中考单选真题
中考英语阅读理解单选题30题
中考英语阅读理解单选题30题1. The author mainly describes the person's ______.A. hobbiesB. achievementsC. personalityD. appearance答案：C。
本题主要考查对人物性格特点的理解。
选项A“hobbies”指爱好；选项B“achievements”指成就；选项D“appearance”指外貌。
文章重点描述的是人物的性格特点，所以选C。
2. According to the passage, we can know that the person is ______.A. braveB. shyC. lazyD. strict答案：A。
文中提到了人物在面对困难时的勇敢表现，可得出其性格勇敢。
选项B“shy”害羞；选项C“lazy”懒惰；选项D“strict”严格，均不符合文中对人物的描述。
3. What kind of person is the character in the passage?A. OptimisticB. PessimisticC. MeanD. Selfish答案：A。
文章中人物在困境中保持积极的态度，展现出乐观的性格。
选项B“Pessimistic”悲观；选项C“Mean”刻薄；选项D“Selfish”自私，均不符合。
4. The person is known for ______.A. being kindB. being intelligentC. being humorousD. being hardworking答案：D。
文中多处提及人物勤奋努力的工作和学习态度。
选项A“being kind”善良；选项B“being intelligent”聪明；选项C“being humorous”幽默，并非重点描述内容。
5. Which of the following is NOT true about the person?A. He is brave.B. He is funny.C. He is hardworking.D. He is quiet.答案：D。
2024年安徽省中考真题数学试卷含答案解析
安徽省2024年中考数学试题学校:___________姓名：___________班级：___________考号：___________一、单选题1．﹣5的绝对值是（）A ．5B ．﹣5C ．15-D ．15【答案】A【分析】根据负数的绝对值等于它的相反数可得答案．【详解】解：|﹣5|=5．故选A ．2．据统计，2023年我国新能源汽车产量超过944万辆，其中944万用科学记数法表示为（）A ．70.94410⨯B ．69.4410⨯C ．79.4410⨯D ．694.410⨯【答案】B【分析】本题考查了科学记数法，先把944万转化为9440000，再根据科学记数法：10n a ⨯（110a ≤<，n 为整数），先确定a 的值，然后根据小数点移动的数位确定n 的值即可，根据科学记数法确定a 和n 的值是解题的关键．【详解】解：944万694400009.4410==⨯，故选：B ．3．某几何体的三视图如图所示，则该几何体为（）A ．B ．C ．D ．【答案】D【分析】本题主要考查由三视图判断几何体，关键是熟悉三视图的定义．【详解】解：根据三视图的形状，结合三视图的定义以及几何体的形状特征可得该几何体为D 选项．故选：D ．4．下列计算正确的是（）A ．356a a a +=B ．632a a a ÷=C ．()22a a -=Da=5．若扇形AOB 的半径为6，120AOB ∠=︒，则 AB 的长为（）A ．2πB ．3πC ．4πD ．6π6．已知反比例函数()0ky k x=≠与一次函数2y x =-的图象的一个交点的横坐标为3，则k 的值为（）A ．3-B ．1-C ．1D ．3【答案】A【分析】题目主要考查一次函数与反比例函数的交点问题，根据题意得出231y =-=-，代入反比例函数求解即可7．如图，在Rt ABC △中，2AC BC ==，点D 在AB 的延长线上，且CD AB =，则BD 的长是（）A B C ．2D ．8．已知实数a ，b 满足10a b -+=，011a b <++<，则下列判断正确的是（）A ．12a -<<B ．112b <<C ．2241a b -<+<D ．1420a b -<+<【答案】C∴442a -<<-，021b <<，∴4421a b -<+<-，选项D 错误，不符合题意；故选：C9．在凸五边形ABCDE 中，AB AE =，BC DE =，F 是CD 的中点．下列条件中，不能推出AF 与CD 一定垂直的是（）A ．ABC AED ∠=∠B ．BAF EAF ∠=∠C ．BCF EDF ∠=∠D ．ABD AEC∠=∠【答案】D【分析】本题考查了全等三角形的判定和性质，等腰三角形“三线合一”性质的应用，熟练掌握全等三角形的判定的方法是解题的关键．利用全等三角形的判定及性质对各选项进行判定，然后根据等腰三角形“三线合一”的性质即可证得结论．【详解】解：A 、连结AC AD 、，∵ABC AED ∠=∠，AB AE =，BC DE =，∴()SAS ACB ADE ≌，∴AC AD=又∵点F 为CD 的中点∴AF CD ⊥，故不符合题意；B 、连结BF EF 、，∵AB AE =，BAF EAF ∠=∠，AF AF =，∴()SAS ABF AEF ≌，∴BF EF =，AFB AFE ∠=∠又∵点F 为CD 的中点，∴CF DF =，∵BC DE =,∴()SSS CBF DEF ≌，∴CFB DFE ∠=∠，∴90CFB AFB DFE AFE ∠+∠=∠+∠=︒，∴AF CD ⊥，故不符合题意；C 、连结BF EF 、，∵点F 为CD 的中点，∴CF DF =，∵BCF EDF ∠=∠，BC DE =，∴()SAS CBF DEF ≌，∴BF EF =，CFB DFE ∠=∠，∵AB AE =，AF AF =，∴()SAS ABF AEF ≌，∴AFB AFE ∠=∠，∴90CFB AFB DFE AFE ∠+∠=∠+∠=︒，∴AF CD ⊥，故不符合题意；D 、ABD AEC ∠=∠，无法得出相应结论，符合题意；故选：D．10．如图，在RtABC △中，90ABC ∠=︒，4AB =，2BC =，BD 是边AC 上的高．点E ，F 分别在边AB ，BC 上（不与端点重合），且DE DF ⊥．设AE x =，四边形DEBF 的面积为y ，则y 关于x 的函数图象为（）A ．B ．C ．D ．∵90ABC ∠=︒，AB =∴22AC AB BC =+=∵BD 是边AC 上的高．二、填空题11．若代数式14-x 有意义，则实数x 的取值范围是．【答案】4x ≠【分析】根据分式有意义的条件，分母不能等于0，列不等式求解即可．【详解】解： 分式有意义的条件是分母不能等于0，∴40x -≠∴4x ≠．故答案为：4x ≠．【点睛】本题主要考查分式有意义的条件，解决本题的关键是要熟练掌握分式有意义的条件．12．，祖冲之给出圆周率的一种分数形式的近似值为227（填“>”或“<”）．13．不透明的袋中装有大小质地完全相同的4个球，其中1个黄球、1个白球和2个红球．从袋中任取2个球，恰为2个红球的概率是．由树状图可得，共有12种等结果，其中恰为∴恰为2个红球的概率为21126=，故答案为：1．14．如图，现有正方形纸片ABCD ，点E ，F 分别在边,AB BC 上，沿垂直于EF 的直线折叠得到折痕MN ，点B ，C 分别落在正方形所在平面内的点B '，C '处，然后还原．（1）若点N 在边CD 上，且BEF α∠=，则C NM '∠=（用含α的式子表示）；（2）再沿垂直于MN 的直线折叠得到折痕GH ，点G ，H 分别在边,CD AD 上，点D 落在正方形所在平面内的点D ¢处，然后还原．若点D ¢在线段B C ''上，且四边形EFGH 是正方形，4AE =，8EB =，MN 与GH 的交点为P ，则PH 的长为．∵MN EF ⊥，∴CC FE '∥，∴12∠=∠，∵四边形ABCD 是正方形，∴90B BCD ∠=∠=︒，∴343290∠+∠=∠+∠=︒，∵四边形ABCD 是正方形，四边形∴90A B C D ∠=∠=∠=∠=∴567690∠+∠=∠+∠=︒，∴57∠=∠，三、解答题15．解方程：223x x -=【答案】13x =，21x =-【分析】先移项，然后利用因式分解法解一元二次方程，即可求出答案．【详解】解：∵223x x -=，∴223=0x x --，∴(3)(1)0x x -+=，∴13x =，21x =-．【点睛】本题考查了解一元二次方程，解题的关键是掌握解一元二次方程的方法进行解题．16．如图，在由边长为1个单位长度的小正方形组成的网格中建立平面直角坐标系xOy ，格点（网格线的交点）A 、B ，C 、D 的坐标分别为()7,8，()2,8，()10,4，()5,4．(1)以点D 为旋转中心，将ABC 旋转180︒得到111A B C △，画出111A B C △；(2)直接写出以B ，1C ，1B ，C 为顶点的四边形的面积；(3)在所给的网格图中确定一个格点E ，使得射线AE 平分BAC ∠，写出点E 的坐标．（2）连接1BB ，1CC ，∵点B 与1B ，点C 与1C 分别关于点∴1DB DB =，1DC DC =，∴四边形11BC B C 是平行四边形，∴122104S CC B ==⨯⨯⨯= （3）∵根据网格信息可得出5AB =∴ABC 是等腰三角形，∴AE 也是线段BC 的垂直平分线，∵B ，C 的坐标分别为，()2,8，(10,4∴点21084,22E ++⎛⎫ ⎪⎝⎭，即()6,6E ．（答案不唯一）17．乡村振兴战略实施以来，很多外出人员返乡创业．某村有部分返乡青年承包了一些田地．采用新技术种植A B ，两种农作物．种植这两种农作物每公顷所需人数和投入资金如表：农作物品种每公顷所需人数每公顷所需投入资金（万元）A48B 39已知农作物种植人员共24位，且每人只参与一种农作物种植，投入资金共60万元．问A B ，这两种农作物的种植面积各多少公顷？【答案】A 农作物的种植面积为3公顷，B 农作物的种植面积为4公顷．【分析】本题考查了二元一次方程组的应用，设A 农作物的种植面积为x 公顷，B 农作物的种植面积为y 公顷，根据题意列出二元一次方程组即可求解，根据题意，找到等量关系，正确列出二元一次方程组是解题的关键．【详解】解：设A 农作物的种植面积为x 公顷，B 农作物的种植面积为y 公顷，由题意可得，43248960x y x y +=⎧⎨+=⎩，解得34x y =⎧⎨=⎩，答：设A 农作物的种植面积为3公顷，B 农作物的种植面积为4公顷．18．数学兴趣小组开展探究活动，研究了“正整数N 能否表示为22x y -（x y ，均为自然数）”的问题．(1)指导教师将学生的发现进行整理，部分信息如下（n 为正整数）：N 奇数4的倍数表示结果22110=-22420=-22321=-22831=-22532=-221242=-22743=-221653=-22954=-222064=-L L一般结论()22211n n n -=--4n =______按上表规律，完成下列问题：（ⅰ）24=（）2-（）2；（ⅱ）4n =______；(2)兴趣小组还猜测：像261014 ，，，，这些形如42n -（n 为正整数）的正整数N 不能表示为22x y -（x y ，均为自然数）．师生一起研讨，分析过程如下：假设2242n x y -=-，其中x y ，均为自然数．分下列三种情形分析：①若x y ，均为偶数，设2x k =，2y m =，其中k m ，均为自然数，则()()()222222224x y k m k m -=-=-为4的倍数．而42n -不是4的倍数，矛盾．故x y ，不可能均为偶数．②若x y ，均为奇数，设21x k =+，21=+y m ，其中k m ，均为自然数，则()()22222121x y k m -=+-+=______为4的倍数．而42n -不是4的倍数，矛盾．故x y ，不可能均为奇数．③若x y ，一个是奇数一个是偶数，则22x y -为奇数．而42n -是偶数，矛盾．故x y ，不可能一个是奇数一个是偶数．由①②③可知，猜测正确．阅读以上内容，请在情形②的横线上填写所缺内容．【答案】(1)（ⅰ）7，5；（ⅱ）()()2211n n +--；(2)()224k m k m -+-【分析】（1）（ⅰ）根据规律即可求解；（ⅱ）根据规律即可求解；（2）利用完全平方公式展开，再合并同类项，最后提取公因式即可；本题考查了平方差公式，完全平方公式，掌握平方差公式和完全平方公式的运算是解题的关键．【详解】（1）（ⅰ）由规律可得，222475=-，故答案为：7，5；（ⅱ）由规律可得，()()22411n n n =+--，故答案为：()()2211n n +--；（2）解：假设2242n x y -=-，其中x y ，均为自然数．分下列三种情形分析：①若x y ，均为偶数，设2x k =，2y m =，其中k m ，均为自然数，则()()()222222224x y k m k m -=-=-为4的倍数．而42n -不是4的倍数，矛盾．故x y ，不可能均为偶数．②若x y ，均为奇数，设21x k =+，21=+y m ，其中k m ，均为自然数，则()()()22222221214x y k m k m k m -=+-+=-+-为4的倍数．而42n -不是4的倍数，矛盾．故x y ，不可能均为奇数．③若x y ，一个是奇数一个是偶数，则22x y -为奇数．而42n -是偶数，矛盾．故x y ，不可能一个是奇数一个是偶数．由①②③可知，猜测正确．故答案为：()224k m k m -+-．19．科技社团选择学校游泳池进行一次光的折射实验，如图，光线自点B 处发出，经水面点E 折射到池底点A 处．已知BE 与水平线的夹角36.9α=︒，点B 到水面的距离 1.20BC =m ，点A 处水深为1.20m ，到池壁的水平距离 2.50m AD =，点B C D ，，在同一条竖直线上，所有点都在同一竖直平面内．记入射角为β，折射角为γ，求sin sin βγ的值（精确到0.1，参考数据：sin 36.90.60︒≈，cos36.90.80︒≈，tan 36.90.75︒≈）．20．如图，O 是ABC 的外接圆，D 是直径AB 上一点，ACD ∠的平分线交AB 于点E ，交O 于另一点F ，FA FE =．(1)求证：CD AB ⊥；(2)设FM AB ⊥，垂足为M ，若1OM OE ==，求AC 的长．【答案】(1)见详解21．综合与实践【项目背景】无核柑橘是我省西南山区特产，该地区某村有甲、乙两块成龄无核柑橘园．在柑橘收获季节，班级同学前往该村开展综合实践活动，其中一个项目是：在日照、土质、空气湿度等外部环境基本一致的条件下，对两块柑橘园的优质柑橘情况进行调查统计，为柑橘园的发展规划提供一些参考．【数据收集与整理】从两块柑橘园采摘的柑橘中各随机选取200个．在技术人员指导下，测量每个柑橘的直径，作为样本数据．柑橘直径用x （单位：cm ）表示．将所收集的样本数据进行如下分组：组别A B C D E x 3.5 4.5x ≤< 4.5 5.5x ≤< 5.5 6.5x ≤< 6.57.5x ≤<7.58.5x ≤≤整理样本数据，并绘制甲、乙两园样本数据的频数直方图，部分信息如下：任务1求图1中a 的值．【数据分析与运用】任务2A ，B ，C ，D ，E 五组数据的平均数分别取为4，5，6，7，8，计算乙园样本数据的平均数．任务3下列结论一定正确的是______（填正确结论的序号）．①两园样本数据的中位数均在C 组；②两园样本数据的众数均在C 组；③两园样本数据的最大数与最小数的差相等．任务4结合市场情况，将C，D两组的柑橘认定为一级，B组的柑橘认定为二级，其它组的柑橘认定为三级，其中一级柑橘的品质最优，二级次之，三级最次．试估计哪个园的柑橘品质更优，并说明理由．根据所给信息，请完成以上所有任务．Y的对角线AC与BD交于点O，点M，N分别在边AD，BC上，且22．如图1，ABCDAM CN =．点E ，F 分别是BD 与AN ，CM 的交点．(1)求证：OE OF =；(2)连接BM 交AC 于点H ，连接HE ，HF ．（ⅰ）如图2，若HE AB ∥，求证：HF AD ∥；（ⅱ）如图3，若ABCD Y 为菱形，且2MD AM =，60EHF ∠=︒，求AC BD的值．23．已知抛物线2y x bx =-+（b 为常数）的顶点横坐标比抛物线22y x x =-+的顶点横坐标大1．(1)求b 的值；(2)点()11,A x y 在抛物线22y x x =-+上，点()11,B x t y h ++在抛物线2y x bx =-+上．（ⅰ）若3h t =，且10x ≥，0t >，求h 的值；（ⅱ）若11x t =-，求h 的最大值．。
中考英语动词综合运用单选题40题
中考英语动词综合运用单选题40题1. My mother __________ the dishes every day, but she didn't do it yesterday.A. washesB. washedC. washD. washing答案：A。
本题考查一般现在时。
my mother 是第三人称单数，一般现在时中，第三人称单数作主语，动词要用第三人称单数形式washes。
B 选项washed 是一般过去时；C 选项wash 是动词原形，用于主语是非第三人称单数的一般现在时；D 选项washing 是现在分词，不能单独作谓语。
2. We __________ to the park last weekend.A. goB. wentC. goesD. going答案：B。
本题考查一般过去时。
last weekend 是一般过去时的标志词，所以要用过去式went。
A 选项go 是动词原形，用于一般现在时；C 选项goes 是第三人称单数形式，用于一般现在时；D 选项going 是现在分词，不能单独作谓语。
3. My father __________ in the factory every day.B. worksC. workedD. working答案：B。
本题考查一般现在时。
my father 是第三人称单数，一般现在时中，第三人称单数作主语，动词要用第三人称单数形式works。
A 选项work 是动词原形，用于主语是非第三人称单数的一般现在时；C 选项worked 是过去式，用于一般过去时；D 选项working 是现在分词，不能单独作谓语。
4. They __________ football yesterday afternoon.A. playB. playedC. playsD. playing答案：B。
本题考查一般过去时。
yesterday afternoon 是一般过去时的标志词，所以要用过去式played。
中考英语单选1000题
中考英语单项选择1000题1 .Tom is not at school. Do you know what happen __?A. with him B .to him C. to he D. for he2 .My mother is _. I have to look after her.A .in the hospital B.At a hospital C .in hospital D. in a hospital3 . Did you hear someone ___at the door?A. knocksB. to knockC. knockedD. knocking4 .The teacher told the children, “it is very important___ careful ___fire.”A. to be; withB. is; withC. being; withD. to be; to5 . She saw ____ boy playing with his dogA eight-year-old B.An eight-years-old C.An eight-year-old D.A eight-years-old6 .The story sounds___ .A. interestinglyB. interestingC. interestedD. danger7. John told me to __ the pictures __ tomorrow.A. take; hereB. bring; thereC. taking; thereD. bring; here8. There __ a lot of __ in the kitchen and it was very__.A. was; smoke; hotB. were; smokes; hotC. was; smoke; hotterD. were; smoke; hotter9. Do you __ drive on the left in England?A. have toB. mustC. shouldD. may10. It is very hot today, please keep the window__.A. openingB. openC. opensD. to open11. --May I play with my dog?--I am afraid not. You can’t play with it __ you finish your homeworkA. whenB. untilC.afterD. because12. I am afraid I won’t __ finish reading the book in two daysA. canB. couldC. be able toD. may13. They have ___.A. enough food to eatB. food enough eatC. enough food eatingD. food enough eating14. --Must I clean the cage today?--No, you___.A. must notB. can notC. need notD. may not15. She ___ so much ___ her mother.A. looks; likeB. looks; forC. looks; afterD. looks forwards; to16. Mr. White likes to live in a __ place.A. quiteB. quietC. quickD. quietly17. Kate has a cat __ Mimi.A. calledB. callC. to callD. calling18. -- May I take my pet to school?-- No, you__.A. may notB. might notC. need notD. can not19. The teacher told the children to keep the classroom__.A. to cleanB. cleansC. cleanD. cleaned20. He doesn’t smoke and hates women __.A. smokesB. smokeC. smokedD. smoking21.-- How often do you clean the fish tank?--____.A. this afternoonB. only onceC. once a monthD. for two days22. Tom’s gold fish died because he gave them ___ food.A. too muchB. much tooC.A fewD. too many23. I __ , because I don’t want to be late for school.A.Am used to getting up earlyB. used to getting up earlyC. was used to getting up earlyD. used to get up early24. I need __ candles. Please pass them to me.A. two moreB. one moreC. more twoD. more one25.All the students in my class did their homework except__.A. Jane and IB. Jane and mineC. I and JaneD. Jane and me26. Will you please give the boy__ to eat?A. favorite somethingB. different anythingC. popular everythingD. something delicious27. Mr. Wang told his son __ football on the road.A. not playB. to not playC. not to playD. doesn’t play28. Both ___ watches were broken.A. Jim and Tom’sB. Jim’s and Tom’sC. Jim’s and TomD. Jim and Tom29.–Don’t forget to bring your son here next time, please.--____.A. No, I don’tB. No, I won’tC. No, I canD. Yes , I do30. I saw the boy__ the classroom.A. enter intoB. enterC. to enter intoD. to enter31. Miss Li is ___ our teacher ___our friend.A. neither; orB. either; orC. not only; but alsoD. either ; nor32. He began learning English. ___ the age of five.A. forB. onC. inD.At33. His job is __ cars.A. to repairB. repairedC. repairsD. repair34. We should protect our eyes __ sunglasses.(考有动作含义的介词)A. in wearB. by wearingC. with wearingD. to wear35. He visited Uncle Li___ a cold morning.A. onB. inC.AtD. for36. They often __ school activities after school.A. joinB. doC. take part inD. play with37. I have seen the movie __ times.A. the number ofB.A number ofC. muchD.A number38. The boy is made__ the room every day.A. cleanB. cleaningC. to cleanD. cleans39. You can find some ___ on the Internet.A. informationsB. informationC. pictureD. story40. The ___ girl is looked well by her grandmotherA. five-years-oldB. five year oldC. five-years oldD. five-year-old41. Great changes ___ in the last ten years.A. have taken placeB. have been taken placeC. took placeD. were taken place42. __ does your brother__ ?A. how; look likeB. What ; look likeC. what; lookD. How ; looks43. You must have left your glasses___.A. somewhere elseB.anywhere elseC. somewhere otherD. some other where44. I will talk with you about it ___time.A. the otherB. othersC.AnotherD. the others45. When I was walking in the street, I saw him ___ his brother.A. to quarrel withB. quarrels withC. quarrel withD. quarreling with46.All the students like the teachers who__ their lessons interesting.A. makesB. makeC. makingD. to make47. we’d better go and tell her the __ news. I am sure she will be very __ it.A. surprised; surprising inB. interested; interesting inC. interesting; interesting atD. surprising; surprised at48. We can watch the TV programmers from other countries __ the satellites.A. becauseB. because ofC. ifD. that49. The teacher told us not___ our dictionaries to school the next day.A. to bringB. to takeC. bringD. take50. I will go to visit my uncle___ next week.A. sometimesB. some timesC. some timeD. sometime51. When I was watching TV, I __ someone calling my name outside.A. heardB. listenC. listen toD. hear52. The policeman asked John __ he knew the victim.(受害者)A. whatB. thatC. ifD. which53. Betty and John have come back, but___ students aren’t here yet.A.AnotherB. the otherC. othersD. the others54. The robbery_____ in Sun Town last Sunday.A. is happenedB. was happenedC. happenedD. happens55. He said that __ eight- year-old child was__.A.A; kidnappedB.An; kidnappedC.A; kidnapedD.An; kidnapped56. Tom asked, “Did you hear___?A. something strangeB. nothing strangeC. strange anythingD.Anything strange57. The boy is __ in __ on the ice.A. interesting; skatingB. interesting; to skateC. interested; skatingD. interested; to skate58. You don’t need ___ if you feel sick.A. to comeB. comeC. comingD. comes59. The house is ___ for us to ___.A. big enough; liveB. enough big; live inC. big enough; live inD. enough big; live60. He finished his sandwich and asked for ____.A. the otherB.AnotherC. otherD. others61. Do you like the cake __ nuts __ it?A. with; inB. have; inC. has; onD. with ; of62. Will you ___ come tomorrow?A. be able toB. canC. mustD. be able63. The used car is ___ 500 dollars.A. costB. payC. worthD. spend64. --- Will you go shopping tonight?--- If you go,___.A. so do IB. so will IC. so I goD. that I will go65. --- Do you still remember ___ me somewhere in ShangHai?--- yes, of course, two years ago.A. seeingB. seeC. to seeD. saw66. __ is really hard ___ them to climb Mount QomolangmA.A. This; isB. it ; forC. This ; forD. it; to67.–Jack hasn’t paid for the school things, has he?-___. His father will pay for him.A. yes, he hasB. no, he hasn’tC. yes, he didD. no, he didn’t68. She is __, but she looks young.A. in her fiftiesB.At her fiftyC. in her fiftyD.At her fifties69. Tom studies__, but his sister __ studies.A. hard; hardB. hardly; hardlyC. hard; hardlyD. hardly; hard70. Do you know the lady__ is interviewing our headmaster?A. whichB. whoC. whomD. whose71. It’s ___ ride from my home to the factory.A. two hours and half’sB. two and half hours’C. two and a half hours’D. two hour and a half’s72. I have __ a raincoat __ an umbrellA. That is why I have to wait until the rain stops.A. neither; norB. either; orC. not only; but alsoD. both; and73. Most of us wondered if girls’football team could ___ boys’football team in the final match.A. beatB. winC. hitD. lose74.–___ is the Summer Palace from here?-- about three kilometers away. You can take the No. 35 bus.A. how longB. how oftenC. how farD. how much75. ___ a heavy snow tomorrow.A. there will haveB. there is going to haveC. there will hasD. there is going to be76. Who will ___ if he ___ come?A. mop it up; won’tB. mop up it; doesn’tC. mop it up; doesn’tD. mop it up; don’t77. ___ cloudy day it is!A. howB. whatC. how aD. what a78. The flood killed ___ peopleA. thousands ofB. thousand ofC. thousandsD. thousand79. This math problem is not easy. I can’t work it out __.A. without heB. with himC. without himD. with he80. This problem is so difficulty that only __ students can work it out.A.A fewB. fewC. littleD.A little81. We all think __ to play the gameA. it is interestedB. that was interestingC. it is interestingD. that interesting82. I think he will prefer the blown trousers. Let’s buy__.A. itB. oneC. onesD. that83. --___is the movie ticket for <a world without thieves>?--About 30 yuanA. how longB. how manyC. how muchD. how soon84. --___will your manager return to the company, please?-- in about three daysA. how longB. how soonC. how oftenD. how much85.–__did it take him to repair the computer?--about 2 daysA. how soonB. how oftenC. how longD. how far86. She taught __ English.A. herB. hersC. herselfD. she87.–if you want to keep fit, you have to eat__ food and do _sports.-- You mean the more exercise I do, the __ I will be.A. less; more; healthierB. more; less; healthC. less; fewer; healthilyD. most; fewest;88. I must return the digital camera to Nancy. I __ it 2 weeks ago.A. lentB. borrowedC. have keptD. have lent89. The number of the boy babies__ much larger than that of the girl babies these years.A.AreB. wasC. isD. were90. I felt sorry that I was late for the meeting. I was so busy _ a novel that I forgot __the meeting.A. to read; looking atB. reading; to useC. to read; seeingD. reading; to look at91. I am not sure if I am going to Tim’s party. I may go to the concert__.A. onlyB. insteadC. earlyD. late92. His mother will go to New York with his brother__ a few days.A. inB.AfterC. withD. before93. His parents couldn’t __ if they would buy a secondhand car.A. describeB. discoverC. decideD. disappear94. When the old woman was in good health, she __ shopping on Sunday.A. was used to goB. used to goingC. used to goD. get used to going95. When I got __ home, I saw my mother __picture on the wall.A. back; putting offB. off; put upC. back; putting upD. off; putting off96.–I know your father __ to a lot of cities, but what about your mother?--my mother? She __ away from my hometown even once.A. has gone; has never goneB. has been; has never goneC. has gone; has never beenD. has been; has never been97.__ of us could understand the article,__ we could hardly find any new words in it.A. few; thoughtB. few; becauseC.A few; soD. few; though98.A group of scientists__ some eggs __ by dinosaurs in the Gobi Desert in the 1920s.A. found; lyingB. founded; laidC. found; lainD. found; laid99. Many of the stars are__ far away __ .A. so; to seeB. very; to be seenC. too; to be seenD. much; to see 100. You __ the flowers, for the earth is __.A. needn’t to water; enough wetB. needn’t water; wet enoughC. mustn’t water; enough wetD. needn’t water; wet enough101. I don’t know __ the computer .A. what to useB. how useC. how to useD. how can use102. He often __ from the Internet for us.A. get informationB. gets informationC. get informationsD. gets informations103. You can __ the umbrella___ .A. take; homeB. take; to homeC. bring; homeD. bring; to home104. The boy is __ the ballA. tall enough catchingB. enough tall catchingC. enough tall to catchD. tall enough to catch105. Jack is good at___.A. playing the pianoB. to play the pianoC. playing pianoD. to play piano 106.–May I put my bike here?-No, you __A. may notB. can’tC. might notD. mayn’t107. He __ a lot of time__ me with my math .A. spends; helpB. spend; helpingC. spend; to helpD. spends; helping 108. I have __ to tell you.A.Anything interestingB. something interestingC. interesting anythingD. interesting something109. Thank you for __ us the news.A. to tellB. tellsC. tellingD. told110. He is very __. He often__ his school things at home.A. careful; leavesB. careless; forgetsC. careful; forgetsD. careless; leaves 111. The soldier saved __ boy.A.An 11 year oldB.An 11-year-oldC.A 11-year-oldD.A 11-years-old 112. Sam likes music very much. He lives __ but he never feels__ .A.Alone; lonelyB.Alone; aloneC. lonely; aloneD. lonely; lonely113. Billy didn’t come to school this morning. What happened __ him?A. withB. forC. toD. in114. She was glad __ her friends againA. seeB. sawC. seeingD. to see115. let’s __ every Monday after schoolA. practise dancingB. practise to danceC. to practise dancingD. to practise to dance116. Will you __ come to me tomorrow?A. canB. couldC. be able toD. may117. There is a lot of __ outside when he is trying to sleep.A. noiseB. noisesC. noisyD. noisily118. Can you hear someone __ in the next room?A. singB. singsC. singingD. sang119. She __ feed the cat. Her parents do it.A. don’t have toB. has not toC. have not toD. does not have to120.–Must I walk the dog in the park now?- no , you __.A. mustn’tB. needn’tC. can’tD. may not121. If you want to ask your sister not to pull y our rabbit’s ears, you should say, “___”.A. you might pull the rabbit’s earsB. Not pull the rabbit’s earsC. Don’t pull the rabbit’s earsD. I don’t let you pull the rabbit’s ears122. He spent the whole afternoon __ booksA. on readingB. in readC. to readD. reading123. There __ for him __ for two days.A.Are enough food; to eatB. is enough food; to eatC.Are food enough; eatingD. is enough food; eating124. If you want to be __ you must take more___.A. healthy; exerciseB. health; exerciseC. healthy; exercisesD. health; exercises125. please __ the new shoes here and __the old ones thereA. bring; takeB. take; bringC. bring; bringD. take; take126. Would you please keep the window __?A. closeB. closedC. closingD. to closed127. __ afraid of the camel! It is friendly !A. Doesn’t beB. Not beC. Don’t beD. Don’t is128. The shirt doesn’t fit me. It’s __ small for me.A. too muchB. much tooC. too manyD. many too129. I have a dog. I think it is __ in the world.A. very cleverB. clevererC. the most cleverD. the cleverest130. Mr. Li teaches __.A. my EnglishB. my with EnglishC. me with EnglishD. me English 131. Each of the children __ his own bicycle.A. haveB. hasC. havingD. to have132. When did audrey __ the film industry(电影工业)?A. joinB. take part inC. took part inD. joined133. Would you like __ actress?A. to be aB. is aC. be anD. to be an134. I would rather__ than go outA. staying at homeB. stay at homeC. to staying at homeD. to stay at home135. __ David __ Jack has such a bag. It must be __.A. Both; and; someone elseB. Either; or; someone elseC. Neither; nor; someone else’sD. Not only; but also; someone else’s136. The boy’s dream is __ a computer engineer.A. beB. to becomeC. becomingD. becomes137. He __ a writer for five years before he came to ChinA.A. had beenB. had becomeC. wasD. became138. The film star __ both a TV series and some well-known films.A. joinB. take part inC. took part inD. joined139. She is not sure__.A. how does she use the computerB. what to use the computerC. how to use the computerD. what she uses the computer140. They didn’t __ the town until last night.A. get inB. reach toC.Arrive inD.Arrive at141. Why is George going to give up__?A. studies EnglishB. studying EnglishC. to study EnglishD. study English142. The old man practises __ 10,000 steps every day.A. to walkB. to walkingC. walkingD. walk143. Can you __ Mr. Johnson’s address for me?A. findB. find outC. looked forD. look for144. She is forgetful. She often __ her books at home.A. leavesB. forgetsC. forgotD. left145. You don’t __ do it if you don’t want to.A. had betterB. ought toC. mustD. have to146. The old man __ the last few years in __ trees in the desert.A. spent; plantingB. spent; to plantC. took; plantingD. took; plant 147. I have __ question to ask you.A. more oneB.Any moreC. some moreD. one more148. The child felt __ when they heard the news.A. happilyB. happyC. sadlyD.Angily149. His parents’death made him__ .A. leaving schoolB. to leave schoolC. leave schoolD. leaves school 150. I am not sure if they __ tomorrow. If they __ tomorrow they will tell me.A. will go hiking; will go hikingB. will go hiking; go hikingC. go hiking; go hikingD. go hiking; will go hiking151. Yesterday I saw __ action film __ Cheng Long.A.A; starringB.An; starredC.An; starringD.A; starred152.–Must we get there before six?-No, you__.A. mustn’tB. may notC. can’tD. don’t have to153. His mother’s __ was a great blow to him.A. diedB. deadC. deathD. die154. There is __ food in the fridge. Let’s go to the supermarket.A.A bitB.A bit ofC. littleD.A little of155.–Would you mind __ care of our child?--__.A. to take; of courseB. taking; certainlyC. to take; certainly notD. taking; of course not156. I don’t know if she __ tomorrow. If it __ , perhaps she’ll come.A. will come; stops rainingB. comes; will stop rainingC. will come; won’t rainD. comes; doesn’t rain157. I found John was very careful. He __ everything__ than I did.A. plans; betterB. planed; bestC. planned; betterD. planned; well158. Hainan is a good place __ for touring __ for surfing. It has the best beaches and waves all the year around.A. neither; norB. not only; but alsoC. either; orD. both; and159. He couldn’t decide__.A. which sweater he boughtB. which sweater did he buyC. which sweater will I buyD. which sweater to buy160. She asked __.A. who was he talking withB. who he is talking withC. who he was talking withD. who is he talking with161. He had a bad cough. the doctor advised him to give up__.A. smokeB. smokingC. to smokeD. smoked162. He is __ at English than Kate.A. betterB. bestC. goodD. well163. If he does the work__, he will make__ mistakes.A. more carefully; fewerB. more careful; lessC. more carefully; fewD. careful; less164. Hawaii is__ island that attracts __ many tourists.A. so beautiful; soB. such beautiful; suchC. quite a beautiful; suchD. such a beautiful; so165. __were sitting at the supper table when I knocked at the door.A. WhiteB. The WhiteC. The WhitesD. Whites166. It’s __ now. let’s go home.A. fifty past fourB. four past fiftyC. fifty to fiveD. ten to five167. --___ do you watch TV, Lin Feng?-- Twice a week.A. how oftenB. how longC. how soonD. how much168. The bu s ticket from Nan Jing to Shanghai __ about 80 yuan.A. costsB. takesC. spendsD. pays169. My father can’t come to parents’meeting. He __ to Beijing on business this morning.A. has goneB. has beenC. wentD. would go170. I __ to answer the question in English. But as you know, I’m not so good at English.A. toldB. was toldC. have toldD. was telling171. Would you please __ him up? He is too tired and let him have a good rest.A. not to wakeB. not wakeC. don’t wakeD. to not wake172. –what a day! It is quite hot today.--___.A. So it is.B. So is it.C. So it doesD. So does it173. Beethoven heard someone playing __ piano while he was walking in the street.A.AB.AnC. theD. /174. My uncle can speak German. He can make friends with __.A. GermanB. GermenC. GermansD. Germens175. There is no__ in the boat, so we have to wait for another one.A. seatsB. roomC. roomsD.A seat176. The wind is blowing more and more strongly. Why not__ the windows__?A. to keep; closeB. to keep; openC. keep; openedD. keep; closed 177. There are a lot of new buildings on __ side of the street.A. everyB. eitherC. bothD.All178. It is a very long day for Jackson. He didn’t get home from school __ six o’clock.A. sinceB.AfterC. untilD. by179. Li Lei looks happy, __ he’s __ his English examA. because; pastB. when; pastC. since; passedD. because; passed 180. No matter __ , we should not change our plan.A. what does it happensB. happens whatC. what is happenedD. what happens181. Mr. Green and Mr. king__ at this school__ they came to China two years ago. A. taught; when B. have taught; since C. have taught; because D. taught; until182. Nobody except Li Ping and Liu Ying __ at school this time yesterday.A. wereB. has beenC. wasD. had been183. These foreign friends have already __ Nanjing for about two days.A. reachedB.Arrived inC. got toD. been in184. I think traveling by train is much cheaper and __ a rushed trip by air.A. far more enjoyable thanB. very much enjoyable thanC. so much enjoyable thanD. much more enjoyable as185. –will you please __ him the pictures as soon as he __ back tomorrow?--With pleasure.A. to give; will comeB. give; comesC. gave; will comeD. giving; come186. The teacher has done his best __ their studies.A. help his students to improveB. to help his students to improveC. helps his students to improveD. helped his students to improve187. She feels like __ TV.A. watchesB. watchC. watchingD. to watch188. Our teacher, Miss Green, __ English on the radio the day before yesterday.A. teachesB. taughtC. teachD. had taught189. Hello, Mr. Green! I want to see you right now. Can you come as __ as possible ?A. manyB. lateC. muchD. soon190. I must return the camera to Li Lei. I __ it for two weeks.A. have boughtB. borrowedC. have keptD. have lent191. The black bag__ be anna’s. she has a blue oneA. shouldB. can’tC. wouldn’tD. could192. __ the morning of July the 5th, we finally __ the town by train.A.At; reachB. on; arrived atC. in; got toD. on; arrived in193. My watch doesn’t work. I have to __ it __ right now.A. make; repairB. have; repairedC. make; to repairD. have; repair 194. We prefer__ at the party rather than__.A. to sing; danceB. to sing; dancingC. sing; to danceD. sing; dance 195. –May I speak to Mr. Black, please?--Sorry, he’s __ Beijing for about three daysA. been toB. gone toC. been inD. gone in196. Parents are more worried about their children’s lessons. In fact, it’s not necessary for them to watch their children__ every night.A. studyB. to studyC. studiesD. studying197. –Have you sent your grandparents an e-mail telling them you arrived already?--No, __ of them can use a computer.A. noneB. bothC. NeitherD.All198. __ interesting work it is!A. HowB. What aC. How anD. What199 . Did you find__ to sit down in the train?A.A roomB. roomsC. roomD. place200.As close friends,they used to walk to school____.A. face to faceB.little by littleC. step by stepD.side by side201 . Would you please tell me ___ the computer?A. what to useB. how to useC. how can useD. what can use202 . Simon heard his neighbor ___ for help at nightA. callsB. callC. callingD. to call203 . I am very busy. I have a lot of clothes___.A. washB. washingC. washedD. to wash204.–Could you teach us how to look after the rabbit?--_____.A. good ideaB. you are welcomeC. no problemD. that’s all right 205 . We look forward to ___ from him soon.A. hearB. hearsC. heardD. hearing206 . It takes him half an hour __ to work by bike.A. goingB. to goC. goD. goes207 . My baby is sleeping. Don’t make ___.A. much noiseB.A lot noiseC. many noiseD. noise208 . The old woman ___ a lot of time___.A. spends; playingB. takes; to playC. spent; to playD. spent; playing 209 . Do you know the young man ___ John?A. to callB. callC. calledD. calling210 . This book is __ for us___.A. enough easy; to understandB. easy enough; to understandC. enough easy; understandingD. easy enough; understanding211 . My car is broken. I __ go to the office on foot.A. mayB. mustC. canD. have to212 . She is __ unusual speaker.A.AB. /C.AnD. the213 . The old man practises ___10,000 steps every day.A. walkB. walkingC. to walkD. walks214 . They will play___ basketball instead of___ piano.A. the; playing theB. /; playC. the; play theD. /; playing the215 . You must have __ the book __.A. forgotten; somewhere elseB. left; somewhere elseC. left; somewhere otherD. forgotten; anywhere else216 . The man was seen __ the car in the garden an hour ago.A. to washB. washesC. washingD. washed217 . We have to put off the sports meeting__ the rain.A. becauseB. ifC. sinceD. because of218 . The girl was seen ___ the office.A. leaveB. to leaveC. leavingD. to left219. The children were__ at the thought of the journey.A. excitingB. excitedC. exciteD. excitedly220 . When he heard the news, he felt__.A. happilyB. sadlyC. happyD. bad221 . The old man is jogging __ a blue sweater.A. putting onB. wearC. inD. with222 . You are so hungry. Would you like__ cake?A.AnotherB. otherC. the othersD. others223 . Please make the girl__.A. to keep quietB. keep quietC. keep quiteD. keeping quiet224. --___ does he take the medicine?。
2024年重庆市中考真题数学试卷(A卷)含答案解析
2024年重庆市中考真题（A卷）数学试题学校:___________姓名：___________班级：___________考号：___________一、单选题1．下列四个数中，最小的数是（）A．2-B．0C．3D．1 2 -2．下列四种化学仪器的示意图中，是轴对称图形的是（）A．B．C．D．【答案】C【分析】此题考查了轴对称图形的概念，根据概念逐一判断即可，如果一个图形沿一条直线折叠，直线两旁的部分能够互相重合，这个图形叫做轴对称图形，这条直线叫做对称轴，这时，我们也可以说这个图形关于这条直线(成轴）对称，熟练掌握知识点是解题的关键．【详解】A、不是轴对称图形，故本选项不符合题意；B、不是轴对称图形，故本选项不符合题意；C、是轴对称图形，故本选项符合题意；D、不是轴对称图形，故本选项不符合题意；故选：C．3．已知点()3,2-在反比例函数()0ky k x=≠的图象上，则k 的值为（ ）A ．3-B ．3C ． 6-D ．64．如图，AB CD ∥，165∠=︒，则2∠的度数是（ ）A ．105︒B ．115︒C ．125︒D ．135︒【答案】B【分析】本题主要考查了平行线的性质，根据平行线的性质得3165∠=∠=︒，由邻补角性质得23180∠+∠=︒，然后求解即可，熟练掌握两直线平行，同位角相等是解题的关键．【详解】解：如图，∵AB CD ∥，∴3165∠=∠=︒，∵23180∠+∠=︒，∴2115∠=︒，故选：B ．5．若两个相似三角形的相似比是1:3，则这两个相似三角形的面积比是（ ）A ．1:3B ．1:4C ．1:6D ．1:9【答案】D【分析】此题考查了相似三角形的性质，根据“相似三角形的面积比等于相似比的平方”解答即可．【详解】解：两个相似三角形的相似比是1:3，则这两个相似三角形的面积比是1:9，故选：D ．6．烷烃是一类由碳、氢元素组成的有机化合物质，下图是这类物质前四种化合物的分子结构模型图，其中灰球代表碳原子，白球代表氢原子．第1种如图①有4个氢原子，第2种如图②有6个氢原子，第3种如图③有8个氢原子，……按照这一规律，第10种化合物的分子结构模型中氢原子的个数是（ ）A ．20B ．22C ．24D ．26【答案】B【分析】本题考查数字的变化类，根据图形，可归纳出规律表达式的特点，再解答即可．【详解】解：由图可得，第1种如图①有4个氢原子，即2214+⨯=第2种如图②有6个氢原子，即2226+⨯=第3种如图③有8个氢原子，即2238+⨯=⋯，∴第10种化合物的分子结构模型中氢原子的个数是：221022+⨯=；故选：B ．7．已知m =m 的范围是（ ）A ．23m <<B ．34m <<C ．45m <<D ．56m <<8．如图，在矩形ABCD 中，分别以点A 和C 为圆心，AD 长为半径画弧，两弧有且仅有一个公共点．若4=AD ，则图中阴影部分的面积为（ ）A ．328π-B ．4π-C ．324π-D ．8π-根据题意可得2AC AD =∵矩形ABCD ，∴AD BC =在Rt ABC △中，AB =9．如图，在正方形ABCD 的边CD 上有一点E ，连接AE ，把AE 绕点E 逆时针旋转90︒，得到FE ，连接CF 并延长与AB 的延长线交于点G ．则FGC E的值为（ ）AB C D 由旋转得,90EA EF AEF =∠=︒，∵四边形ABCD 是正方形，∴90D Ð=°，DC AB ∥，DA =∴D H ∠=∠，10．已知整式1110:n n n n M a x a x a x a --++++ ，其中10,,,n n a a - 为自然数，n a 为正整数，且1105n n n a a a a -+++++= ．下列说法：①满足条件的整式M 中有5个单项式；②不存在任何一个n ，使得满足条件的整式M 有且只有3个；③满足条件的整式M 共有16个．其中正确的个数是（ ）A ．0B ．1C ．2D ．3【答案】D【分析】本题考查的是整式的规律探究，分类讨论思想的应用，由条件可得04n ≤≤，再分类讨论得到答案即可．【详解】解：∵10,,,n n a a - 为自然数，n a 为正整数，且1105n n n a a a a -+++++= ，∴04n ≤≤，当4n =时，则2104345a a a a a +++++=，∴41a =，23100a a a a ====，满足条件的整式有4x ，当3n =时，则210335a a a a ++++=，∴()()3210,,,2,0,0,0a a a a =，()1,1,0,0，()1,0,1,0，()1,0,0,1，满足条件的整式有：32x ，32x x +，3x x +，31x +，当2n =时，则21025a a a +++=，∴()()210,,3,0,0a a a =，()2,1,0，()2,0,1，()1,2,0，()1,0,2，()1,1,1，满足条件的整式有：23x ，22x x +，221x +，22x x +，22x +，21x x ++；当1n =时，则1015a a ++=，∴()()10,4,0a a =，()3,1，()1,3，()2,2，满足条件的整式有：4x ，31x +，3x +，22x +；当0n =时，005a +=，满足条件的整式有：5；∴满足条件的单项式有：4x ，32x ，23x ，4x ，5，故①符合题意；不存在任何一个n ，使得满足条件的整式M 有且只有3个；故②符合题意；满足条件的整式M 共有1464116++++=个．故③符合题意；故选D二、填空题11．计算：011(3)(2π--+＝ ．12．若一个多边形的每一个外角都等于40°，则这个多边形的边数是 ．【答案】9【详解】解：360÷40=9，即这个多边形的边数是9．故答案为：9．13．重庆是一座魔幻都市，有着丰富的旅游资源．甲、乙两人相约来到重庆旅游，两人分别从A 、B 、C 三个景点中随机选择一个景点游览，甲、乙两人同时选择景点B 的概率为 ．由图可知，共有9种等可能的情况，其中甲、乙两人同时选择景点∴甲、乙两人同时选择景点B 的的概率为19，故答案为：19．14．随着经济复苏，某公司近两年的总收入逐年递增．该公司2021年缴税40万元，2023年缴税48.4万元，该公司这两年缴税的年平均增长率是 ．【答案】10%【分析】本题主要考查一元二次方程的应用．设平均增长率为x ，然后根据题意可列方程进行求解．【详解】解：设平均增长率为x ，由题意得：()240148.4x +=，解得：10.110%x ==，2 2.1x =-（不符合题意，舍去）；故答案为：10%．15．如图，在ABC 中，延长AC 至点D ，使CD CA =，过点D 作DE CB ∥，且DE DC =，连接AE 交BC 于点F ．若CAB CFA ∠=∠，1CF =，则BF = ．【答案】3【分析】先根据平行线分线段成比例证AF EF =，进而得22DE CD AC CF ====，4AD =，再证明CAB DEA ≌，得4BC AD ==，从而即可得解．16．若关于x 的不等式组()411321x x x x a -⎧<+⎪⎨⎪+≥-+⎩至少有2个整数解，且关于y 的分式方程13211a y y-=---的解为非负整数，则所有满足条件的整数a 的值之和为 ．17．如图，以AB 为直径的O 与AC 相切于点A ，以AC 为边作平行四边形ACDE ，点D 、E 均在O 上，DE 与AB 交于点F ，连接CE ，与O 交于点G ，连接DG ．若10,8AB DE ==，则AF = ．DG = ．∵以AB 为直径的O 与AC ∴AB AC ⊥，∴90CAB ∠=︒，∵四边形ACDE 为平行四边形，∴∥D E A C ，8AC DE ==，18．我们规定：若一个正整数A 能写成2m n -，其中m 与n 都是两位数，且m 与n 的十位数字相同，个位数字之和为8，则称A 为“方减数”，并把A 分解成2m n -的过程，称为“方减分解”．例如：因为26022523=-，25与23的十位数字相同，个位数字5与3的和为8，所以602是“方减数”，602分解成26022523=-的过程就是“方减分解”．按照这个规定，最小的“方减数”是 ．把一个“方减数”A 进行“方减分解”，即2A m n =-，将m 放在n 的左边组成一个新的四位数B ，若B 除以19余数为1，且22m n k +=（k 为整数），则满足条件的正整数A 为 ．三、解答题19．计算：(1)()()22x x y x y -++；(2)22111a a a a -⎛⎫+÷ ⎪+．20．为了解学生的安全知识掌握情况，某校举办了安全知识竞赛．现从七、八年级的学生中各随机抽取20名学生的竞赛成绩（百分制）进行收集、整理、描述、分析．所有学生的成绩均高于60分（成绩得分用x 表示，共分成四组：A ．6070x <≤；B ．7080x <≤；C ．8090x <≤；D ．90100x <≤），下面给出了部分信息：七年级20名学生的竞赛成绩为：66，67，68，68，75，83，84，86，86，86，86，87，87，89，95，95，96，98，98，100.八年级20名学生的竞赛成绩在C 组的数据是：81，82，84，87，88，89．七、八年级所抽学生的竞赛成绩统计表年级七年级八年级平均数8585中位数86b 众数a 79根据以上信息，解答下列问题：(1)上述图表中=a ______，b =______，m =______；(2)根据以上数据分析，你认为该校七、八年级中哪个年级学生的安全知识竞赛成绩较好？请说明理由（写出一条理由即可）；(3)该校七年级有400名学生，八年级有500名学生参加了此次安全知识竞赛，估计该校七、八年级参加此次安全知识竞赛成绩优秀()90x >的学生人数是多少？【答案】(1)86，87.5，40；(2)八年级学生竞赛成绩较好，理由见解析；(3)该校七、八年级参加此次安全知识竞赛成绩优秀的学生人数是320人．【分析】（1）根据表格及题意可直接进行求解；（2）根据平均分、中位数及众数分析即可得出结果；（3）由题意可得出参加此次竞赛活动成绩优秀的百分比，然后可进行求解；本题主要考查扇形统计图及中位数、众数、平均数，熟练掌握扇形统计图及中位数、众数、平均数是解题的关键．【详解】（1）根据七年级学生竞赛成绩可知：86出现次数最多，则众数为86，八年级竞赛成绩中A 组：2010%2⨯=（人），B 组：2020%4⨯=（人），21．在学习了矩形与菱形的相关知识后，小明同学进行了更深入的研究，他发现，过矩形的一条对角线的中点作这条对角线的垂线，与矩形两边相交的两点和这条对角线的两个端点构成的四边形是菱形，可利用证明三角形全等得到此结论．根据他的想法与思路，完成以下作图与填空：(1)如图，在矩形ABCD中，点O是对角线AC的中点．用尺规过点O作AC的垂线，分别交AB，CD于点E，F，连接AF，CE．（不写作法，保留作图痕迹）(2)已知：矩形ABCD，点E，F分别在AB，CD上，EF经过对角线AC的中点O，且⊥．求证：四边形AECF是菱形．EF AC证明：∵四边形ABCD是矩形，．∴AB CD∠=∠．∴①，OCF OAE∵点O是AC的中点，∴②．∴CFO AEO≅△△（AAS）．∴③．又∵OA OC =，∴四边形AECF 是平行四边形．∵EF AC ⊥，∴四边形AECF 是菱形．进一步思考，如果四边形ABCD 是平行四边形呢？请你模仿题中表述，写出你猜想的结论：④．【答案】(1)见解析(2)①OFC OEA ∠=∠；②OA OC =；③OF OE =；④四边形AECF 是菱形【分析】本题主要考查了矩形的性质，平行四边形的性质与判定，菱形的判定，垂线的尺规作图：（1）根据垂线的尺规作图方法作图即可；（2）根据矩形或平行四边形的对边平行得到OFC OEA ∠=∠，OCF OAE ∠=∠，进而证明()AAS CFO AEO ≌，得到OF OE =，即可证明四边形AECF 是平行四边形．再由EF AC ⊥，即可证明四边形AECF 是菱形．【详解】（1）解：如图所示，即为所求；（2）证明：∵四边形ABCD 是矩形，∴AB CD ．∴OFC OEA ∠=∠，OCF OAE ∠=∠．∵点O 是AC 的中点，∴OA OC =．∴()AAS CFO AEO ≌．∴OF OE =．又∵OA OC =，∴四边形AECF 是平行四边形．∵EF AC ⊥，∴四边形AECF 是菱形．猜想：过平行四边形的一条对角线的中点作这条对角线的垂线，与平行四边形两边相交的两点和这条对角线的两个端点构成的四边形是菱形；证明：∵四边形ABCD 是平行四边形，∴AB CD ．∴OFC OEA ∠=∠，OCF OAE ∠=∠．∵点O 是AC 的中点，∴OA OC =．∴()AAS CFO AEO ≌．∴OF OE =．又∵OA OC =，∴四边形AECF 是平行四边形．∵EF AC ⊥，∴四边形AECF 是菱形．故答案为：①OFC OEA ∠=∠；②OA OC =；③OF OE =；④四边形AECF 是菱形．22．为促进新质生产力的发展，某企业决定投入一笔资金对现有甲、乙两类共30条生产线的设备进行更新换代．(1)为鼓励企业进行生产线的设备更新，某市出台了相应的补贴政策．根据相关政策，更新1条甲类生产线的设备可获得3万元的补贴，更新1条乙类生产线的设备可获得2万元的补贴．这样更新完这30条生产线的设备，该企业可获得70万元的补贴．该企业甲、乙两类生产线各有多少条？(2)经测算，购买更新1条甲类生产线的设备比购买更新1条乙类生产线的设备需多投入5万元，用200万元购买更新甲类生产线的设备数量和用180万元购买更新乙类生产线的设备数量相同，那么该企业在获得70万元的补贴后，还需投入多少资金更新生产线的设备？【答案】(1)该企业甲类生产线有10条，则乙类生产线各有20条；(2)需要更新设备费用为1330万元23．如图，在ABC 中，6AB =，8BC =，点P 为AB 上一点，过点P 作PQ BC ∥交AC 于点Q ．设AP 的长度为x ，点P ，Q 的距离为1y ，ABC 的周长与APQ △的周长之比为2y ．(1)请直接写出1y ，2y 分别关于x 的函数表达式，并注明自变量x 的取值范围；(2)在给定的平面直角坐标系中画出函数1y ，2y 的图象；请分别写出函数1y ，2y 的一条性质；(3)结合函数图象，直接写出12y y >时x 的取值范围．（近似值保留一位小数，误差不超过0.2）（3）解：由函数图象可知，当12y y >时x 的取值范围2.26x <≤．24．如图，甲、乙两艘货轮同时从A 港出发，分别向B ，D 两港运送物资，最后到达A 港正东方向的C 港装运新的物资．甲货轮沿A 港的东南方向航行40海里后到达B 港，再沿北偏东60︒方向航行一定距离到达C 港．乙货轮沿A 港的北偏东60︒方向航行一定距离到达D 港，再沿南偏东30︒方向航行一定距离到达C 港． 1.41≈ 1.73≈，2.45≈）(1)求A ，C 两港之间的距离（结果保留小数点后一位）；(2)若甲、乙两艘货轮的速度相同（停靠B 、D 两港的时间相同），哪艘货轮先到达C 港？请通过计算说明．∴90AEB CEB ∠=∠=︒，由题意可知：45GAB ∠=︒，∴45BAE ∠=︒，∴cos 40cos AE AB BAE =∠=⨯∴tan 202tan CE BE EBC =∠=25．如图，在平面直角坐标系中，抛物线()240y ax bx a =++≠经过点()1,6-，与y 轴交于点C ，与x 轴交于A B ，两点（A 在B 的左侧），连接tan 4AC BC CBA ∠=，，．(1)求抛物线的表达式；(2)点P 是射线CA 上方抛物线上的一动点，过点P 作PE x ⊥轴，垂足为E ，交AC 于点D ．点M 是线段DE 上一动点，MN y ⊥轴，垂足为N ，点F 为线段BC 的中点，连接AM NF ，．当线段PD 长度取得最大值时，求AM MN NF ++的最小值；(3)将该抛物线沿射线CA 方向平移，使得新抛物线经过（2）中线段PD 长度取得最大值时的点D ，且与直线AC 相交于另一点K ．点Q 为新抛物线上的一个动点，当QDK ACB ∠∠=时，直接写出所有符合条件的点Q 的坐标．∴()4,0A -，设直线AC 的解析式为y =代入()4,0A -，得04m =-解得1m =，∴直线AC 的解析式为y =()当0y =时，046x =--，解得32x =-，∴3,02G ⎛⎫- ⎪⎝⎭∵()4,0A -，()0,4C ，∴OA OC =，∴45OAC OCA ∠=∠=︒，∵DR x ∥轴，26．在ABC 中，AB AC =，点D 是BC 边上一点（点D 不与端点重合）．点D 关于直线AB 的对称点为点E ，连接,AD DE ．在直线AD 上取一点F ，使EFD BAC ∠∠=，直线EF 与直线AC 交于点G ．(1)如图1，若60,,BAC BD CD BAD α∠=︒<∠=，求AGE ∠的度数（用含α的代数式表示）；(2)如图1，若60,BAC BD CD ∠=︒<，用等式表示线段CG 与DE 之间的数量关系，并证明；(3)如图2，若90BAC ∠=︒，点D 从点B 移动到点C 的过程中，连接AE ，当AEG △为等腰三角形时，请直接写出此时CG AG 的值．∵EFD BAC ∠∠=，BAC ∠∴60EFD ∠=︒∵1EFD BAD ∠=∠+∠=∠∴160α∠=︒-，∵,AB AC EFD BAC =∠=∠∴=45ABC ∠︒，由轴对称知EAB ∠=∠试题31设BAD BAE β∠=∠=，∴90DAC GAF ∠=∠=︒∴GAE EAF GAF ∠=∠-∠∵GE GA =，。
2024年云南省中考真题数学试卷含答案解析
2024年云南省中考数学试题学校:___________姓名：___________班级：___________考号：___________一、单选题1．中国是最早使用正负数表示具有相反意义的量的国家．若向北运动100米记作100+米，则向南运动100米可记作（）A ．100米B ．100-米C ．200米D ．200-米【答案】B【分析】本题考查了正负数的意义，根据正负数的意义即可求解，理解正负数的意义是解题的关键．【详解】解：若向北运动100米记作100+米，则向南运动100米可记作100-米，故选：B ．2．某市今年参加初中学业水平考试的学生大约有57800人，57800用科学记数法可以表示为（）A ．45.7810⨯B ．357.810⨯C ．257810⨯D ．578010⨯【答案】A【分析】此题考查科学记数法的表示方法．科学记数法的表示形式为10n a ⨯的形式，其中110a ≤<，n 为整数，表示时关键要正确确定a 的值以及n 的值．科学记数法的表示形式为10n a ⨯的形式，其中110a ≤<，n 为整数．确定n 的值时，要看把原数变成a 时，小数点移动了多少位，n 的绝对值与小数点移动的位数相同．当原数绝对值10≥时，n 是正整数；当原数的绝对值1<时，n 是负整数．【详解】解：457800 5.7810=⨯，故选：A ．3．下列计算正确的是（）A ．33456x x x +=B ．635x x x ÷=C ．()327a a =D ．()333ab a b =【答案】D【分析】本题考查了合并同类项、幂的乘方、积的乘方、同底数幂的除法，熟练掌握运算法则是解答的关键．利用合并同类项法则、幂的乘方运算法则、同底数幂的除法运算法则、积的乘方运算法则进行运算，并逐项判断即可．【详解】解：A 、33356x x x +=，选项计算错误，不符合题意；B 、633x x x ÷=，选项计算错误，不符合题意；C 、()326a a =，选项计算错误，不符合题意；D 、()333ab a b =，选项计算正确，符合题意；故选：D ．4在实数范围内有意义，则x的取值范围是（）A ．0x >B ．0x ≥C ．0x <D ．0x ≤5．某图书馆的一个装饰品是由几个几何体组合成的．其中一个几何体的三视图（主视图也称正视图，左视图也称侧视图）如图所示，这个几何体是（）A ．正方体B ．圆柱C ．圆锥D ．长方体【答案】D【分析】本题考查了几何体的三视图，熟悉各类几何体的三视图是解决本题的关键．根据长方体三视图的特点确定结果．【详解】解：根据三视图的特点：几何体的三视图都是长方形，确定该几何体为长方体．故选：D ．6．一个七边形的内角和等于（）A ．540︒B ．900︒C ．980︒D ．1080︒【答案】B【分析】本题考查多边形的内角和，根据n 边形的内角和为()2180n -⋅︒求解，即可解题．【详解】解：一个七边形的内角和等于()72180900-⨯︒=︒，故选：B ．7．甲、乙、丙、丁四名运动员参加射击项目选拔赛，每人10次射击成绩的平均数x 环）和方差2s 如下表所示：甲乙丙丁x9.99.58.28.52s 0.090.650.162.85根据表中数据，从中选择一名成绩好且发挥稳定的运动员参加比赛，应该选择（）A ．甲B ．乙C ．丙D ．丁【答案】A【分析】本题考查根据平均数和方差作决策，重点考查方差的意义．方差是用来衡量一组数据波动大小的量，方差越大，表明这组数据偏离平均数越大，即波动越大，数据越不稳定；反之，方差越小，表明这组数据分布比较集中，各数据偏离平均数越小，即波动越小，数据越稳定．结合表中数据，先找出平均数最大的运动员；再根据方差的意义，找出方差最小的运动员即可．【详解】解：由表中数据可知，射击成绩的平均数最大的是甲，射击成绩方差最小的也是甲，∴中选择一名成绩好且发挥稳定的运动员参加比赛，应该选择甲，故选：A ．8．已知AF 是等腰ABC 底边BC 上的高，若点F 到直线AB 的距离为3，则点F 到直线AC 的距离为（）A ．32B ．2C ．3D ．72【答案】C【分析】本题考查了等腰三角形的性质，角平分线的性质定理，熟练掌握知识点是解题的关键．由等腰三角形“三线合一”得到AF 平分BAC ∠，再角平分线的性质定理即可求解．【详解】解：如图，∵AF 是等腰ABC 底边BC 上的高，∴AF 平分BAC ∠，∴点F 到直线AB ，AC 的距离相等，∵点F 到直线AB 的距离为3，∴点F 到直线AC 的距离为3．故选：C ．9．两年前生产1千克甲种药品的成本为80元，随着生产技术的进步，现在生产1千克甲种药品的成本为60元．设甲种药品成本的年平均下降率为x ，根据题意，下列方程正确的是（）A ．()280160x -=B ．()280160x -=C ．()80160x -=D ．()801260x -=【答案】B【分析】本题考查了一元二次方程的应用，根据甲种药品成本的年平均下降率为x ，利用现在生产1千克甲种药品的成本=两年前生产1千克甲种药品的成本年⨯（1-平均下降率）2，即可得出关于的一元二次方程．【详解】解： 甲种药品成本的年平均下降率为x ，根据题意可得()280160x -=，故选：B ．10．按一定规律排列的代数式：2x ，23x ，34x ，45x ，56x ，L ，第n 个代数式是（）A ．2nx B ．()1nn x-C ．1n nx +D ．()1nn x+【答案】D【分析】本题考查了数列的规律变化，根据数列找到变化规律即可求解，仔细观察和总结规律是解题的关键．【详解】解：∵按一定规律排列的代数式：2x ，23x ，34x ，45x ，56x ，L ，∴第n 个代数式是()1nn x +，11．中华文明，源远流长；中华汉字，寓意深广．下列四个选项中，是轴对称图形的为（）A ．爱B ．国C ．敬D ．业【答案】D【分析】本题主要考查轴对称图形的定义，根据轴对称图形的定义（如果一个平面图形沿一条直线折叠，直线两旁的部分能够互相重合，这个图形就叫做轴对称图形，）进行逐一判断即可．【详解】解：A 、图形不是轴对称图形，不符合题意；B 、图形不是轴对称图形，不符合题意；C 、图形不是轴对称图形，不符合题意；D 、图形是轴对称图形，符合题意；故选：D ．12．在Rt ABC △中，90B Ð=°，已知34AB BC ==，，则tan A 的值为（）A ．45B ．35C ．43D ．3413．如图，CD 是O 的直径，点A 、B 在O 上．若 AC BC=，36AOC ∠= ，则D ∠=（）A ．9B ．18C ．36oD ．4514．分解因式：39a a -=（）A ．()()33a a a -+B ．()29a a +C ．()()33a a -+D ．()29a a -【答案】A【分析】本题考查了提取公因式和公式法进行因式分解，熟练掌握知识点是解题的关键．将39a a -先提取公因式，再运用平方差公式分解即可．【详解】解：()()()329933a a a a a a a -=-=+-，故选：A ．15．某校九年级学生参加社会实践，学习编织圆锥型工艺品．若这种圆锥的母线长为40厘米，底面圆的半径为30厘米，则该圆锥的侧面积为（）A ．700π平方厘米B ．900π平方厘米C ．1200π平方厘米D ．1600π平方厘米【答案】C【分析】本题考查了圆锥的侧面积，先求出圆锥底面圆的周长，再根据圆锥的侧面积计算公二、填空题16．若关于x 的一元二次方程220x x c -+=无实数根，则c 的取值范围是．【答案】1c >/1c<【分析】利用判别式的意义得到Δ=（-2）2-4c ＜0，然后解不等式即可．【详解】解：根据题意得Δ=（-2）2-4c ＜0，解得c ＞1．故答案为：c ＞1．【点睛】本题考查了根的判别式，一元二次方程ax 2+bx +c =0（a ≠0）的根与Δ=b 2-4ac 有如下关系：当Δ＞0时，方程有两个不相等的实数根；当Δ=0时，方程有两个相等的实数根；当Δ＜0时，方程无实数根．17．已知点()2,P n 在反比例函数10y x=的图象上，则n =．18．如图，AB 与CD 交于点O ，且AC BD ∥．若12OA OC AC OB OD BD ++=++，则AC BD=．19．某中学为了丰富学生的校园体育锻炼生活，决定根据学生的兴趣爱好采购一批体育用品供学生课后锻炼使用．学校数学兴趣小组为给学校提出合理的采购意见，随机抽取了该校学生100人，了解他们喜欢的体育项目，将收集的数据整理，绘制成如下统计图：注：该校每位学生被抽到的可能性相等，每位被抽样调查的学生选择且只选择一种喜欢的体育项目．若该校共有学生1000人，则该校喜欢跳绳的学生大约有人．【答案】120【分析】本题考查了条形统计图和扇形统计图，用1000乘以12%即可求解，看懂统计图是解题的关键．【详解】解：该校喜欢跳绳的学生大约有100012%120⨯=人，故答案为：120．三、解答题20．计算：12117sin3062-⎛⎫++---⎪⎝⎭．21．如图，在ABC 和AED △中，AB AE =，BAE CAD ∠=∠，AC AD =．求证：ABC AED ≌△△．【答案】见解析【分析】本题考查了全等三角形的判定和性质，熟练掌握三角形全等的判定定理是解题关键．利用“SAS ”证明ABC AED ≌△△，即可解决问题．【详解】证明： BAE CAD ∠=∠，∴BAE EAC CAD EAC ∠+∠=∠+∠，即BAC EAD ∠=∠，在ABC 和AED △中，AB AEBAC EAD AC AD =⎧⎪∠=∠⎨⎪=⎩，∴()SAS ABC AED ≌．22．某旅行社组织游客从A 地到B 地的航天科技馆参观，已知A 地到B 地的路程为300千米，乘坐C 型车比乘坐D 型车少用2小时，C 型车的平均速度是D 型车的平均速度的3倍，求D 型车的平均速度．【答案】D 型车的平均速度为100km /h【分析】本题考查分式方程的应用，设D 型车的平均速度为km /h x ，则C 型车的平均速度23．为使学生更加了解云南，热爱家乡，热爱祖国，体验“有一种叫云南的生活”．某校七年级年级组准备从博物馆a、植物园b两个研学基地中，随机选择一个基地研学，且每个基地被选到的可能性相等；八年级年级组准备从博物馆a、植物园b、科技馆c三个研学基地中，随机选择一个基地研学，且每个基地被选到的可能性相等．记选择博物馆a为a，选择植物园b为b，选择科技馆c为c，记七年级年级组的选择为x，八年级年级组的选择为y．(1)请用列表法或画树状图法中的一种方法，求(),x y所有可能出现的结果总数；(2)求该校七年级年级组、八年级年级组选择的研学基地互不相同的概率P．24．如图，在四边形ABCD 中，点E 、F 、G 、H 分别是各边的中点，且AB CD ∥，AD BC ∥，四边形EFGH 是矩形．(1)求证：四边形ABCD 是菱形；(2)若矩形EFGH 的周长为22，四边形ABCD 的面积为10，求AB 的长． ∴四边形ABCD 是平行四边形，四边形ABCD 中，点E 、25．A、B两种型号的吉祥物具有吉祥如意、平安幸福的美好寓意，深受大家喜欢．某超市销售A、B两种型号的吉祥物，有关信息见下表：成本（单位：元/个）销售价格（单位：元/个）A型号35aB型号42b若顾客在该超市购买8个A种型号吉祥物和7个B种型号吉祥物，则一共需要670元；购买4个A种型号吉祥物和5个B种型号吉祥物，则一共需要410元．(1)求a、b的值；(2)若某公司计划从该超市购买A、B两种型号的吉祥物共90个，且购买A种型号吉祥物的数量x（单位：个）不少于B种型号吉祥物数量的43，又不超过B种型号吉祥物数量的2倍．设该超市销售这90个吉祥物获得的总利润为y元，求y的最大值．注：该超市销售每个吉祥物获得的利润等于每个吉祥物的销售价格与每个吉祥物的成本的差．26．已知抛物线21y x bx =+-的对称轴是直线2x =．设m 是抛物线21y x bx =+-与x 轴交点的横坐标，记533109m M -=．(1)求b 的值；(2)比较M27．如图，AB 是O 的直径，点D 、F 是O 上异于A 、B 的点．点C 在O 外，CA CD =，延长BF 与CA 的延长线交于点M ，点N 在BA 的延长线上，AMN ABM ∠∠=，AM BM AB MN ⋅=⋅．点H 在直径AB 上，90AHD ∠= ，点E 是线段DH 的中点．(1)求AFB ∠的度数；(2)求证：直线CM 与O 相切：(3)看一看，想一想，证一证：以下与线段CE 、线段EB 、线段CB 有关的三个结论：CE EB CB +<，CE EB CB +=，CE EB CB +>，你认为哪个正确？请说明理由．【答案】(1)90︒(2)见解析(3)CE EB CB +=，理由见解析∴点O在线段AD的中垂线上，=，∵CA CD∴点C在线段AD的中垂线上，⊥，∴OC AD。
2024年吉林省中考真题数学试卷含答案解析
2024年吉林省中考数学试题学校:___________姓名：___________班级：___________考号：___________一、单选题1．若()3-⨯ 的运算结果为正数，则W 内的数字可以为（ ）A ．2B ．1C ．0D ．1-【答案】D【分析】本题主要考查了有理数的乘法计算，根据有理数的乘法计算法则，分别计算出3-与四个选项中的数的乘积即可得到答案．【详解】解：()326-⨯=-，()313-⨯=-，()300-⨯=，()()313-⨯-=，四个算式的运算结果中，只有3是正数，故选：D ．2．长白山天池系由火山口积水成湖，天池湖水碧蓝，水平如镜，群峰倒映，风景秀丽，总蓄水量约达32040000000m ，数据2040000000用科学记数法表示为（ ）A ．102.0410⨯B ．92.0410⨯C ．820.410⨯D ．100.20410⨯3．葫芦在我国古代被看作吉祥之物．下图是—个工艺葫芦的示意图，关于它的三视图说法正确的是（ ）A ．主视图与左视图相同B ．主视图与俯视图相同C ．左视图与俯视图相同D ．主视图、左视图与俯视图都相同【答案】A 【分析】本题主要考查了简单几何体的三视图，根据三视图的定义找到葫芦的三视图即可得到答案．【详解】解：葫芦的俯视图是两个同心圆，且带有圆心，主视图和俯视图都是下面一个较大的圆，中间一个较小的圆，上面是一条线段，故选：A ．4．下列方程中，有两个相等实数根的是（ ）A ．()221x -=-B ．()220x -=C ．()221x -=D ．()222x -=5．如图，在平面直角坐标系中，点A 的坐标为()4,0-，点C 的坐标为()0,2．以OA OC ，为边作矩形OABC ，若将矩形OABC 绕点O 顺时针旋转90︒，得到矩形OA B C '''，则点B '的坐标为（ ）A ．()4,2--B ．()4,2-C ．()2,4D ．()4,2【答案】C【分析】本题主要考查了坐标与图形变化—旋转，矩形的性质等等，先根据题意得到42OA OC ==，，再由矩形的性质可得290AB OC ABC ===︒，∠，由旋转的性质可得42OA OA A B AB '''====，，90OA B ''∠=︒，据此可得答案．【详解】解：∵点A 的坐标为()4,0-，点C 的坐标为()0,2，∴42OA OC ==，，∵四边形OABC 是矩形，∴290AB OC ABC ===︒，∠，∵将矩形OABC 绕点O 顺时针旋转90︒，得到矩形OA B C '''，∴42OA OA A B AB '''====，，90OA B ''∠=︒，∴A B y ''⊥轴，∴点B '的坐标为()2,4，故选：C ．6．如图，四边形ABCD 内接于O ，过点B 作BE AD ∥，交CD 于点E ．若50BEC ∠=︒，则ABC ∠的度数是（ ）A ．50︒B ．100︒C ．130︒D ．150︒【答案】C 【分析】本题考查了平行线的性质，圆的内接四边形的性质，熟练掌握知识点是解题的关键．先根据BE AD ∥得到50D BEC ∠=∠=︒，再由四边形ABCD 内接于O 得到180ABC D ∠+∠=︒，即可求解．【详解】解：∵BE AD ∥，50BEC ∠=︒，∴50D BEC ∠=∠=︒，∵四边形ABCD 内接于O ，∴180ABC D ∠+∠=︒，∴18050130ABC ∠=︒-︒=︒,故选：C ．二、填空题7．当分式11x +的值为正数时，写出一个满足条件的x 的值为 ．8．因式分解：a 2﹣3a=．【答案】a （a ﹣3）【分析】直接把公因式a 提出来即可．【详解】解：a 2﹣3a=a （a ﹣3）．故答案为a （a ﹣3）．9．不等式组2030x x ->⎧⎨-<⎩的解集为 ．【答案】23x <</32x >>【分析】本题主要考查了解一元一次不等式组，先求出每个不等式的解集，再根据 “同大取大，同小取小，大小小大中间找，大大小小找不到（无解）”求出不等式组的解集即可．【详解】解：2030x x ->⎧⎨-<⎩①②解不等式①得：2x >，解不等式②得：3x <，∴原不等式组的解集为23x <<，故答案为：23x <<．10．如图，从长春站去往胜利公园，与其它道路相比，走人民大街路程最近，其蕴含的数学道理是 ．【答案】两点之间，线段最短【分析】本题考查了两点之间线段最短，熟记相关结论即可．【详解】从长春站去往胜利公园，走人民大街路程最近，其蕴含的数学道理是：两点之间，线段最短故答案为：两点之间，线段最短．11．正六边形的每个内角等于°．12．如图，正方形ABCD 的对角线AC BD ，相交于点O ，点E 是OA 的中点，点F 是OD 上一点．连接EF ．若45FEO ∠=︒，则EF BC 的值为 ．13．图①中有一首古算诗，根据诗中的描述可以计算出红莲所在位置的湖水深度，其示意图如图②，其中AB AB '=，AB B C '⊥于点C ，0.5BC =尺，2B C '=尺．设AC 的长度为x 尺，可列方程为 ．【答案】()22220.5x x +=+【分析】本题考查了勾股定理的实际应用，正确理解题意，运用勾股定理建立方程是解题的关键．设AC 的长度为x 尺，则0.5AB AB x '==+，在Rt AB C '△中，由勾股定理即可建立方程．【详解】解：设AC 的长度为x 尺，则0.5AB AB x '==+，∵AB B C '⊥，由勾股定理得：222AC B C AB ''+=，∴()22220.5x x +=+，故答案为：()22220.5x x +=+．14．某新建学校因场地限制，要合理规划体育场地，小明绘制的铅球场地设计图如图所示，该场地由O 和扇形OBC 组成，,OB OC 分别与O 交于点A ，D ．1m OA =，10m OB =，40AOD ∠=︒，则阴影部分的面积为 2m （结果保留π）．三、解答题15．先化简，再求值：()()2111a a a +-++，其中a =16．吉林省以“绿水青山就是金山银山，冰天雪地也是金山银山”为指引，不断加大冰雪旅游的宣传力度，推出各种优惠活动，“小土豆”“小砂糖橘”等成为一道靓丽的风景线，某滑雪场为吸引游客，每天抽取一定数量的幸运游客，每名幸运游客可以从“滑雪”“滑雪圈”“雪地摩托”三个项目中随机抽取一个免费游玩．若三个项目被抽中的可能性相等，用画树状图或列表的方法，求幸运游客小明与小亮恰好抽中同一个项目的概率．由树状图可知共有9种等可能的结果数，小明与小亮恰好抽中同一个项目的结果数有∴幸运游客小明与小亮恰好抽中同一个项目的概率17．如图，在ABCD Y 中，点O 是AB 的中点，连接CO 并延长，交DA 的延长线于点E ，求证：AE BC =．【答案】证明见解析【分析】本题主要考查了全等三角形的性质与判定，平行四边形的性质，先根据平行四边形对边平行推出OAE OBC OCB E ==∠∠，∠∠，再由线段中点的定义得到OA OB =，据此可证明()AAS AOE BOC △≌△，进而可证明AE BC =．【详解】证明：∵四边形ABCD 是平行四边形，∴AD BC ∥，∴OAE OBC OCB E ==∠∠，∠∠，∵点O 是AB 的中点，∴OA OB =，∴()AAS AOE BOC △≌△，∴AE BC =．18．钢琴素有“乐器之王”的美称，键盘上白色琴键和黑色琴键共有88个，白色琴键比黑色琴键多16个．求白色琴键和黑色琴键的个数．【答案】白色琴键52个，黑色琴键36个【分析】本题考查了列一元一次方程解应用题，正确理解题意是解题的关键．设黑色琴键x 个，则白色琴键()16x +个，可得方程()1688x x ++=，再解方程即可．【详解】解：设黑色琴键x 个，则白色琴键()16x +个，由题意得：()1688x x ++=，解得：36x =，∴黑色琴键由：361652+=（个），答：白色琴键52个，黑色琴键36个．19．图①、图②均是44⨯的正方形网格，每个小正方形的顶点称为格点．点A ，B ，C ，D ，E ，O 均在格点上．图①中已画出四边形ABCD ，图②中已画出以OE 为半径的O ，只用无刻度的直尺，在给定的网格中按要求画图．(1)在图①中，面出四边形ABCD 的一条对称轴．(2)在图②中，画出经过点E 的O 的切线．【答案】(1)见解析(2)见解析【分析】本题主要考查了正方形的性质与判定，矩形的性质与判定，切线的判定，画对称轴等等：（1）如图所示，取格点E 、F ，作直线EF ，则直线EF 即为所求；（2）如图所示，取格点G H 、，作直线GH ，则直线GH 即为所求．【详解】（1）解：如图所示，取格点E、F，作直线EF，则直线EF即为所求；，的中点；易证明四边形ABCD是矩形，且E、F分别为AB CD、，作直线GH，则直线GH即为所求；（2）解：如图所示，取格点G H⊥．易证明四边形OGTH是正方形，点E为正方形OGTH的中心，则OE GH20．已知蓄电池的电压为定值，使用蓄电池时，电流I（单位：A）与电阻R（单位：Ω）是反比例函数关系，它的图象如图所示．(1)求这个反比例函数的解析式（不要求写出自变量R的取值范围）．(2)当电阻R为3Ω时，求此时的电流I．-年全国居民人均可支配收入及其增长速度情况如图所示．21．中华人民共和国20192023根据以上信息回答下列问题：-年全国居民人均可支配收入中，收入最高的一年比收入最低的一年多多少元？(1)20192023-年全国居民人均可支配收入的中位数．(2)直接写出20192023(3)下列判断合理的是______（填序号）．-年全国居民人均可支配收入里逐年上升趋势．①20192023-年全国居民人均可支配收入实际增长速度最慢的年份是2020年．因此这5年中，②201920232020年全国居民人均可支配收入最低．【答案】(1)8485元(2)35128元(3)①【分析】本题主要考查了频数分布直方图，频数分布折线图，中位数：（1）用2023年的全国居民人均可支配收入减去2019年全国居民人均可支配收入即可得到答案；（2）根据中位数的定义求解即可；（3）根据统计图的数据即可得到答案．【详解】（1）解：39218307338485-=元，答：20192023-年全国居民人均可支配收入中，收入最高的一年比收入最低的一年多8485元．（2）解：20192023-年这五年的全国居民人均可支配收入分别为30733元，32189元，35128元，36883元，39218元，∴20192023-年全国居民人均可支配收入的中位数为35128元；（3）解：由统计图可知20192023-年全国居民人均可支配收入里逐年上升趋势，故①正确；由统计图可知20192023-年全国居民人均可支配收入实际增长速度最慢的年份是2020年．但这5年中，2019年全国居民人均可支配收入最低，故②错误；故答案为：①．22．图①中的吉林省广播电视塔，又称“吉塔”．某直升飞机于空中A 处探测到吉塔，此时飞行高度873m AB =，如图②，从直升飞机上看塔尖C 的俯角37EAC ∠=︒，看塔底D 的俯角45EAD ∠=︒，求吉塔的高度CD （结果精确到0.1m ）．（参考数据：sin 370.60︒=，cos370.80︒=，tan 370.75︒=）在Rt GAD 中，45EAD ∠=∴873tan DG AG DG EAD===∠在Rt GAC △中，37EAC ∠=∴tan 873CG AG EAC =⋅∠=∴873654.75CD DG CG =-=-23．综合与实践某班同学分三个小组进行“板凳中的数学”的项目式学习研究，第一小组负责调查板凳的历史及结构特点；第二小组负责研究板凳中蕴含的数学知识：第三小组负责汇报和交流，下面是第三小组汇报的部分内容，请你阅读相关信息，并解答“建立模型”中的问题．【背景调查】图①中的板凳又叫“四脚八叉凳”，是中国传统家具，其榫卯结构体现了古人含蓄内敛的审美观．榫眼的设计很有讲究，木工一般用铅笔画出凳面的对称轴，以对称轴为基准向两边各取相同的长度，确定榫眼的位置，如图②所示．板凳的结构设计体现了数学的对称美．【收集数据】小组收集了一些板凳并进行了测量．设以对称轴为基准向两边各取相同的长度为x ，凳面的宽度为mm y ，记录如下：以对称轴为基准向两边各取相同的长度/mm x 16.519.823.126.429.7凳面的宽度/mm y 115.5132148.5165181.5【分析数据】如图③，小组根据表中x ，y 的数值，在平面直角坐标系中描出了各点．【建立模型】请你帮助小组解决下列问题：(1)观察上述各点的分布规律，它们是否在同一条直线上？如果在同一条直线上，求出这条直线所对应的函数解析式；如果不在同一条直线上，说明理由．(2)当凳面宽度为213mm 时，以对称轴为基准向两边各取相同的长度是多少？【答案】(1)在同一条直线上，函数解析式为：533y x =+(2)36mm【分析】本题考查了一次函数的实际应用，待定系数法求函数解析式，已知函数值求自变量，熟练掌握知识点，正确理解题意是解题的关键．（1）用待定系数法求解即可；（2）将213y =代入函数解析式，解方程即可．【详解】（1），解：设函数解析式为：()0y kx b k =+≠，∵当16.5,115.5x y ==，23.1,148.5x y ==，∴16.5115.523.1148.5k b k b +=⎧⎨+=⎩，解得：533k b =⎧⎨=⎩，∴函数解析式为：533y x =+，经检验其余点均在直线533y x =+上，∴函数解析式为533y x =+，这些点在同一条直线上；（2）解：把213y =代入533y x =+得：533213x +=，解得：36x =，∴当凳面宽度为213mm 时，以对称轴为基准向两边各取相同的长度为36mm ．24．小明在学习时发现四边形面积与对角线存在关联，下面是他的研究过程：【探究论证】（1）如图①，在ABC 中，AB BC =，BD AC ⊥，垂足为点D ．若2CD =，1BD =，则ABC S = ______．（2）如图②，在菱形A B C D ''''中，4''=A C ，2B D ''=，则A B C D S ''''=菱形______．（3）如图③，在四边形EFGH 中，EG FH ⊥，垂足为点O ．若5EG =，3FH =，则EFGH S =四边形______；若EG a =，FH b =，猜想EFGH S 四边形与a ，b 的关系，并证明你的猜想．【理解运用】（4）如图④，在MNK △中，3MN =，4KN =，5MK =，点P 为边MN 上一点．小明利用直尺和圆规分四步作图：（ⅰ）以点K 为圆心，适当长为半径画弧，分别交边KN ，KM 于点R ，I ；（ⅱ）以点P 为圆心，KR 长为半径画弧，交线段PM 于点I '；（ⅲ）以点I '为圆心，IR 长为半径画弧，交前一条弧于点R '，点R '，K 在MN 同侧；（ⅳ）过点P 画射线PR '，在射线PR '上截取PQ KN =，连接KP ，KQ ，MQ ．请你直接写出MPKQ S 四边形的值．25．如图，在ABC 中，90C ∠=︒，30B ∠=︒，3cm AC =，AD 是ABC 的角平分线．动点P从点A /s 的速度沿折线AD DB -向终点B 运动．过点P 作PQ AB ∥，交AC 于点Q ，以PQ 为边作等边三角形PQE ，且点C ，E 在PQ 同侧，设点P 的运动时间为()()s 0t t >，PQE V与ABC 重合部分图形的面积为()2cm S ．(1)当点P 在线段AD 上运动时，判断APQ △的形状（不必证明），并直接写出AQ 的长（用含t 的代数式表示）．(2)当点E 与点C 重合时，求t 的值．(3)求S 关于t 的函数解析式，并写出自变量t 的取值范围．∵90C ∠=︒，30B ∠=∴60BAC ∠=︒，∵AD 平分BAC ∠，∴30PAQ BAD ∠=∠=∵PQ AB ∥，∴30APQ BAD ∠=∠=∴PAQ APQ =∠∠，∵PQE V 为等边三角形，∴QE QP =，由（1）得QA QP =∴QE QA =，即22AE AQ t ==∵30PAQ ∠=︒，∴1322PG AP ==∵PQE V 是等边三角形，∴QE PQ AQ ===∴12S QE PG =⋅=∵PQE V 是等边三角形，∴60E ∠=︒，而CE AE AC =-∴tan CF CE =⋅∠∴1S CE CF =⋅∵30DAC ∠=︒DCA ∠=由上知3DC =，∴23AD =，∴此时323PD t =-26．小明利用一次函数和二次函数知识，设计了一个计算程序，其程序框图如图（1）所示，输入x 的值为2-时，输出y 的值为1；输入x 的值为2时，输出y 的值为3；输入x 的值为3时，输出y 的值为6．(1)直接写出k ，a ，b 的值．(2)小明在平面直角坐标系中画出了关于x 的函数图像，如图（2）．Ⅰ．当y 随x 的增大而增大时，求x 的取值范围．Ⅱ．若关于x 的方程230ax bx t ++-=（t 为实数），在04x <<时无解，求t 的取值范围．Ⅲ．若在函数图像上有点P ，Q （P 与Q 不重合）．P 的横坐标为m ，Q 的横坐标为1m -+．小明对P ，Q 之间（含P ，Q 两点）的图像进行研究，当图像对应函数的最大值与最小值均不随m 的变化而变化，直接写出m 的取值范围．则10m -≤≤，综上：10m -≤≤或12m ≤≤．【详解】（1）解：∵20x =-<，∴将2x =-，1y =代入3y kx =+，得：231k -+=，解得：1k =，∵20,30x x =>=>，∴将2,3x y ==，3,6x y ==代入23y ax bx =++得：42339336a b a b ++=⎧⎨++=⎩，解得：12a b =⎧⎨=-⎩；（2）解：Ⅰ，∵1,1,2k a b ===-，∴一次函数解析式为：3y x =+，二次函数解析式为：223y x x =-+当0x >时，223y x x =-+，对称为直线1x =，开口向上，∴1x ≥时，y 随着x 的增大而增大；当0x ≤时，3y x =+，10k =>，∴0x ≤时，y 随着x 的增大而增大，综上，x 的取值范围：0x ≤或1x ≥；Ⅱ，∵230ax bx t ++-=，∴23ax bx t ++=，在04x <<时无解，∴问题转化为抛物线223y x x =-+与直线y t =在04x <<时无交点，∵对于223y x x =-+，当1x =时，2y =∴顶点为()1,2，如图：∴当2t =时，抛物线223y x x =-+与直线y ∴当2t <时，抛物线223y x x =-+与直线y 当4x =，168311y =-+=，∴当11t =时，抛物线223y x x =-+与直线∴当11t ≥时，抛物线223y x x =-+与直线y ∴当2t <或11t ≥时，抛物线223y x x =-+与直线即：当2t <或11t ≥时，关于x 的方程2ax +Ⅲ：∵,1P Q x m x m ==-+，由题意得：11012m m -≤-+≤⎧⎨≤≤⎩，∴12m ≤≤；②当12m <，如图：由题意得：10112m m -≤≤⎧⎨≤-+≤⎩，∴10m -≤≤，综上：10m -≤≤或12m ≤≤．。
中考阅读理解单选题60题
中考阅读理解单选题60题1. Tom is a very kind boy. He always helps his classmates. What can we know about Tom?A. He is lazy.B. He is selfish.C. He is helpful.D. He is unfriendly.答案：C。
本题考查对人物性格的理解。
A 选项“lazy”表示懒惰，与文中说他总是帮助同学不符；B 选项“selfish”表示自私，也不符合他帮助同学的行为；C 选项“helpful”表示乐于助人，符合他总是帮助同学的描述；D 选项“unfriendly”表示不友好，与原文相悖。
通过阅读文段，理解关键信息来判断人物性格。
2. Mary loves reading books. She spends most of her free time in the library. What does Mary like doing?A. Playing sports.B. Watching TV.C. Reading.D. Sleeping.答案：C。
此题考查对人物爱好的判断。
A 选项“Playing sports”意为进行体育运动，文中未提及；B 选项“Watching TV”表示看电视，文中没提到；C 选项“Reading”阅读，与文中她爱读书并在图书馆度过大部分空闲时间相符；D 选项“Sleeping”睡觉，不符合她爱读书的描述。
根据文中关键句判断人物爱好。
3. Jack is a famous singer. He has many fans all over the world. Why is Jack famous?A. Because he is a good actor.B. Because he is a great writer.C. Because he is a popular singer.D. Because he is a wonderful dancer.答案：C。
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中考英语习题集（十一）1. Shanghai is larger than ______ city in India.A. any otherB. the otherC. any2. There are three ways to help you be happier. ______ is to enjoy the things youhave had. ______ is to develop the hobbies you’re interested in. ______ is to volunteer your time t o help the people in trouble.A. One; The other; AnotherB. One; Another; The otherC. One; Other; The other3. --John, thank you for helping me watering flowers in the garden. But could you mind ______ me a clean shirt from my bedroom?--All right, please wait a moment!A. bringingB. takingC. fetching4. –A terrible earthquake hit Japan ______ the afternoon of March 11th. --______ sad news! But I believe natural disaster can’t beat human beings.A. on, WhatB. in, WhatC. on, How5. –When did you the new supermarket open?--Don’t you know it ______ for ten days?A. has openedB. has been openedC. has been open6. –A dream of Red Mansions (<红楼梦>) is famous all around the world. But infact, only the first 80 chapters were written by Cao Xueqin.--So it is. ______ there have been many different endings over the years, ______ a new one with Liu Xinwus was on bookshelves at the end of March, 2011.A. Although; butB. Though; butC. Although; /7. –More than 35 thousand Chinese people have returned from the chaos(混乱) inLibya(利比亚) thanks to the nine-day effort.-- ______ our government has done for the evacuation(撤离)！A. How successfullyB. What successfulC. How successful8. –The annual (周年的) Festival of Sweet Ball- a tradition snack food in northChina, ______ in Qingdao now. --It sounds really good.A. is being heldB. is being happenedC. is being taken place9. –A panda and her young baby have moved into their new home at a wildlifesanctuary (保护区) in Southwest China’s Sichuan Province.--The pair is used to the life in sanctuary ______ they will spend the next two years before being r eleased into the wild.A. whichB. whereC. whom10. –We are so grateful ______ all the teachers ______ their help.--Yes, it is the teachers that give us knowledge and courage.A. to, toB. for, toC. to, for11. –Don’t lose your heart! I’m certain you can get ______ through hard work. --I hope so.A. what you wantB. that you wantC. how you want12. –Tree planting Day is coming. Let’s plant trees in the park, ______?--Good idea. The more, the better.A. will youB. shall weC. won’t we13. –I hear that you haven’t found your lovely cat.--I still hope to find my ______ cat. I ______ it very much.A. losing, missB. missing, missC. missed, lose14. I used to think ______ hard to learn English well. But I find ______ easy tograsp it now.A. it’s, itB. it, it’sC. it, that’s15. Have confidence in yourself, ______ you can realize your dream sooner or later.A. andB. butC. or16. –You have made great progress in English this term.--______. That’s why I got an “A” in the English exam.A. So I haveB. So do IC. So do I17. –How delicious the cakes are! Could I want ______ one? --Certainly. Here you are.A. a thirdB. the thirdC. third18. –The final exam is coming. Everyone seems ______ about it.--Yes, we’d better try our best to prepare it.A. worryB. worriedC. worrying19. –What do you think of your food？--It’s spicy. Because there is ______ garlic in it.A. too manyB. too muchC. much too20. –I am too hungry. I’ve had 4 pieces of bread, and I will have ______ one.--Help yourself, please.A. the fifthB. fiveC. fifth21. --Why do you looks so excited?--My ______ friend and I will go to Andy Lau’s show. It is the first time to look ______ at him.A. closed, closeB. close, closelyC. closed, close22. As students in Grade 9, we should spend most of our time ______. Because wewill have the high school entrance examination in a few months.A. to studyB. on studyingC. studying23. –Congratulations to you, Tom. You’ve got a high mark. Can you give me someadvice on learning methods?--Well, There is no easy way. If you do everything as teachers tell you, youwill ______ succeed in studying.A. tend toB. focus onC. look forward to24. –Tom is really a hard-working student. Do you know why he keeps studying hard?--He studies so hard ______ he wants to enter No.3 High School.A. thatB. becauseC. and25. –Some big snow ______ in Harbin last year which had a bad effect on our life.–Luckily, ______ our government and people’s effort, we overcame that difficulty.A. happened; thanks forB. was happened; thanks toC. happened; thanks to26. There ______ some difficulties on our way to success. I’m sure if we havelots of determination, we won’t ______ by difficulties.A. maybe; be beatenB. may be; be beatenC. may be; beat27. -- _______ wonderful music you are playing! --Thank you! I’m glad you enjoy it.A. WhatB. What aC. How28. Harbin’s subway ______ for a few months. It is really convenient for peoplein Harbin and we are looking forward to ______ another subway in a few years.A. has been open; takingB. has been open; takeC. has been opened; taking29. Nowadays some children often play the computer games too much and usuallyforget to have meals and go to bed. ______, they aren’t in good health.A. As a ruleB. As we knowC. As a result30. Years have passed, but Chinese people still remember those exciting days ______they spent during the Beijing 2008 Olympic Games. --Thanks.A. whenB. whoC. that答案：1.C 2.B 3.C (fetch: go and get) 4.A 5.C 6.C 7.A 8.A 9.B 10.C 11.A 12.B 13.B 14.B 15.A 16.A 17.A 18.B 19.B 20.C 21.B 22.C 23.A (tend to do 倾向于往往倾向于做易于做某事有做……的倾向) 24.B25.C (thanks to为习语介词,thanks不可以改为thank you, to后也不接动词原形,这个短语表示原因,意为“由于”、“多亏”,to表示感谢的对象.如：Thanks to the English language, we can learn a lot from other countries．由于英语这门语言,我们能从其它国家学到很多东西.thanks for是客套用语,thanks相当于 thank you ,意为“因……而感谢”,for强调为何而感谢,其后可接名词或v-ing. Thanks for your help．谢谢你的帮助.Thanks for inviting us to your birthday party．谢谢你邀请我们参加你的生日聚会.) 26. B (determination [dɪˌtɜːmɪ'neɪʃn] n.决心；测定；规定；(正式)决定；定位) 27.A 28.A 29. C 30. C。