From 3e5119693c71bb7adc943d6b481fdf42326c36d3 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sun, 24 Mar 2024 21:59:18 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A5=E8=8B=A5=E5=B9=B2=E7=AD=94?= =?UTF-8?q?=E6=A1=88?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/metadata.txt | 163 +++++---- 工具v2/文本文件/pendingmetadata.txt | 544 ---------------------------- 题库0.3/Problems.json | 60 +-- 3 files changed, 118 insertions(+), 649 deletions(-) diff --git a/工具v2/文本文件/metadata.txt b/工具v2/文本文件/metadata.txt index 4f8b4909..0922553c 100644 --- a/工具v2/文本文件/metadata.txt +++ b/工具v2/文本文件/metadata.txt @@ -1,90 +1,103 @@ ans -018434 -\begin{tikzpicture}[>=latex] -\draw [->] (-1,0) -- (7,0) node [below] {$x$}; -\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$}; +024729 +不是, 如$x=\dfrac{\pi}{3}$时, $\sin (x+\dfrac{2\pi}{3})\ne \sin x$ + +018439 +(1) $\dfrac{2\pi}{3}$; (2) $4\pi$ + +018440 +$\pm \pi$ + +018441 +$\pi$ + +009595 +(1) $2\pi$; (2) $\dfrac{2\pi}{3}$ + +009596 +不是, 如$x=0$时, $\sin (x+\dfrac{\pi}{3})\ne \sin x$ + +021651 +(1) 假; (2) 假;(3) 真. + +018442 +$2+\sqrt{3}$ + +010275 +$\pm \dfrac{\pi}{2}$ + +010284 +$1$ + +010288 +(1) $2$; (2) \begin{tikzpicture} +\draw [->] (-6,0) -- (6,0) node [below] {$x$}; +\draw [->] (0,-3) -- (0,3) 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$(0,\pi)$ - -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] {$3$}; +\foreach \i in {-4,-3,-2,-1,1,2,3,4} +{\draw (\i,0.1) -- (\i,0) node [below] {$\i$};}; +\foreach \i in {-2,-1,1,2} +{\draw (0.1,\i) -- (0,\i) node [left] {$\i$};}; +\draw [dashed] (-5,2) -- (-4,0) -- (-3,2) -- (-2,0) -- (-1,2) -- (0,0) -- (1,2) -- (2,0) -- (3,2) -- (4,0) -- (5,2); +\draw (-6,2) -- (-5,0) -- (-4,2) -- (-3,0) -- (-2,2) -- (-1,0) -- (0,2) -- (1,0) -- (2,2) -- (3,0) -- (4,2) -- (5,0) -- (6,2); \end{tikzpicture} -018436 -$\dfrac{1}{2}$或$-\dfrac{3}{2}$ +018443 +(1) 最大值为$2$, 当且仅当$x=\dfrac{2k\pi}{3}+\dfrac{7\pi}{18}$, $k\in \mathbf{Z}$时取到; 最小值为$-2$, 当且仅当$x=\dfrac{2k\pi}{3}+\dfrac{\pi}{18}$, $k\in \mathbf{Z}$时取到;\\(2) 最大值为$2$, 当且仅当$x=2k\pi+\dfrac{\pi}{6}$, $k\in \mathbf{Z}$时取到; 最小值为$-2$, 当且仅当$x=2k\pi+\dfrac{7\pi}{6}$, $k\in \mathbf{Z}$时取到;\\最大值为$2$, 当且仅当$x=2k\pi+\dfrac{3\pi}{2}$, $k\in \mathbf{Z}$时取到; 最小值为$-\dfrac{1}{4}$, 当且仅当$x=2k\pi+\dfrac{\pi}{6}$或$2k\pi+\dfrac{5\pi}{6}$, $k\in \mathbf{Z}$时取到;\\(4) 最大值为$4$, 当且仅当$x=k\pi+\dfrac{\pi}{6}$, $k\in \mathbf{Z}$时取到; 最小值为$0$, 当且仅当$x=k\pi+\dfrac{2\pi}{3}$, $k\in \mathbf{Z}$时取到 -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} +018444 +应截取$AB=\sqrt{2}r$, $BC=\dfrac{\sqrt{2}}{2}r$, 这时矩形$ABCD$的面积达到最大值$r^2$ -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$(\dfrac{\pi}{6},\dfrac{5\pi}{6})$ +018445 +最大值为$\sqrt{2}$, 取到最大值的$x$的集合为$\{x|x=\dfrac{k\pi}{2}+\dfrac{\pi}{4}, \ k\in \mathbf{Z}\}$; 最小值为$1$, 取到最小值的$x$的集合为$\{x|x=\dfrac{k\pi}{2}, \ k\in \mathbf{Z}\}$ -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 +009598 +(1) 定义域为$\mathbf{R}$, 值域为$[-1,1]$; (2) 定义域为$\mathbf{R}$, 值域为$[\dfrac{1}{2},2]$ -018437 -$(-\dfrac{2\pi}{3},-\dfrac{\pi}{3})\cup (\dfrac{\pi}{3},\dfrac{2\pi}{3})$ +009599 +(1) 最大值为$6$, 最小值为$-4$; (2) 最大值为$\dfrac{3}{2}$, 最小值为$-3$; (3) 最大值为$2$, 最小值为$-2$ -018438 -$(1,3)$ +009600 +$\dfrac{\pi}{4}$ -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} +018446 +当且仅当$\theta=\dfrac{\pi}{6}$时面积$S$最大, $S$的最大值为$\dfrac{50}{3}\sqrt{3}\text{m}^2$ -024726 -$\dfrac{16}{65}$或$\dfrac{56}{65}$ +010286 +最小正周期为$\dfrac{\pi}{2}$, 最大值为$1$, 最小值为$\dfrac{1}{2}$ -040264 -(1) $\dfrac 23 \pi$; (2) 顶角为$120^\circ$的等腰三角形 +018447 +(1) 偶函数, 理由略; (2) 偶函数, 理由略; (3) 既不是奇函数也不是偶函数, 理由略 -024727 -$\dfrac{\sqrt{5}-1}{4}$ +018448 +(1) $\sin \dfrac{6 \pi}{5}<\sin \dfrac{7 \pi}{6}$; (2) $\sin \dfrac{43 \pi}{7}>\sin (-\dfrac{47 \pi}{8})$ + +018449 +$[2k\pi,2k\pi+\pi]$, $k\in \mathbf{Z}$ + +018450 +$[-\dfrac{2\pi}{3},-\dfrac{\pi}{6}]$ + +018451 +$k\pi+\dfrac{\pi}{2}$, $k\in \mathbf{Z}$ + +009601 +(1) 奇函数, 理由略; (2) 偶函数, 理由略; (3) 偶函数, 理由略; (4) 既不是奇函数, 又不是偶函数, 理由略 + +009602 +(1) $\sin (-\dfrac \pi {16})>\sin (-\dfrac \pi {13})$; (2) $\sin 715^\circ<\sin (-724^\circ )$ + +009603 +(1) 严格增区间: $[2k\pi-\dfrac{\pi}{2},2k\pi+\dfrac{\pi}{2}]$, $k\in \mathbf{Z}$; 严格减区间: $[2k\pi+\dfrac{\pi}{2},2k\pi+\dfrac{3\pi}{2}]$, $k\in \mathbf{Z}$;\\(2) 严格增区间: $[2k\pi+\dfrac{\pi}{2},2k\pi+\dfrac{3\pi}{2}]$, $k\in \mathbf{Z}$; 严格减区间: $[2k\pi-\dfrac{\pi}{2},2k\pi+\dfrac{\pi}{2}]$, $k\in \mathbf{Z}$;\\ +(3) 严格增区间: $[\dfrac{2k\pi}{3}-\dfrac{\pi}{12},\dfrac{2k\pi}{3}+\dfrac{\pi}{4}]$, $k\in \mathbf{Z}$; 严格减区间: $[\dfrac{2k\pi}{3}+\dfrac{\pi}{4},\dfrac{2k\pi}{3}+\dfrac{7\pi}{12}]$, $k\in \mathbf{Z}$; + +018452 +(1) $[0,\dfrac{\pi}{6}]$; (2) $[-\sqrt{3}-1,1]$ + +023603 +$[6k\pi+\dfrac{9\pi}{4},6k\pi+\dfrac{21\pi}{4}]$, $k\in \mathbf{Z}$ + +010277 +(1) 奇函数, 理由略; (2) 偶函数, 理由略; (3) 既不是奇函数, 又不是偶函数, 理由略 diff --git a/工具v2/文本文件/pendingmetadata.txt b/工具v2/文本文件/pendingmetadata.txt index 5e53ac06..2faa8048 100644 --- a/工具v2/文本文件/pendingmetadata.txt +++ b/工具v2/文本文件/pendingmetadata.txt @@ -1,546 +1,2 @@ usages -013222 -20240314 2024届高三07班 0.833 FORCE -20240314 2024届高三07班 0.825 - -013228 -20240314 2024届高三07班 0.881 FORCE -20240314 2024届高三07班 0.875 - -013236 -20240314 2024届高三07班 0.857 FORCE -20240314 2024届高三07班 0.850 - -014583 -20240314 2024届高三07班 0.952 FORCE -20240314 2024届高三07班 0.950 - -013223 -20240314 2024届高三07班 0.738 FORCE -20240314 2024届高三07班 0.750 - -014579 -20240314 2024届高三07班 0.786 FORCE -20240314 2024届高三07班 0.775 - -014589 -20240314 2024届高三07班 0.690 FORCE -20240314 2024届高三07班 0.700 - -014075 -20240314 2024届高三07班 0.929 FORCE -20240314 2024届高三07班 0.925 - -014588 -20240314 2024届高三07班 0.905 0.524 0.571 FORCE -20240314 2024届高三07班 0.900 0.525 0.575 - -014578 -20240314 2024届高三07班 0.833 0.940 0.643 FORCE -20240314 2024届高三07班 0.825 0.938 0.650 - -040956 -20240319 2025届高二10班 0.758 FORCE -20240305 2025届高二10班 0.759 - -040958 -20240319 2025届高二10班 0.909 FORCE -20240305 2025届高二10班 0.828 - -040956 -20240319 2025届高二11班 0.778 FORCE -20240305 2025届高二11班 0.875 - -040958 -20240319 2025届高二11班 0.815 FORCE -20240305 2025届高二11班 0.792 - -040956 -20240319 2025届高二01班 0.951 FORCE -20240305 2025届高二01班 1.000 - -040958 -20240319 2025届高二01班 0.902 FORCE -20240305 2025届高二01班 1.000 - -040956 -20240319 2025届高二02班 1.000 FORCE -20240305 2025届高二02班 0.950 - -040958 -20240319 2025届高二02班 0.953 FORCE -20240305 2025届高二02班 0.950 - -040956 -20240319 2025届高二03班 0.950 FORCE -20240305 2025届高二03班 0.946 - -040958 -20240319 2025届高二03班 0.900 FORCE -20240305 2025届高二03班 1.000 - -040956 -20240319 2025届高二04班 0.892 FORCE -20240305 2025届高二04班 0.912 - -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 - -021619 -20240315 2026届高一02班 0.780 FORCE -20240315 2026届高一02班 0.800 - -021620 -20240315 2026届高一02班 0.902 FORCE -20240315 2026届高一02班 0.900 - -021615 -20240315 2026届高一02班 0.829 FORCE -20240315 2026届高一02班 0.825 - -021616 -20240315 2026届高一02班 0.927 FORCE -20240315 2026届高一02班 0.925 - -021618 -20240315 2026届高一02班 0.610 FORCE -20240315 2026届高一02班 0.600 - -021629 -20240315 2026届高一02班 0.976 FORCE -20240315 2026届高一02班 0.975 - -010256 -20240315 2026届高一02班 0.878 FORCE -20240315 2026届高一02班 0.875 - -010259 -20240315 2026届高一02班 0.927 FORCE -20240315 2026届高一02班 0.925 - -010266 -20240315 2026届高一02班 1.000 0.902 FORCE -20240315 2026届高一02班 1.000 0.900 - -003606 -20240315 2026届高一02班 0.878 0.610 FORCE -20240315 2026届高一02班 0.875 0.625 - -021619 -20240315 2026届高一04班 0.872 FORCE -20240315 2026届高一04班 0.868 - -021615 -20240315 2026届高一04班 0.795 FORCE -20240315 2026届高一04班 0.789 - -021616 -20240315 2026届高一04班 0.949 FORCE -20240315 2026届高一04班 0.947 - -021618 -20240315 2026届高一04班 0.410 FORCE -20240315 2026届高一04班 0.395 - -021629 -20240315 2026届高一04班 0.872 FORCE -20240315 2026届高一04班 0.868 - -003606 -20240315 2026届高一04班 0.949 0.718 FORCE -20240315 2026届高一04班 0.947 0.711 - -014532 -20240311 2024届高三06班 0.972 0.889 FORCE -20240311 2024届高三06班 0.971 0.886 - -014533 -20240311 2024届高三06班 0.944 0.889 0.917 FORCE -20240311 2024届高三06班 0.943 0.886 0.914 - -012920 -20240311 2024届高三06班 0.861 FORCE -20240311 2024届高三06班 0.857 - -014534 -20240311 2024届高三06班 0.528 FORCE -20240311 2024届高三06班 0.514 - -012967 -20240311 2024届高三06班 0.889 FORCE -20240311 2024届高三06班 0.886 - -012968 -20240311 2024届高三06班 0.944 FORCE -20240311 2024届高三06班 0.943 - -012933 -20240311 2024届高三06班 0.306 FORCE -20240311 2024届高三06班 0.286 - -013923 -20240311 2024届高三06班 0.833 FORCE -20240311 2024届高三06班 0.829 - -014546 -20240311 2024届高三06班 0.972 FORCE -20240311 2024届高三06班 0.971 - -014540 -20240311 2024届高三06班 1.000 0.833 FORCE -20240311 2024届高三06班 1.000 0.829 - -013007 -20240311 2024届高三06班 0.653 0.736 0.431 FORCE -20240311 2024届高三06班 0.643 0.729 0.443 - -032067 -20240311 2024届高三06班 0.917 0.597 FORCE -20240311 2024届高三06班 0.914 0.586 - -012928 -20240320 2024届高三06班 0.472 FORCE -20240310 2024届高三06班 0.457 - -013919 -20240320 2024届高三06班 0.778 FORCE -20240310 2024届高三06班 0.771 - -012965 -20240320 2024届高三06班 0.722 FORCE -20240310 2024届高三06班 0.714 - -012951 -20240320 2024届高三06班 0.861 FORCE -20240310 2024届高三06班 0.857 - -012955 -20240320 2024届高三06班 0.611 FORCE -20240310 2024届高三06班 0.600 - -032068 -20240320 2024届高三06班 0.889 FORCE -20240310 2024届高三06班 0.886 - -012953 -20240320 2024届高三06班 0.917 FORCE -20240310 2024届高三06班 0.914 - -012981 -20240320 2024届高三06班 0.778 FORCE -20240310 2024届高三06班 0.771 - -012969 -20240320 2024届高三06班 0.778 FORCE -20240310 2024届高三06班 0.771 - -012972 -20240320 2024届高三06班 0.944 0.764 FORCE -20240310 2024届高三06班 0.943 0.757 - -013952 -20240320 2024届高三06班 0.972 0.875 0.694 FORCE -20240310 2024届高三06班 0.971 0.871 0.686 - -012942 -20240312 2024届高三06班 0.529 FORCE -20240312 2024届高三06班 0.515 - -012941 -20240312 2024届高三06班 0.794 FORCE -20240312 2024届高三06班 0.788 - -012976 -20240312 2024届高三06班 0.853 FORCE -20240312 2024届高三06班 0.848 - -032069 -20240312 2024届高三06班 0.500 FORCE -20240312 2024届高三06班 0.515 - -013002 -20240312 2024届高三06班 0.882 FORCE -20240312 2024届高三06班 0.879 - -014550 -20240312 2024届高三06班 0.500 FORCE -20240312 2024届高三06班 0.515 - -012966 -20240312 2024届高三06班 0.941 0.971 FORCE -20240312 2024届高三06班 0.939 0.970 - -013935 -20240312 2024届高三06班 0.853 FORCE -20240312 2024届高三06班 0.848 - -012978 -20240312 2024届高三06班 0.794 FORCE -20240312 2024届高三06班 0.788 - -012947 -20240312 2024届高三06班 0.647 FORCE -20240312 2024届高三06班 0.652 - -012971 -20240312 2024届高三06班 0.985 0.765 FORCE -20240312 2024届高三06班 0.985 0.758 - -032070 -20240312 2024届高三06班 0.647 0.750 FORCE -20240312 2024届高三06班 0.636 0.742 - -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 - -032071 -20240313 2024届高三07班 1.000 0.953 1.000 0.953 1.000 0.884 0.977 0.953 0.860 0.977 0.953 0.953 FORCE -20240313 2024届高三07班 1.000 0.952 1.000 0.952 1.000 0.905 0.976 0.952 0.881 0.976 0.952 0.952 - -040205 -20240313 2024届高三07班 0.930 0.884 FORCE -20240313 2024届高三07班 0.929 0.905 - -021376 -20240313 2024届高三07班 0.977 0.977 FORCE -20240313 2024届高三07班 0.976 0.976 - -021396 -20240313 2024届高三07班 0.907 FORCE -20240313 2024届高三07班 0.905 - -013633 -20240313 2024届高三07班 0.930 FORCE -20240313 2024届高三07班 0.929 - -031354 -20240313 2024届高三07班 0.744 FORCE -20240313 2024届高三07班 0.738 - -031353 -20240313 2024届高三07班 0.814 0.814 0.837 0.721 FORCE -20240313 2024届高三07班 0.833 0.810 0.833 0.714 - -013297 -20240313 2024届高三07班 0.907 FORCE -20240313 2024届高三07班 0.905 - -032072 -20240313 2024届高三07班 0.547 0.860 FORCE -20240313 2024届高三07班 0.548 0.869 - -030424 -20240313 2024届高三07班 0.651 0.628 FORCE -20240313 2024届高三07班 0.655 0.619 - -024644 -20240315 2026届高一07班 0.923 FORCE -20240315 2026届高一07班 0.921 - -024645 -20240315 2026届高一07班 0.897 FORCE -20240315 2026届高一07班 0.895 - -024646 -20240315 2026届高一07班 0.641 FORCE -20240315 2026届高一07班 0.632 - -024647 -20240315 2026届高一07班 0.949 FORCE -20240315 2026届高一07班 0.974 - -024648 -20240315 2026届高一07班 0.949 FORCE -20240315 2026届高一07班 0.947 - -024649 -20240315 2026届高一07班 0.795 FORCE -20240315 2026届高一07班 0.789 - -024650 -20240315 2026届高一07班 0.923 FORCE -20240315 2026届高一07班 0.921 - -024651 -20240315 2026届高一07班 0.897 FORCE -20240315 2026届高一07班 0.895 - -024652 -20240315 2026届高一07班 0.949 FORCE -20240315 2026届高一07班 0.947 - -024653 -20240315 2026届高一07班 0.795 FORCE -20240315 2026届高一07班 0.816 - -024654 -20240315 2026届高一07班 0.872 FORCE -20240315 2026届高一07班 0.868 - -024655 -20240315 2026届高一07班 0.744 FORCE -20240315 2026届高一07班 0.737 - -024657 -20240315 2026届高一07班 0.718 FORCE -20240315 2026届高一07班 0.711 - -024658 -20240315 2026届高一07班 0.744 FORCE -20240315 2026届高一07班 0.737 - -024659 -20240315 2026届高一07班 0.949 0.513 FORCE -20240315 2026届高一07班 0.947 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 - diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 832d5e0f..05f58567 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -274451,7 +274451,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2\\pi$; (2) $\\dfrac{2\\pi}{3}$", "solution": "", "duration": -1, "usages": [], @@ -274473,7 +274473,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "不是, 如$x=0$时, $\\sin (x+\\dfrac{\\pi}{3})\\ne \\sin x$", "solution": "", "duration": -1, "usages": [], @@ -274543,7 +274543,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 定义域为$\\mathbf{R}$, 值域为$[-1,1]$; (2) 定义域为$\\mathbf{R}$, 值域为$[\\dfrac{1}{2},2]$", "solution": "", "duration": -1, "usages": [], @@ -274566,7 +274566,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 最大值为$6$, 最小值为$-4$; (2) 最大值为$\\dfrac{3}{2}$, 最小值为$-3$; (3) 最大值为$2$, 最小值为$-2$", "solution": "", "duration": -1, "usages": [], @@ -274589,7 +274589,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{\\pi}{4}$", "solution": "", "duration": -1, "usages": [], @@ -274611,7 +274611,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 奇函数, 理由略; (2) 偶函数, 理由略; (3) 偶函数, 理由略; (4) 既不是奇函数, 又不是偶函数, 理由略", "solution": "", "duration": -1, "usages": [], @@ -274633,7 +274633,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\sin (-\\dfrac \\pi {16})>\\sin (-\\dfrac \\pi {13})$; (2) $\\sin 715^\\circ<\\sin (-724^\\circ )$", "solution": "", "duration": -1, "usages": [], @@ -274655,7 +274655,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 严格增区间: $[2k\\pi-\\dfrac{\\pi}{2},2k\\pi+\\dfrac{\\pi}{2}]$, $k\\in \\mathbf{Z}$; 严格减区间: $[2k\\pi+\\dfrac{\\pi}{2},2k\\pi+\\dfrac{3\\pi}{2}]$, $k\\in \\mathbf{Z}$;\\\\(2) 严格增区间: $[2k\\pi+\\dfrac{\\pi}{2},2k\\pi+\\dfrac{3\\pi}{2}]$, $k\\in \\mathbf{Z}$; 严格减区间: $[2k\\pi-\\dfrac{\\pi}{2},2k\\pi+\\dfrac{\\pi}{2}]$, $k\\in \\mathbf{Z}$;\\\\\n(3) 严格增区间: $[\\dfrac{2k\\pi}{3}-\\dfrac{\\pi}{12},\\dfrac{2k\\pi}{3}+\\dfrac{\\pi}{4}]$, $k\\in \\mathbf{Z}$; 严格减区间: $[\\dfrac{2k\\pi}{3}+\\dfrac{\\pi}{4},\\dfrac{2k\\pi}{3}+\\dfrac{7\\pi}{12}]$, $k\\in \\mathbf{Z}$;", "solution": "", "duration": -1, "usages": [], @@ -293765,7 +293765,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\pm \\dfrac{\\pi}{2}$", "solution": "", "duration": -1, "usages": [], @@ -293809,7 +293809,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 奇函数, 理由略; (2) 偶函数, 理由略; (3) 既不是奇函数, 又不是偶函数, 理由略", "solution": "", "duration": -1, "usages": [], @@ -293965,7 +293965,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -294009,7 +294009,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "最小正周期为$\\dfrac{\\pi}{2}$, 最大值为$1$, 最小值为$\\dfrac{1}{2}$", "solution": "", "duration": -1, "usages": [], @@ -294056,7 +294056,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2$; (2) \\begin{tikzpicture}\n\\draw [->] (-6,0) -- (6,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {-4,-3,-2,-1,1,2,3,4}\n{\\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};};\n\\foreach \\i in {-2,-1,1,2}\n{\\draw (0.1,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\draw [dashed] (-5,2) -- (-4,0) -- (-3,2) -- (-2,0) -- (-1,2) -- (0,0) -- (1,2) -- (2,0) -- (3,2) -- (4,0) -- (5,2);\n\\draw (-6,2) -- (-5,0) -- (-4,2) -- (-3,0) -- (-2,2) -- (-1,0) -- (0,2) -- (1,0) -- (2,2) -- (3,0) -- (4,2) -- (5,0) -- (6,2);\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -510588,7 +510588,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{2\\pi}{3}$; (2) $4\\pi$", "solution": "", "duration": -1, "usages": [], @@ -510610,7 +510610,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\pm \\pi$", "solution": "", "duration": -1, "usages": [], @@ -510632,7 +510632,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pi$", "solution": "", "duration": -1, "usages": [], @@ -510654,7 +510654,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$2+\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -510676,7 +510676,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 最大值为$2$, 当且仅当$x=\\dfrac{2k\\pi}{3}+\\dfrac{7\\pi}{18}$, $k\\in \\mathbf{Z}$时取到; 最小值为$-2$, 当且仅当$x=\\dfrac{2k\\pi}{3}+\\dfrac{\\pi}{18}$, $k\\in \\mathbf{Z}$时取到;\\\\(2) 最大值为$2$, 当且仅当$x=2k\\pi+\\dfrac{\\pi}{6}$, $k\\in \\mathbf{Z}$时取到; 最小值为$-2$, 当且仅当$x=2k\\pi+\\dfrac{7\\pi}{6}$, $k\\in \\mathbf{Z}$时取到;\\\\最大值为$2$, 当且仅当$x=2k\\pi+\\dfrac{3\\pi}{2}$, $k\\in \\mathbf{Z}$时取到; 最小值为$-\\dfrac{1}{4}$, 当且仅当$x=2k\\pi+\\dfrac{\\pi}{6}$或$2k\\pi+\\dfrac{5\\pi}{6}$, $k\\in \\mathbf{Z}$时取到;\\\\(4) 最大值为$4$, 当且仅当$x=k\\pi+\\dfrac{\\pi}{6}$, $k\\in \\mathbf{Z}$时取到; 最小值为$0$, 当且仅当$x=k\\pi+\\dfrac{2\\pi}{3}$, $k\\in \\mathbf{Z}$时取到", "solution": "", "duration": -1, "usages": [], @@ -510698,7 +510698,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "应截取$AB=\\sqrt{2}r$, $BC=\\dfrac{\\sqrt{2}}{2}r$, 这时矩形$ABCD$的面积达到最大值$r^2$", "solution": "", "duration": -1, "usages": [], @@ -510720,7 +510720,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "最大值为$\\sqrt{2}$, 取到最大值的$x$的集合为$\\{x|x=\\dfrac{k\\pi}{2}+\\dfrac{\\pi}{4}, \\ k\\in \\mathbf{Z}\\}$; 最小值为$1$, 取到最小值的$x$的集合为$\\{x|x=\\dfrac{k\\pi}{2}, \\ k\\in \\mathbf{Z}\\}$", "solution": "", "duration": -1, "usages": [], @@ -510742,7 +510742,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "当且仅当$\\theta=\\dfrac{\\pi}{6}$时面积$S$最大, $S$的最大值为$\\dfrac{50}{3}\\sqrt{3}\\text{m}^2$", "solution": "", "duration": -1, "usages": [], @@ -510764,7 +510764,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 偶函数, 理由略; (2) 偶函数, 理由略; (3) 既不是奇函数也不是偶函数, 理由略", "solution": "", "duration": -1, "usages": [], @@ -510786,7 +510786,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\sin \\dfrac{6 \\pi}{5}<\\sin \\dfrac{7 \\pi}{6}$; (2) $\\sin \\dfrac{43 \\pi}{7}>\\sin (-\\dfrac{47 \\pi}{8})$", "solution": "", "duration": -1, "usages": [], @@ -510808,7 +510808,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$[2k\\pi,2k\\pi+\\pi]$, $k\\in \\mathbf{Z}$", "solution": "", "duration": -1, "usages": [], @@ -510830,7 +510830,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$[-\\dfrac{2\\pi}{3},-\\dfrac{\\pi}{6}]$", "solution": "", "duration": -1, "usages": [], @@ -510852,7 +510852,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$k\\pi+\\dfrac{\\pi}{2}$, $k\\in \\mathbf{Z}$", "solution": "", "duration": -1, "usages": [], @@ -510874,7 +510874,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[0,\\dfrac{\\pi}{6}]$; (2) $[-\\sqrt{3}-1,1]$", "solution": "", "duration": -1, "usages": [], @@ -604333,7 +604333,7 @@ "第三单元" ], "genre": "解答题", - "ans": "(1) 假;(1) 假;(3) 真.", + "ans": "(1) 假; (2) 假;(3) 真.", "solution": "", "duration": -1, "usages": [ @@ -661022,7 +661022,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$[6k\\pi+\\dfrac{9\\pi}{4},6k\\pi+\\dfrac{21\\pi}{4}]$, $k\\in \\mathbf{Z}$", "solution": "", "duration": -1, "usages": [], @@ -688501,7 +688501,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "不是, 如$x=\\dfrac{\\pi}{3}$时, $\\sin (x+\\dfrac{2\\pi}{3})\\ne \\sin x$", "solution": "", "duration": -1, "usages": [],