2026新高一数学资料

新高一数学30天每日练原创可编辑资料ORG·2026.07PAGESTARTHERE｜10分钟开始使用2026—2027学年新高一数学初高中衔接30天每日练（集合函数不等式＋双卷摸底）每日3题＋4次周测＋入学摸底双卷｜答案·错因·学习节奏先确认适用对象与使用场景，再按最短路径完成一次闭环。文档中的表格均可直接替换字段、打印或复制到企业/班级现有模板。快速判断说明01这是什么围绕集合、代数运算、方程不等式、函数语言与图像安排30天训练，每天3题，配周测和双卷摸底。02适合谁初三毕业、新高一学生、家长与初高中衔接教师。03最短怎么开始每天20—25分钟；每7天做一次周测；第15天与第30天完成摸底卷。04会得到什么90道每日练、4次周测、2套摸底、答案与错因清单。05怎么打印/分发按天拆页打印或整册打印；答案部分建议后置发放。使用边界：衔接训练不替代学校课程；含参数与函数题应根据学生基础调整难度。一、30天路线图天数主题完成标准1集合与元素写关键步骤＋标错因＋口头复述1题2集合运算与区间写关键步骤＋标错因＋口头复述1题3代数式与因式分解写关键步骤＋标错因＋口头复述1题4一元二次方程写关键步骤＋标错因＋口头复述1题5不等式与区间写关键步骤＋标错因＋口头复述1题6函数概念与对应写关键步骤＋标错因＋口头复述1题7一次/二次函数图像写关键步骤＋标错因＋口头复述1题8周测一写关键步骤＋标错因＋口头复述1题9绝对值写关键步骤＋标错因＋口头复述1题10分式与定义域写关键步骤＋标错因＋口头复述1题11根式与限制条件写关键步骤＋标错因＋口头复述1题12方程与函数零点写关键步骤＋标错因＋口头复述1题13函数值与值域写关键步骤＋标错因＋口头复述1题14单调性初步写关键步骤＋标错因＋口头复述1题15摸底卷A写关键步骤＋标错因＋口头复述1题16集合包含与子集写关键步骤＋标错因＋口头复述1题17含参数不等式写关键步骤＋标错因＋口头复述1题18函数图像变换写关键步骤＋标错因＋口头复述1题19分段函数写关键步骤＋标错因＋口头复述1题20奇偶性直观写关键步骤＋标错因＋口头复述1题21周测二写关键步骤＋标错因＋口头复述1题22二次不等式写关键步骤＋标错因＋口头复述1题23零点与符号写关键步骤＋标错因＋口头复述1题24函数最值写关键步骤＋标错因＋口头复述1题25实际问题建模写关键步骤＋标错因＋口头复述1题26抽象函数代入写关键步骤＋标错因＋口头复述1题27周测三写关键步骤＋标错因＋口头复述1题28综合纠错写关键步骤＋标错因＋口头复述1题29摸底卷B写关键步骤＋标错因＋口头复述1题30总复盘写关键步骤＋标错因＋口头复述1题

二、30天每日练Day1｜集合与元素1.用列举法表示A={x∈Z｜-2≤x<3}。________________________________________________________________________________________________________________________________________________________________2.判断2、3是否属于集合B={x｜x²-5x+6=0}。________________________________________________________________________________________________________________________________________________________________3.写出小于10的正质数组成的集合。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day2｜集合运算与区间1.A={1,2,3,4}，B={3,4,5}，求A∩B。________________________________________________________________________________________________________________________________________________________________2.求A∪B。________________________________________________________________________________________________________________________________________________________________3.用区间表示-1<x≤4。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day3｜因式分解1.分解x²-9。________________________________________________________________________________________________________________________________________________________________2.分解2x²-8x。________________________________________________________________________________________________________________________________________________________________3.化简(x+2)²-(x-2)²。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

Day4｜一元二次方程1.解x²-5x+6=0。________________________________________________________________________________________________________________________________________________________________2.已知方程x²-4x+m=0有两个相等实根，求m。________________________________________________________________________________________________________________________________________________________________3.若x1+x2=7，x1x2=10，写出对应二次方程。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day5｜不等式与区间1.解2x-3>5。________________________________________________________________________________________________________________________________________________________________2.解-3x≤9。________________________________________________________________________________________________________________________________________________________________3.解不等式组x>1，x≤4。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day6｜函数概念1.判断y²=x是否表示y是x的函数。________________________________________________________________________________________________________________________________________________________________2.函数f(x)=2x-1，求f(3)。________________________________________________________________________________________________________________________________________________________________3.已知f(a)=2a+1=9，求a。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

Day7｜二次函数图像1.写出y=(x-2)²+1的顶点。________________________________________________________________________________________________________________________________________________________________2.y=-x²+4开口方向与最大值。________________________________________________________________________________________________________________________________________________________________3.求y=x²-4x+3的零点。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day8｜周测一1.A={x｜x²-4<0}，用区间表示A。________________________________________________________________________________________________________________________________________________________________2.解x²-5x+4=0。________________________________________________________________________________________________________________________________________________________________3.求y=x²-2x-3的顶点与零点。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day9｜绝对值1.|x|=5，求x。________________________________________________________________________________________________________________________________________________________________2.|x-2|<3，求x范围。________________________________________________________________________________________________________________________________________________________________3.化简|a|（已知a<0）。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

Day10｜分式与定义域1.函数f(x)=1/(x-3)的定义域。________________________________________________________________________________________________________________________________________________________________2.化简(x²-9)/(x-3)。________________________________________________________________________________________________________________________________________________________________3.解1/(x-1)=2。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day11｜根式与限制1.√(x-1)有意义，求x范围。________________________________________________________________________________________________________________________________________________________________2.化简√50。________________________________________________________________________________________________________________________________________________________________3.解√(x+1)=3。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day12｜方程与零点1.函数f(x)=x²-4，求零点。________________________________________________________________________________________________________________________________________________________________2.方程2^x=8，求x。________________________________________________________________________________________________________________________________________________________________3.若f(1)>0，f(2)<0，说明区间(1,2)内可能有什么？________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

Day13｜函数值与值域1.f(x)=x²+1，求f(-2)。________________________________________________________________________________________________________________________________________________________________2.y=2x+3，x∈[0,4]，求值域。________________________________________________________________________________________________________________________________________________________________3.y=(x-1)²，x∈[0,3]，求最小值。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day14｜单调性1.一次函数y=3x-2单调性。________________________________________________________________________________________________________________________________________________________________2.y=-2x+5单调性。________________________________________________________________________________________________________________________________________________________________3.y=x²在[0,+∞)上的单调性。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day15｜摸底卷A准备1.集合、方程、函数各写一个最易错点。________________________________________________________________________________________________________________________________________________________________2.把昨天错题重做1遍。________________________________________________________________________________________________________________________________________________________________3.限时完成卷A前3题。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

Day16｜子集与包含1.A={1,2}，写出所有子集。________________________________________________________________________________________________________________________________________________________________2.若A⊆B且B⊆A，A与B关系？________________________________________________________________________________________________________________________________________________________________3.空集与任意集合关系？________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day17｜含参数不等式1.若(m-1)x>0对x>0恒成立，求m范围。________________________________________________________________________________________________________________________________________________________________2.x²-2mx+m²≥0是否恒成立？________________________________________________________________________________________________________________________________________________________________3.若直线y=(a-2)x+1递增，求a。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day18｜图像变换1.y=x²向右平移2得到什么？________________________________________________________________________________________________________________________________________________________________2.y=|x|向上平移1。________________________________________________________________________________________________________________________________________________________________3.y=2x与y=2x+3位置关系。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

Day19｜分段函数1.f(x)=x+1(x≥0)，-x(x<0)，求f(2)、f(-3)。________________________________________________________________________________________________________________________________________________________________2.判断f(0)。________________________________________________________________________________________________________________________________________________________________3.画出两个分段的关键点。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day20｜奇偶性直观1.f(x)=x²满足f(-x)=?________________________________________________________________________________________________________________________________________________________________2.f(x)=x³满足f(-x)=?________________________________________________________________________________________________________________________________________________________________3.y=x²图像关于什么对称？________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day21｜周测二1.解|x-1|≤2。________________________________________________________________________________________________________________________________________________________________2.求f(x)=1/(x+2)定义域。________________________________________________________________________________________________________________________________________________________________3.判断x³的奇偶性。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

Day22｜二次不等式1.解x²-5x+6>0。________________________________________________________________________________________________________________________________________________________________2.解x²-4≤0。________________________________________________________________________________________________________________________________________________________________3.解-(x-1)(x+2)>0。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day23｜零点与符号1.f(x)=(x-1)(x+3)，写零点。________________________________________________________________________________________________________________________________________________________________2.在区间(-3,1)内f(x)符号。________________________________________________________________________________________________________________________________________________________________3.方程f(x)=0有几个实根？________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day24｜函数最值1.y=x²-4x+7最小值。________________________________________________________________________________________________________________________________________________________________2.y=-x²+6x-5最大值。________________________________________________________________________________________________________________________________________________________________3.y=2x+1，x∈[-2,3]最大值。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

Day25｜实际建模1.长方形周长20，设长x，写面积函数。________________________________________________________________________________________________________________________________________________________________2.出租车起步价10元含3km，超出每km2元，写x>3时费用函数。________________________________________________________________________________________________________________________________________________________________3.利润=收入-成本，用字母表示。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day26｜抽象函数代入1.已知f(x+1)=2x+3，求f(3)。________________________________________________________________________________________________________________________________________________________________2.f(x)=x²+ax，且f(1)=3，求a。________________________________________________________________________________________________________________________________________________________________3.若f(f(1))=5且f(1)=2，求f(2)。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day27｜周测三1.解x²-x-6≤0。________________________________________________________________________________________________________________________________________________________________2.求y=(x+1)²-4最小值与零点。________________________________________________________________________________________________________________________________________________________________3.写出函数图像平移的一条规则。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

Day28｜综合纠错1.重做最常见错因K题1道。________________________________________________________________________________________________________________________________________________________________2.重做最常见错因C题1道。________________________________________________________________________________________________________________________________________________________________3.用一句话解释“定义域先于化简”。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day29｜摸底卷B准备1.复述二次不等式解题步骤。________________________________________________________________________________________________________________________________________________________________2.复述函数零点与方程根关系。________________________________________________________________________________________________________________________________________________________________3.限时完成卷B前3题。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆Day30｜总复盘1.写出30天最稳定的3个知识点。________________________________________________________________________________________________________________________________________________________________2.写出仍需跟进的2个模块。________________________________________________________________________________________________________________________________________________________________3.写下开学第一周的数学行动。________________________________________________________________________________________________________________________________________________________________完成时间：____分钟错因：K/R/C/M/T自评：☆☆☆☆☆

入学摸底卷A建议用时：60分钟满分：100分训练重点：集合、方程、不等式与函数基础姓名：________________班级：________________日期：____年__月__日得分：________分作答规则：先独立限时完成，再核对答案；主观题保留关键过程。订正时至少写出“错因＋正确方法＋一道同类题”。1.A={1,2,3}，B={2,3,4}，求A∩B、A∪B。（8分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________2.解方程x²-7x+12=0。（8分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________3.解不等式组2x-1>3，x≤5。（8分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________4.函数f(x)=x²-2x-3，求顶点和零点。（12分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________5.求函数y=1/(x-2)的定义域。（8分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________6.解|x+1|<3。（10分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________7.解二次不等式x²-x-6≤0。（12分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________8.某商品成本x元，售价为1.3x元，每件另有固定包装费5元，写利润函数。（10分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________9.已知f(x+1)=3x-2，求f(5)。（10分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________10.写一段80字左右说明：为什么高中数学需要保留定义域和步骤？（14分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

入学摸底卷B建议用时：60分钟满分：100分训练重点：函数图像、含参数与综合表达姓名：________________班级：________________日期：____年__月__日得分：________分作答规则：先独立限时完成，再核对答案；主观题保留关键过程。订正时至少写出“错因＋正确方法＋一道同类题”。1.写出集合{x∈Z｜-3<x≤2}。（8分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________2.若直线y=(m-1)x+2递减，求m。（8分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________3.函数y=(x-2)²-1的顶点、对称轴和零点。（12分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________4.解分式方程1/(x-1)+1=3。（10分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________5.解二次不等式-x²+5x-6>0。（12分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________6.已知f(x)=x²+ax+1，且f(1)=4，求a与f(-1)。（10分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________7.将y=x²图像先向左1、再向下4，写解析式。（10分）___________________________________________________________________________________________________________________________________________________