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[]
["小升初模块一标签",{"$nulls":4},"暂定序号","小升初",null,"暂定序号"]
["1数的认识","基本概念认识","整数的认识",null,"位值原理",1,"数论","整除特征",1]
[null,null,"分数的认识",null,"基本进位制",2,null,"数字谜",2]
[null,null,"小数的认识",null,null,3,null,"最值问题",3]
[null,null,"负数的认识",null,null,4,null,"因倍质合综合",4]
[null,null,"百分数的认识",null,null,5,null,"抽屉原理",5]
[null,null,"因数和倍数的认识",null,"“韩信点兵”类",6,null,"进位制",6]
[null,null,"质数和合数的认识",null,null,7,null,"韩信点兵类",7]
[null,null,"奇数和偶数的认识",null,null,8,null,"位值原理",8]
[null,"基本性质规律","分数的基本性质及应用",null,null,9,null,"余数的基本性质",9]
[null,null,"小数的基本性质及应用",null,null,10,null,"带余除法",10]
[null,null,"小数点位置的移动引起小数大小的变化",null,null,11,null,null,11]
[null,null,"奇偶运算性质",null,null,12,null,null,12]
[null,"基本方法","数的互化",null,null,13,null,null,13]
[null,null,"数的读写",null,null,14,null,null,14]
[null,null,"数的大小比较",null,null,15,null,null,15]
[null,null,"数的改写和近似",null,null,16,null,null,16]
[null,null,"倒数",null,null,17,null,null,17]
[null,null,"最大公因数和最小公倍数",null,"分解质因数法求大因小倍",18,null,null,18]
[null,null,"最简分数",null,null,19,null,null,19]
[null,null,"互质",null,null,20,null,null,20]
[null,null,"分解质因数",null,null,21,"几何","等积变形",21]
[null,"常见的量","计量单位的认识及应用",null,null,22,null,"等高模型",22]
[null,null,"单位换算",null,null,23,null,"平移旋转对称的应用",23]
["2数的运算","计算法则","基本运算","计算","等差数列",24,null,"图形的拼组",24]
[null,null,"四则混合运算",null,"大数的计算",25,null,"求图形面积的方法综合",25]
[null,"运算定律","加法交换律",null,"简便计算-分数裂项",26,null,"几何中的比例",26]
[null,null,"加法结合律",null,"简便计算-整体约分",27,null,"圆和扇形综合",27]
[null,null,"乘法交换律",null,"简便计算-连锁约分",28,null,"正方体和长方体综合",28]
[null,null,"乘法结合律",null,"简便计算-换元法",29,null,"圆柱与圆锥综合",29]
[null,null,"乘法分配律",null,"简便计算-分配律",30,null,"格点与割补",30]
[null,null,"简便运算",null,"简便计算-提取公因数"]
[null,null,"加减法的意义和各部分间的关系",null,"数表分析"]
[null,null,"乘除法的意义和各部分间的关系",null,null,31,"应用题","平均数应用题",31]
["3代数与方程","基本认识和性质","等式的基本认识和性质",null,null,32,null,"列方程解应用题",32]
[null,null,"方程的基本认识",null,null,33,null,"牛吃草问题",33]
[null,"基本方法及应用","用字母表示数",null,null,34,null,"经典应用题",34]
[null,null,"代数式及其运算",null,null,35,null,"分百应用题",35]
[null,null,"方程的解",null,null,36,null,"比例应用题",36]
[null,null,"列方程",null,null,37,null,"工程问题",37]
["4比和比例","认识与性质","比的认识和基本性质",null,null,39,null,"经济问题",39]
[null,null,"比例的认识和基本性质",null,null,40,null,"浓度问题",40]
[null,"应用","化简比和求比值",null,null,41,"行程","基本相遇追及",41]
[null,null,"解比例",null,null,42,null,"火车过桥",42]
[null,null,"比例尺",null,null,43,null,"流水行船",43]
[null,null,"正比例和反比例",null,null,44,null,"环形跑道",44]
["5平面几何","图形的基本认识","点、线、角的基本认识",null,null,45,null,"比例法解行程",45]
[null,null,"垂直与平行的特征与性质",null,null,46,null,"多人行程",46]
[null,null,"平面图形（直线型）的基本认识",null,null,47,null,"多次行程",47]
[null,null,"平面图形（圆和扇形）的基本认识",null,null,48,null,"变速行程",48]
[null,"测量与作图","测量与作图",null,null,49,null,"扶梯与发车",49]
[null,"公式计算","平面图形（直线型）周长公式及应用",null,null,50,null,"时钟问题",50]
[null,null,"平面图形（直线型）的内角和",null,null,51,"组合","加乘原理",51]
[null,null,"平面图形（直线型）面积公式及应用",null,null,52,null,"逻辑推理",52]
[null,null,"平面图形（圆和扇形）周长公式及应用",null,null,53,null,"数独、数阵图、幻方",53]
[null,null,"平面图形（圆和扇形）面积公式及应用",null,null,54,null,"体育比赛中的数学",54]
[null,null,"组合图形",null,null,55,null,"计数",55]
[null,"方法","面积关系",null,null,56,null,"容斥原理",56]
[null,"图形与变换","平移、旋转、对称",null,null,57,null,"操作类智巧趣题",57]
[null,"方向与位置","位置",null,null,58,null,"统筹与最优化",58]
[null,null,"方向",null,null,59,null,"找规律与周期",59]
["6立体几何","基本认识","三视图",null,null,60,null,"统计与可能性",60]
[null,null,"长方体正方体的基本认识",null,null,61,null,"统计图和统计表",61]
[null,null,"立体图形展开图",null,null,62,null,"必胜策略",62]
[null,null,"立体图形的容积",null,null,63,null,null,63]
[null,null,"圆柱和圆锥的认识",null,null,64,null,null,64]
[null,"公式计算","长方体和正方体棱长和的计算公式及应用",null,null,65,null,null,65]
[null,null,"长方体和正方体表面积的计算公式及应用",null,null,66,null,null,66]
[null,null,"长方体和正方体体积的计算公式及应用",null,null,67,null,null,67]
[null,null,"圆柱的表面积公式及应用",null,null,68,null,null,68]
[null,null,"圆柱和圆锥的体积公式及应用",null,null,69,null,null,69]
[null,null,"组合体",null,null,70,null,null,70]
[null,"方法","旋转体",null,null,71,null,null,71]
[null,null,"水中浸物",null,null,72,null,null,72]
["7统计与可能性",null,"统计",null,null,73,null,null,73]
[null,null,"可能性",null,null,74,null,null,74]
[]
[]
[]
[]
[]
[{"$nulls":6},"50个左右"]
[]
[{"$nulls":6},"例如行程问题"]
[{"$nulls":6},"怎么延展"]
[{"$nulls":6},"标准如何定？"]

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[]
[null,null,"基础知识点",{"$nulls":4},"小升初技能应用",{"$nulls":9},"刷题建议"]
[null,"出105道",{"$nulls":7},"具体层级"]
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[null,"打散",null,null,null,"改写和近似数",1,null,"数字问题",null,null,1,{"$nulls":4},1]
[null,"25+10",null,null,"数的整除","因数和倍数",1,null,"整除特征",{"$nulls":7},1]
[{"$nulls":5},"2，5，3的倍数特征",1,null,"质数合数综合",null,null,2,null,null,null,1,1]
[{"$nulls":5},"奇数和偶数",1,null,"因数和倍数综合",null,null,2,null,null,null,1,1]
[{"$nulls":5},"质数和合数",1,null,"余数问题",null,null,2,null,null,1,null,1]
[{"$nulls":5},"分解质因数",1,"经典应用题板块（常用数量关系）","具体内容",null,"语言理解","归纳递推","空间想象","转化","计算","逻辑"]
[{"$nulls":5},"最大公因数和最小公倍数",1,null,"和差倍问题",{"$nulls":7},1,"基本数量关系的理解"]
[{"$nulls":4},"小数","小数的基本认识",1,null,"一般复合应用题",{"$nulls":7},1,"解题思路和方法的总结"]
[{"$nulls":5},"小数点移动引起小数大小的变化",1,null,"还原类问题",{"$nulls":7},1]
[{"$nulls":5},"小数的分类",1,null,"盈亏问题","  ",{"$nulls":6},1]
[{"$nulls":4},"分数","分数的基本认识",1,null,"基本分百应用题",{"$nulls":7},1]
[{"$nulls":5},"分数的分类",1,null,"抓不变量-调整比例法",{"$nulls":7},1,"   "]
[{"$nulls":5},"倒数",1,null,"工程问题-交替工作",{"$nulls":7},1]
[{"$nulls":5},"分数的基本性质（约分、通分、最简分数）",1,null,"溶液浓度问题",{"$nulls":7},1]
[{"$nulls":5},"比较大小",1,null,"商品利润问题",{"$nulls":7},1]
[{"$nulls":5},"假分数与带分数的互化",1,null,"基本相遇追及",{"$nulls":7},1]
[{"$nulls":4},"百分数","百分数的基本认识",1,null,"环形跑道和时钟问题",{"$nulls":7},1,"   "]
[{"$nulls":5},"分小百的互化",1,null,"鸡兔同笼类分析",{"$nulls":7},1]
[{"$nulls":5},"成数、折扣",1,"计算板块","具体内容",null,"语言理解","归纳递推","空间想象","转化","计算","逻辑"]
[{"$nulls":5},"税率和利率",1,null,"简便计算技能-裂项",{"$nulls":7},1]
[{"$nulls":4},"正负数","正负数的基本认识",1,null,"简便计算技能-乘法分配律",{"$nulls":7},1]
[null,null,null,"数的运算","基本运算","整数小数加减法",1,null,"简便计算技能-连锁约分",{"$nulls":7},1]
[{"$nulls":5},"分数加减法",1,null,"等量代换",{"$nulls":7},1]
[{"$nulls":5},"整数小数乘除法",1,null,"数列数表",{"$nulls":7},1]
[{"$nulls":5},"分数乘除法",2,null,"定义新运算",{"$nulls":7},1]
[{"$nulls":4},"四则混合运算","混合运算",2]
[{"$nulls":5},"混合运算的逆运算",1,"几何板块","具体内容",null,"语言理解","归纳递推","空间想象","转化","计算","逻辑"]
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[{"$nulls":5},"乘方的运算",1,null,"计算公式的综合应用",{"$nulls":7},1]
[{"$nulls":4},"估算","数的估算",1,null,"技能-差不变求面积",{"$nulls":7},1]
[{"$nulls":4},"带余除法","带余除法",1,null,"技能-整体考虑",{"$nulls":7},1]
[{"$nulls":4},"运算定律","交换律（加法、乘法）"]
[{"$nulls":5},"结合律（加法、乘法）",1,null,"技能-包含与排除",{"$nulls":7},1]
[{"$nulls":5},"乘法分配律",null,null,"立体图形的分割与拼组",{"$nulls":7},1]
[{"$nulls":5},"提取公因数",1]
[{"$nulls":4},"变化规律","和、差的变化规律",1,"组合","具体内容",null,"语言理解","归纳递推","空间想象","转化","计算","逻辑"]
[{"$nulls":5},"积、商的变化规律",1,null,"计数",{"$nulls":7},1]
[{"$nulls":4},"计量单位","常用的计量单位以及换算关系",1,null,"抽屉原理和最不利原则",{"$nulls":7},1]
[null,null,null,"式与方程","用字母表示数","用字母表示数",1]
[{"$nulls":5},"代数求值",1]
[{"$nulls":4},"简易方程","等式、方程的基本概念",1,null,"面积计算技巧-代数法"]
[{"$nulls":5},"解方程",1,null,"面积计算技巧-和差法"]
[null,null,null,"比和比例","比","比的基本认识",1,null,"面积计算技巧-转化法"]
[{"$nulls":5},"比的基本性质、化简比及求比值",1,null,"面积计算技巧-割补拼接法"]
[{"$nulls":5},"按比分配",1,null,"面积计算技巧-差不变原理"]
[{"$nulls":4},"比例","比例的意义和基本性质",1]
[{"$nulls":5},"解比例、组比例",1]
[{"$nulls":5},"比例尺",1]
[{"$nulls":5},"正比例和反比例",1]
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[{"$nulls":5},"平行、垂直的概念与特征",1]
[{"$nulls":4},"角","角的概念、分类"]
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[{"$nulls":4},"三角形","三角形的定义、特征",1]
[{"$nulls":5},"三角形的分类"]
[{"$nulls":5},"内角和计算",1]
[{"$nulls":5},"三角形的周长面积计算",1]
[{"$nulls":4},"四边形","基本直线图形的认识"]
[{"$nulls":5},"平面图形（长方形、正方形、平行四边形、梯形）的周长面积计算",1]
[{"$nulls":4},"圆和扇形","圆的特征"]
[{"$nulls":5},"圆的周长面积计算",1]
[{"$nulls":5},"圆的衍生图形（扇形、圆环等）的周长面积计算",1]
[{"$nulls":4},"组合图形","组合图形的计算",1]
[null,null,null,"立体图形","观察物体","三视图",1]
[{"$nulls":5},"立体图形展开图",1]
[{"$nulls":4},"立体图形的认识","长方体和正方体的特征与关系",1]
[{"$nulls":5},"圆柱和圆锥的特征与关系",1]
[{"$nulls":4},"立体图形的计算","长方体、正方体棱长和、表面积、体积的计算",1]
[{"$nulls":5},"圆柱表面积、体积的计算",2]
[{"$nulls":5},"圆锥体积的计算",1]
[{"$nulls":5},"水中浸物",1]
[null,null,null,"图形与变换","基本认识","平移",1]
[{"$nulls":5},"旋转",1]
[{"$nulls":5},"对称",1]
[null,null,null,"图形与位置","位置","用方向和距离确定物体的位置",1]
[{"$nulls":5},"用数对确定物体的位置"]
[]
[null,null,"统计与可能性","统计","统计表","单式复式统计表",1]
[{"$nulls":4},"统计图","条形、折线、扇形统计图"]
[{"$nulls":4},"数据分析","平均数、众数、中位数"]
[null,null,null,"可能性","语言描述","可能性的描述",1]
[{"$nulls":4},"大小计算","可能性的大小"]
[{"$nulls":4},"应用","游戏规则的公平性"]
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[null,"报告","知识点的漏洞"]
[null,null,"能力的分数"]
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[null,"解决方案","讲法教法问法"]
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[null,null,"列方程解应用题"]

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["计算专题"]
["基本功","整数小数加减法",2,"技能提升","繁分数的计算",1]
[null,"整数小数乘除法",1,null,"混合运算的逆运算",1]
[null,"分数加减法",2,null,"乘法分配律的应用",1]
[null,"分数乘除法",2,null,"提取公因数的应用",1]
[null,"分小百互化",1,null,"分数巧算-连锁约分",1]
[null,"假分数带分数的互化",1,null,"分数巧算-裂项",1]
[null,"求倒数",1,null,"整体代换思想",1]
[null,"括号",1,null,"解分数系数方程",1]
[null,"简单估算",1,null,"定义新运算",1]
[null,"化简比、求比值",1,null,"大小比较",1]
[null,"解基本方程",1,null,"混合运算-带中括号",2]
[null,"解比例方程",1]
[null,"代数求值",1]
[null,"大小比较",1]
[null,"单位换算",1]
[null,"求近似数",1]
["运算性质","奇数偶数运算性质",1]
[null,"0的运算性质",1]
[null,"加减法的意义和各部分间的关系",1]
[null,"乘除法的意义和各部分间的关系",1]
["运算定律","交换律（加法、乘法）",1]
[null,"结合律（加法、乘法）",1]
[null,"乘法分配律",1]
[null,"提取公因数",1]
["混合运算","混合运算-同级混合",1]
[null,"混合运算-四则混合",1]
[]
["组合专题"]
["基本概念和性质","整数的基本认识",null,"规律与特征","数字找规律",1]
[null,"小数的基本认识",null,null,"图形找规律",1]
[null,"有限小数和无限小数",null,null,"数列数表",1]
[null,"因数和倍数的认识",null,null,"涉及日期的周期计算",1]
[null,"质数和合数的认识",null,null,"2/3/5的倍数特征",2]
[null,"奇数和偶数的认识",null,"组合计数","枚举法",1]
[null,"分数的基本认识",null,null,"包含与排除",1]
[null,"分数的基本性质",null,null,"最不利原则",1]
[null,"真分数和假分数"]
[null,"最简分数"]
[null,"负数的认识"]
[null,"最大公因数和最小公倍数"]
[null,"比和比例的基本认识"]
[null,"正比例和反比例"]
[null,"比例尺"]
["统计与可能性","统计图"]
[null,"可能性"]
[]
["图形与空间"]
["平面几何","线段、直线、射线的概念与特征",1,"技能提升","组合图形求周长",1]
[null,"平行、垂直的概念与特征",1,null,"组合图形求面积",2]
[null,"角度",1,null,"公式应用-整体考虑",3]
[null,"三角形的定义、特征",1,null,"面积计算技巧-和差法",4]
[null,"内角和计算",1,null,"面积计算技巧-等高模型",5]
[null,"三角形的周长",1]
[null,"三角形的面积",1]
[null,"四边形（梯形）的周长面积计算",1]
[null,"圆的面积计算",1]
[null,"圆的周长计算",1]
["立体几何","三视图",1]
[null,"立体图形展开图",1]
[null,"长方体、正方体棱长和的计算",1]
[null,"长方体、正方体表面积、体积的计算",1]
[null,"圆柱侧面积、表面积计算",1]
[null,"圆柱体积计算",1]
[null,"圆锥体积的计算",1]
["图形与变换","平移",1]
[null,"旋转",1]
[null,"对称",1]
["图形与位置","用方向和距离确定物体的位置",1]
[]
["数量关系（应用题）"]
["基本功","基本数量关系"]

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[{"$nulls":6},"选项指向的问题","能力分值",{"$nulls":6},"题目所暴露的问题","家长误以为的问题","问题的归属"]
["数论＋组合","题目编号","题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法","题目来源"]
[null,1,"2019年李哮天的生日是星期四，那么2020年李哮天的生日是星期几？","涉及日期的周期计算问题","A","A. 星期四","未掌握周期的计算方案",1,1,{"$nulls":4},"日期周期计算很多学生的痛点，原因在于学生①对于周期的起始点找不准；②没有考虑到闰年的情况；解决方案：加强对找周期起始点的训练",{"$nulls":4},"日期周期计算很多学生的痛点，原因在于学生①对于周期的起始点找不准；②没有考虑到闰年的情况","天省真题改编"]
[{"$nulls":4},"B","B. 星期五","未考虑到闰年的情况"]
[{"$nulls":4},"C","C. 星期六","考虑到了闰年，但没有想到有2种情况"]
[{"$nulls":4},"D","D. 星期四或星期五","考虑到了2种情况，但周期计算错误"]
[{"$nulls":4},"E","E. 星期五或星期六","正确选项"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,2,"一个2020位数A: ，用这个数A去除以3，得到的余数是多少？","整除特征","A","能整除，没有余数","对3的整除特征理解不足",2,1,{"$nulls":4},"属于校内有关3的整除特征的延伸；可重新学习3/9等整除特征的推导过程，并进行一定量的题目训练"]
[{"$nulls":4},"B",1,"正确选项"]
[{"$nulls":4},"C",2,"对3的整除特征理解不足"]
[{"$nulls":4},"D",3,"对3的整除特征掌握不足，且忽略了余数比除数小的要求"]
[{"$nulls":4},"E","数据太大，不会计算","对3的整除特征理解不足"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,3,"将14个完全一样的小球分成三堆，每堆至少2个，有几种分法？","计数","A","10种","正确选项",1,null,null,null,1,null,"分类计数方法未掌握，学生考虑问题不够全面；可加强对分类枚举的训练，培养学生严谨的逻辑思维"]
[{"$nulls":4},"B","16种","未考虑条件“每堆至少2个”"]
[{"$nulls":4},"C","24种","重复计数"]
[{"$nulls":4},"D","78种","未考虑条件“每堆至少2个”，且重复计数"]
[{"$nulls":4},"E","太多了，不想数","学生学业情绪问题"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,4,"三个互不相等的自然数的最大公因数是9，最小公倍数是90，满足要求的三个数一共有多少组？","因数和倍数综合","A","1组",null,2]
[{"$nulls":4},"B","2组"]
[{"$nulls":4},"C","3组","正确选项"]
[{"$nulls":4},"D","4组"]
[{"$nulls":4},"E","无法确定"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,5,"已知a、b均为质数，且有3a+5b=91,求a+b=","质数合数综合","A",null,null,2]
[{"$nulls":4},"B"]
[{"$nulls":4},"C"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,6,"一次数学测验只有两道题，结果全班有12人全对，第一道题有27人做对，第二道题有22人做错，那么两道题都做错的有多少人？","容斥原理","A","5人",{"$nulls":4},2,1,null,"加强对语言的理解和容斥原理中韦恩图工具的掌握"]
[{"$nulls":4},"B","6人"]
[{"$nulls":4},"C","7人","正确选项"]
[{"$nulls":4},"D","10人"]
[{"$nulls":4},"E","15人"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,7,"一个袋子里有一些球，这些球仅只有颜色不同。其中红球10个，白球9个，黄球8个，蓝球2个。李哮天闭着眼睛从中取出若干个，试问他至少要取多少个球，才能保证至少有4个球颜色相同？","最不利原则/极限思想","A","4个",{"$nulls":4},2,1,null,"极限思想；做错需要加强对“至少”“至多”这类词汇的理解"]
[{"$nulls":4},"B","11个"]
[{"$nulls":4},"C","12个","正确选项"]
[{"$nulls":4},"D","16个"]
[{"$nulls":4},"E","29个"]
["几何",null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,8,"已知△ABC的面积是2，△ADE的面积是5，△BDF的面积是15，△CEF的面积是30，那么△DEF的面积是多少？","面积计算技巧-和差法","A",null,"学生不能正确分析所求图形是由哪些已知图形组合而成",1,null,null,null,1,null,"训练图形分解拆解能力"]
[{"$nulls":4},"B"]
[{"$nulls":4},"C",null,"正确选项"]
[{"$nulls":4},"D",null,"学生不能正确分析所求图形是由哪些已知图形组合而成"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,9,"已知AE:AC=1:4,DB:AB=1:3,下列选项正确的是（      ）","面积计算技巧-等高模型","A",null,"学生对三角形的底边与面积关系理解不够",2,{"$nulls":4},1,"在应对小升初的考试中，可提高归纳总结能力"]
[{"$nulls":4},"B"]
[{"$nulls":4},"C"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E",null,"正确选项"]
["应用题",null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,10,"李哮天给班级活动准备纸飞机，前10分钟共折28个，后6分钟每分钟折10个，那么李哮天平均每分钟折纸飞机多少个？下列列式正确的是（     ）","平均数","A",null,"未掌握平均数计算数量关系式",1,null,null,1,null,null,"知识点：平均数应用题的练习；技能：提高语言理解能力"]
[{"$nulls":4},"B",null,"未掌握平均数计算数量关系式"]
[{"$nulls":4},"C",null,"正确选项"]
[{"$nulls":4},"D",null,"未掌握平均数计算数量关系式"]
[{"$nulls":4},"E",null,"未掌握平均数计算数量关系式"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,11,"下面表述正确的是（　　）","常用数量关系","A",null,"学生语言理解能力有待提升，未掌握基本数量关系的表述",1,null,null,1,null,null,"知识点：基本和差倍问题的练习；技能：提高语言理解能力"]
[{"$nulls":4},"B",null,"正确选项"]
[{"$nulls":4},"C",null,"学生语言理解能力有待提升，未掌握基本数量关系的表述"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,12,"科技书有100本，        ，那么文艺书有多少本？如果文艺书本数的列式为，横线上应填（       ）","分数乘法应用题","A","A.比文艺书多","不能准确判断单位“1”的量",1,null,null,1]
[{"$nulls":4},"B","B.比文艺书少","不能准确判断单位“2”的量"]
[{"$nulls":4},"C","C.文艺书比科技书多","正确选项"]
[{"$nulls":4},"D","D.文艺书比科技书少","不能准确找到问题对应的分率"]
[{"$nulls":4},"E","E.不会","学习态度问题"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,13,"看线段图列式，正确的是（　　）","分数除法应用题","A",null,"未能根据分数除法的意义列算式",1,null,null,1]
[{"$nulls":4},"B",null,"未能根据分数除法的意义列算式"]
[{"$nulls":4},"C",null,"未能根据分数除法的意义列算式"]
[{"$nulls":4},"D",null,"正确选项"]
[{"$nulls":4},"E",null,"未能根据分数除法的意义列算式"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题","归纳","计算","空间","语言","逻辑","转化","解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,14,"四年前，爸爸比儿子大36岁，今年，爸爸的年龄是儿子年龄的4倍，父子二人今年各是多少岁？下列对今年爸爸和儿子年龄的数量关系理解正确的是（     ）","年龄问题","A",null,"基本倍数关系出错",1,null,null,null,1]
[{"$nulls":4},"B",null,"基本倍数关系出错+未掌握年龄差不变这一数量关系"]
[{"$nulls":4},"C",null,"正确选项"]
[{"$nulls":4},"D",null,"未掌握年龄差不变这一数量关系"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题",{"$nulls":6},"解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,15,"某学校安排学生住宿，如果每间住12人，那么有34人没有宿舍；如果每间住14人，则空出4间宿舍。求：有多少间宿舍？有学生多少人？若设有x间宿舍，下列列式正确的是（      ）    ","盈亏问题","A",null,"未掌握盈亏问题数量关系"]
[{"$nulls":4},"B",null,"未掌握盈亏问题数量关系"]
[{"$nulls":4},"C",null,"正确选项"]
[{"$nulls":4},"D",null,"未掌握盈亏问题数量关系"]
[{"$nulls":4},"E",null,"未掌握盈亏问题数量关系"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题",{"$nulls":6},"解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,16,"#7. 下列列式正确的选项是（      ）","工程问题","A"]
[{"$nulls":4},"B"]
[{"$nulls":4},"C"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题",{"$nulls":6},"解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,17,null,null,"A"]
[{"$nulls":4},"B"]
[{"$nulls":4},"C"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题",{"$nulls":6},"解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,19,null,null,"A"]
[{"$nulls":4},"B"]
[{"$nulls":4},"C"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题",{"$nulls":6},"解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,20,null,null,"A"]
[{"$nulls":4},"B"]
[{"$nulls":4},"C"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题",{"$nulls":6},"解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,21,null,null,"A"]
[{"$nulls":4},"B"]
[{"$nulls":4},"C"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题",{"$nulls":6},"解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,22,null,null,"A"]
[{"$nulls":4},"B"]
[{"$nulls":4},"C"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E"]
[null,null,"题目内容","知识点","选项","选项内容","对应问题",{"$nulls":6},"解决方法","实际问题","常见问题","学习情绪问题","学科能力问题","解决方法"]
[null,23,null,null,"A"]
[{"$nulls":4},"B"]
[{"$nulls":4},"C"]
[{"$nulls":4},"D"]
[{"$nulls":4},"E"]
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[]
["专项诊断知识点排查表",{"$nulls":7},"题目序号"]
["基本知识点","一级标题","二级标题","三级标题","编号",null,null,null,"A卷","B卷","C卷",null,null,"得分","得分率"]
[null,"1数与量","基本概念认识","整数的认识","1a",1,{"$nulls":4},"#5",null,"第1章",{"$f":"SUM(F4:F29)","v":23},{"$f":"N4/23","v":1}]
[null,null,null,"分数/小数/百分数的认识","1b",1,null,null,"#7",null,null,null,"第2章",{"$f":"SUM(F30:F44)","v":13},{"$f":"N5/13","v":1}]
[null,null,null,"真分数、假分数和带分数","1c",1,null,null,"#8","#2",null,null,"第3章",{"$f":"SUM(F45:F64)","v":17},{"$f":"N6/17","v":1}]
[null,null,null,"负数的认识","1d",1,{"$nulls":4},"#7",null,"第4章",{"$f":"SUM(F65:F66)","v":2},{"$f":"N7/2","v":1}]
[null,null,null,"因数和倍数的认识","1e",{"$nulls":7},"第5章",{"$f":"SUM(F69:F92)","v":17},{"$f":"N8/17","v":1}]
[null,null,null,"质数和合数的认识","1f",1,null,null,"#6",null,null,null,"第6章",{"$f":"SUM(F93:F103)","v":10},{"$f":"N9/10","v":1}]
[null,null,null,"奇数和偶数的认识","1g",1,null,null,null,"#6",null,null,"第7章",{"$f":"SUM(F104:F110)","v":5},{"$f":"N10/5","v":1}]
[null,null,"基本性质规律","分数的基本性质及应用","1h",{"$nulls":7},"第8章",{"$f":"SUM(F111:F113)","v":3},{"$f":"N11/3","v":1}]
[null,null,null,"小数的基本性质及应用","1i",1,null,null,null,"#4",null,null,"SUM",{"$f":"SUM(N4:N11)","v":90},{"$f":"N12/90","v":1}]
[null,null,null,"2，5，3的倍数特征","1j",1,null,null,null,"#17"]
[null,null,"基本方法","数的互化","1k",1,null,null,"#2",null,null,null,"基本版",{"$f":"SUM(N4:N7)","v":55},{"$f":"N14/55","v":1}]
[null,null,null,"数的大小比较","1l",1,{"$nulls":4},"#9",null,"提升版",{"$f":"SUM(N8:N11)","v":35},{"$f":"N15/35","v":1}]
[null,null,null,"数的改写和近似","1m",1,{"$nulls":4},"#4"]
[null,null,null,"倒数","1n",1,{"$nulls":4},"#2"]
[null,null,null,"最大公因数和最小公倍数","1o",1,null,null,"#9"]
[null,null,null,"最简分数","1p",1,null,null,null,"#5"]
[null,null,null,"分解质因数","1q",1]
[null,null,"用字母表示数","用字母表示数带字母的运算","1r",1,null,null,null,"#16"]
[null,null,"简易方程","等式、方程的基本概念","1s"]
[null,null,null,"解方程","1t",1,null,null,"#15"]
[null,null,"比","比的基本认识（份数思想）","1u",1,null,null,null,"#11"]
[null,null,null,"比的基本性质、化简比及求比值","1v",1,{"$nulls":4},"#3"]
[null,null,null,"按比分配","1w",1,null,null,"#17"]
[null,null,"比例","比例的意义和基本性质、解比例、组比例","1x",1,null,null,null,"#15"]
[null,null,null,"比例尺","1y",1,{"$nulls":4},"#16","23题"]
[null,null,null,"正比例和反比例","1z",1,null,null,null,"#19"]
[null,"2数的运算","基本运算","整数小数加减法","2a",1,null,null,"#1"]
[null,null,null,"分数加减法","2b",2,null,null,null,"#1","#1"]
[null,null,null,"整数小数乘除法","2c",1,null,null,"#3"]
[null,null,null,"分数乘除法","2d",1,null,null,"#4"]
[null,null,"混合运算","混合运算-同级混合","2e",1,null,null,null,"#3"]
[null,null,null,"混合运算-四则混合","2f",1,null,null,"#5"]
[null,null,"运算定律","交换律（加法、乘法）","2g"]
[null,null,null,"结合律（加法、乘法）","2h"]
[null,null,null,"乘法分配律","2i",1,null,null,null,"#22"]
[null,null,null,"提取公因数","2j",1,{"$nulls":4},"#11"]
[null,null,"运算性质","奇数偶数运算性质","2k",1,{"$nulls":4},"#6"]
[null,null,null,"0的运算性质","2l"]
[null,null,null,"加减法的意义和各部分间的关系","2m",1,null,null,null,"#9"]
[null,null,null,"乘除法的意义和各部分间的关系","2n",1,{"$nulls":4},"#10"]
[null,null,"计量单位","常用的计量单位以及换算关系","2o",1,{"$nulls":4},"#18",13]
[null,"3图形与空间","平面图形的基本认识","点、线、角的基本认识","3a",1,null,null,"#14"]
[null,null,null,"垂直与平行的特征与性质","3b"]
[null,null,null,"平面图形（直线型）的基本认识","3c",1,null,null,null,"#7"]
[null,null,null,"平面图形（圆和扇形）的基本认识","3d"]
[null,null,"平面图形公式计算","平面图形（直线型）周长公式及应用","3e",1,{"$nulls":4},"#14"]
[null,null,null,"平面图形（直线型）的内角和","3f",1,{"$nulls":4},"#8"]
[null,null,null,"平面图形（直线型）面积公式及应用","3g",2,null,null,"#10","#12"]
[null,null,null,"平面图形（圆和扇形）周长公式及应用","3h",1,null,null,"#11"]
[null,null,null,"平面图形（圆和扇形）面积公式及应用","3i",1,null,null,null,"#13"]
[null,null,"图形与变换","平移、旋转、对称","3j",1,{"$nulls":4},"#17"]
[null,null,"方向与位置","方向和位置","3k",1,{"$nulls":4},"#15"]
[null,null,"立体几何基本认识","三视图","3l",1,null,null,"#20"]
[null,null,null,"长方体正方体的基本认识","3m"]
[null,null,null,"立体图形展开图","3n",1,null,null,null,"#8"]
[null,null,null,"圆柱和圆锥的基本认识","3o"]
[null,null,"立体图形公式计算","长方体和正方体棱长和的计算公式及应用","3p",1,null,null,"#13"]
[null,null,null,"长方体和正方体表面积的计算公式及应用","3q",1,{"$nulls":4},"#12"]
[null,null,null,"长方体和正方体体积的计算公式及应用","3r"]
[null,null,null,"圆柱的表面积公式及应用","3s",1,null,null,null,"#14"]
[null,null,null,"圆柱和圆锥的体积公式及应用","3t",2,null,null,"#12",null,"#13",17]
[null,"4统计与可能性","基本认识","统计","4a",1,{"$nulls":4},"#19"]
[null,null,null,"可能性","4b",1,null,null,null,"#18",null,2]
[{"$nulls":8},"题目序号"]
["技能提升","一级标题","二级标题","三级标题","编号",null,null,null,"A卷","B卷","C卷"]
[null,"5数量关系（应用题）","基本数量关系","用字母表示数量关系","5a",1,{"$nulls":4},"#23",17]
[null,null,null,"生活中常见的率","5b",1,null,null,"#16"]
[null,null,null,"折扣问题","5c",1,null,null,null,"#10"]
[null,null,null,"利润问题","5d",1,null,null,null,"#27"]
[null,null,null,"税收、利息问题","5e",1,{"$nulls":4},"#25"]
[null,null,null,"工作效率类问题","5f",1,null,null,"#18"]
[null,null,null,"合作类问题","5g",1,null,null,"#27"]
[null,null,null,"浓度问题","5h",1,null,null,"#21"]
[null,null,"经典应用题数量关系","平均数问题","5i",1,{"$nulls":4},"#24"]
[null,null,null,"和差倍问题-找1倍量","5j"]
[null,null,null,"年龄问题-差不变","5k",1,null,null,null,"#25"]
[null,null,null,"盈亏问题","5l",1,null,null,"#23"]
[null,null,null,"植树问题","5m"]
[null,null,null,"鸡兔同笼类","5n",1,null,null,null,"#20"]
[null,null,null,"牛吃草问题-分析变化量","5o"]
[null,null,null,"行程问题基本数量关系-s=vt","5p"]
[null,null,null,"平均速度","5q",1,null,null,"#28"]
[null,null,null,"相遇追及类问题","5r"]
[null,null,null,"火车过桥类","5s"]
[null,null,null,"流水行船类","5t"]
[null,null,"分百比应用题","分数乘法应用题","5u",1,null,null,"#19",null,"#20"]
[null,null,null,"分数除法应用题","5v",1,null,null,null,"#21"]
[null,null,null,"比和比例性质的拓展应用","5w",1,null,null,"#22"]
[null,null,null,"比例应用题-调整比例","5x",1]
[null,"6计算提升","简便计算","乘法分配律的应用","6a",1,{"$nulls":4},"#26",10]
[null,null,null,"提取公因数的应用","6b"]
[null,null,null,"分数巧算-连锁约分","6c",1,null,null,null,"#29"]
[null,null,null,"分数巧算-裂项","6d",1,null,null,"#25"]
[null,null,"硬算","解分数系数方程","6e",1,{"$nulls":4},"#28"]
[null,null,null,"混合运算-带中括号","6f",2,null,null,"#30","#28"]
[null,null,"方法技巧","大小比较-特殊值法","6g",1,null,null,null,"#23"]
[null,null,"规律与特征","规律探索","6h",1,{"$nulls":4},"#21"]
[null,null,null,"数列数表","6i",1,null,null,"#29"]
[null,null,null,"涉及日期的周期计算","6j",1,null,null,"#26"]
[null,null,null,"2/3/5的倍数特征","6k"]
[null,"7几何方法","公式应用","公式应用-整体考虑","7a",1,{"$nulls":4},"#30",5]
[null,null,null,"公式应用-圆柱和圆锥的倍比关系","7b",1,{"$nulls":4},"#27"]
[null,null,null,"组合图形求周长","7c",1,null,null,null,"#24"]
[null,null,null,"组合图形求面积-大减小","7d",1,{"$nulls":4},"#22"]
[null,null,"面积计算技巧","面积计算技巧-和差法","7e",1,null,null,null,"#30"]
[null,null,null,"面积计算技巧-等高模型","7f"]
[null,null,null,"面积计算技巧-等积变形","7g"]
[null,"8组合应用","组合计数","枚举法","8a",1,{"$nulls":4},"#29",3]
[null,null,null,"包含与排除","8b",1,null,null,null,"#26"]
[null,null,null,"最不利原则","8c",1,null,null,"#24"]

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[]
["小升初90题"]
["零级标题","一级标题","二级标题","三级标题","编号"]
["基本知识点","1数与量","基本概念认识","整数的认识","1a"]
[null,null,null,"分数/小数/百分数的认识","1b"]
[null,null,null,"真分数、假分数和带分数","1c"]
[null,null,null,"负数的认识","1d"]
[null,null,null,"因数和倍数的认识","1e"]
[null,null,null,"质数和合数的认识","1f"]
[null,null,null,"奇数和偶数的认识","1g"]
[null,null,"基本性质规律","分数的基本性质及应用","1h"]
[null,null,null,"小数的基本性质及应用","1i"]
[null,null,null,"2，5，3的倍数特征","1j"]
[null,null,"基本方法","数的互化","1k"]
[null,null,null,"数的大小比较","1l"]
[null,null,null,"数的改写和近似","1m"]
[null,null,null,"倒数","1n"]
[null,null,null,"最大公因数和最小公倍数","1o"]
[null,null,null,"最简分数","1p"]
[null,null,null,"分解质因数","1q"]
[null,null,"用字母表示数","用字母表示数带字母的运算","1r"]
[null,null,"简易方程","等式、方程的基本概念","1s"]
[null,null,null,"解方程","1t"]
[null,null,"比","比的基本认识（份数思想）","1u"]
[null,null,null,"比的基本性质、化简比及求比值","1v"]
[null,null,null,"按比分配","1w"]
[null,null,"比例","比例的意义和基本性质、解比例、组比例","1x"]
[null,null,null,"比例尺","1y"]
[null,null,null,"正比例和反比例","1z"]
[null,"2数的运算","基本运算","整数小数加减法","2a"]
[null,null,null,"分数加减法","2b"]
[null,null,null,"整数小数乘除法","2c"]
[null,null,null,"分数乘除法","2d"]
[null,null,"混合运算","混合运算-同级混合","2e"]
[null,null,null,"混合运算-四则混合","2f"]
[null,null,"运算定律","交换律（加法、乘法）","2g"]
[null,null,null,"结合律（加法、乘法）","2h"]
[null,null,null,"乘法分配律","2i"]
[null,null,null,"提取公因数","2j"]
[null,null,"运算性质","奇数偶数运算性质","2k"]
[null,null,null,"0的运算性质","2l"]
[null,null,null,"加减法的意义和各部分间的关系","2m"]
[null,null,null,"乘除法的意义和各部分间的关系","2n"]
[null,null,"计量单位","常用的计量单位以及换算关系","2o"]
[null,"3图形与空间","平面图形的基本认识","点、线、角的基本认识","3a"]
[null,null,null,"垂直与平行的特征与性质","3b"]
[null,null,null,"平面图形（直线型）的基本认识","3c"]
[null,null,null,"平面图形（圆和扇形）的基本认识","3d"]
[null,null,"平面图形公式计算","平面图形（直线型）周长公式及应用","3e"]
[null,null,null,"平面图形（直线型）的内角和","3f"]
[null,null,null,"平面图形（直线型）面积公式及应用","3g"]
[null,null,null,"平面图形（圆和扇形）周长公式及应用","3h"]
[null,null,null,"平面图形（圆和扇形）面积公式及应用","3i"]
[null,null,"图形与变换","平移、旋转、对称","3j"]
[null,null,"方向与位置","方向和位置","3k"]
[null,null,"立体几何基本认识","三视图","3l"]
[null,null,null,"长方体正方体的基本认识","3m"]
[null,null,null,"立体图形展开图","3n"]
[null,null,null,"圆柱和圆锥的基本认识","3o"]
[null,null,"立体图形公式计算","长方体和正方体棱长和的计算公式及应用","3p"]
[null,null,null,"长方体和正方体表面积的计算公式及应用","3q"]
[null,null,null,"长方体和正方体体积的计算公式及应用","3r"]
[null,null,null,"圆柱的表面积公式及应用","3s"]
[null,null,null,"圆柱和圆锥的体积公式及应用","3t"]
[null,"4统计与可能性","基本认识","统计","4a"]
[null,null,null,"可能性","4b"]
["技能提升","5数量关系（应用题）","基本数量关系","用字母表示数量关系","5a"]
[null,null,null,"生活中常见的率","5b"]
[null,null,null,"折扣问题","5c"]
[null,null,null,"利润问题","5d"]
[null,null,null,"税收、利息问题","5e"]
[null,null,null,"工作效率类问题","5f"]
[null,null,null,"合作类问题","5g"]
[null,null,null,"浓度问题","5h"]
[null,null,"经典应用题数量关系","平均数问题","5i"]
[null,null,null,"和差倍问题-找1倍量","5j"]
[null,null,null,"年龄问题-差不变","5k"]
[null,null,null,"盈亏问题","5l"]
[null,null,null,"植树问题","5m"]
[null,null,null,"鸡兔同笼类","5n"]
[null,null,null,"牛吃草问题-分析变化量","5o"]
[null,null,null,"行程问题基本数量关系-s=vt","5p"]
[null,null,null,"平均速度","5q"]
[null,null,null,"相遇追及类问题","5r"]
[null,null,null,"火车过桥类","5s"]
[null,null,null,"流水行船类","5t"]
[null,null,"分百比应用题","分数乘法应用题","5u"]
[null,null,null,"分数除法应用题","5v"]
[null,null,null,"比和比例性质的拓展应用","5w"]
[null,null,null,"比例应用题-调整比例","5x"]
[null,"6计算提升","简便计算","乘法分配律的应用","6a"]
[null,null,null,"提取公因数的应用","6b"]
[null,null,null,"分数巧算-连锁约分","6c"]
[null,null,null,"分数巧算-裂项","6d"]
[null,null,"硬算","解分数系数方程","6e"]
[null,null,null,"混合运算-带中括号","6f"]
[null,null,"方法技巧","大小比较-特殊值法","6g"]
[null,null,"规律与特征","规律探索","6h"]
[null,null,null,"数列数表","6i"]
[null,null,null,"涉及日期的周期计算","6j"]
[null,null,null,"2/3/5的倍数特征","6k"]
[null,"7几何方法","公式应用","公式应用-整体考虑","7a"]
[null,null,null,"公式应用-圆柱和圆锥的倍比关系","7b"]
[null,null,null,"组合图形求周长","7c"]
[null,null,null,"组合图形求面积-大减小","7d"]
[null,null,"面积计算技巧","面积计算技巧-和差法","7e"]
[null,null,null,"面积计算技巧-等高模型","7f"]
[null,null,null,"面积计算技巧-等积变形","7g"]
[null,"8组合应用","组合计数","枚举法","8a"]
[null,null,null,"包含与排除","8b"]
[null,null,null,"最不利原则","8c"]

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