收录杨浦二模

This commit is contained in:
WangWeiye 2023-04-06 13:51:08 +08:00
parent eda2fe00da
commit c6021dacd5
3 changed files with 404 additions and 5 deletions

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@ -1,9 +1,9 @@
#修改起始id,出处,文件名 #修改起始id,出处,文件名
starting_id = 40552 starting_id = 14784
raworigin = "" raworigin = ""
filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目9.tex" filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目9.tex"
editor = "20230405\t王伟叶" editor = "20230406\t王伟叶"
indexed = False indexed = True
import os,re,json import os,re,json

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@ -10,7 +10,7 @@ paper_type = 2 # 随后设置一下后续的讲义标题
"""---设置题块编号---""" """---设置题块编号---"""
problems = [ problems = [
"040485,040486,040487,040488,040489,040490,040491,040492,040493,040494,040495,040496","040497,040498,040499,040500","040501,040502,040503,040504,040505" "14784:14795","14796:14799","14800:14804"
] ]
"""---设置结束---""" """---设置结束---"""
@ -24,7 +24,7 @@ if paper_type == 1:
elif paper_type == 2: elif paper_type == 2:
enumi_mode = 1 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号) enumi_mode = 1 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)
template_file = "模板文件/测验周末卷模板.txt" #设置模板文件名 template_file = "模板文件/测验周末卷模板.txt" #设置模板文件名
exec_list = [("标题替换","高三下学期周末卷06")] #设置讲义标题 exec_list = [("标题替换","2023届杨浦区二模")] #设置讲义标题
destination_file = "临时文件/"+exec_list[0][1] # 设置输出文件名 destination_file = "临时文件/"+exec_list[0][1] # 设置输出文件名
elif paper_type == 3: elif paper_type == 3:
enumi_mode = 0 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号) enumi_mode = 0 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)

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@ -364740,6 +364740,405 @@
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"content": "集合$A=\\{x | x^2-2 x-3=0\\}$, $B=\\{x | 2 \\leq x \\leq 4,\\ x \\in\\mathbf{R}\\}$, 则$A \\cap B=$\\blank{50}.",
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"content": "设$\\mathrm{i}$为虚数单位, 则复数$\\dfrac{3+4 \\mathrm{i}}{3-4 \\mathrm{i}}$的虚部是\\blank{50}.",
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"content": "已知等差数列$\\{a_n\\}$中, $a_3=7$, $a_7=3$, 则通项公式为$a_n=$\\blank{50}.",
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"content": "设$(2 x+1)^5=a_5 x^5+a_4 x^4+a_3 x^3+\\cdots+a_1 x+a_0$, 则$a_3=$\\blank{50}.",
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"content": "函数$y=\\ln (2-3 x)$的导数是$y'=$\\blank{50}.",
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"content": "若圆锥的侧面积为$15 \\pi$, 高为 4 , 则圆锥的体积为\\blank{50}.",
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"content": "由函数的观点, 不等式$3^x+\\lg x \\leq 3$的解集是\\blank{50}.",
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"content": "某中学举办思维竞赛, 现随机抽取$50$名参学生的成绩制作成频率分布直方图 (如图), 估计: 学生的平均成绩为\\blank{50}分.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.08, yscale = 50]\n\\draw [->] (80,0) -- (155,0) node [below] {成绩/分};\n\\draw [->] (80,0) -- (80,0.055) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\foreach \\i/\\j in {90/0.03,100/0.04,110/0.015,120/0.01,130/0.005}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (10,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {90/0.03,100/0.04,110/0.015,120/0.01,130/0.005}\n{\\draw [dashed] (\\i,\\j) -- (80,\\j) node [left] {$\\k$};};\n\\draw (140,0) node [below] {$140$};\n\\end{tikzpicture}\n\\end{center}",
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"content": "$\\triangle ABC$内角$A, B, C$的对边是$a, b, c$, 若$a=3$, $b=\\sqrt{6}$, $\\angle A=\\dfrac{\\pi}{3}$, 则$\\angle B=$\\blank{50}.",
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"content": "$F_1, F_2$分别是双曲线$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$的左右焦点, 过$F_1$的直线$l$与双曲线的左右两支分别交于$A, B$两点. 若$\\triangle ABF_2$为等边三角形, 则双曲线的离心率为\\blank{50}.",
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"content": "若存在实数$\\varphi$, 使函数$f(x)=\\cos (\\omega x+\\varphi)-\\dfrac{1}{2}$($\\omega>0$)在$x \\in[\\pi, 3 \\pi]$上有且仅有$2$个零点, 则$\\omega$的取值范围为\\blank{50}.",
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"content": "已知非零平面向量$\\overrightarrow {a}, \\overrightarrow {b}, \\overrightarrow {c}$, 满足$|\\overrightarrow {a}|=5$, $2|\\overrightarrow {b}|=|\\overrightarrow {c}|$, 且$(\\overrightarrow {b}-\\overrightarrow {a}) \\cdot(\\overrightarrow {c}-\\overrightarrow {a})=0$, 则$|\\overrightarrow {b}|$的最小值是\\blank{50}.",
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"content": "已知$a, b \\in \\mathbf{R}$, 则``$a>b$''是``$a^3>b^3$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}",
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"content": "对成对数据$(x_1, y_1)$、$(x_2, y_2)$、$\\cdots \\cdots$、$(x_n, y_n)$用最小二乘法求回归方程是为了使\\bracket{20}.\n\\fourch{$\\displaystyle\\sum_{i=1}^n(y_i-\\overline {y})=0$}{$\\displaystyle\\sum_{i=1}^n(y_i-\\hat{y}_i)=0$}{$\\displaystyle\\sum_{i=1}^n(y_i-\\hat{y}_i)$最小}{$\\displaystyle\\sum_{i=1}^n(y_i-\\hat{y}_i)^2$最小}",
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"content": "下列函数中, 既是偶函数, 又在区间$(-\\infty, 0)$上严格递减的是\\bracket{20}.\n\\fourch{$y=2^{|x|}$}{$y=\\ln (-x)$}{$y=x^{-\\frac{2}{3}}$}{$y=-\\sqrt{x^2}$}",
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"content": "如图, 一个由四根细铁杆$PA$、$PB$、$PC$、$PD$组成的支架($PA$、$PB$、$PC$、$PD$按照逆时针排布), 若$\\angle APB=\\angle BPC=\\angle CPD=\\angle DPA=\\dfrac{\\pi}{3}$, 一个半径为$1$的球恰好放在支架上与四根细铁杆均有接触, 则球心$O$到点$P$的距离是\n\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 1.5]\n\\path [name path = circ, draw] (0,0) circle (1);\n\\filldraw (0,0) node [right] {$O$} circle (0.03);\n\\draw [dashed] (0,0) ellipse (1 and 0.25);\n\\draw [dashed] (0,{-sqrt(2)/2}) ellipse ({sqrt(2)/2} and {sqrt(2)/8});\n\\draw (0,{-sqrt(2)}) node [below] {$P$} coordinate (P);\n\\draw (P) --++ (-1.5,1.5) node [above] {$A$};\n\\draw (P) --++ (-0.6,2.5) node [above] {$B$};\n\\draw (P) --++ (1.5,1.5) node [above] {$C$};\n\\path [name path = PD] (P) --++ (0.6,2.5) node [above] {$D$} coordinate (D);\n\\path [name intersections = {of = PD and circ, by = {M,N}}];\n\\draw (M)--(D)(P)--(N);\n\\draw [dashed] (M)--(N);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$\\sqrt{3}$}{$\\sqrt{2}$}{2}{$\\dfrac{3}{2}$}",
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"content": "已知一个随机变量$X$的分布为: $\\begin{pmatrix}6 & 7 & 8 & 9 & 10 \\\\ 0.1 & a & 0.2 & 0.3 & b\\end{pmatrix}$.\\\\\n(1) 已知$E[X]=\\dfrac{43}{5}$, 求$a, b$的值;\\\\\n(2) 记事件$A: X$为偶数; 事件$B: X \\leq 8$. 已知$P(A)=\\dfrac{1}{2}$, 求$P(B)$, $P(A \\cap B)$, 并判断$A, B$是否相互独立?",
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"content": "四边形$ABCD$是边长为$1$的正方形, $AC$与$BD$交于$O$点, $PA \\perp$平面$ABCD$, 且二面角$P-BC-A$的大小为$45^{\\circ}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 2.5]\n\\draw (0,0,0) node [above right] {$A$} coordinate (A);\n\\draw (1,0,0) node [right] {$D$} coordinate (D);\n\\draw (0,0,1) node [left] {$B$} coordinate (B);\n\\draw (1,0,1) node [right] {$C$} coordinate (C);\n\\draw (0.5,0,0.5) node [below] {$O$} coordinate (O);\n\\draw (0,1,0) node [above] {$P$} coordinate (P);\n\\draw (P)--(B)--(C)--(D)--cycle(P)--(C);\n\\draw [dashed] (P)--(A)--(C)(B)--(D)(B)--(A)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 求点$A$到平面$PBD$的距离;\\\\\n(2) 求直线$AC$与平面$PCD$所成的角.",
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"014802": {
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"content": "如图, 某国家森林公园的一区域$OAB$为人工湖, 其中射线$OA, OB$为公园边界. 已知$OA \\perp OB$, 以点$O$为坐标原点, 以$OB$为$x$轴正方向, 建立平面直角坐标系(单位: 千米), 曲线$AB$的轨迹方程为: $y=-x^2+4$($0 \\leq x \\leq 2$). 计划修一条与湖边$AB$相切于点$P$的直路\n$l$(宽度不计), 直路$l$与公园边界交于点$C, D$两点, 把人工湖围成一片景区$\\triangle OCD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (0,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,5.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {0.5,1,1.5,2,2.5,3,3.5}{\\draw (\\i,0.1)--(\\i,0) node [below] {\\tiny$\\i$};};\n\\foreach \\i in {0.5,1,1.5,2,2.5,3,3.5,4,4.5,5}{\\draw (0.1,\\i)--(0,\\i) node [left] {\\tiny$\\i$};};\n\\draw [domain = 0:2, samples = 100] plot (\\x,{4-\\x*\\x});\n\\filldraw (0,4) circle (0.05) node [below right] {$A$};\n\\filldraw (2,0) circle (0.05) node [above right] {$B$};\n\\filldraw (0.8,3.36) circle (0.05) node [above right] {$P$};\n\\filldraw (0,4.64) circle (0.05) node [above right] {$C$} coordinate (C);\n\\filldraw (2.9,0) circle (0.05) node [above right] {$D$} coordinate (D);\n\\draw ($(C)!-0.1!(D)$) node [left] {$l$}-- ($(C)!1.1!(D)$);\n\\end{tikzpicture}\n\\end{center}\n(1) 若$P$点坐标为$(1,3)$, 计算直路$CD$的长度; (精确到$0.1$千米)\\\\\n(2) 若$P$为曲线$AB$(不含端点)上的任意一点, 求景区$\\triangle OCD$面积的最小值. (精确到$0.1$平方千米)",
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"content": "已知椭圆$C: \\dfrac{x^2}{4 a^2}+\\dfrac{y^2}{3 a^2}=1$($a>0$)的右焦点为$F$, 直线$l: x+y-4=0$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2.5,0) -- (2.5,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\path [name path = elli, draw] (0,0) ellipse (2 and {sqrt(3)});\n\\filldraw (1,0) circle (0.03) node [below] {$F$} coordinate (F);\n\\path [name path = l,draw] (-1.5,2.1) -- (2.1,-1.5);\n\\path [name intersections = {of = l and elli, by = {A,B}}];\n\\draw (A) node [above] {$A$};\n\\draw (B) node [below] {$B$};\n\\end{tikzpicture}\n\\end{center}\n(1) 若$F$到直线$l$的距离为$2 \\sqrt{2}$, 求$a$;\\\\\n(2) 若直线$l$与椭圆$C$交于$A, B$两点, 且$\\triangle ABO$的面积为$\\dfrac{48}{7}$, 求$a$;\\\\\n(3) 若椭圆$C$上存在点$P$, 过$P$作直线$l$的垂线$l_1$, 垂足为$H$, 满足直线$l_1$和直线$FH$的夹角为$\\dfrac{\\pi}{4}$, 求$a$的取值范围.",
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"014804": {
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"content": "已知数列$\\{a_n\\}$是由正实数组成的无穷数列, 满足$a_1=3$, $a_2=7$, $a_n=|a_{n+1}-a_{n+2}|$($n$为正整数).\\\\\n(1) 写出数列$\\{a_n\\}$前$4$项的所有可能取法;\\\\\n(2) 判断: 在满足条件的所有数列$\\{a_n\\}$中, 是否可能存在正整数$k$, 满足$a_k=1$, 并说明理由;\\\\\n(3) $c_n$为数列$\\{a_n\\}$的前$n$项中不同取值的个数, 求$c_{100}$的最小值.",
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"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.",