2026届扬州市九年级数学中考压轴冲刺QS01黑白可打印标准付费预览仿真卷B1第0199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）

QS01黑白可打印仿真卷B1第0199套2026届扬州市九年级数学中考压轴冲刺QS01黑白可打印标准付费预览仿真卷B1第0199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）考试时间：120分钟满分：120分适用对象：扬州市九年级数学中考压轴冲刺备考QS01黑白可打印说明：本卷按整卷限时训练排版，试题区与参考答案区分开，主观题设置学生作答空间，适合课堂训练、周末自测与教师讲评。注意事项：1.答题前请检查页码与题号是否完整；2.选择题答案填入答题栏，填空题写在横线上；3.解答题必须写出必要过程、关键推理和单位；4.作答时保持书写清楚，遇到压轴题先完成可得分步骤。姓名：________________班级：________________得分：________________一、选择题（本大题共8小题，每小题3分，共24分。每题只有一个正确选项）1.计算|－2|＋(1/2)⁰的结果是（）A.1B.2C.3D.42.下列因式分解正确的是（）A.a²－4a＋4=(a－2)²B.a²＋4a＋4=(a＋4)²C.a²－4=(a－4)(a＋1)D.a²＋2a=a(a＋2)＋13.在平面直角坐标系中，点A(－2，3)，B(1，－1)，则线段AB的长为（）A.3B.4C.5D.64.若二次函数y=(k－1)x²的图像开口向上，且经过点P(2，8)，则k的值为（）A.－1B.1C.2D.35.不等式2x－5≤x＋1的解集是（）A.x≤6B.x≥6C.x≤－6D.x≥－66.圆O的半径为5，弦AB到圆心O的距离为3，则弦AB的长为（）A.4B.6C.8D.107.一个不透明袋中有3个红球、2个白球，它们除颜色外完全相同。从中不放回地任取2个球，两个球颜色相同的概率为（）A.1/5B.2/5C.3/5D.4/58.关于x的一元二次方程x²－4x＋m=0有两个相等的实数根，则m的值为（）A.－4B.0C.4D.8选择题答题栏题号12345678答案二、填空题（本大题共10小题，每小题3分，共30分。请把答案写在题中横线上）9.0.00036用科学记数法表示为__________。10.若式子√(a－1)/(a－3)有意义，则a的取值范围是__________。11.方程组x＋y=5，x－y=1的解为__________。12.反比例函数y=12/x的图像经过点(3，m)，则m=__________；当y=2时，x=__________。13.一个多边形的内角和为1260°，则这个多边形的边数是__________。14.一组数据5，6，6，7，8的中位数与众数之和为__________。15.半径为6、圆心角为60°的扇形面积为__________。16.直角三角形的两条直角边分别为6和8，则它的内切圆半径为__________。17.等差数列3，5，7，9，…的前10项和为__________。18.抛物线y=－(x－1)²＋4与x轴两个交点之间的距离为__________。三、解答题（本大题共7小题，共66分。解答应写出文字说明、证明过程或演算步骤）19.（8分）计算与化简：（1）计算：(√12－√3)×√3＋(π－3)⁰；（2）先化简，再说明取值限制：(a²－4)/(a²＋4a＋4)÷(a－2)/(a＋2)。学生作答空间：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（8分）某班50名学生完成一次中考数学限时训练，教师将得分（满分10分）整理如下表。得分5678910人数361114106（1）求这50名学生得分的平均数、中位数和众数；（2）从该班随机抽取1名学生，求其得分大于8分的概率；（3）若全年级480名学生参加同类训练，请估计得分不低于8分的人数。学生作答空间：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（8分）某校九年级组织扬州历史文化研学，租用讲解器有两种收费方案：甲方案收服务费20元，另按每人6元收费；乙方案收服务费50元，另按每人4.5元收费。设参加人数为x人，两种方案总费用分别为y甲、y乙。（1）分别写出y甲、y乙关于x的函数表达式；（2）当参加人数为多少时，两种方案费用相同？（3）若九年级72人参加，应选择哪种方案？可节省多少元？学生作答空间：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（10分）如图形文字描述：在△ABC中，AB=AC=10，BC=12，AD⊥BC，垂足为D。以D为圆心、4为半径作圆，圆与AD交于点E（E在AD上），过E作EF∥BC，分别交AB、AC于F、G。（1）求AD的长；（2）说明△AEF与△ABC相似，并求FG的长；（3）求四边形BFGC的面积。学生作答空间：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.（10分）在平面直角坐标系中，抛物线y=x²－4x＋3与x轴交于A、B两点（A在B左侧），顶点为C。（1）求A、B、C三点坐标；（2）求直线BC的函数表达式，并求它与y轴交点D的坐标；（3）点P在抛物线位于A、B之间的部分上，求△PAB面积的最大值。学生作答空间：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.（10分）某书店为九年级学生准备数学冲刺练习本，进价为每本12元。市场试售发现：当售价为16元时，每天可售出120本；在售价不低于16元且不高于30元的范围内，售价每提高1元，每天少售5本。设每本售价为x元，每天利润为w元。（1）当x=20时，每天售出多少本？每天利润是多少元？（2）写出w关于x的函数表达式；（3）若每天利润不少于900元，求x的取值范围；（4）售价定为多少元时，每天利润最大？最大利润是多少元？学生作答空间：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.（12分）压轴综合题：在平面直角坐标系中，抛物线C：y=－1/2x²＋3x与x轴交于O(0，0)、A(6，0)，顶点为P。点M在抛物线第一象限部分上，设M的横坐标为t（0<t<6），过M作MN⊥x轴，垂足为N。（1）求顶点P的坐标；（2）用含t的式子表示△OMA的面积S，并求S的最大值；（3）若S△OMN:S△MNA=2:1，求t的值及点M坐标；（4）过M作直线MQ∥OP，交x轴于Q。当Q在线段ON上时，求t的取值范围；并求当OQ=QN时点M的坐标。学生作答空间：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________主观题附加作答纸（可用于续写过程、补图、检验与订正）___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案、逐题解析、评分细则与压轴题讲评说明：本区供教师讲评、学生订正与家长督学使用。选择题、填空题给出规范答案；解答题给出关键步骤、易错点与分步得分。一、选择题答案与解析（每小题3分）1.答案：C。解析：|－2|=2，(1/2)⁰=1，两项相加为3。易错点是把非零数的零次幂误认为0。评分：选对得3分，错选或不选不得分。2.答案：A。解析：a²－4a＋4是完全平方公式，等于(a－2)²。B项应为(a＋2)²；C项应为(a－2)(a＋2)；D项不是因式分解。评分：选对得3分，错选或不选不得分。3.答案：C。解析：AB=√[(1＋2)²＋(－1－3)²]=√(9＋16)=5。坐标距离公式中横、纵坐标差都要平方。评分：选对得3分，错选或不选不得分。4.答案：D。解析：点P代入得8=(k－1)×2²，故k－1=2，k=3；此时k－1>0，图像开口向上。评分：选对得3分，错选或不选不得分。5.答案：A。解析：2x－5≤x＋1，移项得x≤6。移项时不等号方向不变，因为没有乘除负数。评分：选对得3分，错选或不选不得分。6.答案：C。解析：连接OA，作OM⊥AB，则M为AB中点。AM=√(5²－3²)=4，所以AB=8。评分：选对得3分，错选或不选不得分。7.答案：B。解析：同色共有C₃²＋C₂²=3＋1=4种，任取2个共有C₅²=10种，概率为4/10=2/5。评分：选对得3分，错选或不选不得分。8.答案：C。解析：两个相等实数根要求判别式Δ=(－4)²－4m=0，解得m=4。评分：选对得3分，错选或不选不得分。二、填空题答案与解析（每小题3分）9.答案：3.6×10⁻⁴。解析：0.00036的小数点向右移动4位得到3.6，所以指数为－4。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。10.答案：a≥1且a≠3。解析：根式要求a－1≥0，分母要求a－3≠0，两条件同时满足。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。11.答案：x=3，y=2。解析：两式相加得2x=6，x=3；代回x＋y=5得y=2。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。12.答案：m=4；x=6。解析：m=12÷3=4；当y=2时，2=12/x，得x=6。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。13.答案：9。解析：(n－2)×180°=1260°，n－2=7，n=9。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。14.答案：12。解析：按从小到大排列后中位数为6，出现次数最多的数据为6，和为12。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。15.答案：6π。解析：扇形面积=60/360×π×6²=6π。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。16.答案：2。解析：斜边为10，直角三角形内切圆半径r=(6＋8－10)/2=2。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。17.答案：120。解析：前10项为3到21，S₁₀=10×(3＋21)/2=120。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。18.答案：4。解析：令－(x－1)²＋4=0，得(x－1)²=4，x=－1或3，两交点距离为4。评分：答案等价且表达规范得3分；符号、范围或单位错误酌情扣1—2分。三、解答题参考答案、评分细则与讲评要点19.（8分）参考答案与解析（1）√12=2√3，所以(√12－√3)×√3=(2√3－√3)×√3=√3×√3=3；又(π－3)⁰=1，原式=4。（2）a²－4=(a－2)(a＋2)，a²＋4a＋4=(a＋2)²。原式=[(a－2)(a＋2)/(a＋2)²]×[(a＋2)/(a－2)]=1。取值限制：a≠－2且a≠2。评分细则：第（1）问化简√12得1分，零次幂得1分，结果得2分；第（2）问因式分解2分，乘除转化与约分1分，取值限制1分。易错点：分式除法要乘倒数，且原分母和除式分母均不能为0。20.（8分）参考答案与解析总分=5×3＋6×6＋7×11＋8×14＋9×10＋10×6=390，平均数=390÷50=7.8。第25、26个数据都落在8分组，中位数为8；人数最多的是8分，众数为8。得分大于8分的人数为10＋6=16，概率为16/50=8/25。得分不低于8分的人数比例为(14＋10＋6)/50=30/50=0.6，估计全年级人数为480×0.6=288。评分细则：平均数计算2分，中位数1分，众数1分，概率2分，估计人数2分。讲评要点：中位数要先定位第25、26个数据，概率要区分“大于8”与“不低于8”。21.（8分）参考答案与解析（1）甲方案：y甲=6x＋20；乙方案：y乙=4.5x＋50。（2）令6x＋20=4.5x＋50，得1.5x=30，x=20。因此20人时两种方案费用相同。（3）当x=72时，y甲=6×72＋20=452，y乙=4.5×72＋50=374，选择乙方案，节省452－374=78元。评分细则：函数表达式各1.5分，共3分；列方程与求解3分；比较费用与节省金额2分。易错点：服务费只收一次，不能按人数重复计算。22.（10分）参考答案与解析