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{"sheet":"原始","index":1,"n_rows":1208,"n_cols":4,"rows_kept":1208,"cut":false,"hidden":false,"merged":[]}
["有理数","知识清单",1]
[null,"知识清单",1]
[null,"正数、负数",2]
[null,"正数、负数",2]
[null,"有理数及其分类",3]
[null,"有理数及其分类",3]
[null,"数轴及其三要素",4]
[null,"相反数",5]
[null,"绝对值",6]
[null,"方法清单",7]
[null,"正、负数的识别方法",8]
[null,"正、负数的应用方法",9,1]
[null,"正、负数的应用方法",9]
[null,"数轴的几何意义",10,1]
[null,"数轴的几何意义的应用方法",10]
[null,"求相反数的方法",11]
[null,"多重符号的化简方法",12,1]
[null,"多重符号的化简方法",12]
[null,"绝对值化简的方法",13]
[null,"绝对值非负性的应用方法",14]
[null,"有理数大小的比较方法",15]
[null,"知识清单",16]
[null,"有理数的加法",17]
[null,"有理数的加法运算律",18]
[null,"有理数的减法",19]
[null,"有理数的乘法",20]
[null,"倒数",21]
[null,"有理数的乘法运算律",22]
[null,"有理数的除法",23]
[null,"方法清单",24]
[null,"几个有理数相加的常用方法",25]
[null,"有理数减法的解题方法",26]
[null,"有理数加减法在实际问题中的应用",27]
[null,"求倒数",28,1]
[null,"求倒数的方法",28]
[null,"有理数乘除法法则的应用",29]
[null,"有理数乘法运算律的运用",30]
[null,"有理数乘除法在实际问题中的应用",31]
[null,"知识清单",32]
[null,"有理数的乘方及表示方法",33]
[null,"有理数乘方的计算法则",34]
[null,"方法清单",35]
[null,"有理数乘方的运算方法",36]
[null,"有理数混合运算的方式",37]
[null,"知识清单",38]
[null,"科学计数法",39]
[null,"方法清单",40]
[null,"用科学计数法表示绝对值较大的数的方法",41]
[null,"由科学记数法求原数",42,1]
[null,"由科学记数法求原数的方法",42]
[null,"科学记数法表示绝对值小于1的数的方法",43]
[null,"精确度的确定方法",44]
["代数式与整式","知识清单",45]
[null,"知识清单",45]
[null,"代数式及其分类",46]
[null,"代数式及其分类",46]
[null,"列代数式",47]
[null,"方法清单",48]
[null,"列代数式的方法",49]
[null,"多位数的表示方法，多项式的项数及次数",50,1]
[null,"多位数的表示方法",50]
[null,"求代数式的值的方法",51]
[null,"列代数式在探索规律问题中的应用方法",52]
[null,"知识清单",53]
[null,"整式",54,1]
[null,"整式",54]
[null,"单项式",55]
[null,"多项式",56]
[null,"方法清单",57]
[null,"整式的识别方法嗯",58]
[null,"利用多项式概念确定字母取值的方法",59]
[null,"知识清单",60]
[null,"同类项",61]
[null,"合并同类项与移项解方程",62,1]
[null,"合并同类项",62]
[null,"去括号与添括号",63]
[null,"化简求值",64,1]
[null,"化简求值",64]
[null,"方法清单",65]
[null,"同类项概念的应用方法",66]
[null,"去括号的方法",67]
[null,"整体代换思想在化简求值中的应用方法",68,1]
[null,"整体代换思想在化简求值中的应用方法",68]
[null,"整式加减中的解错题问题的解决方法",69,1]
[null,"整式加减中的解错题问题的解决方法",69]
["一元一次方程","知识清单",70]
[null,"知识清单",70]
[null,"等式",71]
[null,"等式",71]
[null,"等式的性质",72]
[null,"等式的性质",72]
[null,"方程",73]
[null,"方程与等式的区别与联系",74]
[null,"方程的解与解方法",75]
[null,"方法清单",76]
[null,"等量关系的确定方法",77]
[null,"利用方程的解求待定字母的方法",78]
[null,"知识清单",79]
[null,"一元一次方程",80]
[null,"移项",81,1]
[null,"移项",81]
[null,"去括号与去分母",82]
[null,"解一元一次方程的一般步骤",83]
[null,"方法清单",84]
[null,"一元一次方程概念的应用",85]
[null,"利用合并同类项与移项解方程的方法",86]
[null,"你用去分母解方程的方法",87]
[null,"含小数的一元一次方程的解法",88,1]
[null,"含小数的一元一次方程的解法",88]
[null,"有关同解方程的解题方法",89,1]
[null,"有关同解方程的解题方法",89]
[null,"知识清单",90]
[null,"列一元一次方程解应用题的一般步骤",91]
[null,"设未知数的几种方法",92]
[null,"一元一次方程应用题的常见类型",93]
[null,"方法清单",94]
[null,"列一元一次方程解决工程问题",95,1]
[null,"列一元一次方程解决行程问题",95,1]
[null,"列一元一次方程解决其他问题",95,1]
[null,"列一元一次方程解决配套问题",95]
[null,"用列表法解决增长率、数字等问题",96]
[null,"用图示法解决行程、工程等的问题",97,1]
[null,"用图示法解决行程、工程等的问题",97]
[null,"列一元一次方程解决销售利润问题",98]
[null,"列一元一次方程解决比赛中的积分问题",99]
[null,"列一元一次方程解决储蓄问题",100]
[null,"列一元一次方程解决等积变形问题",101]
[null,"列一元一次方程解决图表信息问题",102]
["实数","知识清单",103]
[null,"知识清单",103]
[null,"算术平方根",104]
[null,"算术平方根",104,1]
[null,"算术平方根",104]
[null,"平方根",105]
[null,"平方根",105]
[null,"平方根与算术平方根的区别与联系",106]
[null,"方法清单",107]
[null,"开平方的方法",108]
[null,"平方根的性质的应用方法",109]
[null,"利用平方根的概念解方程的方法",110]
[null,"知识清单",111]
[null,"立方根",112]
[null,"开立方",113]
[null,"立方根与平方根的区别与联系",114]
[null,"方法清单",115]
[null,"立方根性质的应用方法",116]
[null,"利用立方根的概念解方程的方法",117]
[null,"方根中小数点移动规律的应用。",118,1]
[null,"方根中小数点移动规律的应用。",118]
[null,"知识清单",119]
[null,"无理数",120]
[null,"实数及其分类",121]
[null,"实数的性质",122]
[null,"方法清单",123]
[null,"无理数的识别方法",124]
[null,"无理数估算的方法",125]
[null,"实数与数轴上的点的对应关系的应用方法我",126]
[null,"实数大小的比较方法",127]
[null,"非负数的性质的应用方法",128]
[null,"无理数的小数部分的确定方法。",129]
["平面直角坐标系","知识清单",130]
[null,"知识清单",130]
[null,"有序数对",131]
[null,"有序数对",131]
[null,"平面直角坐标系",132]
[null,"平面直角坐标系",132]
[null,"象限",133]
[null,"象限",133]
[null,"点的坐标的符号特征解题",134,1]
[null,"点的坐标",134]
[null,"方法清单",135]
[null,"有序数对的应用方法",136]
[null,"坐标平面中点的位置的确定。",137,1]
[null,"坐标平面中点的位置的确定。",137]
[null,"用坐标表示地理位置",138,1]
[null,"用坐标表示地理位置的方法",138]
[null,"知识清单",139]
[null,"各象限内点的坐标的符号特征。",140,1]
[null,"根据三视图求几何体的体积和表面积",140,1]
[null,"各象限内点的坐标的符号特征。",140]
[null,"坐标轴上点的坐标的特征",141,1]
[null,"坐标轴上点的坐标的特征",141]
[null,"象限角的平分线上的点的坐标特征",142,1]
[null,"象限角的平分线上的点的坐标特征",142]
[null,"与坐标轴平行的直线上的点的坐标特征。",143,1]
[null,"与坐标轴平行的直线上的点的坐标特征。",143]
[null,"点到坐标轴的距离",144]
[null,"平面直角坐标系内的图形变化。",145]
[null,"方法清单",146]
[null,"利用点的坐标的符号特征解题的方法",147]
[null,"点到坐标轴的距离的应用方法。",148]
[null,"利用图形的平移确定变化的坐标的方法。",149]
[null,"方向角与方位角",150,1]
[null,"利用图形的对称确定变化的坐标方法",150]
["二元一次方程组","知识清单",151]
[null,"知识清单",151]
[null,"二元一次方程",152]
[null,"二元一次方程",152]
[null,"二元一次方程组",153]
[null,"二元一次方程组",153]
[null,"二元一次方程（组）的解",154]
[null,"二元一次方程（组）的解",154]
[null,"方法清单",155]
[null,"二元一次方程的判别方法。",156]
[null,"二元一次方程组的解的应用方法",157]
[null,"求二元一次方程的整数解",158,1]
[null,"求二元一次方程的整数解的方法",158]
[null,"知识清单",159]
[null,"消元",160]
[null,"代入消元法",161]
[null,"加减消元法",162]
[null,"整体消元法",163,1]
[null,"整体消元法",163]
[null,"解二元一次方程组的一般步骤",164,1]
[null,"解二元一次方程组的一般步骤。",164]
[null,"方法清单",165]
[null,"解“看错系数”问题的方法",166]
[null,"利用同解方程组确定字母取值的方法",167]
[null,"利用消元思想解三元一次方程组的方法。",168]
[null,"知识清单",169]
[null,"列二元一次方程组解应用题的一般步骤。",170]
[null,"列二元一次方程组解应用题的常见类型。",171,1]
[null,"列二元一次方程组解应用题的常见类型。",171]
[null,"方法清单",172]
[null,"列二元一次方程组解决增长率问题。",173,1]
[null,"列二元一次方程组解决增长率问题的方法。",173]
[null,"列二元一次方程组解决配套问题。",174,1]
[null,"列二元一次方程组解决配套问题的方法。",174]
[null,"例二元一次方程组解决行程问题",175,1]
[null,"例二元一次方程组解决行程问题的方法",175]
[null,"例二元一次方程组解决几何图形的计算问题",176,1]
[null,"例二元一次方程组解决几何图形的计算问题的方法",176]
[null,"利用二元一次方程组的解进行方案设计的方法。",177]
["一元一次不等式","知识清单",178]
[null,"知识清单",178]
[null,"不等式",179]
[null,"不等式",179]
[null,"不等式的解与解集",180]
[null,"不等式的解与解集",180]
[null,"不等式的基本性质",181]
[null,"解不等式",182,1]
[null,"解不等式",182]
[null,"不等式的性质与等式的性质的区别与联系。",183]
[null,"方法清单",184]
[null,"列不等式的方法",185]
[null,"不等式性质的应用方法。",186]
[null,"利用不等式的性质比较大小的方法。",187]
[null,"知识清单",188]
[null,"一元一次不等式",189]
[null,"一元一次不等式的解集。",190]
[null,"一元一次不等式的解集的表示方法",191]
[null,"解一元一次不等式的一般步骤。",192]
[null,"解一元一次方程解一元一次不等式的区别。",193]
[null,"一元一次不等式的整数解。",194]
[null,"方法清单",195]
[null,"求一元一次不等式特殊解的方法",196]
[null,"确定不等式中字母的取值范围。",197,1]
[null,"确定不等式中字母的取值范围的方法。",197]
[null,"确定一元一次不等式中待定字母的值",198,1]
[null,"确定一元一次不等式中待定字母的值的方法",198]
[null,"知识清单",199]
[null,"一元一次不等式组",200]
[null,"一元一次不等式组的解集。",201]
[null,"解一元一次不等式组的一般步骤。",202]
[null,"一元一次不等式组的整数解。",203]
[null,"方法清单",204]
[null,"一元一次不等式组解集的确定方法。",205]
[null,"求一元一次不等式组的整数解的方法。",206]
[null,"解连续不等式。",207,1]
[null,"解连续不等式的方法。",207]
[null,"一元一次不等式（组）中待定字母的值的确定方法",208]
[null,"一元一次不等式（组）中待定字母的取值范围的确定方法。",209]
[null,"知识清单",210]
[null,"列一元一次不等式（组）解应用题的关键语句",211]
[null,"列一元一次不等式（组）解应用题的一般步骤",212,1]
[null,"列一元一次不等式（组）解应用题的一般步骤",212]
[null,"方法清单",213]
[null,"利用一元一次不等式（组）解决实际问题的方法",214]
[null,"方程（组）与不等式（组）相结合解决实际问题的方法。",215]
[null,"运用一元一次不等式（组）进行方案设计",216,1]
[null,"运用一元一次不等式（组）进行方案设计的方法",216]
["整式的乘除与因式分解","知识清单",217]
[null,"知识清单",217]
[null,"同底数幂的乘法",218]
[null,"同底数幂的乘法",218]
[null,"幂的乘法",219]
[null,"幂的乘法",219]
[null,"积的乘法",220]
[null,"同底数幂的除法",221]
[null,"零指数幂",222]
[null,"负整数指数幂",223]
[null,"方法清单",224]
[null,"同底数幂的运算方法",225]
[null,"幂的乘法的辨别方法",226]
[null,"幂的运算法则的应用",227]
[null,"利用幂的运算法则比较大小的方法。",228]
[null,"负整数指数幂的运算方法。",229]
[null,"知识清单",230]
[null,"单项式与单项式相乘",231]
[null,"单项式与多项式相乘",232]
[null,"多项式与多项式相乘",233]
[null,"乘法公式",234]
[null,"单项式除以单项式",235]
[null,"多项式除以单项式",236]
[null,"整式的混合运算",237,1]
[null,"整式的混合运算",237]
[null,"方法清单",238]
[null,"乘法公式的合理运用",239]
[null,"乘法公式在解决数的计算问题中的巧妙应用。",240]
[null,"乘法公式在变形在解题中的应用",241]
[null,"化简求值中带错值问题的解决方法。",242,1]
[null,"化简求值中带错值问题的解决方法。",242]
[null,"知识清单",243]
[null,"因式分解",244]
[null,"公因式",245]
[null,"提公因式法",246]
[null,"公式法",247]
[null,"因式分解的一般步骤",248]
[null,"方法清单",249]
[null,"因式分解的判断方法",250]
[null,"用提公因式法分解因式。",251,1]
[null,"用提公因式法分解因式。",251]
[null,"用公式法分解因式",252]
["分式与分式方程","知识清单",253]
[null,"知识清单",253]
[null,"分式的定义",254]
[null,"分式的定义",254]
[null,"分式的基本性质",255]
[null,"分式的基本性质",255]
[null,"约分集约分法则",256]
[null,"最简分式",257]
[null,"通分与通分法则",258]
[null,"最简公分母",259]
[null,"约分与通分的联系与区别。",260]
[null,"方法清单",261]
[null,"分式有无意义的判断方法。",262]
[null,"分数的大小比较解决实际问题。",263,1]
[null,"分式值为零的判断方法。",263]
[null,"分式的基本性质的应用。",264]
[null,"约分的技巧与方法",265]
[null,"通分的技巧与方法",266]
[null,"分式的变形求值的方法。",267]
[null,"知识清单",268]
[null,"分式的乘除",269]
[null,"分式的加减",270]
[null,"分式的乘方",271]
[null,"分式的混合运算",272]
[null,"方法清单",273]
[null,"分式的乘除运算的解题方法。",274]
[null,"分式的加减运算的解题方法",275]
[null,"分式的混合运算的解题方法。",276]
[null,"分式化简求值的方法",277]
[null,"利用分数的大小比较解决实际问题的方法。",278]
[null,"知识清单",279]
[null,"分式方程",280]
[null,"解分式方程的一般步骤。",281]
[null,"可化为一元一次方程的分式方程。",282,1]
[null,"可化为一元一次方程的分式方程。",282]
[null,"验根",283]
[null,"方法清单",284]
[null,"解分式方程的方法",285]
[null,"依据分式方程的解确定字母参数。",286,1]
[null,"依据分式方程的解确定字母参数的方法。",286]
[null,"依据分式方程的增根确定字母参数的方法。",287]
[null,"知识清单",288]
[null,"列分式方程解应用题的一般步骤。",289]
[null,"列分式方程解应用题的常见题型。",290]
[null,"方法清单",291]
[null,"列分式方程解决实际问题的方法。",292]
[null,"列分式方程解决实际行程问题的方法。",293]
[null,"列分式方程解决工程问题的方法。",294]
["二次根式","知识清单",295]
[null,"知识清单",295]
[null,"使二次根式有意义的条件",296,1]
[null,"使二次根式有意义的条件。",296]
[null,"使二次根式有意义的条件。",296]
[null,"最简二次根式",297]
[null,"最简二次根式",297]
[null,"二次根式的性质",298]
[null,"方法清单",299]
[null,"二次根式概念的应用方法。",300]
[null,"利用二次根式的非负性解决的方法。",301]
[null,"二次根式根号下方",302]
[null,"的化简方法。P83",303]
[null,"因式的内移和外移的方法。",304]
[null,"知识清单",305]
[null,"二次根式的乘法",306]
[null,"二次根式的除法",307]
[null,"商的算数平方干",308,1]
[null,"商的算数平方干",308]
[null,"二次根式的加减",309]
[null,"二次根式的混合运算",310]
[null,"方法清单",311]
[null,"二次根式加减运算的方法。",312]
[null,"分母有理化的方法",313]
[null,"与二次根式相关的混合运算的方法。",314]
[null,"二次根式的化简求值的方法。",315]
[null,"二次根式比较大小的方法。",316]
["一次函数","知识清单",317]
[null,"知识清单",317]
[null,"常量与变量",318]
[null,"常量与变量",318]
[null,"函数",319]
[null,"函数",319]
[null,"函数自变量的取值范围。",320]
[null,"函数自变量的取值范围。",320]
[null,"函数值",321]
[null,"函数值",321]
[null,"函数的解析式",322]
[null,"函数的表示方法",323]
[null,"函数的图像",324]
[null,"知识清单",325]
[null,"正比例函数",326]
[null,"一次函数",327]
[null,"待定系数法",328]
[null,"方法清单",329]
[null,"一次函数的判断方法",330]
[null,"解成正比例关系问题。",331,1]
[null,"解成正比例关系问题的方法。",331]
[null,"一次函数解析式的确定方法。",332]
[null,"知识清单",333]
[null,"正比例函数的图像特征与性质。",334]
[null,"一次函数的图像特征与性质。",335]
[null,"k,b的符号与直线y=kx+b（k≠0）的关系",336]
[null,"一次函数与正比例函数的区别与联系",337]
[null,"方法清单",338]
[null,"一次函数的图像与性质的应用方法。",339]
[null,"由k，b的值（范围）确定直线的位置及函数增减性",340,1]
[null,"由k，b的值（范围）确定直线的位置及函数增减性的方法",340]
[null,"一次函数图像的平移规律的应用方法。",341]
[null,"计算一次函数图像与坐标轴围成的三角形的面积的方法。",342]
[null,"一次函数图像的交点坐标的实际应用方法。",343]
[null,"知识清单",344]
[null,"一次函数与一元一次方程",345]
[null,"一次函数与二元一次方程组。",346]
[null,"一次函数与一元一次不等式。",347]
[null,"方法清单",348]
[null,"利用一次函数求解方程组或不等式的方法。",349]
["一元二次方程","知识清单",350]
[null,"知识清单",350]
[null,"一元二次方程",351]
[null,"一元二次方程",351]
[null,"一元二次方程的一般形式。",352]
[null,"一元二次方程的一般形式。",352]
[null,"一元二次方程的根",353]
[null,"方法清单",354]
[null,"应用一元二次方程的定义求字母参数。",355,1]
[null,"应用一元二次方程的定义求字母参数的方法。",355]
[null,"一元二次方程的根的应用方法。",356]
[null,"知识清单",357]
[null,"一元二次方程的常见解法",358]
[null,"配方法解一元二次方程的一般步骤。",359,1]
[null,"配方法解一元二次方程的一般步骤。",359]
[null,"一元二次方程的根的判别式。",360]
[null,"公式法解一元二次方程的一般步骤。",361]
[null,"因式分解法解一元二次方程的一般步骤。",362]
[null,"一元二次方程的根与系数的关系。",363]
[null,"方法清单。",364]
[null,"解一元二次方程的方法。",365]
[null,"配方法带二次三项式中的应用方法。",366,1]
[null,"配方法带二次三项式中的应用方法。",366]
[null,"一元二次方程根的判别式的应用方法。",367]
[null,"一元二次方程根与系数的关系的应用方法。",368]
[null,"知识清单",369]
[null,"列一元二次方程解应用题的一般步骤。",370]
[null,"方法清单",371]
[null,"列一元二次方程解决增长率问题。",372,1]
[null,"列一元二次方程解决增长率问题的方法。",372]
[null,"利用一元二次方程解决每每型问题的方法。",373]
[null,"利用一元二次方程解决几何图形问题的方法。",374]
["二次函数","知识清单",375]
[null,"知识清单",375]
[null,"二次函数",376]
[null,"二次函数",376]
[null,"二次函数的一般形式",377]
[null,"二次函数的一般形式",377]
[null,"二次函数的常见表达式。",378]
[null,"二次函数的常见表达式。",378]
[null,"二次函数的顶点坐标及其意义。",379]
[null,"方法清单",380]
[null,"二次函数的识别方法",381]
[null,"用待定系数法求二次函数解析式。",382,1]
[null,"用待定系数法求二次函数解析式的方法。",382]
[null,"知识清单",383]
[null,"抛物线",384]
[null,"二次函数图像的平移",385]
[null,"二次函数的图像特征与性质。",386]
[null,"二次函数的最值",387]
[null,"二次函数图像与a、b、c的关系",388]
[null,"二次函数与一元二次方程的关系。",389]
[null,"二次函数图像的对称性。",390]
[null,"方法清单",391]
[null,"求抛物线的顶点对称轴的方法",392]
[null,"二次函数图像的平移规律的应用方法。",393]
[null,"抛物线对称性的应用方法。",394]
[null,"二次函数的图像特征与系数关系的应用方法。",395]
[null,"二次函数与一元二次方程，不等式综合应用的方法。",396]
["反比例函数","知识清单",397]
[null,"知识清单",397]
[null,"反比例函数",398]
[null,"反比例函数",398]
[null,"反比例函数的一般形式。",399]
[null,"反比例函数的一般形式。",399]
[null,"待定系数法求反比例函数解析式的一般步骤。",400]
[null,"比例关系与反比例函数的区别与联系。",401]
[null,"方法清单",402]
[null,"待定系数法确定反比例函数解析式的方法。",403]
[null,"反比例函数关系式在实际问题中的确定方法。",404]
[null,"知识清单",405]
[null,"双曲线",406]
[null,"反比例函数的图像特征与性质",407]
[null,"反比例函数中k的几何意义",408]
[null,"反比例函数图像的对称性。",409]
[null,"反比例函数与正比例函数的区别与联系",410]
[null,"正比例函数与反比例函数的交点特征。",411]
[null,"方法清单。",412]
[null,"判断点是否在反比例函数的图像上。",413,1]
[null,"判断点是否在反比例函数的图像上的方法。",413]
[null,"与几何知识相结合确定反比例函数解析式。",414,1]
[null,"与几何知识相结合确定反比例函数解析式的方法。",414]
[null,"反比例函数值的大小比较方法",415]
[null,"计算与反比例函数有关的图形面积的方法。",416]
[null,"一次函数与反比例函数综合题的解法。",417]
[null,"一次函数与反比例函数综合题的解法。",417]
["图像的初步认识","知识清单",418]
[null,"知识清单",418]
[null,"常见的立体图形",419]
[null,"常见的立体图形",419]
[null,"立体图形的平面展示图。",420]
[null,"立体图形的平面展示图。",420,1]
[null,"立体图形的平面展示图。",420]
[null,"正方体的平面展示图",421]
[null,"从三个方向看的常见几何体的形状。",422]
[null,"方法清单",423]
[null,"几何体的特征的应用方法。",424]
[null,"截几何体所有在截面的形状的判断方法。",425]
[null,"正方体展开图相对面的确定方法。",426]
[null,"多面体的棱数面数与顶点数之间的关系",427,1]
[null,"多面体的棱数面数与顶点数之间的关系的确定方法。",427]
[null,"知识清单",428]
[null,"直线及其表示方法",429]
[null,"射线及其表示方法",430]
[null,"线段及其表示方法",431]
[null,"直线，射线，线段的区别与联系。",432]
[null,"直线的相关公理",433]
[null,"两点间的距离",434]
[null,"线段最短",435]
[null,"线段的中点",436]
[null,"尺规作图作线段的和差。",437]
[null,"方法清单",438]
[null,"直线，射线，线段的辨别方法。",439]
[null,"线段大小的比较方法",440]
[null,"线段的计数方法",441]
[null,"利用数学思想计算线段长度的方法。",442]
[null,"线段的和差倍分",443]
[null,"知识清单",444]
[null,"角的定义",445]
[null,"角的表示方法",446]
[null,"角的度量",447]
[null,"角平分线",448]
[null,"余角和补角",449]
[null,"方向角与方位角",450]
[null,"方法清单",451]
[null,"角的大小的比较方法",452]
[null,"度分秒的运算方式",453]
[null,"角平分线的应用方法",454]
[null,"余角和补角的性质的应用方法。",455]
[null,"方程思想求角的度数的方法。",456]
[null,"时针和分针夹角的求解方法",457,1]
[null,"时针和分针夹角的求解方法",457]
[null,"相交线与平行线",458]
[null,"相交线",459]
["相交线与平行线","知识清单",460]
[null,"知识清单",460]
[null,"直线的位置关系",461]
[null,"直线的位置关系",461]
[null,"垂线",462]
[null,"垂线",462]
[null,"垂线的性质",463]
[null,"垂线的画法",464]
[null,"垂线段最短",465]
[null,"点到直线的距离",466]
[null,"方法清单",467]
[null,"垂线性质的应用方法",468]
[null,"利用“垂线段最短”解决实际问题的方法",469]
[null,"相交线相关问题规律的探究方法",470,1]
[null,"相交线相关问题规律的探究方法",470]
[null,"相交线中的角",471]
[null,"知识清单",472]
[null,"对顶角",473]
[null,"邻补角",474]
[null,"同位角、内错角与对旁内角",475]
[null,"方法清单",476]
[null,"对顶角、邻补角的识别方法",477]
[null,"同位角、内错角与同旁内角的识别方法",478]
[null,"利用对顶角、邻补角的性质进行角度的计算的方法",479]
[null,"平行线",480]
[null,"知识清单",481]
[null,"平行线",482]
[null,"平行线的画法",483]
[null,"平行公理",484]
[null,"平行线的判定",485]
[null,"平行线的性质",486]
[null,"平行线的判定与性质的区别于联系",487]
[null," 方法清单",488]
[null,"平移",489]
[null,"平移的性质",490]
[null,"作平移图形的一般步骤",491]
[null,"三角形与多边形",492]
[null,"三角形的有关概念",493]
[null,"知识清单",494]
[null,"三角形及其有关概念",495]
[null,"三角形的表示方法",496]
[null,"三角形的分类",497]
[null,"三角形的角平分线",498]
[null,"三角形的中线",499]
[null,"三角形的高",500]
[null,"方法清单",501]
[null,"三角形的相关概念的辨别方法",502]
[null,"利用三角形的角平分线的性质解题的方法",503]
[null,"利用三角形的中线解决面积计算问题的方法",504]
[null,"利用三角形的高的性质解题的方法",505]
[null,"三角形的性质",506]
["三角形与多边形","知识清单",507]
[null,"知识清单",507]
[null,"三角形的三边关系",508]
[null,"三角形的三边关系",508]
[null,"三角形的内角和定理",509]
[null,"三角形的内角和定理",509]
[null,"三角形的外角",510]
[null,"三角形的外角和",511]
[null,"三角形的稳定性",512]
[null,"方法清单",513]
[null,"三角形三边关系的应用方法",514]
[null,"利用三角形的内角和定理判定三角形形状的方法",515]
[null,"三角形外角的应用方法",516]
[null,"多边形的有关概念和性质",517]
[null,"知识清单",518]
[null,"多边形及其组成要素",519]
[null,"正多边形",520]
[null,"凸多边形",521,1]
[null,"凸多边形",521]
[null,"多边形的内角和定理",522]
[null,"多边形的外角和定理",523]
[null,"四边形的不稳定性",524]
[null,"方法清单",525]
[null,"多边形对角线的条数的计算方法",526]
[null,"利用多边形的内角和、外角和求边数的方法",527]
[null,"正多边形的外角和的应用方法",528]
[null,"利用逼近法确定多边形的边数的方法",529]
[null,"全等形与全等三角形",530]
[null,"全等三角形",531]
["全等形与全等三角形","知识清单",532]
[null,"知识清单",532]
[null,"全等形与全等三角形",533]
[null,"全等形与全等三角形",533]
[null,"全等三角形的表示",534]
[null,"全等三角形的表示",534]
[null,"全等变换",535]
[null,"全等变换",535,1]
[null,"全等变换",535]
[null,"全等三角形的性质",536]
[null,"全等三角形的判定",537]
[null,"方法清单",538]
[null,"全等三角形对应边、对应角的确定方法",539]
[null,"利用全等三角形的性质证明线段、角相等的方法",540]
[null,"利用全等三角形的性质解决实际问题的方法",541]
[null,"全等三角形的判定方法的合理选择",542]
[null,"运用“倍长中线”构造全等的方法",543]
[null,"“截长补短”的应用方法",544]
[null,"解探索开放性问题",545,1]
[null,"解探索开放性问题的方法",545]
[null,"轴对称与等腰三角打开形",546]
[null,"图形的轴对称",547]
["轴对称与等腰三角形","知识清单",548]
[null,"知识清单",548]
[null,"轴对称",549]
[null,"轴对称",549]
[null,"轴对称图形",550]
[null,"轴对称图形",550]
[null,"对称轴",551]
[null,"对称轴",551]
[null,"轴对称图形与轴对称的区别与联系。",552]
[null,"轴对称的性质",553]
[null,"轴对称的识别",554]
[null,"做轴对称图形的一般步骤。",555]
[null,"方法清单",556]
[null,"画对称轴的方法",557]
[null,"利用轴对称解决几何最值问题的方法。",558]
[null,"你有方程的思想解决与“翻折”相关的问题的方法。",559]
[null,"线段的垂直平分线。",560]
[null,"知识清单",561]
[null,"线段的垂直平分线",562]
[null,"线段的垂直平分线的性质定理。",563]
[null,"线段的垂直平分线的性质定理的逆定理。",564]
[null,"三角形三边的垂直平分线的性质。",565]
[null,"垂直平分线与角平分线的区别与联系。",566]
[null,"方法清单",567]
[null,"利用线段的垂直平分线性质解题的方法。",568]
[null,"点在线段的垂直平分线上的判断方法。",569]
[null,"线段垂直平分线与角平分线性质相结合解题。",570,1]
[null,"线段垂直平分线与角平分线性质相结合解题的方法。",570]
[null,"等腰三角形",571]
[null,"知识清单",572]
[null,"等腰三角形",573]
[null,"等腰三角形的性质定理。",574]
[null,"等腰三角形的对称轴",575]
[null,"等腰三角形的判定定理。",576]
[null,"方法清单",577]
[null,"利用等腰三角形的概念解题的方法。",578]
[null,"利用等腰三角形的性质解题的方法。",579]
[null,"利用“等角对等边“”证明线段相等的方法。",580]
[null,"等腰三角形与角平分线相结合解题的方法。",581]
[null,"等边三角形",582]
[null,"知识清单",583]
[null,"等边三角形及其性质",584]
[null,"等边三角形的判定",585]
[null,"方法清单",586]
[null,"利用等边三角形的性质进行计算的方法。",587]
[null,"等边三角形的性质在全等证明中的应用方法",588]
[null,"勾股定理",589]
[null,"直角三角形与勾股定理。",590]
["勾股定理","知识清单",591]
[null,"知识清单",591]
[null,"直角三角形的性质",592]
[null,"直角三角形的性质",592]
[null,"勾股定理",593]
[null,"勾股定理",593]
[null,"勾股定理的验证",594]
[null,"勾股定理的验证",594]
[null,"方法清单",595]
[null,"利用直角三角形的性质进行解题的方法。",596]
[null,"构造含30°角的直角三角形进行解题的方法。",597]
[null,"利用勾股定理解决几何体表面最短距离的方法。",598]
[null,"利用勾股定理解决实际问题的方法",599]
[null,"构造直角三角形的方法。",600]
[null,"利用勾股定理解决有关几何图形面积问题的方法。",601]
[null,"勾股定理的逆定理",602]
[null,"知识清单",603]
[null,"勾股数",604]
[null,"勾股定理的逆定理",605]
[null,"方法清单",606]
[null,"有勾股定理的逆定理判断三角形形状。",607,1]
[null,"有勾股定理的逆定理判断三角形形状的方法。",607]
[null,"利用勾股定理的逆定理求不规则图形的面积的方法。",608]
[null,"平行四边形及特殊的平行四边形。",609]
[null,"平形四边形的有关概念及性质。",610,1]
[null,"平形四边形的有关概念及性质。",610]
["平行四边形","知识清单",611]
[null,"知识清单",611]
[null,"平行四边形",612]
[null,"平行四边形",612]
[null,"行四边形的性质定理。",613]
[null,"行四边形的性质定理。",613,1]
[null,"行四边形的性质定理。",613]
[null,"平行线间的距离",614]
[null,"平行四边形的判定定理。",615]
[null,"平行四边形的对称性",616]
[null,"方法清单",617]
[null,"平行四边形的性质进行计算的方法。",618]
[null,"平行线间距离的应用方法。",619]
[null,"平行四边形的判定方法。",620]
[null,"平行四边形与全等相结合在解题中的应用方法",621]
[null,"中位线",622]
[null,"知识清单",623]
[null,"三角形的中位线",624]
[null,"三角形中位线定理",625]
[null,"平行线等分线段定理",626]
[null,"方法清单",627]
[null,"利用三角形中位线进行计算的方法。",628]
[null,"利用三角形中位线证明线段平行的方法。",629]
[null,"矩形",630]
[null,"知识清单",631]
[null,"矩形",632]
[null,"矩形的性质定理",633]
[null,"矩形的判定定理",634]
[null,"矩形的对称轴",635]
[null,"方法清单",636]
[null,"矩形有关性质的应用方法。",637]
[null,"矩形的判定方法",638]
[null,"菱形",639]
[null,"知识清单",640]
[null,"菱形",641,1]
[null,"菱形",641]
[null,"菱形的性质定理",642]
[null,"菱形的判定定理",643,1]
[null,"菱形的判定定理",643]
[null,"菱形的面积公式",644,1]
[null,"菱形的面积公式",644]
[null,"方法清单",645]
[null,"菱形有关性质的应用方法。",646]
[null,"菱形面积的计算方法",647]
[null,"菱形的判定方法",648]
[null,"正方形",649]
[null,"知识清单",650]
[null,"正方形",651]
[null,"正方形的性质",652]
[null,"正方形的判定",653]
[null,"正方形的对称性",654]
[null,"四边形之间的区别与联系。",655]
[null,"方法清单",656]
[null,"正方形性质的应用方法",657]
[null,"正方形的判定方法",658]
[null,"正方形的性质在探索开放性问题中的应用方法。",659]
[null,"图形的旋转",660]
[null,"图形的旋转",661]
["圆形的旋转","知识清单",662]
[null,"知识清单",662]
[null,"旋转的相关概念",663]
[null,"旋转的相关概念",663]
[null,"旋转的性质",664]
[null,"旋转的性质",664]
[null,"做旋转图形的一般步骤。",665]
[null,"做旋转图形的一般步骤。",665]
[null,"平移，旋转与轴对称的区别与联系。",666]
[null,"方法清单",667]
[null,"图形旋转的概念与性质的应用方法。",668,1]
[null,"图形旋转的概念与性质的应用方法。",668]
[null,"旋转中心的确定方法",669]
[null,"与图形旋转相关的作图方法。",670,1]
[null,"与图形旋转相关的作图方法。",670]
[null,"利用图形的平移，旋转，轴对称进行方案设计的方法。",671]
[null,"图形旋转在探索开放性问题中的应用。",672,1]
[null,"图形旋转在探索开放性问题中的应用。",672]
[null,"中心对称",673]
[null,"知识清单",674]
[null,"中心对称",675]
[null,"中心对称图形",676]
[null,"中心对称的基本性质",677]
[null,"做与已知图形成中心对称的图形的一般步骤",678,1]
[null,"做与已知图形成中心对称的图形的一般步骤",678]
[null,"中心对称与中心对称图形的区别与联系。",679]
[null,"方法清单",680]
[null,"对称中心的确定方法",681]
[null,"中心对称的性质的应用方法。",682]
[null,"利用中心对称等分面积的方法。",683]
[null,"圆",684]
[null,"与圆有关的概念",685,1]
[null,"与圆有关的概念",685]
["圆","知识清单",686]
[null,"知识清单",686]
[null,"圆的定义",687]
[null,"圆的定义",687,1]
[null,"圆的定义",687]
[null,"弦与直径",688]
[null,"弦与直径",688,1]
[null,"弦与直径",688]
[null,"圆",689,1]
[null,"弧，半圆，优弧，劣弧等弧。",689]
[null,"同心圆和等圆",690]
[null,"圆心角和圆周角",691]
[null,"三角形的外接圆与外心",692]
[null,"圆内接四边形",693]
[null,"弓形、扇形，面积",694,1]
[null,"弓形、扇形",694]
[null,"方法清单",695]
[null,"弧，弦，半径，直径等概念的区分方法。",696]
[null,"圆心角与圆周角的关系的运用方法。",697]
[null,"圆的基本性质",698]
[null,"知识清单",699]
[null,"圆的对称性",700,1]
[null,"圆的对称性",700]
[null,"垂径定理及其推论",701]
[null,"圆心角，弧，弦与弦心距之间的关系。",702]
[null,"圆周角定理及其推论",703]
[null,"圆内接四边形性质定理。",704]
[null,"方法清单",705]
[null,"运用垂径定理进行有关弦的计算。",706]
[null,"圆心角，弧，弦的关系的应用方法。",707]
[null,"圆周角定理及推论的应用方法",708]
[null,"与圆有关的位置关系。",709,1]
[null,"与圆有关的位置关系。",709]
[null,"知识清单",710]
[null,"点与圆的位置关系",711]
[null,"过已知点的圆",712,1]
[null,"过已知点的圆",712]
[null,"直线与圆的位置关系",713]
[null,"直线与圆的位置关系的性质与判定。",714]
[null,"切线的性质定理",715]
[null,"切线的判定定理",716]
[null,"切线长定理",717]
[null,"三角形的内切圆与内心",718]
[null,"圆外切四边形",719]
[null,"方法清单",720]
[null,"切线的判定和性质的应用方法",721]
[null,"三角形内心和外心的应用方法",722]
[null,"利用切线长定理进行计算的方法。",723]
[null,"解决与圆的位置关系有关的多解问题。",724,1]
[null,"解决与圆的位置关系有关的多解问题的方法。",724]
[null,"圆中常见的辅助线做法。",725]
[null,"圆有关知识在动态问题中的应用。",726,1]
[null,"圆有关知识在动态问题中的应用。",726]
[null,"正多边形与圆的有关计算。",727]
[null,"知识清单",728]
[null,"正多边形与圆的关系",729]
[null,"正多边形的中心与中心角。",730]
[null,"正多边形的半径与边心距。",731]
[null,"正多边形的有关计算",732]
[null,"正边形的对称性",733]
[null,"弧长公式",734]
[null,"扇形面积公式",735]
[null,"圆柱侧面展开图",736,1]
[null,"圆柱侧面展开图",736]
[null,"圆锥侧面展开图",737,1]
[null,"圆锥侧面展开图",737]
[null,"方法清单",738]
[null,"正多边形有关计算的方法。",739]
[null,"弧长、扇形面积与圆锥侧面积的计算方法。",740]
[null,"不规则图形的面积的计算方法。",741]
[null,"运用圆锥侧面积知识解决实际问题。",742,1]
[null,"运用圆锥侧面积知识解决实际问题的方法。",742]
[null,"相似形",743]
[null,"比例线段及有关性质。",744]
["相似形","知识清单",745]
[null,"知识清单",745]
[null,"两条线段的比",746]
[null,"两条线段的比",746]
[null,"比例线段",747]
[null,"两条线段的比",747,1]
[null,"比例线段",747]
[null,"比例的基本性质",748]
[null,"比例的基本性质",748]
[null,"方法清单",749]
[null,"比例性质的应用方法",750]
[null,"作平行线构造成比例线段。",751,1]
[null,"作平行线构造成比例线段的方法。",751]
[null,"证明比例式或等积式。",752,1]
[null,"证明比例式或等积式的方法。",752]
[null,"相似三角形",753]
[null,"知识清单",754]
[null,"相似形",755,1]
[null,"相似形",755]
[null,"相似三角形",756]
[null,"相似比",757]
[null,"相似三角形的性质",758]
[null,"相似三角形的判定",759]
[null,"方法清单",760]
[null,"利用相似三角形的性质进行计算的方法。",761]
[null,"相似三角形的判定方法。",762]
[null,"相似三角形在实际生活中的应用方法。",763]
[null,"利用相似三角形列函数关系式的方法。",764]
[null,"相似三角形在探索开放型问题中的应用方法。",765]
[null,"相似三角形在动态几何问题中的应用方法。",766]
[null,"相似多边形与位似图形。",767]
[null,"知识清单",768]
[null,"相似多边形及其性质",769]
[null,"相似多边形的判定",770]
[null,"位似图形",771,1]
[null,"位似图形",771]
[null,"位似图形的性质",772]
[null,"画位似图形的一般步骤。",773]
[null,"位似变换的坐标特征",774,1]
[null,"位似变换的坐标特征",774]
[null,"方法清单",775]
[null,"相似多边形的判定方法。",776]
[null,"相似多边形性质的应用方法。",777]
[null,"位似图形的识别方法",778]
[null,"位似图形性质的应用方法。",779]
[null,"锐角三角函数",780]
[null,"锐角三角函数",781]
["锐角三角函数","知识清单",782]
[null,"知识清单",782]
[null,"正弦",783]
[null,"正弦",783]
[null,"余弦",784]
[null,"余弦",784,1]
[null,"余弦",784]
[null,"正切",785]
[null,"正切",785,1]
[null,"正切",785]
[null,"特殊角的三角函数值",786]
[null,"锐角三角函数的关系",787]
[null,"锐角三角函数的性质",788]
[null,"方法清单",789]
[null,"利用锐角三角函数的概念求三角函数值。",790]
[null,"利用锐角三角函数的概念求线段长的方法。",791]
[null,"特殊角三角函数值进行计算的方法。",792]
[null,"等角代换法求锐角三角函数值。",793]
[null,"设参数法求锐角三角函数值。",794,1]
[null,"设参数法求锐角三角函数值。",794]
[null,"构造直角三角形求锐角三角函数值。",795]
[null,"解直角三角形",796]
[null,"知识清单",797]
[null,"解直角三角形",798]
[null,"解直角三角形的理论依据。",799]
[null,"解直角三角形的常见类型。",800]
[null,"解直角三角形应用题中的常见概念。",801]
[null,"解直角三角形应用题的一般步骤。",802]
[null,"测量物体的高度的常见模型。",803]
[null,"方法清单",804]
[null,"解直角三角形的方法",805]
[null,"解斜三角形的方法",806]
[null,"双直角三角形问题的解题方法。",807,1]
[null,"双直角三角形问题的解题方法。",807]
[null,"解直角三角形的知识解决视角相关问题的方法。",808]
[null,"利用解直角三角形的知识解决方向角相关问题的方法。",809]
[null,"运用解直角三角形的知识解决坡角坡度相关问题。",810,1]
[null,"运用解直角三角形的知识解决坡角坡度相关问题的方法。",810]
[null,"解直角三角形的知识解决台风相关问题的方法。",811]
[null,"利用解直角三角形的知识测量物体的高度的方法。",812]
[null,"视图与投影",813]
[null,"几何体的视图",814]
["视图与投影","知识清单",815]
[null,"知识清单",815]
[null,"几何体的三视图",816]
[null,"几何体的三视图",816,1]
[null,"几何体的三视图",816]
[null,"常见几何体的三视图",817]
[null,"常见几何体的三视图",817]
[null,"计算一次函数图像与坐标轴围成的三角形的面积。",818,1]
[null,"几何体三视图的画法",818]
[null,"组合体的三视图",819,1]
[null,"组合体的三视图",819]
[null,"方法清单",820]
[null,"几何体的三视图的识别方法。",821]
[null,"由三视图还原几何体。",822,1]
[null,"由三视图还原几何体的方法。",822]
[null,"由三视图确定小正方形的个数。",823,1]
[null,"由三视图确定小正方形的个数的方法。",823]
[null,"根据三视图求几何体的体积和表面积的方法。",824]
[null,"投影",825]
[null,"知识清单",826]
[null,"投影",827]
[null,"平行投影",828]
[null,"平行投影的变化规律",829]
[null,"中心投影",830]
[null,"平行投影与中心投影的区别与联系。",831]
[null,"正投影",832,1]
[null,"正投影",832]
[null,"方法清单",833]
[null,"平行投影与中心投影的识别方法。",834]
[null,"中心投影的应用方法",835]
[null,"利用平行投影确定影长的方法",836]
[null,"利用相似型解决投影问题的方法。",837]
[null,"尺规作图与命题的证明",838]
["尺规作图","知识清单",839]
[null,"知识清单",839]
[null,"尺规作图",840]
[null,"尺规作图",840]
[null,"基本作图",841]
[null,"基本作图",841]
[null,"方法清单",842]
[null,"方法清单",842]
[null,"运用基本作图作三角形",843,1]
[null,"运用基本作图作三角形的方法",843]
[null,"作全等三角形",844,1]
[null,"作全等三角形的方法",844]
[null,"运用基本作图确定特殊位置。",845,1]
[null,"运用基本作图确定特殊位置的方法。",845]
[null,"运用基本作图确定圆心位置。",846,1]
[null,"运用基本作图确定圆心位置的方法。",846]
[null,"命题",847]
[null,"知识清单",848]
[null,"命题",849,1]
[null,"命题",849]
[null,"真命题、假命题",850]
[null,"逆命题",851,1]
[null,"逆命题",851]
[null,"公理、定理",852,1]
[null,"公理、定理",852]
[null,"互逆定理",853,1]
[null,"互逆定理",853]
[null,"方法清单",854]
[null,"命题的识别方法",855,1]
[null,"命题的识别方法",855]
[null,"真假命题的辨别方法",856]
[null,"证明",857]
[null,"知识清单",858]
[null,"证明的含义",859]
[null,"证明的一般步骤",860]
[null,"辅助线",861]
[null,"综合法与分析法",862,1]
[null,"综合法与分析法",862]
[null,"反正法",863]
[null,"面积法",864]
[null,"方法清单",865]
[null,"命题形成的开放性问题的解决方法。",866,1]
[null,"命题形成的开放性问题的解决方法。",866]
[null,"综合法在几何证明中的运用方法。",867,1]
[null,"综合法在几何证明中的运用方法。",867]
[null,"分析法在几何证明中的运用方法。",868]
[null,"面积法在几何证明中的运用方法。",869]
[null,"辅助线在几何证明中的应用方法。",870]
[null,"证明两角相等的常用方法。",871]
[null,"证明线段相等的常用方法。",872]
[null,"数据的收集、整理与描述。",873,1]
[null,"数据的收集、整理与描述。",873]
[null,"数据我的收集与整理。",874,1]
[null,"数据我的收集与整理。",874]
["数据的收集与整理","知识清单",875]
[null,"知识清单",875]
[null,"数据的收集与整理",876]
[null,"数据的收集与整理",876]
[null,"总体、个体、样本与样本容量。",877]
[null,"总体、个体、样本与样本容量。",877]
[null,"普查与抽样调查",878]
[null,"普查与抽样调查",878]
[null,"普查与抽样调查的区别与联系。",879]
[null,"方法清单",880]
[null,"调查方式的选择方法",881]
[null,"抽样调查的和理性的判断方法。",882]
[null,"总体、个体、样文与样本容量的判断方法。",883]
[null,"用样本估计总体的应用方法",884]
[null,"数据的描述",885]
[null,"知识清单",886]
[null,"频数与频率",887]
[null,"组数与组距",888,1]
[null,"组数与组距",888]
[null,"频数分布表",889]
[null,"条形统计图、扇形统计图与折线统计图。",890]
[null,"条形统计、扇形统计图与折线统计图的区别与联系",891]
[null,"频数分布直方图",892]
[null,"频数折线图",893]
[null,"方法清单",894]
[null,"统计图的识别和应用。",895,1]
[null,"统计图的识别和应用的方法。",895]
[null,"综合利用多种统计图解决实际问题的方法。",896]
[null,"补全或绘制统计图的方法。",897]
[null,"频数分布表和频数分布直方图的识别和应用方法。",898]
[null,"数据的分析",899]
[null,"数据的代表",900]
["数据的分析","知识清单",901]
[null,"知识清单",901]
[null,"平均数",902]
[null,"平均数",902]
[null,"加权平均数",903]
[null,"加权平均数",903]
[null,"中位数",904]
[null,"中位数",904]
[null,"众数",905]
[null,"众数",905]
[null,"平均数、中位数、众数的区别与联系。",906]
[null,"平均数、中位数、众数的区别与联系。",906]
[null,"方法清单",907]
[null,"平均数、中位数、众数的计算方法。",908]
[null,"加权平均数的应用方法",909]
[null,"选择合适的统计量解决问题。",910]
[null,"数据的波动",911]
[null,"知识清单",912]
[null,"极差",913]
[null,"方差",914]
[null,"极差与方差的区别与联系。",915]
[null,"标准差",916]
[null,"方法清单",917]
[null,"方差的性质的应用方法。",918]
[null,"极差、方差的应用方法。",919]
[null,"利用方差进行决策的方法。",920]
[null,"概率",921]
[null,"概率的有关概念",922]
["概率","知识清单",923]
[null,"知识清单",923]
[null,"确定事件",924]
[null,"确定事件",924]
[null,"随机事件",925]
[null,"随机事件",925]
[null,"概率的定义",926]
[null,"概率的定义",926]
[null,"几何概率",927]
[null,"公平的游戏",928,1]
[null,"公平的游戏",928]
[null,"方法清单",929]
[null,"利用概率的定义求事件概率的方法。",930]
[null,"几何概率的计算方法",931]
[null,"判评游戏是否公平。",932,1]
[null,"判评游戏是否公平的方法。",932]
[null,"概率的计算方法",933]
[null,"列举法",934]
[null,"画树状图法",935]
[null,"列表法",936]
[null,"频率估计概率",937,1]
[null,"频率估计概率",937]
[null,"模拟实验",938]
[null,"方法清单",939]
[null,"利用树状图法求事件概率的方法。",940]
[null,"利用列表法求事件概率的方法。",941]
[null,"用频率估计概率的方法。",942]
[null,"利用概率解决平均收益问题的方法。",943]
[null,"选择模拟试验的方法",944]
[null,"常见的数学思想",945]
[null,"知识清单",946]
[null,"数形结合思想",947]
[null,"整体思想",948]
[null,"转化思想",949]
[null,"方程思想",950]
[null,"函数思想",951]
[null,"分类讨论思想",952]
[null,"归纳与类比的思想",953]
[null,"不规则图形的面积",null,1]
[null,"测量物体的高度的常见模型。",null,1]
[null,"常见的立体图形",null,1]
[null,"抽样调查的和理性的判断方法。",null,1]
[null,"代数式及其分类",null,1]
[null,"待定系数法",null,1]
[null,"单项式",null,1]
[null,"倒数",null,1]
[null,"列一元二次方程解应用题的一般步骤。",null,1]
[null,"求锐角三角函数值。",null,1]
[null,"去分母解方程",null,1]
[null,"树状图法求事件概率。",null,1]
[null,"数据的波动",null,1]
[null,"数学思想计算线段长度。",null,1]
[null,"同解方程组确定字母取值",null,1]
[null,"图形的对称确定变化的坐标方法",null,1]
[null,"图形的平移，旋转，轴对称进行方案设计。",null,1]
[null,"图形的平移确定变化的坐标。",null,1]
[null,"图形的轴对称",null,1]
[null,"消元思想解三元一次方程组。",null,1]
[null,"与二次根式相关的混合运算。",null,1]