式为()21025y a x =−+，再把点()0,20代入，即可求解； （2）把32x =代入（1）中解析式，即可求解；（3）求得运动员在空中从起跳到达最高点的高度或从最高点到下落的高度，分别把5h =和20h =代入212h gt =，求出t 的值，即可求解． 【小问1详解】解：根据题意得：抛物线的顶点坐标为()1025.00，，∴抛物线的解析式为()21025y a x =−+， 即10,25h k ==， 即该运动员铅垂高度的最大值为25m ；把点()0,20代入()21025y a x =−+得： ()22001025a =−+，解得：120a =−， ∴满足的函数关系式为()21102520y x =−−+； 【小问2详解】解：∵()32,4K 作为标准点，着陆点在K 点或超过K 点视为成绩达标．∴当32x =时，()213210250.8420y =−−+=<， ∴该运动员的成绩不达标；【小问3详解】解：设直线AC 的解析式为y mx n =+， ∵()8,16A ，()32,4K∴816324m n m n += +=解得：1220m n =− = ，所以直线AC 的解析式为1202y x =−+ 联立()212021102520y x y x =−+ =−−+解得：020x y = =或305x y = = ∴抛物线与AC 的交点为()30,5 解：当25205h =−=时，215102t =×，解得：1t =或1−（舍去），当25520h −时，2120102t =×， 解得：2t =或2−（舍去）， ∴该运动员从起跳到落地所用时间为123 3.1+=<，∵运动员要完成“飞天”动作至少在空中要停留3.1秒钟，∴该运动员从起跳到落地不能完成动作．【点睛】本题主要考查了二次函数的实际应用，明确题意，准确得到函数关系式是解题的关键． 25. 若函数G 在()m x n m n ≤≤<上的最大值记为M ，最小值记为N ，且满足2M N −=，则称函数在m x n ≤≤上的“极差函数”．（1）函数①21y x =−；②2y x ，其中函数______是在12x ≤≤上的“极差函数”；（填序号） （2）已知函数G ：()2430y ax ax a a =−+>，①当1a =时，函数G 是在1t x t ≤≤+上的“极差函数”，求t 的值；②函数G 是在221m x m +≤≤+（m 为整数）上的“极差函数”，若M N 为整数，求a 的值． 【答案】（1）① （2）①t 的值为12或52；②a 的值是18 【解析】【分析】（1）当12x ≤≤时，分别计算出两个函数的M ，N 的值，再计算出M N −，然后根据定义进行判断即可；（2）①当1a =时，()224321y x x x =−+=−−，可得抛物线对称轴为直线2x =，顶点坐标为()21−，，分四种情况：1t ≤，312t <≤，322t <≤，2t >，分别列方程可解得t 的值；②求出抛物线()22432y ax ax a a x a =−+=−−的对称轴为直线2x =，由221m m +≤+得m 1≥，从而得到23m +≥，根据函数G 是在221m x m +≤≤+（m 为整数）上的“极差函数”，求出244M am am =−，2N am a =−，从而得到()22442am am am a −−−=，即23420am am a −+−=①，根据M N为整数，可得1m +是4的因数，即可求得3m =，代入①即可求得a 的值．【小问1详解】 解：当12x ≤≤时，①21y x =−对函数①21y x =−， 20k => ，∴当12x ≤≤时，y 随x 的增大而增大，当1x =时，2111y N =×−==，当2x =时，2213y M =×−==，312M N ∴−=−=，∴函数①21y x =−是“极差函数”；对函数②2y x =，10a => ，对称轴为直线0x =，∴当12x ≤≤时，y 随x 的增大而增大，当1x =时，211y N ===，当2x =时，224y M ===，413M N ∴−=−=，∴函数②2y x =不是“极差函数”；故答案为：①；【小问2详解】解：①当1a =时，()224321y x x x =−+=−−，∴抛物线对称轴为直线2x =，顶点坐标为()21−，，当12t +≤，即1t ≤时，()221M t =−−，()()2212111N t t =+−−=−−，∴()()2221112t t −−−−−= ∴ 解得：12t =， 当312t <≤时，()221M t =−−，1N =−， ()()22112t −−−−=∴，解得：2t =+舍去)或2t =（舍去）， 当322t <≤时，()()2212111M t t =+−−=−−，1N =−， ()()21112t −−−−=∴，解得：1t =(舍去)或1t =舍去)，当2t >时，()()2212111M t t =+−−=−−，()221N t =−−，()()2211212t t −−−−−= ∴， 解得：52t =， 综上所述，t 的值为12或52； ②()22432y ax ax a a x a =−+=−− ，∴抛物线的对称轴为直线2x =，221m m +≤+ ，1m ∴≥23m ∴+≥，函数G ：243y ax ax a =−+在221m x m +≤≤+(m 为整数)上的“极差函数”， ()()2221421344M a m a m a am am ∴=+−++=−，()()222423N a m a m a am a =+−++=−，()22442am am am a ∴−−−=，即23420am am a −+−=①，M N为整数， 2244am am am a−∴−为整数， 即41m m +为整数， 44411m m m =−++ ，且m 为整数， ∴1m +是4的因数，又m 1≥，1m ∴=或3m =，而1m =时，M N 不符合题意，舍去，3m ∴=,把3m =代入①得：271220a a a −+−=，解得：18a=，a∴的值是18．【点睛】本题主要考查了二次函数的综合应用，熟练掌握二次函数的图象与性质，理解题中“极差函数”的定义，采用分类讨论的思想解题，是解决此题的关键．。
福建厦门松柏中学初三上期中考数学试卷(,)
2015-2016学年(上)松柏中学九年级期中考试卷
松柏中学2015-2016学年初三（上）期中考英语试卷九年级Units4-6（二）基础知识与运用（每小题1.5分，共30分）V. 选择填空：从A、B、C中，选出一个最佳答案完成句子。
17. — Do you know where Bill is from?— I only remember that he is from ________ European country.A. theB. aC. an18. — How do you often go to school?— I ________ take a bus, but now I ________ walking.A. used to; used toB. was used to; am used toC. used to; am used to19. — Do you think Tina is a very ________ girl?— Yes. And she’s popular with everyone in our class.A. seriousB. strangeC. lively20. They took ________ in their son, for he did quite well in the exam.A. prideB. proudC. influence21. — How nice your shoes are! Where did you buy them?— I bought them in Hong Kong. This pair of shoes ________ hand and it feels very comfortable.A. is made ofB. are made fromC. is made by22. Kate is so busy that she ________ goes shopping.A. oftenB. seldomC. usually23. — What’s the matter with Jack?— He got hurt in the P.E. class yesterday, so he was absent ________ school today.A. inB. offC. from24. Every driver should ________ drinking alcohol (酒精) before driving.A. tryB. avoidC. finish25. No matter ________ you are, you should follow the rules.A. whatB. whenC. who26. Lucy’s birthday party didn’t start ________ all her friends arrived.A. untilB. sinceC. while27. I will try my best to stop my son from ________ the same mistake.A. makeB. madeC. making28. — Can you help me move the desk, Peter?— ________.A. It doesn’t matterB. That’s rightC. My pleasureVI. 完形填空：从A、B、C中，选择一个最佳答案，使短文意思完整。
2015-2016学年（上）松柏中学九年级Unit2练习卷
2015-2016学年（上）松柏中学九年级Unit2练习卷2015-2016学年（上）松柏中学九年级unit2练习卷(⼆) 基础知识与运⽤（每⼩题1.5分，共30分）V. 选择填空：从A、B、C中，选出⼀个最佳答案完成句⼦。
17. — Do you know the boy who is talking to Jane over there?— No, he is completely a ________ to me.A. studentB. strangerC. relative18. Linda still misses her grandpa although he has been ________ for years.A. diedB. deathC. dead19. Jack was very excited because he received lots of ________ on his birthday.A. presentsB. storiesC. candles20. Every time she went shopping, she ended up ________ something she didn’t need.A. buyB. boughtC. buying21. — I have ________ three pounds during the past two months. What should I do?—You’d better eat less and do more exercise.A. washed awayB. set upC. put on22. The doctor warns me ________ more vegetables if I want to keep healthy.A. to eatB. to eatingC. eat23. — It seems that you are worried.— I am wondering ________ they can be here on time today.A. whenB. whetherC. where24. He celebrates two festivals with his family every year. One is the Spring Festival, and ________ ,the Mid-Autumn Festival.A. otherB. othersC. the other25. — ________ do you like best about the Lantern Festival?— I like the lanterns. I think they are fun ________.A. What; to watchB. What; watchingC. How; to watch26. — ________ lovely day it is today!—Yes. Let’s go out and enjoy the sunshine.A. How aB. What aC. How27. — Could you tell me ________?— Usually at the Dragon Boat Festival.A. when do Chinese people eat ZongziB. Why do Chinese people eat ZongziC. when Chinese people eat zongzi28. — I am going to the USA to spend my holidays next month.— ________.A. Sounds like funB. No, not at allC. Don’t w aste timeVI. 完形填空：从A、B、C中，选择⼀个最佳答案，使短⽂意思完整。
units 1-3单元练习(含答案)
Units 1-3一、单选1. --- What’s the of the car at present? --- It’s about 70 kilometers an hour.A. placeB. speedC. priceD. mark2. --- How nice the fish tastes! Could you tell me who taught you to cook it?---To be honest, I learnt it watching TV. I learn to cook many dishes TV.A. by; inB. by; onC. in; onD. in; in3. --- Many women have to __________ their husbands for their livings .--- That may not be true . Many women choose to go out to work themselves .A．put on B. decide on C．depend on D．come on4. When you come across new words in reading, it is not a good idea to in a dictionary at once.A. make up themB. look up themC. make them upD. look them up5. --- What did Tina say? --- Sorry, I didn’t ________ what she said.A. pay attention toB. get on withC. hold on toD. look forward to6. --- I wonder if I can learn English well. ---________. All things are difficult before they are easy.A. I am afraid soB. You’re slowC. It takes timeD. It’s a piece of cake7. ---You look a bit worried . ---It’s raining , but I ________my umbrella at home .A. tookB. broughtC. leftD. forgot8. --- Can you spare time to come to our Thanksgiving party? --- Well, I don’t know ________A. that I can finish my work by thenB. if can I finish the work by thenC. that can I finish the work by thenD. whether I can finish the work by then9. My father wants to know _________ next week .A. when my uncle leavesB. when will my uncle leaveC. when my uncle will leaveD. when does my uncle leave10. ---I haven’t d ecided where to go. Do you have any good ideas ? --- I ________ that we go swimming .A. promiseB. agreeC. realizeD. suggest11. I wonder _______ you would like to come to my birthday party .A. thatB. whetherC. that whetherD. that if12. — Look at the photo I took in Jinghong, Yunnan Province. ____ the Dai people were having!— Wow! They were celebrating the Water Festival.A. What funB. How funC. What a funD. How a fun13. ---Could you tell me____ about Valentine’s Day in Japan?--- Well, not only adults but children celebrate it.A. somethingB. anythingC. everythingD. nothing14. --- I am going back to America for Thanksgiving Day. ---____. And we will miss you.A. Enjoy yourselfB. You’re welcomeC. That’s interestingD. The same to you15.---What do you think of him ? --- He is such a kind man that we all ________ him very much .A. absorbB. acceptC. attractD. admire二、阅读理解（A）Winter solstice, as the name shows, means the coming of winter. As an important solar term in the traditional Chinese calendar, it is also a traditional holiday for Chinese, which is also called “冬节”，“长至节”，“亚岁”, etc. Generally, winter solstice occurs between December 21st and 23rd. According to the traditional Chinese calendar, five days constitutes a pentad and three pentads constitute a solar term. One year is divided into twelve periods and twelve climates which are regarded as twenty-four solar terms. The Winter Solstice is one of twenty-four solar terms. On this day, in the Northern Hemisphere the period of daytime is the shortest of the year and the period of night is longest. . In Northern China during winter solstice there is a custom of eating dumplings.1. There are _________ solar terms in a year.A. twelveB. fiveC. twenty-fourD. thirty-one2. People often eat _________ during winter solsticeA. mooncakesB. dumplingsC. noodlesD. chicken3. Winter solstice is in __________.A. JanuaryB. SeptemberC. OctoberD. December4. On winter solstice the period of night is ________in China.A. the longestB. the shortestC. darkestD. brightest5. Which day has the longest daytime in China?A. The beginning of springB. Summer solsticeC. Grain fullD. The beginning of autumn（B）Life comes in a package. This package includes happiness and sadness, failure and success, hope and despair. Life is a learning process. Experiences in life teach us new lessons and make us a better person. With each passing day we learn to deal with various situations.Love plays a main role in our life. Love makes you feel wanted. Without love a person could become cruel. In the early stage of our life, our parents are the ones who show us with love and care. They teach us about what is right and wrong, good and bad. But we don’t always care about it. It is only after marriage and having kids that a person understands others’ feelings.Happiness can bring people a peaceful mind. No mind is happy without peace. Sadness is the cause of the death of a loved one or the failure. But all of these things will pass away.Failure is the path to success. It helps us to touch the sky, teaches us to survive and shows us a specific way. Success brings in money, pride and self-respect.Hope is what keeps life going. Parents always hope their children will do well. Hope makes us dream. Hope builds in patience. Life teaches us not to despair even in the darkest hour, because after every night there is a day.Life teaches us not to regret over yesterday, for it has passed and is out of our control. Tomorrow is unknown, for it could either be bright or dark. So the only choice is to work hard today, so that we will enjoy a better tomorrow.6. We usually have to accept if we want to be successful.A. loveB. failureC. sadnessD. hope7. In which section can readers probably read the passage?A. Business.B. Travel.C. Lifestyles.D. Education.8. What does the word “despair” mean in Chinese?A. 颓废B. 遗憾C. 悲伤D. 绝望9. What’s the meaning of the last sentence of the whole passage?A. When choosing between “today” and “tomorrow”, you’d better enjoy tomorrow.B. If you work hard today, you’ll have a better life in the future.C. What you can only choose is to work hard today rather than tomorrow.D. The only choice you make is that you should enjoy a better tomorrow.10. What’s the purpose of the passage?A. To encourage people to love each other.B. To tell people how to deal with happiness and sadness.C. To give readers some information about life.D. To remind people to keep having a beautiful dream.B卷一、根据首字母及句意补全单词，并将单词完整地写在答题卷相应题号后1.A______ comes after March and people like to play kind jokes on the first day of that month.2. People usually say dogs are good at k_______ their way home by their sense of smell.3. Our First Lady, Peng Liyuan is also a very famous Chinese f_____ singer.4.Tianfu Square is in the c______ part of our city.5.My cousin h_____ my dictionary behind the plant when I went out of my room for dinner.二、完成对话。
福建省厦门市松柏中学2024-2025学年九年级上学期数学月考试题
福建省厦门市松柏中学2024-2025学年九年级上学期数学月考试题一、单选题1．下面的图形是用数学家名字命名的，其中既是轴对称图形又是中心对称图形的是（ ）A ． 赵爽弦图B ． 笛卡尔心形线C ． 科克曲线D ． 斐波那契螺旋线2．下列各式中，y 是x 的二次函数的为（ ） A ．2y ax bx c =++ B ．21y x =-+C ．y =D ．29y x =-+3．已知x ＝1是方程x 2﹣m ＝0的根，则m 的值可以是（ ） A ．1B ．﹣1C ．2D ．﹣24．抛物线y ＝x 2﹣9的顶点坐标是（ ） A ．(0，﹣9)B ．(﹣3，0)C ．(﹣9，0)D ．(3，0)5．下列对一元二次方程x 2+x+3=0根的情况的判断，正确的是（ ） A ．有两个不相等实数根 B ．有两个相等实数根 C ．没有实数根D ．有且只有一个实数根6．将抛物线y=﹣(x ＋1)2＋3向右平移2个单位再向上平移2个单位后得到的新抛物线的表达式为( )A ．y=﹣(x ＋3)2＋1B ．y=﹣(x ﹣1)2＋5C ．y=﹣(x ＋1)2＋5D ．y=﹣(x ＋3)2＋57．如图，将ABC V 绕点A 逆时针旋转55︒得到ADE V ，若70E ∠=︒且AD BC ⊥于点F ，则BAC ∠的度数为（ ）A ．65︒B ．70︒C ．75︒D ．80︒8．二次函数y=ax 2+bx-c 与一次函数y=ax+c 在同一直角坐标系中图象大致是（ ）A ．B ．C ．D ．9．如图，将一个小球从斜坡的点O 处抛出，小球的抛出路线可以用抛物线2142y x x =-刻画，斜坡可以用直线12y x =刻画．下列结论错误的是（ ）A ．小球落地点与点O 的水平距离为7mB ．当小球抛出高度达到7.5m 时，小球与点O 的水平距离为3mC ．小球与点O 的水平距离超过4m 时呈下降趋势D ．小球与斜坡的距离的最大值为49m 810．已知二次函数2(0)y ax bx c a =++≠，当y t ≥时，2x m ≤--或24x m ≥-+．若(3,)A m p --，(2,)B m q 是抛物线2y ax bx c =++上的两点，且p q >，则m 的取值范围为（ ）A ．513m -<<B ．1m <-或53m >C ．513m -<<D ．53m <-或1m >二、填空题11．方程29x =的解是． 12．已知()211350mm x x +-+-=是关于x 的一元二次方程，则m 的值为．13．若抛物线y ＝（x ﹣2）2+（m +1）的顶点在第一象限，则m 的取值范围为．14．《念奴娇·赤壁怀古》，在苏轼笔下，周瑜年少有为，文采风流，雄姿英发，谈笑间，樯橹灰飞烟灭，然天妒英才，英年早逝，欣赏下面改编的诗歌，“大江东去浪淘尽，千古风流数人物． 而立之年督东吴，早逝英年两位数．十位恰小个位三，个位平方与寿符．”则这位风流人物去世的年龄为岁．15．已知二次函数223y x ax =-+（其中x 是自变量且0a ≠），且21x -≤≤时，y 的最小值为1，则a 的值是．16．设等腰三角形的一腰与底边的长分别是方程x 2﹣6x+a=0的两根，当这样的三角形只有一个时，则a 的取值范围为．三、解答题 17．解方程2210x x --=18．如图，在平行四边形ABCD 中，点M ，N 分别在边AB ，CD 上，且AM CN =．求证：DM BN =．19．先化简，再求值： 2111a a a -⎛⎫+÷ ⎪⎝⎭，其中1a ．20．已知关于x 的一元二次方程x 2﹣4x ﹣m 2＝0． （1）求证：该方程有两个不相等的实数根；（2）若该方程的两个实数根x 1，x 2满足12123x x x x ++＝，求m 的值．21．如图，在五边形ABCDE 中，90ABC AED ∠=∠=︒，120BAE ∠=︒，60CAD ∠=︒，AB AE =．(1)将AED △绕点A 顺时针旋转得到ABF △，使AE 与AB 重合，请画出图形； (2)求证：CD BC DE =+．22．如图，抛物线y ＝x 2+bx +c 与x 轴交于A （﹣1，0）和B 点，与y 轴交于点C （0，﹣3）．（1）求该抛物线的解析式；（2）观察图象，直接写出不等式x 2+bx +c ＞0的解集；（3）设（1）中的抛物线上有一个动点P ，点P 在该抛物线上滑动且满足S △P AB ＝8，请求出此时P 点的坐标．23．2022年9月，教育部正式印发《义务教育课程方案》，《劳动教育》称为一门独立的课程，某学校率先行动，在校园开辟了一块劳动教育基地；一面利用学校的墙（墙的最大可用长度为15米），用长为30米的篱笆，围成矩形养殖园如图1，已知矩形的边CD靠院墙，ADx．和BC与院墙垂直，设AB的长为m(1)当围成的矩形养殖园面积为2100m时，求BC的长；(2)如图2，该学校打算在养殖园饲养鸡、鸭、鹅三种家禽，需要在中间多加上两道篱笆作为隔离网，并与院墙垂直，请问此时养殖园的面积能否达到2100m若能，求出AB的长；若不能，请说明理由．24．项目式学习项目主题：合理设计智慧泉源项目背景：洒水车是城市绿化的生力军，清扫道路，美化市容，降温除尘，方便出行．如图1，一辆洒水车正在沿着公路行驶（平行于绿化带），为绿化带浇水．数学小组成员想了解洒水车要如何把控行驶路线与绿化带之间的距离，才能保证喷出的水能浇灌到整个绿化带．围绕这个问题，该小组开展了“合理设计智慧泉源”为主题的项目式学习．任务一测量建模建立如图2所示的平面直角坐标系，可以把洒水车喷出水的上、下边缘抽象为两条抛物线的部分图象，喷水口H离地面竖直高度h为1.2米．上边缘抛物线最高点A离喷水口的水平距离为2米，高出喷水口0.4米．（1）求上边缘抛物线的函数解析式；任务二推理分析小组成员通过进一步分析发现：当喷头竖直高度调整时，喷头喷出的水柱抛物线形状不发生改变，即下边缘抛物线是由上边缘抛物线向左平移得到的，把绿化带横截面抽象为矩形DEFG ，其水平宽度 1.8DE =米，竖直高度 1.1EF =米，洒水车到绿化带的距离OD 为d 米．（2）求下边缘抛物线与x 轴交点B 的坐标；（3）若 2.2d =米，则洒水车行驶时喷出的水能否浇灌到整个绿化带？请说明理由． 25．已知直线(0)y kx m k =+<与抛物线2y x bx c =++相交于抛物线的顶点P 和另一点Q ，点P 在第四象限．()1若点()2,P c -，点Q 的横坐标为1，求点Q 的坐标；()2过点Q 作x 轴的平行线与抛物线2y x bx c =++的对称轴交于点E ，直线PQ 与y 轴交于点M ，若EQ PE =，22(5)4b c b =-<-，求OMQ V的面积S 的取值范围．。
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松柏中学2015-2016学年初三（上）第一次月考英语试卷九年级Units 1-3（二）基础知识与运用（每小题1.5分，共30分）V. 选择填空：从A、B、C中，选出一个最佳答案完成句子。
17. —I find that learning a language isn’t easy.—I think so. You should be patient. ________.A. It doesn’t matterB. It serves you rightC. It takes time18. He celebrates two festival with his family every year. One is the Spring Festival, and ________, the Mid-Autumn Festival.A. otherB. othersC. the other19. We should often practice ________ English with each other.A. speakingB. spokeC. speak20. I think this movie is ________ interesting. Why not go to another cinema?A. moreB. lessC. fewer21. —How will you improve your English pronunciation?—________ watching English movie.A. WithB. ByC. Under22. —________ lovely day it is today!—Yes. Let’s go out and enjoy the sunshine!A. How aB. What aC. How23. You can’t improve your spoken English ________ to practice it every day.A. unlessB. butC. since24. —Have you asked the policeman ________?—Yes, he told us to turn left onto Main street. It’s on the right.A. where can we find a bankB. when we can get to the nearest bank实用文档 1C. how to get to the nearest bank25. We live near a big supermarket, so it’s very ________ for us to do some shopping.A. noisyB. boringC. convenient26. Jimmy ________ in Shanghai for seven years. Now he lives abroad with his father.A. studiesB. studiedC. has studied27. —It seems that you are worried.—I am wondering ________ they can be here on time today.A. whenB. whetherC. where28. —Let’s go to Water World for a trip tomorrow, OK?—________. Where did you suggest going?A. Pardon me?B. I don’t knowC. I agree with youⅥ.完形填空:从A、B、C中选择一个最佳答案, 使短文意思完整.The first note I ever wrote for my mother said “Hi, Mom! Have a nice day! Love, Marie!” I was twelve when I wrote it, and I folded the 29 into her change purse (零钱包).My mother worked as a cleaner in a clothing factory. I knew that when she 30 meals in the dining hall, she would have to look for change in her purse. I didn’t know that she would keep that note, and always carry it with her.From the day that I 31 folded the small piece of paper into my mother’s change purse, she and I left each other 32 notes. They would be put in the fridge, under a lamp, or beside the TV set. I even found one hidden in my shoe. From the outside, our notes may have been general records of our days, ideas and wishes. But to my mother and 33 , they were a lifeline — a communication with each other that no one else shared.On October 20, 2009, my mother died after a long illness. I stood near her bed, holding her hand. I didn’t cry the day my mom died, 34 I didn’t cry a week later when I went to collect her things. I was so thankful that she no longer had aches and pains.Recently, I 35 a note that my mom had left me. It had been hidden in the pages of my favorite childhood book for years. It read “Dear Marie, I love you always. Miss you a lot. Don’t forget me. Be 36 ! Love, Mom.” That day, I cried.29. A. note B. book C. diary30. A. prepared B. bought C. cooked31. A. carefully B. wisely C. quickly32. A. funny B. beautiful C. secret33. A. her B. me C. us34. A. and B. but C. because实用文档 235. A. found B. invented C. looked for36. A. patient B. strict C. happy（三）阅读理解（每小题2分，共50分）VII.阅读以下五篇短文，根据文章内容选择最佳答案作答37-61小题。
ANews ReviewAPEC Blue People in Beijing got the saying after the APEC meeting in Beijing. It refers to (指) the clear blue sky during the meeting. To get such a blue sky, many factories in Beijing and nearby cities stopped work, and the number of cars on the road was cut.A Warning Ticket A 24-year-old woman in Nanjing was given a warning ticket for eating food on the subway. Eating is not allowed on Nanjing subway. Up to now, 2,698 people have been punished (惩罚) because of their eating, smoking or selling goods on the subway.A Teacher-free Exam Recently, students at Ningbo Huamao Foreign Language School in Zhejiang took their mid-term exam — a teacher-free exam. After handing out the exam papers, the teachers left the classroom, leaving the students to take the exam without being watched. They only came back to collect the papers at the end.A Tomato Fight Do you want a tomato shower? Come to the “tomato fight” in Spain! Once every year, people in the town of Bunol throw tomatoes at each other. Don’t worry. It’s not a real fight. People do this only for fun.37. APEC Blue refers to ________ in Beijing during the APEC meeting.A. the factoriesB. the clear blue skyC. the cars on the road38. A 24-year-old woman in Nanjing was given a warning ticket for ________ on the subway.A. drinkingB. smokingC. eating food39. In a teacher-free exam, students take their exam ________.A. without being watchedB. at the end of the termC. without giving answers40. In the town of Bunol, Spain, people throw tomatoes at each other ________.A. to have funB. to enjoy dinnerC. to start a fight41. You may probably read the passage above in ________.A. a science reportB. a short novelC. a newspaperBOur new foreign colleagues (同事) are going to arrive very soon, and here are some tips to communicate with them politely.How close do you stand when you talk to a friend? You can stand close to people in the Middle East but don’t stand too close to North Americans! Give them more personal space.Do you know How to touch people correctly? Chinese girls often walk arm in arm with their friends. South Americans sometimes hold your arm when they talk to you, so you can’t move away! But in Britain many people don’t like other people实用文档 3。