From 2f5dc8d7d97cd1575376201a4b023a4c819c2989 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Mon, 18 Mar 2024 13:10:32 +0800 Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A0=E4=B8=80=E4=BA=9Bremark?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/metadata.txt | 1919 +--------------------------------- 题库0.3/Problems.json | 14 +- 2 files changed, 20 insertions(+), 1913 deletions(-) diff --git a/工具v2/文本文件/metadata.txt b/工具v2/文本文件/metadata.txt index 4619f684..cb3e3cdb 100644 --- a/工具v2/文本文件/metadata.txt +++ b/工具v2/文本文件/metadata.txt @@ -1,1919 +1,26 @@ -ans +remark -008393 -$\dfrac{2\pi}{3}$ +021608 +(20240313主要错因) 方法不会, 凑答案 -024718 -$4$ - -024720 -$-4$ - -003773 -(1) $\dfrac{\pi}{3}$; (2) $\dfrac{3\sqrt{3}}{2}$ - -006360 -B - -013849 -B - -031580 -A - -ans - -018409 -$AC\approx 14.6\text{km}$, $BC\approx 22.4\text{km}$ - -018410 -$a=2R\sin A$, $b=2R\sin B$, $c=2R\sin C$ - -018411 -(1) 证明略; (2) 证明略 - -009580 -$b\approx 7.66$, $c\approx 6.74$, $S\approx 16.58$ - -010260 -证明略 +024615 +(20240313主要错因) (1)考虑不周全, 漏解 018412 -$\frac{5+10\sqrt 2}{3}$ +(20240313主要错因) 没能正确说明判断角A的余弦值的符号的过程、 018413 -$\frac{1}{2}$ +(20240313主要错因) (2)方法不会; 直接用正弦定理把边替换成角的正弦值, 没乘上$2R$ -018414 -$c=2,A=60^\circ,B=75^\circ$ +021615 +(20240314主要错因) 未考虑到角的余弦值有两种情况, 漏解; 计算错误 -018415 -$B=60^\circ,C=90^\circ,c=4;B=120^\circ,C=30^\circ,c=2$ +021618 +(20240314主要错因) 考虑不周全, 没考虑到形成三角形要满足的条件; 方法复杂, 没想到找到最大角, 而是把三个角的余弦值都算了出来 -018416 -$\frac{15\sqrt{7}}{4}$ +003606 +(20240314主要错因) (2)对于多解问题不知道如何判断是否要舍解; 以及没掌握从小角入手来求解边的方法; 计算错误 -009582 -$\sqrt{13}$ -009583 -$B=30^\circ,C=105^\circ,c=3\sqrt2+\sqrt6$ -009584 -$-\frac{1}{4}$ - -010256 -$-\frac{1}{7}$ - -010259 -$a=b=2$ - -010266 -$\frac{3}{5};84$ - -024621 -$2\sin(2x-\dfrac{\pi}{6})+1$ - -024618 -(1) $\sqrt{2}\sin (\alpha+\dfrac{\pi}{4})$; (2) $2\sin(\alpha-\dfrac{\pi}{6})$; (3) $2\sin (\alpha+\dfrac{5\pi}{6})$; (4) $5\sin (\alpha+\varphi)$, $\cos\varphi = \dfrac{3}{5}$, $\sin\varphi = \dfrac{4}{5}$, ($\varphi \in [-\pi,\pi)$); (5) $13\sin(\alpha+\varphi)$, $\cos\varphi = \dfrac{12}{13}$, $\sin\varphi = -\dfrac{5}{13}$, ($\varphi \in [-\pi,\pi)$) - -040114 -$\dfrac{7}{25}$ - -040120 -$\dfrac{1}{3}$ - -ans - -012360 -$\dfrac{\pi}{3}$ - -023093 -$\frac{\pi}{4}$或$\frac{3\pi}{4}$. - -023094 -$3\pi$. - -023095 -$4\sqrt{3}$. - -023096 -$\sqrt{2}$. - -023097 -\textcircled{1},\textcircled{3}. - -023098 -$5$. - -023099 -$21$. - -023100 -$32\pi$. - -023101 -$3\sqrt{3}$. - -023102 -$6$. - -023103 -$\frac{\pi}{6}$. - -023104 -A. - -023105 -C. - -023106 -(1)略；(2)$arccos\frac{31}{34}$;(3)$\pi-arctan\frac{\sqrt{51}}{12}$. - -023107 -(1)略；(2)$\frac{1}{6}$;(3)$[\frac{21}{2},15]$. - -009305 -(1)$x^15$,$-15x^14$,$105x^13$,$-455x^12$\\ -(2)$-2099520a^9b^14$ - -009306 -(1)$\dfrac{105}{8}$;(2)$-252$ - -009309 -$120$ - -009308 -证明略 - -009317 -(1)第$18$,$19$项；\\ -(2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$ - -009319 -证明略 - -021093 -(1)$\dfrac{1}{45}$;(2)$\dfrac{7}{10}$ - -022919 -(1)$\dfrac{1}{36}$;(2)$\dfrac{1}{18}$;(3)$\dfrac{5}{12}$ - -021095 -(1)$\dfrac{1}{68880}$;(2)$\dfrac{1}{11480}$ - -021096 -$\dfrac37$ - -021097 -$\dfrac{1}{12}$ - -021098 -$\dfrac{18}{25}$ - -021099 -$\dfrac{2}{5}$ - -021101 -$\dfrac{11}{12}$ - -021102 -$\dfrac{3439}{10000}$ - -021103 -$\dfrac{n!}{n^n}$ - -021104 -$\dfrac{1}{15}$ - -021105 -$\dfrac15$ - -021106 -(1)$\dfrac{11}{42}$;(2)$\dfrac{31}{42}$ - -021107 -(1)$\dfrac{1279}{1785}$;(2)$\dfrac{59049}{139075300}$ - -021108 -(1)$\{5,7,9\}$;(2)$\{0,2,4,5,6,7,8,9\}$;(3)$\emptyset$ - -021109 -B - -021110 -(1)$\{1,2,3,4\}$;(2)A - -021111 -(1)$\{1,2,3,4\}$;(2)A - -021112 -充分非必要 - -021113 -(1)$A\cup B$;(2)$A \cap \overline{B}$;(3)$(A \cap \overline{B}) \cup(\overline{A} \cap B) $ - -021114 -$B\subseteq \overline{A}$,$\overline{A}\cup \overline{B}=\omega$ - -021116 -(1)$\dfrac12$;(2)$\dfrac56$;(3)$\dfrac23$;(4)$\dfrac56$ - -021117 -(1)不是;(2)$0.94$ - -021125 -(1)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)\cup (A \cap B \cap C)$; -(2)$\overline{A\cap B \cap C }$; -(3)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)$ - -021118 -$\dfrac47$,$\dfrac27$,$\dfrac17$,$\dfrac67$,$\dfrac67$,$\dfrac57$ - -019932 -(1)$\dfrac34$;(2)$\dfrac1{13}$;(3)$\dfrac12$;(4)$\dfrac{51}{52}$ - -021119 -$\dfrac45$ - -021120 -$\dfrac35$ - -021121 -$\dfrac14$,$\dfrac16$,$\dfrac14$ - -021122 -$0.9$,$0.1$ - -018762 -证明略 - -021126 -大数定律 - -021127 -$\dfrac{73}{75}$ - -021128 -$\dfrac34$,$\dfrac{9}{44}$,$\dfrac{9}{220}$.$\dfrac{1}{220}$ - -021129 -(1)$0.46$;(2)$0.51$;(3)$0.97$ - -021130 -(1)$0.852$;(2)$25560$;(3)$5869$ - -021131 -(1)$0.1,0.06,0.025,0.02,0.02,0.02$;(2)$0.02$;(3)$40$ - -021132 -(1)$30\%$;(2)$53\%$;(3)$73\%$;(4)$14\%$;(5)$90\%$;(6)$10\%$; - -021133 -(1)$\dfrac13$;(2)$\dfrac14$ - -021134 -C - -021135 -(1)$\dfrac56$;(2)$\dfrac16$;(3)$\dfrac23$;(4)$\dfrac12$ - -021136 -(1)$0.995$;(2)$0.095$ - -021137 -(1)$7:1$;(2)$11:5$ - -021138 -$0.328$ - -021139 -$(\dfrac23,1)$ - -021140 -(1)$\dfrac38$,$\dfrac23$;(2)$\dfrac{21}{32}$ - -021141 -D - -021142 -D - -021143 -A - -021144 -A - -021145 -\textcircled{2} - -021146 -总体是$2487$万人的年龄，样本是$24000$个常住居民的年龄，样本量是$24000$ - -021147 -观测，观测，实验 - -021148 -不可靠，样本容量太小，样本不一定具有代表性 - -021149 -$2$ - -021150 -$122$ - -021151 -$a=b=10.5$ - -021152 -平均值是$17$,方差是$27$ - -021153 -平均数是$72.0$，中位数是$70$，方差是$74.9$ - -021154 -$\dfrac{n}{N}$ - -021155 -B - -021156 -20 - -021157 -C - -021158 -$4467$ - -021159 -(1)抽签法;(2)分层抽样 - -021160 -$49,04,40,36,16,08,06,55,33,69$ - -021161 -样本容量为$92$，抽样人数为$31$ - -021162 -略 - -021163 -分层抽样，高一抽$18$人，高二抽$22$人，高三抽$10$人 - -021164 -C - -021165 -$4$,$5.14$ - -021166 -$0.32$,$96$ - -021167 -$300$ - -021168 -集中，分散，$6.88$,$12.43$ - -021169 -\begin{tabular}{c|ccccccc} -8 & 9 \\ -9 & 3 & 4 & 6 & 7 \\ -10 & 0 & 0 & 1 & 1 & 3 & 5 & 8\\ -11 & 0 & 2 -\end{tabular} - -021170 -略 - -021171 -略 - -021172 -D - -021173 -$35$ - -021174 -$12$ - -021177 -C - -021179 -\textcircled{1},\textcircled{2} - -021180 -A - -021175 -甲更准，乙更稳定 - -021176 -(1)$3.47$,(2)$2773$ - -021178 -$100$ - -021181 -(1)$9.5$;(2)不能 - -021182 -平均成绩是$89.6$，总体方差是$12.09$ - -023356 -$A\subset C\subset B \subset E \subset D \subset G$;$E \subset F \subset G$ - -023357 -全错 - -023358 -$\dfrac{72\sqrt{21}}7$ - -023359 -(1)$\dfrac16$;(2) - -023360 -$2\sqrt{15}$或$4\sqrt{6}$ - -023361 -略 - -023362 -$\frac{b^2-a^2}{\sqrt{a^2+b^2} \cdot \sqrt{a^2+b^2+c^2}}$. - -023363 -(1) $\frac{1}{2}$; (2) $\frac{\pi}{3}$. - -023364 -(1) 略; (2) $\arcsin{\frac{3\sqrt{2}}{10}}$; (3) $\frac{24\sqrt{41}}{41}$ - -023365 -略 - -023366 -$\sqrt{41}$ - -023367 -(1) 略; (2) $\frac{\pi}{4}$. - -023368 -$8\sqrt{3}$. - -003494 -(1) 略; (2) $3$; (3) $108\sqrt{3}$. - -023369 -(1) $48$; (2) $16\sqrt{3}+8\sqrt{21}+40$ - -023370 -(1) 略; (2) $\frac{1}{3}$; (3) $\frac{\sqrt{2}}{2}+\frac{\sqrt{6}}{2}$. - -023108 -C - -023109 -1; 4. - -023110 -8; 4. - -023111 -$M \in a$,$M \notin \alpha$. - -023112 -$\{1,4,6\}$. - -023113 -$D$. - -023114 -$C$. - -023115 -$A$. - -023116 -1个或者无数个 - -023117 -平行四边形 - -023118 -10 - -023119 -\textcircled{1}, \textcircled{2} ,\textcircled{4}, \textcircled{5}. - -023120 -$D$. - -012345 -$D$. - -023121 -(1)略；(2)略. - -023122 -略. - -023123 -略. - -023124 -$\frac{5(\sqrt{6}-1)}{2} $. - -023125 -$\sqrt{2}+2\sqrt{13}$. - -023126 -(1) F ; (2) F; (3) F; (4) T; (5) T; (6) T; (7) T; (8) F. - -023127 -(1) T ; (2) F; (3) F; (4) F; (5) F. - -023128 -异面或者平行. - -023129 -(1) 平行; (2) 异面. - -023130 -相交或者平行. - -023131 -充分不必要. - -023132 -4个. - -023133 -$45^{\circ}$; $30^{\circ}$或$60^{\circ}$. - -023134 -(1) $\frac{\pi}{3}$; (2) $\arccos \frac{\sqrt{10}}{10}$; (3) $\arccos \frac{\sqrt{10}}{5}$. - -023135 -\textcircled{1} \textcircled{4}. - -023136 -$\frac{a}{3}$. - -012345 -D - -023137 -B - -023138 -略. - -023139 -略. - -023140 -$\frac{\pi}{4}$或$\frac{\pi}{3}$. - -023141 -(1) 点 $P$ 在$C$点; (2) 点 $P$ 在距离$C$点$\frac{16}{5}$. - -023142 -$\frac{\sqrt{39}}{2}$. - -016740 -1. - -016731 -8. - -023143 -$\arctan\frac{1}{5}$或者$\arctan\frac{4}{5}$. - -023144 -$\arctan\frac{2\sqrt{5}}{5}$. - -017767 -2 - -023145 -$\sqrt{6}$. - -023146 -$\frac{\sqrt{3}}{3}$. - -023147 -$[ 30,90 ]$. - -023148 -(1) $\frac{\sqrt{15}}{5}$; (2) $\frac{\pi}{6}$. - -023149 -$\frac{\sqrt{3}}{2}$. - -023150 -$\frac{2}{3}$. - -023151 -(1) $\arctan \frac{\sqrt{5}}{5}$; (2) $\arccos \frac{\sqrt{30}}{10}$; (3) 在 $BC$ 边上存在一点 $G$, $BG$的值为1. - -023152 -(1) 略; (2) $\arcsin \frac{\sqrt{21}}{7}$; (3) 存在 $P$, 使得 $DE \parallel $ 平面 $BMP$, $\dfrac{AP}{DP}$ 的值3. - -031552 -$\frac{\sqrt{10}}{5}$ - -003489 -(1) $\arcsin \frac{\sqrt{6}}{3}$; (2) $\arcsin \frac{\sqrt{3}}{3}$; (3) $\frac{\pi}{4}$. - -023153 -(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{\sqrt{6}}{6}$; (3) $\frac{\sqrt{6}}{6}$. - -003456 -$\frac{3\sqrt{5}}{5}$. - -003457 -$\frac{\pi}{3}$或$\frac{2\pi}{3}$. - -023154 -1或3. - -023155 -$\frac{\pi}{3}$. - -023156 -\textcircled{1}\textcircled{2}\textcircled{3}\textcircled{5}. - -023157 -B - -023158 -B - -023159 -A - -023160 -$\frac{\pi}{3}$. - -023161 -4.3 - -023162 -(1) 略; (2) $\frac{\sqrt{3}}{2}$; (3) $\arcsin \frac{2\sqrt{5}}{5}$. - -023163 -(1) $\frac{\pi}{2}$; (2) $\frac{\pi}{3}$. - -023164 -(1) 四边形 $MNDC$为矩形; (2) $\arctan \frac{\sqrt{2}}{2}$; (3) $\frac{\sqrt{2}}{2}$. - -023165 -(1) 异面直线 $D_1E$ 与 $A_1D$ 所成角的大小不会随点 $E$ 的移动而改变, 所成角为$\frac{\pi}{2}$; \\(2) 点 $E$距离点 $A$ 为$2-\sqrt{3}$, 二面角 $D_1-EC-D$ 的大小为 $\dfrac{\pi}{4}$; \\(3) 直线 $AD_1$ 平行于 平面 $B_1DE$. - -023166 -\textcircled{2}\textcircled{3} - -023167 -$75^{\circ}$ - -010502 -arctan$\frac{\sqrt{5}}{5}$ - -023168 -arccos$\frac{2}{3}$ - -023169 -$\frac{\pi}{4}$ - -023170 -$\sqrt{41}$或$13$ - -023171 -$6$或$1.5$ - -023172 -$30^{\circ}$ - -023173 -$3.5cm$ - -023174 -$\frac{\sqrt{2}}{2}$ - -023175 -B - -023176 -$A$ - -023177 -$D$ - -023178 -$(1)$略；$(2)\frac{\sqrt{14}}{14}$ - -023179 -$(1)\frac{\pi}{6};(2)arccos\frac{\sqrt{3}}{3}$ - -023180 -$(1)$略；$(2)arctan\frac{\sqrt{6}}{2}$;$(3)$略；$(4)\frac{\sqrt{2}}{6}$ - -023181 -无 - -011402 -A - -023182 -B. - -023183 -2. - -023184 -5. - -023185 -$\sqrt{29}$. - -023186 -$\frac{\pi}{6}$. - -023187 -$\frac{15\sqrt{3}}{2}$ - -017677 -$DM\perp PC$（或$BM\perp PC$) - -023188 -\textcircled{1}\textcircled{2}\textcircled{4} - -023189 -(1)略；(2)$arccos\frac{\sqrt{15}}{5}$ - -023190 -(1)略；(2)6. - -023191 -$S=\begin{cases}\frac{1}{2cos\alpha},\quad\alpha\in(0,arctan\sqrt{2}]\\ \frac{\sqrt{2}-cot\alpha}{sin\alpha},\alpha\in(arctan\sqrt{2},\frac{\pi}{2}]\end{cases}$ - -023192 -(1)略；(2)$\frac{2\sqrt{6}}{3}$. - -023193 -$8$. - -023194 -$arctan\frac{\sqrt{3}}{2}$. - -023195 -$64.$ - -023196 -$arctan\sqrt{2}$. - -023197 -$10.$ - -023198 -$(1)$外心；$(2)$内心；$(3)$垂心. - -023199 -$\sqrt{3}$ - -023200 -$48$. - -023201 -$\frac{6}{7}$. - -023202 -A. - -023203 -$S=32,V=16$. - -023204 -$\frac{2\sqrt{11}}{11}$. - -023205 -$(1)$略；$(2)\frac{5}{3}$. - -023206 -$(1)V=a^2;(2)$\textcircled{1}$\frac{\sqrt{51}}{9}$;\textcircled{2}$\frac{\sqrt{30}}{3}$. - -023207 -$\sqrt{29}$. - -023208 -$\frac{\sqrt{6}}{3}$. - -023209 -$arctan\frac{\sqrt{5}}{5}$. - -023210 -$arccos\frac{2}{3}$. - -023211 -$\frac{\pi}{6}$. - -023212 -$\frac{15\sqrt{3}}{2}$. - -023213 -$3\pi^2$或$\frac{9}{2}\pi^2$. - -023214 -$\frac{\sqrt{3}}{2}a$. - -023215 -$\pi$. - -023216 -$\sqrt{2}:1$. - -023217 -$1:4:9$. - -023218 -$\frac{8}{3}\pi$. - -023219 -$12:15:20$. - -023220 -$576$. - -023221 -$\theta_{min}=\pi-arctan\frac{4}{3}$,此时$P$ 在线段 $A_1C_1$ 的中点. - -023222 -略. - -023223 -$(1)$略；$(2)arctan\sqrt{2}$;$(3)$是，$\frac{\sqrt{6}}{24}$. - -023224 -$P^{6}_{20-m}$. - -023225 -$60$. - -023226 -$48$. - -023227 -$6$. - -023228 -$3$. - -023229 -$156$. - -023230 -$103$. - -023231 -$48$. - -023232 -$(\frac{2}{3},1)$. - -023233 -$a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2 - \end{cases}$. - -023234 -(1)$m=9$;(2)$k_{n}=3^{n+1}+2$. - -023235 -$(-\frac{1}{11},-\frac{1}{19})$. - -023236 -(1)略；(2)$S_{n}=\frac{2}{3}-(n+\frac{2}{3})(\frac{1}{4})^{n}$;(3)$(-\infty,-5]\cup[1,+\infty)$. - -023237 -$1716$. - -023238 -5或8. - -023239 -$x=15,y=5$. - -023240 -21. - -023241 -6. - -016908 -12. - -023242 -540. - -023243 -2880. - -023244 -200. - -023245 -$-1$. - -023246 -$2^{n-1},n\in \mathbf{N}$且$n\ge1$. - -023247 -$2^{n-1},n\in \mathbf{N}$且$n\ge1$. - -023248 -$7(\frac{1}{3})^{n-1}-6,n\in \mathbf{N}$且$n\ge1$. - -023249 -$765$. - -023250 -(1)58409520;(2)6275430;(3)64684945;(4)64682995. - -023251 -$92$. - -023252 -(1)$a_n=\frac{2}{n+1}$;(2)$a_n=2\cdot3^{n-1}-1$;(3)$a_n=2^n-1$;(4)$a_n=\begin{cases}2,n=4k-3 \\-3,n=4k-2\\-\frac{1}{2},n=4k-1\\\frac{1}{3},n=4k\end{cases}\ \ \ \ \ ( k\in \mathbf{N}$且$k\ge1)$ - -023253 -(1)不是；(2)最大项为$a_3=a_4=20$. - -022570 -(1)$2$;(2)存在，$N=22$. - -022572 -$S_n=(n-1)\cdot3^n+1$. - -023254 -(1)第$16$项；(2)$b_n=3\cdot2^n+1$. - -023255 -(1)略；(2)$a_n=\begin{cases} - \frac{1}{2},n=1\\-\frac{1}{2n(n-1)},n\geq2 -\end{cases}$ - -023256 -$\frac{3}{5}$ - -023257 -$\frac{3}{7}$ - -023258 -$\frac{1}{35}$ - -031430 -$\frac{14}{33}$ - -017716 -$\frac{3}{10}$ - -017041 -$\frac{3}{4}$ - -023259 -$\frac{2}{7}$ - -023260 -$\frac{2}{27}$ - -023261 -$\frac{9}{10}$ - -023262 -$-49$ - -023263 -$12$ - -023264 -$\frac{5}{6}$ - -023265 -(1) $d_1, d_2, d_3$ 的值分别为2,3,6;\\ -(2) 略; (3) 略. - -023266 -$0.54$ - -023267 -$\dfrac{5}{36}$; $\dfrac{5}{12}$ - -023268 -$\dfrac{3}{8}$; $\dfrac{7}{8}$ - -023269 -$0.88$ - -023270 -$0.9$ - -023271 -$7$或$8$ - -002651 -$7$ - -023272 -(1) F; (2) F; (3) T; (4) F. - -023273 -(1) $\dfrac{4}{15}$; (2) $\dfrac{11}{15}$ - -023274 -(1) $\dfrac{70}{323}$; (2) $\dfrac{728}{969}$; (3) $\dfrac{27}{128}$ - -023275 -(1) $\dfrac{211}{3456}$; (2) $\dfrac{7}{10}$; (3) $\dfrac{1}{15}$ - -023276 -(1) $c_n=2n-1$; (2) $S_n=1+(n-1)3^n$ - -023277 -$18$ - -023278 -B - -023279 -A - -023280 -C - -023281 -B - -023282 -C - -023283 -$55$ - -023284 -$50$; $1015$ - -023285 -$3$ - -023286 -$n=1$时, $a_n=5$; $n \geq 2$时, $a_n=2n-2$ - -023287 -$2^n+3$ - -023288 -$1049410$ - -023289 -$19$ - -023290 -(1) $0.5$; (2) $\frac{3}{16}$; (3) 略 - -023291 -(1) $\{a_n\}-3n+15$; (2) $T_n=\frac{1}{6}(\frac{3}{2}-\frac{1}{n+1}-\frac{1}{n+2})$ - -023292 -(1) $P_3=-2p^3+3p^2$; $P_4=4p^3-3p^4$; (2) 当$0\sqrt{3}$ - -040995 -(1)$y=-\sqrt12+\sqrt34$;(2)$x+4y=0$(点在已知椭圆内);(3)$x^2+x+2y^2=0$ - -040996 -$6\sqrt{5}$ - -021204 -$\dfrac{\sqrt{2}}{2}$ - -021205 -$2\sqrt{37}$,$2$ - -021206 -$\dfrac{x^2}{25}+\dfrac{y^2}{75}=1$ - -021207 -$\dfrac{x^2}{12}+\dfrac{y^2}{9}=1$或$\dfrac{x^2}{9}+\dfrac{y^2}{12}=1$ - -021208 -$[-\sqrt{34},\sqrt{34}]$ - -021209 -$\dfrac{\pi}3$ - -040997 -$b\sqrt{a^2-b^2}$ - -040998 -$8\sqrt{3}$ - -021212 -$P(-6,-4)$,$d=\dfrac{22}{\sqrt{73}}$ - -021200 -$\dfrac{x^2}{4}+y^2=1$ - -021201 -$-\dfrac{5\sqrt{7}}{4}0)$;(3)$x^2-\dfrac{y^2}{3}=1$ - -021223 -$\dfrac{x^2}{20}-\dfrac{y^2}{16}=1$ - -021224 -$\dfrac{x^2}{33-12\sqrt{6}}-\dfrac{y^2}{12\sqrt{6}-8}=1$或$\dfrac{y^2}{16}-\dfrac{x^2}{9}=1$ - -021225 -不正确，正确结果为$17$ - -021226 -$\dfrac{x^2}{115600}-\dfrac{y^2}{134400}=1$ - -021227 -D - -021228 -$(-3,6)$ - -021229 -$m<-2$ - -021230 -$\dfrac{41}{4}$ - -021231 -$32+2m$ - -021232 -$|PF_1|=\dfrac{c}{a}x_0+a$,$|PF_2|=\dfrac{c}{a}x_0-a$ - -021233 -$x^2-\dfrac{y^2}{4}=1$ - -041001 -(1)$\dfrac{y^2}{18}-\dfrac{x^2}{18}=1$,$\sqrt{2}$;(2)$(\pm 2\sqrt{3},0)$,$\arctan{2\sqrt{2}}$ - -041002 -A,A,B,B - -041003 -(1))$\dfrac{x^2}{3}-\dfrac{y^2}{5}=1$;(2))$\dfrac{y^2}{81}-\dfrac{x^2}{9}=1$或)$x^2-\dfrac{y^2}{9}=1$ - -021242 -$\dfrac{x^2}{3}-\dfrac{y^2}{12}=1$ - -021243 -$y=\pm \dfrac{\sqrt{2}}{4}x$ - -021244 -证明略 - -041004 -(1)$\dfrac{x^2}{\dfrac{81}{13}}-\dfrac{y^2}{\dfrac{36}{13}}=1$;(2)$2$或$\dfrac{2\sqrt{3}}{3}$; (3)$(\dfrac 52,\dfrac 72)$;(4)$(\pm \sqrt{7},0)$ - -041005 -D,A,D - -021251 -$a^2$ - -021263 -$\dfrac{y^2}{36}-\dfrac{x^2}{81}=1(x\neq 0)$ - -021252 -$\dfrac{c}{a}$ - -021253 -$y=\pm \sqrt{2}x$ - -021254 -$0$ - -008917 -$\dfrac{x^2}{4}-\dfrac{y^2}{5}=1$(x>0) - -021255 -$\dfrac{2\sqrt{3}}{3}$ - -021256 -$\dfrac{14\sqrt{3}}{3}$ - -041006 -$3$ - -021258 -$x^2-4y^2=\pm \dfrac{36}{5}$ - -021259 -$(-\dfrac{\sqrt{15}}{3},-1)$ - -021260 -(1)椭圆:$k<4$,双曲线：$4\dfrac{\sqrt{6}}{2},e\neq \sqrt{2}$;(2)$\dfrac{17}{13}$ - -ans - -022801 -$[0,1]$ - -022802 -$\sqrt{5}$ - -022803 -$2\sqrt{2}-1$ - -022804 -$\pm 1$ - -022805 -$2n-3$ - -022806 -$1$ - -022807 -$36$ - -012041 -$240$ - -022808 -若 \textcircled{1}\textcircled{3},则\textcircled{2}(或者若 \textcircled{2}\textcircled{3},则\textcircled{1}) - -012042 -$(-1,1)$ - -022809 -$\dfrac{4\sqrt{3}}{3}$ - -022810 -A - -022811 -D - -022812 -A - -022813 -$(1)\dfrac{\pi}{4});(2)4-\sqrt{2}$ - -022814 -(1)$\dfrac{\pi}{3}$;(2)$\arctan\dfrac{\sqrt{2}}{2}$;(3)$\dfrac{1}{2}$ - -004486 -(1) 约为$6.7^\circ$; (2) 最小值为$256$ - -022815 -(1) $\dfrac{x^2}{2}+y^2=1$; (2) $k=\pm\dfrac{1}{2}$ - -022816 -(1) $\dfrac{1}{1},\dfrac{2}{1},\dfrac{1}{2},\dfrac{3}{1},\dfrac{2}{2},\dfrac{1}{3},\dfrac{4}{1},\dfrac{3}{2},\dfrac{2}{3},\dfrac{1}{4}$; (2) $1008\dfrac{28}{65}$ - -019810 -$\{2,4\}$ - -019811 -$x=\log_23$ - -031267 -$4\pi$ - -012389 -$n^2$ - -019814 -$2$ - -019815 -$\dfrac{\pi}{6}$ - -009322 -$72$ - -019817 -$\dfrac{2\sqrt{2}}{3}$ - -019818 -$\dfrac{3}{10}$ - -019819 -$-3$ - -040079 -$1078$ - -019822 -B - -019823 -A - -004565 -B - -022817 -(1) $\arctan\dfrac{2}{5}$; (2) $V=4$ - -022818 -(1) $a=0$; (2) $a-\dfrac{1}{4}$ - -022819 -(1)7小时；(2)17小时 - -022820 -(1)$4\sqrt{2}-6$;(2)$y=-\dfrac{\sqrt{2}}{2}x$ - -022821 -(1) $1,2,3,a_n=n$;(2)略 - -022822 -$\sqrt{2}$ - -022823 -3 - -022824 -$1+\ln x$ - -022825 -$\sqrt{5}\pi$ - -022826 -0 - -022827 -80 - -022828 -$-\dfrac{1}{4}$ - -022829 -$\dfrac{y^2}{9}-\dfrac{x^2}{1}=1$ - -022830 -$\dfrac{9}{20}$ - -022831 -8 - -022832 -$\dfrac{\sqrt{5}}{2}$ - -022833 -D - -022834 -A - -022835 -C - -022836 -(1) $\dfrac{16}{3}$;(2) $\arcsin\dfrac{2\sqrt{2}}{3}$ - -004506 -(1) $1$;(2)$2$ - -022837 -(1)$3.1$秒；（2）20米/秒，72千米/小时 - -022838 -（1）$\dfrac{8}{3}$;(2)略 - -022839 -（1）$a_1=1;a_2=0$或$1$；$a_3=0$或$1$;(2)115,证明略 - -022840 -$\{1,2\}$ - -022841 -$\dfrac{\pi}{3}$ - -022842 -$\dfrac{\pi}{3}$ - -022843 -$-2$ - -022844 -$512$ - -022845 -$\dfrac{2\pi}{3}$ - -022846 -$-3$ - -022847 -$\dfrac{x^2}{9}-\dfrac{y^2}{16}=1$ - -022848 -$(0,\dfrac{1}{3})\bigcup (\dfrac{1}{3},\dfrac{2}{3})$ - -022849 -$2:-1:1:1$ - -022850 -$\dfrac{\sqrt{3}}{2}$ - -022851 -C - -022852 -C - -022853 -A - -022854 -(1)12;(2)略 - -022855 -（1）$AB=\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$1$平方米；（2）$AB=2\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$2$平方米 - -022856 -（1）$2020$;(2)$(-\infty,\log_2\dfrac{9}{10}]$ - -022857 -（1）证明略；(2)关于直线$y=x$对称，$x$范围为$[-1,+\infty)$,$y$范围为$[-1,+\infty)$,证明略 - -022858 -（1）例：$f(x)=\sin\dfrac{\pi x}{4}$,证明略；（2）证明略 - -022859 -$(0,2))$ - -004512 -$\sqrt{2}$ - -022860 -$(x+\dfrac{3}{2})^2+y^2=9$ - -022861 -$2n+1$ - -004558 -$15$ - -019885 -$2\pi$ - -022862 -$0.25$ - -022863 -$3\sqrt{3}$ - -022864 -$[0,\dfrac{\sqrt{3}}{3}]$ - -004521 -$(-\infty,-1]$ - -022865 -A - -022866 -A - -004524 -C - -022867 -(1)证明略；（2）$ED=\dfrac{\sqrt{6}}{3}a$ - -004527 -(1)$T=\pi $;严格增区间为$[k\pi-\dfrac{\pi}{3},k\pi+\dfrac{\pi}{6}],k\in\mathbf{Z}$;(2)$3\sqrt{3}$ - -022868 -(1)15户；（2）$x=5$时，$f(x)$最大值为$2.12>2.1$,可以达到 - -022869 -（1）$1$; (2)$(0,\arctan\dfrac{1}{2})$ - -022870 -(1)$6$; (2)正确，证明略 - -019887 -$-\dfrac{1}{4}$ - -019888 -$\dfrac{1}{2}$ - -019889 -3 - -019890 -$[-\dfrac{1}{2},\dfrac{1}{2}]$ - -023003 -C - -019891 -A - -023004 -4 - -023005 -B - -023006 -C - -019900 -1 - -019901 -3 - -019902 -2 - -019903 -$-\dfrac{1}{2}$ - -019904 -D - -004438 -C diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 5ec4bb2e..40dd00b3 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -113558,7 +113558,7 @@ ], "same": [], "related": [], - "remark": "", + "remark": "(20240314主要错因) (2)对于多解问题不知道如何判断是否要舍解; 以及没掌握从小角入手来求解边的方法; 计算错误", "space": "4em", "unrelated": [] }, @@ -509161,7 +509161,7 @@ ], "same": [], "related": [], - "remark": "批改时注意学生应有判断并舍去钝角的过程", + "remark": "批改时注意学生应有判断并舍去钝角的过程\\\\\n(20240313主要错因) 没能正确说明判断角A的余弦值的符号的过程、", "space": "4em", "unrelated": [] }, @@ -509195,7 +509195,7 @@ ], "same": [], "related": [], - "remark": "", + "remark": "(20240313主要错因) (2)方法不会; 直接用正弦定理把边替换成角的正弦值, 没乘上$2R$", "space": "4em", "unrelated": [] }, @@ -601729,7 +601729,7 @@ ], "same": [], "related": [], - "remark": "", + "remark": "(20240313主要错因) 方法不会, 凑答案", "space": "", "unrelated": [] }, @@ -601977,7 +601977,7 @@ ], "same": [], "related": [], - "remark": "", + "remark": "(20240314主要错因) 未考虑到角的余弦值有两种情况, 漏解; 计算错误", "space": "", "unrelated": [] }, @@ -602094,7 +602094,7 @@ ], "same": [], "related": [], - "remark": "", + "remark": "(20240314主要错因) 考虑不周全, 没考虑到形成三角形要满足的条件; 方法复杂, 没想到找到最大角, 而是把三个角的余弦值都算了出来", "space": "4em", "unrelated": [] }, @@ -683686,7 +683686,7 @@ "related": [ "021613" ], - "remark": "", + "remark": "(20240313主要错因) (1)考虑不周全, 漏解", "space": "", "unrelated": [] },