收录2023届宝山高三二模
This commit is contained in:
parent
2fd5a651db
commit
85e17e0d18
|
|
@ -1,5 +1,5 @@
|
|||
#修改起始id,出处,文件名
|
||||
starting_id = 14996
|
||||
starting_id = 15017
|
||||
raworigin = ""
|
||||
filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目11.tex"
|
||||
editor = "202304012\t王伟叶"
|
||||
|
|
|
|||
|
|
@ -369205,6 +369205,405 @@
|
|||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015017": {
|
||||
"id": "015017",
|
||||
"content": "已知集合$A=(1,3)$, $B=[2,+\\infty)$, 则$A \\cap B=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题1",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015018": {
|
||||
"id": "015018",
|
||||
"content": "不等式$\\dfrac{x}{x-1}<0$的解集为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题2",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015019": {
|
||||
"id": "015019",
|
||||
"content": "若幂函数$y=x^a$的图像经过点$(\\sqrt[3]{3}, 3)$, 则此幂函数的表达式为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题3",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015020": {
|
||||
"id": "015020",
|
||||
"content": "已知复数$(m^2-3 m-1)+(m^2-5 m-6) \\mathrm{i}=3$(其中$\\mathrm{i}$为虚数单位), 则实数$m=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题4",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015021": {
|
||||
"id": "015021",
|
||||
"content": "已知数列$\\{a_n\\}$的递推公式为$\\begin{cases}a_n=2 a_{n-1}+1(n \\geq 2) \\\\ a_1=2\\end{cases}$, 则该数列的通项公式$a_n=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题5",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015022": {
|
||||
"id": "015022",
|
||||
"content": "在$(x+\\dfrac{2}{x})^6$的展开式中, 常数项为\\blank{50}.(结果用数字作答)",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题6",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015023": {
|
||||
"id": "015023",
|
||||
"content": "从装有$3$个红球和$4$个蓝球的袋中, 每次不放回地随机摸出一球. 记``第一次摸球时摸到红球''为$A$, ``第二次摸球时摸到蓝球''为$B$, 则$P(B | A)=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题7",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015024": {
|
||||
"id": "015024",
|
||||
"content": "若数列$\\{a_n\\}$为等差数列, 且$a_2=2$, $S_5=20$, 则该数列的前$n$项和为$S_n=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题8",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015025": {
|
||||
"id": "015025",
|
||||
"content": "$\\triangle ABC$的内角$A$、$B$、$C$的对边分别为$a$、$b$、$c$, 若$a \\sin \\dfrac{A+C}{2}=b \\sin A$, 则$B=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题9",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015026": {
|
||||
"id": "015026",
|
||||
"content": "如图是某班一次数学测试成绩的茎叶图(图中仅列出$[50,60),[90,100)$的数据)和频率分布直方图, 则$x-y=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\foreach \\i/\\j in {0/5,1/4,2/5,3/6,4/8,5/9}\n{\\draw (\\i,0) node {$\\j$};};\n\\foreach \\i/\\j in {0/9,1/2,2/4}\n{\\draw (\\i,-4) node {$\\j$};};\n\\draw (0,-1) node {$6$};\n\\draw (0,-2) node {$7$};\n\\draw (0,-3) node {$8$};\n\\draw (0.5,1) -- (0.5,-5);\n\\end{tikzpicture}\n\\phantom{宝山二模2023}\n\\begin{tikzpicture}[>=latex, xscale = 0.05, yscale = 60]\n\\draw [->] (40,0) -- (42,0) -- (44,-0.003) -- (46,0.003) -- (48,0)-- (120,0) node [below] {分数};\n\\draw [->] (40,0) -- (40,0.05) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (40,0) node [below left] {$O$};\n\\foreach \\i/\\j in {50/0.02,60/0.024,70/0.036,80/0.012,90/0.008}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (10,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {50/0.02,60/0.024,70/0.036,80/0.012/x,90/0.008/y}\n{\\draw [dashed] (\\i,\\j) -- (40,\\j) node [left] {$\\k$};};\n\\draw (100,0) node [below] {$100$};\n\\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题10",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015027": {
|
||||
"id": "015027",
|
||||
"content": "已知函数$f(x)=\\dfrac{1}{a^x+1}-\\dfrac{1}{2}$($a>0$且$a \\neq 1)$, 若关于$x$的不等式$f(a x^2+b x+c)>0$的解集为$(1,2)$, 其中$b \\in(-6,1)$, 则实数$a$的取值范围是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题11",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015028": {
|
||||
"id": "015028",
|
||||
"content": "已知非零平面向量$\\overrightarrow {a}, \\overrightarrow {b}$不平行, 且满足$\\overrightarrow {a} \\cdot \\overrightarrow {b}=\\overrightarrow {a}^2=4$, 记$\\overrightarrow {c}=\\dfrac{3}{4} \\overrightarrow {a}+\\dfrac{1}{4} \\overrightarrow {b}$, 则当$\\overrightarrow {b}$与$\\overrightarrow {c}$的夹角最大时, $|\\overrightarrow {a}-\\overrightarrow {b}|$的值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题12",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015029": {
|
||||
"id": "015029",
|
||||
"content": "若$\\alpha: x^2=4$, $\\beta: x=2$, 则$\\alpha$是$\\beta$的\\bracket{20}条件.\n\\fourch{充分非必要}{必要非充分}{充要}{既非充分又非必要}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题13",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015030": {
|
||||
"id": "015030",
|
||||
"content": "已知定义在$\\mathbf{R}$上的偶函数$f(x)=|x-m+1|-2$, 若正实数$a$、$b$满足$f(a)+f(2 b)=m$, 则$\\dfrac{1}{a}+\\dfrac{2}{b}$的最小值为\\bracket{20}.\n\\fourch{$\\dfrac{9}{5}$}{$9$}{$\\dfrac{8}{5}$}{$8$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题14",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015031": {
|
||||
"id": "015031",
|
||||
"content": "将正整数$n$分解为两个正整数$k_1$、$k_2$的积, 即$n=k_1 \\cdot k_2$, 当$k_1$、$k_2$两数差的绝对值最小时, 我们称其为最优分解. 如$20=1 \\times 20=2 \\times 10=4 \\times 5$, 其中$4 \\times 5$即为$20$的最优分解, 当$k_1$、$k_2$是$n$的最优分解时, 定义$f(n)=|k_1-k_2|$, 则数列$\\{f(5^n)\\}$的前$2023$项的和为\\bracket{20}.\n\\fourch{$5^{1012}$}{$5^{1012}-1$}{$5^{2023}$}{$5^{2023}-1$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题15",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015032": {
|
||||
"id": "015032",
|
||||
"content": "在空间直角坐标系$O-x y z$中, 已知定点$A(2,1,0)$、$B(0,2,0)$和动点$C(0, t, t+2)$($t \\geq 0$). 若$\\triangle OAC$的面积为$S$, 以$O$、$A$、$B$、$C$为顶点的锥体的体积为$V$, 则$\\dfrac{V}{S}$的最大值为\\bracket{20}.\n\\fourch{$\\dfrac{2}{15} \\sqrt{5}$}{$\\dfrac{1}{5} \\sqrt{5}$}{$\\dfrac{4}{15} \\sqrt{5}$}{$\\dfrac{4}{5} \\sqrt{5}$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题16",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015033": {
|
||||
"id": "015033",
|
||||
"content": "已知函数$f(x)=\\sin x \\cos x-\\sqrt{3} \\cos ^2 x+\\dfrac{\\sqrt{3}}{2}$.\\\\\n(1) 求函数$y=f(x)$的最小正周期和单调区间;\\\\\n(2) 若关于$x$的方程$f(x)-m=0$在$x \\in[0, \\dfrac{\\pi}{2}]$上有两个不同的实数解, 求实数$m$的取值范围.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题17",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015034": {
|
||||
"id": "015034",
|
||||
"content": "四棱锥$P-ABCD$的底面是边长为$2$的菱形, $\\angle DAB=60^{\\circ}$, 对角线$AC$与$BD$相交于点$O$, $PO \\perp$底面$ABCD$, $PB$与底面$ABCD$所成的角为$60^{\\circ}$, $E$是$PB$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [below] {$O$} coordinate (O);\n\\draw ({sqrt(3)},0,0) node [right] {$C$} coordinate (C);\n\\draw ($(C)!2!(O)$) node [left] {$A$} coordinate (A);\n\\draw (0,0,1) node [below] {$B$} coordinate (B);\n\\draw ($(B)!2!(O)$) node [above] {$D$} coordinate (D);\n\\draw (0,{sqrt(3)},0) node [above] {$P$} coordinate (P);\n\\draw ($(P)!0.5!(B)$) node [left] {$E$} coordinate (E);\n\\draw (A)--(B)--(C)--(P)--cycle(P)--(B);\n\\draw [dashed] (A)--(C)(B)--(D)--(E)(P)--(O)(P)--(D)(A)--(D)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求异面直线$DE$与$PA$所成角的大小 (结果用反三角函数值表示);\\\\\n(2) 证明: $OE\\parallel$平面$PAD$, 并求点$E$到平面$PAD$的距离.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题18",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015035": {
|
||||
"id": "015035",
|
||||
"content": "下表是某工厂每月生产的一种核心产品的产量$x$($4 \\leq x \\leq 20$, $x \\in \\mathbf{Z}$)(件) 与相应的生产成本$y$(万元)的四组对照数据.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$x$& 4 & 6 & 8 & 10 \\\\\n\\hline$y$& 12 & 20 & 28 & 84 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 试建立$x$与$y$的线性回归方程;\\\\\n(2) 研究人员进一步统计历年的销售数据发现, 在供销平衡的条件下, 市场销售价格会波动变化. 经分析, 每件产品的销售价格$q$(万元) 是一个与产量$x$相关的随机变量, 分布为$\\begin{pmatrix} 100-x&90-x&80-x\\\\ \\dfrac{1}{4}&\\dfrac{1}{2}&\\dfrac{1}{4} \\end{pmatrix}$, 假设产品月利润$=$月销售量$\\times$销售价格$-$成本(其中月销售量$=$生产量). 根据(1)进行计算, 当产量$x$为何值时, 月利润的期望值最大? 最大值为多少?",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题19",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015036": {
|
||||
"id": "015036",
|
||||
"content": "已知拋物线$\\Gamma: y^2=4 x$.\\\\\n(1) 求抛物线$\\Gamma$的焦点$F$的坐标和准线$l$的方程;\\\\\n(2) 过焦点$F$且斜率为$\\dfrac{1}{2}$的直线与抛物线$\\Gamma$交于两个不同的点$A$、$B$, 求线段$AB$的长;\\\\\n(3) 已知点$P(1,2)$, 是否存在定点$Q$, 使得过点$Q$的直线与抛物线$\\Gamma$交于两个不同的点$M$、$N$(均不与点$P$重合), 且以线段$MN$为直径的圆恒过点$P$? 若存在, 求出点$Q$的坐标; 若不存在, 请说明理由.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题20",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015037": {
|
||||
"id": "015037",
|
||||
"content": "直线族是指具有某种共同性质的直线的全体. 如: 方程$y=k x+1$中, 当$k$取给定的实数时, 表示一条直线; 当$k$在实数范围内变化时, 表示过点$(0,1)$的直线族(不含$y$轴). 记直线族$2(a-2) x+4 y-4 a+a^2=0$(其中$a \\in \\mathbf{R}$)为$\\Psi$, 直线族$y=3 t^2 x-2 t^3$(其中$t>0)$为$\\Omega$.\\\\\n(1) 分别判断点$A(0,1), B(1,2)$是否在$\\Psi$的某条直线上, 并说明理由;\\\\\n(2) 对于给定的正实数$x_0$, 点$P(x_0, y_0)$不在$\\Omega$的任意一条直线上, 求$y_0$的取值范围(用$x_0$表示);\\\\\n(3) 直线族的包络被定义为这样一条曲线: 直线族中的每一条直线都是该曲线上某点处的切线, 且该曲线上每一点处的切线都是该直线族中的某条直线. 求$\\Omega$的包络和$\\Psi$的包络.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届宝山区高三二模试题21",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"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.",
|
||||
|
|
|
|||
Reference in New Issue