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"会用绝对值的几何意义求解一些基本的含绝对值的不等式.", "predecessor": [] }, "K0117002B": { "id": "K0117002B", "unit_obj": "D01004B", "content": "会用分类讨论的思想求解一些基本的含绝对值的不等式.", "predecessor": [ "K0117001B" ] }, "K0118001B": { "id": "K0118001B", "unit_obj": "D01003B", "content": "知道算术平均值和几何平均值的概念.", "predecessor": [] }, "K0118002B": { "id": "K0118002B", "unit_obj": "D01003B", "content": "经历平均值不等式的证明过程, 理解取等号的条件.", "predecessor": [ "K0118001B", "K0111003B" ] }, "K0118003B": { "id": "K0118003B", "unit_obj": "D01003B", "content": "能运用平均值不等式比较大小、证明一些简单的不等式.", "predecessor": [ "K0118002B" ] }, "K0119001B": { "id": "K0119001B", "unit_obj": "D01003B", "content": "会运用平均值不等式求解较简单的最大值和最小值问题.", "predecessor": [ "K0118002B" ] }, "K0119002B": { "id": "K0119002B", "unit_obj": "D01003B", "content": "会运用平均值不等式解决一些现实情境中的最大值和最小值问题.", "predecessor": [ "K0119001B" ] }, "K0120001B": { "id": "K0120001B", "unit_obj": "D01003B", "content": "经历三角不等式的证明过程, 理解取等号的条件.", "predecessor": [ "K0111003B" ] }, "K0120002B": { "id": "K0120002B", "unit_obj": "D01003B", "content": "会运用三角不等式证明一些简单的不等式.", "predecessor": [ "K0120001B" ] }, "K0120003B": { "id": "K0120003B", "unit_obj": "D01003B", "content": "会运用三角不等式求解一些简单的最大值或最小值问题.", "predecessor": [ "K0120001B" ] }, "K0201001B": { "id": "K0201001B", "unit_obj": "D02001B", "content": "理解零次幂与负整数幂的定义及运算性质.", "predecessor": [] }, "K0201002B": { "id": "K0201002B", "unit_obj": "D02001B", "content": "理解根式及其相关的概念.", "predecessor": [ "K0201001B" ] }, "K0201003B": { "id": "K0201003B", "unit_obj": "D02001B", "content": "会根据定义求实数的$n$次方根.", "predecessor": [ "K0201002B" ] }, "K0201004B": { "id": "K0201004B", "unit_obj": "D02001B", "content": "理解底数为正实数$a$的有理数指数幂的定义$a^{m/n}=(a^{m})^{1/n}$,经历等价定义$a^{m/n}= (a^{1/n})^{m}$的推导过程.", "predecessor": [ "K0201001B", "K0201002B" ] }, "K0202001B": { "id": "K0202001B", "unit_obj": "D02001B", "content": "经历在个别情形下验证底数为正实数的有理数指数幂的三条运算性质的过程.", "predecessor": [ "K0201001B", "K0201004B" ] }, "K0202002B": { "id": "K0202002B", "unit_obj": "D02001B", "content": "会运用底数为正实数的有理数指数幂的定义及运算性质进行幂与根式的互化以及解决相关的化简、计算等问题.", "predecessor": [ "K0201004B", "K0202001B" ] }, "K0202003B": { "id": "K0202003B", "unit_obj": "D02001B", "content": "理解底数为负实数的有理数指数幂的定义, 进而理解底数为实数的有理数指数幂的定义.", "predecessor": [ "K0202002B" ] }, "K0203001B": { "id": "K0203001B", "unit_obj": "D02001B", "content": "知道底数为正实数的无理数指数幂的定义.", "predecessor": [ "K0202002B" ] }, "K0203002B": { "id": "K0203002B", "unit_obj": "D02001B", "content": "熟记底数为正实数的实数指数幂的三条运算性质.", "predecessor": [ "K0202002B", "K0202001B" ] }, "K0203003B": { "id": "K0203003B", "unit_obj": "D02001B", "content": "经历有理数指数幂的基本不等式: ``当实数$a>1$, 有理数$s>0$时, 不等式$a^s>1$成立''的推导过程.", "predecessor": [ "K0202003B" ] }, "K0203004B": { "id": "K0203004B", "unit_obj": "D02001B", "content": "知道幂的基本不等式: ``当$a>1$, $s>0$时, $a^s>1$''.", "predecessor": [ "K0203002B" ] }, "K0203005B": { "id": "K0203005B", "unit_obj": "D02001B", "content": "会应用底数为正实数的实数指数幂的定义、运算性质以及幂的基本不等式, 解决底数为正实数的实数指数幂的较复杂的表达式的化简、不等式的证明等问题.", "predecessor": [ "K0202002B", "K0203001B", "K0203002B", "K0203004B" ] }, "K0204001B": { "id": "K0204001B", "unit_obj": "D02001B", "content": "理解对数的定义.", "predecessor": [] }, "K0204002B": { "id": "K0204002B", "unit_obj": "D02001B", "content": "会理解、熟记并应用一些常用的对数等式: ``$a^{\\log_aN}=N$, $\\log_a1=0$, $\\log_aa=1$''.", "predecessor": [ "K0204001B" ] }, "K0204003B": { "id": "K0204003B", "unit_obj": "D02001B", "content": "知道常用对数、常数$e$以及自然对数的含义.", "predecessor": [ "K0204001B" ] }, "K0204004B": { "id": "K0204004B", "unit_obj": "D02001B", "content": "会进行指数式与对数式的互化, 以及对数式的化简.", "predecessor": [ "K0204001B", "K0204003B" ] }, "K0205001B": { "id": "K0205001B", "unit_obj": "D02001B", "content": "经历推导对数运算性质$1$: ``当$M>0$,$N>0$时, $\\log_a(MN)=\\log_aM+\\log_aN$''；性质$2$: ``当$M>0$,$N>0$时, $\\log_a(M/N)=\\log_aM-\\log_aN$''；性质$3$: ``当$N>0$时, 对任何给定的实数$c$, $\\log_a(N^{c})=c\\log_aN$''的过程, 并熟记这三条运算性质.", "predecessor": [ "K0204001B", "K0203002B" ] }, "K0205002B": { "id": "K0205002B", "unit_obj": "D02001B", "content": "会运用对数的定义以及运算性质解决简单的求值、化简以及生活实际问题.", "predecessor": [ "K0204001B", "K0205001B" ] }, "K0206001B": { "id": "K0206001B", "unit_obj": "D02001B", "content": "经历推导对数换底公式的过程.", "predecessor": [ "K0205001B", "K0204003B", "K0204002B" ] }, "K0206002B": { "id": "K0206002B", "unit_obj": "D02001B", "content": "会运用对数的运算性质以及换底公式解决较复杂的求值、化简以及证明等相关问题.", "predecessor": [ "K0205001B", "K0206001B" ] }, "K0206003B": { "id": "K0206003B", "unit_obj": "D02001B", "content": "会推导并会运用例7的结论: ``当$a>0$, $a\\neq1$, 且$N>0$, $m\\neq0$时, $\\log_a^{m}N^{n}=n/m\\log_aN$''.", "predecessor": [ "K0206001B", "K0205001B", "K0204002B" ] }, "K0207001B": { "id": "K0207001B", "unit_obj": "D02002B", "content": "理解幂函数的定义(包含幂函数定义域的概念).", "predecessor": [] }, "K0207002B": { "id": "K0207002B", "unit_obj": "D02002B", "content": "会根据具体的幂指数$a$求解幂函数$y=x^{a}$的定义域.", "predecessor": [ "K0207001B", "K0202003B" ] }, "K0207003B": { "id": "K0207003B", "unit_obj": "D02002B", "content": "会根据函数定义域, 利用计算器合理采点, 并能通过描点法作出幂函数$y=x^{1/2}$, $y=x^{3}$, $y=x^{-2/3}$的大致图像.", "predecessor": [ "K0207002B" ] }, "K0207004B": { "id": "K0207004B", "unit_obj": "D02002B", "content": "会用图像上任意一点关于原点(或关于$y$轴)的对称点仍落在图像上证明函数的图像关于原点(或$y$轴)对称.", "predecessor": [ "K0207003B" ] }, "K0208001B": { "id": "K0208001B", "unit_obj": "D02002B", "content": "会用不等式的常用性质证明当$x>0$时, 幂函数的函数值总大于$0$.", "predecessor": [ "K0111001B" ] }, "K0208002B": { "id": "K0208002B", "unit_obj": "D02002B", "content": "会经历作图猜想证明具体的幂函数图像在第一象限的单调性.", "predecessor": [ "K0203004B", "K0207003B" ] }, "K0208003B": { "id": "K0208003B", "unit_obj": "D02002B", "content": "知道幂函数的图像过定点$(1,1)$.", "predecessor": [] }, "K0208004B": { "id": "K0208004B", "unit_obj": "D02002B", "content": "会用幂函数的单调性判断两个幂的大小.", "predecessor": [ "K0208002B" ] }, "K0208005B": { "id": "K0208005B", "unit_obj": "D02002B", "content": "理解函数图像的平移与解析式的关系, 并会以此为依据作出分式线性函数的大致图像.", "predecessor": [] }, "K0209001B": { "id": "K0209001B", "unit_obj": "D02002B", "content": "理解指数函数的定义(包含指数函数定义域为$\\mathbf{R}$).", "predecessor": [ "K0202003B", "K0203001B" ] }, "K0209002B": { "id": "K0209002B", "unit_obj": "D02002B", "content": "会求解有关指数型函数的定义域.", "predecessor": [ "K0202002B", "K0203001B" ] }, "K0209003B": { "id": "K0209003B", "unit_obj": "D02002B", "content": "会根据函数定义域, 利用计算器合理采点, 并能通过描点法作出指数函数$y=2^{x}$, $y=3^{x}$, $y=(1/2)^{x}$的大致图像.", "predecessor": [ "K0209001B" ] }, "K0210001B": { "id": "K0210001B", "unit_obj": "D02002B", "content": "会结合图像, 了解指数函数函数值恒大于$0$.", "predecessor": [ "K0209003B" ] }, "K0210002B": { "id": "K0210002B", "unit_obj": "D02002B", "content": "知道指数函数图像过定点$(0,1)$.", "predecessor": [ "K0209003B" ] }, "K0210003B": { "id": "K0210003B", "unit_obj": "D02002B", "content": "会证明指数函数$y=a^{x}$与$y=(1/a)^{x}$($a>0$且$a\\neq1$)的图像关于$y$轴对称.", "predecessor": [ "K0203002B", "K0209003B" ] }, "K0210004B": { "id": "K0210004B", "unit_obj": "D02002B", "content": "会利用幂的基本不等式证明指数函数的单调性.", "predecessor": [ "K0203004B" ] }, "K0210005B": { "id": "K0210005B", "unit_obj": "D02002B", "content": "会作出指数函数的大致图像, 能根据其图像特征叙述其函数性质.", "predecessor": [ "K0209003B", "K0210001B", "K0210002B", "K0210004B" ] }, "K0210006B": { "id": "K0210006B", "unit_obj": "D02002B", "content": "会利用指数函数的单调性判断两个数的大小.", "predecessor": [ "K0210005B" ] }, "K0211001B": { "id": "K0211001B", "unit_obj": "D02002B", "content": "会利用指数函数的单调性解决相关不等式等问题.", "predecessor": [ "K0210005B" ] }, "K0211002B": { "id": "K0211002B", "unit_obj": "D02002B", "content": "会利用指数函数的性质解决其他如最值问题等数学问题和实际生活问题.", "predecessor": [ "K0210005B" ] }, "K0212001B": { "id": "K0212001B", "unit_obj": "D02002B", "content": "理解对数函数的定义(包含对数函数定义域为$(0,+\\infty)$).", "predecessor": [ "K0204001B" ] }, "K0212002B": { "id": "K0212002B", "unit_obj": "D02002B", "content": "会求解有关对数型函数的定义域.", "predecessor": [ "K0212001B" ] }, "K0212003B": { "id": "K0212003B", "unit_obj": "D02002B", "content": "会根据函数定义域, 利用计算器合理采点, 并能通过描点法作出对数函数$y=\\log_2x,y=\\log_3x,y=\\log_{1/2}x$的大致图像.", "predecessor": [ "K0212001B" ] }, "K0213001B": { "id": "K0213001B", "unit_obj": "D02002B", "content": "会利用对数运算性质, 证明函数$y=\\log_ax,y=\\log_{1/a}x$的图像关于$x$轴对称.", "predecessor": [ "K0212003B", "K0206001B" ] }, "K0213002B": { "id": "K0213002B", "unit_obj": "D02002B", "content": "知道对数函数的图像过定点$(1,0)$.", "predecessor": [ "K0204002B" ] }, "K0213003B": { "id": "K0213003B", "unit_obj": "D02002B", "content": "会联系幂的基本不等式, 利用反证法证明对数的基本不等式.", "predecessor": [ "K0203004B", "K0204001B", "K0107003B" ] }, "K0213004B": { "id": "K0213004B", "unit_obj": "D02002B", "content": "会类比指数函数的单调性的证明, 利用对数的基本不等式证明对数函数的单调性.", "predecessor": [ "K0210004B", "K0213003B" ] }, "K0213005B": { "id": "K0213005B", "unit_obj": "D02002B", "content": "会结合图像以及指数与对数互为逆运算的性质, 探究并证明对数函数$y=\\log_ax$和指数函数$y=a^{x}$的图像关于直线$y=x$对称.", "predecessor": [ "K0204001B", "K0210005B", "K0212003B" ] }, "K0213006B": { "id": "K0213006B", "unit_obj": "D02002B", "content": "了解逆运算和反函数的概念.", "predecessor": [ "K0213005B" ] }, "K0213007B": { "id": "K0213007B", "unit_obj": "D02002B", "content": "会作出对数函数的大致图像, 能根据其图像特征叙述函数性质.", "predecessor": [ "K0212003B", "K0213001B", "K0213002B", "K0213004B" ] }, "K0213008B": { "id": "K0213008B", "unit_obj": "D02002B", "content": "会利用对数函数的单调性判断两个数的大小.", "predecessor": [ "K0213007B" ] }, "K0214001B": { "id": "K0214001B", "unit_obj": "D02002B", "content": "会利用对数函数的单调性估算对数型无理数(如$\\log_23$).", "predecessor": [ "K0213007B" ] }, "K0214002B": { "id": "K0214002B", "unit_obj": "D02002B", "content": "会利用对数函数的单调性解决其他相关不等式等数学问题和生活中的实际问题.", "predecessor": [ "K0213007B" ] }, "K0215001B": { "id": "K0215001B", "unit_obj": "D02003B", "content": "理解函数的概念, 体会函数即数与数之间的对应关系, 理解函数的定义(包含自变量、函数值、定义域、值域的概念).", "predecessor": [ "K0101001B" ] }, "K0215002B": { "id": "K0215002B", "unit_obj": "D02003B", "content": "知道定义域和对应关系为函数的两个要素.", "predecessor": [ "K0215001B" ] }, "K0215003B": { "id": "K0215003B", "unit_obj": "D02003B", "content": "会求函数的自然定义域.", "predecessor": [ "K0215001B", "K0207002B", "K0209002B", "K0212002B", "K0104001B" ] }, "K0215004B": { "id": "K0215004B", "unit_obj": "D02003B", "content": "理解两个函数相同的定义, 并会判断两个函数是否是同一函数.", "predecessor": [ "K0215002B" ] }, "K0215005B": { "id": "K0215005B", "unit_obj": "D02003B", "content": "会根据已学习过的一些简单函数的值域, 利用复合求解稍为复杂函数的值域.", "predecessor": [ "K0213007B", "K0210005B" ] }, "K0216001B": { "id": "K0216001B", "unit_obj": "D02003B", "content": "知道函数可以用解析式、图像、列表等方式表示.", "predecessor": [ "K0215001B" ] }, "K0216002B": { "id": "K0216002B", "unit_obj": "D02003B", "content": "理解函数的图像的概念.", "predecessor": [ "K0215001B" ] }, "K0216003B": { "id": "K0216003B", "unit_obj": "D02003B", "content": "会合理利用计算器采点, 通过描点法作出不熟悉函数的大致图像.", "predecessor": [ "K0216002B" ] }, "K0216004B": { "id": "K0216004B", "unit_obj": "D02003B", "content": "会利用函数的定义判断坐标系中的图像是否为函数图像.", "predecessor": [ "K0215001B" ] }, "K0216005B": { "id": "K0216005B", "unit_obj": "D02003B", "content": "了解并能根据实际情况运用函数的分段表示法.", "predecessor": [ "K0216001B", "K0215002B" ] }, "K0216006B": { "id": "K0216006B", "unit_obj": "D02003B", "content": "知道取整符号$[x]$的含义, 并作出取整函数的大致图像.", "predecessor": [ "K0216003B", "K0216005B" ] }, "K0217001B": { "id": "K0217001B", "unit_obj": "D02003B", "content": "知道基于点集的平面图形关于直线成轴对称, 以及关于点成中心对称的定义.", "predecessor": [ "K0207003B" ] }, "K0217002B": { "id": "K0217002B", "unit_obj": "D02003B", "content": "会推导``函数的图像关于$y$轴成轴对称''的等价的代数表达形式, 即偶函数的定义.", "predecessor": [ "K0217001B" ] }, "K0217003B": { "id": "K0217003B", "unit_obj": "D02003B", "content": "会类比偶函数的定义得到``函数的图像关于原点成中心对称''的等价的代数表达形式, 即奇函数的定义.", "predecessor": [ "K0217002B" ] }, "K0217004B": { "id": "K0217004B", "unit_obj": "D02003B", "content": "会运用奇函数、偶函数的定义, 证明一些较为简单的函数是奇函数或是偶函数.", "predecessor": [ "K0217002B", "K0217003B" ] }, "K0218001B": { "id": "K0218001B", "unit_obj": "D02003B", "content": "会运用奇函数、偶函数的定义, 通过赋值法或分析定义域, 判断较为复杂(如含参数)的函数的奇偶性问题.", "predecessor": [ "K0217004B" ] }, "K0219001B": { "id": "K0219001B", "unit_obj": "D02003B", "content": "理解函数单调性的定义.", "predecessor": [ "K0210004B", "K0213004B" ] }, "K0219002B": { "id": "K0219002B", "unit_obj": "D02003B", "content": "会运用函数单调性的定义证明一次函数、二次函数、反比例函数的单调性.", "predecessor": [ "K0219001B" ] }, "K0219003B": { "id": "K0219003B", "unit_obj": "D02003B", "content": "会运用函数单调性的定义以及已知的基本初等函数的单调性, 判断较为复杂的函数单调性.", "predecessor": [ "K0210004B", "K0213004B", "K0219001B" ] }, "K0220001B": { "id": "K0220001B", "unit_obj": "D02003B", "content": "理解单调函数、单调区间的定义.", "predecessor": [ "K0219001B" ] }, "K0220002B": { "id": "K0220002B", "unit_obj": "D02003B", "content": "会求函数的单调区间.", "predecessor": [ "K0220001B" ] }, "K0220003B": { "id": "K0220003B", "unit_obj": "D02003B", "content": "能直观地感知奇偶性可用于分析单调性并能说理.", "predecessor": [ "K0220001B", "K0217002B", "K0217003B" ] }, "K0221001B": { "id": "K0221001B", "unit_obj": "D02003B", "content": "理解函数最大值、最小值的定义.", "predecessor": [ "K0215001B" ] }, "K0221002B": { "id": "K0221002B", "unit_obj": "D02003B", "content": "会运用最值的定义, 解决函数的最值问题, 以及含参数的函数最值问题(函数对应关系含参数或者定义域含参数)的数学问题.", "predecessor": [ "K0220002B", "K0221001B" ] }, "K0222001B": { "id": "K0222001B", "unit_obj": "D02004B", "content": "会将现实情境转化为数学模型, 并能分析其中量与量之间的关系.", "predecessor": [] }, "K0222002B": { "id": "K0222002B", "unit_obj": "D02004B", "content": "在建立好的数学模型中, 能合理选取变量, 建立变量之间的函数关系, 并能结合实际写出函数的定义域.", "predecessor": [ "K0222001B", "K0215001B" ] }, "K0223001B": { "id": "K0223001B", "unit_obj": "D02004B", "content": "知道函数零点的定义.", "predecessor": [ "K0215001B", "K0108002B" ] }, "K0223002B": { "id": "K0223002B", "unit_obj": "D02004B", "content": "会用函数的观点求解一元二次方程.", "predecessor": [ "K0223001B", "K0109001B" ] }, "K0223003B": { "id": "K0223003B", "unit_obj": "D02004B", "content": "会用函数的观点求解一元二次不等式.", "predecessor": [ "K0223001B", "K0112002B" ] }, "K0223004B": { "id": "K0223004B", "unit_obj": "D02004B", "content": "会用函数的观点求解较为复杂的方程.", "predecessor": [ "K0223001B", "K0219003B" ] }, "K0223005B": { "id": "K0223005B", "unit_obj": "D02004B", "content": "会用函数的观点求解较为复杂的不等式.", "predecessor": [ "K0223001B", "K0219003B" ] }, "K0224001B": { "id": "K0224001B", "unit_obj": "D02004B", "content": "知道零点存在定理, 会用零点存在定理判断连续函数在区间上存在零点.", "predecessor": [ "K0223001B", "K0216003B" ] }, "K0224002B": { "id": "K0224002B", "unit_obj": "D02004B", "content": "理解并会运用二分法寻求连续函数在某个区间上的零点的近似值.", "predecessor": [ "K0224001B" ] }, "K0225001B": { "id": "K0225001B", "unit_obj": "D02004B", "content": "理解反函数的定义.", "predecessor": [ "K0213006B", "K0215002B", "K0215005B" ] }, "K0225002B": { "id": "K0225002B", "unit_obj": "D02004B", "content": "会判断一个函数是否存在反函数.", "predecessor": [ "K0225001B", "K0219003B" ] }, "K0225003B": { "id": "K0225003B", "unit_obj": "D02004B", "content": "知道反函数与原来函数定义域与值域的关系.", "predecessor": [ "K0213006B", "K0215002B", "K0215005B" ] }, "K0225004B": { "id": "K0225004B", "unit_obj": "D02004B", "content": "会根据反函数与原来函数自变量与函数值的关系, 求解反函数或原来函数的自变量或函数值.", "predecessor": [ "K0225003B" ] }, "K0225005B": { "id": "K0225005B", "unit_obj": "D02004B", "content": "会求一个具体函数的反函数.", "predecessor": [ "K0225001B", "K0225002B", "K0225003B" ] }, "K0226001B": { "id": "K0226001B", "unit_obj": "D02004B", "content": "经历命题``在平面直角坐标系中, 点$P(a,b)$与点$P'(b,a)$关于直线$y=x$成轴对称''的推导过程.", "predecessor": [] }, "K0226002B": { "id": "K0226002B", "unit_obj": "D02004B", "content": "会利用命题``在平面直角坐标系中, 点$P(a,b)$与点$P'(b,a)$关于直线$y=x$成轴对称''证明性质: ``互为反函数的两函数的图像关于$y=x$成轴对称''.", "predecessor": [ "K0225001B", "K0226001B" ] }, "K0226003B": { "id": "K0226003B", "unit_obj": "D02004B", "content": "能根据性质: ``互为反函数的两函数的图像关于$y=x$成轴对称'', 作出具体函数的反函数的大致图像.", "predecessor": [ "K0226002B" ] }, "K0226004B": { "id": "K0226004B", "unit_obj": "D02004B", "content": "能根据性质: ``互为反函数的两函数的图像关于$y=x$成轴对称''与命题``在平面直角坐标系中, 点$P(a,b)$与点$P'(b,a)$关于直线$y=x$成轴对称'', 求解函数与其反函数的图像上点的相关问题.", "predecessor": [ "K0226002B", "K0226001B" ] }, "K0226005B": { "id": "K0226005B", "unit_obj": "D02004B", "content": "会探究具体函数与其反函数的基本性质之间的区别与联系.", "predecessor": [ "K0225001B", "K0225003B", "K0219001B", "K0217004B" ] }, "K0226006B": { "id": "K0226006B", "unit_obj": "D02004B", "content": "了解符号$f^{-1}(ax+b)$的含义.", "predecessor": [] }, "K0227001X": { "id": "K0227001X", "unit_obj": "D02005X", "content": "经历现实情境中变速运动的平均速度与瞬时速度的定义, 感悟极限思想.", "predecessor": [] }, "K0227002X": { "id": "K0227002X", "unit_obj": "D02005X", "content": "计算已知位移表达式的运动过程中平均速度的极限, 得到某一时刻的瞬时速度, 理解瞬时速度的含义.", "predecessor": [] }, "K0227003X": { "id": "K0227003X", "unit_obj": "D02005X", "content": "从瞬时速度的计算过程中抽象出导数的定义, 理解位移在某一时刻的导数就是该时刻的瞬时速度.", "predecessor": [] }, "K0227004X": { "id": "K0227004X", "unit_obj": "D02005X", "content": "结合导数理解函数的瞬时变化率的概念.", "predecessor": [] }, "K0227005X": { "id": "K0227005X", "unit_obj": "D02005X", "content": "会对不超过二次的多项式函数通过定义求在自变量取具体值时的导数.", "predecessor": [] }, "K0228001X": { "id": "K0228001X", "unit_obj": "D02005X", "content": "了解一般曲线的切线可定义为割线的极限情形.", "predecessor": [] }, "K0228002X": { "id": "K0228002X", "unit_obj": "D02005X", "content": "在具体的情境中, 直观地通过列举斜率数据, 验证圆上一点处用割线极限定义的切线与平面几何中定义的切线是一致的.", "predecessor": [] }, "K0228003X": { "id": "K0228003X", "unit_obj": "D02005X", "content": "用代数语言描述函数图像上某点处割线斜率的极限, 进而结合导数的定义, 理解切线的斜率就是函数在该点处的导数.", "predecessor": [] }, 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"unit_obj": "D03002B", "content": "理解可以通过终边的旋转、对称等方式, 利用诱导公式研究平面上的坐标变换.", "predecessor": [ "K0301004B", "K0306001B", "K0307001B", "K0304001B" ] }, "K0308001B": { "id": "K0308001B", "unit_obj": "D03002B", "content": "能够从已知特殊三角值的角的正弦、余弦、正切值求角的集合, 并能简单应用.", "predecessor": [ "K0306001B", "K0307001B", "K0304001B" ] }, "K0308002B": { "id": "K0308002B", "unit_obj": "D03002B", "content": "能借助角的三角比的特殊值解简单的三角方程.", "predecessor": [ "K0308001B" ] }, "K0308003B": { "id": "K0308003B", "unit_obj": "D03002B", "content": "掌握锐角的反三角函数表示, 并能用计算器求出近似值.", "predecessor": [ "K0303001B" ] }, "K0308004B": { "id": "K0308004B", "unit_obj": "D03002B", "content": "借助单位圆, 能用反三角符号表示的锐角表示一般角.", "predecessor": [ "K0308003B", "K0304001B" ] }, "K0308005B": { "id": "K0308005B", "unit_obj": "D03002B", "content": "会解具体的最简三角方程(指$\\sin x=\\sin \\alpha$, $\\cos x=\\cos \\alpha$, $\\tan x=\\tan\\alpha$).", "predecessor": [ "K0308004B", "K0308002B" ] }, "K0309001B": { "id": "K0309001B", "unit_obj": "D03002B", "content": 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"K0718001X": { "id": "K0718001X", "unit_obj": "D07006X", "content": "会通过联立方程组研究直线与双曲线的公共点个数, 并从形的角度掌握直线与双曲线的位置关系.", "predecessor": [] }, "K0718002X": { "id": "K0718002X", "unit_obj": "D07006X", "content": "在现实情境中能把与双曲线有关的问题抽象为数学模型, 建立坐标系, 应用双曲线的标准方程求解.", "predecessor": [] }, "K0719001X": { "id": "K0719001X", "unit_obj": "D07007X", "content": "经历从具体情境(天文学、物理学等方面)抽象出抛物线, 并借助信息技术等工具绘制出抛物线的这一过程, 了解抛物线的直观图像.", "predecessor": [] }, "K0719002X": { "id": "K0719002X", "unit_obj": "D07007X", "content": "能用语言描述抛物线的定义, 推导抛物线的标准方程, 包括证明以所求方程的任意一组解为坐标的点都在该抛物线上.", "predecessor": [] }, "K0719003X": { "id": "K0719003X", "unit_obj": "D07007X", "content": "知道抛物线的焦点、准线的概念, 掌握四种类型(顶点在原点, 焦点在坐标轴上)抛物线的标准方程.", "predecessor": [] }, "K0719004X": { "id": "K0719004X", "unit_obj": "D07007X", "content": "在简单情境中, 会根据焦点、准线或其他条件求出抛物线的标准方程.", "predecessor": [] }, "K0719005X": { "id": "K0719005X", "unit_obj": "D07007X", "content": "通过回顾初中熟知的\"二次函数的图像是抛物线\"这一结论, 了解二次函数的图像经平移后符合四种标准类型抛物线之一的定义.", "predecessor": [] }, "K0719006X": { "id": "K0719006X", "unit_obj": "D07007X", "content": "会根据抛物线的定义将线段长度作转化证明一些平面几何的命题.", "predecessor": [] }, "K0720001X": { "id": "K0720001X", "unit_obj": "D07007X", "content": "知道用标准方程描述的抛物线关于其中一条坐标轴对称, 知道抛物线顶点的概念, 了解抛物线有且只有一条对称轴.", "predecessor": [] }, "K0720002X": { "id": "K0720002X", "unit_obj": "D07007X", "content": "能根据抛物线的标准方程得到抛物线上点的横、纵坐标的范围.", "predecessor": [] }, "K0720003X": { "id": "K0720003X", "unit_obj": "D07007X", "content": "会通过联立方程组研究直线与抛物线的公共点个数,并从形的角度掌握直线与抛物线的位置关系.", "predecessor": [] }, "K0720004X": { "id": "K0720004X", "unit_obj": "D07007X", "content": "在现实情境中能把与抛物线有关的问题抽象为数学模型, 建立坐标系, 应用抛物线的标准方程求解.", "predecessor": [] }, "K0720005X": { "id": "K0720005X", "unit_obj": "D07007X", "content": "了解抛物线的光学性质.", "predecessor": [] }, "K0721001X": { "id": "K0721001X", "unit_obj": "D07008X", "content": "通过具体的反例, 进一步理解说明一个方程与一条曲线对应时, 需要进行正反两个方面的验证.", "predecessor": [] }, "K0721002X": { "id": "K0721002X", "unit_obj": "D07008X", "content": "掌握求简单的轨迹方程的三个基本步骤(建立合适的坐标系, 根据曲线的特征推导方程, 验证以方程的解为坐标的点都在所求曲线上).", "predecessor": [] }, "K0721003X": { "id": "K0721003X", "unit_obj": "D07008X", "content": "在具体的问题中, 了解如何根据图形的几何特征选取合适的坐标系.", "predecessor": [] }, "K0721004X": { "id": "K0721004X", "unit_obj": "D07008X", "content": "对于线段的定比分点的轨迹等问题, 能用``等价''符号简化曲线与方程对应的证明过程.", "predecessor": [] }, "K0722001X": { "id": "K0722001X", "unit_obj": "D07008X", "content": "借助具体的科学情境, 理解用参数方程来描述曲线的优势.", "predecessor": [] }, "K0722002X": { "id": "K0722002X", "unit_obj": "D07008X", "content": "理解参数方程的概念和相关名词(参数, 参变量, 普通方程).", "predecessor": [] }, "K0722003X": { "id": "K0722003X", "unit_obj": "D07008X", "content": "能通过问题中自然给出的参数将轨迹用参数方程表示.", "predecessor": [] }, "K0722004X": { "id": "K0722004X", "unit_obj": "D07008X", "content": "能通过消参($x,y$中至少有一个变量是参数的一次函数)将参数方程化为普通方程, 并解决曲线上的范围的界定问题.", "predecessor": [] }, "K0722005X": { "id": "K0722005X", "unit_obj": "D07008X", "content": "能借助圆或椭圆的参数方程, 将含有一个约束条件的双变量的问题化为仅含一个自由变量的问题.", "predecessor": [] }, 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"id": "K0724003X", "unit_obj": "D07008X", "content": "会利用余弦的定义求圆心在极径上, 经过原点的圆的极坐标方程.", "predecessor": [] }, "K0724004X": { "id": "K0724004X", "unit_obj": "D07008X", "content": "会分情况讨论, 根据正弦定理推导不过原点的直线的极坐标方程.", "predecessor": [] }, "K0724005X": { "id": "K0724005X", "unit_obj": "D07008X", "content": "会结合物理意义推导等速螺线(阿基米德螺线)的极坐标方程.", "predecessor": [] }, "K0725001X": { "id": "K0725001X", "unit_obj": "D07008X", "content": "能根据正弦和余弦的定义, 推导极坐标转换为直角坐标的公式.", "predecessor": [] }, "K0725002X": { "id": "K0725002X", "unit_obj": "D07008X", "content": "能用公式将具体点的极坐标转换为直角坐标.", "predecessor": [] }, "K0725003X": { "id": "K0725003X", "unit_obj": "D07008X", "content": "通过求解方程, 掌握将点的直角坐标转换为极坐标的公式, 理解其中极角的选取与正切值及点的具体位置均有关.", "predecessor": [] }, "K0725004X": { "id": "K0725004X", "unit_obj": "D07008X", "content": "能用公式将具体点的直角坐标转换为极坐标.", "predecessor": [] }, "K0725005X": { "id": "K0725005X", "unit_obj": "D07008X", "content": "会用$x=\\rho \\cos\\theta$, $y=\\rho \\sin \\theta$代入的方法, 在熟悉的情境下将曲线的简单的直角坐标方程转化为极坐标方程.", "predecessor": [] }, "K0725006X": { "id": "K0725006X", "unit_obj": "D07008X", "content": "通过将$\\rho^2$化为$x^2+y^2$, $\\rho\\cos\\theta$化为$x$, $\\rho\\sin\\theta$化为$y$, 在熟悉的情境下将曲线的极坐标方程转换为直角坐标方程.", "predecessor": [] }, "K0725007X": { "id": "K0725007X", "unit_obj": "D07008X", "content": "了解椭圆, 抛物线, 双曲线的方程在以其(一个)焦点为极点的极坐标系中能统一为相同的形式.", "predecessor": [] }, "K0801001B": { "id": "K0801001B", "unit_obj": "D08001B", "content": "通过具体事例, 认识随机现象在自然界、社会中普遍存在, 理解随机现象的概念.", "predecessor": [] }, "K0801002B": { "id": "K0801002B", "unit_obj": "D08001B", "content": "通过具体事例, 理解随机试验的概念.", "predecessor": [] }, "K0801003B": { "id": "K0801003B", "unit_obj": "D08001B", "content": "初步了解概率论的起源与发展历史, 了解描述性的概率的概念.", "predecessor": [] }, "K0801004B": { "id": "K0801004B", "unit_obj": "D08001B", "content": "能够区分一个现象是随机现象还是确定性现象.", "predecessor": [] }, "K0801005B": { "id": "K0801005B", "unit_obj": "D08001B", "content": "通过具体情境, 了解随机试验中含有的随机性.", "predecessor": [] }, "K0802001B": { "id": "K0802001B", "unit_obj": "D08001B", "content": "了解样本空间, 基本事件(或样本点)的定义, 知道基本事件不能同时发生.", "predecessor": [] }, "K0802002B": { "id": "K0802002B", "unit_obj": "D08001B", "content": "了解在随机现象中, 样本空间的选取可以不唯一.", "predecessor": [] }, "K0802003B": { "id": "K0802003B", "unit_obj": "D08001B", "content": "能够写出随机现象的样本空间, 理解随机事件的含义.", "predecessor": [] }, "K0802004B": { "id": "K0802004B", "unit_obj": "D08001B", "content": "会用集合语言表达随机事件.", "predecessor": [] }, "K0802005B": { "id": "K0802005B", "unit_obj": "D08001B", "content": "理解必然事件和不可能事件的概念, 了解它们对应的子集与样本空间的关系. 会判断一个事件是确定事件还是不确定事件.", "predecessor": [] }, "K0802006B": { "id": "K0802006B", "unit_obj": "D08001B", "content": "能在熟悉的情境中写出随机试验的样本空间.", "predecessor": [] }, "K0803001B": { "id": "K0803001B", "unit_obj": "D08001B", "content": "基于生活经验, 直观地理解随机试验结果的等可能性.", "predecessor": [] }, "K0803002B": { "id": "K0803002B", "unit_obj": "D08001B", "content": "通过具体实例, 理解古典概率模型的两个基本假设: 有限, 等可能. 会基于枚举计数计算古典概率模型中简单随机事件的概率.", "predecessor": [] }, "K0803003B": { 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