2026届珠海市九年级数学中考三模QS01会员专享黑白可打印训练卷B1第0036套（含参考答案、逐题解析、评分细则、压轴题讲评与学生作答空间）

珠海市九年级数学中考三模QS01黑白可打印训练卷B1第0036套2026届珠海市九年级数学中考三模QS01会员专享黑白可打印训练卷B1第0036套（含参考答案、逐题解析、评分细则、压轴题讲评与学生作答空间）数学试题卷考试时间：120分钟满分：120分适用对象：珠海市九年级版式：QS01黑白可打印注意事项：1.本卷分选择题、填空题、解答题三部分，共25题。请先检查页码、题号与印刷是否清楚。2.选择题每题只有一个正确选项；填空题直接写出最简结果；解答题需写出必要的计算、推理或说明。3.试题区提供学生作答空间，参考答案与逐题解析在试题卷后另页呈现，训练时请先独立完成。4.本卷按中考三模整卷节奏设计，建议限时完成，完成后依据评分细则自评或用于课堂讲评。答题栏（选择题）：题号12345678910答案一、选择题（本大题共10小题，每小题3分，共30分）每题只有一个正确选项，请将答案填入上方答题栏。1.计算(−2)²−|−3|的结果是（）A.−7B.1C.5D.72.函数y=√(3−x)+1/(x−2)中，自变量x的取值范围是（）A.x≤3B.x≠2C.x≤3且x≠2D.x≥3且x≠23.一组数据5，6，6，7，8，8，8的中位数和众数分别是（）A.6，8B.7，7C.7，8D.8，74.一元二次方程x²−4x+3=0的两个根是（）A.1和3B.−1和−3C.2和3D.−1和35.反比例函数y=k/x的图象经过点(2，−3)，则该函数图象经过的象限是（）A.第一、三象限B.第一、二象限C.第二、三象限D.第二、四象限6.两条平行线被第三条直线所截，若一对同旁内角中的一个角为58°，则另一个角为（）A.58°B.112°C.122°D.132°7.抛物线y=(x−1)²−4的顶点坐标和对称轴分别是（）A.(1，−4)，x=1B.(−1，−4)，x=−1C.(1，4)，x=1D.(−1，4)，x=−18.一个圆锥的底面半径为3cm，母线长为5cm，则它的侧面积为（）A.8πcm²B.15πcm²C.30πcm²D.45πcm²9.袋中有3个红球和2个白球，除颜色外完全相同。从中不放回地任取2个球，两个都是红球的概率是（）A.3/10B.2/5C.1/2D.3/510.若△ABC∽△DEF，且AB:DE=2:3，则△ABC与△DEF的面积比是（）A.2:3B.4:9C.3:2D.9:4二、填空题（本大题共6小题，每小题3分，共18分）请把最简结果填写在横线上，结果含单位时不要遗漏单位。11.因式分解：a²−4a+4=________。答：________________________________________12.方程2/(x−1)=3的解为x=________。答：________________________________________13.一列数2，5，8，11，…，按此规律，第20个数是________。答：________________________________________14.不等式组2x−1≤5，x+3>1的解集是________。答：________________________________________15.直角三角形的两条直角边长分别为6和8，则其内切圆半径为________。答：________________________________________16.半径为5的圆中，弦AB长为8，则圆心到弦AB的距离为________。答：________________________________________三、解答题（本大题共9小题，共72分）解答应写出文字说明、证明过程或演算步骤。17.（6分）计算与方程组（1）计算：√12+(−2)²−|1−√3|；（2）解方程组：2x+y=7，x−y=2。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（6分）先化简，再求值先化简(a²−4)/(a²−2a)÷(a+2)/a，再从a=3代入求值。请同时写出a的取值限制。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.（7分）统计与估计为了解九年级学生周末数学整理错题的时间，某班随机记录40名学生的整理时间，得到如下分组统计表。请根据表中数据回答问题。整理时间t（分钟）30≤t<6060≤t<9090≤t<120120≤t<150合计人数61216640（1）判断中位数所在的时间组；（2）用组中值估计平均整理时间；（3）若全年级共有900名学生，估计整理时间不少于90分钟的人数。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（7分）一次函数应用某蓄水池原有水50m³，打开排水阀后，水量y（m³）与排水时间x（分钟）近似成一次函数关系。已知10分钟后水量为25m³。（1）求y关于x的函数表达式，并写出实际取值范围；（2）当水量剩20m³时，已排水多少分钟；（3）若排水到剩余水量不超过10m³即需停止检修，最迟应在第几分钟停止。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（8分）概率与游戏规则四张卡片上分别写有1，2，3，4，背面完全相同。随机不放回地抽取两张，记两张卡片上的数字之和为S。（1）列出所有等可能结果，并求S为奇数的概率；（2）若规定“S为奇数甲胜，S为偶数乙胜”，这个游戏是否公平？说明理由；（3）请设计一个只利用两张卡片数字差的公平规则。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（8分）矩形中的线段与面积在矩形ABCD中，AB=8，AD=6。点E在边BC上，且BE=2，连接AE、DE。设A在左下角，B在右下角，C在右上角，D在左上角。（1）求AE的长；（2）求△ADE的面积；（3）若F为AE的中点，求DF的长。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.（10分）二次函数与线段最值已知抛物线y=x²−4x+3，直线l：y=x−1。（1）求抛物线的对称轴、顶点坐标及与x轴的交点；（2）求直线l与抛物线的交点A、B；（3）设P(t，t−1)是线段AB上一点，过P作PQ∥y轴交抛物线于Q，求线段PQ长度的最大值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.（10分）圆的切线与相似已知⊙O半径为5，点P在圆外，OP=13。过点P作⊙O的两条切线PA、PB，A、B为切点，连接AB，OP交AB于M。（1）求PA的长；（2）证明OP⊥AB；（3）求AB的长和PM的长。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.（10分）压轴综合：二次函数与动点抛物线经过A(−1，0)、B(5，0)、C(0，5)三点。点P(t，−t²+4t+5)在第一象限内的抛物线上，过P作PF∥y轴交直线BC于F，0<t<5。（1）求抛物线的函数表达式和顶点坐标；（2）用含t的式子表示PF，并求PF的最大值；（3）当PF=6时，求点P的坐标；（4）对于（3）中的两个点P，分别连接AP并交y轴于E，求E的坐标，比较CE的长度。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________附加演算与检查空间（黑白打印预留）本页用于补充演算、重做关键步骤和检查整卷。建议先检查选择题是否看清限定条件，再检查填空题结果是否最简，最后检查解答题是否写出必要过程、单位、取值范围与结论。自查要点：①分式与根式是否写出限制条件；②几何题是否说明垂直、平行、相似或全等的依据；③函数题是否写清点的坐标、取值范围和最值过程；④概率题是否确认每个结果等可能；⑤统计估计题是否说明组中值或样本比例的使用。需重点回看题号：________________________________________预计可追回分值：____________分____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案、逐题解析与评分细则本区按题号顺序给出参考答案、解析思路、易错提醒与步骤得分点。教师讲评时可结合学生卷面过程酌情扣分，结果正确但关键过程缺失的题目不宜给满分。一、选择题答案与解析1.答案：B。解析：(−2)²=4，|−3|=3，所以4−3=1。评分细则：答出B3分。易错点：注意概念、条件或符号，避免凭印象作答。2.答案：C。解析：√(3−x)要求3−x≥0，即x≤3；分母x−2不能为0，即x≠2，合并得x≤3且x≠2。评分细则：写出x≤31分；写出x≠2并合并2分。易错点：注意概念、条件或符号，避免凭印象作答。3.答案：C。解析：数据按从小到大排列已给出，共7个数，第4个数为7，所以中位数为7；出现次数最多的是8，所以众数为8。评分细则：中位数判断正确1分；众数判断正确并选C2分。易错点：注意概念、条件或符号，避免凭印象作答。4.答案：A。解析：x²−4x+3=(x−1)(x−3)，令其等于0，得x=1或x=3。评分细则：正确分解1分；得到两个根并选A2分。易错点：注意概念、条件或符号，避免凭印象作答。5.答案：D。解析：将点(2，−3)代入y=k/x，得−3=k/2，所以k=−6。k<0时，反比例函数图象在第二、四象限。评分细则：求出k=−61分；判断象限并选D2分。易错点：注意概念、条件或符号，避免凭印象作答。6.答案：C。解析：两直线平行，同旁内角互补。另一个角为180°−58°=122°。评分细则：写出互补关系1分；算得122°并选C2分。易错点：注意概念、条件或符号，避免凭印象作答。7.答案：A。解析：y=(x−1)²−4为顶点式，顶点坐标是(1，−4)，对称轴是x=1。评分细则：顶点坐标正确1分；对称轴正确并选A2分。易错点：注意概念、条件或符号，避免凭印象作答。8.答案：B。解析：圆锥侧面积公式为S=πrl，底面半径r=3，母线l=5，所以S=15πcm²。评分细则：写出或使用S=πrl1分；计算并选B2分。易错点：注意概念、条件或符号，避免凭印象作答。9.答案：A。解析：不放回抽取两个红球的概率为(3/5)×(2/4)=3/10。也可用组合数：从5个球中取2个共有10种，取2个红球有3种。评分细则：列出概率或组合思路1分；结果3/10并选A2分。易错点：注意概念、条件或符号，避免凭印象作答。10.答案：B。解析：相似三角形面积比等于相似比的平方。边长比为2:3，所以面积比为4:9。评分细则：知道面积比为平方比1分；结果4:9并选B2分。易错点：注意概念、条件或符号，避免凭印象作答。二、填空题答案与解析11.答案：(a−2)²。解析：a²−4a+4是完全平方三项式，等于(a−2)²。评分细则：写出完全平方形式3分。易错点：结果应化为最简形式，分式题需关注限制条件。12.答案：5/3。解析：2/(x−1)=3，两边乘以x−1，得2=3x−3，3x=5，x=5/3，且x≠1，符合题意。评分细则：去分母并列出2=3x−31分；求得x=5/3并检验2分。易错点：结果应化为最简形式，分式题需关注限制条件。13.答案：59。解析：数列每次增加3，第n个数为2+3(n−1)=3n−1，第20个数为60−1=59。评分细则：找出公差3或通项1分；求出592分。易错点：结果应化为最简形式，分式题需关注限制条件。14.答案：−2<x≤3。解析：由2x−1≤5得x≤3；由x+3>1得x>−2，合并得−2<x≤3。评分细则：分别解两个不等式2分；正确合并1分。易错点：结果应化为最简形式，分式题需关注限制条件。15.答案：2。解析：斜边长为√(6²+8²)=10。直角三角形内切圆半径r=(两直角边和−斜边)/2=(6+8−10)/2=2。评分细则：求出斜边101分；代入公式得22分。易错点：结果应化为最简形式，分式题需关注限制条件。16.答案：3。解析：圆心到弦的垂线平分弦，半弦长为4。设圆心到弦的距离为d，则d²+4²=5²，d=3。评分细则：利用垂径定理得到半弦41分；勾股求得32分。易错点：结果应化为最简形式，分式题需关注限制条件。三、解答题答案、解析与评分细则17.参考答案：（1）5+√3；（2）x=3，y=1。解析：（1）√12=2√3，(−2)²=4，因为1−√3<0，所以|1−√3|=√3−1。原式=2√3+4−(√3−1)=5+√3。

（2）由x−y=2得y=x−2，代入2x+y=7，得2x+x−2=7，3x=9，x=3，y=1。评分细则：得分点分值写出√12=2√3和绝对值化简2分计算得5+√31分代入或加减消元得到x=32分求出y=1并写成方程组解1分易错提醒：过程题以步骤为主要给分依据，最终结果应与题目条件相互检验。18.参考答案：化简结果为1；当a=3时，原式=1；限制：a≠0，a≠2，a≠−2。解析：原式=(a²−4)/(a²−2a)×a/(a+2)。因a²−4=(a−2)(a+2)，a²−2a=a(a−2)，所以原式=[(a−2)(a+2)]/[a(a−2)]×a/(a+2)=1。分式和除式有意义时，a不能为0、2、−2。a=3符合限制，故代入值为1。评分细则：得分点分值写出乘以倒数1分正确分解a²−4与a²−2a2分约分得到11分写出三个限制1分代入a=3得11分易错提醒：过程题以步骤为主要给分依据，最终结果应与题目条件相互检验。19.参考答案：中位数所在组为90≤t<120；平均整理时间约91.5分钟；估计900名学生中约495人整理时间不少于90分钟。解析：40名学生的第20、21个数据决定中位数。前两组累计人数为6+12=18，前3组累计人数为34，所以第20、21个数据都落在90≤t<120这一组。用组中值估计平均数：45×6+75×12+105×16+135×6=3660，3660÷40=91.5。整理时间不少于90分钟的人数占(16+6)/40=22/40=55%，所以900×55%=495。评分细则：得分点分值判断中位数组2分使用组中值列式2分求出平均数91.5分钟1分求出比例55%1分估计人数4951分易错提醒：过程题以步骤为主要给分依据，最终结果应与题目条件相互