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@@ -1,110 +1,1264 @@
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[
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{
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- "source": "P01",
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- "target": "P02",
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+ "source": "R01",
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+ "target": "R02",
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"type": "successor",
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- "comment": "知识点之间存在必要的学习衔接,用于帮助学生更顺畅地理解后续内容。"
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+ "comment": "理解整数和自然数后,进一步学习有理数分类。"
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},
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{
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- "source": "P02",
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- "target": "P03",
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+ "source": "R02",
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+ "target": "R03",
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"type": "successor",
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- "comment": "知识点之间存在必要的学习衔接,用于帮助学生更顺畅地理解后续内容。"
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+ "comment": "掌握有理数的种类后才能理解加减法的规则。"
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},
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{
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- "source": "P03",
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- "target": "P04",
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+ "source": "R02",
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+ "target": "R04",
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"type": "successor",
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- "comment": "知识点之间存在必要的学习衔接,用于帮助学生更顺畅地理解后续内容。"
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+ "comment": "乘除法基于有理数分类与符号理解。"
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},
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{
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- "source": "P04",
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- "target": "P05",
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+ "source": "R03",
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+ "target": "R04",
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"type": "successor",
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- "comment": "知识点之间存在必要的学习衔接,用于帮助学生更顺畅地理解后续内容。"
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+ "comment": "加减法是乘除法学习的基础。"
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},
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{
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- "source": "P05",
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- "target": "P06",
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+ "source": "R04",
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+ "target": "R05",
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"type": "successor",
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- "comment": "因式分解建立在乘法公式的理解基础上,掌握乘法公式有助于学生快速看出可分解结构。"
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+ "comment": "幂与指数运算基于乘法定义。"
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},
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{
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- "source": "P06",
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- "target": "F01",
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+ "source": "R03",
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+ "target": "A01",
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+ "type": "prerequisite",
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+ "comment": "理解有理数运算后才能学习代数式。"
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+ },
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+ {
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+ "source": "A01",
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+ "target": "A02",
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+ "type": "successor",
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+ "comment": "代数式概念是整式概念的基础。"
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+ },
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+ {
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+ "source": "A02",
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+ "target": "A03",
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+ "type": "successor",
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+ "comment": "整式分类后进入同类项合并学习。"
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+ },
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+ {
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+ "source": "A03",
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+ "target": "A04",
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+ "type": "successor",
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+ "comment": "掌握同类项后学习整式加减(去括号)。"
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+ },
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+ {
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+ "source": "A04",
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+ "target": "A05",
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+ "type": "successor",
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+ "comment": "整式加减是多项式乘法的基础。"
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+ },
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+ {
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+ "source": "A05",
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+ "target": "A06",
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+ "type": "successor",
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+ "comment": "特殊乘法公式在整式乘法基础上发展而来。"
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+ },
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+ {
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+ "source": "A06",
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+ "target": "A07",
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+ "type": "successor",
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+ "comment": "因式分解的公式法依赖乘法公式。"
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+ },
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+ {
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+ "source": "A07",
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+ "target": "A08",
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"type": "successor",
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- "comment": "分式化简通常需要先把分子分母因式分解,这是学生顺利完成约分的关键步骤。"
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+ "comment": "基础因式分解掌握后才能学习复杂技巧,如分组分解、十字相乘。"
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+ },
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+ {
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+ "source": "A08",
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+ "target": "A09",
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+ "type": "successor",
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+ "comment": "综合因式分解依赖多种因式分解方法的整合。"
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+ },
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+ {
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+ "source": "A07",
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+ "target": "F02",
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+ "type": "crosslink",
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+ "comment": "分式约分必须依赖因式分解。"
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+ },
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+ {
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+ "source": "A08",
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+ "target": "F06",
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+ "type": "crosslink",
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+ "comment": "复杂分式化简需要高级因式分解技巧。"
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},
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{
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"source": "F01",
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"target": "F02",
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"type": "successor",
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- "comment": "完成分式化简后,学生才能进行分式的加减乘除运算,这是题目的常见流程。"
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+ "comment": "理解分式基础后进入分式约分。"
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},
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{
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"source": "F02",
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- "target": "E05",
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+ "target": "F03",
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+ "type": "successor",
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+ "comment": "约分完成后才能进行通分。"
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+ },
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+ {
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+ "source": "F03",
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+ "target": "F04",
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"type": "successor",
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- "comment": "处理含分式的一元二次方程前,需要先完成分式运算的化简与统一。"
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+ "comment": "通分后才能进行分式加减。"
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},
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{
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- "source": "E01",
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- "target": "E02",
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+ "source": "F02",
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+ "target": "F05",
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"type": "successor",
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- "comment": "理解一元一次方程后,学生才能掌握方程组的求解方法,如代入法或加减法。"
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+ "comment": "分式乘除依赖因式约分。"
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},
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{
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- "source": "E02",
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- "target": "E05",
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+ "source": "F04",
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+ "target": "F06",
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"type": "successor",
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- "comment": "部分二次方程可通过构造方程组模型来理解,因此方程组经验有助于学生理解二次方程。"
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+ "comment": "分式运算基础完成后进入综合化简。"
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},
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{
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- "source": "H01",
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- "target": "H02",
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+ "source": "R07",
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+ "target": "RS01",
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+ "type": "prerequisite",
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+ "comment": "平方根建立在平方运算基础之上。"
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+ },
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+ {
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+ "source": "RS01",
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+ "target": "RS03",
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"type": "successor",
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- "comment": "掌握函数的基本概念后,学生才能理解一次函数的表示与图像特征。"
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+ "comment": "平方根性质引出根式基本性质。"
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},
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{
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- "source": "H02",
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- "target": "H03",
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+ "source": "RS03",
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+ "target": "RS04",
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"type": "successor",
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- "comment": "理解一次函数的变化特征有助于学生更好地理解二次函数的曲线规律。"
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+ "comment": "根式的基本性质用于根式化简。"
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},
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{
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- "source": "H03",
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- "target": "H04",
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+ "source": "RS04",
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+ "target": "RS05",
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"type": "successor",
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- "comment": "理解二次函数图像后,学生才能准确判断最值与开口方向。"
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+ "comment": "根式化简后进行混合运算。"
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},
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{
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- "source": "E05",
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- "target": "H04",
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+ "source": "A01",
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+ "target": "M01A",
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+ "type": "crosslink",
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+ "comment": "代数式基础用于实际情境的数量关系表达。"
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+ },
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+ {
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+ "source": "M01A",
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+ "target": "M01B",
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"type": "successor",
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- "comment": "求二次函数的最值往往依赖方程求顶点或开口方向,因此二次方程能力影响最值判断。"
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+ "comment": "从表达数量关系进入建模关系分析。"
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},
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{
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- "source": "H04",
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- "target": "F05",
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+ "source": "M01B",
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+ "target": "M01C",
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"type": "successor",
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- "comment": "压轴综合题往往以二次函数最值作为关键突破点,因此掌握最值是完成压轴题的重要能力。"
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+ "comment": "复杂代数式建模基于简单建模能力。"
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+ },
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+ {
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+ "source": "A04",
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+ "target": "E01A",
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+ "type": "prerequisite",
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+ "comment": "整式运算能力是学习一元一次方程基础。"
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+ },
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+ {
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+ "source": "A06",
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+ "target": "E05C",
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+ "type": "crosslink",
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+ "comment": "部分二次方程可通过因式分解求解。"
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+ },
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+ {
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+ "source": "RS04",
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+ "target": "H03",
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+ "type": "crosslink",
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+ "comment": "根式化简常用于二次函数顶点式相关计算。"
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},
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{
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- "source": "P06",
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- "target": "E05",
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+ "source": "A05",
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+ "target": "H02",
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"type": "crosslink",
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- "comment": "部分一元二次方程可通过因式分解直接求解,因此因式分解能力影响方程求解效率。"
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+ "comment": "一次函数代数式运算依赖整式运算。"
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},
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{
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- "source": "P06",
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+ "source": "A07",
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"target": "H04",
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"type": "crosslink",
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- "comment": "二次函数的解析式常需因式分解才能看出顶点与最值特征,因此因式分解是函数最值的重要辅助。"
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+ "comment": "二次函数最值常通过因式分解观察图像特征。"
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+ },
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+ {
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+ "source": "A04",
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+ "target": "E01A",
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+ "type": "prerequisite",
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+ "comment": "整式加减能力是一元一次方程移项与化简的基础。"
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+ },
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+ {
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+ "source": "A03",
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+ "target": "E01B",
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+ "type": "prerequisite",
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+ "comment": "同类项合并直接用于方程化简。"
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+ },
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+ {
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+ "source": "R03",
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+ "target": "E01A",
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+ "type": "prerequisite",
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+ "comment": "有理数加减是方程等式变形的根基。"
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+ },
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+ {
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+ "source": "E01A",
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+ "target": "E01B",
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+ "type": "successor",
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+ "comment": "掌握等式性质后才能熟练移项与合并同类项。"
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+ },
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+ {
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+ "source": "E01B",
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+ "target": "E01C",
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+ "type": "successor",
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+ "comment": "进行方程检验必须在化简后进行。"
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+ },
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+ {
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+ "source": "E01A",
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+ "target": "E02A",
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+ "type": "prerequisite",
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+ "comment": "方程组代入法需要一元一次方程的基础。"
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+ },
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+ {
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+ "source": "E01B",
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+ "target": "E02B",
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+ "type": "prerequisite",
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+ "comment": "加减法消元依赖方程移项与合并技巧。"
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+ },
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+ {
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+ "source": "E02A",
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+ "target": "E02C",
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+ "type": "successor",
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+ "comment": "掌握代入法后进入实际问题的建模应用。"
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+ },
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+ {
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+ "source": "E02B",
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+ "target": "E02C",
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+ "type": "successor",
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+ "comment": "加减法方法熟练后可用于应用方程组求解。"
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+ },
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+ {
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+ "source": "E01A",
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+ "target": "E03A",
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+ "type": "prerequisite",
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+ "comment": "不等式性质基于等式变形思想。"
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+ },
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+ {
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+ "source": "E03A",
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+ "target": "E03B",
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+ "type": "successor",
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+ "comment": "不等式性质掌握后进入不等式求解。"
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+ },
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+ {
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+ "source": "E03B",
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+ "target": "E03C",
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+ "type": "successor",
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+ "comment": "解集的表示必须在求解后进行。"
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+ },
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+ {
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+ "source": "E03C",
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+ "target": "E03D",
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+ "type": "successor",
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+ "comment": "不等式组的解集建立在单个不等式解集基础上。"
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+ },
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+ {
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+ "source": "F03",
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+ "target": "E04B",
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+ "type": "prerequisite",
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+ "comment": "分式方程去分母必须先掌握通分。"
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},
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{
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"source": "F02",
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- "target": "E04",
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+ "target": "E04B",
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+ "type": "prerequisite",
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+ "comment": "分式约分用于方程去分母后化简。"
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+ },
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+ {
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+ "source": "E04B",
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+ "target": "E04C",
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+ "type": "successor",
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+ "comment": "去分母后需检验增根,这是分式方程核心步骤。"
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+ },
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+ {
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+ "source": "E04A",
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+ "target": "E04B",
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+ "type": "successor",
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+ "comment": "理解分式方程基本概念后进入求解过程。"
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+ },
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+ {
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+ "source": "A06",
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+ "target": "E05C",
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+ "type": "prerequisite",
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+ "comment": "因式分解是部分一元二次方程求解的基础方法。"
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+ },
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+ {
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+ "source": "R05",
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+ "target": "E05A",
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+ "type": "prerequisite",
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+ "comment": "指数运算性质用于二次项处理与配平方化简。"
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+ },
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+ {
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+ "source": "E01B",
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+ "target": "E05A",
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+ "type": "prerequisite",
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+ "comment": "配方法需要熟练的一次项移项技巧。"
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+ },
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+ {
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+ "source": "E05A",
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+ "target": "E05B",
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+ "type": "successor",
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+ "comment": "求根公式由配方法推导而来,因此配方法是求根公式的基础。"
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+ },
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+ {
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+ "source": "E05B",
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+ "target": "E05E",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "根的分布判断依赖判别式与求根公式。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "E05B",
|
|
|
+ "target": "E05D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "韦达定理建立在求根公式与二次方程根的性质之上。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "E05C",
|
|
|
+ "target": "E05D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "部分韦达定理题可通过构造因式快速求解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "E05D",
|
|
|
+ "target": "H04",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "二次函数最值常依赖顶点坐标与韦达定理的结合。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "E01A",
|
|
|
+ "target": "APP_E1",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "行程问题建模以简单方程为基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "APP_E1",
|
|
|
+ "target": "APP_E4",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "行程模型常可转化为几何方程模型。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "E02C",
|
|
|
+ "target": "APP_E2",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "工程问题通常建立方程组。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "F06",
|
|
|
+ "target": "APP_E3",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "溶液浓度问题常涉及复杂分式化简。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "E05A",
|
|
|
+ "target": "APP_E4",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "几何方程建模常需用到配方法求关键点位置。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "E05B",
|
|
|
+ "target": "APP_E4",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "复杂几何模型需应用求根公式判断距离与位置关系。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "H02",
|
|
|
+ "target": "E02C",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "函数代数结构可用于建立二元一次方程组模型。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "A09",
|
|
|
+ "target": "E05A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "复杂二次方程常需先进行代数式综合化简才能求解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "RS03",
|
|
|
+ "target": "E05B",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "根式化简用于求根公式中根号部分的处理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G01A",
|
|
|
+ "target": "G01B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "点线面的概念是角的定义基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G01B",
|
|
|
+ "target": "G01C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "角的分类后学习角的度量。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G01C",
|
|
|
+ "target": "G01D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "掌握角度量后可理解对顶角与邻补角关系。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G01D",
|
|
|
+ "target": "G02A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "理解对顶角等概念后才能进入平行线判定。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G02A",
|
|
|
+ "target": "G02B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "平行线判定后学习其性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G02B",
|
|
|
+ "target": "G02C",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平移是平行线性质的几何变换基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G02B",
|
|
|
+ "target": "G03A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "平行线性质是理解三角形角关系的基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03A",
|
|
|
+ "target": "G03B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "三角形分类后学习三角形内角和与外角定理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03B",
|
|
|
+ "target": "G03C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "内角关系掌握后可学习三角形不等式与稳定性。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03C",
|
|
|
+ "target": "G03D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "三角形基本性质掌握后才能深入研究角平分线性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03D",
|
|
|
+ "target": "G03E",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "角平分线与中线、重心性质直接关联。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03B",
|
|
|
+ "target": "G03F",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "三角形角与边关系是全等三角形判定基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03F",
|
|
|
+ "target": "G03G",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "全等判定后进入几何证明与辅助线构造应用。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03F",
|
|
|
+ "target": "G04A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "四边形性质可以用全等三角形证明其定理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G04A",
|
|
|
+ "target": "G04B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "了解四边形分类后进入平行四边形判定。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G04B",
|
|
|
+ "target": "G04C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "判定后学习平行四边形性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G04C",
|
|
|
+ "target": "G04D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "矩形是平行四边形的特例,需先学性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G04C",
|
|
|
+ "target": "G04E",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "菱形性质依赖平行四边形性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G04D",
|
|
|
+ "target": "G04F",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "正方形兼具矩形与菱形所有性质,是综合性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G04E",
|
|
|
+ "target": "G04F",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "正方形也是菱形的特例。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03F",
|
|
|
+ "target": "G05A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "圆的性质中大量使用全等三角形(如等弧等弦)。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05A",
|
|
|
+ "target": "G05B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "弦与圆心距关系基于圆的基本结构。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05B",
|
|
|
+ "target": "G05C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "切线性质基于弦和圆心距关系。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05C",
|
|
|
+ "target": "G05D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "圆周角定理依赖切线与弦所构图形分析。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05D",
|
|
|
+ "target": "G05E",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "掌握圆周角定理后可学习扇形弧长与面积计算。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03D",
|
|
|
+ "target": "G06A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "角平分线常作为辅助线使用于几何证明。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03F",
|
|
|
+ "target": "G06A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "全等构造中常通过辅助线使用延长、平移等技巧。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G02C",
|
|
|
+ "target": "G06A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平移用于构造平行辅助线。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G06A",
|
|
|
+ "target": "G06B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "使用辅助线需要结合数形结合解决复杂应用。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G06B",
|
|
|
+ "target": "G06C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "数形结合能力是几何证明与推理的核心基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03F",
|
|
|
+ "target": "SIM01A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "相似三角形概念依赖全等三角形的边角对应关系。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G02B",
|
|
|
+ "target": "SIM02D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平行线分线段比例是相似三角形的重要来源。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03B",
|
|
|
+ "target": "PY01A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "理解三角形角关系后才能学习直角三角形性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05D",
|
|
|
+ "target": "SIM03A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "圆周角定理常用于相似三角形辅助关系构造。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G06C",
|
|
|
+ "target": "SIM03D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "几何综合证明能力直接影响相似压轴题的推理链。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G04C",
|
|
|
+ "target": "M04C1",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "三角形面积计算需用到平行四边形面积转化。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05E",
|
|
|
+ "target": "M04C3",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "扇形面积公式来自圆的弧长和圆周角关系。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03B",
|
|
|
+ "target": "H01",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "三角形角度计算常用于函数图像斜率判断与倾斜角。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05D",
|
|
|
+ "target": "H01",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "圆周角定理常用于函数图像几何性质的推导与证明。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04A1",
|
|
|
+ "target": "M04B1",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "长度单位的理解是计算三角形周长的基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04A1",
|
|
|
+ "target": "M04B2",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "掌握线段长度后才能正确计算四边形周长。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04A1",
|
|
|
+ "target": "M04B3",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "圆周长计算需要长度单位理解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03A",
|
|
|
+ "target": "M04B1",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "三角形周长计算依赖三边概念与分类。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G04A",
|
|
|
+ "target": "M04B2",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "四边形周长计算依赖四边形基本分类与性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05A",
|
|
|
+ "target": "M04B3",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "圆的基本性质是圆周长公式的来源。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04A2",
|
|
|
+ "target": "M04C1",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "面积单位是三角形面积计算的基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04A2",
|
|
|
+ "target": "M04C2",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "面积单位理解是平行四边形和梯形面积公式的基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04A2",
|
|
|
+ "target": "M04C3",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "扇形面积计算依赖面积单位与比例理解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04A2",
|
|
|
+ "target": "M04C4",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "组合图形面积需要单位面积理解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03B",
|
|
|
+ "target": "M04C1",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "三角形内角与高的位置关系是面积公式实际使用的关键。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G04C",
|
|
|
+ "target": "M04C2",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平行四边形性质与面积公式联系紧密。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05D",
|
|
|
+ "target": "M04C3",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "扇形面积公式来源于圆周角定理与弧长比例关系。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04C1",
|
|
|
+ "target": "M04C4",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "掌握基础三角形面积后才能处理组合图形面积。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04C2",
|
|
|
+ "target": "M04C4",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "平行四边形与梯形面积用于组合图形的拆分与构造。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04C3",
|
|
|
+ "target": "M04C4",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "扇形面积常出现在组合图形面积问题中。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04A3",
|
|
|
+ "target": "M04D1",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "立方体与长方体体积单位依赖体积单位理解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04A3",
|
|
|
+ "target": "M04D3",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "圆柱体积公式依赖体积单位理解。"
|
|
|
+ },
|
|
|
+
|
|
|
+ {
|
|
|
+ "source": "M04D1",
|
|
|
+ "target": "M04D2",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "棱柱体积是长方体体积的推广。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04D1",
|
|
|
+ "target": "M04D4",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "长方体展开图是理解一般立体展开的基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05A",
|
|
|
+ "target": "M04D3",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "圆柱体积公式来源于圆面积公式。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04C3",
|
|
|
+ "target": "M04D3",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "扇形面积计算用于圆柱侧面积构造理解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G02C",
|
|
|
+ "target": "M04E1",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平移是图形变换的基础,且长度保持性对度量重要。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03B",
|
|
|
+ "target": "M04E2",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "旋转常用于三角形角度变化分析。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G01D",
|
|
|
+ "target": "M04E3",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "对顶角、邻补角等角关系是轴对称角度变化理解基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04E1",
|
|
|
+ "target": "M04E4",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "平移掌握后进入三大变换组合应用。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04E2",
|
|
|
+ "target": "M04E4",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "旋转是图形变换综合的重要部分。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04E3",
|
|
|
+ "target": "M04E4",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "掌握轴对称后进入综合变换。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04C4",
|
|
|
+ "target": "M04F1",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "复杂组合图形常通过代数建模处理几何量关系。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04D3",
|
|
|
+ "target": "M04F1",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "结合立体几何量与代数求未知量。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04E4",
|
|
|
+ "target": "M04F2",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "几何变换作为中考图形综合计算的重要技巧。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02D",
|
|
|
+ "target": "M04F2",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "相似三角形中常通过面积比例求组合图形面积。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY01A",
|
|
|
+ "target": "M04F2",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "勾股定理在图形度量综合计算中极为常用。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03F",
|
|
|
+ "target": "SIM01A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "全等三角形中的对应边和对应角概念是相似三角形的基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G02B",
|
|
|
+ "target": "SIM01A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平行线的对应角、内错角关系常用于构造相似三角形。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM01A",
|
|
|
+ "target": "SIM01B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "理解相似概念后,首先学习AA相似判定。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM01A",
|
|
|
+ "target": "SIM01C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "相似的边角对应关系用于SAS比例判定。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM01A",
|
|
|
+ "target": "SIM01D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "SS比例判定基于相似概念中的边比关系。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G02B",
|
|
|
+ "target": "SIM01B",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平行线形成对应角相等,因此产生AA相似。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03B",
|
|
|
+ "target": "SIM01B",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "三角形内角和的使用在AA相似判定中极其常见。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM01B",
|
|
|
+ "target": "SIM01E",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "掌握基础相似判定后进行综合构造与转换。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM01C",
|
|
|
+ "target": "SIM01E",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "边比+夹角的判定常用于中考构造相似。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM01D",
|
|
|
+ "target": "SIM01E",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "SS比例判定后进入构造性质应用。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM01B",
|
|
|
+ "target": "SIM02A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "一旦判定相似,首先得到边比性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02A",
|
|
|
+ "target": "SIM02B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "边比平方得到面积比,是相似性质核心。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02B",
|
|
|
+ "target": "SIM02C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "面积比推广到体积比,尽管为初步认识。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G02B",
|
|
|
+ "target": "SIM02D",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "平行线分线段比例是相似性质的重要来源。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02A",
|
|
|
+ "target": "SIM02D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "比例线段定理可由相似三角形性质推导。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02A",
|
|
|
+ "target": "SIM02E",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "掌握边比后进入复杂比例构造与代数结合。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02D",
|
|
|
+ "target": "SIM02E",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "比例线段是几何综合比例链的关键。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G03B",
|
|
|
+ "target": "PY01A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "三角形角关系是理解直角三角形的基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY01A",
|
|
|
+ "target": "PY01B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "勾股逆定理基于勾股正定理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY01A",
|
|
|
+ "target": "PY01C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "勾股数来自勾股定理的特殊整数解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY01A",
|
|
|
+ "target": "PY01D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "直角三角形性质依赖勾股定理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY01A",
|
|
|
+ "target": "PY02A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "距离公式的本质就是勾股定理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY01A",
|
|
|
+ "target": "PY02B",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "最短路径问题多通过反射法构造直角应用勾股定理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY01D",
|
|
|
+ "target": "PY02C",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "复杂图形中的直角关系常依赖直角三角形性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02A",
|
|
|
+ "target": "PY02D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "几何结构中常结合相似三角形与勾股定理求量。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY01A",
|
|
|
+ "target": "PY02D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "勾股定理与相似性质是中考压轴题的核心组合。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02D",
|
|
|
+ "target": "PY02D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平行线比例定理常用于构造相似与勾股联合结构。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G06A",
|
|
|
+ "target": "SIM03A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "辅助线构造是相似构造的关键技能。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM01E",
|
|
|
+ "target": "SIM03A",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "掌握相似判定与构造后进入压轴构造策略。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02A",
|
|
|
+ "target": "SIM03B",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "比例关系链构建基于相似性质。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM02D",
|
|
|
+ "target": "SIM03B",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平行线比例定理常用于构建多段比例链。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY01A",
|
|
|
+ "target": "SIM03C",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "构造直角常用于建立相似结构或比例关系。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G06A",
|
|
|
+ "target": "SIM03C",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "通过作垂线等构造直角是几何技巧基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM03A",
|
|
|
+ "target": "SIM03D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "辅助线技巧用于几何综合压轴题。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM03B",
|
|
|
+ "target": "SIM03D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "比例链是中考压轴几何题的核心结构。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "SIM03C",
|
|
|
+ "target": "SIM03D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "直角构造与比例链结合用于综合推理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "PY02D",
|
|
|
+ "target": "SIM03D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "相似 + 勾股联合构成中考压轴题最重要模型。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04C1",
|
|
|
+ "target": "PY02A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "面积相关问题常需要使用勾股定理解高或距离。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04C4",
|
|
|
+ "target": "SIM03D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "组合图形面积题中大量运用相似与勾股联合推理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "G05D",
|
|
|
+ "target": "SIM03D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "圆周角定理常用于构造相似或直角结构。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST01A",
|
|
|
+ "target": "ST01B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "获取数据后才能进行分类整理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST01B",
|
|
|
+ "target": "ST01C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "频数与频率基于数据分类整理。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST01C",
|
|
|
+ "target": "ST02A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "频数与频率是平均数和加权平均数的重要基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST01C",
|
|
|
+ "target": "ST02B",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "中位数离不开对数据排序与频率分布的理解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST01C",
|
|
|
+ "target": "ST02C",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "众数来源于频数最高的分类。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST02A",
|
|
|
+ "target": "ST03A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "极差分析在平均数基础上理解数据波动。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST03A",
|
|
|
+ "target": "ST03B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "方差是对数据波动程度更深入的度量。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST03B",
|
|
|
+ "target": "ST03C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "标准差基于方差的平方根定义。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST01C",
|
|
|
+ "target": "ST04A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "条形图展示频数分布。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST01C",
|
|
|
+ "target": "ST04B",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "折线图展示趋势变化,基于频数或频率。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST01C",
|
|
|
+ "target": "ST04C",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "扇形图展示频率比例。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST04A",
|
|
|
+ "target": "ST04D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "掌握基本统计图后进入综合分析图表。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST04B",
|
|
|
+ "target": "ST04D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "折线图趋势分析是综合图表解读的重要组成。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST04C",
|
|
|
+ "target": "ST04D",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "扇形图比例为综合图表解读提供关键信息。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST01A",
|
|
|
+ "target": "ST05A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "概率研究之前必须理解随机性来源于数据过程。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST05A",
|
|
|
+ "target": "ST05B",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "随机事件概念后学习古典概率(等可能模型)。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST05A",
|
|
|
+ "target": "ST05C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "实验概率来自随机事件的重复试验。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST05B",
|
|
|
+ "target": "ST05D",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "树状图和列表法构建样本空间用于古典概率计算。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST05C",
|
|
|
+ "target": "ST05D",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "实验概率可通过树状图辅助分析复杂事件的频率。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST02A",
|
|
|
+ "target": "ST06A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "平均数是统计综合题的核心基础。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST02B",
|
|
|
+ "target": "ST06A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "中位数常用于数据趋势判断。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST03C",
|
|
|
+ "target": "ST06A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "标准差用于判断数据稳定性(新课标核心)。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST04D",
|
|
|
+ "target": "ST06A",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "综合统计图分析常出现在数据统计综合题中。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST05B",
|
|
|
+ "target": "ST06B",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "古典概率用于概率综合题第一阶段分析。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST05D",
|
|
|
+ "target": "ST06B",
|
|
|
+ "type": "prerequisite",
|
|
|
+ "comment": "树状图+列表法用于概率综合题中的多阶段概率。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST05C",
|
|
|
+ "target": "ST06B",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "实验概率用于概率综合题中的概率估计与修正。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST06A",
|
|
|
+ "target": "ST06C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "统计判断能力用于现实情境中的概率估计模型。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "ST06B",
|
|
|
+ "target": "ST06C",
|
|
|
+ "type": "successor",
|
|
|
+ "comment": "概率分析能力用于综合的统计概率融合问题。"
|
|
|
+ },
|
|
|
+
|
|
|
+ {
|
|
|
+ "source": "E02C",
|
|
|
+ "target": "ST06A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "统计量求解中经常将平均数等量转化为方程求解。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "H01",
|
|
|
+ "target": "ST06A",
|
|
|
+ "type": "crosslink",
|
|
|
+ "comment": "折线图趋势判断与函数图像的变化率密切相关。"
|
|
|
+ },
|
|
|
+ {
|
|
|
+ "source": "M04C4",
|
|
|
+ "target": "ST06C",
|
|
|
"type": "crosslink",
|
|
|
- "comment": "处理应用题(如行程、浓度)前,学生通常需要先完成相关的分式运算化简。"
|
|
|
+ "comment": "几何面积变化常结合概率出现于中考融合题。"
|
|
|
}
|
|
|
]
|