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@ -40,10 +40,10 @@ $x=0\quad (-3\leq y \leq 3)$
$\dfrac{4}{3}$ $\dfrac{4}{3}$
040952 040952
\\（1）$l$的斜率不存在$x=10$，舍\\（2）$5x-12y-38=0$或$3x+4y-34=0$ \\(1)$l$的斜率不存在$x=10$, 舍\\(2)$5x-12y-38=0$或$3x+4y-34=0$
040953 040953
\\(1)相交；\\(2)$\sqrt{3}x-y+1-\sqrt{3}=0$或$-\sqrt{3}x-y+1+\sqrt{3}=0$\\(3)$x(x-1)+(y-1)^2=0 (x\neq1)$ \\(1)相交; \\(2)$\sqrt{3}x-y+1-\sqrt{3}=0$或$-\sqrt{3}x-y+1+\sqrt{3}=0$\\(3)$x(x-1)+(y-1)^2=0 (x\neq1)$
040954 040954
\\(1)$(x-1)^2+(y-\dfrac{1}{2})^2=\dfrac{5}{4}$\\(2)m=3 或 m=$-\dfrac{1}{3}$ \\(1)$(x-1)^2+(y-\dfrac{1}{2})^2=\dfrac{5}{4}$\\(2)m=3 或 m=$-\dfrac{1}{3}$
@ -145,7 +145,7 @@ $y=\dfrac{1}{2}x\pm\dfrac{\sqrt{66}}{2}$
$x^2-\dfrac{y^2}{15}=1\quad(x\geq0)$ $x^2-\dfrac{y^2}{15}=1\quad(x\geq0)$
041063 041063
$\\(1)k\geq0$时，双曲线\\(2)$k=0$时，$y=0$\\(3)$k\leq0$且$k\neq-1$时，椭圆\\(4)$k=-1$时，圆 $\\(1)k\geq0$时, 双曲线\\(2)$k=0$时, $y=0$\\(3)$k\leq0$且$k\neq-1$时, 椭圆\\(4)$k=-1$时, 圆
041064 041064
$\\m=4\\S=\sqrt{3}$ $\\m=4\\S=\sqrt{3}$
@ -195,10 +195,10 @@ A.
C. C.
023106 023106
(1)略；(2)$\arccos\frac{31}{34}$;(3)$\pi-\arctan\frac{\sqrt{51}}{12}$. (1)略; (2)$\arccos\frac{31}{34}$;(3)$\pi-\arctan\frac{\sqrt{51}}{12}$.
023107 023107
(1)略；(2)$\frac{1}{6}$;(3)$[\frac{21}{2},15]$. (1)略; (2)$\frac{1}{6}$;(3)$[\frac{21}{2},15]$.
009305 009305
(1)$x^{15}$,$-15x^{14}$,$105x^{13}$,$-455x^{12}$\\ (1)$x^{15}$,$-15x^{14}$,$105x^{13}$,$-455x^{12}$\\
@ -214,7 +214,7 @@ $120$
证明略 证明略
009317 009317
(1)第$18$,$19$项；\\ (1)第$18$,$19$项; \\
(2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$ (2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$
009319 009319
@ -376,13 +376,13 @@ A
\textcircled{2} \textcircled{2}
021146 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$24000$ 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 021147
观测，观测，实验 观测, 观测, 实验
021148 021148
不可靠，样本容量太小，样本不一定具有代表性 不可靠, 样本容量太小, 样本不一定具有代表性
021149 021149
$2$ $2$
@ -397,7 +397,7 @@ $a=b=10.5$
平均值是$17$,方差是$27$ 平均值是$17$,方差是$27$
021153 021153
平均数是$72.0$，中位数是$70$，方差是$74.9$ 平均数是$72.0$, 中位数是$70$, 方差是$74.9$
021154 021154
$\dfrac{n}{N}$ $\dfrac{n}{N}$
@ -421,13 +421,13 @@ $4467$
$49,04,40,36,16,08,06,55,33,69$ $49,04,40,36,16,08,06,55,33,69$
021161 021161
样本容量为$92$，抽样人数为$31$ 样本容量为$92$, 抽样人数为$31$
021162 021162
略 略
021163 021163
分层抽样，高一抽$18$人，高二抽$22$人，高三抽$10$人 分层抽样, 高一抽$18$人, 高二抽$22$人, 高三抽$10$人
021164 021164
C C
@ -442,7 +442,7 @@ $0.32$,$96$
$300$ $300$
021168 021168
集中，分散，$6.88$,$12.43$ 集中, 分散, $6.88$,$12.43$
021169 021169
\begin{tabular}{c|ccccccc} \begin{tabular}{c|ccccccc}
@ -477,7 +477,7 @@ C
A A
021175 021175
甲更准，乙更稳定 甲更准, 乙更稳定
021176 021176
(1)$3.47$,(2)$2773$ (1)$3.47$,(2)$2773$
@ -489,7 +489,7 @@ $100$
(1)$9.5$;(2)不能 (1)$9.5$;(2)不能
021182 021182
平均成绩是$89.6$，总体方差是$12.09$ 平均成绩是$89.6$, 总体方差是$12.09$
023356 023356
$A\subset C\subset B \subset E \subset D \subset G$;$E \subset F \subset G$ $A\subset C\subset B \subset E \subset D \subset G$;$E \subset F \subset G$
@ -582,7 +582,7 @@ $D$.
$D$. $D$.
023121 023121
(1)略；(2)略. (1)略; (2)略.
023122 023122
略. 略.
@ -780,13 +780,13 @@ $A$
$D$ $D$
023178 023178
$(1)$略；$(2)\frac{\sqrt{14}}{14}$ $(1)$略; $(2)\frac{\sqrt{14}}{14}$
023179 023179
$(1)\frac{\pi}{6};(2)arccos\frac{\sqrt{3}}{3}$ $(1)\frac{\pi}{6};(2)arccos\frac{\sqrt{3}}{3}$
023180 023180
$(1)$略；$(2)arctan\frac{\sqrt{6}}{2}$;$(3)$略；$(4)\frac{\sqrt{2}}{6}$ $(1)$略; $(2)arctan\frac{\sqrt{6}}{2}$;$(3)$略; $(4)\frac{\sqrt{2}}{6}$
023181 023181
无 无
@ -813,22 +813,22 @@ $\frac{\pi}{6}$.
$\frac{15\sqrt{3}}{2}$ $\frac{15\sqrt{3}}{2}$
017677 017677
$DM\perp PC$（或$BM\perp PC$) $DM\perp PC$(或$BM\perp PC$)
023188 023188
\textcircled{1}\textcircled{2}\textcircled{4} \textcircled{1}\textcircled{2}\textcircled{4}
023189 023189
(1)略；(2)$arccos\frac{\sqrt{15}}{5}$ (1)略; (2)$arccos\frac{\sqrt{15}}{5}$
023190 023190
(1)略；(2)6. (1)略; (2)6.
023191 023191
$S=\begin{cases}\frac{1}{2cos\alpha},\quad\alpha\in(0,arctan\sqrt{2}]\\ \frac{\sqrt{2}-cot\alpha}{sin\alpha},\alpha\in(arctan\sqrt{2},\frac{\pi}{2}]\end{cases}$ $S=\begin{cases}\frac{1}{2cos\alpha},\quad\alpha\in(0,arctan\sqrt{2}]\\ \frac{\sqrt{2}-cot\alpha}{sin\alpha},\alpha\in(arctan\sqrt{2},\frac{\pi}{2}]\end{cases}$
023192 023192
(1)略；(2)$\frac{2\sqrt{6}}{3}$. (1)略; (2)$\frac{2\sqrt{6}}{3}$.
023193 023193
$8$. $8$.
@ -846,7 +846,7 @@ $arctan\sqrt{2}$.
$10.$ $10.$
023198 023198
$(1)$外心；$(2)$内心；$(3)$垂心. $(1)$外心; $(2)$内心; $(3)$垂心.
023199 023199
$\sqrt{3}$ $\sqrt{3}$
@ -867,7 +867,7 @@ $S=32,V=16$.
$\frac{2\sqrt{11}}{11}$. $\frac{2\sqrt{11}}{11}$.
023205 023205
$(1)$略；$(2)\frac{5}{3}$. $(1)$略; $(2)\frac{5}{3}$.
023206 023206
$(1)V=a^2;(2)$\textcircled{1}$\frac{\sqrt{51}}{9}$;\textcircled{2}$\frac{\sqrt{30}}{3}$. $(1)V=a^2;(2)$\textcircled{1}$\frac{\sqrt{51}}{9}$;\textcircled{2}$\frac{\sqrt{30}}{3}$.
@ -921,7 +921,7 @@ $\theta_{min}=\pi-arctan\frac{4}{3}$,此时$P$ 在线段 $A_1C_1$ 的中点.
略. 略.
023223 023223
$(1)$略；$(2)arctan\sqrt{2}$;$(3)$是，$\frac{\sqrt{6}}{24}$. $(1)$略; $(2)arctan\sqrt{2}$;$(3)$是, $\frac{\sqrt{6}}{24}$.
023224 023224
$P^{6}_{20-m}$. $P^{6}_{20-m}$.
@ -961,7 +961,7 @@ $a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2
$(-\frac{1}{11},-\frac{1}{19})$. $(-\frac{1}{11},-\frac{1}{19})$.
023236 023236
(1)略；(2)$S_{n}=\frac{2}{3}-(n+\frac{2}{3})(\frac{1}{4})^{n}$;(3)$(-\infty,-5]\cup[1,+\infty)$. (1)略; (2)$S_{n}=\frac{2}{3}-(n+\frac{2}{3})(\frac{1}{4})^{n}$;(3)$(-\infty,-5]\cup[1,+\infty)$.
023237 023237
$1716$. $1716$.
@ -1015,19 +1015,19 @@ $92$.
(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$k\ge1)$ (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 023253
(1)不是；(2)最大项为$a_3=a_4=20$. (1)不是; (2)最大项为$a_3=a_4=20$.
022570 022570
(1)$2$;(2)存在，$N=22$. (1)$2$;(2)存在, $N=22$.
022572 022572
$S_n=(n-1)\cdot3^n+1$. $S_n=(n-1)\cdot3^n+1$.
023254 023254
(1)第$16$项；(2)$b_n=3\cdot2^n+1$. (1)第$16$项; (2)$b_n=3\cdot2^n+1$.
023255 023255
(1)略；(2)$a_n=\begin{cases} (1)略; (2)$a_n=\begin{cases}
\frac{1}{2},n=1\\-\frac{1}{2n(n-1)},n\geq2 \frac{1}{2},n=1\\-\frac{1}{2n(n-1)},n\geq2
\end{cases}$ \end{cases}$
@ -1563,7 +1563,7 @@ $\dfrac{x^2}{20}-\dfrac{y^2}{16}=1$
$\dfrac{x^2}{33-12\sqrt{6}}-\dfrac{y^2}{12\sqrt{6}-8}=1$或$\dfrac{y^2}{16}-\dfrac{x^2}{9}=1$ $\dfrac{x^2}{33-12\sqrt{6}}-\dfrac{y^2}{12\sqrt{6}-8}=1$或$\dfrac{y^2}{16}-\dfrac{x^2}{9}=1$
021225 021225
不正确，正确结果为$17$ 不正确, 正确结果为$17$
021226 021226
$\dfrac{x^2}{115600}-\dfrac{y^2}{134400}=1$ $\dfrac{x^2}{115600}-\dfrac{y^2}{134400}=1$
@ -1647,7 +1647,7 @@ $x^2-4y^2=\pm \dfrac{36}{5}$
$(-\dfrac{\sqrt{15}}{3},-1)$ $(-\dfrac{\sqrt{15}}{3},-1)$
021260 021260
(1)椭圆:$k<4$,双曲线：$4<k<9$;(2)$\dfrac{x^2}{3}-\dfrac{y^2}{2}=1$ (1)椭圆:$k<4$,双曲线: $4<k<9$;(2)$\dfrac{x^2}{3}-\dfrac{y^2}{2}=1$
021261 021261
(1)$(\sqrt{6},-\sqrt{3})\cup(\sqrt{3},\sqrt{3})\cup(\sqrt{3},\sqrt{6})$;(2)$\pm 1$ (1)$(\sqrt{6},-\sqrt{3})\cup(\sqrt{3},\sqrt{3})\cup(\sqrt{3},\sqrt{6})$;(2)$\pm 1$
@ -1655,3 +1655,435 @@ $(-\dfrac{\sqrt{15}}{3},-1)$
021267 021267
(1)$e>\dfrac{\sqrt{6}}{2},e\neq \sqrt{2}$;(2)$\dfrac{17}{13}$ (1)$e>\dfrac{\sqrt{6}}{2},e\neq \sqrt{2}$;(2)$\dfrac{17}{13}$
ans
032128
$(0,1]$
032129
$\dfrac{\pi}{3}$
032130
$-\dfrac{5}{2}i$
032131
$-\dfrac{1}{2}$
032132
$y=-\dfrac{1}{4}$
032133
1
032134
$\dfrac{1}{3}$
032135
44
032136
$35+2\sqrt{82}$
032137
643
032138
1289
032139
24
032140
B
032141
A
032142
C
032143
C
032144
(1)略; (2)$\sqrt{2}$
032145
(1)95.8;(2)0.72
032146
(1)直角三角形; (2)$4+4\sqrt{2}$
032147
(1)$\sqrt{2}$;(2)略; (3)$(9x^2+5y^2)^2+162x^2-50y^2=0(y\neq 0)$
032148
(1)略; (2)$a\geq \dfrac{1}{8}$时, $f(x)$在$(0,+\infty )$单调增; $0<a<\dfrac{1}{8}$时, $f(x)$在$(0,\dfrac{1-\sqrt{1-8a}}{4a})$单调增,在$(\dfrac{1-\sqrt{1-8a}}{4a},\dfrac{1+\sqrt{1-8a}}{4a})$单调减, 在$(\dfrac{1+\sqrt{1-8a}}{4a},+\infty )$单调增; (3)$a\leq \dfrac{e}{2}$
032089
$(-\infty,2]$
032090
$2$
032091
$(0,4)$
032092
$10$
032093
$(-\infty,\dfrac{9}{4})$
032094
A
032095
(1)$\pi$;(2)最大值为$1$, 最小值$-2$
032096
(1)证明略; (2)$[1,+\infty)$;(3)存在, 例如: $r(x)=4\sqrt{x},r(x)=\dfrac{1}{4}\log_2(x+1)$等
031023
$2\sqrt{2}\pi$
032097
$(-1,\dfrac{5}{27})$
031157
B
030711
(1)$M=10+mx-x-10\sqrt{x},1\leq x\leq 16,x\in \mathbf{N}$;(2)$[\dfrac{7}{2},\dfrac{9}{4}]$
032098
(1)$\dfrac{x^2}{4}+\dfrac{y^2}{3}=1$;(2)6;(3)$3x+4y-2=0$
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

156
题库0.3/Problems.json
View File

@ -267051,7 +267051,7 @@
"H20250331-二项式定理(2)" "H20250331-二项式定理(2)"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)第$18$,$19$项；\\\\\n(2)$\\mathrm{C}_{35}^{27}3^{27}x^{27}$", "ans": "(1)第$18$,$19$项; \\\\\n(2)$\\mathrm{C}_{35}^{27}3^{27}x^{27}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -494164,7 +494164,7 @@
"W20250306-2025届高二上学期周末卷06" "W20250306-2025届高二上学期周末卷06"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "$DM\\perp PC$（或$BM\\perp PC$)", "ans": "$DM\\perp PC$(或$BM\\perp PC$)",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -588256,7 +588256,7 @@
"H20250338-总体与样本、数据的获取" "H20250338-总体与样本、数据的获取"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "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$24000$", "ans": "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$24000$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -588292,7 +588292,7 @@
"H20250338-总体与样本、数据的获取" "H20250338-总体与样本、数据的获取"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "观测，观测，实验", "ans": "观测, 观测, 实验",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -588328,7 +588328,7 @@
"H20250338-总体与样本、数据的获取" "H20250338-总体与样本、数据的获取"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "不可靠，样本容量太小，样本不一定具有代表性", "ans": "不可靠, 样本容量太小, 样本不一定具有代表性",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -588510,7 +588510,7 @@
"H20250338-总体与样本、数据的获取" "H20250338-总体与样本、数据的获取"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "平均数是$72.0$，中位数是$70$，方差是$74.9$", "ans": "平均数是$72.0$, 中位数是$70$, 方差是$74.9$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -588793,7 +588793,7 @@
"H20250339-抽样方法" "H20250339-抽样方法"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "样本容量为$92$，抽样人数为$31$", "ans": "样本容量为$92$, 抽样人数为$31$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -588869,7 +588869,7 @@
"H20250339-抽样方法" "H20250339-抽样方法"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "分层抽样，高一抽$18$人，高二抽$22$人，高三抽$10$人", "ans": "分层抽样, 高一抽$18$人, 高二抽$22$人, 高三抽$10$人",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -589043,7 +589043,7 @@
"H20250340-统计图表" "H20250340-统计图表"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "集中，分散，$6.88$,$12.43$", "ans": "集中, 分散, $6.88$,$12.43$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -589280,7 +589280,7 @@
"H20250341-统计估计" "H20250341-统计估计"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "甲更准，乙更稳定", "ans": "甲更准, 乙更稳定",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -589507,7 +589507,7 @@
"H20250341-统计估计" "H20250341-统计估计"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "平均成绩是$89.6$，总体方差是$12.09$", "ans": "平均成绩是$89.6$, 总体方差是$12.09$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -590763,7 +590763,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "不正确，正确结果为$17$", "ans": "不正确, 正确结果为$17$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -591824,7 +591824,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)椭圆:$k<4$,双曲线：$4<k<9$;(2)$\\dfrac{x^2}{3}-\\dfrac{y^2}{2}=1$", "ans": "(1)椭圆:$k<4$,双曲线: $4<k<9$;(2)$\\dfrac{x^2}{3}-\\dfrac{y^2}{2}=1$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -634004,7 +634004,7 @@
"W20250310-2025届高二上学期周末卷10" "W20250310-2025届高二上学期周末卷10"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)$2$;(2)存在，$N=22$.", "ans": "(1)$2$;(2)存在, $N=22$.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -642094,7 +642094,7 @@
"A20240502-2024届高三上124分守护卷02" "A20240502-2024届高三上124分守护卷02"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)7小时；(2)17小时", "ans": "(1)7小时; (2)17小时",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -642751,7 +642751,7 @@
"A20240503-2024届高三上124分守护卷03" "A20240503-2024届高三上124分守护卷03"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)$3.1$秒；（2）20米/秒，72千米/小时", "ans": "(1)$3.1$秒; (2)20米/秒, 72千米/小时",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -642787,7 +642787,7 @@
"A20240503-2024届高三上124分守护卷03" "A20240503-2024届高三上124分守护卷03"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "（1）$\\dfrac{8}{3}$;(2)略", "ans": "(1)$\\dfrac{8}{3}$;(2)略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -642823,7 +642823,7 @@
"A20240503-2024届高三上124分守护卷03" "A20240503-2024届高三上124分守护卷03"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "（1）$a_1=1;a_2=0$或$1$；$a_3=0$或$1$;(2)115,证明略", "ans": "(1)$a_1=1;a_2=0$或$1$; $a_3=0$或$1$;(2)115,证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -643317,7 +643317,7 @@
"A20240504-2024届高三上124分守护卷04" "A20240504-2024届高三上124分守护卷04"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "（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", "ans": "(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",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -643343,7 +643343,7 @@
"A20240504-2024届高三上124分守护卷04" "A20240504-2024届高三上124分守护卷04"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "（1）$2020$;(2)$(-\\infty,\\log_2\\dfrac{9}{10}]$", "ans": "(1)$2020$;(2)$(-\\infty,\\log_2\\dfrac{9}{10}]$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -643379,7 +643379,7 @@
"A20240504-2024届高三上124分守护卷04" "A20240504-2024届高三上124分守护卷04"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "（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", "ans": "(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",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -643403,7 +643403,7 @@
"A20240504-2024届高三上124分守护卷04" "A20240504-2024届高三上124分守护卷04"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "（1）例：$f(x)=\\sin\\dfrac{\\pi x}{4}$,证明略；（2）证明略", "ans": "(1)例: $f(x)=\\sin\\dfrac{\\pi x}{4}$,证明略; (2)证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -643659,7 +643659,7 @@
"A20240505-2024届高三上124分守护卷05" "A20240505-2024届高三上124分守护卷05"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)证明略；（2）$ED=\\dfrac{\\sqrt{6}}{3}a$", "ans": "(1)证明略; (2)$ED=\\dfrac{\\sqrt{6}}{3}a$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -643685,7 +643685,7 @@
"A20240505-2024届高三上124分守护卷05" "A20240505-2024届高三上124分守护卷05"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)15户；（2）$x=5$时，$f(x)$最大值为$2.12>2.1$,可以达到", "ans": "(1)15户; (2)$x=5$时, $f(x)$最大值为$2.12>2.1$,可以达到",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -643711,7 +643711,7 @@
"A20240505-2024届高三上124分守护卷05" "A20240505-2024届高三上124分守护卷05"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "（1）$1$; (2)$(0,\\arctan\\dfrac{1}{2})$", "ans": "(1)$1$; (2)$(0,\\arctan\\dfrac{1}{2})$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -643739,7 +643739,7 @@
"A20240505-2024届高三上124分守护卷05" "A20240505-2024届高三上124分守护卷05"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)$6$; (2)正确，证明略", "ans": "(1)$6$; (2)正确, 证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -650656,7 +650656,7 @@
"E20250302-2025届高二上学期测验卷02" "E20250302-2025届高二上学期测验卷02"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)略；(2)$\\arccos\\frac{31}{34}$;(3)$\\pi-\\arctan\\frac{\\sqrt{51}}{12}$.", "ans": "(1)略; (2)$\\arccos\\frac{31}{34}$;(3)$\\pi-\\arctan\\frac{\\sqrt{51}}{12}$.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -650679,7 +650679,7 @@
"E20250302-2025届高二上学期测验卷02" "E20250302-2025届高二上学期测验卷02"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)略；(2)$\\frac{1}{6}$;(3)$[\\frac{21}{2},15]$.", "ans": "(1)略; (2)$\\frac{1}{6}$;(3)$[\\frac{21}{2},15]$.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -651003,7 +651003,7 @@
"W20250301-2025届高二上学期周末卷01" "W20250301-2025届高二上学期周末卷01"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)略；(2)略.", "ans": "(1)略; (2)略.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -652333,7 +652333,7 @@
"W20250305-2025届高二上学期周末卷05" "W20250305-2025届高二上学期周末卷05"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "$(1)$略；$(2)\\frac{\\sqrt{14}}{14}$", "ans": "$(1)$略; $(2)\\frac{\\sqrt{14}}{14}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -652379,7 +652379,7 @@
"W20250305-2025届高二上学期周末卷05" "W20250305-2025届高二上学期周末卷05"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "$(1)$略；$(2)arctan\\frac{\\sqrt{6}}{2}$;$(3)$略；$(4)\\frac{\\sqrt{2}}{6}$", "ans": "$(1)$略; $(2)arctan\\frac{\\sqrt{6}}{2}$;$(3)$略; $(4)\\frac{\\sqrt{2}}{6}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -652588,7 +652588,7 @@
"W20250306-2025届高二上学期周末卷06" "W20250306-2025届高二上学期周末卷06"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)略；(2)$arccos\\frac{\\sqrt{15}}{5}$", "ans": "(1)略; (2)$arccos\\frac{\\sqrt{15}}{5}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -652611,7 +652611,7 @@
"W20250306-2025届高二上学期周末卷06" "W20250306-2025届高二上学期周末卷06"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)略；(2)6.", "ans": "(1)略; (2)6.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -652660,7 +652660,7 @@
"W20250306-2025届高二上学期周末卷06" "W20250306-2025届高二上学期周末卷06"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)略；(2)$\\frac{2\\sqrt{6}}{3}$.", "ans": "(1)略; (2)$\\frac{2\\sqrt{6}}{3}$.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -652798,7 +652798,7 @@
"W20250307-2025届高二上学期周末卷07" "W20250307-2025届高二上学期周末卷07"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "$(1)$外心；$(2)$内心；$(3)$垂心.", "ans": "$(1)$外心; $(2)$内心; $(3)$垂心.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -652961,7 +652961,7 @@
"W20250307-2025届高二上学期周末卷07" "W20250307-2025届高二上学期周末卷07"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "$(1)$略；$(2)\\frac{5}{3}$.", "ans": "$(1)$略; $(2)\\frac{5}{3}$.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -653379,7 +653379,7 @@
"W20250308-2025届高二上学期周末卷08" "W20250308-2025届高二上学期周末卷08"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "$(1)$略；$(2)arctan\\sqrt{2}$;$(3)$是，$\\frac{\\sqrt{6}}{24}$.", "ans": "$(1)$略; $(2)arctan\\sqrt{2}$;$(3)$是, $\\frac{\\sqrt{6}}{24}$.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -653688,7 +653688,7 @@
"W20250309-2025届高二上学期周末卷09" "W20250309-2025届高二上学期周末卷09"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)略；(2)$S_{n}=\\frac{2}{3}-(n+\\frac{2}{3})(\\frac{1}{4})^{n}$;(3)$(-\\infty,-5]\\cup[1,+\\infty)$.", "ans": "(1)略; (2)$S_{n}=\\frac{2}{3}-(n+\\frac{2}{3})(\\frac{1}{4})^{n}$;(3)$(-\\infty,-5]\\cup[1,+\\infty)$.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -654092,7 +654092,7 @@
"W20250310-2025届高二上学期周末卷10" "W20250310-2025届高二上学期周末卷10"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)不是；(2)最大项为$a_3=a_4=20$.", "ans": "(1)不是; (2)最大项为$a_3=a_4=20$.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -654117,7 +654117,7 @@
"W20250310-2025届高二上学期周末卷10" "W20250310-2025届高二上学期周末卷10"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)第$16$项；(2)$b_n=3\\cdot2^n+1$.", "ans": "(1)第$16$项; (2)$b_n=3\\cdot2^n+1$.",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -654140,7 +654140,7 @@
"W20250310-2025届高二上学期周末卷10" "W20250310-2025届高二上学期周末卷10"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "(1)略；(2)$a_n=\\begin{cases}\n\\frac{1}{2},n=1\\\\-\\frac{1}{2n(n-1)},n\\geq2\n\\end{cases}$", "ans": "(1)略; (2)$a_n=\\begin{cases}\n\\frac{1}{2},n=1\\\\-\\frac{1}{2n(n-1)},n\\geq2\n\\end{cases}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -714342,7 +714342,7 @@
"第二单元" "第二单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1)$M=10+mx-x-10\\sqrt{x},1\\leq x\\leq 16,x\\in \\mathbf{N}$;(2)$[\\dfrac{7}{2},\\dfrac{9}{4}]$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -721699,7 +721699,7 @@
"第六单元" "第六单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$2\\sqrt{2}\\pi$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -724861,7 +724861,7 @@
"第七单元" "第七单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "B",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -749536,7 +749536,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(-\\infty,2]$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -749566,7 +749566,7 @@
"第六单元" "第六单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -749596,7 +749596,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(0,4)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -749626,7 +749626,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$10$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -749656,7 +749656,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(-\\infty,\\dfrac{9}{4})$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -749686,7 +749686,7 @@
"第七单元" "第七单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "A",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -749724,7 +749724,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1)$\\pi$;(2)最大值为$1$, 最小值$-2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -749754,7 +749754,7 @@
"第二单元" "第二单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1)证明略; (2)$[1,+\\infty)$;(3)存在, 例如: $r(x)=4\\sqrt{x},r(x)=\\dfrac{1}{4}\\log_2(x+1)$等",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -749785,7 +749785,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(-1,\\dfrac{5}{27})$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -749807,7 +749807,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1)$\\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1$;(2)6;(3)$3x+4y-2=0$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -750665,7 +750665,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(0,1]$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -750700,7 +750700,7 @@
"第六单元" "第六单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{\\pi}{3}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -750737,7 +750737,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-\\dfrac{5}{2}i$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -750772,7 +750772,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-\\dfrac{1}{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -750807,7 +750807,7 @@
"第七单元" "第七单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$y=-\\dfrac{1}{4}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -750844,7 +750844,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "1",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -750879,7 +750879,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{1}{3}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -750914,7 +750914,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "44",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -750950,7 +750950,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$35+2\\sqrt{82}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -750985,7 +750985,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "643",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751020,7 +751020,7 @@
"第四单元" "第四单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "1289",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751056,7 +751056,7 @@
"第七单元" "第七单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "24",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751091,7 +751091,7 @@
"第五单元" "第五单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "B",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751128,7 +751128,7 @@
"第五单元" "第五单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "A",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751163,7 +751163,7 @@
"第七单元" "第七单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "C",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751198,7 +751198,7 @@
"第六单元" "第六单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "C",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751233,7 +751233,7 @@
"第六单元" "第六单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1)略; (2)$\\sqrt{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751269,7 +751269,7 @@
"第八单元" "第八单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1)95.8;(2)0.72",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751304,7 +751304,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1)直角三角形; (2)$4+4\\sqrt{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751341,7 +751341,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1)$\\sqrt{2}$;(2)略; (3)$(9x^2+5y^2)^2+162x^2-50y^2=0(y\\neq 0)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -751376,7 +751376,7 @@
"第二单元" "第二单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1)略; (2)$a\\geq \\dfrac{1}{8}$时, $f(x)$在$(0,+\\infty )$单调增; $0<a<\\dfrac{1}{8}$时, $f(x)$在$(0,\\dfrac{1-\\sqrt{1-8a}}{4a})$单调增,在$(\\dfrac{1-\\sqrt{1-8a}}{4a},\\dfrac{1+\\sqrt{1-8a}}{4a})$单调减, 在$(\\dfrac{1+\\sqrt{1-8a}}{4a},+\\infty )$单调增; (3)$a\\leq \\dfrac{e}{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -778930,7 +778930,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "\\\\（1）$l$的斜率不存在$x=10$，舍\\\\（2）$5x-12y-38=0$或$3x+4y-34=0$", "ans": "\\\\(1)$l$的斜率不存在$x=10$, 舍\\\\(2)$5x-12y-38=0$或$3x+4y-34=0$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -778963,7 +778963,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "\\\\(1)相交；\\\\(2)$\\sqrt{3}x-y+1-\\sqrt{3}=0$或$-\\sqrt{3}x-y+1+\\sqrt{3}=0$\\\\(3)$x(x-1)+(y-1)^2=0 (x\\neq1)$", "ans": "\\\\(1)相交; \\\\(2)$\\sqrt{3}x-y+1-\\sqrt{3}=0$或$-\\sqrt{3}x-y+1+\\sqrt{3}=0$\\\\(3)$x(x-1)+(y-1)^2=0 (x\\neq1)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [
@ -782516,7 +782516,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "$\\\\(1)k\\geq0$时，双曲线\\\\(2)$k=0$时，$y=0$\\\\(3)$k\\leq0$且$k\\neq-1$时，椭圆\\\\(4)$k=-1$时，圆", "ans": "$\\\\(1)k\\geq0$时, 双曲线\\\\(2)$k=0$时, $y=0$\\\\(3)$k\\leq0$且$k\\neq-1$时, 椭圆\\\\(4)$k=-1$时, 圆",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [ "usages": [