录入2023届奉贤二模试题, 单元标签及答案
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#修改起始id,出处,文件名
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#修改起始id,出处,文件名
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starting_id = 15164
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starting_id = 15227
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raworigin = ""
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raworigin = ""
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filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目11.tex"
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filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目11.tex"
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editor = "20230414\t王伟叶"
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editor = "20230414\t王伟叶"
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@ -1,320 +1,86 @@
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ans
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tags
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15122
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15227
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$\{0,1,2\}$
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第一单元
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15123
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$1$
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15124
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15228
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$\sqrt{5}$
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第五单元
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15125
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$\dfrac{x^2}{\frac{11}3}+\dfrac{y^2}{\frac{11}2}=1$($\dfrac{3x^2}{11}+\dfrac{2y^2}{11}=1$)
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15126
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15229
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$-\dfrac 23$
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第八单元
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15127
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$3$
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15128
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15230
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$(0,\dfrac 12]$
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第六单元
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15129
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$(\dfrac 14,\dfrac{\sqrt{3}}4)$
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15130
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15231
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$y=0.186x+11.571$
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第八单元
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15131
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$\dfrac{\sqrt{2}}2$
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15132
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15232
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$95.4$(或者$95.5$也可以)
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第一单元
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15133
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$1+2\lg 2$
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15134
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15233
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C
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第八单元
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15135
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B
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15136
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15234
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A
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第八单元
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15137
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D
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15138
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15235
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(1) 证明略; (2) $2^{n+2}-4-3n$
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第七单元
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15139
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(1) $\dfrac 23$; (2) 证明略
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15140
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15236
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(1) $2\sqrt{3}$; (2) $\sqrt{2}$
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第三单元
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15141
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(1) 分布为$\begin{pmatrix}0 & 1 & 2 \\ \dfrac 15 & \dfrac 35 & \dfrac 15\end{pmatrix}$, 期望为$1$; (2) $\chi^2\approx 0.595$, 脑瘤病患在左右侧的部位与习惯在哪一侧接听手机电话无关
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15142
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15237
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(1) $2x-y-2\ln 2=0$; (2) $-a-\dfrac 12$; (3) 有且仅有一个零点
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第五单元
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15143
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15238
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$(-1,1)$
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第二单元
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15144
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$\pi$
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15145
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15239
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$2$
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第七单元
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15146
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$9$
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15147
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15240
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$(-\infty,0)\cup [\dfrac 13,+\infty)$
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第三单元
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15148
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$-\dfrac 17$
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15149
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15241
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$36\pi$
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第九单元
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15150
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$14$
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15151
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15242
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$68$
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第四单元
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15152
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$3$
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15153
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15243
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$(-\dfrac 12,0)$
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第四单元
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15154
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$3\sqrt{5}$
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15155
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15244
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A
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第六单元
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15156
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D
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15157
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15245
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B
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第二单元
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15158
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D
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15159
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15246
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(1) 证明略; (2) $8\sqrt{3}$
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第三单元
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15160
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(1) $[1,+\infty)$; (2) $10216$
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15161
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15247
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(1) $\dfrac 13$; (2) $1.2$
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第七单元
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15162
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(1) $2$; (2) $(-1,\dfrac 74)$; (3) 是定值$\sqrt{6}$
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15163
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(1) $(1,+\infty)$; (2) $[-1,\dfrac 32]$; (3) 证明略
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15164
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$\{-1,1\}$
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15165
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$10$
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15166
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$\dfrac 12$
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15167
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$18\pi$
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15168
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$2$
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15169
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$0.2$
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15170
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$12$
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15171
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$\dfrac 14$
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15172
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$[-2,+\infty)$
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15173
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$\sqrt{2}$
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15174
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$[\dfrac 76,\dfrac{15}2]$
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15175
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$\dfrac{-3\pm \sqrt{6}}6$
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15176
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D
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15177
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C
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15178
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B
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15179
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C
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15180
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(1) $\dfrac 13$; (2) $8\sqrt{2}$
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15181
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(1) 证明略; (2) $\dfrac{4\sqrt{21}}{21}$
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15182
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(1) $0.01998$; (2) 分布为$\begin{pmatrix}0 & 1 & 2 & 3 \\ 0.00000 & 0.00030 & 0.02940 & 0.97030 \end{pmatrix}$, 期望为$2.97$
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15183
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(1) 离心率为$\dfrac{\sqrt{5}}2$, 渐近线方程为$y=\pm \dfrac 12 x$; (2) $1$; (3) 证明略
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15184
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(1) $-4$; (2) 存在切线$l_2$与$l_1$垂直, 理由略; (3) $(\dfrac{3-\sqrt{5}}{2},\dfrac 12]\cup [2,\dfrac{3+\sqrt{5}}{2})$
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15185
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$\{2,4\}$
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15186
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$(-\infty,1)$
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15187
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$0.2$
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15188
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$(1,+\infty)$
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15189
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$\dfrac{2\sqrt{2}}3\pi$
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15190
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$1$
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15191
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$0.8$
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15192
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$4$
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15193
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$3$
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15194
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$[-1,1]$
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15195
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$3$
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15196
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$\dfrac{\sqrt{21}}{14}$
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15197
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D
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15198
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A
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15199
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C
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15200
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B
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15201
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(1) 证明略; (2) 分布为$\begin{pmatrix} 0 & 1 & 2 \\ \dfrac 3{10} & \dfrac 35 & \dfrac{1}{10}\end{pmatrix}$, 期望为$\dfrac 45$
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15202
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(1) 证明略; (2) $60^\circ$
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15203
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(1) $\lambda \approx 29.21$, 估计到$2023$年底该地新能源汽车保有量约$40.3$万辆; (2) $\hat{\lambda}\approx 29.67$, $\hat{r}\approx 0.32$
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15204
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(1) $\dfrac{x^2}4+\dfrac{y^2}3=1$; (2) $1$; (3) 值恒为$-3$, 证明略
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15205
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(1) 振幅为$\sqrt{2}$, 周期为$2\pi$, 初相位为$\dfrac{\pi}{4}$; (2) $(\dfrac{\pi}{3},\dfrac{5\pi}3]$; (3) $(0,1)$
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15206
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$\{1\}$
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15207
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$5$
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15208
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$-1$
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15209
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$0.94$
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15210
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$-\dfrac{24}{7}$
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15211
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$28$
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15212
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$50$
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15213
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$\dfrac 13$
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15214
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$\dfrac 8{11}$
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15215
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$9$
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15216
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$\dfrac{\sqrt{2}}2$
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15217
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$\sqrt{15}a$
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15218
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B
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15219
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B
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15220
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C
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15221
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B
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15222
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(1) $\dfrac \pi 3$; (2) $\dfrac 32$
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15223
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||||||
(1) 证明略; (2) $\arctan\dfrac{2\sqrt{5}}5$
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15224
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(1) $43.3$亿元; (2) (i) 全款购车两年后资产总额为$0.0322a$万元, 分期付款购车两年后资产总额为$0.0233a$万元, 应选择全款购车; (ii) $a<21.2134$, 这一措施对购买A, B, C车型有效
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15225
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(1) $C_1:\dfrac{x^2}2+y^2=1$, $C_2:\dfrac{x^2}2-y^2=1$; (2) $y=\dfrac 12 x$或$y=-\dfrac 12 x$; (3) $2$
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15226
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(1) $g(x)=f(h(x))$; (2) 导函数为$2(2x)^{2x}(1+\ln (2x))$, 最小值为$(\dfrac 1{\mathrm{e}})^{\frac 1{\mathrm{e}}}$; (3) 证明略
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@ -11,7 +11,7 @@ problems_dict = {
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"第九单元":"014791,014797,014811,014812,014823,014844,015009,015026,015035,015051,015077,015094,015098,015106,015119,015130,015141,015145,015151,015177,015197,015203,015219"
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"第九单元":"014791,014797,014811,014812,014823,014844,015009,015026,015035,015051,015077,015094,015098,015106,015119,015130,015141,015145,015151,015177,015197,015203,015219"
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}
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}
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20230414 2023届高三二模(14区, 缺奉贤徐汇)
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20230414 2023届高三二模(15区, 缺徐汇)
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problems_dict = {
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problems_dict = {
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"2023届高三杨浦区二模试题":"14784:14804",
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"2023届高三杨浦区二模试题":"14784:14804",
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"2023届高三崇明区二模试题":"14805:14825",
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"2023届高三崇明区二模试题":"14805:14825",
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@ -26,7 +26,8 @@ problems_dict = {
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"2023届普陀区高三二模试题":"15143:15163",
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"2023届普陀区高三二模试题":"15143:15163",
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||||||
"2023届闵行区高三二模试题":"15164:15184",
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"2023届闵行区高三二模试题":"15164:15184",
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||||||
"2023届长宁区高三二模试题":"15185:15205",
|
"2023届长宁区高三二模试题":"15185:15205",
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||||||
"2023届松江区高三二模试题":"15206:15226"
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"2023届松江区高三二模试题":"15206:15226",
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||||||
|
"2023届奉贤区高三二模试题":"15227:15247",
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}
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}
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|
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20230414 2022学年第二学期高一高二材料收集
|
20230414 2022学年第二学期高一高二材料收集
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@ -374685,6 +374685,447 @@
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"remark": "",
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"remark": "",
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"space": "12ex"
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"space": "12ex"
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},
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},
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"015227": {
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"id": "015227",
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"content": "已知集合$A=\\{1,2\\}, B=\\{a, 3\\}$, 若$A \\cap B=\\{2\\}$, 则$a=$\\blank{50}.",
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"objs": [],
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"tags": [
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"第一单元"
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],
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"genre": "填空题",
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"ans": "$2$",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届奉贤区高三二模试题1",
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"edit": [
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"20230414\t王伟叶"
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],
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||||||
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"same": [],
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||||||
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"related": [],
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"remark": "",
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||||||
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"space": ""
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||||||
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},
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"015228": {
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||||||
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"id": "015228",
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||||||
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"content": "已知$x \\in \\mathbf{R}$, $y \\in \\mathbf{R}$, 且$x+\\mathrm{i}=y+y \\mathrm{i}, \\mathrm{i}$是虚数单位, 则$x+y=$\\blank{50}.",
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"objs": [],
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||||||
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"tags": [
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||||||
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"第五单元"
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||||||
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],
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||||||
|
"genre": "填空题",
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||||||
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"ans": "$2$",
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||||||
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"solution": "",
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||||||
|
"duration": -1,
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||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题2",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
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||||||
|
"015229": {
|
||||||
|
"id": "015229",
|
||||||
|
"content": "$(2 x+1)^5$的二项展开式中$x^2$项的系数为\\blank{50}(用数值回答).",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第八单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$40$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题3",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015230": {
|
||||||
|
"id": "015230",
|
||||||
|
"content": "已知圆柱的上、下底面的中心分别为$O_1$, $O_2$, 过直线$O_1O_2$的平面截该圆柱所得的截面是面积为$8$的正方形, 则该圆柱的侧面积为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$8\\pi$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题4",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015231": {
|
||||||
|
"id": "015231",
|
||||||
|
"content": "某校高中三年级$1600$名学生参加了区第一次高考模拟统一考试, 已知数学考试成绩量$X$服从正态分布$N(100, \\sigma^2)$(试卷满分为$150$分). 统计结果显示, 数学考试成绩在$80$分到$120$分之间的人数约为总人数的$\\dfrac{3}{4}$, 则此次统考中成绩不低于$120$分的学生人数约为\\blank{50}人.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第八单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$200$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题5",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015232": {
|
||||||
|
"id": "015232",
|
||||||
|
"content": "已知两个正数$a, b$的几何平均值为$1$, 则$a^2+b^2$的最小值为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第一单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$2$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题6",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015233": {
|
||||||
|
"id": "015233",
|
||||||
|
"content": "设某种动物活到$20$岁的概率为$0.8$, 活到$25$岁的概率为$0.4$. 现有一只$20$岁的该种动物, 它活到$25$岁的概率是\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第八单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$0.5$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题7",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015234": {
|
||||||
|
"id": "015234",
|
||||||
|
"content": "已知随机变量$X$的分布为$\\begin{pmatrix}1 & 2 & 3 \\\\ \\dfrac{1}{2} & \\dfrac{1}{3} & \\dfrac{1}{6}\\end{pmatrix}$, 且$Y=a X+3$, 若$E[Y]=-2$, 则实数$a=$\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第八单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$-3$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题8",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015235": {
|
||||||
|
"id": "015235",
|
||||||
|
"content": "设圆$x^2+y^2-2 x-4 y+4=0$与双曲线$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$的渐近线相切, 则该双曲线的渐近线方程为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第七单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$3x\\pm 4y=0$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题9",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015236": {
|
||||||
|
"id": "015236",
|
||||||
|
"content": "$\\triangle ABC$的内角$A, B, C$的对边分别为$a, b, c$, 若$\\triangle ABC$的面积为$\\dfrac{a^2+b^2-c^2}{4}$, 则$C=$\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第三单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$\\dfrac\\pi 4$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题10",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015237": {
|
||||||
|
"id": "015237",
|
||||||
|
"content": "在集合$\\{1,2,3,4\\}$中任取一个偶数$a$和一个奇数$b$构成一个以原点为起点的向量$\\overrightarrow {\\alpha}=(a, b)$, 从所有得到的以原点为起点的向量中任取两个向量为邻边作平行四边形, 面积不超过$4$的平行四边形的个数是\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第五单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$3$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题11",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015238": {
|
||||||
|
"id": "015238",
|
||||||
|
"content": "已知$y=f(x)$为$\\mathbf{R}$上的奇函数, 且当$x \\geq 0$时, $f(x)=\\dfrac{x^2}{2}+\\dfrac{25}{4} \\ln (x+1)+\\dfrac{12}{\\pi} \\cos \\dfrac{\\pi}{3} x+a$, 则$y=f(x)$的驻点为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第二单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$\\pm \\dfrac 32$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题12",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015239": {
|
||||||
|
"id": "015239",
|
||||||
|
"content": "``$a=2$''是``直线$y=-a x+2$与直线$y=\\dfrac{a}{4} x-1$垂直''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第七单元"
|
||||||
|
],
|
||||||
|
"genre": "选择题",
|
||||||
|
"ans": "A",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题13",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015240": {
|
||||||
|
"id": "015240",
|
||||||
|
"content": "下列函数中, 以$\\pi$为周期且在区间$(\\dfrac{\\pi}{2}, \\pi)$上是严格增函数的是\\bracket{20}.\n\\fourch{$f(x)=|\\cos 2 x|$}{$f(x)=|\\sin 2 x|$}{$f(x)=|\\cos x|$}{$f(x)=|\\sin x|$}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第三单元"
|
||||||
|
],
|
||||||
|
"genre": "选择题",
|
||||||
|
"ans": "C",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题14",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015241": {
|
||||||
|
"id": "015241",
|
||||||
|
"content": "某校一个课外学习小组为研究某作物种子的发芽率$y$和温度$x$(单位: ${ }^{\\circ} \\text{C}$)的关系, 在$20$个不同的温度条件下进行种子发芽实验, 由实验数据$(x_i, y_i)$($i=1,2, \\cdots, 20$)得到下面的散点图:\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.2, yscale = 0.5]\n\\foreach \\i/\\j in {24.584/4.712,34.971/5.412,28.833/5.164,17.519/4.140,26.540/4.970,33.338/5.315,23.496/4.898,10.435/1.571,10.260/1.424,30.130/5.160,22.395/4.805,23.658/4.630,22.717/4.700,27.019/5.071,16.696/3.939,19.019/4.382,31.128/5.205,19.833/4.356,12.683/3.085,20.028/4.331}\n{\\filldraw (\\i,\\j) circle (0.15 and 0.06);};\n\\foreach \\i in {0,10,20,30,40}\n{\\draw (\\i,0.2) -- (\\i,0) node [below] {$\\i$} coordinate (\\i);};\n\\foreach \\i in {20,40,60,80,100}\n{\\draw (40,{\\i/16}) -- (0,{\\i/16}) node [left] {$\\i\\%$};};\n\\draw (42,0) node [below right] {温度/${}^\\circ\\text{C}$} (40,0) -- (0,0) node [left] {$0$} -- (0,{100/16});\n\\draw (-6,3) node [rotate = 90] {发芽率};\n\\end{tikzpicture}\n\\end{center}\n由此散点图, 在$10^{\\circ} \\text{C}$至$40^{\\circ} \\text{C}$之间, 下面四个回归方程类型中最适合作为发芽率$y$和温度$x$的回归方程类型的是\\bracket{20}.\n\\fourch{$y=a+b x$}{$y=a+b x^2$}{$y=a+b \\mathrm{e}^x$}{$y=a+b \\ln x$}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第九单元"
|
||||||
|
],
|
||||||
|
"genre": "选择题",
|
||||||
|
"ans": "D",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题15",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015242": {
|
||||||
|
"id": "015242",
|
||||||
|
"content": "设$S_n$是一个无穷数列$\\{a_n\\}$的前$n$项和, 若一个数列满足对任意的正整数$n$, 不等式$\\dfrac{S_n}{n}<\\dfrac{S_{n+1}}{n+1}$恒成立, 则称数列$\\{a_n\\}$为和谐数列, 有下列$3$个命题:\\\\\n\\textcircled{1} 若对任意的正整数$n$均有$a_n<a_{n+1}$, 则$\\{a_n\\}$为和谐数列;\\\\\n\\textcircled{2} 若等差数列$\\{a_n\\}$是和谐数列, 则$S_n$一定存在最小值;\\\\\n\\textcircled{3} 若$\\{a_n\\}$的首项小于零, 则一定存在公比为负数的一个等比数列是和谐数列.\\\\\n以上$3$个命题中真命题的个数有\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{$3$}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第四单元"
|
||||||
|
],
|
||||||
|
"genre": "选择题",
|
||||||
|
"ans": "D",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题16",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"015243": {
|
||||||
|
"id": "015243",
|
||||||
|
"content": "已知等差数列$\\{a_n\\}$的公差不为零, $a_1=25$, 且$a_1, a_{11}, a_{13}$成等比数列.\\\\\n(1) 求$\\{a_n\\}$的通项公式;\\\\\n(2) 计算$\\displaystyle\\sum_{k=1}^{20} a_{3 k-2}$.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第四单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "(1) $a_n=27-2n$; (2) $-640$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题17",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
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||||||
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"remark": "",
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"space": "12ex"
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},
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"015244": {
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"id": "015244",
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"content": "如图, 在四棱锥$P-ABCD$中, $AB\\parallel CD$, 且$\\angle BAP=\\angle CDP=90^{\\circ}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,-1) node [below] {$D$} coordinate (D);\n\\draw (0,0,1) node [below] {$A$} coordinate (A);\n\\draw (2,0,1) node [below] {$B$} coordinate (B);\n\\draw (2,0,-1) node [right] {$C$} coordinate (C);\n\\draw (0,{sqrt(3)},0) node [above] {$P$} coordinate (P);\n\\draw (A)--(B)--(C)--(P)--cycle(P)--(B);\n\\draw [dashed] (A)--(D)--(C)(D)--(P);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: 平面$PAB \\perp$平面$PAD$;\\\\\n(2) 若$PA=PD=AB=DC, \\angle APD=90^{\\circ}$, 且四棱锥$P-ABCD$的体积为$\\dfrac{8}{3}$, 求$PB$与平面$ABCD$所成的线面角的大小.",
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"objs": [],
|
||||||
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"tags": [
|
||||||
|
"第六单元"
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||||||
|
],
|
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|
"genre": "解答题",
|
||||||
|
"ans": "(1) 证明略; (2) $30^\\circ$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题18",
|
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"edit": [
|
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|
"20230414\t王伟叶"
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|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"015245": {
|
||||||
|
"id": "015245",
|
||||||
|
"content": "设函数$y=f(x)$的定义域是$\\mathrm{R}$, 它的导数是$f'(x)$. 若存在常数$m$($m \\in \\mathbf{R}$), 使得$f(x+m)=-f'(x)$对一切$x$恒成立, 那么称函数$y=f(x)$具有性质$P(m)$.\\\\\n(1) 求证: 函数$y=\\mathrm{e}^x$(其中$\\mathrm{e}$为自然对数的底数)不具有性质$P(m)$;\\\\\n(2) 判别函数$y=\\sin x$是否具有性质$P(m)$. 若具有求出$m$的取值集合; 若不具有请说明理由.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第二单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "(1) 证明略; (2) 当且仅当$m=2k\\pi-\\dfrac\\pi 2$, $k\\in \\mathbf{Z}$时, $y=\\sin x$具有性质$P(m)$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题19",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"015246": {
|
||||||
|
"id": "015246",
|
||||||
|
"content": "某小区有块绿地, 绿地的平面图大致如下图所示, 并铺设了部分人行通道. 小区物业根据居民需求, 决定在绿地修建一个休息亭.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 1.8]\n\\draw (0,0) coordinate (O);\n\\draw (1,0) coordinate (A);\n\\draw (2,0) coordinate (B);\n\\draw (2,{sqrt(3)}) coordinate (C);\n\\draw (-1,{sqrt(3)}) coordinate (D);\n\\draw (-0.5,{sqrt(3)/2}) coordinate (E);\n\\fill [pattern = north east lines] (A) arc (0:120:1) -- (D)--(C)--(B)--cycle;\n\\draw [dashed] (A) arc (0:120:1) -- (O) -- cycle;\n\\draw (A)--++ (0,-0.1) --++ (1.1,0) --++ (0,{sqrt(3)+0.2}) --++ ({-3.1-0.1*sqrt(3)},0) --++ (-60:{1+0.1*sqrt(3)}) coordinate (E1) -- (E);\n\\draw [dashed] (A) ++ (0,-0.1) --++ ({-1-0.1/sqrt(3)},0) -- (E1);\n\\draw (A)--(B)--(C)--(D)--(E);\n\\end{tikzpicture}\n\\end{center}\n为了简单起见, 现作如下假设:\n假设\\textcircled{1} 绿地是由线段$AB, BC, CD, DE$和弧$\\overset\\frown{EA}$围成的, 其中$\\overset\\frown{EA}$是以$O$点为圆心, 圆心角为$\\dfrac{2 \\pi}{3}$的扇形的弧, 见图 1;\\\\\n假设\\textcircled{2} 线段$AB, BC, CD, DE$所在的路行人是可通行的, 圆弧$\\overset\\frown{EA}$暂时未修路;\\\\ \n假设\\textcircled{3} 路的宽度在这里暂时不考虑;\\\\\n假设\\textcircled{4} 路用线段或圆弧表示, 休息亭用点表示.\n图1至图3中的相关边、角满足以下条件: 直线$BA$与$DE$的交点是$O$, $AB\\parallel CD$, $\\angle ABC=\\dfrac{\\pi}{2}$. $DE=EO=OA=AB=200$米. 根据不同的设计方案解决相应问题, 结果精确到米.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (1,0) node [below] {$A$} coordinate (A);\n\\draw (2,0) node [below] {$B$} coordinate (B);\n\\draw (2,{sqrt(3)}) node [right] {$C$} coordinate (C);\n\\draw (-1,{sqrt(3)}) node [left] {$D$} coordinate (D);\n\\draw (-0.5,{sqrt(3)/2}) node [below left] {$E$} coordinate (E);\n\\draw [dashed] (A) arc (0:120:1) -- (O) -- cycle;\n\\draw (O) node [above right] {\\tiny$\\dfrac{2\\pi}3$};\n\\path (O) -- (A) node [midway, below] {\\tiny$200$};\n\\path (A) -- (B) node [midway, below] {\\tiny$200$};\n\\path (E) -- (D) node [midway, sloped, below] {\\tiny$200$};\n\\draw (A)--(B)--(C)--(D)--(E);\n\\draw (A) node [below = 0.4] {图1};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (1,0) node [below] {$A$} coordinate (A);\n\\draw (2,0) node [below] {$B$} coordinate (B);\n\\draw (2,{sqrt(3)}) node [right] {$C$} coordinate (C);\n\\draw (-1,{sqrt(3)}) node [left] {$D$} coordinate (D);\n\\draw (-0.5,{sqrt(3)/2}) node [below left] {$E$} coordinate (E);\n\\draw [dashed] (A) arc (0:120:1) -- (O) -- cycle;\n\\draw [very thick] (A) arc (0:120:1);\n\\draw [very thick] (60:1) node [below] {$Q$} coordinate (Q) -- (C);\n\\draw (O) node [above right] {\\tiny$\\dfrac{2\\pi}3$};\n\\path (O) -- (A) node [midway, below] {\\tiny$200$};\n\\path (A) -- (B) node [midway, below] {\\tiny$200$};\n\\path (E) -- (D) node [midway, sloped, below] {\\tiny$200$};\n\\draw (A)--(B)--(C)--(D)--(E);\n\\draw (A) node [below = 0.4] {图2};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (1,0) node [below] {$A$} coordinate (A);\n\\draw (2,0) node [below] {$B$} coordinate (B);\n\\draw (2,{sqrt(3)}) node [right] {$C$} coordinate (C);\n\\draw (-1,{sqrt(3)}) node [left] {$D$} coordinate (D);\n\\draw (-0.5,{sqrt(3)/2}) node [below left] {$E$} coordinate (E);\n\\draw [dashed] (A) arc (0:120:1) -- (O) -- cycle;\n\\draw [very thick] (75:1) node [below] {$P$} coordinate (P) arc (75:120:1);\n\\draw [very thick] (P) -- ($(B)!(P)!(C)$) node [right] {$M$} coordinate (M);\n\\draw [very thick] (P) -- ($(C)!(P)!(D)$) node [above] {$N$} coordinate (N);\n\\draw (O) node [above right] {\\tiny$\\dfrac{2\\pi}3$};\n\\path (O) -- (A) node [midway, below] {\\tiny$200$};\n\\path (A) -- (B) node [midway, below] {\\tiny$200$};\n\\path (E) -- (D) node [midway, sloped, below] {\\tiny$200$};\n\\draw (A)--(B)--(C)--(D)--(E);\n\\draw (A) node [below = 0.4] {图3};\n\\end{tikzpicture}\n\\end{center}\n(1) 假设休息亭建在弧$\\overset\\frown{EA}$的中点, 记为$Q$, 沿$\\overset\\frown{EA}$和线段$QC$修路, 如图2所示. 求$QC$的长;\\\\\n(2) 假设休息亭建在弧$\\overset\\frown{EA}$上的某个位置, 记为$P$, 作$PM \\perp BC$交$BC$于$M$, 作$PN \\perp CD$交$DC$于$N$. 沿$\\overset\\frown{EP}$、线段$PM$和线段$PN$修路, 如图3所示. 求修建的总路长$\\overset\\frown{EP}+PM+PN$的最小值;\\\\\n(3) 请你对(1)和(2)涉及到的两种设计方案做个简明扼要的评价.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第三单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "(1) 约$346$米($200\\sqrt{3}$米); (2) 约$651$米($\\angle AOP=\\dfrac\\pi 2$); (3) 方案1涉及到的设计方案总路径是$\\dfrac{400\\pi}{3}+200 \\sqrt{3} \\approx 765$米, 比起方案2显然不是最优(短)路径; 方案2涉及到的设计方案显然相对于方案1是相对不便捷(不利于$AB$段附近居民前往)等等. 说明: 可以从多个角度考虑, 但以下两个指标是主要的衡量指标: 一修的路相对短, 二修的路相对便于居民出行, 若学生自己有一个评价标准, 并根据自己的标准并给予自圆其说适当给予评分\n譬如说: 有的同学直接连接$OC$, 休息亭建立在$OC$与$\\overset\\frown{EA}$的交点处, 将$\\overset\\frown{EA}$与$QC$全部修好, 这样更短($\\dfrac{400}{3} \\pi+200 \\approx 619$米)也相对便捷等等",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题20",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"015247": {
|
||||||
|
"id": "015247",
|
||||||
|
"content": "已知椭圆$C: \\dfrac{x^2}{4}+\\dfrac{y^2}{b^2}=1$($b>0$), $A(0, b)$, $B(0,-b)$, 椭圆$C$内部的一点$T(t, \\dfrac{1}{2})$($t>0$). 过点$T$作直线$AT$交椭圆于$M$, 作直线$BT$交椭圆于$N$, $M$、$N$是不同的两点.\\\\\n(1) 若椭圆$C$的离心率是$\\dfrac{\\sqrt{3}}{2}$, 求$b$的值;\\\\\n(2) 设$\\triangle BTM$的面积是$S_1$, $\\triangle ATN$的面积是$S_2$, 若$\\dfrac{S_1}{S_2}=5$, 当$b=1$时, 求$t$的值;\\\\\n(3) 若点$U(x_u, y_u), V(x_v, y_v)$满足$x_u<x_v$且$y_u>y_v$, 则称点$U$在点$V$的左上方. 求证: 当$b>\\dfrac{1}{2}$时, 点$N$在点$M$的左上方.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第七单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "(1) $1$或$4$; (2) $1$; (3) 证明略",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届奉贤区高三二模试题21",
|
||||||
|
"edit": [
|
||||||
|
"20230414\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
"020001": {
|
"020001": {
|
||||||
"id": "020001",
|
"id": "020001",
|
||||||
"content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",
|
"content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",
|
||||||
|
|
|
||||||
Reference in New Issue