2026届九年级数学中考二模A卷模拟试卷（含答案详解与评分标准）

九年级数学中考二模A卷请保持卷面整洁，答题步骤清楚。2026届九年级数学中考二模A卷模拟试卷（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分题型选择题填空题解答题总分分值24分18分78分120分注意事项1.本卷共24题，分选择题、填空题和解答题三部分。请在规定时间内完成全卷。2.答题前请将学校、班级、姓名、考号填写清楚。选择题请把选项填入答题表。3.计算题应写出主要过程；几何证明应写明依据；结果能化简的应化简。4.作图可先用铅笔，确定后加深；不得在题目旁写与答案无关的内容。选择题答题表题号12345678答案一、选择题（本大题共8小题，每小题3分，共24分）1.（3分）计算|−3|+(−2)²的结果是（）A.1B.5C.7D.−12.（3分）把0.00035用科学记数法表示为（）A.3.5×10⁻³B.35×10⁻⁵C.3.5×10⁻⁴D.35×10⁻⁴3.（3分）多项式x²−5x+6分解因式正确的是（）A.(x−2)(x−3)B.(x+2)(x−3)C.(x−1)(x−6)D.(x+2)(x+3)4.（3分）一个不透明袋中有3个红球、2个黄球、5个蓝球，这些球除颜色外完全相同。从中任取1个球，取到的球不是蓝球的概率是（）A.1/5B.1/2C.3/5D.2/55.（3分）点在一次函数y=−2x+3的图象上的是（）A.(0，−3)B.(1，1)C.(2，1)D.(−1，−1)6.（3分）菱形的两条对角线长分别为8cm和6cm，则这个菱形的面积是（）A.14cm²B.20cm²C.24cm²D.48cm²7.（3分）若关于x的一元二次方程x²+2x+k=0有实数根，则k的取值范围是（）A.k≤1B.k<1C.k≥1D.k>18.（3分）一个圆锥的底面半径为3cm，母线长为5cm，则它的侧面积是（）A.8πcm²B.12πcm²C.10πcm²D.15πcm²二、填空题（本大题共6小题，每小题3分，共18分）9.（3分）计算：√18−√8=__________。10.（3分）方程(x−2)/3=(x+1)/5的解为x=__________。11.（3分）若一元二次方程x²−4x+m=0有两个相等的实数根，则m=__________。12.（3分）一组数据7，9，9，10，12，14的众数是__________。13.（3分）正六边形的一个外角的度数是__________。14.（3分）半径为4cm、圆心角为90°的扇形面积是__________cm²。三、解答题（本大题共10小题，共78分）15.（6分）先化简，再求值：〔x/(x−2)²−1/(x−2)〕÷〔2/(x−2)〕，其中x=4。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________16.（6分）解不等式组：2x−1≤5，(x+3)/2>1，并写出它的所有整数解。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________17.（6分）某校九年级进行一分钟跳绳抽测，随机抽取50名学生，成绩分组和人数如下表。成绩x（次）120≤x<140140≤x<160160≤x<180180≤x<200人数816188（1）求样本中成绩不低于160次的学生所占百分比；（2）若全校九年级共有600名学生，估计成绩不低于160次的学生人数。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（6分）某地出租车收费标准为：3千米以内收费10元；超过3千米的部分，每千米收费2.4元。设行驶路程为x千米（x>3），车费为y元。求：（1）y关于x的函数表达式；（2）行驶8千米应付多少元；（3）若一次乘车付费34元，行驶路程是多少千米。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.（8分）在△ABC中，AB=AC，点D、E在BC上，且BD=CE。求证：（1）AD=AE；（2）∠BAD=∠CAE。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（8分）已知：P为⊙O外一点，PA、PB分别与⊙O相切于A、B两点，OP=10cm，⊙O半径为6cm。求：（1）切线长PA；（2）四边形PAOB的面积。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（8分）已知二次函数y=x²−4x+3。求：（1）图象的顶点坐标和对称轴；（2）图象与x轴的交点坐标；（3）当y≤0时，x的取值范围。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（8分）同一时刻，直立木杆高1.5m，影长2m；教学楼的影长为18m。（1）求教学楼的高度；（2）若在教学楼顶安装一根旗杆后，总影长变为22m，求旗杆的高度。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.（11分）在平面直角坐标系中，矩形ABCD的顶点为A(0，0)，B(8，0)，C(8，6)，D(0，6)。点P从A出发沿AB向B运动，点Q从B出发沿BC向C运动，二者同时出发，速度均为1个单位/秒，运动时间为t秒（0≤t≤6）。（1）写出P、Q两点的坐标；（2）求△DPQ的面积S与t的函数关系式；（3）求S的最小值及对应的t值；（4）当S=24时，求t的值。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.（11分）某文创店销售纪念笔，单件进价为10元。市场调查显示：售价为20元/件时，每天可售80件；售价每提高1元，每天少售4件。设售价为x元/件（20≤x≤35），日销售量为q件，日利润为W元。（1）写出q关于x的函数表达式；（2）写出W关于x的函数表达式；（3）售价为多少元时日利润最大？最大日利润是多少元？（4）若计划日利润不低于864元，求售价x的取值范围。作答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析评分说明：本卷满分120分。选择题每题3分，只有一个正确选项；填空题每题3分，结果等价且化简正确可得满分；解答题按关键过程、计算结果和书写结论分步给分。解答题中，若使用与参考解法不同但推理正确的方法，应按相同知识点和关键结论给分；若前一步计算错误但后续方法正确，可按实际完成的有效过程给相应过程分。板块题号范围分值主要考查内容选择题1—824分数与式、概率、函数、几何基础填空题9—1418分二次根式、方程、统计、几何量解答题15—2478分运算、证明、函数、相似、综合应用题号分值评分重点156分分式通分、除法转化、约分、代入求值166分两个不等式分别求解，公共解集和整数解完整176分读表求人数，计算百分比，用样本估计总体186分根据分段收费建立一次函数，代入和反解均需写过程198分利用等腰三角形底角相等，判定三角形全等并推出结论208分切线垂直半径，勾股定理求切线长，面积分割计算218分配方法求顶点，因式分解求交点，结合图象判断范围228分同一时刻物高与影长成比例，两次比例计算要区分总高度2311分建立坐标，列面积函数，配方求最值，解方程并检验范围2411分建立销售量和利润函数，配方求最大值，解利润不等式一、选择题答案与解析题号12345678答案CCABBCAD1.|−3|表示−3到0的距离，值为3；(−2)²=4，两个结果相加为7。其余选项未同时满足绝对值和乘方运算规则，选C。评分：选C得3分。2.科学记数法要求写成a×10ⁿ，且1≤a<10。0.00035的小数点向右移动4位得到3.5，因此指数为−4，故0.00035=3.5×10⁻⁴，选C。评分：选C得3分。3.二次项系数为1，常数项为6，一次项系数为−5。寻找两个数2和3，其积为6、和为5，所以x²−5x+6=(x−2)(x−3)，选A。评分：选A得3分。4.随机取1个球时，每个球被取到的可能性相同。不是蓝球包含红球和黄球，共3+2=5个，总球数为10个，概率为5/10=1/2，选B。评分：选B得3分。5.判断点是否在函数图象上，只需检验横坐标代入后所得纵坐标是否一致。把x=1代入y=−2x+3，得y=1，故(1，1)在图象上，选B。评分：选B得3分。6.菱形的两条对角线互相垂直，面积等于两条对角线乘积的一半。故S=8×6÷2=24cm²，选C。评分：选C得3分。7.一元二次方程有实数根的条件是判别式Δ≥0。本题中Δ=2²−4×1×k=4−4k，令4−4k≥0，得k≤1，选A。评分：选A得3分。8.圆锥侧面展开后是扇形，其面积公式可写为S=πrl，其中r为底面半径，l为母线长。代入r=3，l=5，得S=15πcm²，选D。评分：选D得3分。二、填空题答案与解析9.答案：√2。解析：√18−√8=3√2−2√2=√2。评分：填√2得3分。10.答案：13/2。解析：5(x−2)=3(x+1)，5x−10=3x+3，2x=13，x=13/2。评分：结果正确得3分。11.答案：4。解析：两个相等实数根时Δ=0，(−4)²−4m=0，m=4。评分：结果正确得3分。12.答案：9。解析：数据中9出现2次，其他数各出现1次，众数为9。评分：结果正确得3分。13.答案：60°。解析：正n边形的一个外角为360°/n，正六边形外角为360°/6=60°。评分：结果正确得3分。14.答案：4π。解析：扇形面积S=(90/360)×π×4²=4πcm²。评分：结果正确得3分。三、解答题答案详解与评分标准15.解：〔x/(x−2)²−1/(x−2)〕÷〔2/(x−2)〕=〔x/(x−2)²−(x−2)/(x−2)²〕×(x−2)/2=〔2/(x−2)²〕×(x−2)/2=1/(x−2)。当x=4时，原式=1/(4−2)=1/2。给定的x=4满足x≠2，代入有效。评分标准：通分正确得2分；把除法转化为乘法并约分正确得2分；代入x=4求值得1分；写出最终结论得1分。若未注明x≠2但化简过程正确，不扣过程分。16.解：由2x−1≤5，得2x≤6，x≤3。由(x+3)/2>1，得x+3>2，x>−1。所以不等式组的解集为−1<x≤3。若用数轴表示，−1处为空心点，3处为实心点，中间部分为公共解。整数解为0，1，2，3。评分标准：分别求出两个不等式的解各得