wangweiye
/
mathdeptv2
Archived
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

K03单元的课时目标添加predecessor

This commit is contained in:
wangweiye7840 2024-03-19 14:04:52 +08:00
parent c393496061
commit e220fc9af1
1 changed files with 275 additions and 75 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

350
题库0.3/LessonObj.json
View File

@ -1555,241 +1555,349 @@
"id": "K0301002B",
"unit_obj": "D03001B",
"content": "会判断角在平面直角坐标系中的位置.",
"predecessor": []
"predecessor": [
"K0301001B"
]
},
"K0301003B": {
"id": "K0301003B",
"unit_obj": "D03001B",
"content": "角的加减运算与角终边的旋转之间的关系.",
"predecessor": []
"predecessor": [
"K0301001B",
"K0301002B"
]
},
"K0301004B": {
"id": "K0301004B",
"unit_obj": "D03001B",
"content": "终边有特殊位置关系的角之间的等量关系.",
"predecessor": []
"predecessor": [
"K0301003B"
]
},
"K0302001B": {
"id": "K0302001B",
"unit_obj": "D03001B",
"content": "了解弧度制, 能进行一般的角度制与弧度制的转化.",
"predecessor": []
"predecessor": [
"K0301001B"
]
},
"K0302002B": {
"id": "K0302002B",
"unit_obj": "D03001B",
"content": "掌握弧度制下扇形的弧长和面积公式.",
"predecessor": []
"predecessor": [
"K0302001B"
]
},
"K0302003B": {
"id": "K0302003B",
"unit_obj": "D03001B",
"content": "在弧度制下会用代数方法表示和研究角.",
"predecessor": []
"predecessor": [
"K0302001B"
]
},
"K0303001B": {
"id": "K0303001B",
"unit_obj": "D03001B",
"content": "掌握任意角的用比值给出的正弦、余弦、正切、余切的定义.",
"predecessor": []
"predecessor": [
"K0301001B"
]
},
"K0303002B": {
"id": "K0303002B",
"unit_obj": "D03001B",
"content": "掌握不同象限的角的正弦、余弦、正切和余切的符号.",
"predecessor": []
"predecessor": [
"K0301002B",
"K0303001B"
]
},
"K0304001B": {
"id": "K0304001B",
"unit_obj": "D03001B",
"content": "理解角的终边和单位圆的交点的坐标与角的正弦、余弦、正切和余切的关系.",
"predecessor": []
"predecessor": [
"K0303001B"
]
},
"K0304002B": {
"id": "K0304002B",
"unit_obj": "D03001B",
"content": "经历$\\sin^2\\alpha+\\cos^2\\alpha=1$; $\\tan\\alpha=\\dfrac{\\sin\\alpha}{\\cos\\alpha}$; $\\cot\\alpha=\\dfrac{\\cos\\alpha}{\\sin\\alpha}$; $\\tan\\alpha\\cdot \\cot\\alpha=1$的推导.",
"predecessor": []
"predecessor": [
"K0303001B"
]
},
"K0304003B": {
"id": "K0304003B",
"unit_obj": "D03001B",
"content": "会用$\\sin^2\\alpha+\\cos^2\\alpha=1$; $\\tan\\alpha=\\dfrac{\\sin\\alpha}{\\cos\\alpha}$; $\\cot\\alpha=\\dfrac{\\cos\\alpha}{\\sin\\alpha}$; $\\tan\\alpha\\cdot \\cot\\alpha=1$解决``已知一个三角比的值, 求其他三角比的值''的问题.",
"predecessor": []
"predecessor": [
"K0304002B",
"K0303002B"
]
},
"K0305001B": {
"id": "K0305001B",
"unit_obj": "D03001B",
"content": "会用同角三角函数的基本关系式($\\sin^2\\alpha+\\cos^2\\alpha=1$; $\\tan\\alpha=\\dfrac{\\sin\\alpha}{\\cos\\alpha}$; $\\cot\\alpha=\\dfrac{\\cos\\alpha}{\\sin\\alpha}$; $\\tan\\alpha\\cdot \\cot\\alpha=1$), 在熟悉的情境中, 解决一些三角恒等式的化简与证明问题.",
"predecessor": []
"predecessor": [
"K0304002B",
"K0303002B"
]
},
"K0306001B": {
"id": "K0306001B",
"unit_obj": "D03002B",
"content": "借助单位圆的对称性, 经历利用定义推导出第一组诱导公式(有关$k\\pi\\pm \\alpha$)的正弦、余弦、正切和余切的过程.",
"predecessor": []
"predecessor": [
"K0301004B",
"K0304001B"
]
},
"K0306002B": {
"id": "K0306002B",
"unit_obj": "D03002B",
"content": "会利用第一组诱导公式(有关$k\\pi\\pm \\alpha$)进行简单的求值、化简与证明.",
"predecessor": []
"predecessor": [
"K0306001B"
]
},
"K0307001B": {
"id": "K0307001B",
"unit_obj": "D03002B",
"content": "借助单位圆的对称性, 经历利用定义推导出第二组诱导公式(有关$(k+\\dfrac 12)\\pi\\pm \\alpha$)的正弦、余弦、正切和余切的过程.",
"predecessor": []
"predecessor": [
"K0301004B",
"K0304001B"
]
},
"K0307002B": {
"id": "K0307002B",
"unit_obj": "D03002B",
"content": "会通过``奇变偶不变, 符号看象限''来记忆诱导公式.",
"predecessor": []
"predecessor": [
"K0306001B",
"K0307001B"
]
},
"K0307003B": {
"id": "K0307003B",
"unit_obj": "D03002B",
"content": "会利用第二组诱导公式(有关$(k+\\dfrac 12)\\pi\\pm \\alpha$)进行简单的求值、化简与证明.",
"predecessor": []
"predecessor": [
"K0307001B"
]
},
"K0307004B": {
"id": "K0307004B",
"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": []
"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": []
"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": []
"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": []
"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": []
"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": []
"predecessor": [
"K0308004B",
"K0308002B"
]
},
"K0309001B": {
"id": "K0309001B",
"unit_obj": "D03002B",
"content": "经历两角差的余弦公式的坐标法的推导过程, 知道两角差的余弦公式的意义.",
"predecessor": []
"predecessor": [
"K0304001B"
]
},
"K0309002B": {
"id": "K0309002B",
"unit_obj": "D03002B",
"content": "两角差的余弦推导两角和的余弦.",
"predecessor": []
"predecessor": [
"K0309001B",
"K0306002B"
]
},
"K0309003B": {
"id": "K0309003B",
"unit_obj": "D03002B",
"content": "会灵活选择角, 用两角和差的余弦公式求值及化简.",
"predecessor": []
"predecessor": [
"K0309001B",
"K0309002B"
]
},
"K0310001B": {
"id": "K0310001B",
"unit_obj": "D03002B",
"content": "了解两角差的余弦公式推导两角和与差的正弦、正切公式的路径, 并经历推导过程.",
"predecessor": []
"predecessor": [
"K0309001B",
"K0307003B",
"K0306002B"
]
},
"K0310002B": {
"id": "K0310002B",
"unit_obj": "D03002B",
"content": "会灵活选择角, 用两角和、差的正弦和正切公式求值及化简.",
"predecessor": []
"predecessor": [
"K0310001B"
]
},
"K0311001B": {
"id": "K0311001B",
"unit_obj": "D03002B",
"content": "理解可以通过终边的旋转、对称等方式, 利用两角和、差的正弦、余弦公式研究平面上的坐标变换.",
"predecessor": []
"predecessor": [
"K0303001B",
"K0301004B",
"K0310002B",
"K0309003B"
]
},
"K0311002B": {
"id": "K0311002B",
"unit_obj": "D03002B",
"content": "会用辅助角公式将$a\\sin\\alpha+b\\cos\\alpha$型的表达式整理为$A\\sin(\\alpha+\\varphi)$及$A\\cos(\\alpha+\\varphi)$的形式, 并能明确给出辅助角$\\varphi$的正弦与余弦值.",
"predecessor": []
"predecessor": [
"K0310002B",
"K0309003B"
]
},
"K0312001B": {
"id": "K0312001B",
"unit_obj": "D03002B",
"content": "经历利用两角和公式, 推导出二倍角的正弦、余弦、正切公式的过程, 并了解它们的内在联系.",
"predecessor": []
"predecessor": [
"K0310002B",
"K0309003B"
]
},
"K0312002B": {
"id": "K0312002B",
"unit_obj": "D03002B",
"content": "熟悉二倍角余弦公式的三种不同形式.",
"predecessor": []
"predecessor": [
"K0312001B",
"K0305001B"
]
},
"K0312003B": {
"id": "K0312003B",
"unit_obj": "D03002B",
"content": "利用二倍角公式, 进行求值、化简和证明.",
"predecessor": []
"predecessor": [
"K0312002B"
]
},
"K0313001B": {
"id": "K0313001B",
"unit_obj": "D03002B",
"content": "能运用所学公式进行简单的恒等变换, 推导半角公式.",
"predecessor": []
"predecessor": [
"K0312002B"
]
},
"K0313002B": {
"id": "K0313002B",
"unit_obj": "D03002B",
"content": "能运用所学公式进行简单的恒等变换, 推导积化和差公式.",
"predecessor": []
"predecessor": [
"K0309003B",
"K0310002B"
]
},
"K0313003B": {
"id": "K0313003B",
"unit_obj": "D03002B",
"content": "能运用所学公式进行简单的恒等变换, 推导和差化积公式.",
"predecessor": []
"predecessor": [
"K0309003B",
"K0310002B",
"K0313002B"
]
},
"K0314001B": {
"id": "K0314001B",
"unit_obj": "D03003B",
"content": "经历用坐标法推导三角形面积公式$S=\\dfrac{1}{2}ab\\sin C$等的过程.",
"predecessor": []
"predecessor": [
"K0303001B"
]
},
"K0314002B": {
"id": "K0314002B",
"unit_obj": "D03003B",
"content": "利用三角形面积公式推导得到正弦定理.",
"predecessor": []
"predecessor": [
"K0314001B"
]
},
"K0314003B": {
"id": "K0314003B",
"unit_obj": "D03003B",
"content": "会用正弦定理解决``ASA''型的解三角形问题.",
"predecessor": []
"predecessor": [
"K0314002B"
]
},
"K0314004B": {
"id": "K0314004B",
"unit_obj": "D03003B",
"content": "会用正弦定理及面积公式证明三角形中关于边、角和面积的恒等式.",
"predecessor": []
"predecessor": [
"K0314001B",
"K0314002B"
]
},
"K0314005B": {
"id": "K0314005B",
@ -1801,163 +1909,234 @@
"id": "K0314006B",
"unit_obj": "D03003B",
"content": "利用圆周角均相等推导含$2R$的正弦定理的过程.",
"predecessor": []
"predecessor": [
"K0314005B"
]
},
"K0315001B": {
"id": "K0315001B",
"unit_obj": "D03003B",
"content": "经历用坐标法推导余弦定理的过程.",
"predecessor": []
"predecessor": [
"K0314001B"
]
},
"K0315002B": {
"id": "K0315002B",
"unit_obj": "D03003B",
"content": "熟悉并记忆余弦定理.",
"predecessor": []
"predecessor": [
"K0315001B"
]
},
"K0315003B": {
"id": "K0315003B",
"unit_obj": "D03003B",
"content": "会用余弦定理解``SSS''``SAS''型的解三角形问题.",
"predecessor": []
"predecessor": [
"K0315002B"
]
},
"K0315004B": {
"id": "K0315004B",
"unit_obj": "D03003B",
"content": "能够灵活运用正弦定理、余弦定理解决``SSA''型的解三角形问题, 并能正确取舍解得结果.",
"predecessor": []
"predecessor": [
"K0314003B",
"K0315003B"
]
},
"K0316001B": {
"id": "K0316001B",
"unit_obj": "D03003B",
"content": "会灵活运用正弦定理和余弦定理证明三角形中的等式.",
"predecessor": []
"predecessor": [
"K0314002B",
"K0315002B"
]
},
"K0316002B": {
"id": "K0316002B",
"unit_obj": "D03003B",
"content": "会灵活运用正弦定理和余弦定理判断三角形的形状.",
"predecessor": []
"predecessor": [
"K0314003B",
"K0315003B",
"K0315004B"
]
},
"K0317001B": {
"id": "K0317001B",
"unit_obj": "D03003B",
"content": "能用正弦定理、余弦定理解决简单的实际问题.",
"predecessor": []
"predecessor": [
"K0314003B",
"K0315003B",
"K0315004B"
]
},
"K0317002B": {
"id": "K0317002B",
"unit_obj": "D03003B",
"content": "能将有关测量的问题转化为解三角形问题, 并灵活运用正弦定理和余弦定理求解.",
"predecessor": []
"predecessor": [
"K0317001B"
]
},
"K0318001B": {
"id": "K0318001B",
"unit_obj": "D03004B",
"content": "建立正弦函数的概念.",
"predecessor": []
"predecessor": [
"K0303001B",
"K0215001B"
]
},
"K0318002B": {
"id": "K0318002B",
"unit_obj": "D03004B",
"content": "经历描点, 平移绘制正弦函数图像的过程.",
"predecessor": []
"predecessor": [
"K0318001B",
"K0216003B"
]
},
"K0318003B": {
"id": "K0318003B",
"unit_obj": "D03004B",
"content": "会用五点法绘制正弦函数、与正弦函数相关的函数的大致图像.",
"predecessor": []
"predecessor": [
"K0318002B"
]
},
"K0319001B": {
"id": "K0319001B",
"unit_obj": "D03004B",
"content": "结合诱导公式理解正弦函数的周期性.",
"predecessor": []
"predecessor": [
"K0306002B"
]
},
"K0319002B": {
"id": "K0319002B",
"unit_obj": "D03004B",
"content": "直观地理解周期函数的定义.",
"predecessor": []
"predecessor": [
"K0319001B",
"K0318002B"
]
},
"K0319003B": {
"id": "K0319003B",
"unit_obj": "D03004B",
"content": "能用``数学语言''准确地给出周期函数的定义.",
"predecessor": []
"predecessor": [
"K0319001B"
]
},
"K0319004B": {
"id": "K0319004B",
"unit_obj": "D03004B",
"content": "会证明正弦函数的最小正周期是$2\\pi$.",
"predecessor": []
"predecessor": [
"K0319003B",
"K0318002B"
]
},
"K0319005B": {
"id": "K0319005B",
"unit_obj": "D03004B",
"content": "了解函数$y=A\\sin(\\omega x+\\varphi)$的周期, 并会粗略地说明道理.",
"predecessor": []
"predecessor": [
"K0319003B",
"K0306002B"
]
},
"K0320001B": {
"id": "K0320001B",
"unit_obj": "D03004B",
"content": "借助单位圆理解正弦函数的值域与最值.",
"predecessor": []
"predecessor": [
"K0304001B"
]
},
"K0320002B": {
"id": "K0320002B",
"unit_obj": "D03004B",
"content": "能运用正弦函数的值域与最值解决简单的正弦型函数的相应问题.",
"predecessor": []
"predecessor": [
"K0320001B"
]
},
"K0320003B": {
"id": "K0320003B",
"unit_obj": "D03004B",
"content": "会将与正弦有关的现实情境中的问题转化为正弦函数的最值问题, 并加以解决.",
"predecessor": []
"predecessor": [
"K0320002B"
]
},
"K0321001B": {
"id": "K0321001B",
"unit_obj": "D03004B",
"content": "会判断并证明与正弦函数相关的函数的奇偶性.",
"predecessor": []
"predecessor": [
"K0306002B"
]
},
"K0321002B": {
"id": "K0321002B",
"unit_obj": "D03004B",
"content": "会借助单位圆及函数图像, 直观地理解正弦函数的单调性.",
"predecessor": []
"predecessor": [
"K0304001B",
"K0318002B"
]
},
"K0321003B": {
"id": "K0321003B",
"unit_obj": "D03004B",
"content": "能求$y=A\\sin(\\omega x+\\varphi)$型函数的单调区间, 其中$A>0$, $\\omega>0$.",
"predecessor": []
"predecessor": [
"K0321002B"
]
},
"K0321004B": {
"id": "K0321004B",
"unit_obj": "D03004B",
"content": "能求$y=A\\sin(\\omega x+\\varphi)$型函数的单调区间, 其中$A$与$\\omega$不全大于零.",
"predecessor": []
"predecessor": [
"K0321003B",
"K0307002B"
]
},
"K0322001B": {
"id": "K0322001B",
"unit_obj": "D03004B",
"content": "建立余弦函数的概念.",
"predecessor": []
"predecessor": [
"K0307003B"
]
},
"K0322002B": {
"id": "K0322002B",
"unit_obj": "D03004B",
"content": "借助正弦函数的相关性质, 掌握余弦函数的奇偶性、周期性、单调性、值域与最值等性质及其图像特征.",
"predecessor": []
"predecessor": [
"K0322001B",
"K0321001B",
"K0319004B",
"K0321002B",
"K0320001B"
]
},
"K0322003B": {
"id": "K0322003B",
"unit_obj": "D03004B",
"content": "会将与余弦函数有关的问题借助第二诱导公式转化为正弦函数有关的问题.",
"predecessor": []
"predecessor": [
"K0307003B"
]
},
"K0323001B": {
"id": "K0323001B",
@ -1969,49 +2148,70 @@
"id": "K0323002B",
"unit_obj": "D03004B",
"content": "会用三角函数解决简单的与周期变化有关的实际问题, 体会可利用三角函数构建刻画周期变化事物的数学模型.",
"predecessor": []
"predecessor": [
"K0323001B"
]
},
"K0323003B": {
"id": "K0323003B",
"unit_obj": "D03004B",
"content": "了解函数$y=A\\sin(\\omega x+\\varphi)$参数的变化对函数图像的影响.会用五点作图法作出函数的大致图像.",
"predecessor": []
"predecessor": [
"K0323001B",
"K0318003B"
]
},
"K0324001B": {
"id": "K0324001B",
"unit_obj": "D03004B",
"content": "类比正弦函数, 建立正切函数的概念.",
"predecessor": []
"predecessor": [
"K0318001B",
"K0303001B"
]
},
"K0324002B": {
"id": "K0324002B",
"unit_obj": "D03004B",
"content": "类比正弦函数, 借助单位圆画出正切函数的图像.",
"predecessor": []
"predecessor": [
"K0318002B",
"K0304001B"
]
},
"K0324003B": {
"id": "K0324003B",
"unit_obj": "D03004B",
"content": "直观地掌握正切函数的图像特征.",
"predecessor": []
"predecessor": [
"K0324002B"
]
},
"K0324004B": {
"id": "K0324004B",
"unit_obj": "D03004B",
"content": "直观地理解正切函数的周期性与值域.",
"predecessor": []
"predecessor": [
"K0306002B",
"K0324003B"
]
},
"K0324005B": {
"id": "K0324005B",
"unit_obj": "D03004B",
"content": "会用代数语言表示正切函数的奇偶性及单调性.",
"predecessor": []
"predecessor": [
"K0306002B",
"K0220002B"
]
},
"K0324006B": {
"id": "K0324006B",
"unit_obj": "D03004B",
"content": "能借助正切函数的单调性求$y=A\\tan(\\omega x+\\varphi)$的单调区间.",
"predecessor": []
"predecessor": [
"K0324005B"
]
},
"K0401001X": {
"id": "K0401001X",