录入宝山2023届二模答案

工具/文本文件/metadata.txt

@@ -1,64 +1,64 @@
 ans
 
-14996
+15017
-$\{0,1\}$
+$[2,3)$
 
-14997
+15018
-$-\dfrac 12+\dfrac 32\mathrm{i}$
+$(0,1)$
 
-14998
+15019
-$40\pi$
+$y=x^3$
 
-14999
+15020
-$270$
+$-1$
 
-15000
+15021
-$0.1$
+$3\cdot 2^{n-1}-1$
 
-15001
+15022
-$2$
+$160$
 
-15002
+15023
-$\dfrac 12$
+$\dfrac 23$
 
-15003
+15024
-$\dfrac{4\sqrt{6}}{25}$
+$n(n-1)$
 
-15004
+15025
-$2\sqrt{2}-1$
+$\dfrac\pi 3$
 
-15005
+15026
-$[\dfrac{5\pi}6,\dfrac{11\pi}6)$
+$0.004$
 
-15006
+15027
-$\dfrac 14$
+$(1,2)$
 
-15007
+15028
-$(1,3]$
+$4$
 
-15008
+15029
 B
 
-15009
+15030
 A
 
-15010
+15031
-D
+B
 
-15011
+15032
-D
+C
 
-15012
+15033
-(1) $\dfrac{121}9$; (2) $S_n$的最大值为$3$, 当且仅当$n=2$或$3$时取得
+(1) 最小正周期为$\pi$, 函数在$[k\pi-\dfrac{\pi}{12},k\pi+\dfrac{5\pi}{12}]$($k\in \mathbf{Z}$)上为增函数, 在$[k\pi-\dfrac{5\pi}{12},k\pi+\dfrac{11\pi}{12}]$($k\in \mathbf{Z}$)上为减函数; (2) $[\dfrac{\sqrt{3}}2,1)$
 
-15013
+15034
-(1) 证明略; (2) $\dfrac{\sqrt{6}}6$
+(1) $\arccos \dfrac{\sqrt{2}}4$; (2) 证明略, 距离为$\dfrac{\sqrt{15}}5$
 
-15014
+15035
-(1) $\dfrac{41}{42}$; (2) $\dfrac{12}{5}>\dfrac{116}{75}$, 故应该先答人文历史题, 再答地理环境题
+(1) $\hat{y}=11.2x-42.4$; (2) 当产量为$20$件时, 月利润的期望最大, 最大期望为$1218.4$万元.
 
-15015
+15036
-(1) $\dfrac{\sqrt{6}}3$; (2) $\dfrac 43$或$\dfrac{4\sqrt{6}}9$; (3) 存在, $P$的坐标为$(1,1)$
+(1) 焦点为$(1,0)$, 准线为$x=-1$; (2) $20$; (3) 存在定点, 坐标为$(5,-2)$
 
-15016
+15037
-(1) $O(0,0)$是的, $A(2,0)$不是; (2) 证明略; (3) $\{(a,b)|b=-a\text{或}b=a^3-a, \ a\ne 0\}$   
+(1) $A$点在$y=1$上, $B$点不在$\Psi$的任何一条直线上; (2) $(x_0^3,+\infty)$; (3) $\Omega$的包络是曲线$y=x^3$($x>0$), $\Psi$的包络是抛物线$y=\dfrac{x^2}{4}+1$

题库0.3/Problems.json

@@ -370280,7 +370280,7 @@
             "第一单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[2,3)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370301,7 +370301,7 @@
             "第一单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,1)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370322,7 +370322,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$y=x^3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370343,7 +370343,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370364,7 +370364,7 @@
             "第四单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3\\cdot 2^{n-1}-1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370385,7 +370385,7 @@
             "第八单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$160$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370406,7 +370406,7 @@
             "第八单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac 23$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370427,7 +370427,7 @@
             "第四单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$n(n-1)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370448,7 +370448,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac\\pi 3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370469,7 +370469,7 @@
             "第九单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0.004$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370490,7 +370490,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(1,2)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370511,7 +370511,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370532,7 +370532,7 @@
             "第一单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370553,7 +370553,7 @@
             "第二单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370574,7 +370574,7 @@
             "第四单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370595,7 +370595,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370616,7 +370616,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 最小正周期为$\\pi$, 函数在$[k\\pi-\\dfrac{\\pi}{12},k\\pi+\\dfrac{5\\pi}{12}]$($k\\in \\mathbf{Z}$)上为增函数, 在$[k\\pi-\\dfrac{5\\pi}{12},k\\pi+\\dfrac{11\\pi}{12}]$($k\\in \\mathbf{Z}$)上为减函数; (2) $[\\dfrac{\\sqrt{3}}2,1)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370637,7 +370637,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\arccos \\dfrac{\\sqrt{2}}4$; (2) 证明略, 距离为$\\dfrac{\\sqrt{15}}5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370658,7 +370658,7 @@
             "第九单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\hat{y}=11.2x-42.4$; (2) 当产量为$20$件时, 月利润的期望最大, 最大期望为$1218.4$万元.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370679,7 +370679,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 焦点为$(1,0)$, 准线为$x=-1$; (2) $20$; (3) 存在定点, 坐标为$(5,-2)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -370700,7 +370700,7 @@
             "第二单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $A$点在$y=1$上, $B$点不在$\\Psi$的任何一条直线上; (2) $(x_0^3,+\\infty)$; (3) $\\Omega$的包络是曲线$y=x^3$($x>0$), $\\Psi$的包络是抛物线$y=\\dfrac{x^2}{4}+1$",
         "solution": "",
         "duration": -1,
         "usages": [],