2023年江苏省南京市中考模拟试卷(含答案)

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2023年江苏省南京市中考数学真题模拟试卷附解析

2023年江苏省南京市中考数学真题模拟试卷学校：__________ 姓名：__________ 班级：__________ 考号：__________注意事项： 1．答题前填写好自己的姓名、班级、考号等信息 2．请将答案正确填写在答题卡上一、选择题1．口ABCD 的周长为36 cm ，AB=BC=2cm ，则AD ，CD 的长度分别为（） A ．12 cm ，6 cmB ．8 cm ，10 cmC ．6 cm ，12 cmD ．10 cm ，8 cm2．利用因式分解计算2009200822-，则结果是（） A ．2B ．1C ．20082D ．-1 3．经过任意三点中的两点共可以画出的直线条数是（）A ．一条或三条B ．三条C ．两条D ．一条4．长方形的周长是36（cm ），长是宽的2倍，设长为x （cm ），则下列方程正确的是（） A ．x+2 x =36B ．1362x x +=C ．2（x +2x ）=36D ．12()362x x +=5．下列各个变形正确的是（） A ．由 7x=4x-3，移项，得 7x-4x=3B ．由 3（2x-1）=1+ 2（x-3），去括号，得6x-1 =1+2x-3C ．由 2（2x-1）-3（x-3）= 1，去括号，得4x-2-3x-9= 1D ．由 2（x+1）=x+8，去括号，移项，合并，得x=66．两个有理数和的绝对值与这两个数绝对值的和相等，那么这两个数（） A ．都是正数B. 两数同号或有一个数为 0 C ．都是负数 D ．无法确定二、填空题7．如图，有6张牌，从中任意抽取两张，点数和是奇数的概率是________．8．在Rt △ABC 中,已知∠C=90°,若∠A=30°3,则∠B=______, b=______，c=______．9．一次函数21y x =-+的图象，经过抛物线21(0)y x mx m =++≠的顶点，则 m= ． 10．如图,在矩形ABCD 中，M 是BC 的中点，且MA ⊥MD ．•若矩形ABCD•的周长为48cm ，•则矩形ABCD 的面积为 cm 2．11．在平面直角坐标系中．点A(x-l ，2-x)在第四象限，则实数x 的取值范围是 . 12．如图，方格纸上有A 、B 两点．若以B 为原点，建立平面直角坐标系，则点A 的坐标为(6，3)；若以A 为原点建立平面直角坐标系，则点B 的坐标为 .13．请举出一个主视图和俯视图相同，但是左视图不同的几何体： . 14．如图，AB ∥CD ，EG 平分∠BEF.∠2 = 60°，则∠1= .15．x= 时，分式)1)(3(3+--x x x 的值是0.16．观察下列各式： (x-1(x+1)=x 2-1 (x-1)(x 2+x+1)=x 3-1 (x-1）(x 3+x 2+x+1)=x 4-1根据规律可得(x-1)(x n-1+……+x+1)= (其中n 为正整数）． 17．填空：(1)已知5n a =,则3n a = ； (2)已知530()x a a =，则x = ；(3)若2434()()x y m m m ==，则x= ,y= ．18．观察下面的等式，①111122⨯=-；②222233⨯=-；③333344⨯=-；④444455⨯=-……第n个等式可表示为．19．图中有线段条，分别是线段、、、、、．图中共有射线条．20．宁波市2008年初中毕业生学业考试各科的满分值如下：科目语文数学英语科学社政体育满分值1201201101508030若把表中各科满分值按比例绘成扇形统计图，则表示数学科学的扇形的圆心角应是度（结果保留3个有效数字）．21．如图，∠A+∠B+∠C+∠D+∠E+∠F 的度数为．三、解答题22．Rt △ABC 中，∠C=90°，cosB=32,求a:b:c 等于多少？23．如图，一次函数y kx b =+的图象与反比例函数my x=的图象相交于 A ．B 两点， (1)利用图中条件，求反比例函数和一次函数的解析式；(2)根据图象写出使一次函数的值小于反比例函数的值的取值范围．24．如图所示，在梯形ABCD 中，AD ∥BC ，AB=DC ，∠D=120°．对角线CA 平分∠BCD ，且梯形的周长为20，求AC 的长及梯形的面积．25．给出下面三种边长相等的正多边形：要求选取其中的至少两种正多边形，使这几种正多边形能围绕一个顶点镶嵌成不留空隙的平面图形，请画出两种不同镶嵌方法的示意图．26．按由大到小的顺序排列下列各数： 1332312721752 1117523273223>>>27．如图，点E 、D 分别是等边△ABC 中以C 点为顶点的一边延长线和另一边反向延长线上的点，且BE=CD ，DB 的延长线交AE 于F ．（1）请说明△ABE ≌△BCD 的理由；（2）求∠AFB 的度数．28．若a ，b 互为相反数，求3223a a b ab b +++的值.29．25(精确到0.001 ).30．8箱苹果，以每箱５千克为准，称重记录如下：（超过记为正数，单位：千克） 1.5，－１，3，0， 0.5，－1.5，2，－0.5321CA BEDF这8箱苹果的总重量是多少？【参考答案】学校：__________ 姓名：__________ 班级：__________ 考号：__________注意事项：1．答题前填写好自己的姓名、班级、考号等信息2．请将答案正确填写在答题卡上一、选择题1．B2．C3．A4．D5．D6．B二、填空题7．88．1560°，12，389．一410．1282x >12．(-6,-3)13．答案不唯一，如横放的圆柱14．60°15．-316．1-n x 17．(1)125；(2)6；(3)8,618．11n nn n n n ⨯=-++19． 6；线段CO 、CA 、CB 、OA 、OB 、AB ；820．70.821．360°三、解答题 22．3:5:2．23．（1）由题意得，m=2×3=6． ∴6y x=，∴当 x=-1 时，n=-6． ∴23|6k b k b =+⎧⎨-=-+⎩，∴24k b =⎧⎨=-⎩，∴24y x =-(2)当 x<—1 或 0<x<3 时，一次函数的值大于反比例函数的值24．AC=S 梯形略26．>>>．（1）略；（2）60°28．29．12，-=≈12)10.178 30．44千克。

2023年中考数学第二次模拟考试卷及答案解析(南京卷)

2023年中考数学第二次模拟考试卷及答案解析（南京卷）第Ⅰ卷一、选择题（本大题共6小题，每小题2分，共12分．在每小题给出的四个选项中，只有一个选项是符合题目要求的）1．8的相反数是（）A ．8-B ．8C ．18D ．18-【答案】A【分析】根据只有符号不同的两个数互为相反数进行解答即可得．【详解】解：8的相反数是8-，故选A ．【点睛】本题考查了相反数的定义，掌握相反数的定义是解题的关键．2．截止北京时间2022年6月11 5.32亿例，5.32亿用科学记数法表示为（）A ．85.3210⨯B ．753.210⨯C ．90.53210⨯D ．75.3210⨯【答案】A【分析】利用科学记数法的表示方法进行解题即可．【详解】解：5.32亿=5.32810⨯故选A ．【点睛】本题考查科学记数法的表示方法：10n a ⨯，其中110a ≤＜．3．某工程甲单独完成要25天，乙单独完成要20天．若乙先单独干10天，剩下的由甲单独完成，设甲、乙一共用x 天完成，则可列方程为（）A ．101012025x ++=B ．101012520x ++=C ．101012520x -+=D ．101012520x -+=【答案】D【分析】设甲、乙一共用x 天完成，根据题意，列出方程，即可求解．【详解】解：设甲、乙一共用x 天完成，根据题意得：101012520x -+=．故选：D【点睛】本题主要考查了一元一次方程的应用，明确题意，准确得到等量关系是解题的关键．4．如图1，点A ，B ，C 是数轴上从左到右排列的三个点，分别对应的数为5-，b ，4，某同学将刻度尺如图2放置，使刻度尺上的数字0对齐数轴上的点A ，发现点B 对应刻度1.8cm ，点C 对齐刻度5.4cm ．则数轴上点B 所对应的数b 为（）A ．3B ．1-C ．2-D ．3-【答案】C 【分析】结合图1和图2求出1个单位长度=0.6cm ，再求出求出AB 之间在数轴上的距离，即可求解；【详解】解：由图1可得AC =4-（-5）=9，由图2可得AC =5.4cm ，∴数轴上的一个长度单位对应刻度尺上的长度为=5.4÷9=0.6（cm ），∵AB =1.8cm ，∴AB =1.8÷0.6＝3（单位长度），∴在数轴上点B 所对应的数b =-5+3=-2；故选：C【点睛】本题考查了数轴，利用数形结合思想解决问题是本题的关键．5．不透明的袋子中装有红、绿小球各一个，除颜色外两个小球无其他差别，从中随机摸出一个小球，放回并摇匀，再从中随机摸出一个小球，那么第一次摸到红球、第二次摸到绿球的概率是（）A．14B．13C．12D．34【答案】A【分析】首先根据题意画出树状图，由树状图求得所有等可能的结果与第一次摸到红球，第二次摸到绿球的情况，然后利用概率公式求解即可求得答案．【详解】解：画树状图得：∵共有4种等可能的结果，第一次摸到红球，第二次摸到绿球有1种情况，∴第一次摸到红球，第二次摸到绿球的概率为1 4，故选：A．【点睛】本题考查了画树状法或列表法求概率，列出所有等可能的结果是解决本题的关键．6．已知四边形ABCD两条对角线相交于点E，AB＝AC＝AD，AE＝3，EC＝1，则BE•DE 的值为（）A．6B．7C．12D．16【答案】B【分析】根据AB＝AC＝AD，可知点D、C、B在以点A为圆心的圆上，延长CA交⊙A于点F ，连接DF ，EF =AF +AE =AC +AE ，再证明△FDE ∽△BCE ，EF DE BE CE=，即BE •DE ＝CE •EF ，则问题得解．【详解】∵AB ＝AC ＝AD ，∴点D 、C 、B 在以点A 为圆心的圆周上运动，如图，延长CA 交⊙A 于点F ，连接DF ，∵AE ＝3，EC ＝1，∴AC ＝AF ＝AE +CE ＝3+1＝4，即EF ＝AE +AF ＝3+4＝7，∵∠F =∠CBD ，∠FDB =∠FCB ，∴△FDE ∽△BCE ，∴EF DE BE CE=，即BE •DE ＝CE •EF ＝1×7＝7，故选：B ．【点睛】本题考查了圆周角定理、相似三角形的判定与性质等知识，根据AB ＝AC ＝AD ，确定点D 、C 、B 在以点A 为圆心的圆上，是解答本题的关键．第Ⅱ卷二、填空题（本大题共10小题，每小题2分，共20分）7．函数y =x 的取值范围是_____．【答案】1x ≥【分析】根据二次根式有意义的条件，列出不等式，即可求解．【详解】解：根据题意得，10x -≥，解得1x ≥．故答案为1x ≥．【点睛】本题主要考查函数的自变量取值范围，掌握二次根式有意义的条件，是解题的关键．8．分解因式：6x 2y ﹣3xy ＝_____．【答案】()321xy x -【分析】直接提取公因式进行因式分解即可．【详解】解：原式=()321xy x -．故答案为：()321xy x -．【点睛】本题主要考查因式分解，熟练掌握因式分解的方法是解题的关键．9．设一个圆锥的底面积为10，它的侧面展开后平面图为一个半圆，则此圆锥的侧面积是____________.【答案】20【分析】根据圆锥底面周长得到半径和母线的关系，然后计算侧面积即可；【详解】解：∵侧面展开图是半圆，∴2l rππ=∴2l r=∵210r π=∴222112)22102022S l r r πππ====⨯=侧（故答案为20；【点睛】本题考查了圆锥的侧面积，掌握并熟练使用相关知识，同时注意解题中需注意的事项是本题的解题关键．10．已知二次函数y ＝（x －m ）2，当x ≤1时，y 随x 的增大而减小，则m 的取值范围是__________．【答案】m 1≥【分析】先根据二次函数的解析式判断出函数的开口方向，再由当x ≤1时，函数值y 随x 的增大而减小可知二次函数的对称轴x ＝m ≥1．【详解】解：∵二次函数y ＝（x ﹣m ）2，中，a ＝1＞0，∴此函数开口向上，∵当x ≤1时，函数值y 随x 的增大而减小，∴二次函数的对称轴x ＝m ≥1．故答案为：m ≥1．【点睛】本题考查的是二次函数的性质，熟知二次函数的增减性是解答此题的关键．11．如图，已知函数y x b =+和3y ax =+的图象交点为P ，则不等式3x b ax +>+的解集为______．【答案】x ＞1【分析】根据图象直接解答即可．【详解】解：从图象上得到函数y=x+b 和y=ax+3的图象交点P ，点P 的横坐标为1，在x ＞1时，函数y=x+b 的值大于y=ax +3的函数值，故可得不等式x+b ＞ax +3的解集x ＞1．故答案为：x ＞1．【点睛】此题考查了一次函数与一元一次不等式，认真体会一次函数与一元一次方程及一元一次不等式之间的内在联系是解决本题的关键．12．某校规定学生体育成绩满分为100分，将课外活动成绩、期中成绩、期末成绩的比按2∶3∶5计算学期成绩若小明这学期的三项成绩分别为90分、90分、96分，则小明本学期的体育成绩为____________分．【答案】93【分析】根据加权平均数的计算方法进行计算即可．【详解】解：23590909693235235235⨯+⨯+⨯=++++++，故答案为：93．【点睛】本题考查加权平均数的意义和计算方法，理解加权平均数的意义，掌握加权平均数的计算方法是正确解答的前提．13．如图，点E ，F 在BC 上，BE ＝CF ，∠A ＝∠D ．请添加一个条件________________，使△ABF ≌△DCE 【答案】∠B ＝∠C (答案不唯一)【分析】求出BF =CE ，再根据全等三角形的判定定理判断即可．【详解】解：∵BE =CF ，∴BE +EF =CF +EF ，∴BF =CE ，添加∠B =∠C ，在△ABF 和△DCE 中，B C A D BF CE ∠∠⎧⎪∠∠⎨⎪⎩＝＝＝，∴△ABF ≌△DCE （AAS ），故答案为：∠B =∠C （答案不唯一）．【点睛】本题考查了全等三角形的判定定理，能熟记全等三角形的判定定理是解此题的关键．14．如图，O 的半径为2cm ，正六边形内接于O ，则图中阴影部分面积为______．【答案】23π【分析】如图，连接BO ，CO ，OA ．由题意得，△OBC ，△AOB 都是等边三角形，证明△OBC 的面积=△ABC 的面积，可得图中阴影部分的面积等于扇形OBC 的面积，再利用扇形的面积公式进行计算即可．【详解】解：如图，连接BO ，CO ，OA ．由题意得，△OBC ，△AOB 都是等边三角形，∴∠AOB =∠OBC =60°，∴OA BC ∥，∴△OBC 的面积=△ABC 的面积，∴图中阴影部分的面积等于扇形OBC 的面积=260223603ππ⨯=．故答案为：23π【点睛】本题考查正多边形与圆、扇形的面积公式、平行线的性质等知识，解题的关键是学会用转化的扇形思考问题，属于中考常考题型．15．已知在ABC 中，=AB AC ，=30C ∠︒，AB AD ⊥，2cm AD =，则BC 的长等于________．【答案】6【分析】过A 作AE BC ⊥交BC 于E ，根据=AB AC ，=30C ∠︒得到30B ∠=︒，由AB AD ⊥可得4BD =，再根据勾股定理求出AB ，即可得到BE ，即可得到答案．【详解】解：过A 作AE BC ⊥交BC 于E ，∵=AB AC ，=30C ∠︒，∴30B ∠=︒，∵AB AD ⊥，2cm AD =，∴4BD =，在Rt ABD ∆中，AB ==，∵AE BC ⊥，30B ∠=︒，∴AE∴3BE ==，∵=AB AC ，AE BC ⊥，∴26BC BE ==，故答案为6，．【点睛】本题考查等腰三角形性质，含30︒角的直角三角形性质及勾股定理，解题的关键是求出AB ．16．如图，等腰ABC 的底边BC 长为4，面积是12，腰AC 的垂直平分线EF 分别交AC ，AB 边于E F ，点．若点D 为BC 边的中点，点M 为线段EF 上一动点，则CDM V 的周长最小值为：____．【答案】8【分析】连接AD ，由于ABC 是等腰三角形，点D 是BC 边的中点，故AD BC ⊥，再根据三角形的面积公式求出AD 的长，再根据EF 是线段AC 的垂直平分线可知，点C 关于直线EF 的对称点为点A ，故AD 的长为AM MD +的最小值，由此即可得出结论【详解】解：连接AD ，AM ，∵ABC 是等腰三角形，点D 是BC 边的中点，∴AD BC ⊥，∵EF 是线段AC 的垂直平分线，∴点C 关于直线EF 的对称点为点A ，∴AD 与EF 的交点为点M 时，CDM V 的周长最小，故AD 的长为AM MD +的最小值，在ABC 中，4BC =，12ABC S =△，∴1•412212ABC S BC AD AD ⨯==⨯= ，122CD BC ==解得6AD =，∴CDM V 的周长最小为：628AM MD BC AD BC ++≥+=+=，故答案为：8【点睛】本题考查的是轴对称﹣最短路线问题，熟知等腰三角形三线合一的性质是解答此题的关键．三、解答题（本大题共11小题，共88分，解答时应写出文字说明、证明过程或演算步骤等）17．（7分）已知6a +3的立方根是3，3a +b ﹣1的算术平方根是4．(1)求a ，b 的值；(2)求b 2﹣a 2的平方根．【答案】(1)4；5(2)±3【分析】（1）运用立方根和算术平方根得出方程求解即可得；（2）先求出代数式的值，然后计算平方根即可．【详解】（1）解：∵63a +的立方根是3，31a b +-的算术平方根是4，∴6327a +=，3116a b +-=，∴4a =，5b =；（2）解：由（1）知4a =，5b =，∴2222549b a -=-=，∵9的平方根为3±，∴22b a -的平方根为3±．【点睛】本题考查了平方根、算术平方根、立方根及解方程，理解题意，根据题意得出方程是解题关键．18．（7分）先化简，再求值：22441111x x x x x x ⎛⎫-+-+÷ ⎪--⎝⎭，其中4x =-．【答案】112x -，19【分析】先将括号内的通分加减，再根据除以不为零的数等于乘以这个数的倒数，最后约分化简即可，把4x =-的值代入即可求解．【详解】解：原式()222221(21)211111121x x x x x x x x x x x ⎛⎫-+---=-÷=⨯ ⎪-----⎝⎭112x=-，将4x =-代入112x-，得1112(4)9=-⨯-．【点睛】本题主要考查分式的化简求值，掌握乘法公式在分式中的运算是解题的关键．19．（7分）请把下面证明过程补充完整．如图，AD BE ，13∠=∠，2B ∠=∠，求证：DE AC ∥．证明：∵AD BE （已知），∴2∠+__________180=︒（__________）．∵2B ∠=∠（已知），∴180B DCB ∠+∠=︒（__________），∴__________ AB （__________），∴3∠=__________（__________）．∵13∠=∠（已知），∴1∠=__________（等量代换），∴DE AC ∥（内错角相等，两直线平行）．【答案】DCB ∠；两直线平行，同旁内角互补；等量代换；CD ；同旁内角互补，两直线平行；4∠；两直线平行，内错角相等；4∠【分析】已知AD BE ，可以得出2180DCB ∠+∠=︒，结合2B ∠=∠可以得出CD AB ∥，可以得出3=4∠∠，由已知13∠=∠，即可得到结论．【详解】证明：∵AD BE （己知）∴2180DCB ∠+∠=︒（两直线平行，同旁内角互补）∵2B ∠=∠（已知）∴180B DCB ∠+∠=︒（等量代换）∴CD AB ∥（同旁内角互补，两直线平行）∴34∠∠=（两直线平行，内错角相等）∵13∠=∠（已知）∴14∠=∠（等量代换）∴∥DE AC （内错角相等，两直线平行）【点睛】本题主要考查平行线的性质和判定，熟记平行线的判定定理和性质，并灵活运用是解题的关键．20．（8分）新冠疫情期间，学生居家上网课，为了解我市初中生每周锻炼身体的时长t （单位：小时）的情况，在全市随机抽取部分初中生进行调查，按五个组别：A 组()34t ≤<，B 组()45t ≤<，C 组()56t ≤<，D 组()67t ≤<，E 组()78t ≤<进行整理，绘制如下两幅不完整的统计图，根据图中提供的信息，解决下列问题：(1)这次抽样调查的学生总人数为______；(2)抽取的学生中，每周锻炼身体的时长大于等于6小于7的频数是______；(3)求C 组所在扇形的圆心角．【答案】(1)500(2)150(3)115.2︒【分析】（1）由B 组人数及其所占百分比可得学生总人数；（2）根据总人数分别减去A 、B 、C 、E 组的人数即可得出答案；（3）先求出C 组所占总人数的百分比，再用360︒乘以C 组所占总人数的百分比即可．【详解】（1）10020=500÷％（人）故答案为：500．（2）每周锻炼身体的时长大于等于6小于7的频数:5005010016040150----=（人）故答案为：150．（3）C 组所占总人数的百分比为：160100=32500⨯％％C 组所在扇形的圆心角：36032=115.2︒⨯︒％∴C 组所在扇形的圆心角为115.2︒．【点睛】本题考查了频数分布直方图、扇形统计图，理解两个统计图中数量之间的关系是解决问题的前提，掌握频率=频数÷总数是正确解答的关键．21．（8分）为了解某校中学生有多少人已患上近视眼，判断下列选取对象的方案是否恰当?不恰当的请说明理由．(1)在学校门口数有多少人戴眼镜；(2)在低年级的学生中随机抽取一个班作调查；(3)从每个年级每个班级都随机抽取几个学生作调查．【答案】(1)不恰当，理由见解析(2)不恰当，理由见解析(3)恰当【分析】根据选取的样本是否具有代表性依次判断即可求解．【详解】（1）不恰当；因为可能有住校学生没调查到．（2）不恰当；因为低年级学生的视力一般比高年级学生好．（3）样本具有代表性，因此恰当．【点睛】本题考查了样本的代表性，解题关键是掌握选取的样本应该具有代表性，要求学生能根据实际情况进行判断．22．（7分）如图，在半径为10cm 的⊙O 中，AB 是⊙O 的直径，CD 是过⊙O 上一点C 的直线，且AD ⊥DC 于点D ，AC 平分∠BAD ，点E 是BC 的中点，OE ＝6cm ．(1)求证：CD 是⊙O 的切线；(2)求AD 的长．【答案】(1)见解析(2)365AD =【分析】（1）连接OC ，由AC 平分∠BAD ，OA ＝OC ，可得∠DAC ＝∠OCA ，AD ∥OC ，根据AD ⊥DC ，即可证明CD 是⊙O 的切线；（2）由OE 是△ABC 的中位线，得AC ＝12，再证明△DAC ∽△CAB ，AD AC AC AB =，即121220AD =，从而得到AD 365=．【详解】（1）证明：连接OC ，如图：∵AC 平分∠BAD ，∴∠DAC＝∠CAO，∵OA＝OC，∴∠CAO＝∠OCA，∴∠DAC＝∠OCA，∴AD∥OC，∵AD⊥DC，∴CO⊥DC，∵OC是⊙O的半径，∴CD是⊙O的切线；（2）解：∵E是BC的中点，且OA＝OB，∴OE是△ABC的中位线，AC＝2OE，∵OE＝6，∴AC＝12，∵AB是⊙O的直径，∴∠ACB＝90°＝∠ADC，又∠DAC＝∠CAB，∴△DAC∽△CAB，∴AD ACAC AB=，即121220AD=，∴AD36 5 =．【点睛】本题考查圆的切线的判定定理，相似三角形的判定及性质等知识，解题的关键是熟练应用圆的相关性质，转化圆中的角和线段．23．（8分）某书店计划同时购进A，B两类图书，已知购进3本A类图书和4本B类图书共需288元；购进6本A类图书和2本B类图书共需306元．A，B两类图书每本的进价各是多少元？【答案】A类图书每本的进价是36元，B类图书每本的进价是45元．【分析】根据“购进3本A 类图书和4本B 类图书共需288元；购进6本A 类图书和2本B 类图书共需306元”列出方程组进行计算即可．【详解】解：设A 类图书每本的进价是a 元，B 类图书每本的进价是b 元．根据题意得：3428862306a b a b +⎧⎨+⎩＝＝，解得3645a b ⎧⎨⎩＝＝，答：A 类图书每本的进价是36元，B 类图书每本的进价是45元．【点睛】本题考查二元一次方程组的应用，解题的关键是找到等量关系列出二元一次方程．24．（8分）胜利黄河大桥犹如一架巨大的竖琴，凌驾于滔滔黄河之上，使黄河南北“天堑变通途”.已知主塔AB 垂直于桥面BC 于点B ，其中两条斜拉索AD AC 、与桥面BC 的夹角分别为60︒和45︒，两固定点D 、C 之间的距离约为33m ，求主塔AB 的高度（结果保留整数，参1.73≈≈）【答案】主塔AB 的高度约为78m ．【分析】在Rt △ABD 中，利用正切的定义求出=AB ，然后根据∠C ＝45°得出AB ＝BC ，列方程求出BD ，即可解决问题．【详解】解：∵AB ⊥BC ，∴∠ABC ＝90°，在Rt △ABD 中，tan 60AB BD =⋅︒=，在Rt △ABC 中，∠C ＝45°，∴AB ＝BC ，33BD =+，∴)3312BD ⨯==m ，∴AB ＝BC ＝)3313333782BD ⨯+=+≈m ，答：主塔AB 的高度约为78m ．【点睛】本题考查了解直角三角形的应用，熟练掌握正切的定义是解题的关键．25．（8分）如图，抛物线y ＝34x 2+bx +c 交x 轴于A ，B 两点，交轴于点C ，点A ，B 的坐标分别为（-1，0），（4，0）．(1)求抛物线的解析式；(2)点P 是直线BC 下方的抛物线上一动点，求△CPB 的面积最大时点P 的坐标；(3)若M 是抛物线上一点，且∠MCB ＝∠ABC ，请直接写出点M 的坐标．【答案】(1)239344y x x =--(2)92,2P ⎛⎫- ⎪⎝⎭(3)M 的坐标为()3,3-或531125,749⎛⎫ ⎪⎝⎭【分析】（1）待定系数法求解即可；（2）待定系数法求直线BC 的解析式，如图1，过P 作PD AB ⊥交BC 于D ，设239,344P m m m ⎛⎫-- ⎪⎝⎭，则3,34D m m ⎛⎫- ⎪⎝⎭，2134622CPB S DP m m =⨯=-+ ，求解CPB △面积最大时的m 值，进而可得P 点坐标；（3）由题意知，分两种情况求解；①如图2，作CD AB ∥，两直线平行，内错角相等，可知直线CD 与抛物线的交点即为点M ，根据二次函数的对称性求解M 的坐标即可；②如图2，作直线CE 使ECB ABC =∠∠交AB 于F ，可知直线CE 与抛物线的交点即为点M ，根据勾股定理求出F 点坐标，待定系数法求CE 的解析式，联立求交点坐标即可．【详解】（1）解：将,A B 点坐标代入抛物线解析式得230434404b c b c ⎧-+=⎪⎪⎨⎪⨯++=⎪⎩解得943b c ⎧=-⎪⎨⎪=-⎩∴抛物线的解析式为239344y x x =--．（2）解：当0x =时，=3y -∴()0,3C -设直线BC 的解析式为y kx b =+，将,B C 两点坐标代入得403k b b +=⎧⎨=-⎩解得343k b ⎧=⎪⎨⎪=-⎩∴直线BC 的解析式334y x =-如图1，过P 作PD AB ⊥交BC 于D ，设239,344P m m m ⎛⎫-- ⎪⎝⎭，则3,34D m m ⎛⎫- ⎪⎝⎭∴2334PD m m =-+∴2134622CPB S DP m m =⨯=-+ ()23262m =--+∵302-<，04m <<∴2m =时，CPB △面积最大∴92,2P ⎛⎫- ⎪⎝⎭．（3）解：由题意知，分两种情况求解；①如图2，作CD AB ∥，∵CD AB∥∴ABC DCB∠=∠∴直线CD 与抛物线的交点即为点M∵,C M 关于抛物线的对称轴直线9343224x -=-=⨯对称∴()3,3M -；②如图2，作直线CE 使ECB ABC =∠∠交AB 于F∵ECB ABC=∠∠∴直线CE 与抛物线的交点即为点M∴FC FB=设OF a =，则4FC FB a==-在Rt COF 中，由勾股定理得222OC FC OF =-，即()22234a a =--解得78a =∴7,08F ⎛⎫ ⎪⎝⎭设直线CE 的解析式为y kx b =+，将,C F 点坐标代入得7083k b b ⎧+=⎪⎨⎪=-⎩解得2473k b ⎧=⎪⎨⎪=-⎩∴直线CE 的解析式为2437y x =-∴联立2243739344y x y x x ⎧=-⎪⎪⎨⎪=--⎪⎩解得03x y =⎧⎨=-⎩或537112549x y ⎧=⎪⎪⎨⎪=⎪⎩∴531125,749M ⎛⎫ ⎪⎝⎭；综上所述，MCB ABC ∠=∠时，点M 的坐标为()3,3-或531125,749⎛⎫ ⎪⎝⎭．【点睛】本题考查了待定系数法求二次函数解析式，二次函数与面积综合，二次函数与角度综合．解题的关键在于对知识的灵活运用．26．（9分）在菱形ABCD 中，∠ABC ＝60°，P 是直线BD 上一动点，以AP 为边向右侧作等边 APE （A ，P ，E 按逆时针排列），点E 的位置随点P 的位置变化而变化．（1）如图1，当点P 在线段BD 上，且点E 在菱形ABCD 内部或边上时，连接CE ，则BP 与CE 的数量关系是，BC 与CE 的位置关系是；（2）如图2，当点P 在线段BD 上，且点E 在菱形ABCD 外部时，（1）中的结论是否还成立？若成立，请予以证明；若不成立，请说明理由；（3）当点P 在直线BD 上时，其他条件不变，连接BE ．若AB ＝BE ＝写出 APE 的面积．【答案】（1）BP ＝CE ，CE ⊥BC ；（2）仍然成立，见解析；（3）【分析】（1）连接AC ，根据菱形的性质和等边三角形的性质证明△BAP ≌△CAE 即可证得结论；（2）（1）中的结论成立，用（1）中的方法证明△BAP ≌△CAE 即可；（3）分两种情形：当点P 在BD 的延长线上时或点P 在线段DB 的延长线上时，连接AC 交BD 于点O ，由∠BCE ＝90°，根据勾股定理求出CE 的长即得到BP 的长，再求AO 、PO 、PD 的长及等边三角形APE 的边长可得结论．【详解】解：（1）如图1，连接AC ，延长CE 交AD 于点H ，∵四边形ABCD是菱形，∴AB＝BC，∵∠ABC＝60°，∴△ABC是等边三角形，∴AB＝AC，∠BAC＝60°；∵△APE是等边三角形，∴AP＝AE，∠PAE＝60°，∴∠BAP＝∠CAE＝60°﹣∠PAC，∴△BAP≌△CAE（SAS），∴BP＝CE；∵四边形ABCD是菱形，∴∠ABP＝12∠ABC＝30°，∴∠ABP＝∠ACE＝30°，∵∠ACB＝60°，∴∠BCE＝60°+30°＝90°，∴CE⊥BC；故答案为：BP＝CE，CE⊥BC；（2）（1）中的结论：BP＝CE，CE⊥AD仍然成立，理由如下：如图2中，连接AC，设CE与AD交于H，∵菱形ABCD，∠ABC＝60°，∴△ABC和△ACD都是等边三角形，∴AB＝AC，∠BAD＝120°，∠BAP＝120°+∠DAP，∵△APE是等边三角形，∴AP＝AE，∠PAE＝60°，∴∠CAE＝60°+60°+∠DAP＝120°+∠DAP，∴∠BAP＝∠CAE，∴△ABP≌△ACE（SAS），∴BP＝CE，∠ACE＝∠ABD＝30°，∴∠DCE＝30°，∵∠ADC＝60°，∴∠DCE+∠ADC＝90°，∴∠CHD＝90°，∴CE⊥AD；∴（1）中的结论：BP＝CE，CE⊥AD仍然成立；（3）如图3中，当点P在BD的延长线上时，连接AC交BD于点O，连接CE，BE，作EF⊥AP于F，∵四边形ABCD是菱形，∴AC⊥BD BD平分∠ABC，∵∠ABC＝60°，AB＝∴∠ABO＝30°，∴AO＝12AB OB＝3，∴BD＝6，由（2）知CE⊥AD，∵AD∥BC，∴CE⊥BC，∵BE＝BC＝AB＝∴CE8，由（2）知BP＝CE＝8，∴DP＝2，∴OP＝5，∴AP，∵△APE是等边三角形，∴S△AEP（2＝如图4中，当点P在DB的延长线上时，同法可得AP∴S △AEP 34（312＝3【点睛】此题是四边形的综合题，重点考查菱形的性质、等边三角形的性质、全等三角形的判定与性质、勾股定理等知识点，解题的关键是正确地作出解题所需要的辅助线，将菱形的性质与三角形全等的条件联系起来，此题难度较大，属于考试压轴题．27．（11分）【解决问题】如图①，在四边形ABCD 中，90DAB ABC ∠=∠=︒，点E 是边AB 的中点，90DEC ∠=︒，求证：DE 平分ADC ∠．(提示：延长DE 交射线CB 于点)F 【应用】如图②，在矩形ABCD 中，点F 是边BC 上的一点，将ABF △沿直线AF 折叠，若点B 落在边DC 的中点E 处，则sin BAF ∠=______．【拓展】在矩形ABCD 中，AD AB >，点E 为边AD 的中点，将ABE 沿直线BE 折叠，得到FBE ，延长BF 交直线CD 于点G ，直线EF 交边BC 于点.H 若1CG =，2DG =，直接写出HF 的长．【答案】【解决问题】见解析；【应用】12；【拓展】64或24【分析】解决问题如图①，延长DE 交射线CB 于点F ，证明(ASA)DAE FBE ≌△△，可得DE FE =，ADE F ∠=∠，进而可以解决问题；应用如图②，延长FE 交AD 延长线于点Q ，证明(ASA)CEF DEQ ≌△△，可得FE QE =，再(SAS)AEF AEQ ≌△△，可得FAE QAE ∠=∠，所以30FAB FAE QAE ∠=∠=∠=︒，进而可得sin BAF ∠的值；拓展分两种情况画图讨论：①当点G 在DC 边上时，②当点G 在DC 延长线上时，然后证明(SAS)BAE QDE ≌△△，可得ABE Q ∠=∠，AB DQ =，证明FBH CBG ∽△△，可得FH BF CG BC =，进而可以求出FH 的长．【详解】解决问题证明：如图①，延长DE 交射线CB 于点F ，点E 是边AB 的中点，AE BE ∴=，在DAE 和FBE 中，90A EBF AE BE AED BEF ∠=∠=︒⎧⎪=⎨⎪∠=∠⎩，∴(ASA)DAE FBE ≌△△，DE FE ∴=，ADE F ∠=∠，90DEC =︒∠ ，CE DF ∴⊥，CD CF ∴=，CDE F ∴∠=∠，ADE CDE ∴∠=∠，DE ∴平分ADC ∠；应用解：如图②，延长FE 交AD 延长线于点Q ，点E 是边CD 的中点，CE DE ∴=，在CEF △和DEQ 中，90C EDQ CE DE CEF DEQ ∠=∠=︒⎧⎪=⎨⎪∠=∠⎩，∴(ASA)CEF DEQ ≌△△，FE QE ∴=，由翻折可知：90AEF B ∠=∠=°，90AEF AEQ ∴∠=∠=︒，在AEF △和AEQ △中，90FE QE AEF AEQ AE AE =⎧⎪∠=∠=︒⎨⎪=⎩，∴(SAS)AEF AEQ ≌△△，FAE QAE ∴∠=∠，由翻折可知：FAE FAB ∠=∠，30FAB FAE QAE ∴∠=∠=∠=︒，1sin sin302BAF ∴∠=︒=；故答案为：12；拓展解：①如图，在矩形ABCD 中，AD AB >，当点G 在DC 边上时，延长AE 交CD 延长线于点Q，点E 为边AD 的中点，AE DE ∴=，在BAE 和QDE △中，90A QDE AE DE AEB DEQ ∠=∠=︒⎧⎪=⎨⎪∠=∠⎩，∴(SAS)BAE QDE ≌△△，ABE Q ∴∠=∠，AB DQ =，将ABE 沿直线BE 折叠，得到FBE ，ABE FBE ∴∠=∠，90A EFB ∠=∠=︒，FB AB =，Q FBE ∴∠=∠，GB BQ ∴=，1CG = ，2DG =，3AB CD DQ CG DG ∴===+=，5GQ GD DQ ∴=+=，5GB ∴=，BC ∴=，90BFH C ∠=∠=︒ ，FBH CBG ∠=∠，∴FBH CBG ∽△△，FH BF CG BC∴=，1FH ∴FH ∴=②如图，在矩形ABCD 中，AD AB >，当点G 在DC 延长线上时，延长BE 交CD 延长线于点Q ，同①得BAE ≌()QDE ASA ，ABE Q ∴∠=∠，AB DQ =，将ABE 沿直线BE 折叠，得到FBE ，ABE FBE ∴∠=∠，Q FBE ∴∠=∠，GB BQ ∴=，1CG = ，2DG =，1AB CD DQ DG CG ∴===-=，3GQ GD DQ ∴=+=，3GB ∴=，BC ∴==同①FBH CBG ∽△△，FH BF CG BC∴=，1FH ∴=，4FH ∴=．综上所述：HF 【点睛】本题属于四边形的综合题，全等三角形的判定与性质，相似三角形是判定与性质，等腰三角形的性质，翻折变换，锐角三角函数，解决本题的关键是得到FBH CBG ∽△△．。

【中考冲刺】2023年江苏省南京市中考模拟英语试卷(附答案)

2023年江苏省南京市中考模拟英语试题学校:___________姓名：___________班级：___________考号：___________一、单项选择1．June is the sixth month of the year. It comes ________ May and July.A．on B．before C．in D．between 2．Tai chi, part of Chinese culture, is an exercise which helps people improve ________ in health.A．themselves B．ourselves C．itself D．myself 3．It’s great that we can buy train tickets over the phone without going out. It ________ us a lot of time.A．lends B．misses C．saves D．takes4．The weather ________ rainy and cloudy in the past few days. I hope the sun will come out soon.A．was B．is C．will be D．has been 5．In the past, people thought it was a ________ idea to send e-mails and read news online, but now it is part of our everyday life.A．simple B．popular C．terrible D．fresh6．For Mike, the price is ________ important thing when he shops for jeans. He cares even more about the shape, the color and the size.A．more B．the most C．less D．the least 7．— How wonderful the school concert is! I wonder ________ our school will hold it next year.— Sure. It’s our school tradition!A．how B．if C．where8．It’s well-known that black tea ________ in China more than 600 years ago.A．is invented B．was invented C．invents D．invented9．I love the weekends because I ________ get up early on Saturdays and Sundays. A．needn't B．mustn't C．can't D．shouldn't 10．—I dislike summer here. It ________ rains heavily in the afternoon.—I don’t think so. The rain stops in a short time and then everyone feels cooler.A．rarely B．seldom C．usually D．hardly 11．Judy is such a confident girl that she believes she can ________ the hard task if she triesher best.A．carry out B．turn out C．pick out D．break out 12．Which of the following sentences has a different sentence structure from the other three? A．Children fly kites happily in spring.B．I like eating ice cream in summer.C．Farmers harvest crops in autumn.D．Everything looks beautiful with snow.13．Look at the text on public signs. What kind of method is used to organize ideas?A．Time order.B．Space order.C．General to specific.D．Specific to general.14．—Loneliness may be one of the biggest problems in our society these years.—________, especially among the old people. We should care more about them. A．That’s true B．That’s a good idea C．I don’t think so D．That’s not the case15．—What about watching the Dragon Boat Race this afternoon?— ________ I guess it will be fun.A．Forget it.B．No way.C．What for?D．Why not?二、完形填空Before words were words, a boy named Yes lived in a small kingdom. Yes was good at everything and whenever someone asked Yes for help, he would ____16____ help. However, his brother, No, was not much good at anything.One day Yes asked his brother to watch the animals while he went to find some food toeat. ____17____ doing what Yes asked, No lay down and fell asleep.It just so happened that the King had a personal road nearby, and he traveled on it often. When the animals wandered（漫步）onto the road, the King’s carriage（马车）was____18____. The King wondered why the animals had been allowed on his road. Yes was always ____19____, so he told the King the whole story.The King was so angry that he decided that Yes and No were to work in the castle as his servants（佣人）to ____20____ them. However, soon the King realized that only Yes would be of any use to him as a servant. Whenever the King asked No to bring him ____21____, it would get thrown away, broken, or eaten.One day, the King sent the brothers to help pick the food for a big party. The first cook came up the gate and yelled（喊叫）, “I bring my delicious ____22____ for the King’s banquet（宴会）!” The King heard this and thought that pie would be ____23____ for such an event. He didn’t want anything to happen to the pie, so he yelled “Yes!” and then asked him to get it.The next cook stepped up to the gate. “I offer the King some soup!” he said. The King didn’t like soup and he knew just how to get rid of（摆脱）it. “No!” he yelled and No dropped the soup ____24____ the King could even smell it.This went on for hours. If the king liked a dish, he would yell “Yes!”. If he did not, everyone would hear aloud “NO!” and the dish would be destroyed moments later by a servant.Pretty soon this became _____25_____ around the Kingdom. If people didn’t want something, they would say “No.” And if they liked what someone was offering, they would say “Yes.”16．A．bravely B．impatiently C．curiously D．gladly 17．A．Because of B．Instead of C．Proud of D．Full of 18．A．breaking out B．running away C．passing by D．cutting in 19．A．honest B．generous C．organized D．creative 20．A．contact B．punish C．praise D．attack 21．A．something B．anything C．everything D．nothing 22．A．pie B．sandwich C．soup D．salad 23．A．ready B．perfect C．sorry D．famous 24．A．after B．when C．before D．until25．A．traditional B．impossible C．serious D．popular三、阅读单选Welcome to 2022 Summer Fun Club!Are you looking for something that can add colour to your summer holiday? If yes, here are the summer courses that you cannot miss!Each course offers summer students the chance to learn new skills!You will have an unforgettable summer filled with fun, happiness and new friendships!26．Which course should Nick join if he wants to be more confident?A．Acting for Fun.B．Little Writers.C．Teenagers Can Cook.D．Space Explorers.27．What can students do in the writing course?A．Write stories and other text types.B．Give talks on short story writing. C．Get to know the importance of acting.D．Learn about the solar system by reading.28．What is the purpose of the text?A．To ask students to act with their parents in public.B．To attract students to join 2022 Summer Fun Club.C．To encourage students to cook meals for their parents.D．To introduce some famous space explorers to students.Your English teacher has introduced a play to your class. Read the play.Characters: Sarah, student, 13 years oldJason, student, 14 years oldBetty, student, 15 years oldCindy, student, 14 years oldTime: One Sunday afternoon in springPlace: Sunshine Park(The four teenagers have just finished the picnic. They are tidying up.)Sarah: Wow! That was a great picnic. I’m so full that I can hardly move.Jason: That’s no excuse for not tidying up, Sarah. Come over here and help me pack up the leftover food. Betty, can you put out the fire, please? And clean up the place.Betty: (Speaking unhappily to herself) How can I always get the dirty and difficult jobs? It’s not fair.(Betty throws a bit of water on the fire. Then she picks up the ashes with an old newspaper and wants to throw them into the long grass.)Sarah: (Sounding surprised) What are you doing, Betty? _______Jason: Whoops...the paper has caught fire.Sarah: And the grass...Jason, Cindy, help! Help!(Jason and Cindy come over quickly. They help put out the fire completely.)Betty: Oh, no. What have I done?Cindy: You know that we should do everything carefully, don’t you?Betty: (With her head in her hands) Yes. What have I done? What have I done? 29．The words in brackets such as “(The four teenagers have just finished the picnic They are tidying up.)” tell ________.A．how the writer acts in the playB．when and where the story happensC．what the characters are saying to each otherD．what the characters are doing and how they are acting30．Which of the following sentences should be put in the blank?A．You seem surprised!B．How interesting it is!C．Don’t worry about it!D．That’s very dangerous!31．How does Betty feel when she says “What have I done? What have I done?”?A．She feels proud.B．She feels guilty.C．She feels relaxed.D．She feels lucky.In ancient times, people tried to explain the world around them based on what they saw. People in ancient times saw that the sun came up from one side of the earth, moved across the sky and went down to the other side. Based on this observation, they believed that the sun travels around the earth. Going directly from observation to conclusion is called non-scientific thinking.Here is an example of non-scientific thinking. Maybe you had a sick stomach, and ate a candy bar. An hour later, you found that you felt much better. You might conclude that it was the candy bar that made you feel better. But there are other possible reasons for the observation. Maybe you had taken some medicine an hour earlier, and it took a while to work. Maybe enough time had passed, and you would have felt better without eating the candy bar. Non-scientific thinking happens all the time.The scientific method is a way of thinking that helps you to avoid making incorrect conclusions. It helps you to avoid non-scientific thinking. It reminds you to treat your first conclusion as one of several possible conclusions. It reminds you to gather evidence（证据）to support your conclusion. The four steps in the scientific method begin by questioning an observation, and end with a conclusion that is based on evidence. First, you can ask a question about your observation, such as, “What makes a sick stomach feel better?” Second, state a possible answer to the question, such as, “A candy bar makes a sick stomach feel better.” Third, test your guess, this can be done in many different ways. You could wait until you have a sick stomach again, eat a candy bar, and see what happens. Finally, think and conclude—think about what happened when you tested and you can make a conclusion. 32．The underlined word “observation” in Paragraph 1 means “________”.A．watching carefully B．giving examples C．guessing quickly D．making conclusions33．The purpose of the example in the second paragraph is to ________.A．ask readers to take some medicine as early as they canB．help readers understand what non-scientific thinking isC．show how to make conclusions directly from observationsD．conclude that eating a candy bar can make people feel better34．The last paragraph mainly talks about ________.A．what makes non-scientific thinkingB．an example of non-scientific thinkingC．ways to make a sick stomach feel betterD．how to use the scientific method correctly35．The text is most probably taken from ________.A．an advertisement B．a movie poster C．a guide book D．a science magazineDennis didn’t feel like sleeping. He had gone to bed at the same time every night for as long as he could remember. He was tired of going to bed when his parents told him to. So one night, when fall seemed over, but it wasn’t yet winter, he decided he would stay up!What Dennis didn’t realize is that staying awake at night is hard when your body needs to sleep. He tried everything he could think of to stop himself from falling asleep. He tried counting wolves（if counting sheep makes you sleepy, then counting wolves must surely do the opposite）, but unfortunately it made him even more tired. He started to suspect that it was the counting, and not the choice of animal, that made people sleepy.Dennis was just about ready to give up when he heard a squeak（吱吱叫）from his hamster（仓鼠）Charlie. He went over to Charlie’s cage, but it was empty. Dennis followed the sounds of squeaking until he found Charlie on the floor, looking behind the door. Dennis noticed that something back there was throwing things at Charlie! Coins, balls of paper, and even some stones were flying in Charlie’s direction, as he squeaked.“What’s there, Charlie?” Dennis asked as he picked up the hamster and walked towards the door.What he saw made him wonder if he had actually fallen asleep and not realized it.“It’s a…it’s a rabbit!” he said. No bigger than Charlie（and no smaller）, the rabbit wore a yellow shirt, a tiny pair of green pants, and a hat.“Why are you throwing things at my hamster, rabbit?” asked Dennis.“Why do you keep a vicious（凶猛的）hamster as a pet, human?” asked the rabbit. “Charlie is not vicious! More importantly, why are you in my room, rabbit?” asked Dennis. “That is an interesting question, human.”“My name is not ‘human’, it’s Dennis.” Dennis said angrily. “I already know your name.And rabbits have names too!”Dennis didn’t say anything for a moment, and neither did the rabbit. It was an awkward （尴尬的）silence for everyone except Charlie who, as usual, had fallen asleep shortly after Dennis picked him up.“Well, what is your name then?” asked Dennis.36．When did the story take place?A．One night in late autumn.B．One late afternoon in summer. C．One afternoon in early spring.D．One early morning in winter. 37．Why does the writer uses the punctuation mark “…” in the sentence “It’s a…it’s a rabbit!”?A．To show his certainty of this subject.B．To hide his limited knowledge in animals.C．To express Dennis’ surprise at the rabbit.D．To display Dennis’ worry about his hamster.38．Which is the right order of the following events?a. Dennis heard the sounds of squeaking.b. The rabbit threw balls of paper at Charlie.c. Dennis tried to count wolves to stay awake.d. Charlie fell asleep shortly after Dennis picked him up.A．c-d-a-b B．d-a-c-b C．d-c-a-b D．c-b-a-d 39．What is the best title for the story?A．Dennis’ lovely hamster B．Ways to stay up lateC．Dennis’ unusual night D．Advice on falling asleep 40．According to the last paragraph, what would most probably happen next?A．The rabbit would run away at once.B．The rabbit would tell Dennis his name. C．The rabbit would throw things at Dennis.D．The rabbit would fall asleep with Dennis.四、根据汉语提示填空41．—What’s the _____ (日期) today, Millie?—It’s 17 June. Oh, tomorrow is Dragon Boat Festival.42．These days, citizens must show their health codes and travel codes before entering________ places. （公共）43．Students should always go over what they have learned in time after class in order to________ better. （理解）44．It’s reported that the Phase I Project of Nanjing Metro Line 10 is ________（预料）to be completed and opened to traffic in 2024.45．Larry, my American friend, has learned to use ________（筷子）well and can eat beef noodles the way most Chinese people do.五、用所给单词的正确形式填空46．Chinese love their “Lucky Bamboo” plants and you will see them often in _______ (they) homes and offices.47．I want to keep pets, but my mother is worried about if I can look after them ________ (proper).48．Amazing China wins high praise from the public. I think the documentary is well worth ________ (watch).49．Millie is ________ (sure) whether the School Sports Festival will be held tomorrow because of the bad weather.50．Eileen Gu won China’s ________ (three) gold medal and her first gold medal of the Beijing Winter Olympic Games on February 8.六、选择适当的单词补全对话请根据对话内容、从下列方框中选择适当的单词或短语填空，使对话内容完整正确。

2023年江苏省南京市中考数学模拟预测卷+答案解析

2023年江苏省南京市中考数学模拟预测卷一、选择题：本题共6小题，每小题3分，共18分。

在每小题给出的选项中，只有一项是符合题目要求的。

1.二次根式中字母x的取值范围是()A. B. C. D.2.如果点在平面直角坐标系的第三象限内，那么x的取值范围在数轴上可表示为()A. B.C. D.3.如图是近一年来某企业产值增长率的折线统计图，下列信息正确的是()A.2022年4月份该企业产值最低B.2022年9月份是该企业产值最大的月份C.2022年11月份比2022年10月份产值低D.2022年4月至2023年3月该企业产值一直在增大4.下列运算正确的是()A. B. C. D.5.已知a，b是一元二次方程的两根，则的值为()A.4B.C.2D.16.学习《设计制作长方体形状的包装纸盒》后，小宁从长方形硬纸片上截去两个矩形图中阴影部分，再沿虚线折成一个无盖的长方体纸盒．纸片长为30cm，宽为18cm，，则该纸盒的容积为()A. B. C. D.二、填空题：本题共10小题，每小题3分，共30分。

7.的相反数是_____.8.计算：______.9.2022年11月30日，神舟十五号飞船载乘3名航天员成功与神舟十四号航天员乘组上演“太空相会”．航天员的宇航服加入了气凝胶，可以抵御太空的高温．气凝胶是一种具有纳米多孔结构的新型材料，其颗粒尺寸通常小于，将数据用科学记数法表示为_____.10.若关于x的方程有两个相等的实数根，则m的值是_____.11.如图，用一个圆心角为的扇形围成一个无底的圆锥，如果这个圆锥底面圆的半径为2cm，则这个扇形的半径是_______12.如图，已知菱形ABCD的边长为4，，E为AB的中点，F为CE的中点，AF与DE相交于点G，则GF的长等于_________.13.如图，将沿BC边上的中线AD平移到的位置，已知的面积为9，阴影部分三角形的面积为4，若，则_______.14.在平面直角坐标系中、反比例函数的图象与边长是4的正方形OABC的两边AB，BC分别相交于M，N两点，三角形OMN的面积为，若动点P在x轴上，则的最小值是___.15.如图，二次函数的图象与x轴的负半轴交于点A，对称轴为直线下面结论：①；②；③；④为实数其中正确的是_____只填序号16.如图，E为正方形ABCD的边CD上一点不与C、重合，将沿直线BE翻折到，延长EF交AD于点G，点O是过B、E、G三点的圆劣弧EG上一点，则__________三、计算题：本大题共1小题，共6分。

2023年江苏省南京市中考数学必刷模拟试卷附解析

2023年江苏省南京市中考数学必刷模拟试卷学校：__________ 姓名：__________ 班级：__________ 考号：__________注意事项： 1．答题前填写好自己的姓名、班级、考号等信息 2．请将答案正确填写在答题卡上一、选择题1．如图，DE ∥BC ，点D 、E 分别在 AB 、AC 上，且AD : AB= 1 : 3 , CE=4，则 AC 的长为（） A ．6B ．5C ．7D ． 832．已知函数2y ax bx c =++的图象如图所示，那么函数解析式为（）A ．223y x x =-++ B ．223y x x =-- C ．223y x x =-+ D ．223y x x =-+- 3．下面的函数是反比例函数的是（） A ．13+=x yB ．x x y 22+=C ．2x y =D ．xy 2=4．在对2006个数据进行整理的频数分布表中，各组频数之和与频率之和分别等于（） A ．2006，1B ．2006，2006C ．1，2006D ．1，15．下列所给的边长相同的正多边形的组合中，不能镶嵌平面的是（） A ．正三角形与正方形组合 B ．正三角形与正六边形组合 C ．正方形与正六边形组合D ．正三角形、正方形、正六边形组合6．了解全市八年级学生身高在某一范围内的学生所占比例的大小，需知道相应样本的（） A ．平均数B ．方差C ．众数D ．频数分布7．如图，天平右盘中的每个砝码的质量都是1g ，则图中显示出某药品A 的质量范围是（） A ．大于2 g B ．小于3 gC ．大于2 g 或小于3 gD ．大于2 g 且小于3 g8．在平面直角坐标系中，下列各点关于y 轴的对称点在第一象限的是（） A ．(21)，B ．(21)-，C ．(21)-，D ．(21)--，9．点P在第二象限，若该点到2轴的距离为3，到有y轴的距离为1，则点P的坐标是（）A．（-1，3）B．（3-，1）C．（3，-l）D．（1，3）10．直线142y x=-与x轴的交点坐标为（）A．（0，一4）B．（一4，0）C．（0，8）D．（8，O）11．在平面直角坐标系中，若点P（m-2，m）在第二象限．则m的取值范围为（）A． 0<m<2 B．m>0 C．m<2 D．m>212．平行线之间的距离是指（）A．从一条直线上的一点到另一条直线的垂线段B．从一条直线上的一点到另一条直线的垂线段的长度C．从一条直线上的一点到另一条直线的垂线的长度D．从一条直线上的一点到另一条直线上的一点间线段的长13．如果x的相反数比13-的倒数大4，由此可列出方程（）A．1()43x-+-=B．1()43x---=C．(3)4x---=D．(3}4x-+-=14．光年是天文学中的距离单位，1 光年大约是9 500 000 000 000千米，用科学记数法可表示为（）A．1095010⨯千米B．119510⨯千米C．129.510⨯千米D．130.9510⨯千米二、填空题15．已知正比例函数232ky kx-=的函数值y随着x的增大而减小，则k= ．16．若一个底面为正方形的直棱柱的侧面展开图是一个边长为4的正方形，则这个直棱柱的表面积是，体积是．17．等腰三角形一边长为2 cm，另一边长为5cm，它的周长是 cm．18．在△ABC中，∠A=48°，∠B=66°，AB=2．7 cm，则AC= cm．19．如图，∠1=75°，∠2 =75°，∠3 = 105°，那么∠4 = ,可推出的平行关系有 . 20．如图，如果 AB∥CD，∠1 = 57°，那么∠AEC= ．21．如图(1)硬纸片ABCD 的边长是4cm，点E、F分别是AB、BC边的中点，若沿左图中的虚线剪开，拼成如图 (2}所示的一栋“小别墅”，则图中阴影部分的面积和是 cm 2.解答题22．164的立方根是，()29-的平方根是，-5是的平方根． 23．用“>”或“<”连结下列各数：(1) 16- -4.2；(2)314-23．三、解答题24．根据如图回答下列问题.(1)这幅画大约是在一天中什么时候完成的？ (2)画出此时旗杆的影子.(3)若旗杆高6 m ，影长为 3m ，建筑物的影长为 l2m ，求建筑物的高.25．某校有A 、B 两个餐厅，甲、乙、丙三名学生各自随机选择其中的一个餐厅用餐. (1)求甲、乙、丙三名学生在同一个餐厅用餐的概率； (2)求甲、乙、丙三名学生中至少有一人在B 餐厅用昝的概率.26．如图，在△ABC 中，AB=5，AC=7，∠B=60°，求BC 的长．60︒CB A27．如图所示，已知：AD=BC，AD∥BC , AE⊥BD，CF⊥BD，E，F为垂足．求证：四边形AECF是平行四边形．28．如图，将△ABC先向上平移5格得到△A′B′C′，再以直线MN为对称轴，将△A′B′C′作轴对称变换，得到△A″B″C″，作出△A′B′C′和△A″B″C″．29．某校八年一班的一节数学活动课安排了测量操场上悬挂国旗的旗杆的高度.甲、乙、丙三个学习小组设计的测量方案如图所示：甲组测得图中BO=60米，OD=3.4米，CD=1.7米；乙组测得图中，CD=1.5米，同一时刻影长FD=0.9米，EB=18米；丙组测得图中，EF∥AB、FH∥BD，BD=90米，EF=0.2米，人的臂长(FH)为0.6米，请你任选一种方案，利用实验数据求出该校旗杆的高度.30．在一次“寻宝”游戏中，寻宝人已经找到了坐标为(3，2)和(3，一2)的A、B两个标志点(如图)，并且知道藏宝地点的坐标为(4，4)，除此外不知道其他信息．如何确定直角坐标系找到“宝藏”?与同伴进行交流．【参考答案】学校：__________ 姓名：__________ 班级：__________ 考号：__________注意事项：1．答题前填写好自己的姓名、班级、考号等信息2．请将答案正确填写在答题卡上一、选择题1．A2．A3．D4．A5．C6．D7．D8．C9．A10．D11．A12．B13．C14．C二、填空题 15． -216．18，417．1218．2.719．105°；1l ∥2l 、3l ∥4l20．57°21．422． 14，9 ，5 23．(1)> (2)<三、解答题 24．(1)由影子在建筑物的东边可知，此时太阳西去，应该是下午.(2)连结建.筑物的顶端A 和其影子的顶端B 得直线 AB ，过族杆的顶端 C 作直线CD ∥AB 交地面于 D ，则 D 与旗杆底部E 的连线为其影子.(3)∵旗杆和影子长以及建筑物和影子长成比例，∴建筑物的高612243h⨯==m．25．所有可能出现结果如下：(1)甲、乙、丙三名学生在同一餐厅用餐的概率是14；(2)甲、乙、丙三名学生中至少有一人在 B餐厅用餐的概率是78 26．如图，作AD⊥BC于D，则AD=AB·sin60°=532，BD=AB·cos60°=52，CD227511 4942AC AD=-=-=，∴BC=BD+CD=8．27．先证明△ADE≌△CBF(AAS)，得AE=CF，则AE∥CF28．略29．该校的旗杆为30米．30．略．提示：连结AB，AB长就是4个单位长度，作AB的中垂线即为x轴，向左移3个单位长度，再作x轴的垂线即y轴，从而可确定“宝藏”位置。

2023年江苏省南京市中考数学全真模拟考试试卷A卷附解析

2023年江苏省南京市中考数学全真模拟考试试卷A卷学校：__________ 姓名：__________ 班级：__________ 考号：__________注意事项：1．答题前填写好自己的姓名、班级、考号等信息2．请将答案正确填写在答题卡上一、选择题如图是一个正方体纸盒的平面展开图，每一个正方形内部都有一个单项式．当折成正方体后，“？”所表示的单项式与对面正方形上的单项式是同类项，则“？”所表示的单项式是（）A．b B．c C．d D．e2．如图，以□ABCD对角线的交点为坐标原点，以平行于AD边的直线为x轴，建立直角坐标系.若点 D的坐标为（3，2），则点B的坐标为（）A．（3,2）B．（2,3）C．（-3,-2）D．（-2,-3）3．一个正方形的对角线长为2 cm，则它的面积是（）A．2 cm2 8．4 cm2C．6 cm2D．8 cm24．一个容量为80的样本，最大值是141，最小值是50，取组距为10，则可以分（）A．10组B．9组C．8组D．7组5．某初中毕业班的每一个同学都将自己的相片向全班其他同学各送一张表示留念，全班共送了2550张相片，如果全班有x名学生，根据题意，列出方程为（）A．x（x+1）=2550 B．x（x-1）=2550C．2x（x+1）=2550 D．x （x-1）=2550×26．估算728-的值在（）A． 7和8之间B． 6和7之间C． 3和4之间D． 2和3之间7．不等式组111xx-<⎧⎨≥-⎩的解集在数轴上表示正确的是（）A．B．C．D．8．甲、乙、丙、丁四位数选手各l0次射击成绩的平均数都是8环，众数和方差如下表，则这四个人中水平发挥最稳定的是（）选手田乙丙丁众数（环） 9 8 8 i0方差（环2）0.035 0．Ol5 0.025 0.27A ．甲B ．乙C ．丙D ．丁9．已知：如图，∠A0B 的两边 0A 、0B 均为平面反光镜，∠A0B=40．在0B 上有一点P,从P 点射出一束光线经0A 上的Q 点反射后,反射光线QR 恰好与0B 平行,则∠QPB 的度数是（） A ．60°B ．80°C ．100 °D ．120°10．己在△ABC 中，∠A=55°，∠C=42°，则∠B 的数为（） A ． 42° B ．55° C ．83° D ．97° 11．用长为4 cm 、5 cm 、6 cm 的三条线段围成三角形的事件是（） A ．随机事件 B ．必然事件 C ．不可能事件 D ．以上都不是 12．若关于x 的方程230m mx m ++-=是一元一次方程，则这个方程的解是（）A ．1B ．-lC ．-4D ．4二、填空题13．用6个球（除颜色外没有区别）设计满足以下条件的游戏：摸到白球的概率为12，摸到红球的概率为13，摸到黄球的概率为16.则应有个白球，个红球，个黄球. 14．某集团公司计划生产化肥 500t ，则每天生产化肥 y(t)与生产天数 x(天)之间的函数． 15．在函数y=2x+4中，若-3≤x ≤-l ，则y 的取值范围是．16．若33320x x y +++-=，则点P(x ，y)在第象限，点Q(x+1，y-2)在． 17．一次函数(26)5y m x =-+中，y 随x 增大而减小，则m 的取值范围是． 18．图中的几何体是面体．19．方程组⎩⎨⎧=-=+13y x y x 的解为_________．20．如图，已知 AB 、CD 相交于点0, OE ⊥AB. ∠EOC=28°, 则∠AOD= .21．某校共有教师100名，现按职称(高级、一级、其它职称)制成统计图，则其它职称的教师占％．三、解答题22．小明、小亮和小张三入准备下象棋，他们约定用“抛硬币”的游戏方式来确定哪两个人先下棋，规则如下：游戏规则:三人手中各持有一枚质地均匀的硬币，他们同时将手中硬币抛落到水平地面为一个回合，落地后，三枚硬币中，恰有两枚正面向上或者反面向上的两人先下棋；若三枚硬币均为正面向上或反面向上，则不能确定其中哪两人先下棋.(1)请你完成下面表示游戏一个回合所有可能出现的结果的树状图.树状图为:(2)求一个回合能确定两人先下棋的概率.23．为举办毕业联欢会，小颖设计了一个游戏：游戏者分别转动如图的两个可以自由转动的转盘各一次，当两个转盘的指针所指字母相同时，他就可以获得一次指定．．一位到会者为大家表演节目的机会．(1）利用树状图或列表的方法（只选其中一种）表示出游戏可能出现的所有结果；(2)若小亮参加一次游戏，则他能获得这种指定机会的概率是多少？24．如图，已知反比例函数8y x=-和一次函数2y x =-+的图象交于A 、B 两点，求：（1）A 、B 两点的坐标；（2）若O 为坐标原点，求△AOB 的面积．25．如图，用同样规格黑白两色的正方形瓷砖铺设长方形地面，请观察下列图形，并解答有关问题：(1）第n 个图形铺设地面所用瓷砖的总块数为 (用含n 的代数式表示）； (2）上述铺设方案，铺一块这样的长方形地面共用了506块瓷砖，求此时n 的值； (3）是否存在黑瓷砖与白瓷砖块数相等的情形？请通过计算加以说明．n=1n=2n=326．如图甲，正方形被划分成16个全等的三角形，将其中若干个三角形涂黑，且满足下列条件：(1）涂黑部分的面积是原正方形面积的一半；(2）涂黑部分成轴对称图形．如图乙是一种涂法，请在图1～3中分别设计另外三种涂法．（在所设计的图案中，若涂黑部分全等，则认为是同一种涂法，如图乙与图丙）27．根据频数直方图（如图）回答问题：(1）总共统计了多少名学生的心跳情况?(2）哪些次数段的学生数最多?占多大比例?(3）如果半分钟心跳次数为x，且3039≤次属于正常范围，心跳次数属于正常的学生占多x大比例?(4）说说你从频数折线图中获得的信息．28．分别写出下列函数解析式，并指出式中的常量与变量：(1)居民用电平均每度0．52元，则电费y(元)与用电量x（度）之间的函数解析式；(2)小昕用50元钱购买6元／件的某种商品，则剩余的钱y(元)与购买这种商品x(件)之间的函数解析式．29．图中有三棱柱的展开图吗?30．解方程组：(1）37528y xx y=-⎧⎨+=⎩；（2）32352x yx y-=-⎧⎨-=⎩；(3)2783810x yx y-=⎧⎨-=⎩【参考答案】学校：__________ 姓名：__________ 班级：__________ 考号：__________注意事项：1．答题前填写好自己的姓名、班级、考号等信息2．请将答案正确填写在答题卡上一、选择题1．D2．C3．A4．A5．B6．D7．B8．B9．B10．C11．B12．C二、填空题 13． 3,2,114．500y x=15． -2≤y ≤216．二，y 轴上17．m ＜318．五19．21x y =⎧⎨=⎩ 20． 62°21．65三、解答题 22． (1)如解图.(2) 34P =（确定）． 23．(1）可列表如下：转盘１转盘２ＡＢＣＣ（Ａ，Ｃ）（Ｂ，Ｃ）（Ｃ，Ｃ）Ｄ（Ａ，Ｄ）（Ｂ，Ｄ）（Ｃ，Ｄ）（2）由上表可知，小亮能获得这种指定机会的概率是1624．(1)由28y x y x =-+⎧⎪⎨=-⎪⎩得2280x x --=，解得：x 1 = 4，x 2 =－2x 1 = 4时，y 1 =-2；x 2 =-2 时，y 2 =4，∴A 、B 坐标分别是(4，一2)和(—2，4)． (2)设直线 AB 与 x 轴交于C ，则点 C 的坐标为(2，0)．112422622AOB AOC OBC S S S ∆∆∆=+=⨯⨯+⨯⨯=． 25．解：（1）652++n n ；(2）256506n n ++=，解得1220,25n n ==-（舍） (3）不存在．由2(1)(56)(1)n n n n n n +=++-+，解得3332n ±= 因为n 不为正整数，所以不存在黑白瓷砖数相等的情形．26．不同涂法的图案列举如下：27．⑴总共统计了 27人的心跳情况；（2）30～33这个次数段的学生数最多，约占26% ；（3）约占56%；（4）从折线统计图中可知：呈中间高两边低的趋势，就是说心跳正常的人数较多．28．(1)y=0．52x ；常量0．52；变量x 、y ；(2)y=50-6x ；常量：50，6；变量：x 、y29．①、②、③都是30．(1)21xy=⎧⎨=-⎩，(2)13xy=⎧⎨=⎩，（3）6545xy⎧=⎪⎪⎨⎪=-⎪⎩。

2023-2024学年江苏省南京市学校九年级(下)中考数学模拟试卷02+答案解析

2023-2024学年江苏省南京市学校九年级（下）中考数学模拟试卷02一、选择题：本题共6小题，每小题3分，共18分。

在每小题给出的选项中，只有一项是符合题目要求的。

1.2022年10月31日，搭载空间站梦天实验舱的长征五号B遥四运载火箭，在我国文昌航天发射场发射成功．长征五号B运载火箭可提供1078t起飞推力．已知1t起飞推力约等于10000N，则长征五号B运载火箭可提供的起飞推力约为( )A. B. C. D.2.如图，数轴上A，B，C，D，E五个点分别表示数1，2，3，4，5，则表示数的点应在( )A. 线段AB上B. 线段BC上C. 线段CD上D. 线段DE上3.若一个等腰三角形的腰长为3，则它的周长可能是( )A. 5B. 10C. 15D. 204.折返跑是一种跑步的形式．如图，在一定距离的两个标志物①、②之间，从①开始，沿直线跑至②处，用手碰到②后立即转身沿直线跑至①处，用手碰到①后继续转身跑至②处，循环进行，全程无需绕过标志物．小华练习了一次的折返跑，用时在整个过程中，他的速度大小随时间变化的图象可能是( )A.B.C.D.5.如图，在四边形ABCD中，，，，，若线段MN 在边AD上运动，且，则的最小值是( )A. B. C. D. 106.如图，数学活动课上，为测量学校旗杆高度，小菲同学在脚下水平放置一平面镜，然后向后退保持脚、镜和旗杆底端在同一直线上，直到她刚好在镜子中看到旗杆的顶端．已知小菲的眼睛离地面高度为，同时量得小菲与镜子的水平距离为2m，镜子与旗杆的水平距离为10m，则旗杆高度为( )A. B. 8m C. D.二、填空题：本题共10小题，每小题3分，共30分。

7.计算：__________；__________.8.使分式有意义的x的取值范围是__________.9.计算__________.10.分解因式：__________.11.计算：__________.12.某青年排球队有12名队员，年龄的情况如下表：年龄/岁1819202122人数35211则这12名队员年龄的中位数是__________岁．13.学校提倡“低碳环保，绿色出行”，小明和小亮分别选择步行和骑自行车上学，两人各自从家同时同向出发，沿同一条路匀速前进．如图所示，和分别表示两人到小亮家的距离和时间的关系，则出发__________________ h后两人相遇．14.已知曲线、分别是函数，的图象，边长为6的正的顶点A在y轴正半轴上，顶点B、C在x轴上在C的左侧，现将绕原点O顺时针旋转，当点B在曲线上时，点A恰好在曲线上，则k的值为__________.15.半径为5cm的圆内接正五边形一边所对劣弧的长为___________16.如图，在菱形纸片ABCD中，点E在边AB上，将纸片沿CE折叠，点B落在处，，垂足为若，，则__________三、解答题：本题共11小题，共88分。

【中考冲刺】2023年江苏省南京市中考模拟英语试卷 (附答案)

2023江苏省南京市中考模拟英语试题学校:___________姓名：___________班级：___________考号：___________一、单项选择1．The 19th Asian Games will take place in Hangzhou ________ September this summer. A．in B．at C．on D．with 2．Nobody taught my grandpa how to use Wechat. He learned it all by ________. A．herself B．her C．him D．himself 3．—Millie, I can’t solve the problems by myself. What should I do?—Maybe working in groups is a good ________.A．survey B．report C．method D．organization 4．—What do you think of Jerry’s advice on how to remember English words?—Very ________. I would try it.A．expensive B．practical C．natural D．strange 5．According to the new traffic rules, people ________ wear a helmet when riding an e-bike. A．might B．may C．can D．must 6．With the help of 5G technology, the apps on the smart phone can provide ________ functions for the users than before.A．many B．more C．most D．less 7．（2017 • 上海中考）The museum ____________ next month to celebrate the Science & Technology Festival.A．is decorated B．will decorate C．is decorating D．will be decorated8．If you have trouble reading these words, you can ________ them over and over again until you are comfortable with them.A．remind B．refuse C．repeat D．return9．My father can always ________ the jobs that other people think difficult and work at them slowly until they get done.A．take on B．take out C．take away D．take off 10．—Is your brother at home, Cathy?—No, he ________ in the health club.A．exercises B．exercised C．is exercising D．was exercising 11．Doing voluntary work is a great way for me to help others. _________, I can meet someinteresting people who turn to be lifelong friends.A．However B．Instead C．Otherwise D．Moreover 12．—Could you tell me ________?—The famous table tennis coach Liu Guoliang.A．when you will watch the game B．who you admire mostC．why you want to watch the game D．what sport you like best13．Miss Li advised the students who are weak in English ________ aloud every morning. A．read B．reading C．to read D．reads14．A study has found that plants feel pain ________ they are touched or hurt.A．what B．when C．where D．who 15．—Would you please come to our party tonight?—________! I have to prepare for the coming English speech contest.A．Go ahead B．With pleasure C．My pleasure D．What a pity 二、完形填空阅读下面短文，从短文后所给各题的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

2023年南京市中考英语模拟试题与答案

2023年南京市中考英语模拟试题与答案第一部分：听力理解（共20小题；每小题1分，满分20分）第一节（共5小题；每小题1分，满分5分）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选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. What did the woman buy for Jack?- A. A book. B. A toy car. C. A soccer ball.2. How much does the man need to pay for the shoes?- A. $14. B. $17. C. $20.3. What will the weather be like tomorrow?- A. Sunny. B. Cloudy. C. Rainy.4. Where is the woman's brother?- A. In Canada. B. In China. C. In the United States.5. What was the man doing during the vacation?- A. Visiting his grandparents. B. Traveling around the world.C. Attending summer camp.第二节（共15小题；每小题1分，满分15分）听下面5段对话。

每段对话后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

每段对话读两遍。

听第6段材料，回答第6、7题。

6. What is Judy waiting for?- A. A friend. B. The bus. C. Her mother.7. Where does Judy’s friend live?- A. In the city. B. In the countryside. C. In a small town.听第7段材料，回答第8、9题。

2023年江苏省南京市中考数学全优模拟试卷附解析

2023年江苏省南京市中考数学全优模拟试卷学校：__________ 姓名：__________ 班级：__________ 考号：__________注意事项：1．答题前填写好自己的姓名、班级、考号等信息2．请将答案正确填写在答题卡上一、选择题1．在ABC △中，90C AC BC ∠=，，的长分别是方程27120x x -+=的两个根，ABC△内一点P 到三边的距离都相等．则PC 为（）A ．1B ．2C ．322D ．222．过⊙O 内一点M 的最长的弦长为4cm ，最短的弦长为2cm ，则OM 的长为（）A ．3cmB ．2cmC . 1cmD ． 3cm 3．一个五边形能画出的对角线条数为（） A ．2条B ．3条C ．4条D ．5条 4．在频数分布直方图中，每个小长形的高度等于（）A ．组距B ．组数C ．每小组的频率D ．每小组的频数 5．若干名工人某天生产同一种零件，生产的零件数整理成条形图（如图所示）．设他们生产零件的平均数为a ，中位数为b ，众数为c ，则a ，b ，c 的大小关系为．6．如图，宽为 50 cm 的矩形图案由 10个全等的小长方形拼成，其中一个小长方形的面积为（）A ．400cm 2B ．500 cm 2C ．600 cm 2D ．4000 cm 27．小王身上只有 2元和 5元两种面值的人民币，他买一件学习用品要支付27元，则付款的（）A ．1种B ．2种C ．3种D ．4种8．4个红球、3个白球、2个黑球放入一个不透明的袋子里，从中摸出8个球，恰好红球、白球、黑球都摸到，这件事情（）A ．可能发生B ．不可能发生C ．很可能发生D ．必然发生9．下列四个图中，能用∠ 1、∠AOB、∠O三种方法表示同一个角的是（）A．B．C． D．10．下列四个图中，能表示线段x=a+c-b的是（）A． B．C． D．11．图甲、乙所示分别是我国l997～2000年全国初中在校生人数和全国初中学校数统计图，由图可知，从l997年到2000年，我国初中在校生人数和学校数分别（）A．逐年增加，逐年增加B．逐年增加，逐年减少C．逐年减少，逐年减少D．逐年减少，逐年增加二、填空题12．如图，AB 是半圆的直径，点 P在 AB 的延长线上，PM 切半圆0于M点，若OA=a，PM=3a，则△PMB的周长是．13．盒子里装有大小形状相同的3个白球和2个红球，搅匀后从中揍出一个球，放回搅匀后，再接出第二个球，则取出的恰是两个红球的概率是．）m 的树被台风吹断，树顶者地面后与地面恰成60°角，14．如图所示，一株高为（633则树顶着地处与树根的距离为 m．15．如图，在△ABC 中, 内接正方形EFGH ，BC=16，AD ⊥BC 于D ，AD=8，则正方形EFGH 的边长为． 16．点A(5，2-)关于直角坐标系原点对称的点的坐标是，关于y 轴对称的点的坐标是，关于x 轴对称的点的坐标是．17．矩形的对角线相交成的钝角为l20°，宽等于4 cm ，则对角线的长为．18．如图，直线AB CD ∥，EF CD ⊥，F 为垂足．如果20GEF =∠，那么1∠的度数是 °．19．轮船在静水中每小时行驶akm ，水流的速度为每小时bkm ，则轮船在逆流中行驶skm 需要小时.解答题20．要将右面图形中的甲图变为乙图，应先将甲图进行变换，然后再进行变换，就可以得到乙图．21．某市在端年节准备举行划龙舟大赛，预计15个队共330人参加．已知每个队一条船，每条船上人数相等，且每条船上有1人击鼓，1人掌舵，其余的人同时划桨．设每条船上划桨的有x 人，那么可列出一元一次方程为．22．已知 x= 2007，则22231()(2)122x x x --+-+= ．23．计算： (-0.1)× (-0.001) ×(-100)×1000= ．三、解答题24．某校八年级将举行班级乒乓球对抗赛，每个班必须选派出一对男女混合双打选手参赛，八年级一班准备在小娟、小敏、小华三名女选手和小明、小强两名男选手中，选男、女选手各一名组成一对参赛，一共能够组出哪几对？如果小敏和小强的组合是最强组合，那么采用随机抽签的办法，恰好选出小敏和小强参赛的概率是多少？25．已知抛物线2y ax = 经过点A(12，-2) (1)求a 的值，并写出这个二次函数的解析式；(2)说出这个二次函数的顶点坐标、对称轴、开口方向.26．画出如图所示几何体的主视图、左视图和俯视图．27．若3a b +2a b - ab 的值.28．计算下列各题(1))9()11()4()3(--+--+- (2)()39112-⨯÷- (3)⎪⎭⎫ ⎝⎛+-⨯-654331112 (4)[2 – 5 ×(21-)2 ]÷)41(- (5)32725.0-()212--(6) 用计算器计算: )]2(222[413-⨯+--π.(精确到0.01)29．某酒店客房部有三人间、双人间客房，收费数据如下表：一些三人普通间和双人普通间客房．若每问客房正好住满，且一天共花去住宿费1510元，则旅游团住了三人普通间和双人普通间客房各多少间?(只要求列出方程，不解方程)30．先化简，再求值. 22222222(22)[(33)(33)]x y xy x y x y x y xy---++-，其中12x=-，2y=．【参考答案】学校：__________ 姓名：__________ 班级：__________ 考号：__________注意事项：1．答题前填写好自己的姓名、班级、考号等信息2．请将答案正确填写在答题卡上一、选择题1．B2．A3．D4．D5．b>a>c6．A7．C8．D9．D10．D11．B二、填空题12．(23)a +13． 42514． 315．16316． (-5，2)，(-5，2-)，(5，2)17．8 cm18．70 19．b a s-20．旋转，平移或平移，旋转21．15(x+2)=33022．123．-10三、解答题24．共 6 对，恰好选出小敏和小强的概率是16． 25．（1）把点(12，-2) 的坐标代入2y ax =得212()2a -=∴a =—8.∴这个二次函数的解析式28y x =-(2)顶点为 (0，0)，对称抽为 y 轴.因为a=-8<0，所以开口向下. 26．27．22()()144a b a b ab +--==28． (1)-9； (2) 27； (3)-19； (4)-3 ； (5)-14.5； (6) -6.91 29．设三人普通间共住了x 人，则双人普通间共住了 (50x -)人，由题意得5015050%14050%151032x x -⨯⨯+⨯⨯=30． 22x y xy -+ ,122-。

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2023年江苏省南京市中考模拟试卷（含答案）一、单项选择。

1 . Mr. Li always has his own special _______ to make his lessons lively.A.surveysB.instructions C . works D. methods2. Many people find that listening to some good music helps _______ when they are low.A. himB. herC.themD. us3.--- How do you find your company?---A little worried. We ground as a _______ leader in the field of IT with the others speeding up development.A.are losingB.were losingC.lostD.have lost4.Look at the floor, Tom! _______ you watch TV while having a meal?A.ShouldB.CouldC.MustD.May5.He just looked at me and there was an expression in his eyes I couldn’t _______.A.readB.senseC.tellD.notice6.No rules all things, will not be long. Without proper lessons, you could _______ a lot of bad habits when playing the piano.A.give upB.catch upC.keep upD.pick up7. The workers are made _______ ten hours a day.A . work B.to work C . working D. worked8.---- I hear that you have bought a smart car. Does the car give you any good _______ for your money?--- Certainly.A.valueB.priceC.wealthD.cost9.As we stayed at home for two months, papers fell into piles. People are always as busy as a bee on weekdays, so they _______ spend their weekend on housework.A.widelyB.probablyC.mostlyD.wisely10. The 24th Winter Olympic Games _______ in Bejjing on February 2, 2022.A. Is held B . will be held C . was held D. are hold11.You've watched the boring soap opera thousands of times! Why don't you go outside and find something _______ doing?efulB.cheerfulC.enjoyableD.worth12.---Your head teacher has set up a Wechat group. Could you tell _______?---It is more convenient to communicate with our parents.A. when it was set upB. why did he set it upC.how did he set it upD.what it is used for13.In England, if you think that other people are always in a better situation than you, even when they are not, we say“_______”.A.the grass is always greener on the other sideB.every dog has its dayC.the early bird catches the wormD.actions speak louder than words14.Do you know the boy _______ mother is an excellent teacher?A. whichB.who C . whose D.what15. ---I missed the basketball game last Saturday because I had an exam.---_______, but it will be repeated on TV.A.Take it easyB. You are lucky C . That's wonderful D. Never mind二、完形填空。

When we see well, we do not think about our eyes very often．It is only when we cannot see perfectly that we ___16___ how important our eyes are．People who are near-sighted can only see things that are very close to their eyes. Everything else seems ___17___．A person ___18___ does a lot of work, such as writing, reading and sewing become near－sighted then.People who are far-sighted suffer from just the ___19___ problem．They can see things that are far away, but they have ___20___ in reading a book unless they hold it at arm’s length．If they want to do much ___21___, they must get glasses, too．Other people do not see clearly because their eyes are not exactly the right shape. They have what is called astigmatism(散光)．This, too, can be corrected by glasses．Some people’s eyes become ___22___ because of cataracts(白内障)．Long ago these people often became blind．Now, however, it is possible to operate on the cataracts and remove them．Having two good eyes is important for judging distances．___23___ eye sees things from a slightly different angle(角度)．To prove this to ___24___, look at an object our of one eye; then look at the same object out of your other eye．You will find the object’s relation to the background and other things around it has changed．The difference between these two different eye views ___25___ us to judge(判断) how far away an object is．People who have only one eye cannot judge distance as people with two eyes do．16.A. remind B. receive C. review D. realize17.A. unhappy B. unpleasant C. unclear D. unfair18. A. what B. who C when D. which19.A. right B. same C. wrong D. opposite20. A. difficulty B. fun C. time D. experience21.A. shopping B. cleaning C. reading D. fishing22. A. cloudy B. sunny C. windy D. rainy23. A. Each B. Every C.Both D. All24.A. yourself B. himself C. herself D. myself25.A. helps B. makes C. encourages D. agrees三、阅读理解。

A26. What is Julie's advice?A. Getting a pen friend.B. Watching some English films.C. Reading English newspapers.D. Joining an English Speaking Club.27. Who is poor at learning English grammar?A. Julie.B.Li Lei.C. Betty.D. Sam.28. Where can Zhao Xin find a pen friend?A. At school.B. In the newspaper.C. On the Internet.D. In the English Speaking Club.BAre you sometimes a little tired and sleepy in the early afternoon? Sometimes a task that takes you five minutes in the morning may take fifteen minutes in the afternoon? Many people feel this way after lunch. They may think that eating lunch is the cause of the sleepiness. If this were the case, why wouldn't we feel just as sleepy after eating a large breakfast or after dinner? The truth is that this sleepiness is unrelated to meals and is due to another cause.The real reason lies inside your bodies. At that time, about eight hours after you wake up-your body temperature goes down. This is what makes you slow down and feel sleepy. Scientists have tested sleep habits in experiments where there was no night or day. The people in these experiments almost always followed a similar sleeping pattern (模式). They slept for one long period and then for one short period about eight hours later.In many parts of the world, people take naps (午睡) in the middle of the day. This is especially true in warmer climates where the heat makes work difficult in the early afternoon. Researchers are now saying that naps are good for everyone in any climate.A daily nap gives one a more rested body and mind and therefore is good for health in general. In countries where naps are traditional, people often suffer less from problems such as heart disease.Many working people, unfortunately, have no time to take naps. Though doctors may advise taking naps, employers do not allow it! If you do have the chance, however, here are a few tips about making the most of your nap. Remember that the best time to take a nap is about eight hours after you get up. A short sleep too late inthe day may only make you feel more tired and sleepy afterward. This can also happen if you sleep for too long.If you're feeling down, try taking a nap to lift your spirits. Napping, or even just resting for an hour without falling asleep, can brighten your outlook.29. Why do people feel sleepy in the early afternoon according to the passage?A. They eat too much for lunch.B. They sleep too little at night.C. The weather becomes a lot warmer.D. Their body temperature becomes lower.30. What can we learn from the passage?A. A late nap may make people more tired.B. Taking naps can help treat heart disease.C.People spend more time finishing a task in the morning.D. It's difficult for people to follow a similar sleeping pattern.31. Which of the following would be the best title for the passage?A. Is a Long Nap Really Good for You?B. Benefits for Your Best NapC. Tips for Napping at WorkD. Can Napping Lift You Up?CIf you are a recent social science graduate who has had to listen to jokes about unemployment(失业) from your computer major(专业课) classmates, you may have had the last laugh. There are many advantages for the social science major because this high-tech“Information Age”requires people who are flexible(灵活的) and whohave good communication skills.There are many social science majors in large companies who fill important positions. For example, a number of research studies found that social science majors had achieved greater managerial ( 管理的) success than those who had technical training or pre-professional courses. Studies show that social science majors are mostsuitable for change, which is the leading feature(特点) of the kind of high-speed, high-pressure, high-tech world we now live in.Social science majors are not only experiencing success in their long-term company jobs, but they are also finding jobs more easily. A study showed that many companies had filled a large percentage of their entry-level(入门的) positions with social science graduates. The study also showed that the most important quality in aperson who was looking for a job was communication skills, noted as "very important", by 92 percent of the companies. Social science majors have these skills, often without knowing how important they are. It is probably because of these skills that they have been offered different kinds of positions.Finally, although some social science majors may still find it more difficult than their technically trained classmates to land the first job, recent graduates report that they don't regret their choice of study.32. By saying that "you may have had the last laugh’" in the first paragraph, the author means that you may have_______.A.shared the jokes with computer majorsB. achieved as much as computer majorsC. stopped joking about computer majorsD. found jobs more easily than computer majors33. Compared with graduates of other subjects, social science graduates_______.A. are ready to change when situations changeB. are better able to deal with difficultiesC. are equally good at computer skillsD. are likely to give others pressure(压力)34.The underlined word “land" in the last paragraph probably means _______.A. keep for some timeB. successfully getC. start at onceD. lose regretfully35.According to the text, what has made it easy for social science graduates to find jobs?A. Willingness to take low-paid jobs.B. Readiness to get high-tech knowledge.C. Skills in expressing themselves.D. Part-time work experience.DSome people think only school children do not agree with their parents, however, it is not true.Communication is a problem for parents and children of all ages. If it's hard for you to communicate with your parents, don't worry about it. Here is some advice for you to bridge the generation gap (代沟).Don't argue (争辩) with your parents. Don't get to your parents when you are angry. Your parents probably won't consider your ideas if you are shouting at them. And you can't express (表达) yourself well if you are angry. Firstly keep calm. Then make sure you understand why you are unhappy. Next think about what you want to say to them. If you don't want to talk with them face to face, try writing a letter.Try to reach a compromise (和解). Perhaps you and your parents disagree on something. You can keep your opinions to yourself and try to accept each other. Michael's mother didn't agree with him about buying a toy. They argued about it. But she finally agreed with him. Michael bought the toy, but only played it on certain days.Of course, your parents might disagree with you on something. In these situations, it is especially important to show love and respect (尊敬) to them. It will help keep your relationship strong.Talk about your values. The values of your parents are probably different from yours. Tell your parents what you care about, and why. Understanding your values might help them see your purposes in life.A good relationship with your parents can make you a better and happier person. It is a pleasure to have a try!36. How many pieces of advice does the writer give us to keep a good relationship with our parents?A.2.B.3.C.4.D.5.37. According to the passage, _______have a communication problem.A. parents and teachersB. teachers and their studentsC. parents and children of all agesD. only school kids and their parents38.The underlined word “bridge" in the passage means “ _______”.A.建立B.通过C.消除D.到达39. If the values of your parents are different from yours, you'd better_______.A. argue with themB. keep away from themC. reach an agreement with themD. talk about your values to them40. What is the best title of the passage?A. How to be good parentsB. How to be a good childC. How to bridge the generation gapD. How to deal with family problems四、填空。