【广州】2017-2018广东广州越秀黄冈中学初三上期中考试试卷
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黄冈中学广州学校2017-2018学年度上学期九年级数学问卷一、选择题(本大题共10小题,每小题3分,满分30分.在每小题给出的四个选项中,只有一项是符合题目要求的.)1.如果 a 的取值范围是( )A. a ≥0B.a ≤0C. a ≥3D.a ≤32.下列平面图形中,既是轴对称图形,又是中心对称图形的是( )A. B. C. D.3.关于x 的一元二次方程2x 2+ax =5的一个根是1,则a 的值是( )A. 0B.1C. 3D.24.用配方法解方程x 2−2x −3=0,配方后的方程式 ( )A. (x −1)2=8B.(x −1)2=2C. (x +1)2=4D.(x −1)2=45.若抛物线y =2x 2平移后得到抛物线y =2x 2+1,则平移方式为( )A. 向左平移1个单位B. 向右平移1个单位C. 向上平移1个单位D. 向下平移1个单位6.关于x 的一元二次方程x 2+x −2=0的根的情况是( )A. 有两个不相等的实数根B. 有两个相等的实数根C. 无实数根D. 无法判断7.三角形两边的长是3和4,第三边的长是方程x 2−12x +35=0的根,则该三角形的周长为( )A. 14B.12C. 12或14D.以上都不对8.设二次函数y =(x −3)2−4图象的对称轴为直线l ,若点M 在直线l 上,则点M 的坐标可能是( )A. (1,0)B. (3,0)C. (-3,0)D. (0,-4)9.如图,在Rt△ABC中,∠ACB=90°,∠ABC=30°,将△ABC绕点C顺时针旋转至△A’B’C,使点A’恰好落在AB上,则旋转角度为()A. 30°B.45°C.60°D.90°10.如图,为二次函数y=ax2+bx+c的图象,给出下列说法:①ab<0;②方程ax2+bx+c=0的根为x1=−1,x2=3;③a+b+c>0;④当x>1时,y随x值的增大而增大;⑤当y>0时,−1<x<3;⑥2a+b<0。
2017学年第一学期初三级期中考英语科问卷总分:110 时间:120分钟一.语法选择(共15题;每小题1分,满分15分)阅读下面短文,按照句子结构的语法行和上下文连贯的要求,从1-15各题所给的A、B、C和D项中选出最佳选项,并在答题卡上将该项涂黑。
About the importance of good health, nobody can explain better than ____1____ doctor. They are the people who really know the importance of keeping fit and ____2____. I am saying this because my doctor is an angel. Every time I put on an extra pound, he will remind me____3____ what it is happening to my body. If we do not need to visit any doctor we think we are very healthy. ____4____ that is not true. We may look healthy but we don’t know clearly what ____5____ inside. However, there are many different ways we ____6____ make sure that we look inside as ____7____ as we do outside.The first and easiest step is keeping a good and ____8____ diet.Next ____9____ sleeping well. Sleep early. Make sure you get nine hours of sleep.Do not skip your breakfast. It is one of the most important ____10____ of the day. Eat your regular meals, and it will do you good to eat healthily even during breaks.____11____ your body every day. Go ____12____ a swim, or walk, or just play a game of football or tennis. Try your best not to get stressed ____13____ it’s bad for your health.Remember ____14____ washing your hands, and then you won’t catch any infection.Get away from your bad habit. Don’t smoke. Some wine does your body good while most of it does harm. Be wise and don’t drink ____15____.1. mine B. yours C. his D. your2. healthy B. health C. healthily D. unhealthy3. on B. at C. of D. with4. So B. And C. However D. But5. happens B. is happening C. was happening D. happened6. A. should B. can C. must D. may not7. A. good B. well C. better D. stronger8. A. balance B. balancing C. balanced D. balances9. A. to be B. is C. do D. does10. A. meals B. a meal C. meal D. some meals11. A. To exercise B. Exercising C. Exercise D. Exercised12. A. to B. for C. / D. in13. A. when B. so C. though D. because14. A. to keep B. keeping C. keep D. keeps15. A. too many B. any C. too little D. too much二.完形填空(共10小题;每小题1.5分,共15分)体裁:记叙文话题:金钱与法律难度:★★阅读下面短文,掌握其大意,然后从16-25各题所给的A、B、C和D项中,选出最佳选项,并在答题卡上将该项涂黑。
-广州市第二中学2017学年第一学期中段考初三年级 物理 科目 试卷 第一部分(选择题共36分)一、选择题(每题3分,共36分)1.如图所示为内燃机的能流图,则内燃机的效率可表示为( )A .12345100%E E E E E Eη=⨯++++B .3100%E E η=⨯ C .2345100%E E E E Eη=⨯+++D .1100%EE η=⨯【答案】B 【分析】本题考查热机的效率.根据热机效率的定义式100%E E η=⨯有用燃气内能,已知内燃机的能流图,即可求解.【解析】热机的效率是指热机用来做有用功的能量与燃料完全燃烧释放能量之比,即100%E E η=⨯有用燃气内能,1E 、2E 、4E 、5E 均是损耗能量,真正用来做有用功的能量是2E ,因此内燃机的效率为3100%E Eη=⨯. 故选B .2.下列关于热现象的说法正确的是( )A .用力想掰断一把尺子,发现很难掰断,这是因为在掰尺的过程中,分子间引力增大,斥力消失B .能量守恒定律表明,我们有机会可以做出一种不需要动力就能源源不断地对外做功的机器C .两个互相接触的物体之间 热传递,一定是因为他们内能相同D .两个温度不同的物体互相接触,一定会发生热传递【答案】D【解析】A .分子引力与斥力是同时存在的; B .能量守恒定律表明,永动机是不存在的; C .热传递的发生条件是存在着温差;D .只要存在温差,相互接触就会发生热传递. 故选D .3.如图所示的四种机械装置中,不能省力的装置是( )A .自行车的脚踏板B .旗杆顶的滑轮C .水管上的水龙头D .大门上的门把手【答案】B正确率:64%,易错项:A【解析】本题考查杠杆的概念与分类.动力臂大于阻力臂的杠杆属于省力杠杆;阻力臂大于动力臂的杠杆属于费力杠杆.A 、C 、D 选项,自行车的脚踏板、水管上的水龙头以及大门上的门把手在使用过程中动力臂均大于阻力臂,属于省力杠杆,可以省力,故A 、C 、D 错误;B 选项,旗杆顶的定滑轮在使用过程中动力臂等于阻力臂,既不省力也不费力,只能用来改变力的方向,故B 正确. 故选B .4.如图是一种切甘蔗用的铡刀示意图,下列有关说法正确的是( )A .刀刃很薄可以增大压力B .铡刀实质上是一种费力杠杆C .甘蔗放在a 点比b 点更容易被切断D .手沿1F 方向用力比沿2F 方向更省力正确率:54%,易错项:D 【解析】选项分析:A 项,刀刃很薄是通过减小接触面积来增大压强的,故A 错误;B 项,观察图,铡刀在使用时动力臂大于阻力臂,实质上是一种省力杠杆,故B 错误;C 项,观察图,甘蔗放在a 点比b 点时的阻力臂更小,则由杠杆的平衡条件可知,动力会越小,更易被切断,故C 正确;D 项,手沿1F 方向用力比沿2F 方向时的动力臂要小,根据杠杆平衡条件可知,需要的动力越大,更费力,故D 错误. 故选C .5.山区里的山夫挑着物体上山时,行走的路线是S 形,目的是( )A .做更少的功B .尽量省力C .减小上山移动距离D .工作中养成的生活习惯【答案】B【解析】根据功的原理.Fs Gh =,挑着物体上山时,做功不变,山区里的挑夫挑着物体上山时,行走的路线呈"S "形,目的是增大距离S .减少F ,省力,故A 、C 、D 错误,B 正确. 故选B .6.如图所示,在水平拉力F 的作用下,物体A 匀速向右滑动时,轻质弹簧测力计示数为10N ,不计滑轮与绳之间摩擦,则作用在滑轮上的水平拉力F 和物体A 与水面之间的摩擦力f 的大小分别是( )A .=20N F ,20N f =B .=10N F ,20N f =C .20N F =,10N f =D .10N F =,10N f =【答案】C【解析】图中实质是一个动滑轮,绳子两端的力相等,都为10N ,轴上的力F 等于绳子两端的力的和为20N ;物体匀速运动,则绳子对物体的拉力和地面对物体的摩擦力是一对平衡力,大小相等. 故选C .7.质量和初温相同的铜块和铁块放入沸水中煮相当长的时间后,取出来把他们放置在两杯相同的很大杯的冰水混合物中.又经过一段足够长的时间(冰水混合物的冰还没有完全熔化),两杯中剩下的冰的质量( )(c c <铜铁). A .一样多B .铜那杯多C .铁那杯多D .无法确定【答案】B【解析】质量和初温相同的铜块与铁块放入沸水中相当长时间,证明两个物体的温度相同,由于冰水混合物的冰还没熔化完,所以两个杯子末温都是0C ︒. 因为Q cm t =∆,且c c <铜铁.所以铁块放出的热量多,即铁球的杯中冰吸收的热量多,所以铜球的杯子中冰多. 8.如图所示的四个实物图中,与如图中电路图对应的是( )A .B .C .D .【答案】D【解析】电路图可知,两个灯泡并联,且电流表测1L . 故选D .9.如图所示电路中,以下哪个操作可能会造成元件损坏( ) A .闭合开关B .把小灯泡2L 拧出来再闭合开关C .把小灯泡2L 换成电流表再闭合开关D .把小灯泡2L 换成电压表再闭合开关【答案】C【解析】由图可知,1L 两端被导线连接,当2L 变成电流表时,相当于整条电路没有用电器,故闭合开关,电源短路,故C 正确. 故选C .10.如果毛皮和橡胶棒摩擦,毛皮会失去电子.如图所示,一根毛皮摩擦过的橡胶棒靠近用细线挂住的轻细吸管A 端时,吸管发生了转动.对吸管A 端带电性质判断正确的是( )A .若相互吸引,一定带正电B .若相互吸引,一定带负电C .若相互排斥,一定带正电D .若相互排斥,一定带负电【答案】D正确率:71%,易错项:A 【解析】本题考查磁现象.A 、B 项.因为橡胶棒带负电,根据同极相斥,异极相吸原理,若相互吸引,则吸管A 端带正电或者不带电,故A 、B 错误;C、D项.如果相互排斥,根据同极相斥,异极相吸原理,则吸管A端一定带负电,故C错误,D正确.故选D.11.美国科研人员2016年2月11日宣布,他们利用激光干涉引力波天文台(LIGO)于去年9月在地球上首次探测到引力波,在爱因斯坦的描述中,有质量的物体会使它周围的时空发生扭曲,物体质量越大,时空就扭曲的越厉害.当有质量的两物体加速旋转的时候,他们周围的时空会发生起伏,这种“时空扰动”以波的形式向外传播,这就是“引力波”.引力波探测是难度最大的尖端技术之一,因为只有质量非常大的天体加速运动时才会产生较容易探测的引力波.引力波和物质之间的相互作用极度微弱,因此它的衰减也是极度缓慢的,根据上述材料做下列推断.其中正确的是()A.引力波极容易被探测到B.引力波在宇宙中传播时会迅速衰减C.只有质量非常大的天体加速运动,才能产生引力波D.引力波可以在真空和空气中传播【答案】D【解析】材料可知,引力波知道现在才能检测到,故A错误;引力波和物体之司的相互作用极度微弱,故衰减极度缓慢,故B错误;只有质量非常大的天体加速运动,才能产生比较容易检测到的引力波,故C错误.故选D.12.卫生间安装了换气扇和照明灯,有时需要换气扇独立工作,有时需要照明灯独立工作,有时需要二者同时工作.如图所示的电路中,符合要求是()A.B.C.D .【答案】B【解析】由题可以知道,换气扇和照明灯可以单独工作,也可以同时工作,所以换气扇和照明灯并联并且都有单独开关控制. 故选B .第二部分 非选择题(共64分)二、填空题(共24分,每空1分,15题图1分,其他画图2分)13.(3分)分析以下电路图.在图中的方框中按要求填写开关的名字,要求:干路开关为S ,开关1S 控制1L ,开关2S 控制2L .【答案】如图.14.(4分)用橡胶棒摩擦毛皮,橡胶棒能够吸引纸屑,说明带电体具有__________的性质.如果用摩擦过的橡胶棒接触验电器金属小球(如图所示),验电器的金属箔片张开,这是因为箔片带__________(同/异)种电荷,__________(正/负)电荷从橡胶棒转移到箔片.从以上现象还可推理出:金属小球和金属箔片之间是通过__________(导体/绝缘体)相连.【答案】吸引轻小物体;同;负电荷;导体【解析】用毛衣摩擦过的塑料棒带了电荷,因为带电体能够吸引轻小物体,所以当其靠近碎纸屑时,碎纸屑会被吸引过来.当验电器与带电的塑料棒接触后,验电器的金属箔片上都带了同种电荷,因为同种电荷相互排斥,所以两个金属箔片会张开角度.摩擦起电的实质是电子从一个物体转移到另一个物体,即摩擦起电的实质是电子在物质间转移.电子带负电荷.导体上带大量自由电子,故能转移电子的是导体.15.(4分)学校运动会初赛中,小芳同学用60N的力投出实心球在空中画了一条优美的弧线.若实心球重为20N,投球出手高度为1.8m,小芳投出了6m的距离,球最高点距地面2.6m,则球在离手后空中飞行到球落地的过程中,小芳对球所做的功为___________J,重力做的功为___________J.请在图中画出小球运动到最高点时所受的力(忽略空气阻力).如果此时所有外力都消失,小球将___________.【答案】036如图:匀速直线运动.【解析】离手后,小芳对球没有作用力,故做功为0J;,可知,重力做功为36J,离手高度为1.8m,重力大小为20N,由W Gh离手后,忽略空气阻力,小球只受重力作用,故如图:所有力消失,小球处于平衡状态,故做匀速直线运动.16.(5分)如图所示,杆杆在竖直向下拉力F的作用下将一躯体缓慢匀速提升,如表是提升物体时采集到的信息:(1(2)若实际拉力F 为100N ,杆杆的物体做的有用功是___________J ;拉力做的总功是___________J ;请画出物体在虚线位置时,杠杆的阻力2F ,和动力臂1L . 【答案】(1)80N .(2) 8J 9J 如图:【解析】(1)当杠杆从水平位置匀速转到图示位置,如图所示:OC 为阻力臂,OD 为动力臂,因为OCA ODB ''△∽△,所以OC OAOD OBL L L L '=', 又因为OD OC FL GL =,阻力大小不变(物重G 不变),所以当杠杆匀速运动时,动力F 的大小不变,所以OB OA FL GL =, 所以40N 0.8m80N 0.4mOA OB GL F L ⨯===. (2)由表中数据可知,0.1m s =,0.2m h =,=90N 0.1m=9J W F s '=⨯总,=40N 0.2m=8J W Gh =⨯有用.如图所示:17.(3分)(1)当一固体被加热时,其分子运动更加剧烈,分子间的束缚随之减弱,以致有的分子能脱离了固体,较自由地“游动”,呈流动性,其宏观表现就是该物体的___________(选填物态变化名称). (2)5月31日是“世界无烟日”,吸烟危害健康,即使只有很少人吸烟,整个场所会充满烟味,这说明分子___________.(3)液体温度越高,蒸发越快,从微观的角度来说,这是因为___________. 【答案】(1)熔化.(2)无时无刻部在做无规则的运动.(3)分子的热运动与温度有关,温度越高,热运动越剧烈.【解析】(1)固体加热时,变得有流动性,证明固体变成液体,熔化了. (2)分子无时无刻都在做无规则的运动,所以人可以闻到烟味,是扩散现象. (3)分子的热运动与温度有关,温度越高,热运动越剧烈,所以蒸发快.18.(2分)(1)一定质量的气味从外界吸收53.010J ⨯的热量,内能增加54.010J ⨯,这可能是因为____________.(2)用凉水冷却滚烫的鸡蛋,鸡蛋的温度降低,这是通过__________的方式改变鸡蛋的内能. 【答案】(1)有一部分内能是通过做功增加的. (2)热传递.【解析】改变内能的方法有两个:热传递与做功.19.(3分)小明设计了一种用工作电压力为1.5V 的发光二极管(符号)做成的发光棒,电源电压3V 恒定,如图所示是发光棒控制部分的横截面,A 处是个缝隙,可以放入小片,B处是开关,当B 处开关闭合,A 处不放小片时,发光棒正常发光;当B 处开关闭合,A 处放入小片时,发光棒不发光;当B 处开关断开,A 处是否放入小片,发光棒都不发光.根据以上现象,小片可以选用的材料是___________(填选:A 铜片、B 铁片、C 塑料片、D 橡胶片),请在图方框中作出此设计的电路图,A 可以看作是一个开关.【答案】C D 如图或A B ;如图【解析】由题意有,要两个开关同时闭台,灯才亮,故两个开关串联.三、计算题(共l2分,每题6分.) 20.某款汽车油箱内可承装50kg 的汽油.装满箱油可从西安开到延安,改装为新型高效混合燃气车后,装满“油箱”的是30.2m 的混合燃气,汽车只用半箱燃气就可跑到延安(汽油的热值74.610J/kg q =⨯汽油,新型混合燃气的热值93=11.510J/m q ⨯混合燃气)试计算:(l )完全燃烧50kg 汽油能释放出多少热量?(2)若汽油机的效率为20%,从西安开到延安汽车做了多少有用功? (3)新型高效混合燃气汽车的效率为多少? 【答案】【解析】(1)50kg 的汽油完全燃烧放出的热量为: 79=50kg 4.610J/kg=2.310J Q m q =⨯⨯⨯汽油油放汽.(2)根据题意可以知道,从本溪开到承德汽车做的有用功为:98==20% 2.310J=4.610J W Q η⨯⨯⨯有用汽油机放.(3)燃气燃烧放热3939=0.2m 0.511.510J/m 1.510J Q V q =⨯⨯⨯=⨯燃气燃放气.汽车两种情况下运动的路程相同,即有用功相同做混合燃气汽车的效率为: 894.610J=100%=100%40%1.1510JW Q η⨯⨯⨯=⨯有用燃气汽车放.21.如图所示电路中,电表B 、C 、D 为电流表或电压表,如图B 、C 、D 的示数分别为1.6、2.5和0.7(单位是A 或V ),则:(1)在电表B 、C 、D 中,哪个是电流表?哪个是电压表? (2)灯1L 、2L 两端的电压各是多少? (3)通过1L 、2L 的电流各是多少?【解析】(1)从图中可以知道,B 与电源串联,故B 为电流表,示数为1.6A ;D 与灯泡1L 串联,故D 也为电流表,示数为0.7A ;C 与灯泡2L 并联,故C 为电压表,示数为2.5V . (2)并联电路各支路两端电压相等,因为1L 、2L 并联,故灯1L 、2L 两端的电压为12 2.5V V V ==.(3)电流表B 测干路中电流,故 1.6A I =,电流表D 测1L 中电流,故通过1L 的电流是10.7A I =; 因为并联电路中干路电流等于各支路电流之和,故通过2L 的电流为21 1.6A 0.7A 0.9A I I I =-=-=.四、实验、探究题(共20分,每空1分,画图2分)22.(6分)二中物理兴趣小组在探究滑轮机械效率的实验中,采用如图所示的实验装置测量滑轮组的机械效率,相关数据记录在下表中:重物时,应竖直向上___________拉动弹簧测力计.(2)第三次实验中,滑轮组的机械效率为_________________.(3)分析比较第一、二两次实验数据,有用功1W 有_________2W 有(选填“<”,“>”或“=”).某位同学认为,为了减少实验误差,滑轮组的机械效率应取三次测量的平均值吗,你认为该同学想法错误的原因是_________. 【答案】(1)刻度尺 匀速直线.(2)83.3%. (3)<勾码的重力改变了,机械效率会改变,求平均值无意义.【解析】(1)需要用到刻度尺测量移动的速度. (2)由图知,3n =,故绳端移动的距离为60cm ,故10N 0.2m=83.3%4N 60mW Gh W Fs η⨯===⨯有总. (3)由W Gh =有,可知,第一次有用功小于第二次的有用功; 由W W W η=+有有额,可知勾码的重力改变了,机械效率会改变,求平均值无意义.23.(5分)在“探究不同物质吸热情况”的实验中,某班同学做出以下实验步骤: (1)实验所需的器材有:加热器、温度计、天平、电源、__________、水和煤油. (2)实验中得到如下一组数据:. ②比较分析1、2号烧杯的实验记录,可以得出的初步结论是:__________.③比较分析__________号烧杯的实验记录,可以得出的初步结论是:质量相等的同种物质,升高不同的温度,吸收热量不同.④实验说明物体吸收热量的多少不仅与物体的质量和升高的温度有关,还与___________有关. 【答案】(1)秒表.(2)①质量相等的不同物质,升高相同的温度,吸收的热量不同. ②质量不同的相同物质,升高相同的温度,吸收的热量不同. ③3、4. ④物质的种类.(1)实验中需要用天平测质量、温度计测温度,秒表测量加热时间,很明显题目中给出的器材缺少秒表.(2)①比较分析1、3号烧杯的实验记录,可以得出的初步结论是:质量相等的不同物质,升高相同的温度,吸收的热量不同.②1、2号烧杯的液体种类都是水,初温和末温即升高的温度相同,质量不同,加热时间即吸收的热量不同,所以可以得出质量不同的相同物质,升高相同的温度,吸收的热量不同.③3、4号烧杯中的液体种类都是煤油,初温相同,末温不同,即升高的温度不同,而加热时间不同即吸收的热量不同.所以说明了质量相等的同种物质,升高不同的温度,吸收的热量不同.④1、3号烧杯中的液体种类不同,初温、末温、液体的质量都相同,但加热时间即吸收的热量不同,说明了物体吸收热量的多少还与物体的种类有关.24.(9分)二中某班同学对串、并联电路电流规律进行了研究.(l )小明在连接电路时,开关必须__________,按图所示电路连接完各元件,闭合开关后,观察到灯泡2L 比等泡1L 要亮一点,为了验证“串联电路中,越靠近电源正极灯泡越亮”的结论是否正确,请你设计一个实验,在图丙的方框中画出该实验所用的电路图.(2)小明在图中的A 点串联接入一个电流表,闭合开关后发现电流表如图甲所示,出现的原因是__________;更正后,正确使用电流表,如图乙所示,其读数是__________A .(3)为了进一步研究,小明又设计了如图所示的并联电路来研究并联电路电流规律.小明测完一组数据后得出结论.此做法错谡的原因是_______________________.(4)如图所示,当只闭合1S 时.发光的灯是________:当1S 、2S 均闭合时,发光的是________.此时电流表1A 测的是________的电流(填对应的小灯泡名称).(5)小明利用如图所示的电路检验并联电路干路电流是否等于各支路电话之和,其中有一根导线接错了,接错的是___________(填导线的对应编号).【答案】(1)断开如图:(2)正负接线柱接反了 0.8A .(3)只有一组数据,存在偶然性,结论没有普遍性.(4)1L1L 3L 2L 3L .【解析】(l )在连接电路时,必须断开开关:小明认为”串联电路中,越靠近电源正极灯泡越亮”,我 们可以交换一下这两个灯的位置,让电流先经过灯1L ,后经过灯2L ,观察两个灯泡的亮度情况,电路图如下图所示,如果泡1L 比灯泡2L 要亮一点,则小明的观点正确,如果泡2L 比灯泡1L 要亮一点,小明的观点错误.(2)由图所示电流表可以知道,电流表指针反向偏转,这是因为电流表正负接线柱接反造成的. (3)只有一组数据,存在偶然性,结论没有普遍性. (4)等效电路图为:由图可知,1S 闭合,只有1L 亮.两个开关都闭合,则三盏灯都亮,电流表1A 测2L 、3L .【解析】要探究并联电路的电流关系,应将两灯泡并联三个电流表分别测量干路和支路电流,所以需通过改动2L 与负极相连的导线,将负极与灯泡2L 相连的导线改接左下电流表的负接线柱,导线3接错了,正确的电路图如图所示:(5)因此,本题正确答案是:3. 五、材料题(8分) 25.阅读短文,回答问题.汽车发动机发动机是汽车的动力源,汽油机以汽油为燃料,使活塞在气缸中往复运动,一个工作循环经历进气、压缩、做功和排气四个冲程,汽油机的性能和气缸排量有关,气缸排量指活塞一个冲程中活塞在气缸内通过的容积,它取决于活塞的面积和活塞上下运动的距离(冲程长度).如果发动机有若干个气缸,所有气缸“工作容积”之和称为发动机排量,实际汽车往往采用多缸发动机.如图所示发动机有4个气缸(图中标注1、2、3、4),通过连杆把4个气缸的活塞连在一根曲轴上,这4个气缸顺序排列不定,其代表着吸气、压缩、做功和排气冲程.(1)汽油机做功冲程将内能转化为__________能.(2)如图所示,仿照内燃机做功冲程的示意图,画出吸气冲程活塞运动的箭头方向和气缸门的开闭情况.(3)结合短文和图示,若四缸发动中1号气缸在做功冲程中,4号气缸所处的冲程是__________. (4)若汽车发动机以恒定功率输出,在爬坡的时候换用低速挡,目的是___________,请写出你的判断依据是__________.(5)当发动机转速为3000r /min 时,则发动机一个工作循环所需要的时间为___________s ;假设做功冲程燃气对活塞的平均压强是0p ,发动机排量为V 排,效率为 ,则发动机转速为n 时(n 的单位是r/s ),该轿车的输出功率P 与发动机排量V 排的关系式为__________. 答案:(1)内能. (2)(3)吸气冲程.(4)增大牵引力;输出功率P 等于牵引力F 与速度v 的乘积,当速度小时,牵引力大. (5)0.04s012P nPV =排.【解析】(1)内燃机就是将内能转化为机械能的机器. (2)吸气冲程,进气门打开,排气门关闭.(3)四汽缸发动机,各个汽缸的做功过程错开,在飞轮转动的每半周里,都有一个汽缸在做功,其他三个汽缸分别在吸气、压缩和排气冲程,据此可以知道四缸发动机中1号汽缸在做功冲程中.4号汽缸所处的是吸气冲程.(4)增大牵引力;输出功率P 等于牵引力F 与速度v 的乘积,当速度小时,牵引力大.(5)在发动机中,飞轮转2周完成一个工作循环所以发动机转速为3000r /min 时,完成1500个工作循环,每个工作循环所需要的时间为60s 0.04s 1500t ==. 设做功冲程燃气对活塞的平均压强为0p ,发动机排量为V 排,则一个活塞的排气量14V 排,做功冲程燃气对一个活塞的平均压力:0F p S =. 每个做功冲程燃气对一个活塞做的功:00014W FL p SL p V ===排, 发动机转速为n 时,燃气对活塞做功的功率:00112=42W P n PV nPV t ==⨯排排.。
123(4(5(6(78(either(4)solve (5)avoid(6)91:so2:hot3:that4:don't(1)1:How2:delicious(2)1:is2:spoken(3)1:was2:the3:first4:man(4)1:did2:not3:begin4:until(5)1:impossible2:as3:fast4:as(6)1:helps2:with(7)范文一(升级版):Stress drives us to think positively and study carefully, so that we will review what we learn in time to avoid forgetting. However, with too much stress, we may have difficulty in sleep and 10五、完成句子六、书面表达always feel very tired. Also, it's possible that we fear exams and then failures will come.I think we can do something to deal with exam stress, like taking exercise and having a rest after each class. Besides, talking to our parents is helpful too, because their support will give us more confidence.范文二(基础版):Stress makes us think more and study carefully. Also, with stress, we will review the knowledge, so that we will not forget it. However, too much stress is not good, because we can't fall asleep and may feel very tired. Also, we will be afraid of exams and fail them.I think we can take more exercise to deal with stress. We should take a rest after class. Also, it is useful for us to talk to our parents, because they will give us support and we will feel relaxed.。
14. A.being told B.telling C.being telling D.was told5. A.AsB.SoC.BecauseD.Though 6. ed to playing es to play ed to play ing to play 7. A.happiness B.happy C.happily D.the happier 8. A.at B.in C.to D./9. A.from B.of C.with D.on 10. A.cook B.cooking C.to cooking D.cooked 11. A.are selling B.sell C.would sell D.were selling 12. A.not B.not do C.don't D.aren't 13. A.a B.an C.the D./14. A.he B.him C.his D.himself 15. A.andB.butC.soD.or1. A.neighbours B.people C.birds D.children2. A.louder B.noisier C.more terrible D.more beautiful3. A.buy B.catch C.kill D.draw4. A.lucky B.silent C.frightened D.strong5. A.cared for B.looked at C.listened to D.played with6. A.washed B.cleaned ed D.ate7. A.excited eless C.shocked D.boring8. A.story B.truth C.way D.experience9. A.dieB.playC.singD.stayWhen I was a boy of twelve, I lived in South Carolina with my family. Every morning many 1 would come and rest in the tree and sing. There isn't any sound that can be 2 than the song of the birds. I decided to 3 a young bird and keep it in a cage so that I could have my own musician. I finally caught one and put it in a cage. The bird was 4 and cried loudly, but finally it became quiet in its new home. I felt happy and 5 my little musician carefully, giving it food and water.The next day, the bird's mother flew to the cage with food in her mouth. The baby bird 6 up everything she brought. But the following morning, I found it lying on the bottom of the cage, dead. I was very 7 ! What had happened?Arthur Wayne, a famous scientist, happened to hear me crying over the death of my bird.He told me the 8 . "A mother bird, finding her young child in a cage, will sometimes bring it poisonous food. She thinks it's better for her young to 9 than to live in a cage."Since than, I never catch any birds or put them in a cage. All the birds have the right to 10 in the sky.210. A.jump B.fly C.dance D.eatAWhen I was young, my mom used to give the family a funny special treat from time to time — she would make breakfast food for dinner.I remember she did so one night. She had been at work all day but wanted to do something special for us all.On that evening, my mom put a plate of eggs, sausages and very burnt toast in front of my dad. I waited to see if anyone noticed. But my dad just took his toast, smiled at my mom and asked me how my day at school had been. I don't remember what I told him that night. But I do remember watching him put butter and jelly on that toast. He ate it up as usual, every single bite.After dinner, I remember hearing my mom apologize to my dad for burning the toast. I'll never forget what he said: "Honey, I love burnt toast."Later that night, I went to kiss Daddy good night. I asked him if he really liked his toast burnt. He wrapped (抱紧)me in his arms and said: "Your mommy worked very hard today.She's really tired. And besides – a bit of burnt toast never hurts anyone!"Life is full of imperfect things. Nobody is perfect either. I'm not the best at anything. I forget birthdays and other important events just like everyone else does. But I've learned something important from my father. Understanding is the basis of everything, whether between a husband and wife, a parent and child or just between two friends. Remember, burnt toast never hurts anyone. It's the people with the kind thoughts who make life worth living.3A.B.C.D.The writer's father during the dinner.ate up all the burnt toast liked to eat the burnt toast threw away the burnt toast didn't notice the burnt toast(1)A.B.C.D.What does the underlined word "apologize" mean?辩白谢罪道歉辩护(2)A.From what the father said to his son, we know the father .could understand his wife(3)二、阅读理解B.C.D.always argued with his wife was a good cook worked hard every dayA.B.C.D.Which of the following is TRUE according to the passage?My dad loves to eat burnt toast.Burnt toast never hurts anyone except me.My dad quite understands that nobody is perfect including my mum, so he loves burnt toast.My mum loves to make burnt toast.(4)A.B.C.D.What is the best title of the passage?Life is imperfect The father and the son A big dinnerBurnt toast never hurts anyone(5)Paul Walker, the star of the "Fast & Furious" movie series, died on Saturday in a car crash that killed one other person north of Los Angeles. He was 40.A statement on the actor's Facebook page said he was a passenger in a friend's car and that Walker was in the area to attend a charity event for his organization Reach Out Worldwide."We are shocked and sad beyond belief by this news, " the statement said.Walker was working on "Fast & Furious 7" at the time of his death. He also starred in the film "Hours", which is set for release this month. "All of us at Universal are heart-broken, "Universal Pictures said in a statement, "Paul was truly one of the most beloved and respected members of our studio family for 14 years, and this loss is very big to us, to everyone involved with the "Fast & Furious" film and to countless fans."Walker grew up in a working class. He's the oldest of five children. Walker's mother began taking him to auditions (试镜)as a child. He was a child model beginning at the age of 2.Walker has said the early coming into show business wasn't to start him on a career path,but as a way to help support the family.After a lot of TV roles as a child in the 1980s, Walker played a main role in the 1998comedy "Meet the Deedles". Supporting roles in the films "Pleasant Ville", "Varsity Blues" and "She is All That" followed.His performance in "The Skulls" caught the eye of producer Moritz, who made him star in "Fast & Furious" , and the film became an unexpected hit."Your humble spirit was felt from the start, " said Ludacris. "Wherever you went you always left a mark—we were like brothers."4A.B.C.D.Paul Walker lost his life because of .a big fire a charity events a car accident too much work(1)A.B.C.D.When Walker was caught in the car crash, he .was driving his own car with a friend was going to attend a charity event was working on the film "Fast & Furious 6"was starring in the film, "Hours"(2)A.B.C.D.How did the members of Universal Pictures feel about Walker's death?Beloved.Respected.Pitiful.Sad.(3)A.B.C.D.The passage mainly wants to tell us .Walker grew up in a working class Walker starred in many films Walker's performance was excellent it's a pity Walker died in a car crash (4)A.B.C.D.Which of the following is the correct order?a. Many people were sorry about Paul's death.b. Paul was born as the oldest of five children.c. Paul became a child model when he was two years old.d. Walker died in a car crash.e. Walker starred in "Fast & Furious" after his performance in "The Skulls" .b-a-c-e-d b-c-e-d-a c-b-e-a-d e-a-b-d-c(5)CThe surface of the Earth is made of many large pieces, or plates, which are moving very slowly. Most earthquakes happen at the edges of these plates, where they grate (摩擦)against one another.5In some place, the plates are moving all the time, so small tremors (小地震)happen almost every day. Many of them are too small to be felt by humans.In other places, the plates try to move past one another, but they get stuck. The stress builds up for many years until finally the plates break and a powerful earthquake happens.In 1935, US scientist Charles Richter developed the Richter scale (里氏震级)to measure how strong an earthquake is. Its scale is from 0 to 10. The higher the number, the bigger the earthquake. Most earthquakes are between 3 and 4 on the Richter scale. The biggest earthquake in history was in 1960 in Chile the Mid-Atlantic Ridge.There are three areas in the world where most earthquake happen: the Ring of Fire, the Alpide belt and the Mid-Atlantic Ridge.The Ring of Fire, which is also called the circum-Pacific belt, is the world's most active earthquake zone. It's an area circling the Pacific Ocean, where about 90 percent of the world's earthquakes and 81 percent of the world's largest earthquakes happen. Indonesia and Japan are on the Ring of Fire.A.B.C.D.Which of the following is NOT TRUE ?The Earth's plates are moving slowly every day.Earthquakes often happen at the edges of the Earth's plates.Small tremors happen almost every day in some places.A powerful earthquake happens whenever the plates get stuck.(1)A.B.C.D.What is the Richter scale used for?Predicting whether there is an earthquake.Measuring how strong an earthquake is.Recording how fast the plates are moving.Telling people how to avoid an earthquake.(2)A.B.C.D.Where did the biggest earthquake in history happen?In the US.In Chile.In Indonesia.In Japan.(3)A.B.C.D.What is the world's most active earthquake zone?.The circum-Pacific belt.The Alpide belt.The Mid-Atlantic Ridge.What damages an earthquake causes.(4)A.B.What does the story mainly talk about?How to predict an earthquake.What to do in an earthquake.(5)C.D.How an earthquake happens. What damages an earthquake causes.Some Children's Festivals in AmericaKansas City Jiggle JamIt is the largest family music festival in the Midwest. There are two music stages (舞台).Children and parents can also enjoy different activities, like playing musical instruments,painting pictures and cooking.Houston Children's FestivalThis festival started in 1988. It is the largest children's festival in the USA. Every year,about fifty thousand people from all over the country would come to join it. There are six music stages in the festival. Children and their parents can enjoy different music shows there.Seattle International Children's FestivalThis music festival started in 1986. It is held in Seattle every year. This festival brings musicfrom different countries all over the world together, like China, England and many other countries.Greater Good Music, Art & Children's Festival This festival brings many children's music and art activities together. It is open for three days.And it is different from other music festivalsbecause it raises money for some children's organizations.6 A.B.C.D.There are music stages at Kansas City Jiggle Jam.two three five six(1)A.B.C.D.Kids can at the Houston Children's Festival.paint pictures cookenjoy different music shows play musical instruments(2) brings music from different countries all over the world together.(3)A.B.C.D.Houston Children's Festival Kansas City Jiggle Jamk Greater Good MusicSeattle International Children's FestivalA.B.C.D.Which of the following is NOT TRUE about Greater Good Music, Art & Children'sFestival?It is open for three days.It brings some art activities.It's not the same as other music festivals.It raises money for some kids in poor areas.(4)A.B.C.D.What do you think the passage is?A poster for some children's festivals.An introduction to some children's festivals.A report about some children's festivals.Advice on attending some children's festivals.(5)A.B.C.D.E. A 90-year-old Kenyan grandmother has become the world's oldest elementary school student. Priscilla Sitienei is from a small village in Kenya. 1Ms.Sitienei has spent most of her life working as a nurse. She wanted to be able to read and write so she could do well in her work. Sitienei said she never had a chance to go to school when she was young.2 She wants all the children in her village to study.When Ms. Sitienei first tried to go to school, the head teacher David did not think it was a good idea. 3 David said, "I'm very proud of her. She is loved by every pupil. They all want to learn and play with her." He also said, "She is doing well at her age. 4 "Sitienei had a message for children everywhere, saying, " 5 " She added. "With education, you can be whatever you want—a doctor or a pilot."Now he is very happy that Sitienei is at school.She is studying at the local elementary school to learn to read and write.I can say I have seen a big difference in this school since she came.I want to say to the children of the world, especially girls, that education will be your wealth (财富).She said she knows she is old but she hopes she will set an example to children.7三、任务型阅读单词拼写。
2017-2018学年广东省广州市越秀区九年级(上)期中数学试卷一、选择题(本大题共10小题,每小题3分,共30分.在每小题给出的四个选项中,只有一项是符合题目要求的)1.下列图形中,是中心对称图形的是()A.B.C.D.2.一元二次方程x2+x+6=0的根的情况是()A.有两个相等的实数根B.有两个不相等的实数根C.只有一个实数根D.没有实数根3.二次函数y=﹣2(x+1)2﹣5的最大值是()A.﹣1B.1C.﹣5D.54.方程x(x+4)=0的根是()A.x1=0,x2=﹣4B.x1=0,x2=4C.x=﹣4D.x=45.一个正方形绕其中心至少旋转(),才能与自身重合.A.45°B.90°C.135°D.180°6.若关于x的方程x2+mx﹣15=0有一根是3,则方程的另一根是()A.﹣5B.5C.﹣2D.27.如图,△ABC绕点O逆时针旋转100°后得到△A′B′C′,若∠AOB=35°,则∠A′OB=()A.35°B.65°C.100°D.135°8.关于x的方程ax2+bx+c=0(a≠0)的两个根为﹣5和1,则抛物线y=ax2+bx+c(a≠0)的对称轴是()A.x=﹣4B.x=﹣3C.x=﹣2D.x=﹣19.某一型号飞机着陆后滑行的距离S(单位:米)关于滑行的时间t(单位:秒)之间的函数解析式是S=﹣1.5t2+60t,则该型号飞机着陆后滑行()秒才能停下来.A.600B.300C.40D.2010.如图,抛物线y=(x﹣h)2与x轴只有一个交点M,且与平行于x轴的直线l交于A、B两点,若AB=3,则点M到直线l的距离是()A.B.C.D.二、填空题(本大题共6小题,每小题3分,共18分)11.点P(﹣5,﹣7)关于原点对称的点的坐标是.12.设x1,x2是方程x2+3x﹣1=0的两个根,则x1+x2=.13.抛物线y=﹣x2+6的顶点坐标是.14.某种商品的标价为400元/件,经过两次降价后的价格为324元/件,并且两次降价的百分率相同,则该商品每次降价的百分率为.15.将抛物线y=x2+4x+4向右平移3个单位长度,再向下平移2个单位长度,得到抛物线的解析式是.16.如图,在平面直角坐标系中O是原点,矩形OABC的对角线相交于点P,顶点C的坐标是(0,3),∠ACO=30°,将矩形OABC绕点O顺时针旋转150°后点P的对应点P′的坐标是.三、解答题(本大题共9小题,共102分.解答应写出必要的文字说明、推理过程或演算步骤)17.(9分)解方程:x2+6x+8=0.18.(9分)已知抛物线y=﹣(x﹣2)2+3.(1)写出抛物线的开口方向、对称轴和顶点坐标;(2)当y随x的增大而增大时,求x的取值范围.19.(10分)如图,在边长为1的正方形网格中,△ABC的三个顶点均在格点上.(1)画出△ABC绕点C逆时针旋转90°后的三角形,点A的对应点为A′,点B的对应点为B′,连接BB′;(2)在(1)所画图形中,∠B′BC的度数是.20.(10分)如图,利用一面墙(墙的长度不限),另三边用20米长的篱笆围成一个矩形场地.若围成矩形场地的面积为50米2,求矩形场地的长和宽.21.(12分)已知关于x的方程x2+5x﹣p2=0.(1)求证:无论p取何值,方程总有两个不相等的实数根;(2)设方程的两个实数根为x1、x2,当x1+x2=x1x2时,求p的值.22.(12分)如图,二次函数y=﹣x2+bx+c的图象经过(2,0)、(0,8)两点.(1)求二次函数的解析式;(2)当x取何范围的值时,二次函数的图象位于x轴上方.23.(12分)将边长为2的正方形ABCD与边长为2的正方形AEFG如图放置,AD与AE在同一直线上,AB与AG在同一直线上,连接DG、BE.(1)求证:DG=BE;(2)把正方形AEFG绕点A旋转,当点F恰好落在AB边所在的直线上时,求BE的长.24.(14分)已知抛物线y1=ax2+bx+c(ab≠0)经过原点,顶点为A.(1)若点A的坐标是(﹣2,﹣4),①求抛物线的解析式;②把抛物线在第三象限之间的部分图象记为图象G,若直线y=﹣x+n与图象G有两个不同的交点,求n的取值范围;(2)若直线y2=ax+b经过点A,当1<x<2时,比较y1与y2的大小.25.(14分)如图,△ABC是边长为4的等边三角形,点D是线段BC的中点,∠EDF=120°,把∠EDF绕点D旋转,使∠EDF的两边分别与线段AB、AC交于点E、F.(1)当DF⊥AC时,求证:BE=CF;(2)在旋转过程中,BE+CF是否为定值?若是,求出这个定值;若不是,请说明理由;(3)在旋转过程中,连接EF,设BE=x,△DEF的面积为S,求S与x之间的函数解析式,并求S 的最小值.2017-2018学年广东省广州市越秀区九年级(上)期中数学试卷参考答案与试题解析一、选择题(本大题共10小题,每小题3分,共30分.在每小题给出的四个选项中,只有一项是符合题目要求的)1.下列图形中,是中心对称图形的是()A.B.C.D.【分析】根据轴对称图形和中心对称图形的概念对各选项分析判断即可得解.【解答】解:A、不是中心对称图形,故本选项错误;B、不是中心对称图形,故本选项错误;C、是中心对称图形,不是轴对称图形,故本选项正确;D、不是中心对称图形,故本选项错误.故选:C.【点评】本题考查了中心对称图形与轴对称图形的概念.中心对称图形是要寻找对称中心,旋转180度后两部分重合.2.一元二次方程x2+x+6=0的根的情况是()A.有两个相等的实数根B.有两个不相等的实数根C.只有一个实数根D.没有实数根【分析】先计算判别式的值,然后根据判别式的意义判断方程根的情况.【解答】解:△=12﹣4×1×6=﹣23<0,所以方程没有实数根.故选:D.【点评】本题考查了根的判别式:一元二次方程ax2+bx+c=0(a≠0)的根与△=b2﹣4ac有如下关系:当△>0时,方程有两个不相等的实数根;当△=0时,方程有两个相等的实数根;当△<0时,方程无实数根.3.二次函数y=﹣2(x+1)2﹣5的最大值是()A.﹣1B.1C.﹣5D.5【分析】所给形式是二次函数的顶点式,易知其顶点坐标是(﹣1,﹣5),由a=﹣2<0可知:当x=﹣1时,函数有最大值﹣5.【解答】解:∵y=﹣2(x+1)2﹣5中a=﹣2<0,∴此函数的顶点坐标是(﹣1,﹣5),有最大值﹣5,即当x=﹣1时,函数有最大值﹣5.故选:C.【点评】本题考查了二次函数的最值,解题关键是掌握二次函数顶点式,并会根据顶点式求最值.4.方程x(x+4)=0的根是()A.x1=0,x2=﹣4B.x1=0,x2=4C.x=﹣4D.x=4【分析】根据方程得出两个一元一次方程,求出方程的解即可.【解答】解:x(x+4)=0,x=0或x+4=0,x1=0,x2=﹣4,故选:A.【点评】本题考查了解一元二次方程,能把一元二次方程转化成一元一次方程是解此题的关键.5.一个正方形绕其中心至少旋转(),才能与自身重合.A.45°B.90°C.135°D.180°【分析】正方形是中心对称图形,它的对称中心是两条对角线的交点,然后根据旋转角及旋转对称图形的定义作答.【解答】解:∵360°÷4=90°,∴正方形绕中心至少旋转90度后能和原来的图案互相重合.故选:B.【点评】本题考查了旋转角的定义及求法,对应点与旋转中心所连线段的夹角叫做旋转角.6.若关于x的方程x2+mx﹣15=0有一根是3,则方程的另一根是()A.﹣5B.5C.﹣2D.2【分析】设方程的另一根为x1,根据两根之积等于,即可得出关于x1的一元一次方程,解之即可得出结论.【解答】解:设方程的另一根为x1,根据题意得:3×x1=﹣15,解得:x1=﹣5.故选:A.【点评】本题考查了根与系数的关系:x1,x2是一元二次方程ax2+bx+c=0(a≠0)的两根时,x1+x2=﹣,x1•x2=.牢记两根之积等于是解题的关键.7.如图,△ABC绕点O逆时针旋转100°后得到△A′B′C′,若∠AOB=35°,则∠A′OB=()A.35°B.65°C.100°D.135°【分析】先根据旋转的性质得到∠AOA′=100°,然后计算∠AOA′﹣∠AOB即可.【解答】解:∵△ABC绕点O逆时针旋转100°后得到△A′B′C′,∴∠AOA′=100°,∴∠A′OB=∠AOA′﹣∠AOB=100°﹣35°=65°.故选:B.【点评】本题考查了旋转的性质:对应点到旋转中心的距离相等;对应点与旋转中心所连线段的夹角等于旋转角;旋转前、后的图形全等.8.关于x的方程ax2+bx+c=0(a≠0)的两个根为﹣5和1,则抛物线y=ax2+bx+c(a≠0)的对称轴是()A.x=﹣4B.x=﹣3C.x=﹣2D.x=﹣1【分析】根据题意和一元二次方程和抛物线的关系,可以求得该抛物线的对称轴,本题得以解决.【解答】解:∵关于x的方程ax2+bx+c=0(a≠0)的两个根为﹣5和1,∴抛物线y=ax2+bx+c(a≠0)与x轴的交点坐标为(﹣5,0),(1,0),∴该抛物线的对称轴为直线x==﹣2,故选:C.【点评】本题考查抛物线与x轴的交点、二次函数的性质,解答本题的关键是明确题意,利用二次函数的性质解答.9.某一型号飞机着陆后滑行的距离S(单位:米)关于滑行的时间t(单位:秒)之间的函数解析式是S=﹣1.5t2+60t,则该型号飞机着陆后滑行()秒才能停下来.A.600B.300C.40D.20【分析】飞机停下时,也就是滑行距离最远时,即在本题中需求出s最大时对应的t值.【解答】解:由题意,s=﹣1.5t2+60t,=﹣1.5(t2﹣40t+400﹣400)=﹣1.5(t﹣20)2+600,即当t=20秒时,飞机才能停下来.故选:D.【点评】本题考查了二次函数的应用.解题时,利用配方法求得t=20时,s取最大值.10.如图,抛物线y=(x﹣h)2与x轴只有一个交点M,且与平行于x轴的直线l交于A、B两点,若AB=3,则点M到直线l的距离是()A.B.C.D.【分析】函数顶点坐标M为(h,0),设:点M到直线l的距离为a,则:y=(x﹣h)2=a,求出A、B坐标即可求解.【解答】解:函数顶点坐标M为(h,0),设:点M到直线l的距离为a,则:y=(x﹣h)2=a,解得:x=h,即:A(h﹣,0),B(h,0),∵AB=3,∴h+﹣(h﹣)=3,解得:a=,故选:B.【点评】本题考查的是函数与x轴的交点,是一道基本题.二、填空题(本大题共6小题,每小题3分,共18分)11.点P(﹣5,﹣7)关于原点对称的点的坐标是(5,7).【分析】让两点的横纵坐标均互为相反数可得所求的坐标.【解答】解:∵两点关于原点对称,∴横坐标为5,纵坐标为7,故点P(﹣5,﹣7)关于原点对称的点的坐标是:(5,7).故答案为:(5,7).【点评】此题主要考查了关于原点对称的坐标的特点:两点的横坐标互为相反数;纵坐标互为相反数.12.设x1,x2是方程x2+3x﹣1=0的两个根,则x1+x2=﹣3.【分析】直接根据根与系数的关系求解.【解答】解:根据题意得x1+x2=﹣3.故答案为﹣3.【点评】本题考查了根与系数的关系:若二次项系数不为1,则常用以下关系:x1,x2是一元二次方程ax2+bx+c=0(a≠0)的两根时,x1+x2=,x1x2=.13.抛物线y=﹣x2+6的顶点坐标是(0,6).【分析】已知解析式是抛物线的顶点式,根据顶点式的坐标特点,直接写出顶点坐标.【解答】解:因为y=﹣x2+6是抛物线的顶点式,根据顶点式的坐标特点可知,顶点坐标为(0,6).故答案为(0,6).【点评】此题考查了二次函数顶点式的性质:抛物线y=a(x﹣h)2+k的顶点坐标为(h,k).14.某种商品的标价为400元/件,经过两次降价后的价格为324元/件,并且两次降价的百分率相同,则该商品每次降价的百分率为10%.【分析】设该商品每次降价的百分率为x,根据该商品的标价及经过两次降价后的价格,即可得出关于x的一元二次方程,解之取其中小于1的值即可得出结论.【解答】解:设该商品每次降价的百分率为x,根据题意得:400(1﹣x)2=324,解得:x1=0.1=10%,x2=1.9(不合题意,舍去).答:该商品每次降价的百分率为10%.故答案为:10%.【点评】本题考查了一元二次方程的应用,找准等量关系,正确列出一元二次方程是解题的关键.15.将抛物线y=x2+4x+4向右平移3个单位长度,再向下平移2个单位长度,得到抛物线的解析式是y=(x﹣1)2﹣2.【分析】先把y=x2+4x+4配成顶点式得到抛物线的顶点坐标为(﹣2,0),再根据点平移的规律,点(﹣2,0)经过平移后所得对应点的坐标为(1,﹣2),然后利用顶点式写出平移后的抛物线的解析式.【解答】解:y=x2+4x+4=(x+2)2,此抛物线的顶点坐标为(﹣2,0),把点(﹣2,0)向右平移3个单位长度,再向下平移2个单位长度后所得对应点的坐标为(1,﹣2),所以平移后得到的抛物线的解析式为y=(x﹣1)2﹣2.故答案是:y=(x﹣1)2﹣2.【点评】本题考查了二次函数图象与几何变换:由于抛物线平移后的形状不变,故a不变,所以求平移后的抛物线解析式通常可利用两种方法:一是求出原抛物线上任意两点平移后的坐标,利用待定系数法求出解析式;二是只考虑平移后的顶点坐标,即可求出解析式.16.如图,在平面直角坐标系中O是原点,矩形OABC的对角线相交于点P,顶点C的坐标是(0,3),∠ACO=30°,将矩形OABC绕点O顺时针旋转150°后点P的对应点P′的坐标是(0,﹣).【分析】根据已知条件得到OC=3,解直角三角形求得AC===2,OA=AC=,根据矩形的性质得PC=PA,根据勾股定理得到OP==,根据旋转的性质即可得到结论.【解答】解:∵点C的坐标是(0,3),∴OC=3,∵∠ACO=30°,∠AOC=90°,∴AC===2,∴OA=AC=,∴A(,0),∵四边形OABC是矩形,∴PC=PA,∴P(,),∴OP==,∵∠ACO=30°,∠AOC=90°,∴∠AOP=60°,∵将矩形OABC绕点O顺时针旋转150°后点P的对应点P′落在y轴的负半轴上,∴OP′=OP=,∴点P′的坐标是(0,﹣),故答案为:(0,﹣).【点评】本题考查了矩形的性质,坐标与图形变化﹣旋转,解直角三角形,正确的找到点P′的位置是解题的关键.三、解答题(本大题共9小题,共102分.解答应写出必要的文字说明、推理过程或演算步骤)17.(9分)解方程:x2+6x+8=0.【分析】先把方程左边进行因式分解得到(x+2)(x+4)=0,然后解一元一次方程即可.【解答】解:∵x2+6x+8=0,∴(x+2)(x+4)=0,∴x+2=0或x+4=0,∴x1=﹣2,x2=﹣4.【点评】本题主要考查了因式分解法解一元二次方程的知识,解答本题的关键是掌握因式分解法解一元二次方程的一般步骤:①移项,使方程的右边化为零;②将方程的左边分解为两个一次因式的乘积;③令每个因式分别为零,得到两个一元一次方程;④解这两个一元一次方程,它们的解就都是原方程的解.18.(9分)已知抛物线y=﹣(x﹣2)2+3.(1)写出抛物线的开口方向、对称轴和顶点坐标;(2)当y随x的增大而增大时,求x的取值范围.【分析】(1)由二次函数的顶点式,根据二次函数的性质解决问题;(2)由(1)中抛物线的对称轴方程及开口方向即可判断出y随x的增大而增大时x的值.【解答】解:(1)y=﹣(x﹣2)2+3.所以抛物线的开口向下,抛物线的对称轴为直线x=2,顶点坐标为(2,3);(2)∵抛物线开口向下,∴在对称轴的右侧y随x的增大而增大,∵抛物线的对称轴x=2,∴当x<2时y随x的增大而增大.【点评】本题考查的是二次函数的性质,熟知二次函数的图象与系数的关系、抛物线的顶点坐标、对称轴方程及函数的增减性是解答此题的关键.19.(10分)如图,在边长为1的正方形网格中,△ABC的三个顶点均在格点上.(1)画出△ABC绕点C逆时针旋转90°后的三角形,点A的对应点为A′,点B的对应点为B′,连接BB′;(2)在(1)所画图形中,∠B′BC的度数是45°.【分析】(1)将点A与点B分别绕点C逆时针旋转90°得到其对应点,再与点C首尾顺次连接即可得;(2)根据旋转的定义和性质知∠BCB′=90°,BC=B′C,再由等腰直角三角形的性质可得答案.【解答】解:(1)如图所示,△A′B′C即为所求;(2)∵∠BCB′=90°,BC=B′C,∴∠B′BC=45°,故答案为:45°.【点评】本题主要考查作图﹣旋转变换,解题的关键是熟练掌握旋转变换的定义与性质,并据此得出变换后的对应点.20.(10分)如图,利用一面墙(墙的长度不限),另三边用20米长的篱笆围成一个矩形场地.若围成矩形场地的面积为50米2,求矩形场地的长和宽.【分析】设所围矩形ABCD的长AB为x米,则宽AD为(20﹣x)米,根据矩形面积的计算方法列出方程求解.【解答】解:设矩形与墙平行的一边长为xm,则另一边长为(20﹣x)m.根据题意,得(20﹣x)x=50,解方程,得x=10.当x=10时,(20﹣x)=5.答:矩形的长为10m,宽为5m.【点评】考查了一元二次方程的应用,解答此题要注意以下问题:(1)矩形的一边为墙,且墙的长度不超过45米;(2)根据矩形的面积公式列一元二次方程并根据根的判别式来判断是否两边长相等.21.(12分)已知关于x的方程x2+5x﹣p2=0.(1)求证:无论p取何值,方程总有两个不相等的实数根;(2)设方程的两个实数根为x1、x2,当x1+x2=x1x2时,求p的值.【分析】(1)求出根的判别式△=25+p2,根据判别式的意义即可得出无论p取何值,方程总有两个不相等的实数根;(2)根据根与系数的关系求出两根和与两根积,再代入x1+x2=x1x2,得到一个关于p的一元二次方程,解方程即可.【解答】(1)证明:△=52﹣4(﹣p2)=25+p2,∵无论p取何值时,总有p2≥0,∴25+p2>0,∴无论p取何值时,方程总有两个不相等的实数根;(2)解:由题意可得,x1+x2=﹣5,x1x2=﹣p2,∵x1+x2=x1x2,∴﹣5=﹣p2,∴p=±.【点评】本题考查了根的判别式和根与系数的关系,注意熟记以下知识点:(1)一元二次方程ax2+bx+c=0(a≠0)的根与△=b2﹣4ac有如下关系:①当△>0时,方程有两个不相等的实数根;②当△=0时,方程有两个相等的实数根;③当△<0时,方程无实数根.上面的结论反过来也成立.(2)一元二次方程ax2+bx+c=0(a≠0)的两实数根分别为x1,x2,则有x1+x2=﹣,x1•x2=.22.(12分)如图,二次函数y=﹣x2+bx+c的图象经过(2,0)、(0,8)两点.(1)求二次函数的解析式;(2)当x取何范围的值时,二次函数的图象位于x轴上方.【分析】(1)把(2,0)、(0,8)代入二次函数表达式,即可求解;(2)令y=0,解得:x=2或﹣4,即可求解.【解答】解:(1)把(2,0)、(0,8)代入二次函数表达式,解得:b=﹣2,c=8,故:函数的表达式为:y=﹣x2﹣2x+8;(2)令y=0,解得:x=2或﹣4,从图象可以看出:﹣4<x<2时,函数在x轴上方.【点评】本题考查的是函数与坐标轴的交点,涉及到二次函数的基本性质,难度不大.23.(12分)将边长为2的正方形ABCD与边长为2的正方形AEFG如图放置,AD与AE在同一直线上,AB与AG在同一直线上,连接DG、BE.(1)求证:DG=BE;(2)把正方形AEFG绕点A旋转,当点F恰好落在AB边所在的直线上时,求BE的长.【分析】(1)依据四边形ABCD和四边形AEFG为正方形,即可得到AG=AE,AD=AB,∠DAG =∠BAE=90°,判定△ABE≌△ADG(SAS),即可得到DG=BE;(2)分两种情况进行讨论:点F在BA的延长线上;点F在射线AB上,即可得到BE的长.【解答】解:(1)∵四边形ABCD和四边形AEFG为正方形,∴AG=AE,AD=AB,∠DAG=∠BAE=90°,∴△ABE≌△ADG(SAS),∴DG=BE;(2)分两种情况:①如图,当点F在BA的延长线上时,连接EG,交AF于O,则∠AOE=90°,∵AE=2,AB=2,∴AO=EO=,∴Rt△BOE中,AE===2;②如图,当点F在射线AB上时,AF=2=AB,∴点F与点B重合,∴BE=FE=2;综上所述,BE的长为2或2.【点评】本题是考查了正方形的性质,全等三角形的判定与性质,旋转的性质,勾股定理的综合运用.利用分类讨论思想是解题的关键.24.(14分)已知抛物线y1=ax2+bx+c(ab≠0)经过原点,顶点为A.(1)若点A的坐标是(﹣2,﹣4),①求抛物线的解析式;②把抛物线在第三象限之间的部分图象记为图象G,若直线y=﹣x+n与图象G有两个不同的交点,求n的取值范围;(2)若直线y2=ax+b经过点A,当1<x<2时,比较y1与y2的大小.【分析】(1)①设抛物线的解析式为:y1=a(x+2)2﹣4,根据抛物线y1=ax2+bx+c(ab≠0)经过原点,得到0=4a﹣4,于是得到结论;②在y1=x2+2x中,令y1=0,则x2+2x=0,得到抛物线与x轴的交点为:(﹣2,0),(0,0);解不等式得到n>﹣,当直线y=﹣x+n过点(﹣2,0),则n=﹣2,于是得到结论;(2)将函数y1的解析式配方,即可找出其顶点坐标,将顶点坐标代入函数y2的解析式中,即可得出a、b的关系,再根据ab≠0,用a表示出b,两函数解析式做差,即可得出y1﹣y2=a(x﹣2)(x﹣1),根据x的取值范围可得出(x﹣2)(x﹣1)<0,分a>0或a<0两种情况考虑,即可得出结论.【解答】解:(1)①∵顶点A(﹣2,﹣4),∴设抛物线的解析式为:y1=a(x+2)2﹣4,∵抛物线y1=ax2+bx+c(ab≠0)经过原点,∴0=4a﹣4,∴a=1,∴抛物线的解析式为:y1=x2+4x;②在y1=x2+2x中,令y1=0,则x2+2x=0,解得:x1=0,x2=﹣2,∴抛物线与x轴的交点为:(﹣2,0),(0,0);解得,x2+3x﹣n=0,∵抛物线在第三象限之间的部分图象记为图象G,若直线y=﹣x+n与图象G有两个不同的交点,∴△=9+4n>0,∴n>﹣,当直线y=﹣x+n过点(﹣2,0),则n=﹣2,∴n的取值范围为:﹣<x<﹣2;(2)∵抛物线y1=ax2+bx+c(ab≠0)经过原点,∴y1=ax2+bx=a(x+)2﹣,∴函数y1的顶点为(﹣,﹣),∵函数y2的图象经过y1的顶点,∴﹣=a(﹣)+b,即b=﹣,∵ab≠0,∴﹣b=2a,∴b=﹣2a,∴y1=ax2﹣2ax=ax(x﹣2),y2=ax﹣2a,∴y1﹣y2=a(x﹣2)(x﹣1).∵1<x<2,∴x﹣2<0,x﹣1>0,(x﹣2)(x﹣1)<0.当a>0时,a(x﹣2)(x﹣1)<0,y1<y2;当a<0时,a(x﹣2)(x﹣1)>0,y1>y2.【点评】本题考查了二次函数与不等式(组),解题的关键是分a>0或a<0两种情况考虑.本题属于中档题,难度不大.25.(14分)如图,△ABC是边长为4的等边三角形,点D是线段BC的中点,∠EDF=120°,把∠EDF绕点D旋转,使∠EDF的两边分别与线段AB、AC交于点E、F.(1)当DF⊥AC时,求证:BE=CF;(2)在旋转过程中,BE+CF是否为定值?若是,求出这个定值;若不是,请说明理由;(3)在旋转过程中,连接EF,设BE=x,△DEF的面积为S,求S与x之间的函数解析式,并求S 的最小值.【分析】(1)根据四边形内角和为360°,可求∠DEA=90°,根据“AAS”可判定△BDE≌△CDF,即可证BE=CF;(2)过点D作DM⊥AB于M,作DN⊥AC于N,如图2,易证△MBD≌△NCD,则有BM=CN,DM=DN,进而可证到△EMD≌△FND,则有EM=FN,就可得到BE+CF=BM+EM+CF=BM+FN+CF=BM+CN=2BM=2BD×cos60°=BD=BC=2;(3)过点F 作FG ⊥AB ,由题意可得S △DEF =S △ABC ﹣S △AEF ﹣S △BDE ﹣S △BCF ,则可求S 与x 之间的函数解析式,根据二次函数最值的求法,可求S 的最小值.【解答】解:(1)∵△ABC 是边长为4的等边三角形,点D 是线段BC 的中点,∴∠B =∠C =60°,BD =CD ,∵DF ⊥AC ,∴∠DFA =90°,∵∠A +∠EDF +∠AFD +∠AED =180°,∴∠AED =90°,∴∠DEB =∠DFC ,且∠B =∠C =60°,BD =DC ,∴△BDE ≌△CDF (AAS )(2)过点D 作DM ⊥AB 于M ,作DN ⊥AC 于N ,则有∠AMD =∠BMD =∠AND =∠CND =90°.∵∠A =60°,∴∠MDN =360°﹣60°﹣90°﹣90°=120°.∵∠EDF =120°,∴∠MDE =∠NDF .在△MBD 和△NCD 中,,∴△MBD ≌△NCD (AAS )BM =CN ,DM =DN .在△EMD 和△FND 中,,∴△EMD ≌△FND (ASA )∴EM =FN ,∴BE +CF =BM +EM +CF =BM +FN +CF =BM +CN=2BM =2BD ×cos60°=BD =BC =2(3)过点F 作FG ⊥AB ,垂足为G ,∵BE =x∴AE =4﹣x ,CF =2﹣x ,∴AF =2+x ,∵S △DEF =S △ABC ﹣S △AEF ﹣S △BDE ﹣S △BCF ,∴S =BC ×AB ×sin60°﹣AE ×AF ×sin60°﹣BE ×BD ×sin60°﹣CF ×CD ×sin60°=4﹣×(4﹣x )×(2+x )×﹣×x ×2×﹣×(2﹣x )×2×∴S =(x ﹣1)2+∴当x =1时,S 最小值为【点评】本题主要考查了等边三角形的判定与性质、四边形的内角和定理、全等三角形的判定与性质、三角函数的定义、特殊角的三角函数值等知识,通过证明三角形全等得到BM =CN ,DM =DN ,EM =FN 是解决本题的关键.。
2017学年第一学期期中检测九年级数学问卷一、选择题(本大题共10小题,每小题3分,共30分.每小题给出的四个选项中,只有一项是符合题目要求的)1.下列图形中,是中心对称图形的是().A .B .C .D .2.一元二次方程260x x ++=的根的情况是().A .有两个相等的实数根B .有两个不相等的实数根C .只有一个实数根D .没有实数根3.二次函数22(1)5y x =-+-的最大值是().A .1-B .1C .5-D .54.方程(4)0x x +=的根是().A .10x =,24x =-B .10x =,24x =C .4x =-D .4x =5.一个正方形绕其中心至少旋转(),才能与自身重合.A .45︒B .90︒C .135︒D .180︒6.若关于x 的方程2150x mx +-=有一根是3,则方程的另一根是().A .5-B .5C .2-D .27.如图,ABC △绕点O 逆时针旋转100︒后得到A B C '''△,若35AOB =︒∠,则A OB '=∠().A .35︒B .65︒C .100︒D .135︒8.关于x 的方程20(0)ax bx c a ++=≠有两个根为5-和1,则抛物线2(0)y ax bx c a =++≠的对称轴是().A .4x =-B .3x =-C .2x =-D .1=-9.某一型号飞机着陆后滑行的距离S (单位:米)关于滑行的时间t (单位:秒)之间的函数解析式是21.560S t t =-+,则该型号飞机着陆后滑行()秒才能停下来.AB COA'C'A .600B .300C .40D .2010.如图,抛物线2()y x h =-与x 轴只有一个交点M ,且与平行于x 轴的直线l 交于A 、B 两点,若3AB =,则点M 到直线l 的距离是().A .73B .94C .115D .136二、填空题(共大题共6小题,每小题3分,共18分)11.点(5,7)P --关于原点对称的点的坐标是__________.12.已知1x 、2x 是方程2310x x +-=的两个实数根,则12x x +=__________.13.抛物线26y x =-+的顶点坐标是__________.14.某种商品的标价为400元/件,经过两次降价后的价格为324元/件,且两次降价的百分率相同,则该种商品每次降价的百分率是__________.15.将抛物线244y x x =++向右平移3个单位长度,再向下平移2个单位长度,得到抛物线的解析式是__________.16.如图,在平面直角坐标系中O 是原点,矩形OABC 的对角线相交于点P ,顶点C 的坐标是(0,3),30ACO =︒∠,将矩形OABC 绕点O 顺时针旋转150︒后点P 的对应点P '的坐标是__________.三、解答题(共大题共9小题,共102分.解答应写出文字说明、推理过程或推演步骤) 17.(本小题满分9分)解方程:2680x x ++=.18.(本小题满分9分)已知抛物线21(2)34y x =--+. (1)写出抛物线的开口方向、对称轴和顶点坐标.(2)当y 随x 的增大而增大时,求x 的取值范围.19.(本小题满分10分)如图,在边长为1的正方形网格中,ABC △的三个顶点均在格点上.(1)画出ABC △绕点C 逆时针旋转90︒后的三角形,点A 的对应点为A ',点B 的对应点为B ',连接BB '.(2)在(1)所画图形,B BC '∠的度数__________.20.(本小题满分10分)如图,利用一面墙(墙的长度不限),另三边用20米长的篱笆围成一个矩形场地.若围成矩形场地的面积为50米2,求矩形场地的长和宽.21.(本小题满分12分)已知关于x 的方程250x x p 2+-=.(1)求证:无论p 取何值,方程总有两个不相等的实数根.(2)设方程的两个实数根为1x 、2x ,当1212x x x x +=时,求p 的值.22.(本小题满分12分)如图,二次函数2y x bx c =-++的图象经过(2,0)、(0,8)两点.(1)求二次函数的解析式.(2)当x 取何范围的值时,二次函数的图象位于x 轴上方.A BC23.(本小题满分12分)将边长为ABCD 与边长为2的正方形AEFG 如图放置,AD 与AE 在同一直线上,AB 与AG 在同一直线上,连接DG 、BE .(1)求证:DG BE =.(2)把正方形AEFG 绕点A 旋转一周,当点F 恰好落在AB 边所在的直线上时,求BE 的长.24.(本小题满分14分)已知抛物线21(0)y ax bx c ab =++≠经过原点,顶点为A .(1)若点A 的坐标是(2,4)--.①求抛物线的解析式.②把抛物线在第三象限之间的部分图象记为图象G ,若直线y x n =-+与图象G 有两个不同的交点,求n 的取值范围.(2)若直线2y ax b =+经过点A ,当12x <<时,比较1y 与2y 的大小.25.(本小题满分14分)如图,ABC △是边长为4的等边三角形,点D 是线段BC 的中点,120EDF =︒∠,把EDF ∠绕点D 旋转,使EDF ∠的两边分别与线段AB 、AC 交于点E 、F .(1)当DF AC ⊥时,求证:BE CF =.(2)在旋转过程中,BE CF +是否为定值?若是,求出这个定值;若不是,请说明理由. (3)在旋转过程中,连接EF ,设BE x =,DEF △的面积为S ,求S 与x 之间的函数解析式,并求S 的最小值. G FE C BA DF EC B AD。
1下列词语书写全对的一项是2依次填入下列句子横线上的词语,最恰当的一项是3下列句子中,有语病的一项是4D.今年国庆节期间,无论高速公路是否收费,预计广东省内的自驾游车辆都不会减少。
A.B.C.D.下列说法有误的一项:《我的叔叔于勒》选自莫泊桑的短篇小说集《羊脂球》,莫泊桑是法国19世纪著名的批判现实主义作家,与俄国作家契诃夫、美国作家欧亨利被称为“世界三大短篇小说巨匠”。
毛泽东《沁园春·雪》写景辽阔,江山尽收眼底,论史则百代帝王遣上笔端,其气魄之大,前无古人。
鲁迅作品《故乡》中的主要人物闰土,是五四运动后十年间中国农村经济萧条衰败的悲惨景象的真实写照。
《战国策》是西汉末年刘向根据战国史书整理编辑的,一共有33篇,分为东周、西周、秦齐、楚、赵、魏、韩、燕、宋、卫、中山十二策。
5 著名作家严文井对寓言有如下形象的表述,请用简明直白的语言概括寓言的两个特点和寓言的作用。
寓言是一个魔袋,袋子很小,却能从里面取出很多东西来,甚至能取出比袋子大得多的东西;寓言是一个怪物,当它朝你走来时,分明是一个故事,生动活泼,而当它转身要走的时候,却突然变成了一个哲理,严肃认真;寓言是一座奇妙的桥梁,走过它,你的行囊里就装满了很多好东西,你也长大了,变得美丽了。
特点:① ②作用:6 A.B.C.D.E.F.选出下列古诗文默写正确的两项宫中府中,俱为一体,陟罚藏否,不宜异同。
老夫聊发少年狂,左牵黄,右擎仓。
后值倾覆,奉命于败军之际,受任于危难之间,尔来二十有一年矣。
池上碧台三四点,叶底黄鹂一两声,日长飞絮轻。
已是黄昏独自愁,更著风和雨。
晨起动征铎,客行悲故乡。
7补充下列古诗文的上下据,任选四句补充完整。
8过尽千帆皆不是, 。
(1) ,只有香如故。
(2)了却君王天下事, 。
(3) ,欲语泪先流。
(4)鸡声茅店月,。
(5)(6),西北望,射天狼。
完成下列古诗默写。
9“面朝黄土背朝天”写的是古代劳动人民在烈日下辛苦劳作的情景。
广东省2018届九年级数学上学期期中试题【说明】1.全卷满分为120分。
考试用时为100分钟。
2.答题必须用黑色字迹钢笔或签字笔作答,答案必须写在答题卡各题目的指定区域内相应位置上;不准使用铅笔和涂改液。
不按以上要求作答的答案无效。
一、选择题(本大题10小题,每小题3分,共30分.在每小题列出的四个选项中,只有一个是正确的,请将下列各题的正确答案填写在答题卡相应位置上)1、下列四个圆形图案中,分别以它们所在圆的圆心为旋转中心,顺时针旋转120°后,能与原图形完全重合的是()A. B. C. D.2、一元二次方程的二次项系数、一次项系数、常数项分别是A.,, B.,, C.,, D.,,3、若将抛物线y=x2-2x+1沿着x轴向左平移1个单位,再沿y轴向下平移2个单位,则得到的新抛物线的顶点坐标是( )A.(0,2 ) B.(0,-2) C.(1,2) D.(-1,2)4、关于x的一元二次方程有两个相等的实数根,则m的值是()A. 不存在B、4;C、0; D、0或4;5、二次函数y=ax2+bx的图象如图所示,那么一次函数y=ax+b的图象大致是()A.B.C. D.6、甲、乙、丙三家超市为了促销一种定价相同的商品,甲超市先降价20%,后又降价10%;乙超市连续两次降价15%;丙超市一次降价30%.那么顾客到哪家超市购买这种商品更合算()A.甲B.乙 C.丙 D.一样7、若点A(﹣4,y1),B(﹣1,y2),C(1,y3)在抛物线y=﹣(x+2)2﹣1上,则()A.y1<y3<y2 B.y2<y1<y3 C.y3<y2<y1 D.y3<y1<y28、在一次篮球联赛中,每个小组的各队都要与同组的其他队比赛两场,然后决定小组出线的球队.如果某一小组共有x个队,该小组共赛了90场,那么列出正确的方程是()A. B. x(x﹣1)=90 C.D. x(x+1)=90 9、某商品现在的售价为每件60元,每星期可卖出300件.市场调查反映,如果调整商品售价,每降价1元,每星期可多卖出20件.设每件商品降价x元后,每星期售出商品的总销售额为y元,则y与x的关系式为()A.y=60(300+20x) B.y=(60﹣x)(300+20x)C.y=300(60﹣20x) D.y=(60﹣x)(300﹣20x)10、定义:如果一元二次方程满足,那么我们称这个方程为“凤凰”方程. 已知是“凤凰”方程,且有两个相等的实数根,则下列结论正确的是()A. B. C. D.二、填空题(本大题6小题,每小题4分,共24分.请将下列各题的正确答案填写在答题卡相应位置上)11、方程有两个不等的实数根,则a的取值范围是________。
黄冈中学2017-2018学年九年级上学期期中考试数学试题一、选择题 (本大题有10个小题,每小题3分,共30分.)1.已知关于x的方程x2+3x+a=0有一个根为﹣2,则a的值为()A.5 B. 2 C.﹣2 D.﹣52.已知关于x的一元二次方程x2+2x﹣(m﹣2)=0有实数根,则m的取值范围是()A.m>1 B.m<1 C.m≥1 D.m≤13.二次函数y=x2﹣2x+4化为y=a(x﹣h)2+k的形式,下列正确的是()A.y=(x﹣1)2+2 B.y=(x﹣2)2+4 C.y=(x﹣2)2+2 D.y=(x﹣1)2+34.有x支球队参加篮球比赛,共比赛了45场,每两队之间都比赛两场,则下列方程中符合题意的是()A.x(x﹣1)=45 B. x(x+1)=45 C. x(x﹣1)=45 D.x(x+1)=455.下列汽车标志中,既是轴对称图形又是中心对称图形的是()A. B. C. D.6. 抛物线y=x2+2x+3的对称轴是()A.直线x=1 B.直线x=﹣1 C.直线x=﹣2 D.直线x=27. 如图,在⊙O中, =,∠AOB=44°,则∠ADC的度数是()A.44° B.34° C.22° D.12°8.如图,在正方形ABCD中,△ABE经旋转,可与△CBF重合,AE的延长线交FC于点M,以下结论正确的是()A.AM⊥FC B.BF⊥CF C.BE=CE D.FM=MC9.如图,⊙O的半径为2,△ABC是⊙O的内接三角形,连接OB、OC.若∠BAC与∠BOC互补,则弦BC的长为()A.4 B.3 C.2 D.10. 一次函数y=ax+b (a≠0)与二次函数y=ax 2+bx+c (a≠0)在同一平面直角坐标系中的图象可能是( )A .B .C .D .二、填空题 (本大题有5个小题,每小题3分,共15分.)11. 一元二次方程x 2+3x ﹣4=0的两根分别为 .12. 已知x 1,x 2是关于x 的方程x 2+ax ﹣2b=0的两实数根,且x 1+x 2=﹣2,x 1•x 2=1,则a+b 的值是 .13. 已知二次函数y=(x ﹣1)2+4,若y 随x 的增大而增大,则x 的取值范围是 . 14.如图,四边形ABCD 内接于⊙O,∠DAB=120°,连接OC ,点P 是半径OC 上任意一点,连接DP ,BP ,则∠BPD 可能为 度(写出一个即可).15.如图,Rt △OAB 的顶点A (﹣4,8)在抛物线y=ax 2上,将Rt △OAB 绕点O 顺时针旋转90°,得到△OCD ,边CD 与该抛物线交于点P ,则点P 的坐标为 .16.如图,已知正方形ABCD 的边长为6,E 、F 分别是AB 、BC 边上的点,且∠EDF=45°,将△DAE 绕点D 逆时针旋转90°,得到△DCM .若AE=2,则FM 的长为 .第16题图第14题图第15题图三、解答题(本大题共9个小题,计69分.)17.(本题满分6分)先化简,再求值:(1﹣)÷﹣,其中x2+x﹣2=0.18.(本题满分6分)已知关于x的一元二次方程x2﹣6x+(2m+1)=0有实数根.(1)求m的取值范围;(2)如果方程的两个实数根为x1,x2,且2x1x2+x1+x2≥20,求m的取值范围.19.(本题满分6分)如图,平面直角坐标系内,小正方形网格的边长为1个单位长度,△ABC的三个顶点的坐标分别为A(﹣1,3),B(﹣4,0),C(0,0)(1)画出将△ABC向上平移1个单位长度,再向右平移5个单位长度后得到的△A1B1C1;(2)画出将△ABC绕原点O顺时针方向旋转90°得到△A2B2O;(3)在x轴上存在一点P,满足点P到A1与点A2距离之和最小,请直接写出P点的坐标.OGF EDA20.(本题满分6分)某地2014年为做好“精准扶贫”,授入资金1280万元用于一滴安置,并规划投入资金逐年增加,2016年在2014年的基础上增加投入资金1600万元.从2014年到2016年,该地投入异地安置资金的年平均增长率为多少?21.(本题满分7分)某中学课外兴趣活动小组准备围建一个矩形苗圃园,其中一边靠墙,另外三边周长为30米的篱笆围成.已知墙长为18米(如图所示),设这个苗圃园垂直于墙的一边长为x 米. (1)若苗圃园的面积为72平方米,求x ;(2)若平行于墙的一边长不小于8米,这个苗圃园的面积有最大值和最小值吗?如果有,求出最大值和最小值;如果没有,请说明理由;22.(本题满分8分)正方形ABCD 内接于⊙O,如图所示,在劣弧上取一点E ,连接DE 、BE ,过点D 作DF∥BE 交⊙O 于点F ,连接BF 、AF ,且AF 与DE 相交于点G ,求证: (1)四边形EBFD 是矩形; (2)DG=BE .18m 苗圃园 21题图23.(本题满分10分)某片果园有果树80棵,现准备多种一些果树提高果园产量,但是如果多种树,那么树之间的距离和每棵树所受光照就会减少,单棵树的产量随之降低.若该果园每棵果树产果y (千克),增种果树x(棵),它们之间的函数关系如图所示.(1)求y与x之间的函数关系式;(2)在投入成本最低的情况下,增种果树多少棵时,果园可以收获果实6750千克?(3)当增种果树多少棵时,果园的总产量w(千克)最大?最大产量是多少?24.(本题满分10分)如图,已知△ABC是等腰三角形,顶角∠BAC=α(α<60°),D是BC边上的一点,连接AD,线段AD绕点A顺时针旋转α到AE,过点E作BC的平行线,交AB于点F,连接DE,BE,DF.(1)求证:BE=CD;(2)若AD⊥BC,试判断四边形BDFE的形状,并给出证明.25.(本题满分13分)在平面直角坐标系中,现将一块等腰直角三角板ABC放在第二象限,斜靠在两坐标轴上,且点A(0,2),点C(﹣1,0),如图所示:抛物线y=ax2+ax﹣2经过点B.(1)求点B的坐标;(2)求抛物线的解析式;(3)在抛物线上是否还存在点P(点B除外),使△ACP仍然是以AC为直角边的等腰直角三角形?若存在,求所有点P的坐标;若不存在,请说明理由.答案一、选择题 (本大题有10个小题,每小题3分,共30分.)1.已知关于x的方程x2+3x+a=0有一个根为﹣2,则a的值为( B )A.5 B. 2 C.﹣2 D.﹣52.已知关于x的一元二次方程x2+2x﹣(m﹣2)=0有实数根,则m的取值范围是( C )A.m>1 B.m<1 C.m≥1 D.m≤13.二次函数y=x2﹣2x+4化为y=a(x﹣h)2+k的形式,下列正确的是( D )A.y=(x﹣1)2+2 B.y=(x﹣2)2+4 C.y=(x﹣2)2+2 D.y=(x﹣1)2+34.有x支球队参加篮球比赛,共比赛了45场,每两队之间都比赛两场,则下列方程中符合题意的是( A )A.x(x﹣1)=45 B. x(x+1)=45 C. x(x﹣1)=45 D.x(x+1)=455.下列汽车标志中,既是轴对称图形又是中心对称图形的是( D )A. B. C. D.6. 抛物线y=x2+2x+3的对称轴是( B )A.直线x=1 B.直线x=﹣1 C.直线x=﹣2 D.直线x=27. 如图,在⊙O中, =,∠AOB=44°,则∠ADC的度数是( C )A.44° B.34° C.22° D.12°8.如图,在正方形ABCD中,△ABE经旋转,可与△CBF重合,AE的延长线交FC于点M,以下结论正确的是( A )A.AM⊥FC B.BF⊥CF C.BE=CE D.FM=MC9.如图,⊙O 的半径为2,△ABC 是⊙O 的内接三角形,连接OB 、OC .若∠BAC 与∠BOC 互补,则弦BC 的长为( C ) A . 4 B .3 C .2 D .10.一次函数y=ax+b (a≠0)与二次函数y=ax 2+bx+c (a≠0)在同一平面直角坐标系中的图象可能是( D )A .B .C .D .二、填空题 (本大题有5个小题,每小题3分,共15分.)11. 一元二次方程x 2+3x ﹣4=0的两根分别为 .(1和-4)12. 已知x 1,x 2是关于x 的方程x 2+ax ﹣2b=0的两实数根,且x 1+x 2=﹣2,x 1•x 2=1,则a+b 的值是 . (23) 13. 已知二次函数y=(x ﹣1)2+4,若y 随x 的增大而增大,则x 的取值范围是 .(x >1) 14.如图,四边形ABCD 内接于⊙O,∠DAB=120°,连接OC ,点P 是半径OC 上任意一点,连接DP ,BP ,则∠BPD 可能为 度(写出一个即可).(60~120之间的任意一个数)15.如图,Rt △OAB 的顶点A (﹣4,8)在抛物线y=ax 2上,将Rt △OAB 绕点O 顺时针旋转90°,得到△OCD ,边CD 与该抛物线交于点P ,则点P 的坐标为 .(22,4)第8题图第7题图第9题图第15题图16.如图,已知正方形ABCD 的边长为6,E 、F 分别是AB 、BC 边上的点,且∠EDF=45°,将△DAE 绕点D 逆时针旋转90°,得到△DCM .若AE=2,则FM 的长为 .(5)三、解答题(本大题共9个小题,计69分.) 17.(本题满分6分)先化简,再求值:(1﹣)÷﹣,其中x 2+x ﹣2=0.解:原式=•﹣=﹣=, ……………2分解方程x 2+x ﹣2=0,得x 1=1,x 2=-2(不合题意,舍去), ……………5分 ∴原式=3412142=⨯+.……………6分 18.(本题满分6分)已知关于x 的一元二次方程x 2﹣6x+(2m+1)=0有实数根.(1)求m 的取值范围;(2)如果方程的两个实数根为x 1,x 2,且2x 1x 2+x 1+x 2≥20,求m 的取值范围. 解:(1)根据题意得△=(﹣6)2﹣4(2m+1)≥0,解得m≤4;……………3分(2)根据题意得x 1+x 2=6,x 1x 2=2m+1, 而2x 1x 2+x 1+x 2≥20,所以2(2m+1)+6≥20,解得m≥3,而m≤4,所以m 的范围为3≤m≤4.……………6分19.(本题满分6分)如图,平面直角坐标系内,小正方形网格的边长为1个单位长度,△ABC 的三个顶点的坐标分别为A (﹣1,3),B (﹣4,0),C (0,0)(1)画出将△ABC 向上平移1个单位长度,再向右平移5个单位长度后得到的△A 1B 1C 1; (2)画出将△ABC 绕原点O 顺时针方向旋转90°得到△A 2B 2O ;(3)在x 轴上存在一点P ,满足点P 到A 1与点A 2距离之和最小,请直接写出P 点的坐标.第16题图第14题图解:(1)如图所示,△A1B1C1为所求做的三角形;……………2分(2)如图所示,△A2B2O为所求做的三角形;……………4分(3)∵A2坐标为(3,1),A3坐标为(4,﹣4),∴A2A3所在直线的解析式为:y=﹣5x+16,令y=0,则x=,∴P 点的坐标(,0).……………6分20.(本题满分6分)某地2014年为做好“精准扶贫”,授入资金1280万元用于一滴安置,并规划投入资金逐年增加,2016年在2014年的基础上增加投入资金1600万元.从2014年到2016年,该地投入异地安置资金的年平均增长率为多少?解:设该地投入异地安置资金的年平均增长率为x,根据题意,……………1分得:1280(1+x)2=1280+1600,……………3分解得:x=0.5或x=﹣2.25(舍),……………5分答:从2014年到2016年,该地投入异地安置资金的年平均增长率为50%;……………6分21.(本题满分7分)某中学课外兴趣活动小组准备围建一个矩形苗圃园,其中一边靠墙,另外三边周长为30米的篱笆围成.已知墙长为18米(如图所示),设这个苗圃园垂直于墙的一边长为x米.(1)若苗圃园的面积为72平方米,求x;(2)若平行于墙的一边长不小于8米,这个苗圃园的面积有最大值和最小值吗?如果有,求出最大值和最小值;如果没有,请说明理由;18m苗圃园21题图解:(1)苗圃园与墙平行的一边长为(30-2x)米.依题意可列方程O G F E D CB A x (30-2x )=72,即x 2-15x +36=0.……………2分解得x 1=3,x 2=12.……………3分(2)依题意,得8≤30-2x ≤18.解得6≤x ≤11.……………4分面积S =x (30-2x )=-2(x -152)2+2252(6≤x ≤11).……………5分 ①当x =152时,S 有最大值,S 最大=2252;……………6分 ②当x =11时,S 有最小值,S 最小=11×(30-22)=88.……………7分22.(本题满分8分)正方形ABCD 内接于⊙O,如图所示,在劣弧上取一点E ,连接DE 、BE ,过点D 作DF∥BE 交⊙O 于点F ,连接BF 、AF ,且AF 与DE 相交于点G ,求证:(1)四边形EBFD 是矩形;(2)DG=BE .证明:(1)∵正方形ABCD 内接于⊙O,∴∠BED=∠BAD=90°,∠BFD=∠BCD=90°,又∵DF∥BE,∴∠EDF+∠BED=180°,∴∠EDF=90°,∴四边形EBFD 是矩形;……………4分(2)∵正方形ABCD 内接于⊙O,∴的度数是90°,∴∠AFD=45°, 又∵∠GDF=90°,∴∠DGF=∠DFC=45°,∴DG=DF,又∵在矩形EBFD 中,BE=DF ,∴BE=DG.……………8分23.(本题满分10分)某片果园有果树80棵,现准备多种一些果树提高果园产量,但是如果多种树,那么树之间的距离和每棵树所受光照就会减少,单棵树的产量随之降低.若该果园每棵果树产果y (千克),增种果树x (棵),它们之间的函数关系如图所示.(1)求y 与x 之间的函数关系式;(2)在投入成本最低的情况下,增种果树多少棵时,果园可以收获果实6750千克?(3)当增种果树多少棵时,果园的总产量w (千克)最大?最大产量是多少?解:(1)设函数的表达式为y=kx+b ,该一次函数过点(12,74),(28,66),得,解得,∴该函数的表达式为y=﹣0.5x+80,……………3分(2)根据题意,得,(﹣0.5x+80)(80+x)=6750,解得,x1=10,x2=70∵投入成本最低.∴x2=70不满足题意,舍去.∴增种果树10棵时,果园可以收获果实6750千克.……………6分(3)根据题意,得w=(﹣0.5x+80)(80+x)=﹣0.5 x2+40 x+6400=﹣0.5(x﹣40)2+7200∵a=﹣0.5<0,则抛物线开口向下,函数有最大值∴当x=40时,w最大值为7200千克.∴当增种果树40棵时果园的最大产量是7200千克.……………10分24.(本题满分10分)如图,已知△ABC是等腰三角形,顶角∠BAC=α(α<60°),D是BC边上的一点,连接AD,线段AD绕点A顺时针旋转α到AE,过点E作BC的平行线,交AB于点F,连接DE,BE,DF.(1)求证:BE=CD;(2)若AD⊥BC,试判断四边形BDFE的形状,并给出证明.证明:(1)∵△ABC是等腰三角形,顶角∠BAC=α(α<60°),线段AD绕点A顺时针旋转α到AE,∴AB=AC,∴∠BAE=∠CAD,在△ACD和△ABE中,,∴△ACD≌△ABE(SAS),∴BE=CD;……………5分(2)∵AD⊥BC,∴BD=CD,∴BE=BD=CD,∠BAD=∠CAD,∴∠BAE=∠BAD,在△ABD和△ABE中,,∴△ABD≌△ABE(SAS),∴∠EBF=∠DBF,∵EF∥BC,∴∠DBF=∠EFB,∴∠EBF=∠EFB,∴EB=EF,∴BD=BE=EF=FD,∴四边形BDFE为菱形.……………10分25.(本题满分13分)在平面直角坐标系中,现将一块等腰直角三角板ABC放在第二象限,斜靠在两坐标轴上,且点A(0,2),点C(﹣1,0),如图所示:抛物线y=ax2+ax﹣2经过点B.(1)求点B的坐标;(2)求抛物线的解析式;(3)在抛物线上是否还存在点P(点B除外),使△ACP仍然是以AC为直角边的等腰直角三角形?若存在,求所有点P的坐标;若不存在,请说明理由.解:(1)过点B作BD⊥x轴,垂足为D,∵∠BCD+∠ACO=90°,∠ACO+∠CAO=90°,∴∠BCD=∠CAO,又∵∠BDC=∠COA=90°,CB=AC,∴△BCD≌△CAO,∴BD=OC=1,CD=OA=2,∴点B的坐标为(﹣3,1); (3)分(2)抛物线y=ax2+ax﹣2经过点B(﹣3,1),则得到1=9a﹣3a﹣2,解得a=,所以抛物线的解析式为y=x2+x﹣2;……………7分(3)假设存在点P,使得△ACP仍然是以AC为直角边的等腰直角三角形:①若以点C为直角顶点;则延长BC至点P1,使得P1C=BC,得到等腰直角三角形△ACP1,过点P1作P1M⊥x轴,∵CP1=BC,∠MCP1=∠BCD,∠P1MC=∠BDC=90°,∴△MP1C≌△DBC.∴CM=CD=2,P1M=BD=1,可求得点P1(1,﹣1);②若以点A为直角顶点;则过点A作AP2⊥CA,且使得AP2=AC,得到等腰直角三角形△ACP2,过点P2作P2N⊥y轴,同理可证△AP2N≌△CAO,∴NP2=OA=2,AN=OC=1,可求得点P2(2,1),③以A为直角顶点的等腰Rt△ACP的顶点P有两种情况.即过点A作直线L⊥AC,在直线L上截取AP=AC时,点P可能在y轴右侧,即现在解答情况②的点P2;点P也可能在y轴左侧,即还有第③种情况的点P3.因此,然后过P3作P3G⊥y轴于G,同理:△AGP3≌△CAO,∴GP3=OA=2,AG=OC=1,∴P3为(﹣2,3);经检验,点P1(1,﹣1)与点P2(2,1)都在抛物线y=x2+x﹣2上,点P3(﹣2,3)不在抛物线上.……………13分。
2017-2018学年上学期广州九年级上期中测试英语卷(含答案)2017学年第一学期初三级期中考英语科问卷总分:110 时间:120分钟一.语法选择(共15题;每小题1分,满分15分)阅读下面短文,按照句子结构的语法行和上下文连贯的要求,从1-15各题所给的A、B、C和D项中选出最佳选项,并在答题卡上将该项涂黑。
About the importance of good health, nobody can explain better than ____1____ doctor. They are the people who really know the importance of keeping fit and ____2____. I am saying this because my doctor is an angel. Every time I put on an extra pound, he will remind me____3____ what it is happening to my body. If we do not need to visit any doctor we think we are very healthy. ____4____ that is not true. We may look healthy but we don’t know clearly what ____5____ inside. However, there are many different ways we ____6____ make sure that we look inside as ____7____ as we do outside.The first and easiest step is keeping a good and ____8____ diet.Next ____9____ sleeping well. Sleep early. Make sure you get nine hours of sleep.Do not skip your breakfast. It is one of the most important ____10____ of the day. Eat your regular meals, and it will do you good to eat healthily even during breaks.____11____ your body every day. Go ____12____ a swim, or walk, or just play a game of football or tennis. Try your best not to get stressed ____13____ it’s bad for your health.Remember ____14____ washing your hands, and then youwon’t catch any infection.Get away from your bad habit. Don’t smoke. Some wine does your body good while most of it does harm. Be wise and don’t drink ____15____.1. mine B. yours C. his D. your2. healthy B. health C. healthily D. unhealthy3. on B. at C. of D. with4. So B. And C. However D. But5. happens B. is happening C. was happening D. happened6. A. should B. can C. must D. may not7. A. good B. well C. better D. stronger8. A. balance B. balancing C. balanced D. balances9. A. to be B. is C. do D. does10. A. meals B. a meal C. meal D. some meals11. A. To exercise B. Exercising C. Exercise D. Exercised12. A. to B. for C. / D. in13. A. when B. so C. though D. because14. A. to keep B. keeping C. keep D. keeps15. A. too many B. any C. too little D. too much二.完形填空(共10小题;每小题1.5分,共15分)体裁:记叙文话题:金钱与法律难度:★★阅读下面短文,掌握其大意,然后从16-25各题所给的A、B、C 和D项中,选出最佳选项,并在答题卡上将该项涂黑。
广外外校2017——2018学年度第一学期期中考试初三年级语文试卷考试时间:120分钟满分:150分命题人:徐晓琳本试卷7页,答题卷2面,试卷分三部分,共25小题,注意事项:1.答卷前,考生务必在答题卡上用黑色字迹的钢笔或签字笔填写自己的考生号、姓名,再用2B铅笔把对应号码的标号涂黑。
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第一部分积累与运用一、(6小题,20分)1.下列词语中,加粗字读音全对..的一项是()(3分)A.狡黠.xiá哭丧.(sàng)襁.褓qiáng 一抔.黄土póuB.畸.形jī拮据.jù栈.桥zhàn 义愤填膺.yīngC.抽噎.yē执拗.ào 恣睢.(suī)咬文嚼.字juéD.阴霾.mái 窒.息zhì挑剔.(tī)廓然无累.lěi2.下面词语中没有..错别字的一组是(3分)A.隔膜愕然瑟缩心无旁鹜B.殒落谀词嬉闹红妆素裹C.凌驾驱除禁锢歇斯底里D.暗哑扶掖颧骨莫明其妙3、下列句子中加粗词语使用正确的一项是()(3分)A.德国肠出血性大肠杆菌疫情引发欧洲国家恐慌,一些国家的农产品市场也遭到重创,据称,作为德国重要蔬菜供应地的法国,其黄瓜等蔬菜的销售量一泻千里。
B.“低碳”生活方式潜移默化地改变着人们的日常行为习惯,并逐步成为生活新时尚。
C.为迎接中国——亚欧博览会这一规格高、规模大、影响广的重要展会,我市召开环境综合治理工作会议,决定投资10亿元,力争让首府改头换面,发生巨大变化。
2017-2018学年广东省广州市越秀区培正中学九年级(上)期中物理试卷一、单项选择题(36分,每题3分)1.(3分)下列餐具中,通常情况下属于导体的是()A.玻璃杯B.不锈钢汤匙C.瓷碗D.竹筷2.(3分)四个悬挂着的带电草球,相互作用情况如图所示,那么D球()A.带与A球不同种的电荷B.带与B球不同种的电荷C.带与C球不同种的电荷D.一定带正电荷3.(3分)扩散现象的发生是由于()A.分子在不停息地做无规则运动B.分子之间存在引力C.分子之间的斥力大于引力D.物质是由分子组成的4.(3分)如图所示实验或事例,属于内能转化为机械能的是()A.水蒸气将软木塞冲出B.搓手取暖C.钻木取火D.由滑梯上滑下臀部会有灼热感5.(3分)如图是某物质由液态变为固态过程温度随时间变化的图象,下列说法正确的是()A.t4时刻物体内能为零B.t2、t3时刻物体内能相等C.t2时刻物体内能比t3小D.t1时刻物体分子动能比t2时大6.(3分)如图所示的四幅电路中,电流表能够测灯L1电流的是()A.B.C.D.7.(3分)某装置的能量流向图如图所示,据此推测该装置可能是()A.热机B.滑轮组C.电灯D.电热水器8.(3分)小明直接用水桶装着水从一楼提到三楼的家中,克服水的重力所做的功和克服桶的重力所做的功分别是()A.总功和有用功B.总功和额外功C.有用功和额外功 D.均是有用功9.(3分)小灯泡的结构如图,按图中连接能让完好的2.5V 的灯泡点亮的是()A.B.C.D.10.(3分)如果电路中出现如图所示的情形,物理学中称之为短路,这样的后果很严重,这时灯泡会()A.变暗B.变得更亮C.正常发光D.不能发光11.(3分)如图所示为汽油机工作过程的示意图,其中表示做功冲程的是()A.B.C.D.12.(3分)如图所示的电蚊拍,具有灭蚊和照明等功能。
当开关S1闭合、S2断开时,只有灭蚊网通电起到灭蚊作用;当开关S1和S2都闭合时,灭蚊网与灯都通电,同时起到灭蚊和照明作用。
广州市育才实验学校2017学年第一学期期中检测九年级数学试卷一、选择题(本大题每题3分,共30分)1.下列图形既是轴对称图形又是中心对称图形的是(). A . B . C .D .2.一元二次方程23450x x --=的一次项系数是().A .3B .4C .5-D .4-3.将二次函数2361y x x =-+化成顶点式是().A .23(3)26y x =--B .23(3)8y x =--C .23(1)2y x =--D .23(1)y x =-4.如图,ABC △内接于⊙O ,且OB OC ⊥,则A ∠的度数是(). A .90︒ B .50︒ C .45︒ D .30︒5.已知关于x 的方程2410x x c -++=有两个相等的实数根,则常数c 的值为().A .1-B .0C .1D .36.已知点(12,1)M m m --关于原点的对称点在第一象限,则m 的取值范围在数轴上表示正确的是(). A .B .C .D .7.若二次函数225y x ax =-++的图象关于直线4x =对称,则y 的最值是().A .最小值21B .最小值24C .最大值21D .最大值248.要组织一次篮球邀请赛,参赛的每个队之间的都要比赛一场,计划安排15场比赛,设比赛组织者应邀请x 个队参赛,则x 满足的关系式为(). A .1(1)152x x += B .1(1)152x x -= C .(1)15x x += D .(1)15x x -=9.如图,在平面直角坐标系中,⊙O 的半径是1,直线AB 与x 轴交于点(,0)P x ,且与x 轴正方向夹角为45︒,若AB 与⊙O 有公共点,则x 值的范围是().等腰梯形平行四边形等边三角形菱形C BAOA .11x -≤≤B.x C.x < D.0x ≤10.如图,在Rt ABC △中,90ACB =︒∠,将ABC △绕顶点C 逆时针旋转得到A B C '''△,M 是BC 的中点,P 是A B ''的中点,连接PM ,若2BC =,30BAC =︒∠,则线段PM 的最大值是(). A .4 B .3 C .2 D .1二、填空题(本大题每题3分,共18分)11.方程(3)(9)0x x --=的根是__________.12.在⊙O 中,弦AB 的长恰好等于半径,弦AB 所对的圆心角为__________.13.一元二次方程220x mx m ++=的两个实根分别为1x ,2x ,若121x x +=,则12x x =__________.14.二次函数22(1)1y a x x a =--+-的图象经过原点,则a 的值为__________.15.如图,在矩形ABCD 中,1AB =,2AD =,将AD 绕点A 顺时针旋转,当点D 落在BC 上点D '时,则DAD '=∠__________度.16.如图,AB 是⊙O 的弦,C 是AB 上一点,90AOC =︒∠,8OA =,6OC =,则AB =__________.PM AB CA'B'D'D AB CA B C O三、解答题(共大题共102分,需要写出必要的过程,作图要求用黑色签字笔或2B 铅笔..完成) 17.(本小题满分8分)解方程(1)2(5)90x --=.(2)2253x x +=.18.(本小题满分10分)如图,ABC 在平面直角坐标系内,顶点的坐标分别为(1,5)A -,(4,2)B -,(2,2)C -. (1)画出ABC △关于原点O 对称的222A B C △.并直接写出点2A 、2B 、2C 的坐标.(2)线段2AA 的长度为__________.19.(本小题满分10分)已知二次函数2y x bx c =++的图象经过点(0,2)和(1,1)-,求图象的顶点坐标和对称轴.20.(本小题满分10分)已知关于x 的一元二次方程2(2)230a x ax a -+++=有实数根.(1)求a 的取值范围.(2)当a 取最大数值时,解此一元二次方程.21.(本小题满分12分)为了响应十九大党中央提出的“精准扶贫”,2017年,某市开始实施“旧物循环计划”,为旧物品二次利用提供了公益平台,输送到贫因地区,预计到2017年底,全年回收旧物3万件,随着定值力度的加大,2019年全年回收旧物预计达6.75万件,若每年回收旧物的增大率相同. (1)求每年回收旧物的增长率.(2)按着这样的增长速度,请计算2020年全年回收旧物能超过10万件吗?22.(本小题满分12分)如图,⊙O 中,直径CD ⊥弦AB 于E ,AM BC ⊥于M ,交CD 于N ,连AD . (1)求证:AD AN =.(2)若AE =1ON =,求⊙O 的半径.EC AD M N23.(本小题满分12分)如图,已知二次函数2(0)y ax bx c a =++≠的图象经过(1,0)A -、(4,0)B 、(0,2)C 三点.(1)求二次函数的解析式.(2)点D 是该二次函数图象上的一点,且满足DBA CAO =∠∠,求点D 的坐标.24.(本小题满分14分)如图,已知ABC △和ADE △都是等腰直角三角形,90ACB ADE ==︒∠∠,点F 为BE 的中点,连接CF ,DF .(1)如图1,当点D 在AB 上,点E 在AC 上时.①证明:BFC △是等腰三角形.②请判断线段CF ,DF 的关系?并说明理由.(2)如图2,将图1中ADE △绕点A 旋转到图2位置时,请判断(1)中②的结论是否仍然成立?并证明你的判断.25.(本小题满分14分)如图,将矩形纸片ABCD 沿直线MN 折叠,顶点B 恰好与CD 边上的动点P 重合(点P 不与点C ,D 重合),折痕为MN ,点M ,N 分别在边AD ,BC 上,连接MB ,MP ,BP ,BP 与MN 相交于点F .(1)求证:NMD BPC =∠∠.(2)①在图2中,作出经过M ,D ,P 三点的⊙O (保留作图痕迹).②设4AB =,随着点P 在CD 上的运动,若①中的⊙O 恰好与BM ,BC 同时相切,求此时DP 的长.图1DA B C F 图2D A BC E F图1F PD A B C M N 图2F M C B A D P 备用图D A B C。
二、语言知识与运用(共两节,满分20分)第一节单项选择(共10小题,每小题1分,满分10分)16.He has breakfast at seven, ________ ?A.has heB. does heC. hadn’t heD. doesn’t he17.The important thing is ________ there on time.A.to gettingB. gotC. to getD. get18.He always kept ______ when he was asked about it.A.to be silentB. silenceC. silentD. silently19.Though he is quite busy, ________ he often helps me with my English.A.butB. howeverC. soD. yet20.His father suggests that he _______ his homework before watching TV.A.will finishB. finishesC. finishD. has finished21.There is ________ news about his movie star in the newspaper. Where can I get some?A.manyB. a fewC. a lotD. little22.A: you look very nice in your new dress today.B: Oh, really? I ______ it when I was on sale.A.buyB.boughtC. have boughtD. will buy23.A: Jack, your toys should be in right order.B: OK, I’ll ________ them _______ right now.A.put; downB. put; awayC. put; upD. put; on24.Maybe you can hardly believe it. A 70-year-old man _______ me at tennis.A.wonB. succeededC. beatD. hit25.A: I feel really tired.B: _________.A.Lucky you.B. You’d better work harder.C. Why not go and have a rest?D. Congratulations第二节语法选择(共10小题,每小题1分,满分10分)What will you do when you want to have something but without money?Last summer holiday, Jack, a 16-year-old boy, 26 wanted to have a nice bike. He asked his parents for the money and they said he must get it by himself. But 27 could he get it?On his way home one day, he 28 about this. Not many people wanted to ask children 29 for them. Maybe he could sweep away snow for the neighbors. 30 it was not winter. He had to wait a long time for that. He couldn't ___31 grass for their gardens, because he was not old enough to do such work.Just at the moment, he saw Tom, one of his classmates, selling books in a book shop."I could do that," he thought. He asked Tom 32 questions. He learned that 33 took Tom about three hours a day to do the job and he could get twenty dollars each week. And Tom gave him the telephone number of the book shop manager.Jack almost flew home. "Mum. I have 34 good news to tell you." Jack said. After he had told his mother what he thought, she said, "I think it's a good idea.""I 35 the manager tomorrow." said Jack, "After all, I'm going to be a businessman." Jack'smother looked happily at him and smiled.26. A. which B. that C. whom D. who27. A. where B. which C. how D. what28. A. thinks B. will think C. was thinking D. is thinking29. A. work B. to work C. working D. worked30. A. But B. If C. So D. However31. A. cuts B. cut C. cutting D. be cut32. A. little B. a little C. few D. a few33. A. it B. its C. this D. that34. A. \ B. a C. an D. the35. A. call B. called C. will call D. was calling三、完形填空(共10小题,每小题1分,满分10分)Tyrone curry of white center, Washington, loves his _ 36_ jobs at evergreen high school. One is keeping the_ 37 _clean and the other is coaching a running team. So five years ago, when he won almost 3.4 million dollars in the Washington state lottery(彩票),he decided not to _ 38__a thing. He still goes to work everyday, making the floors _ 39__, and then heading outside to coach the team in their running exercises. The only difference? __40__athletes will soon run on a new track(跑道)Long before curry _ 41__ the money, he’d already made a decision. “ten years ago , I said I was going to put a track here,” he saidEither this month, curry gave the school a check of 40000 dollars to _ 42__a track“ Tyrone goes above and beyond in the sports he teaches,” high school senior Devant Botello said,”It’s a _43 _feeling. All I can say is thanks.”But curry believes his students give him _ 44__ than he has given them. “T hey do things for you. They keep you young.” He saidCurry will finally retire this June. He has _ 45__for 34 years. But he’s planning to run for the school board and the chances are, he won’t miss a single track meet.36A two B three C four D five37A house B supermarket C school D park38A smell B waste C make D change39A dirty B clean C warm D cold40A her B his C your D my41A borrowed B lent C won D saved42A build B find C buy D sell43A deep B bad C terrible D good44A less B worse C more D better45A lived B worked C drove D studied四、阅读理解(共20小题,每小题2分,满分40分)ALong, long ago people made fires from lightening (闪电). But they had to keep the fire burning, for they couldn’t start it again if there was no lightening. Later, they found out hitting two pieces of stone together could make a spark (火花). The spark could fire dry leaves. In this way they could make the fire again if it went out. Then people also learned to make a fire by rubbing (摩擦). They made a hole on a piece of wood and put a smaller stick into the hole. They turned the stick again and again. After a few minutes they got a fire.A years went by, people learned other ways to make a fire. Sometimes they used the heat from the sun. They held a piece of glass in the right way and made a piece of paper on fire.About two centuries ago, people began to make matches. Matches brought people a quick and easy way to make fires. Today matches are still being used, but people have more new ways to make fires. One of them is to use an electric fire starter. Of course an electric fire starter is much more expensive than a box of matches. But it is very useful.46. From the text we know that a spark can _______.A. fire any leavesB. burn anythingC. burn dry leavesD. keep fire burning47. We can also get a fire by ________.A. making a hole on a big piece of woodB. putting a smaller stick into the holeC. turning the stick hard for a whileD. all above together48. Matches have been used ________.A. for about two thousand yearsB. for about two hundred yearsC. since people began to use fire for cookingD. since people used the heat from the sun49. From the text, we know that _______.A. electric fire starters are widely usedB. people haven’t used matches since they had electric fire startersC. today there are only two ways to make fireD. some forest fires happen from lightening50. Which of the following is the right order of the ways to make fires that people got to know?a. with a matchb. from the sunc. from lighteningd. by rubbinge. with an electric fire starterA. a, b, c, d, eB. b, c, a, e, dC. c, d, b, a, eD. d, a, c, b, eBWhen I was ten my dad helped me buy my first ten-speed bicycle from Allen. I put up $60 of my grass cutting and snow shoveling (铲) money and my dad put up the other half I would pay him back over the next six months. Although it was not in the latest style, it was my ticket to the adult world.I spent that summer and autumn riding happily. My sister Liz, a prisoner(囚犯,俘虏) of her five-speed bicycle, never had a chance to keep up. Just before the Christmas deadline to pay my dad back, we were hit with several snowstorms. This allowed me to shovel enough driveways (车道) to pay off my debt. I was now officially a bike owner; it was a feeling unlike any other.On that Christmas morning, my dad gave me a used portable (便携式的) record player. I was excited. However, my joy was short-lived after my dad called my sister to the kitchen. “We have one more gift for you. ”he said as he opened the door that led to the garage. There, on the steps, stood a new ten-speed bicycle.“It’s not fair,”I complained. “I worked so hard for my bike. and it’s not even new. Then Liz gets a new bike. She didn’t have to do anything for it. ”My dad smiled. “She didn’t have to do anything for it because it’s not really for her,”he said. What did that mean? I didn’t want her bike. By spring Liz and I were riding all over town together now that she could keep up. As we grew, Liz and I became true friends.Still I wasn’t smart enough to figure out what my dad meant until years later. That new bike was not a gift for Liz —it was a gift for me. He’d given me the gift of my sister’s company, the ability to stay together rather than drift apart (逐渐疏远) in the face of my ability to travel. He gave me my best friend.51. What do we know about the author’s bike?A.It was worth $120. B.Allen bought it for him.C.It was very fashionable. D.He didn’t like it actually.52. Why did the author think he was officially a bike owner?A.He had paid off his debt.B.He had learned to ride a bike.C.He could also own Liz’s bike.D.He could sell his bike to Liz.53. Why was the author’s Christmas joy short-lived?A.His sister got a new record player.B.His father didn’t care about him.C.The record player wasn’t new.D.His sister got a better gift.54. Hearing his father say “it’s not really for her (Paragraph 4)”, the author probably felt ________. A.moved B.satisfied C.puzzled D.disappointed55. The author finally realized that ________.A.the new bike actually belonged to himB.the new bike wasn’t bought by his fatherC.his father actually gave him a more valuable giftD.his father loved his sister more as a matter of factCIn every country, there are thousands of people who want to help out. Many join organizations run (管理) by their governments, for example, the Peace Corps in the United States and V oluntary Service Overseas in Britain. Since the powerful (猛烈的) earthquake took place in Sichuan, more than 200 thousand volunteers across China have been helping there! They do all kinds of work or come up with ways to help improve life. Some offer their professional skills for free. Others have no qualifications (资历), but they love to work hard to help.One of the most famous volunteers in the world was Mother Teresa. She could be the best volunteer because she gave her life to helping the poorest people of Calcutta. She helped the homeless, cared for the sick, gave out food, and became the mother of those without families.Now more and more teenagers actively look for volunteering opportunities, too. They volunteer because they think it will be fun or they will learn something. They also like the idea of being helpful to others, even if it is just handing out books for the teacher. As they get older, these reasons are still the same, but there are other important reasons for volunteering such as learning on-the-job, getting work experience, and improving their social life.All volunteers bring joy to the people they help in so many ways. They might read books to the blind, fix up broken homes, find ways to get water for villages. Could you be a volunteer? What kind of volunteer work could you do? There is someone in the world who needs you.56. The Peace Corps is __ in the United States.A.a city B.an organization C.a volunteer D.a school57. The word those in the passage means __ .A.the homeless B.the sick C.the poor D.the kids58. What is NOT the reason for teenagers to be volunteers according to the passage?A.They want to make more friends.B.They want to be helpful.C.It helps them get work experience.D.It can improve their social life.59. Which of the following is true according to the passage?A.V olunteers need qualifications.B.V olunteers offer their help without any pay.C.Young kids can’t be volunteers.D.Some volunteers bring joy to others.60. What is the main idea of this passage?A.The world needs volunteers.B.Mother Teresa was a great volunteer.C.V olunteers do all kinds of work.D.There are different ways of volunteering.DWhat exactly is a lie? Is it anything we say which we know is untrue? Or is it something more than that? For example, suppose a friend wants to borrow some money from you. You say "I wish I could help you, but I am short of money myself." In fact, you are not short of money but your friend is in the habit of not paying his debts and you don't want to hurt his feelings by reminding him of this. Is this really a lie?Professor Jerald Jellison of the University of southern California has made a scientific study of lying. According to him, women are better liars than men, particularly when telling a "white lie", such as when a woman at a party tells another woman that she likes her dress when she really thinks it's terrible. However,this is only one side of the story. Other researchers say that men are more likely to tell more serious lies, such as making a promise that they have no intention of carrying out. This is the kind of lie politicians and businessmen are supposed to be particularly skilled at: the lie from which the liar hopes to profit or gain in some way.Research has been done into the way people's behavior changes in a number of small, unimportant ways when they lie. It has been found that if they are sitting down at the time, they tend to move about in their chairs more than usual. To the trained observer they are saying "I wish I were somewhere else now". They also tend to touch certain parts of the face, particularly the nose. One explanation of this may be that lying causes a slight increase in blood pressure. The tip of the nose is very sensitive to changes and the increased pressure makes it itch.Another gesture that gives liars away is what the writer Decmond Morris in his book Man Watchingcalls the "mouth cover". He says that there are several typical forms of this,such as covering part of the mouth with the fingers, touching the upper lip or putting a finger of the hand at one side off the mouth. Such a gesture can be understood as an unconscious (未察觉的) attempt on the part of the liar to stop himself from lying.Of course, such gestures as rubbing the nose or covering the mouth, moving about in a chair can not be taken as proof that the speaker is lying. They simply tend to happen more often in this situation. It is one gesture alone that gives the liar away but a whole number of things, and in particular the context (上下文) which the lie is told.61. According to the passage, a white lie seems to be a lie _____.A. that other people believeB. that other people don't believeC. told in order not to hurt someone's feelingsD. told in order to take advantage of someone62. Research suggests that women _____.A. are better at telling less serious lies than menB. generally lie for more than men doC. often make promises they intend to breakD. lie at parties more often than men do63. Researchers find that when a person tells lies _____.A. his blood pressure increases measurablyB. he looks very seriousC. he is likely to make some small changes in his behaviorD. he uses his unconscious mind64. The writer of the passage _____.A. hates lyingB. enjoys lyingC. often tells a lieD. tries to study about lying65. Which of the following is not mentioned in the passage as a sign of lying?A. Touching one's earsB. Rubbing the noseC. Moving in a chairD. Covering the mouth五、写作(共三节,满分30分)第一节单词拼写(共5小题,每小题1分,满分5分)根据下列句子和所给单词的首字母写出所缺单词。
2017学年上学期广州中学九年级11月月考语文试卷本试卷共8页,分三部分,共23小题,满分150分。
考试用时120分钟。
注意事项:1.答题前,考生务必在答题卡上用黑色字迹的钢笔或签字笔填写自己的考生号、姓名;同时填写考场试室号、座位号,再用2B铅笔把对应这两个号码的标号涂黑。
2.选择题答案用2B铅笔填涂;将答题卡上选择题答题区中对应题目选项的答案信息点涂黑;如需改动,用橡皮擦干净后,在选涂其他答案;答案不能答在试卷上。
3.非选择题答案必须用黑色字迹的钢笔或签字笔写在答题卡各题目指定区域内的相应位置上:如需改动,先划掉原来的答案,然后再写上新的答案,改动后的答案也不能超出指定的区域;不准使用铅笔、圆珠笔和涂改液。
不按以上要求作答的答案无效。
第一部分积累与运用(共35分)一、基础部分(6,题,20分)1.下列加粗的字注音正确的一项是()A.潮汛.(xùn)煞.白(shà)恣.睢(zī)拮.据(jié)B.栈.桥(zhàn)汲.取(qí)诘.难(jié)滞.碍(zhì)C.狡黠.(jié)诓.骗(kuāng)抽噎.(yē)阔绰.(chuò)D.惘.然(wǎng)模.式(mó)沙哑.(yǎ)嗤.笑(chī)2.下列词语书写全部正确的一项是()(3分)A.愕然牡蛎歇斯底里掷之不理B.彷徨阐述格物治知斩钉截铁C.要诀渺茫修身齐家豁然贯通D.藻饰伦理狂忘自大轻而易举ù3.下列加粗词语运用不恰当的一项是()(3分)A.只要锲而不舍....地努力,就能沿着自己的目标一步步前进。
B.他犯了罪,他的家人给法官送去一份厚礼,其目的的是不言而喻....的。
C.他的发言听起来味同嚼...蜡.,实在让人提不起兴趣。
D.宋濂学有所成,关键在于自己学习的寻章摘句....和努力勤奋。
4.下列句子中没有语病的一项是()(3分)A.十六岁的武亦姝登上《在中国诗词大会》第二季冠军的宝座,靠的是对古诗文的真心热爱、潜心记诵、丰厚积累取得的。
2017-2018学年广州市中学九年级(上)期中数学试卷.细心选一选A. =3B. =0C. =1 或=3D. =3 或=03. (3分)设1, 2是一元二次方程2+3-4=0的两个根,则1+2的值是(A. 3 B, - 3 C. 4 D, - 44. (3分)如图,在圆 O 中,圆心角/ BOC=100° ,那么/ BAC=(AA. 6B. 5C. 4D. 39. (3分)已知A ( - 1, yi ), B (2, y 是抛物线y= - (+2) 2+1上的两点,则必,y2的大小关系( )A. y i>y 2B. y i >y ?C. y i<y 2 D . y i< y 210. (3分)二次函数y=a 2+b+c (aw0)的图象如图所示,则下列说法不正确的是()C. 70°D. 75° 1. (3分)将图所示的图案按顺时针方向旋转 90°后可以得到的图案是(2. (3分)方程2-3=0的解是( )A. b2-4ao 0B. a> 0C. c> 0D.会<C二.耐心填一填11.(3分)已知抛物线y=-2 (-i)2+3,当时,y随的增大而减小.12.(3分)如图,AB是圆O的直径,点C在圆。
上,若/ A=40° ,则/ B的度数为13.(3分)已知点A (-3, b)与点B (a, 2)关于原点对称,则a+b=.14.(3分)二次函数y=2-2-3的图象如图所示.当y<0时,自变量的取值范围是15.(3分)已知点P (3, 2),将OP绕点O逆时针旋转90°到OP',那么点P'的坐标是.16.(3分)一个足球被从地面向上踢出,它距地面的高度h (m)与足球被踢出后经过的时问t (s)之间具有函数关系h=at2+19.6t,已知足球被踢出后经过4s落地,则足球距地面的最大高度是m .三.用心答一答17.解方程(1)2-4-5=0(2)2( T) + - 1=0.18.已知关于的方程:32-+1=0的一根是=1,求的值以及方程的另一个根.19.抛物线y=22+b+c 经过(-3, 0), (1, 0)两点(1)求抛物线的解析式,并求出其开口方向和对称轴(2)用配方法求出该抛物线的顶点坐标.20.已知△ ABC,点A (― 3, 1), B (― 1, — 1), C (0, 2)(1)作出△ ABC;(2)利用关于原点对称的点的坐标的关系作出与^ ABC关于原点对称的^ A' B' C';(3)写出AA' B' C三个顶点的坐标.21.如图小张想用总长60m的篱笆围成矩形ABCD场地,其中AD边靠墙,墙体最多能用30m,矩形ABCD的面积S (m2)随矩形边长AB设为(m)的变化而变化.(1)求S与之间的函数关系(2)当为多少m时,矩形的面积是400m2?此时长宽分别是多少m?A\............ D31 -------------r22.已知关于的方程(-1) 2+2+2=0(1)求证:无论为何值,方程总有实数根(2)设1, 2是上述方程的两个实数根,记£占+工3S的值能为6吗?若能,求X1 x2 1 *出此时的值,若不能请说明理由.23.在△ ABC中,A A=90 , AC=AB,点D再射线BA上(不与B, A重合),连接CD,将CD绕点D顺时针旋转90°得到DE ,连接BE.(1)如图1,点D在BA边上.依题意补全图1作DFXBA交CB与点F,若AC=6, DF=2 , 求BE的长(2)如图2,点D在BA边的延长线上,用等式表示线段CB, BD, BE之间的数量关系(直接写出结论)24.如图,在平面直角坐标系中,点B (- 1, -1), A (3, -3),抛物线尸其经过A, O, B三点,连接OA, OB, AB,线段AB交y轴于点C.(1)求点C的坐标;(2)若点P为线段OA上的一个动点(不与O, A重合),直线PC与抛物线交于D, E两点(点D在y轴右侧),连接OD , AD①当4OPC为等腰三角形,求点P的坐标;②求4AOD面积的最大值,并求出此时点D的坐标.25.如图1点M为轴上的一点,圆M与轴交于点B, A,与y轴交于点C, D,设C (0,正),A (3, 0)(1)求点M的坐标(2)如图2所示,点F为弧AC的上的任一点,点E为弧CF上的中点,AF , DE交于点G, 求AG的长(3)如图3所示,连BC, AC,做/ ACG的平分线CF交圆M于点E,连接BE,求冬的BE图却郅12017-2018学年广东省广州市中学九年级(上)期中数学试卷参考答案与试题解析2. (3分)方程2-3=0的解是( )A. =3B. =0C. =1 或=3D. =3 或=0【解答】解:2-3=0(-3) =0「• =0 或-3=0,♦ ♦ 1=0 , 2=3 .故选:D .3. (3分)设1, 2是一元二次方程2+3-4=0的两个根,则1+2的值是(A. 3B. - 3C. 4D. - 4.细心选一选故选:B.,得到的图案【解答】解:.「i, 2是一元二次方程2+3-4=0的两个根,••1+2= - 3,故选:B.4.(3分)如图,在圆O中,圆心角/ BOC=100° ,那么/ BAC=(【解答】解::圆心角/ BOC=100° , ・./BAC=50° .故选:A.5.(3分)抛物线y=2 (-3) 2+1的顶点坐标是( )A. (3, 1)B. (3, T)C. (-3, 1)D. (-3, T)【解答】解:由y=2 (-3) 2+1,根据顶点式的坐标特点可知,顶点坐标为(3, 1).故选:A.6.(3分)将抛物线y= (-1) 2+3向左平移1个单位,再向右平移3个单位得到的解析式是( )A. y= (-2) 2B. y= (-2) 2+6C. y=2D. y=2+6【解答】解:二.向左平移1个单位,再向上平移3个单位,「. y= (-1+1) 2+3+3 .故得到的抛物线的函数关系式为:y=2+6.故选:D .7.(3分)某商品原价200元,连续两次降价a%后售彳介为148元,下列所列方程正确的是(A. 200 (1+a%) 2=148B. 200 (1 - a%) 2=148C. 200 (1 -2a%) =148D. 200 ( 1-3%) 二148【解答】解:依题意得两次降价后的售价为200 (1-a%)• .200 (1-a%)2=148.故选:B.8.(3分)如图,AB是。
2017-2018学年度九年级上学年期中测试卷(2017.10.20)一、选择题(每小题2分,共20分)1、在常温干燥的情况下,下列餐具属于导体的是A.陶瓷碗B.塑料筷子 C.玻璃果盘 D.不锈钢勺2、两个物体相接触,热量不再从一个物体传递给另一个物体是由于()A.具有相同的比热容 B.具有相同的温度C.具有相同的热量 D.具有相同的质量3、如图所示的电路中,闭合开关,下列说法正确的是()A.两灯泡是串联的 B.开关只能控制L2C.电流表测总电流 D.电流表测L1的电流4、如图所示,关于电流表和电压表的使用方法中正确的是()A. B. C. D.5、小亮同学想设计一个通过电表示数反映压敏电阻所受压力大小的电路,要求压力增大时电表示数增大.已知压敏电阻的阻值是随所受压力的增大而减小的.以下电路不符合要求的是()A. B. C. D.6、下列说法正确的是()A.长导线的电阻比短导线的电阻大 B.只有正电荷的定向移动才能形成电流C.金属导体中大量电子定向移动的方向就是电流方向 D.甲、乙两灯的两端电压相等,甲、乙两灯可能是串联7、如图所示电路,当开关闭合,两灯正常发光,使用中发现两灯突然熄灭,电流表无示数,电压表示数增大,则故障可能是()A.灯L1被短路 B.灯L2被短路 C.灯L1断路 D.灯L2断路7、 9、 10、8、关于电流、电压和电阻的关系,下列说法正确的是()A.导体电阻跟导体两端的电压成正比,跟导体中的电流成反比 B.有电流通过这段导体,这段导体两端一定有电压C.通过导体的电流越大,这段导体的电阻一定越小 D.两个电阻中的电流相等,则两电阻一定是串联9、在如图所示电路中,电源电压不变,当滑动变阻器的滑片P向右移动的过程中,下列说法正确的是()A.电流表的示数变小 B.电压表的示数变小 C.电流表的示数不变 D.电压表的示数变大10、如图所示电路,电源电压保持不变,其中R0、R1为定值电阻,闭合开关,当把滑动变阻器的滑片从右端调到左端过程中,下列说法中正确的是()A.电流表A示数变小 B.电压表V1示数变小 C.电压表V2示数变小 D.R0两端的电压变小二、填空题(每空1分,共12分)11、某导体两端的电压为4V时,通过的电流为0.5A,则导体的电阻为_______Ω,当某导体两端的电压为0时,则导体的电阻为_______Ω。
黄冈中学广州学校2017—2018学年第一学期期中考试
九年级数学
一、选择题(本大题共10小题,每小题3分,共30分.在每小题给出的四个选项中,只有一个符合题意)
1
a 的取值范围是().
A .0a ≥
B .0a ≤
C .3a ≥
D .3a ≤
2.下列平面图形中,既是轴对称图形,又是中心对称图形的是().
A .
B .
C .
D .
3.关于x 的一元二次方程225x ax +=的一个根是1,则a 的值是().
A .0
B .1
C .3
D .3-
4.用配方法解方程2230x x --=,配方后的方程是().
A .2(1)8x -=
B .2(1)2x -=
C .2(1)4x +=
D .2(1)4x -=
5.将抛物线22y x =平移后得到抛物线221y x =+,则平移方式为().
A .向左平移1个单位
B .向右平移1个单位
C .向上平移1个单位
D .向下平移1个单位
6.关于x 的一元二次方程220x x +-=的根的情况是().
A .有两个不相等的实数根
B .有两个相等的实数根
C .无实数根
D .无法判断
7.三角形两边长是3和4,第三边的长是方程212350x x -+=的根,则该三角形的周长为().
A .14
B .12
C .12或14
D .以上都不对
8.设二次函数2(3)4y x =--图象的对称轴为直线l ,若点M 在直线l 上,则点M 的坐标可能是().
A .(1,0)
B .(3,0)
C .(3,0)-
D .(0,4)-
9.如图,在Rt ABC △中,90ACB ∠=︒,30ABC ∠=︒,将ABC △绕点C 顺时针旋转至A B C '''△,使点A '恰好落在AB 上,则旋转角度为().
A
B C B'
A'
A .30︒
B .45︒
C .60︒
D .90︒
10.如图,为二次函数2y ax bx c =++的图象,给出下列说法:①0ab <;②方程20ax bx c ++=的根为11x =-,23x =;③0a b c ++>;④当1x >时,y 随x 值的增大而增大;⑤当0y >时,13x -<<;⑥20a b +<.其中,正确的说法有()个.
A .2
B .3
C .4
D .5
二、填空题:(本大题共6小题,每小题3分,共18分.只要求写出最后的结果) 11.把方程2215x x -=化为一般形式是____________.
12.点(1,2)P -关于原点对称的点P '的坐标是____________.
13.如图,AB 是⊙O 的弦,半径2OA =,120AOB ∠=︒,则弦AB 的长是____________.
14.抛物线223y x bx =-+的对称轴是1x =,则b 的值为___________.
15.若(0)n n ≠是关于x 的方程20x mx n 2++=的根,则m n +的值为__________.
16.若抛物线2(1)232y m x mx m =-++-的顶点在坐标轴上,则m 的值为__________.
三、解答题(本大题共9小题,共102分.作答时应写出文字说明、推理依据、演算步骤) 17.(9分)解方程:
(1)2320x x -+=.
(2)(1)(1)2(3)8x x x +-++=.
18.(9分)若关于x 的一元二次方程2430x x k -+-=有两个实数根1x ,2x .
(1)求k 的取值范围.
(2)当123x x =时,求两根及k 的值.
19.(10分)已知二次函数24y ax x c =-+的图像经过点(1,1)A --和点(3,9)B -. (1)求二次函数表达式.
A
B
O
(2)写出该抛物线的对称轴及顶点坐标.
20.(10分)如图,在每个小正方形的边长均为1个单位长度的方格纸中,有一个ABC △和一点O ,ABC △的顶点和点O 均与小正方形的顶点重合.
(1)在方格纸中,以点O 为旋转中心,将ABC △绕点O 顺时针旋转90︒得到111A B C △,请画出111A B C △.
(2)在方格纸中,建立平面直角坐标系,已知点(2,4)A -,将ABC △绕点O 旋转180︒得到222A B C △,请画出222A B C △,并写出点2B 的坐标.
21.(10分)如图,AB 是⊙O 的直径,AC 、BC 是⊙O 的弦,直径DE AC ⊥于点P .若点D 在优弧 ABC 上,8AB =,3BC =,求DP 的长.
22.(12分)如图所示,一个农户要建一个矩形猪舍,猪舍的一边利用长为12m 的房墙,另外三边用25m 长的建筑材料围成,为了方便进出,在垂直于房墙的一边留一个1m 宽的门.
(1)所围成矩形猪舍的长、宽分别是多少时,猪舍面积为280m ?
(2)为做好猪舍的卫生防疫,现需要对围成的矩形进行硬底化,若以房墙的长为矩形猪舍一边的长,且已知硬底化的造价为60元/平方米,请你帮助农户计算矩形猪舍硬底化需要的费用.
23.(12分)已知二次函数2y ax bx c =++的图象经过点(2,5)-,顶点为(1,4)-,直线l 的解析式为2y x m =+.
(1)求抛物线的解析式.
(2)若直线l 与抛物线只有一个公共点P ,求点P 的坐标.
D
A B C E F
O
(3)设抛物线与x 轴的交点分别为A 、B ,求在(2)的条件下PAB △的面积.
24.(14分)如图1,在ABC △中,36A ∠=︒,AB AC =,ABC ∠的平分线BE 交AC 于E .
(1)求证:AE BC =.
(2)如图(2),过点E 作EF BC ∥交AB 于F .将AEF △绕点A 逆时针旋转角(0144)αα︒<<︒得到AE F ''△,连结CE '、BF ',求证:CE BF ''=.
(3)在(2)的旋转过程中是否存在CE AB '∥?若存在,求出相应的旋转角α;若不存在,请说明理由.
25.(14分)已知,如图抛物线23(0)y ax ax c a =++>与y 轴交于点C ,与x 轴交于A 、B 两点,点A 在点B 左侧,点B 的坐标为(1,0),3OC OB =.
(1)求抛物线的解析式.
(2)若点D 是线段AC 下方抛物线上的动点,求四边形ABCD 面积的最大值. (3)若点E 在x 轴上,点P 在抛物线上,是否存在以点A ,C ,E ,P 为顶点且以AC 为一边的平行四边形?若存在,求点P 的坐标;若不存在,请说明理由.
图1()36°
E
C B A
图2()F'E'36°F E C B A 备用图A B
C
E F
36°。