diff --git a/工具v2/文本文件/metadata.txt b/工具v2/文本文件/metadata.txt index 13f3a9d0..4f8b4909 100644 --- a/工具v2/文本文件/metadata.txt +++ b/工具v2/文本文件/metadata.txt @@ -1,204 +1,90 @@ -usages +ans -040956 -20240319 2025届高二10班 0.758 FORCE -20240305 2025届高二10班 0.759 +018434 +\begin{tikzpicture}[>=latex] +\draw [->] (-1,0) -- (7,0) node [below] {$x$}; +\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw [domain = 0:{2*pi}, samples = 100] plot (\x,{1-sin(\x*180/pi)}); +\draw (0,1) node [left] {$1$} (0,2) node [left] {$2$}; +\draw [dashed] ({pi/2*3},2) -- (0,2); +\draw ({pi/2},0) node [below] {$\frac{\pi}{2}$} ({pi*3/2},0) node [below] {$\frac{3\pi}{2}$}; +\draw (pi,0) node [below] {$\pi$} (2*pi,0) node [below] {$2\pi$}; +\draw [dashed] (2*pi,0) --++ (0,1) -- (0,1) (pi,0) --++ (0,1) (3*pi/2,0) --++ (0,2); +\end{tikzpicture} +取值范围为$(0,\pi)$ -040958 -20240319 2025届高二10班 0.909 FORCE -20240305 2025届高二10班 0.828 +018435 +\begin{tikzpicture}[>=latex] +\draw [->] (-2,0) -- (5.5,0) node [below] {$x$}; +\draw [->] (0,-0.5) -- (0,3.5) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw [domain = -pi/2:{3*pi/2}, samples = 100] plot (\x,{2-sin(\x*180/pi)}); +\draw [dashed] (-pi/2,0) --++ (0,3) --++ (2*pi,0) --++ (0,-3) (0,2) --++ (pi,0) --++ (0,-2) (0,1) --++ (pi/2,0) --++ (0,-1); +\draw (-pi/2,0) node [below] {$\frac{\pi}{2}$} (pi/2,0) node [below] {$\frac{\pi}{2}$} (pi,0) node [below] {$\pi$} (3*pi/2,0) node [below] {$\frac{3\pi}{2}$}; +\draw (0,1) node [left] {$1$} (0,2) node [above right] {$2$} (0,3) node [above right] {$3$}; +\end{tikzpicture} -040956 -20240319 2025届高二11班 0.778 FORCE -20240305 2025届高二11班 0.875 +018436 +$\dfrac{1}{2}$或$-\dfrac{3}{2}$ -040958 -20240319 2025届高二11班 0.815 FORCE -20240305 2025届高二11班 0.792 +009592 +\begin{tikzpicture}[>=latex] +\draw [->] (-3.5,0) -- (3.5,0) node [below] {$x$}; +\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$}; +\draw (0,0) node [below right] {$O$}; +\draw [domain = -pi:pi, samples = 100] plot (\x,{sin(\x*180/pi)}); +\draw [dashed] (-pi/2,0) --++ (0,-1) -- (0,-1) (pi/2,0) --++ (0,1) -- (0,1); +\draw (-pi/2,0) node [above] {$-\frac{\pi}{2}$} (pi/2,0) node [below] {$\frac{\pi}{2}$}; +\draw (0,1) node [left] {$1$} (0,-1) node [right] {$-1$}; +\end{tikzpicture} -040956 -20240319 2025届高二01班 0.951 FORCE -20240305 2025届高二01班 1.000 +009593 +\begin{tikzpicture}[>=latex] +\draw [->] (-0.5,0) -- (7,0) node [below] {$x$}; +\draw [->] (0,-1) -- (0,2) node [left] {$y$}; +\draw (0,0) node [below right] {$O$}; +\draw [domain = 0:2*pi, samples = 100] plot (\x,{1/2-sin(\x*180/pi)}); +\draw [dashed] (2*pi,0.5) -- (0,0.5) (pi/2,0) --++ (0,-0.5) -- (0,-0.5) (3*pi/2,0) --++ (0,1.5) -- (0,1.5); +\draw (3*pi/2,0) node [below] {$\frac{3\pi}{2}$} (pi/2,0) node [above] {$\frac{\pi}{2}$}; +\draw (0,0.5) node [left] {$\frac{1}{2}$} (0,1.5) node [left] {$\frac{3}{2}$} (0,-0.5) node [left] {$-\frac{1}{2}$}; +\end{tikzpicture} +$y>0$时$x$的取值范围为$[0,\dfrac{\pi}{6})\cup (\dfrac{5\pi}{6},2\pi]$; $y<0$时$x$的取值范围为$(\dfrac{\pi}{6},\dfrac{5\pi}{6})$ -040958 -20240319 2025届高二01班 0.902 FORCE -20240305 2025届高二01班 1.000 +009594 +\begin{tikzpicture}[>=latex,scale = 0.5] +\draw [->] (-7,0) -- (7,0) node [below] {$x$}; +\draw [->] (0,-1.5) -- (0,3.5) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw [dashed, domain = -7:7, samples = 100] plot (\x,{sin(\x/pi*180)}); +\draw [domain = -7:7, samples = 100] plot (\x,{2+sin(\x/pi*180)}); +\end{tikzpicture} +$y=2+\sin x$的图像由$y=\sin x$的图像向上平移$2$单位得到 -040956 -20240319 2025届高二02班 1.000 FORCE -20240305 2025届高二02班 0.950 +018437 +$(-\dfrac{2\pi}{3},-\dfrac{\pi}{3})\cup (\dfrac{\pi}{3},\dfrac{2\pi}{3})$ -040958 -20240319 2025届高二02班 0.953 FORCE -20240305 2025届高二02班 0.950 +018438 +$(1,3)$ -040956 -20240319 2025届高二03班 0.950 FORCE -20240305 2025届高二03班 0.946 +023601 +\begin{tikzpicture}[>=latex, scale = 0.6] +\draw [->] (-7,0) -- (7,0) node [below] {$x$}; +\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw [domain = 0:2*pi,samples = 200] plot (\x,{sin(\x/pi*180)}) plot (-\x,{sin(\x/pi*180)}); +\draw [dashed] (pi/2,0) --++ (0,1) -- (-pi/2,1) --++ (0,-1) (3*pi/2,0) --++ (0,-1) -- (-3*pi/2,-1) --++ (0,1); +\draw (0,1) node [below left] {$1$} (0,-1) node [below left] {$-1$}; +\draw (pi/2,0) node [below] {$\frac{\pi}{2}$} (-pi/2,0) node [below] {$-\frac{\pi}{2}$}; +\draw (3*pi/2,0) node [below] {$\frac{3\pi}{2}$} (-3*pi/2,0) node [below] {$-\frac{3\pi}{2}$}; +\end{tikzpicture} -040958 -20240319 2025届高二03班 0.900 FORCE -20240305 2025届高二03班 1.000 +024726 +$\dfrac{16}{65}$或$\dfrac{56}{65}$ -040956 -20240319 2025届高二04班 0.892 FORCE -20240305 2025届高二04班 0.912 +040264 +(1) $\dfrac 23 \pi$; (2) 顶角为$120^\circ$的等腰三角形 -040958 -20240319 2025届高二04班 0.892 FORCE -20240305 2025届高二04班 0.853 - -040956 -20240319 2025届高二05班 0.795 FORCE -20240305 2025届高二05班 0.857 - -040958 -20240319 2025届高二05班 0.795 FORCE -20240305 2025届高二05班 0.771 - -040956 -20240319 2025届高二07班 0.932 FORCE -20240305 2025届高二07班 0.857 - -040958 -20240319 2025届高二07班 0.909 FORCE -20240305 2025届高二07班 0.929 - -040956 -20240319 2025届高二09班 0.895 FORCE -20240305 2025届高二09班 0.800 - -040958 -20240319 2025届高二09班 0.947 FORCE -20240305 2025届高二09班 0.875 - - - -014586 -20240322 2024届高三01班 0.969 FORCE -20240110 2024届高三01班 0.939 - -014587 -20240322 2024届高三01班 0.656 FORCE -20231206 2024届高三01班 0.500 - -014083 -20240318 2024届高三11班 0.760 FORCE -20231201 2024届高三11班 0.778 - -014585 -20240318 2024届高三11班 0.840 FORCE -20240103 2024届高三11班 0.419 - -014083 -20240318 2024届高三12班 0.826 FORCE -20231201 2024届高三12班 0.762 - -014585 -20240318 2024届高三12班 0.826 FORCE -20240103 2024届高三12班 0.783 - -014083 -20240318 2024届高三05班 0.714 FORCE -20231201 2024届高三05班 0.577 - -014585 -20240318 2024届高三05班 0.714 FORCE -20240103 2024届高三05班 0.516 - -014083 -20240318 2024届高三06班 0.743 FORCE -20231201 2024届高三06班 0.793 - -014083 -20240318 2024届高三07班 0.658 FORCE -20231201 2024届高三07班 0.611 - -014585 -20240318 2024届高三07班 0.737 FORCE -20240103 2024届高三07班 0.513 - -014083 -20240318 2024届高三08班 0.737 FORCE -20231201 2024届高三08班 0.765 - -014585 -20240318 2024届高三08班 0.789 FORCE -20240103 2024届高三08班 0.526 - -024676 -20240322 2026届高一10班 0.641 FORCE -20231024 2026届高一10班 0.634 - -024676 -20240322 2026届高一12班 0.825 FORCE -20231024 2026届高一12班 0.738 - -024676 -20240322 2026届高一01班 0.450 FORCE -20231024 2026届高一01班 0.829 - -024676 -20240322 2026届高一02班 0.900 FORCE -20231024 2026届高一02班 0.674 - -024676 -20240322 2026届高一03班 0.825 FORCE -20231024 2026届高一03班 0.605 - -024676 -20240322 2026届高一04班 0.829 FORCE -20231024 2026届高一04班 0.651 - -024676 -20240322 2026届高一05班 0.359 FORCE -20231024 2026届高一05班 0.829 - -024676 -20240322 2026届高一06班 0.850 FORCE -20231024 2026届高一06班 0.800 - -024676 -20240322 2026届高一07班 0.395 FORCE -20231024 2026届高一07班 0.357 - -024676 -20240322 2026届高一09班 0.784 FORCE -20231024 2026届高一09班 0.585 - -002376 -20240318 2025届高二10班 1.000 FORCE -20240311 2025届高二10班 0.969 - -002376 -20240318 2025届高二11班 0.962 FORCE -20240311 2025届高二11班 0.920 - -002376 -20240318 2025届高二01班 0.949 FORCE -20240311 2025届高二01班 0.950 - -002376 -20240318 2025届高二02班 1.000 FORCE -20240311 2025届高二02班 0.950 - -002376 -20240318 2025届高二03班 0.868 FORCE -20240311 2025届高二03班 1.000 - -002376 -20240318 2025届高二04班 0.971 FORCE -20240311 2025届高二04班 0.974 - -002376 -20240318 2025届高二05班 1.000 FORCE -20240311 2025届高二05班 0.944 - -002376 -20240318 2025届高二07班 0.875 FORCE -20240311 2025届高二07班 0.837 - -002376 -20240318 2025届高二09班 0.848 FORCE -20240311 2025届高二09班 0.865 +024727 +$\dfrac{\sqrt{5}-1}{4}$ diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 4901e552..60db32bd 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -274382,7 +274382,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex]\n\\draw [->] (-3.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -pi:pi, samples = 100] plot (\\x,{sin(\\x*180/pi)});\n\\draw [dashed] (-pi/2,0) --++ (0,-1) -- (0,-1) (pi/2,0) --++ (0,1) -- (0,1);\n\\draw (-pi/2,0) node [above] {$-\\frac{\\pi}{2}$} (pi/2,0) node [below] {$\\frac{\\pi}{2}$};\n\\draw (0,1) node [left] {$1$} (0,-1) node [right] {$-1$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -274407,7 +274407,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex]\n\\draw [->] (-0.5,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = 0:2*pi, samples = 100] plot (\\x,{1/2-sin(\\x*180/pi)});\n\\draw [dashed] (2*pi,0.5) -- (0,0.5) (pi/2,0) --++ (0,-0.5) -- (0,-0.5) (3*pi/2,0) --++ (0,1.5) -- (0,1.5);\n\\draw (3*pi/2,0) node [below] {$\\frac{3\\pi}{2}$} (pi/2,0) node [above] {$\\frac{\\pi}{2}$};\n\\draw (0,0.5) node [left] {$\\frac{1}{2}$} (0,1.5) node [left] {$\\frac{3}{2}$} (0,-0.5) node [left] {$-\\frac{1}{2}$};\n\\end{tikzpicture}\n$y>0$时$x$的取值范围为$[0,\\dfrac{\\pi}{6})\\cup (\\dfrac{5\\pi}{6},2\\pi]$; $y<0$时$x$的取值范围为$(\\dfrac{\\pi}{6},\\dfrac{5\\pi}{6})$", "solution": "", "duration": -1, "usages": [], @@ -274429,7 +274429,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-7,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [dashed, domain = -7:7, samples = 100] plot (\\x,{sin(\\x/pi*180)});\n\\draw [domain = -7:7, samples = 100] plot (\\x,{2+sin(\\x/pi*180)});\n\\end{tikzpicture}\n$y=2+\\sin x$的图像由$y=\\sin x$的图像向上平移$2$单位得到", "solution": "", "duration": -1, "usages": [], @@ -510478,7 +510478,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:{2*pi}, samples = 100] plot (\\x,{1-sin(\\x*180/pi)});\n\\draw (0,1) node [left] {$1$} (0,2) node [left] {$2$};\n\\draw [dashed] ({pi/2*3},2) -- (0,2);\n\\draw ({pi/2},0) node [below] {$\\frac{\\pi}{2}$} ({pi*3/2},0) node [below] {$\\frac{3\\pi}{2}$};\n\\draw (pi,0) node [below] {$\\pi$} (2*pi,0) node [below] {$2\\pi$};\n\\draw [dashed] (2*pi,0) --++ (0,1) -- (0,1) (pi,0) --++ (0,1) (3*pi/2,0) --++ (0,2);\n\\end{tikzpicture}\n取值范围为$(0,\\pi)$", "solution": "", "duration": -1, "usages": [], @@ -510500,7 +510500,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (5.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -pi/2:{3*pi/2}, samples = 100] plot (\\x,{2-sin(\\x*180/pi)});\n\\draw [dashed] (-pi/2,0) --++ (0,3) --++ (2*pi,0) --++ (0,-3) (0,2) --++ (pi,0) --++ (0,-2) (0,1) --++ (pi/2,0) --++ (0,-1);\n\\draw (-pi/2,0) node [below] {$\\frac{\\pi}{2}$} (pi/2,0) node [below] {$\\frac{\\pi}{2}$} (pi,0) node [below] {$\\pi$} (3*pi/2,0) node [below] {$\\frac{3\\pi}{2}$};\n\\draw (0,1) node [left] {$1$} (0,2) node [above right] {$2$} (0,3) node [above right] {$3$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -510522,7 +510522,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1}{2}$或$-\\dfrac{3}{2}$", "solution": "", "duration": -1, "usages": [], @@ -510544,7 +510544,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\dfrac{2\\pi}{3},-\\dfrac{\\pi}{3})\\cup (\\dfrac{\\pi}{3},\\dfrac{2\\pi}{3})$", "solution": "", "duration": -1, "usages": [], @@ -510566,7 +510566,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$(1,3)$", "solution": "", "duration": -1, "usages": [], @@ -660975,7 +660975,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-7,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:2*pi,samples = 200] plot (\\x,{sin(\\x/pi*180)}) plot (-\\x,{sin(\\x/pi*180)});\n\\draw [dashed] (pi/2,0) --++ (0,1) -- (-pi/2,1) --++ (0,-1) (3*pi/2,0) --++ (0,-1) -- (-3*pi/2,-1) --++ (0,1);\n\\draw (0,1) node [below left] {$1$} (0,-1) node [below left] {$-1$};\n\\draw (pi/2,0) node [below] {$\\frac{\\pi}{2}$} (-pi/2,0) node [below] {$-\\frac{\\pi}{2}$};\n\\draw (3*pi/2,0) node [below] {$\\frac{3\\pi}{2}$} (-3*pi/2,0) node [below] {$-\\frac{3\\pi}{2}$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -688428,7 +688428,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{16}{65}$或$\\dfrac{56}{65}$", "solution": "", "duration": -1, "usages": [], @@ -688455,7 +688455,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{5}-1}{4}$", "solution": "", "duration": -1, "usages": [], @@ -756855,7 +756855,7 @@ "第三单元" ], "genre": "解答题", - "ans": "(1) $\\dfrac 23 \\pi$; (2) 等腰钝角三角形", + "ans": "(1) $\\dfrac 23 \\pi$; (2) 顶角为$120^\\circ$的等腰三角形", "solution": "", "duration": -1, "usages": [],