67.What does the writer give the “battery” example to tell us?A.The difficulty of garbage sorting.B.The importance of garbage sorting.C.How to sort ourgarbage.D.What harmful waste is.68.What will people do to take a free bus ride in Indonesia?A.Take plastic bottles to the station.B.Put bottles in a machine.C.Put garbage into different bins.D.Geta notice on the door.69.Which bin should“newspapers"”go to?DDoRccyclablcWeeHarmful70. Which is the best title for the passage?A.Different Countries,Different PoliciesB.Sort Garbage, Save the EarthC.Less Garbage, Cleaner EnvironmentD.Clean Shanghai, Beautiful China第二节阅读表达（共5题；每题2分，满分10分）阅读下面短文，简略回答问题。Puberty(青春期) is the stage of life when young people leave childhood and head into adulthood.It is a diffcult process for teenagers because it has an effct on both their minds and bodies. Theyneed to understand what is going on with their bodies,how to deal with those changes and how to starttaking responsibility for themselves.A young person may begin puberty at 8, while another may not start puberty until 14 or 15. Inthe age of 18.During these years,the body develops in many ways.Feelings can also change quickly.Teenage boys at this stage often take unnecessary risks.Their focus is on having fun and beingaccepted by others.They need to think before they act and make good decisions for themselves.A girl's personality often does not develop in the same way as a boy's.Teenage girls sometimes lose confidence in themselves.They are no longer certain about theirownfeelings.Yet they are usually afraid to tell theirparents or teachers about their problems.For thisreason, teenage girls should be encouraged to discuss things with trusted adults.Parents, schools and communitiescan doalot tocare for andhelp young peopleIt is everyone'sresponsibility tomake sure that young people grow intohealthy adults.71.Why is puberty a difficult process for teenagers?72.When is puberty usually complete for teenagers?73.Who needs to think before they act and make good decisions for themselves?74.What does the writer think of the development of a girl's personality and a boy's?75.Do you think it is necessary for teenage girls and teenage boys to talk about their problems toothers? Why or why not?英语试卷第7页（共8页）

67.What does the writer give the “battery” example to tell us?A.The difficulty of garbage sorting.B.The importance of garbage sorting.C.How to sort ourgarbage.D.What harmful waste is.68.What will people do to take a free bus ride in Indonesia?A.Take plastic bottles to the station.B.Put bottles in a machine.C.Put garbage into different bins.D.Geta notice on the door.69.Which bin should“newspapers"”go to?DDoRccyclablcWeeHarmful70. Which is the best title for the passage?A.Different Countries,Different PoliciesB.Sort Garbage, Save the EarthC.Less Garbage, Cleaner EnvironmentD.Clean Shanghai, Beautiful China第二节阅读表达（共5题；每题2分，满分10分）阅读下面短文，简略回答问题。Puberty(青春期) is the stage of life when young people leave childhood and head into adulthood.It is a diffcult process for teenagers because it has an effct on both their minds and bodies. Theyneed to understand what is going on with their bodies,how to deal with those changes and how to starttaking responsibility for themselves.A young person may begin puberty at 8, while another may not start puberty until 14 or 15. Inthe age of 18.During these years,the body develops in many ways.Feelings can also change quickly.Teenage boys at this stage often take unnecessary risks.Their focus is on having fun and beingaccepted by others.They need to think before they act and make good decisions for themselves.A girl's personality often does not develop in the same way as a boy's.Teenage girls sometimes lose confidence in themselves.They are no longer certain about theirownfeelings.Yet they are usually afraid to tell theirparents or teachers about their problems.For thisreason, teenage girls should be encouraged to discuss things with trusted adults.Parents, schools and communitiescan doalot tocare for andhelp young peopleIt is everyone'sresponsibility tomake sure that young people grow intohealthy adults.71.Why is puberty a difficult process for teenagers?72.When is puberty usually complete for teenagers?73.Who needs to think before they act and make good decisions for themselves?74.What does the writer think of the development of a girl's personality and a boy's?75.Do you think it is necessary for teenage girls and teenage boys to talk about their problems toothers? Why or why not?英语试卷第7页（共8页）

B.V3A.12C.22亿用小（2）如图2，延长GE交边CD于点H，DH15.计算：（2025-π)-√12+（√3+1）（√3-1）建立面直角坐标系xOy，格点（网格线的交点）A,B,C的坐标分别为A(1.3)，B(3,2)，c（1,0)。（1）将△ABC先向下移2个单位长度，再向左移3个单位长度，作出移后的△ABC（点A，B'，C'分别为点A，B，C的对应点）;（2）直接写出△ABB的面积；（3）在所给的网格图中第四象限确定一个格点D，使得ADB=90°，写出点D的坐标。不四、（本大题共2小题，每小题8分，满分16分）交于点C（1，3）17.如图，直线y=x+b与x轴交于点A，与y轴交于点B，与反比例函数y=（1）求k的值与点A的坐标；（2）过点B作BD⊥AC交x轴于点D，求AD的长。18.观察以下等式：第1个等式：x（++第2个等式：x（1+3+数学试卷共4页第2页

B.V3A.12C.22亿用小（2）如图2，延长GE交边CD于点H，DH15.计算：（2025-π)-√12+（√3+1）（√3-1）建立面直角坐标系xOy，格点（网格线的交点）A,B,C的坐标分别为A(1.3)，B(3,2)，c（1,0)。（1）将△ABC先向下移2个单位长度，再向左移3个单位长度，作出移后的△ABC（点A，B'，C'分别为点A，B，C的对应点）;（2）直接写出△ABB的面积；（3）在所给的网格图中第四象限确定一个格点D，使得ADB=90°，写出点D的坐标。不四、（本大题共2小题，每小题8分，满分16分）交于点C（1，3）17.如图，直线y=x+b与x轴交于点A，与y轴交于点B，与反比例函数y=（1）求k的值与点A的坐标；（2）过点B作BD⊥AC交x轴于点D，求AD的长。18.观察以下等式：第1个等式：x（++第2个等式：x（1+3+数学试卷共4页第2页

信息第耕前信息卷数学命中率高①重点中学、教育强区考前猜题信息卷（一）玫师用卷线）剪开，得到的剪开图是所以函数f（x）=e2.故选C.0已知直线:3x-y=0，l2：3x+y=0，点M到记点M的轨迹为曲线命题立意本题考查合情推理；意在考查逻辑推r，若r与曲线y=√a-x有四个交点，则aB理和直观想象的核心素养。的取值范围为试题解析因为纸带是由一个长方形纸条一端B.(9.+00)A.(3,+00)D.(1,9)扭曲180°后粘贴而成的封闭环，沿着三等分线C.(1,3)剪开时，会一次性剪完纸带的所有三等分线，命题立意本题考查求双曲线的轨迹方程，判断所以剪开图是两个套在一起的环，并且两个环两曲线交点的个数：意在考查逻辑推理、直观想象和数学运算的核心素养。的宽度是原纸带环宽度的正确剪开图是选试题解析设M（x，y），由题意得项B.故选B./106函数f（x）=一1的零点个数至多为13x+yl=9，所以9x²一y²=±9，e√1010即x2A.0B.1C.2D.3±1命题立意本题考查求函数零点或方程根的个所以点M的轨迹为两个双曲线，其方程分别数，指数函数和对数函数图象的应用；意在考为xx²=1查逻辑推理、数学建模和直观想象的核心素养。=1的实半轴长为1，Inx试题解析由f（x）=-1=0，得lnx=ex²=1的实半轴长为3，9Inx所以函数f（x）=—1的零点个数可转化由y=√a-x²，得x²+y²=a（y≥0），表示以原点为圆心，a为半径的圆的上半圆，为函数y=lnx和y=e的图象的交点个数，若曲线r与半圆x²+y²=a（y≥0）有四个函数y=1nx在区间（0，+oo）上单调递增，交点，当a

Use your senses.Whilecrafting,itsessential thatyou ueyour senses.Thatmightmean enjoyingthefeel ofthewoolinyourhandsasyouknit,delightinginthevividcolorsofyourpaint,orlisteningtothe sound your crafting makes.39Specifically,notice touch, sensation,colors,patterns and anyothersensory detail.Whenyoufullyfocusoncrafting,itisnolongerjust aboutmaking things,butbecomesa waytomoments,you canfind calm and joy.40A.Set the scene.B.Plan the time.C.Also,pick calm moments for crafting joy.D.This works because craftingrequiresfocused attention.E.Focus your attention on every detail of the experience as youcraft.F.Moreover,takea minute tobein the present momentbeforeyou restart.G.Startcraftingtoday,anddiscoveritspowertobringpeacetoyourmind第三部分语言运用（共两节，满分30分）第一节（共15小题；每小题1分，满分15分）阅读下面短文，从每题所给的A、B、C、D四个选项中选出最佳选项。Acitychild’ssummerisspentin thestreetinfrontof hishome.All through thesummervacations,I41silently aside andoccasionallywatchedenviously theotherboysplayingbaseball.Iwasneverasked to takepartevenwhen one teamhad amember42not out of special cruelty,butbecausethey43_Iwouldbenogoodat it.Iwouldneverforgetthatwonderful evening.Thebaseball44abouteightoreight thirtywhenthere or46to.There the boyswould mostly talk about theirgamesand then47_oneby one.Itwhich boy49the silence.“What's in those books you're always reading?" he asked casually."Stories,"Ianswered50Ijustsattherein silence.But thatdayI told themfortwohours thestoryIwasreadingatthemoment.They listened 51_.The next night andmany nights thereafter,akind of unspoken ritualtook place.Sometimes,in order to52_myvictory more completely,I cheated.Iwould stop at themost53partofastory and tell them itwould have tobe54thefollowingevening.Itwasnottrue,of course.I enjoyed the long summer evenings until school began in the fall,which55in mymemory.41.A.satB.walkedC.helpedD.read42.A.missingB.comingC.speakingD.training43.A.admittedB.assumedC.guaranteedD.confirmed英语试卷第8页（共10页）

第三部分专题训练变式训练32

（5分）→正确利用绝对值三角不等式进行放缩即可给1分。解法二因为点M(x,y）,N(x,y)在椭圆 :=1(a>b>0)上,a²+b²(2分)一x=1，=1每正确写a²b²b²出一个给1分。设=cos α，² = cos αcos β+ sin αsin β=cos(α-β),(11)(2)(i)由 L(()分。由题可得椭圆在点M(x,)处的切线的方程为yy=1,b²a64线垂直A,A2+B,B2=0)(7分）一→写出两条切线的方程给1分,得到当切线,的斜率都存在且都不为O时,设l与l交于点P(xp,p）（x,≠±α且再给1分。yp≠±b）,过点 P的椭圆 的切线方程为-y,=k(-xp)(k≠0),[y-yp=k(x-xp)由得(a²k²+b²)x²+2a²k（yp-kxp)x+a²(yp-hxp)²-a²b²=0,²则△=[2a²k(yp-hxp)]²-4(a²k²+b²)[a²(yp-kxp)²-a²b²] =0,→联立方程，得到一元二次方程给1分,根据直线与椭圆的位置关系得整理得（x²-a²)k²-2xpypk+y-b²=0。(9分)-到（x²-a²)k²-2xpypk+y²-b²=0y²-b²显然k,b,是上述方程的两个根,故k,k,=-1再给1分。y-b²所以x²+y²=a²+b²(xp≠±a且yp≠±b)。(11分)当切线，l中一条切线的斜率不存在，一条切线的斜率为0时,可得点P的坐标为α²+b²(xp≠±a且yp≠±b)再给1分。(a,b)或(-a,b)或(a,-b)或(-α,-b),此时点P也满足x²+y=α²+b²。（12分）→缺少切线斜率为0或切线斜率不存综上,x+y²=a²+b²，在的情况扣1分。防范措施：一定要考虑切线的斜率是故曲线 R的方程为x²+y²=α²+b²。(13分)否存在、是否为0。(ii)易知 B(0,b）,由(i)知曲线 R是以坐标原点为圆心，√α²+b为半径的圆,→根据最大值、最小值列方程组,每正因为B与曲线R上的点之间的距离的最大值为3,最小值为1，确列出1个方程给1分。得分关键：圆内一定点到圆心的距[√a²+b²+b=3（15分）离为d,圆的半径为r,则该点与圆上所以l√a²+6²-b=1的点的距离的最小值为r-d,最大值为r+d。得α=√3,b=1,所以椭圆的方程为+y²=1。(17分）求出α=√3，b=1给1分，写出椭圆3厂的方程再给1分。

中考导向总复模拟样卷数学（八）·视图与图形变化7.如图题号一二三得分四五六七八总分注意事项：1.本卷满分150分，答题时间120分钟。2.答题前请将密封线内的项目填写清楚。8.三根一、选择题（本大题共10小题，每小题4分，满分40分）合理每小题都给出A，B，C，D四个选项，其中只有一个是符合题目要求的。号位座迹.用数学知识可以解释为9.若A.点动成线CB.线动成面AC.面动成体D.面与面相交得线答第1题图要2.如图，三个图形中既是轴对称图形又是中心对称图形的个数是第2题图10.名姓不A.0个B.1个C.2个D.3个3.如图，将半圆绕直径所在的虚线旋转一周，得到的立体图形是丙线封B4.如图所示的手提水果篮，其俯视图是D级班5.如图，从正面看三棱柱得到的图形是ABD6.如图是某几何体的三视图，该几何体是BCDA.圆柱B.五棱柱C.长方体D.五棱锥数学总复模拟样卷（八）第1页REDMI K5O ULTRA2025.04.2123:24

。（①要将沉重的箱子推上陡峭的岩石和坦地面。②自然环境恶劣。③小屋是个简陋的方形盒，全铺黑色油毡，周围散布动物户骨。④生活设施糟糕间和景物角度，直观展现岛上的荒芜；“海岸构成一幅死亡与腐败的荒凉画面”直接点明环境的恶劣。作用：渲染了压抑、悲凉的氛围，烘托“我们”初到此地的失望，为后文写生活的艰难做铺垫。说“炉子没问题”，可看出他积极乐观、冷静坚强。10．参考答案（以“积极乐观”为例）：文中“我”的丈夫面对糟糕的炉子和艰苦的环境，坚信炉子是好的，小屋会舒适，展现出积极乐观。在生活中，我们也会遇到各种困难，如考试失利、比赛失败等，这时我们应像文中丈夫一样，保持积极心态，才能更好地应对挑战，走出困境。(二）(10分)11.答案：事实：B、D；观点：A、C12.参考答案：。历史悠久，有近300年历史。。包容性强，吸纳多种艺术元素。。题材贴近生活，受观众喜爱。。不断创新，演出形式多样且关注时代。·13．参考答案（判断同学乙）：信息真实可信。文本一提到常香玉在豫剧表演上技艺精湛，且积极投身传承推广，具有高尚爱国情怀；同学乙分享的信息与文本相符，很多艺术文献有记载也能增加可信度。三、古诗文阅读 （15分)14.答案：。（1）同“避”，躲避。(2)比。(3)②15．参考答案：这种做法不是可以停止了吗？这就叫做丧失了人固有的羞恶之心。论述做铺垫；激发读者阅读兴趣。