2021年广西壮族自治区来宾市中考数学真题 (一).pdf

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1、2021年广西来宾市中考数学试卷一、选 择 题（本大题共12小题，共36分）1.下列各数是有理数的是（）A.兀 B.V2 C.V32.如图是一个几何体的主视图，则该几何体是（）A.D.0B.C.D.3.如图，小明从4入口进入博物馆参观，参观后可从B,C,。三个出口走出，他恰好从C出口走出的概率是（）c.月入口D|4.我国天问一号火星探测器于2 0 2 1 年 5 月 1 5 日成功着陆火星表面.经测算，地球跟火星最远距离约4 0 0 0 0 0 0 0 0 千米，其中数据4 0 0 0 0 0 0 0 0 科学记数法表示为（）A.4 x 1 09 B.4 0 x 1 07 C.4 x 1 08

2、 D.0.4 x 1 095.如图是某市一天的气温随时间变化的情况，下列说法正确的是（）C.最高温比最低温高8 C D.0 时至8 时气温呈下降趋势6 .下列运算正确的是（）A.a2-a3=a5 B.(a2)3=AC.a6-i-a2=a3 D.3 a2 2a=a27 .平面直角坐标系内与点P（3,4）关于原点对称的点的坐标是（）8.A.(-3,4)B.(-3,-4)C.(3,-4)D.(4,3)如图，。0 的半径O B 为 4,。工4 8 于点。，BAC=3 0 ,A.V 2B.V 3则O D的长是（C.2D.39.一次函数y =2 x +1 的图象不经过（）A.第一象限 B.第二象限 C.第

3、三象限 D.第四象限第2页，共28页1 0 .仇章算术少是人类科学史上应用数学的“算经之首”，书中记载：今有三人共车，二车空；二人共车，九人步.问：人与车各几何？译文：若 3人坐一辆车，则两辆车是空的；若 2人坐一辆车，则 9人需要步行，问：人与车各多少？设有x 辆车，人数为必 根据题意可列方程组为（）(y=3 x-2 (y=3(x -2)(y=3 x-2(y =2%+9 (y =2%4-9 (y=2x 9y =3(%2)y =2x 91 1 .如图，矩形纸片A3 C D,AD：4 8 =&：1,点 E,尸分别在AO,B C上,把纸片如图沿所折叠，点 A,8的对应点分别为力，B,连接A4 并延

4、长交线段CO 于点G,则芫的值为（）A.立2B1DT1 2 .定义一种运算：=则不等式（2 乂 +1）*（2-03的解集是（）A.%1 或x g B.-1 x 1 或 或X -1二、填 空 题（本大题共6 小题，共 18分）1 3 .要使分式上有意义，则 x的取值范围是1 4 .分解因式：a2-4b2=1 5.如图，从楼顶A处看楼下荷塘C处的俯角为4 5。，看楼下荷塘。处的俯角为6 0,已知楼高A 8为 3 0 米，则荷塘的宽C。为 米（结果保留根号）.1 6 .某校举行“党在我心中”演讲比赛，评委将从演讲内容，演讲能力，演讲效果三个方面给选手打分，各项成绩均按百分制计，然后再按演讲内容占50

5、%,演讲能力占4 0%,演讲效果占1 0%,计算选手的综合成绩(百分制).小婷的三项成绩依次是84,95,9 0,她 的 综 合 成 绩 是 .1 7.如图，从一块边长为2,乙4=120。的菱形铁片上剪出一个扇形，这个扇形在以A 为圆心的圆上(阴影部分)，且圆弧与BC,CQ分别相切于点E,F,将剪下来的扇形围成一个圆锥，则圆锥的底面圆半径是1 8.如图，已知点4(3,0),8(1,0),两点C(-3,9),。(2,4)在抛物线y=/上，向左或向右平移抛物线后,C,。的对应点分别为C,D.当四边形ABC。的周长最小时，抛物线的解析式为三、解答题(本大题共8 小题，共 66分)1 9.计算：23x

6、(-i+l)-(l-3).20.分式方程：5?=看+1。2 1.如图，四边形A8CQ中，A B/CD,乙 B=)，连接AC.求证：ATlfiCsA CDA；(2)尺规作图：过 点 C 作 AB的垂线，垂足为E(不要求写作法，保留作图痕迹)；(3)在(2)的条件下，已知四边形ABCD的面积为20,AB=5,求 CE的长.第4 页，共 28页2 2.某水果公司以10元/g 的成本价新进2000箱荔枝，每箱质量5依，在出售荔枝前，需要去掉损坏的荔枝，现随机抽取20箱，去掉损坏荔枝后称得每箱的质量(单位：kg)如下：4.7 4.8 4.6 4.5 4.8 4.9 4.8 4.7 4.8 4.74.8

7、4.9 4.7 4.8 4.5 4.7 4.7 4.9 4.7 5.0整理数据：质量(kg)4.54.64.74.84.95.0数量(箱)217a31分析数据：平均数众数中位数4.75bC(1)直接写出上述表格中a,b,C的值.(2)平均数、众数、中位数都能反映这组数据的集中趋势，请根据以上样本数据分析的结果，任意选择其中一个统计量，估算这2000箱荔枝共损坏了多少千克？(3)根据(2)中的结果，求该公司销售这批荔枝每千克定为多少元才不亏本(结果保留一位小数)？2 3.【阅读理解】如图，lb，AABC的面积与D8C的面积相等吗？为什么？解：相等.在ABC和D8C中，分别作Z E l.%，DF

8、1 12,垂足分别为E,F./.AEF=乙DFC=90,AE/D F.W/，2,四边形AEFD是平行四边形,AE=DF.又5A.BC=：BC AE,SDBC=BC-DF.SMBC=SADBC【类比探究】如图，在正方形48C。的右侧作等腰ACDE,CE=D1的面积.解：过点E 作EF J.CD于点F,连接AF.请将余下的求解步骤补充完整.【拓展应用】如图，在正方形A8CD的右侧作正方形C E FG,点 8,接 80,BF,D F,直接写出ABD尸的面积.A D*rBE F C B C B图 图9,AD=4,连接A E,求ADEC,E 在同一直线上，AD=4,连C E图第6页，共28页24.202

9、2年北京冬奥会即将召开，激起了人们对冰雪运动的极大热情.如图是某跳台滑雪训练场的横截面示意图，取某一位置的水平线为x 轴，过跳台终点A作水平线的垂线为y 轴，建立平面直角坐标系，图中的抛物线G：丫 =-去 产+：%+1近似表示滑雪场地上的一座小山坡，某运动员从点。正上方41Z o米处的A 点滑出，滑出后沿一段抛物线C2：y=：/+取+，运动.O(1)当运动员运动到离A 处的水平距离为4 米时，离水平线的高度为8 米，求抛物线的函数解析式(不要求写出自变量x 的取值范围)；(2)在(1)的条件下，当运动员运动的水平距离为多少米时，运动员与小山坡的竖直距离为1米？(3)当运动员运动到坡顶正上方，且

10、与坡顶距离超过3 米时，求人的取值范围.2 5.如图，在AABC中，4D_LBC于点。，BC=14,AD=8,80=6,点E是 上 一 动 点(不 与 点A,。重合)，在ADC内作矩形EFG”，点尸在QC上，点G,在AC上，设0E=x,连接BE.(1)当矩形EFG”是正方形时，直接写出EF的长；(2)设 ABE的面积为5 ,矩形EFGH的面积为5 2,令 丁 =兴，求y关于x的函数解析式(不要求写出自变量32X的取值范围);(3)如图，点P(a,b)是(2)中得到的函数图象上的任意一点，过点尸的直线/分别与x轴正半轴，y轴正半轴交于M,N两点，求A0MN面积的最小值，并说明理由.第8页，共28

11、页2 6.如图，已知A。，EF是。的直径，AD=6位,。与MBC的边4B,0 c分别交于点E,M,连接CC并延长，与4尸的延长线交于点G,AFE=/.0CD.(1)求证：CC是。的切线;(2)若GF=1,求cos乙4EF的值;(3)在(2)的条件下，若乙4BC的平分线8H交CO于点H,连接4H交。于点N,求瑞的值.2021年广西玉林市中考数学试卷一、选择题：本大题共12小题，每小题3分，共36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，把正确答案的标号填（涂）在答题卡内相应的位置上.1.计算：-1+2的结果是（）A.1 B-1C.3 D.-32.我市今年中考报名人数接近101000

12、人，将数据101000用科学记数法表示是（）A.10.1 X104 B.1.01X105C.1.01X106 D.0.101 Xio63.如图是某几何体的三视图，则该几何体是（）A.圆锥 B.圆柱C.长方体 D.三棱柱4.下列计算正确的是（）A.6 75+a5=10B.-3(a-b)=-3a-3bC.(ab)3ab 3D.心+2=45.甲、乙两人进行飞镖比赛，每人各投6 次，他们的成绩如下表（单位：环）：甲6,7,8,8,9,9乙5,6,x,9,9,10如果两人的比赛成绩的中位数相同，那么乙的第三次成绩x是（）A.6 环 B.7 环C.8 环 D.9 环6.如图，ABC底边8 c 上的高为加，

13、PQR底 边 0 R 上的高为例，则 有（）第10页，共28页55/55。入 12/B C Q RA.h=h2 B.hhi D.以上都有可能7.学习圆的性质后，小铭与小熹就讨论起来，小铭说：“被直径平分的弦也与直径垂直”，小熹说：“用反例就能说明这是假命题”.下列判断正确的是（）A.两人说的都对B.小铭说的对，小熹说的反例不存在C.两人说的都不对D.小铭说的不对，小熹说的反例存在8.一个不透明的盒子中装有2 个黑球和4 个白球，这些球除颜色外其他均相同，从中任意摸出3 个球，下列事件为必然事件的是（）A.至少有1 个白球 B.至少有2 个白球C.至少有1个黑球 D.至少有2 个黑球9.已知关于

14、x 的一元二次方程：/-”+胆=0 有两个不相等的实数根xi,X 2,则（）A.Xl+X20 B.XlX2-1 D.X1X2=8,则k的值是.1 8.如图，在正六边形A 8 C D E F 中，连接对角线A ,AE,AC,DF,DB,A C 与 B D 交于点M,AE与。尸交于点为M M N 与 A D 交于点、O,分别延长A B,CC于点G,设 A B=3.有以下结论：M N A D MN=2 D 4G 的重心、内心及外心均是点M四边形项CQ绕点。逆时针旋转3 0 与四边形A 8 D E 重合则所有正确结论的序号是三、解答题：本大题共8 小题，满分共66分。解答应写出证明过程或演算步理（含相

15、应的文字说明），将解答写在答题卡上。1 9.(6 分)计 算：V 1 6+(4-TT)+(-1)-1-6s i n 3 0 .2 0.（6分）先化简再求值：（a-2+工）2 2,其中。使反比例函数）一 曳的图象分别位于第二、四a I a|x象限.2 1.(8 分)如图，在A B C 中，。在 A C 上，DE/BC,DF/AB.(1)求证：/X D F C s X A E D：e(2)若 C D 1.A C,求D F C.的值.3 SAAED第14页，共28页2 2.（8 分）“五一”后某校组织了八年级学生参加建党1 0 0 周年知识竞赛，为了了解学生对党史知识的掌握情况，学校随机抽取了部分同

16、学的成绩作为样本，把成绩按不及格、合格、良好、优秀四个等级分别进行统计，并绘制了如下不完整的条形统计图与扇形统计图：请根据图中提供的信息解答下列问题：（1）根据给出的信息，将这两个统计图补充完整（不必写出计算过程）；（2）该校八年级有学生6 5 0 人，请估计成绩未达到“良好”及以上的有多少人？（3）“优秀”学生中有甲、乙、丙、丁四位同学表现突出，现从中派2人参加区级比赛，求抽到甲、乙两人的概率.2 3.（8分）如图，。与等边aABC的边A C,AB分别交于点 ,E,AE是直径，过点。作。尸，BC于点F.（1）求证：DF是OO的切线;（2）连接E F,当 EF是。0的切线时，求OO的半径r 与

17、等边AABC的边长。之间的数量关系.2 4.（8分）某市垃圾处理厂利用焚烧垃圾产生的热能发电.有A,8两个焚烧炉，每个焚烧炉每天焚烧垃圾均为1 0 0 吨，每焚烧一吨垃圾，4焚烧炉比B焚烧炉多发电5 0 度，A,8焚烧炉每天共发电5 5 0 0 0 度.（1）求焚烧一吨垃圾，A焚烧炉和B焚烧炉各发电多少度？（2）若经过改进工艺，与改进工艺之前相比每焚烧一吨垃圾，A焚烧炉和B焚烧炉的发电量分别增加“和 2 4 ,贝 I J A,8焚烧炉每天共发电至少增加（5+）%,求”的最小值.2 5.（1 0 分）如图，在四边形A B C Q 中，对角线AC与 8。交于点。，已知O A=O C,O B=O D

18、,过点。作分别交A B、D C 于点E,F,连接。E,BF.（1）求证：四边形。E 8 F 是菱形：（2）设 A O a E F,AD+AB=2,B D=4 ,求 A 尸的长.第16页，共28页2 6.（1 2分）已知抛物线：y=a -3ax-4a（a 0）与x轴交点为A,B（A在B的左侧），顶点为。.（1）求点A,B的坐标及抛物线的对称轴；（2）若直线y=与抛物线交于点M,N,且M,N关于原点对称，求抛物线的解析式；（3）如图，将（2）中的抛物线向上平移，使得新的抛物线的顶点O 在直线/：y=2 上，设直线/与8），轴的交点为O,原抛物线上的点P平移后的对应点为点。，若O P=O Q,求点P

19、,。的坐标.2021年普通高中招生考试试卷英 语注意事项：1.本试卷共10页，六个大题，满 分 120分，考试时间100分钟。2.本试卷上不要答题，请按答题卡上注意事项的要求直接把答案填写在答题卡上。答在试卷上的答案无效。一、听力理解（20小题，每小题1 分，共 20分）第一节听下面5 段对话。每段对话后有一个小题，从题中所给的A、B、C 三个选项中选出最佳答案。每段对话读两遍。1.What is the weather like now?A.Hot.B.Warm.C.Cold2.What kind of music does the woman like?A.Rock music.B.Pop

20、 music.C.Country music.3.What is Sally Brown?A.A teacher.B.A doctor.C.A writer.4.Where are the speakers?A.In a library.B.In a bookstore.C.In a classroom.5.What did the woman do last weekend?A.She went fishing.B.She went camping.C.She went bike riding.第二节听下面几段对话或独白。每段对话或独白后有几个小题，从题中所给的A、B、C 三个选项中选出最佳

21、答案。每段对话或独白读两遍。听下面一段对话，回答第6 至第7 两个小题。6.How much does the man pay for his juice?第18页，共28页A.10 yuan.B.15 yuan.C.20 yuan.7.What does the man take at last?A.Orange juice.B.Lemon juice.C.Apple juice.听下面一段对话，回答第8 至第9 两个小题。8.Whom does the boy plan to ravel with?A.His mother.B.His father.C.His friend.9.When

22、is the boy leaving for Xian?A.On July 3.B.On July5.C.On July 7.听下面一段独白，回答第10至 第 12三个小题。10.How long will the activity last?A.3 days.B.5 days.C.7 days.11.How will the students get to the village school?A.On foot.B.By bike.C.By bus.12.Which group will play sports with children?A.Group One.B.Group Two.C

23、.Group Three.听下面一段对话，回答第13至 第 15三个小题。13.Whats the possible relationship between the two speakers?A.Guide and tourist.B.Mother and son.C.Friends.14.Where will they go tomorrow?A.To the museum.B.To e cinema.C.To the school.15.When will they meet?A.A 8:00 a.m.B.At 8:30 a.m.C.At 9:00 a.m.第三节听下面一篇短文。按照你所

24、听内容的先后顺序将下列图片排序。短文读两遍。16.17.18.19.20.二、阅读理解（20小题，每小题2 分，共 40分）阅读下面四篇语言材料，然后按文后要求做题。ACreate Your Own Story CompetitionIf you love to write,draw and create stories,heres your chance!Come and join in the Create Your Own Story Competition（13-19 September 2021）All you have to do is to create your own sto

25、ries.1 st place2nd place3rd to 6th places1 dictionary and 20 books1 dictionary and 10 books1 dictionary and 5 books、二 The competition is only open to the students in Grand Middle School./靠 Please write a story in at least 300 wordsj Pictures are not necessary but stories with creative pictures will

26、get extra（额 夕 卜 的）points.Get an entry form（参赛表格）from www.GrandMiddleSchooL.org/createyourownstory.The closing date:September 20,2021.The best stories will be posted on www.GrandMiddleSchool.org/beststories.Everyone will have thechance to vote（投票）for their favorite stories from 23 to 25 September 202

27、1.Names of winners will also be posted on www.GrandMiddleSchooLorg/beststones on September 30,2021.Please call 1800 6221 4422 or visit www.GrandMiddleSchool.org/siorycompefition for moreinformation.根据材料内容选择最佳答案。第20页，共28页21.If you win the 5th place,what prizes will you get?A.1 dictionary and 5 books.

28、B.1 dictionary and 10 books.C.1 dictionary and 15 books.D.1 dictionary and 20 books.22.Jimmy is refused to take part in the competition probably b e c a u s e.A.he creates the story all by himselfB.his story has more than 300 wordsC.his story doesnt have any picturesD.He isnt from Grand Middle Schoo

29、l23.When can you vote for your favorite stories?A.On September 13.B.On September 20.C.On September 24.D.On September 30.24.What can you find on www.GrandMiddleSchool.or/storycompetitionlA.Best stories.B.More information.C.An entry form.D.Names of winners.25.Who is the text written for?A.Students.B.T

30、eachers.C.Parents.D.Artists.“Oh,boys,dont throw stones at the poor bird,“said an old grey-headed man.“Sir,said a little one,H she makes such a loud noise that we cant bear her.“I am afraid the stone will rebound（反弹）and hurt you as long as you live!“Rebound!We dont understand you,sir!”“Well,I will te

31、ll you a true story.“Fifty years ago,I liked throwing stones because I had no other boy to playwith and I became very skillful.One day I went to work for an old couple whowere very friendly to everybody,even to the birds.And the birds seemed to lovethe old couple,too.For seven years a bird had come

32、and built her nest（鸟巢）in the“same place.She and her mate had just returned on the day I went to work and theold couple welcomed them happily.During the day,I thought I would try my skill upon her.Suddenly the birdflew to a tree near me.I found a nice stone,and I threw it with my best skill.It hit th

33、e bird on the head and shedropped dead!“I was sorry the moment I saw her fall off the tree.But it was too late.All day long her mate flew about,andchirped（发喟啾声）so sadly that he made my heart ache.I said nothing to the old couple but one of theirgrandchildren told them about it.Though the old couple

34、never said a word to me,I knew that they were very sad.Icould never look them in the eye and tell them how sorry I was.They have been dead for many,many years,andso has the poor bird.But dont you see how that stone rebounded,and hit me?For fifty years I have stillremembered it though I have never sp

35、oken of it before.But if what I have told you will stop you,I will be happy.”The boys at once dropped the stones in their hands and the bird had no more trouble from them.根据材料内容选择最佳答案。26.Why did the boy throw stones at the bird according to what the little boy said?A.Because they wanted to catch the

36、 bird.B.Because they thought the bird was noisy.C.Because they wanted to practice their skills.D.Because they thought throwing stones was fun.27.Which word can best describe the old couple?A.Kind.B.Strict.C.Proud.D.Funny.28.The underlined word They refers to.A.the birds B.the old couple C.the boys D

37、.the grandchildren29.How did the old man stop the boys from throwing stones at the bird?A.By driving away the bird.B.By taking away their stones.C.By playing jokes on the boys.D.By telling the boys his own story.30.What can we learn from the text?A.Dont hurt others,or you will hurt yourself.B.Try to

38、 save others and you will feel happier.C.Keep practicing and you will be very skillful.D.Dont waste time,or you will achieve nothing.C第22页，共28页Every living thing needs to reproduce.Reproducing means creating more members of your group.In orderfor plants to reproduce,they have to spread their seeds（种

39、子）to other areas.Plants have developed all kinds ofways to do this.The simplest way is gravity.Many seeds are inside of fruit.When a piece of fruit gets too heavy,it falls froma tree to the ground.Sometimes animals will pick up the fruit and drop it in another area.That helps move theseed even farth

40、er away.Apples spread this way.Other plants use wind to spread their seeds.Dandelions are a good example of this.Dandelion seeds are solight that when wind blows,it carries dandelion seeds to new places.Maple（枫树）seeds also use wind.Theirseeds are connected with long,thin leaves that look likewings.W

41、hen the seed falls from the tree,its wings”help it fly farther from the tree.Some animals help plants spread their seeds.The animals eat the seeds.While the seed is in the animafsbody,it stays whole.when the seed leaves the animal,its in a new place.Ants also help spread seeds.Some seeds have a spec

42、ial smell that attracts ants.The ants bring the seeds backto their home,which of course is underground.They only eat part of the seed.They leave the rest of the seedunderground.After that,the seed can start growing.根据材料内容选择最佳答案。31.What does the word“gravity mean in the second paragraph?A.The action

43、that makes animals drop seeds.B.The help that moves seeds even farther away.C.The need that comes from animals and plants.D.The force that causes fruit to fall to the ground.32.How do maples spread their seeds?A.They use ants.B.They use wind.C.They use smells.D.They use animals.33.What do ants do to

44、 help spread seeds?a.They only eat part of the seed.b.They help seeds fall from the tree.c.They carry seeds to the underground home.d.They pick up the fruit and move it far away.e.They leave the rest of the seed underground.A.b,d,e B.a,b,d C.a,c,e D.b,c,d34.What is the theme（主 题）of the text?A.Natare

45、.B.Culture.C.Education.D.Technology.35.Whats the best title for the text?A.How Plants Spread Seeds?B.Why Animals Pick Up Seeds?C.How Wind Helps Seeds Spread?D.Why Seeds Have a Special Trip?DA mind map is basically a tool that connects information around a central subject.It canhelp you make a knowle

46、dge bank to solve problems.A student recently said,“I thought mindmapping would take a lot of time to do but in fact it saves me time.36How to make a mind map?Now follow these steps for making wonderful mind maps.37 Why?Because starting in the center lets your brain spread out in alldirections and e

47、xpress itself more freely and naturally.Use a picture for your central idea.Why?Because a picture is worth a thousand words and helps you useyour imagination.38 It helps get your attention and makes you work excitedly!Connect your main branches（分支）to the central picture and connect your second-and-t

48、hird-level branches to thefirst and second levels,etc.Why?Because your brain works by connection.39 If you connect the branches,you will understand and remember a lot more easily.Use one key word every line.Why?Because every single key word can make you learn more clearly andeasily.40 Why?Because ea

49、ch picture,just like the central picture,is also worth a thousand words.So,if youhave 10 pictures in your mind map,they are already worth 10,000 words of notes.Try to use more colors.Why?Because colors are as exciting to your brain as pictures.Color adds greatenergy to your creative thinking,and is

50、fun!根据材料内容，从下面五个选项中选出能填入文中空缺处的最佳选项，使文章意通顺、内容完整。A.Start in the center of a page.B.Use pictures as many as possible.第24页，共28页C.A central picture is more interesting.D.I dont have to read my notes over and over again.E.It likes to connect two,or three,or four things together.三、完形填空（15小题，每小题1分，共15分）先通读短