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录入黄浦青浦虹口2023届二模答案

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WangWeiye 2023-04-14 15:17:06 +08:00
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commit 7f95a6cc64
2 changed files with 232 additions and 100 deletions
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208
工具/文本文件/metadata.txt
View File

@ -1,64 +1,196 @@
ans
15038
$0$
15059
$\{3,5\}$
15039
$(1,2)$
15060
$\pi$
15040
$y=\pm \dfrac 43 x$
15061
$81$
15041
$\dfrac\pi 4$
15062
$-5$
15042
$10$
15063
$(x-1)^2+y^2=4$
15043
$3-\mathrm{i}$
15064
$40$
15044
$-19$
15065
$-2$
15045
$\dfrac 12$
15066
$(300+100\sqrt{2})\pi$
15046
$8$
15067
$\dfrac{2\pi}{3}$
15047
$(0,\dfrac 56]$
15068
$\dfrac{11}{32}$
15048
$(2-\sqrt{2},3)$
15069
$4$
15049
$\sqrt{29}-2$
15070
$[-2,2]$
15050
15071
B
15072
A
15073
D
15051
15074
C
15052
15075
(1) $\dfrac{16}{65}$; (2) 周长为$32$, 面积为$24$
15076
(1) 证明略; (2) 距离为$\dfrac{\sqrt{2}}2$, 所成角为$\arcsin\dfrac{\sqrt{10}}{10}$
15077
(1) \begin{tabular}{|c|c|c|c|} \hline & 生产标兵 & 非生产标兵 & 总计\\\hline
$35$周岁及以上组 & $20$ & $60$ & $80$\\\hline
$35$周岁以下组 & $30$ & $50$ & $80$ \\\hline
总计& $50$ & $110$ & $160$ \\ \hline
\end{tabular}, $\chi^2\approx 2.91$, 因此没有$95\%$的把握认为是否为生产标兵与工人所在的年龄有关; (2) 估计该厂工人中$35$周岁以下占$40\%$, 该厂生产标兵中$35$周岁以下占$50\%$
15078
(1) $y=\pm 2\sqrt{2}x$; (2) 最大值为$\dfrac 14$, 此时$\angle AF_1B$的正切值为$-\dfrac{24}{7}$; (3) 证明略
15079
(1) $h_1(x)$是, $h_2(x)$不是; (2) $y=ax^2+(4-2a)x+a$($0<a<2$); (3) $2\sqrt{3}$
15080
平行或相交
15081
$5$
15082
$(\sqrt{3},0)$
15083
$\sqrt{3}x-y+\sqrt{3}+3=0$
15084
$[3,+\infty)$
15085
$16\pi$
15086
$(-\dfrac 12,\dfrac 23)\cup (3,+\infty)$
15087
$0$
15088
$100\sqrt{2}$
15089
$(-\dfrac 1{11},-\dfrac 1{19})$
15090
$\dfrac{\sqrt{10}}5$
15091
$[0,\dfrac\pi 3]\cup [\dfrac{2\pi}3,\pi]$
15092
C
15093
C
15094
B
15053
15095
D
15096
(1) 最小正周期为$\pi$, 对称轴的方程为$x=\dfrac\pi 6+\dfrac{k\pi}2$, $k\in \mathbf{Z}$; (2) $(0,\dfrac 32]$
15097
(1) 证明略; (2) $\dfrac{\sqrt{5}}3$
`1
15098
(1) $a=0.26$, $b=0.38$; (2) $\dfrac 23$; (3) $X$的分布为$\begin{pmatrix} 0 & 1 & 2 \\ \dfrac 5{14} & \dfrac{15}{28} & \dfrac 3{28} \end{pmatrix}$, 期望为$\dfrac 34$
15099
(1) $x_3^2+\dfrac 14$; (2) $(-1,1)$; (3) 证明略
15100
(1) 证明略; (2) $1$; (3) 证明略
15101
$\{0,2\}$
15102
$(2,+\infty)$
15103
$3-\mathrm{i}$
15104
$5$
15105
$\dfrac 17$
15106
$32.5$
15107
$4$
15108
$(-\infty,-5]\cup \{0\}\cup [5,+\infty)$
15109
$\dfrac 65$
15110
$48\pi$
15111
$\dfrac{x^2}3-y^2=1$
15112
$\dfrac 52$
15113
A
15114
D
15115
C
15116
B
15054
(1) $2$; (2) $2+\dfrac 23\sqrt{3}$
15117
(1) $\begin{cases}2, & n=1, \\ 2^{n-1}, & n\ge 2;\end{cases}$ (2) $m=11$
15055
(1) $\arctan \dfrac 12$; (2) 证明略, 距离为$\dfrac{2\sqrt{5}}5$
15118
(1) 证明略; (2) $\dfrac{\sqrt{3}}4$
15056
(1) 分布为$\begin{pmatrix}600 & 900 \\ \dfrac 35 & \dfrac 25\end{pmatrix}$; (2) 当$n$为$600$时, $Y$的期望达到最大值, 最大值为$3000$元
15057
(1) $\dfrac{x^2}{4}+y^2=1$; (2) $x^2+y^2=6-2\sqrt{5}$; (3) $\sqrt{5}-1$
15119
(1) $\chi^2\approx 35.4$, 有$99.9\%$的把握认为电解电容质量与铝箔质量有关; (2) 约为$0.846$
15058
(1) $\lambda=-1$; (2) $k=1$; (3) $(-\infty,-1)$
15120
(1)$\dfrac{x^2}2+y^2=1$; (2) $x\pm \dfrac{\sqrt{14}}7y-1=0$; (3) 证明略
15121
(1) 在$(-\pi,0]$和$[\pi,2\pi]$上均为严格增函数, 在$[0,\pi]$和$[2\pi,3\pi)$上均为严格减函数, 极小值为$-\dfrac{1}{\mathrm{e}^\pi}$, 极大值为$1$与$\dfrac{1}{\mathrm{e}^{2\pi}}$; (2) $(-\infty,2]$; (3) 证明略

124
题库0.3/Problems.json
View File

@ -371162,7 +371162,7 @@
"第一单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\{3,5\\}$",
"solution": "",
"duration": -1,
"usages": [],
@ -371183,7 +371183,7 @@
"第三单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\pi$",
"solution": "",
"duration": -1,
"usages": [],
@ -371204,7 +371204,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$81$",
"solution": "",
"duration": -1,
"usages": [],
@ -371225,7 +371225,7 @@
"第五单元"
],
"genre": "填空题",
"ans": "",
"ans": "$-5$",
"solution": "",
"duration": -1,
"usages": [],
@ -371246,7 +371246,7 @@
"第七单元"
],
"genre": "填空题",
"ans": "",
"ans": "$(x-1)^2+y^2=4$",
"solution": "",
"duration": -1,
"usages": [],
@ -371267,7 +371267,7 @@
"第四单元"
],
"genre": "填空题",
"ans": "",
"ans": "$40$",
"solution": "",
"duration": -1,
"usages": [],
@ -371288,7 +371288,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$-2$",
"solution": "",
"duration": -1,
"usages": [],
@ -371309,7 +371309,7 @@
"第六单元"
],
"genre": "解答题",
"ans": "",
"ans": "$(300+100\\sqrt{2})\\pi$",
"solution": "",
"duration": -1,
"usages": [],
@ -371330,7 +371330,7 @@
"第三单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{2\\pi}{3}$",
"solution": "",
"duration": -1,
"usages": [],
@ -371351,7 +371351,7 @@
"第八单元"
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"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{11}{32}$",
"solution": "",
"duration": -1,
"usages": [],
@ -371372,7 +371372,7 @@
"第五单元"
],
"genre": "填空题",
"ans": "",
"ans": "$4$",
"solution": "",
"duration": -1,
"usages": [],
@ -371393,7 +371393,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$[-2,2]$",
"solution": "",
"duration": -1,
"usages": [],
@ -371414,7 +371414,7 @@
"第七单元"
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"ans": "B",
"solution": "",
"duration": -1,
"usages": [],
@ -371435,7 +371435,7 @@
"第八单元"
],
"genre": "选择题",
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"ans": "A",
"solution": "",
"duration": -1,
"usages": [],
@ -371456,7 +371456,7 @@
"第六单元"
],
"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
@ -371477,7 +371477,7 @@
"第四单元"
],
"genre": "选择题",
"ans": "",
"ans": "C",
"solution": "",
"duration": -1,
"usages": [],
@ -371498,7 +371498,7 @@
"第三单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $\\dfrac{16}{65}$; (2) 周长为$32$, 面积为$24$",
"solution": "",
"duration": -1,
"usages": [],
@ -371519,7 +371519,7 @@
"第六单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) 距离为$\\dfrac{\\sqrt{2}}2$, 所成角为$\\arcsin\\dfrac{\\sqrt{10}}{10}$",
"solution": "",
"duration": -1,
"usages": [],
@ -371540,7 +371540,7 @@
"第九单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) \\begin{tabular}{|c|c|c|c|} \\hline & 生产标兵 & 非生产标兵 & 总计\\\\\\hline\n$35$周岁及以上组 & $20$ & $60$ & $80$\\\\\\hline\n$35$周岁以下组 & $30$ & $50$ & $80$ \\\\\\hline\n总计& $50$ & $110$ & $160$ \\\\ \\hline\n\\end{tabular}, $\\chi^2\\approx 2.91$, 因此没有$95\\%$的把握认为是否为生产标兵与工人所在的年龄有关; (2) 估计该厂工人中$35$周岁以下占$40\\%$, 该厂生产标兵中$35$周岁以下占$50\\%$",
"solution": "",
"duration": -1,
"usages": [],
@ -371561,7 +371561,7 @@
"第七单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $y=\\pm 2\\sqrt{2}x$; (2) 最大值为$\\dfrac 14$, 此时$\\angle AF_1B$的正切值为$-\\dfrac{24}{7}$; (3) 证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -371582,7 +371582,7 @@
"第二单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $h_1(x)$是, $h_2(x)$不是; (2) $y=ax^2+(4-2a)x+a$($0<a<2$); (3) $2\\sqrt{3}$",
"solution": "",
"duration": -1,
"usages": [],
@ -371603,7 +371603,7 @@
"第六单元"
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"genre": "填空题",
"ans": "",
"ans": "平行或相交",
"solution": "",
"duration": -1,
"usages": [],
@ -371624,7 +371624,7 @@
"第五单元"
],
"genre": "填空题",
"ans": "",
"ans": "$5$",
"solution": "",
"duration": -1,
"usages": [],
@ -371645,7 +371645,7 @@
"第五单元"
],
"genre": "填空题",
"ans": "",
"ans": "$(\\sqrt{3},0)$",
"solution": "",
"duration": -1,
"usages": [],
@ -371666,7 +371666,7 @@
"第七单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\sqrt{3}x-y+\\sqrt{3}+3=0$",
"solution": "",
"duration": -1,
"usages": [],
@ -371687,7 +371687,7 @@
"第一单元"
],
"genre": "填空题",
"ans": "",
"ans": "$[3,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
@ -371708,7 +371708,7 @@
"第六单元"
],
"genre": "填空题",
"ans": "",
"ans": "$16\\pi$",
"solution": "",
"duration": -1,
"usages": [],
@ -371729,7 +371729,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$(-\\dfrac 12,\\dfrac 23)\\cup (3,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
@ -371750,7 +371750,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$0$",
"solution": "",
"duration": -1,
"usages": [],
@ -371771,7 +371771,7 @@
"第六单元"
],
"genre": "填空题",
"ans": "",
"ans": "$100\\sqrt{2}$",
"solution": "",
"duration": -1,
"usages": [],
@ -371792,7 +371792,7 @@
"第四单元"
],
"genre": "填空题",
"ans": "",
"ans": "$(-\\dfrac 1{11},-\\dfrac 1{19})$",
"solution": "",
"duration": -1,
"usages": [],
@ -371813,7 +371813,7 @@
"第七单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{\\sqrt{10}}5$",
"solution": "",
"duration": -1,
"usages": [],
@ -371834,7 +371834,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$[0,\\dfrac\\pi 3]\\cup [\\dfrac{2\\pi}3,\\pi]$",
"solution": "",
"duration": -1,
"usages": [],
@ -371855,7 +371855,7 @@
"第五单元"
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"genre": "选择题",
"ans": "",
"ans": "C",
"solution": "",
"duration": -1,
"usages": [],
@ -371876,7 +371876,7 @@
"第八单元"
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"genre": "选择题",
"ans": "",
"ans": "C",
"solution": "",
"duration": -1,
"usages": [],
@ -371897,7 +371897,7 @@
"第九单元"
],
"genre": "选择题",
"ans": "",
"ans": "B",
"solution": "",
"duration": -1,
"usages": [],
@ -371918,7 +371918,7 @@
"第四单元"
],
"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
@ -371939,7 +371939,7 @@
"第三单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) 最小正周期为$\\pi$, 对称轴的方程为$x=\\dfrac\\pi 6+\\dfrac{k\\pi}2$, $k\\in \\mathbf{Z}$; (2) $(0,\\dfrac 32]$",
"solution": "",
"duration": -1,
"usages": [],
@ -371960,7 +371960,7 @@
"第六单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) $\\dfrac{\\sqrt{5}}3$\n`1\n15098\n(1) $a=0.26$, $b=0.38$; (2) $\\dfrac 23$; (3) $X$的分布为$\\begin{pmatrix} 0 & 1 & 2 \\\\ \\dfrac 5{14} & \\dfrac{15}{28} & \\dfrac 3{28} \\end{pmatrix}$, 期望为$\\dfrac 34$",
"solution": "",
"duration": -1,
"usages": [],
@ -372003,7 +372003,7 @@
"第七单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $x_3^2+\\dfrac 14$; (2) $(-1,1)$; (3) 证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -372024,7 +372024,7 @@
"第二单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) $1$; (3) 证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -372045,7 +372045,7 @@
"第一单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\{0,2\\}$",
"solution": "",
"duration": -1,
"usages": [],
@ -372066,7 +372066,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$(2,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
@ -372087,7 +372087,7 @@
"第五单元"
],
"genre": "填空题",
"ans": "",
"ans": "$3-\\mathrm{i}$",
"solution": "",
"duration": -1,
"usages": [],
@ -372108,7 +372108,7 @@
"第七单元"
],
"genre": "填空题",
"ans": "",
"ans": "$5$",
"solution": "",
"duration": -1,
"usages": [],
@ -372129,7 +372129,7 @@
"第三单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac 17$",
"solution": "",
"duration": -1,
"usages": [],
@ -372150,7 +372150,7 @@
"第九单元"
],
"genre": "填空题",
"ans": "",
"ans": "$32.5$",
"solution": "",
"duration": -1,
"usages": [],
@ -372171,7 +372171,7 @@
"第三单元"
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"genre": "填空题",
"ans": "",
"ans": "$4$",
"solution": "",
"duration": -1,
"usages": [],
@ -372192,7 +372192,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$(-\\infty,-5]\\cup \\{0\\}\\cup [5,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
@ -372213,7 +372213,7 @@
"第八单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac 65$",
"solution": "",
"duration": -1,
"usages": [],
@ -372234,7 +372234,7 @@
"第六单元"
],
"genre": "填空题",
"ans": "",
"ans": "$48\\pi$",
"solution": "",
"duration": -1,
"usages": [],
@ -372255,7 +372255,7 @@
"第七单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{x^2}3-y^2=1$",
"solution": "",
"duration": -1,
"usages": [],
@ -372276,7 +372276,7 @@
"第五单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac 52$",
"solution": "",
"duration": -1,
"usages": [],
@ -372297,7 +372297,7 @@
"第五单元"
],
"genre": "选择题",
"ans": "",
"ans": "A",
"solution": "",
"duration": -1,
"usages": [],
@ -372318,7 +372318,7 @@
"第八单元"
],
"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
@ -372339,7 +372339,7 @@
"第二单元"
],
"genre": "选择题",
"ans": "",
"ans": "C",
"solution": "",
"duration": -1,
"usages": [],
@ -372360,7 +372360,7 @@
"第四单元"
],
"genre": "选择题",
"ans": "",
"ans": "B",
"solution": "",
"duration": -1,
"usages": [],
@ -372381,7 +372381,7 @@
"第四单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $\\begin{cases}2, & n=1, \\\\ 2^{n-1}, & n\\ge 2;\\end{cases}$ (2) $m=11$",
"solution": "",
"duration": -1,
"usages": [],
@ -372402,7 +372402,7 @@
"第六单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) $\\dfrac{\\sqrt{3}}4$",
"solution": "",
"duration": -1,
"usages": [],
@ -372423,7 +372423,7 @@
"第九单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $\\chi^2\\approx 35.4$, 有$99.9\\%$的把握认为电解电容质量与铝箔质量有关; (2) 约为$0.846$",
"solution": "",
"duration": -1,
"usages": [],
@ -372444,7 +372444,7 @@
"第七单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1)$\\dfrac{x^2}2+y^2=1$; (2) $x\\pm \\dfrac{\\sqrt{14}}7y-1=0$; (3) 证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -372465,7 +372465,7 @@
"第二单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) 在$(-\\pi,0]$和$[\\pi,2\\pi]$上均为严格增函数, 在$[0,\\pi]$和$[2\\pi,3\\pi)$上均为严格减函数, 极小值为$-\\dfrac{1}{\\mathrm{e}^\\pi}$, 极大值为$1$与$\\dfrac{1}{\\mathrm{e}^{2\\pi}}$; (2) $(-\\infty,2]$; (3) 证明略",
"solution": "",
"duration": -1,
"usages": [],