2026届浙江省九年级数学中考二模模拟试卷（含答案详解与评分标准）

2026届浙江省九年级数学中考二模模拟试卷（含答案详解与评分标准）学校________班级________姓名________考号________考试时间120分钟满分120分考试节点中考二模适用对象2026届九年级注意事项：1．本试卷为浙江省九年级数学中考二模考前检测用卷，满分120分，考试时间120分钟。2．答题前，请将学校、班级、姓名、考号填写清楚；选择题答案填写在答题栏内。3．解答题应写出必要的文字说明、证明过程或演算步骤；作图题可先用铅笔作图，再用黑色字迹笔描清。4．全卷共三大题、22小题。选择题10小题，每小题3分，共30分；填空题6小题，每小题3分，共18分；解答题6小题，共72分。题型选择题填空题解答题总分题号1—1011—1617—22分值30分18分72分120分一、选择题（本大题共10小题，每小题3分，共30分。每小题只有一个正确选项）1．在实数-2，0，1/3，√5中，最小的数是（）A．-2B．0C．1/3D．√52．2026年浙江省某市预计参加中考人数约为6.82×10⁴人，将这个数写成普通计数法为（）A．6820B．68200C．682000D．0.6823．下列运算正确的是（）A．a³+a²=a⁵B．(a²)³=a⁶C．a⁶÷a²=a³D．(-2a)²=-4a²4．若式子√(x-3)在实数范围内有意义，则x的取值范围是（）A．x>3B．x≥3C．x<3D．x≤35．如图形语言描述：两条直线a∥b，直线c分别与它们相交，若一组同位角中较小的角为65°，则与它相邻的内角为（）A．25°B．65°C．115°D．130°6．从写有数字1，2，3，4的四张完全相同卡片中任意抽取一张，放回后再抽取一张，则两次抽到的数字之和为偶数的概率是（）A．1/4B．1/3C．1/2D．3/47．若关于x的一元二次方程x²-4x+m=0有两个不相等的实数根，则m的取值范围是（）A．m<4B．m≤4C．m>4D．m≥48．某班一次数学二模专项练习的成绩分布如下表，则该组数据的众数是（）成绩/分80859095人数51294A．80B．85C．90D．959．如图形语言描述：在⊙O中，弦AB的长为8，圆心O到弦AB的距离为3，则⊙O的半径为（）A．3B．4C．5D．610．已知二次函数y=x²-2x-3的图象与x轴交于A，B两点，与y轴交于C点。若点P在抛物线上且△ABP的面积为6，则符合条件的点P的个数是（）A．1B．2C．3D．4选择题答题栏：题号12345678910答案二、填空题（本大题共6小题，每小题3分，共18分）11．分解因式：x²-9=__________．12．若点P(2,m)在反比例函数y=6/x的图象上，则m=__________．13．一个多边形的内角和为1080°，则这个多边形的边数为__________．14．已知一组数据7,8,9,a,11的平均数为9，则a=__________．15．如图形语言描述：在Rt△ABC中，∠C=90°，AC=6，BC=8，点D是斜边AB的中点，则CD=__________．16．已知二次函数y=x²-4x+k的图象与x轴只有一个公共点，则k=__________．三、解答题（本大题共6小题，共72分。解答应写出文字说明、证明过程或演算步骤）17．（10分）为检验二模前基础运算掌握情况，完成下列各题：（1）计算：|-3|+(π-2026)⁰-√16+(-1)²；（2）解不等式组：{2x-1≥3,x+4<3x}，并把解集在数轴上表示出来。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（10分）某校九年级开展“二模前函数与统计专项训练”。从九年级学生中随机抽取40名学生的训练成绩，整理成如下频数表：成绩x/分60≤x<7070≤x<8080≤x<9090≤x≤100合计频数41018840（1）求被抽取学生成绩不低于80分的频率；（2）若该校九年级共有600名学生，请估计成绩不低于90分的学生人数；（3）在成绩不低于90分的学生中随机选2名参加经验交流。若其中男生5名、女生3名，请用列表或画树状图的方法求恰好选到1名男生和1名女生的概率。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）如图形语言描述：在△ABC中，AB=AC，点D是BC的中点。点E，F分别在AB，AC上，且AE=AF，连接ED，FD，EF。（1）求证：△ADE≌△ADF；（2）若AB=AC=10，BC=12，AE=6，求EF的长；（3）在第（2）问条件下，求四边形EBCF的面积。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）某文具店在二模复习阶段销售一种错题本。已知每本进价为8元，按每本12元销售时，每天可售出120本。经市场调查，售价每提高1元，每天少售出10本。设每本售价为x元，每天销售利润为w元。（1）当x=14时，每天可售出多少本？每天利润是多少元？（2）求w与x之间的函数表达式，并写出自变量x的实际取值范围；（3）若该店希望每天利润达到560元，并且尽量让学生负担较低的售价，应将售价定为多少元？____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（14分）如图形语言描述：AB是⊙O的直径，点C在⊙O上，过点C作⊙O的切线l，过点A作AD⊥l，垂足为D，连接AC，BC，OC。（1）求证：∠ACD=∠ABC；（2）若AB=10，BC=6，求AC的长；（3）在第（2）问条件下，求AD的长。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析说明：本答案给出主要解法和评分标准。不同解法只要逻辑正确、结果准确，可参照相应步骤给分；选择题与填空题每题均按题目分值给分。一、选择题答案与关键理由（每小题3分，共30分）题号12345678910答案ABBBCCABCD1．答案：A。负数小于零和正数，且-2小于其余三个数。2．答案：B。6.82×10⁴=68200。3．答案：B。幂的乘方法则：(a²)³=a⁶。其余选项分别混淆合并同类项、同底数幂除法和积的乘方符号。4．答案：B。二次根式有意义需被开方数非负，即x-3≥0，所以x≥3。5．答案：C。平行线同位角相等，所给角为65°；与它相邻的内角互为邻补角，故为180°-65°=115°。6．答案：C。两次抽取共有4×4=16种等可能结果。和为偶数需同奇偶：奇奇2×2=4种，偶偶2×2=4种，共8种，概率8/16=1/2。7．答案：A。判别式Δ=(-4)²-4m=16-4m。两个不相等实根需Δ>0，得m<4。8．答案：B。众数是出现次数最多的数据。表中85分对应人数12人，最多。9．答案：C。圆心到弦的垂线平分弦，半弦为4，半径r=√(3²+4²)=5。10．答案：D。抛物线与x轴交点满足(x-3)(x+1)=0，故AB=4。面积S=1/2·AB·|y_P|=6，得|y_P|=3。当y=3时，x²-2x-6=0有两个实根；当y=-3时，x²-2x=0有两个实根，所以共有4个符合条件的点。二、填空题答案与解析（每小题3分，共18分）11．答案：(x+3)(x-3)。平方差公式：x²-9=x²-3²=(x+3)(x-3)。12．答案：3。将P(2,m)代入y=6/x，得m=6/2=3。13．答案：8。设边数为n，则(n-2)×180°=1080°，解得n=8。14．答案：10。平均数为9，则7+8+9+a+11=45，得a=10。15．答案：5。直角三角形斜边中线等于斜边的一半，AB=√(6²+8²)=10，故CD=5。16．答案：4。图象与x轴只有一个公共点，判别式Δ=(-4)²-4k=0，得k=4。三、解答题答案、解析与评分标准（共72分）17．（10分）（1）|-3|+(π-2026)⁰-√16+(-1)²=3+1-4+1=1。评分标准：正确写出|-3|=3、(π-2026)⁰=1、√16=4、(-1)²=1各1分，计算结果1分，共5分。（2）由2x-1≥3得x≥2；由x+4<3x得x>2。两个条件同时成立，解集为x>2。数轴上用空心圆表示2，向右画线。评分标准：每个不等式解法各2分，写出公共解集1分，数轴表示正确1分；本小问满分5分，若只写x≥2或x>2的一个条件，最多得2分。18．（10分）（1）不低于80分的人数为18+8=26人，频率为26/40=0.65。（2）不低于90分的频率为8/40=0.2，估计全校人数为600×0.2=120人。（3）把5名男生记为M₁,M₂,M₃,M₄,M₅，3名女生记为G₁,G₂,G₃。从8人中任取2人共有C₈²=28种等可能结果；恰好1名男生和1名女生共有5×3=15种结果，所以概率为15/28。评分标准：第（1）问人数与频率各1分，共2分；第（2）问频率1分、估计人数2分，共3分；第（3）问列举或组合总数2分、有利结果2分、概率1分，共5分。19．（12分）（1）因为AB=AC，D是BC的中点，所以AD是等腰三角形底边上的中线，也是顶角平分线，即∠EAD=∠DAF。又AE=AF，AD为公共边，所以△ADE≌△ADF。（2）由AB=AC且AE=AF，得AE/AB=AF/AC=6/10=3/5，所以EF∥BC，△AEF∽△ABC。于是EF/BC=AE/AB=3/5，故EF=12×3/5=36/5。（3）因为AB=AC=10，D为BC的中点，所以BD=6，且AD⊥BC。在Rt△ABD中，AD=√(10²-6²)=8。由相似可知点E,F到A的比例为3/5，故EF到BC的距离为AD×(1-3/5)=16/5。四边形EBCF为梯形，面积S=((BC+EF)/2)×16/5=(12+36/5)×8/5=768/25。评分标准：第（1）问写出等腰三角形三线合一2分，利用边角边证明全等2分，共4分；第