收录2023年新高考II卷试题
This commit is contained in:
parent
01039ab886
commit
11bd38e170
|
|
@ -1,8 +1,8 @@
|
|||
#修改起始id,出处,文件名
|
||||
starting_id = 18061
|
||||
starting_id = 18082
|
||||
raworigin = ""
|
||||
filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目12.tex"
|
||||
editor = "20230608\t王伟叶"
|
||||
filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目14.tex"
|
||||
editor = "20230610\t王伟叶"
|
||||
indexed = True
|
||||
IndexDescription = "试题"
|
||||
|
||||
|
|
|
|||
|
|
@ -463644,6 +463644,446 @@
|
|||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"018082": {
|
||||
"id": "018082",
|
||||
"content": "在复平面内, $(1+3 \\mathrm{i})(3-\\mathrm{i})$对应的点位于\\bracket{20}.\n\\fourch{第一象限}{第二象限}{第三象限}{第四象限}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题1",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018083": {
|
||||
"id": "018083",
|
||||
"content": "设集合$A=\\{0,-a\\}$, $B=\\{1, a-2,2 a-2\\}$, 若$A \\subseteq B$, 则$a=$\\bracket{20}.\n\\fourch{$2$}{$1$}{$\\dfrac{2}{3}$}{$-1$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题2",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018084": {
|
||||
"id": "018084",
|
||||
"content": "某学校为了解学生参加体育运动的情况, 用比例分配的分层随机抽样法作抽样调查, 拟从初中部和高中部两层共抽取$60$名学生, 已知该校初中部和高中部分别有$400$和$200$名学生, 则不同的抽样结果共有\\bracket{20}种.\n\\fourch{$C_{400}^{45} \\cdot C_{200}^{15}$}{$C_{400}^{20} \\cdot C_{200}^{40}$}{$C_{400}^{30} \\cdot C_{200}^{30}$}{$C_{400}^{40} \\cdot C_{200}^{20}$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题3",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018085": {
|
||||
"id": "018085",
|
||||
"content": "若$f(x)=(x+a) \\ln \\dfrac{2 x-1}{2 x+1}$为偶函数, 则$a=$\\bracket{20}.\n\\fourch{$-1$}{$0$}{$\\dfrac{1}{2}$}{1}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题4",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018086": {
|
||||
"id": "018086",
|
||||
"content": "已知椭圆$\\dfrac{x^2}{3}+y^2=1$的左、右焦点分别为$F_1, F_2$, 直线$y=x+m$与$C$交于$A$、$B$两点, 若$\\triangle F_1AB$的面积是$\\triangle F_2AB$的面积的$2$倍, 则$m=$\\bracket{20}.\n\\fourch{$\\dfrac{2}{3}$}{$\\dfrac{\\sqrt{2}}{3}$}{$-\\dfrac{\\sqrt{2}}{3}$}{$-\\dfrac{2}{3}$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题5",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018087": {
|
||||
"id": "018087",
|
||||
"content": "已知函数$f(x)=a \\mathrm{e}^x-\\ln x$在区间$(1,2)$上单调递增, 则$a$的最小值为\\bracket{20}.\n\\fourch{$\\mathrm{e}^2$}{$\\mathrm{e}$}{$\\mathrm{e}^{-1}$}{$\\mathrm{e}^{-2}$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题6",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018088": {
|
||||
"id": "018088",
|
||||
"content": "已知$\\alpha$为锐角, $\\cos \\alpha=\\dfrac{1+\\sqrt{5}}{4}$, 则$\\sin \\dfrac{\\alpha}{2}=$\\bracket{20}.\n\\fourch{$\\dfrac{3-\\sqrt{5}}{8}$}{$\\dfrac{-1+\\sqrt{5}}{8}$}{$\\dfrac{3-\\sqrt{5}}{4}$}{$\\dfrac{-1+\\sqrt{5}}{4}$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题7",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018089": {
|
||||
"id": "018089",
|
||||
"content": "记$S_n$等比数列$\\{a_n\\}$的前$n$项和, 若$S_4=-5$, $S_6=21S_2$, 则 $S_8=$\\bracket{20}.\n\\fourch{$120$}{$85$}{$-85$}{$-120$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题8",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018090": {
|
||||
"id": "018090",
|
||||
"content": "已知圆锥的顶点为$P$, 底面圆心为$O$, $AB$为底面的直径, $\\angle APB=120^{\\circ}$, $AP=2$, 点$C$在底面圆周上, 且二面角$P-AC-O=45^{\\circ}$, 则\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [above] {$P$} coordinate (P);\n\\draw (-30:2) node [right] {$B$} coordinate (B);\n\\draw (-150:2) node [left] {$A$} coordinate (A);\n\\draw (A) arc (180:360:{sqrt(3)} and {sqrt(3)/8});\n\\draw [dashed] (A) arc (180:0:{sqrt(3)} and {sqrt(3)/8});\n\\draw ($(A)!0.5!(B)$) node [right] {$O$} coordinate (O);\n\\draw [dashed] (P)--(O)--(A);\n\\draw (O) ++ (-110:{sqrt(3)} and {sqrt(3)/8}) node [below] {$C$} coordinate (C);\n\\draw [dashed] (A)--(C)--(O);\n\\draw (A)--(P)--(B)(C)--(P);\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} 该圆锥的体积为$\\pi$;\\\\\n\\textcircled{2} 该圆锥的侧面积为$4 \\sqrt{3} \\pi$;\\\\\n\\textcircled{3} $AC=2 \\sqrt{2}$;\\\\\n\\textcircled{4} $\\triangle PAC$的面积为$\\sqrt{3}$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题9",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018091": {
|
||||
"id": "018091",
|
||||
"content": "设$O$为坐标原点, 直线$y=-\\sqrt{3}(x-1)$过抛物线 $C: y^2=2 p x$($p>0$)的焦点, 且与$C$交于$M$、$N$两点, $l$为$C$的准线, 则\\blank{50}.\\\\\n\\textcircled{1} $p=2$; \\textcircled{2} $|MN|=\\dfrac{8}{3}$; \\textcircled{3} 以$MN$为直径的圆与$l$相切; \\textcircled{4} $\\triangle OMN$为等腰三角形.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题10",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018092": {
|
||||
"id": "018092",
|
||||
"content": "若函数$f x=a \\ln x+\\dfrac{b}{x}+\\dfrac{c}{x^2}$($a \\neq 0$)既有极大值又有极小值, 则\\blank{50}.\\\\\n\\textcircled{1} $b c>0$; \\textcircled{2} $a b>0$; \\textcircled{3} $b^2+8 a c>0$; \\textcircled{4} $a c<0$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题11",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018093": {
|
||||
"id": "018093",
|
||||
"content": "在信道内传输$0$, $1$信号, 信号的传输相互独立, 发送$0$时, 收到$1$的概率为$\\alpha$($0<\\alpha<1$), 收到$0$的概率为$1-\\alpha$; 发送$1$时, 收到$0$的概率为$\\beta$($0<\\beta<1$), 收到$1$的概率为$1-\\beta$. 考虑两种传输方案: 单次传输和三次传输. 单次传输是指每个信号只发送$1$次; 三次传输是指每个信号重复发送$3$次. 收到的信号需要译码, 译码规则如下: 单次传输时, 收到的信号即为译码: 三次传输时, 收到的信号中出现次数多的即为译码(例如, 若依次收到$1,0,1$, 则译码为$1$). 以下说法中正确的是\\blank{50}.\\\\\n\\textcircled{1} 采用单次传输方案, 若依次发送$1,0,1$, 则依次收到$1,0,1$的概率为$(1-\\alpha)(1-\\beta)^2$;\\\\\n\\textcircled{2} 采用三次传输方案, 若发送$1$, 则依次收到$1,0,1$的概率为$\\beta(1-\\beta)^2$;\\\\\n\\textcircled{3} 采用三次传输方案, 若发送$1$, 则译码为$1$的概率为$\\beta(1-\\beta)^2+(1-\\beta)^3$;\\\\\n\\textcircled{4} 当$0<\\alpha<0.5$时, 若发送$0$, 则采用三次传输方案译码为$0$的概率大于采用单次传输方案译码为$0$的概率.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题12",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018094": {
|
||||
"id": "018094",
|
||||
"content": "已知向量$\\overrightarrow{a}, \\overrightarrow{b}$满足$|\\overrightarrow{a}-\\overrightarrow{b}|=\\sqrt{3},|\\overrightarrow{a}+\\overrightarrow{b}|=|2 \\overrightarrow{a}-\\overrightarrow{b}|$, 则$|\\overrightarrow{b}|=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题13",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018095": {
|
||||
"id": "018095",
|
||||
"content": "底面边长为$4$的正四棱锥被平行于其底面的平面所截, 截去一个底面边长为 $2$, 高为$3$的正四棱锥, 所得棱台的体积为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题14",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018096": {
|
||||
"id": "018096",
|
||||
"content": "已知直线$x-m y+1=0$与$\\odot C: (x-1)^2+y^2=4$交于$A, B$两点, 写出满足``$\\triangle ABC$面积为$\\dfrac{8}{5}$''的$m$的一个值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题15",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018097": {
|
||||
"id": "018097",
|
||||
"content": "已知函数$f(x)=\\sin (\\omega x+\\varphi)$, 如图$A, B$是直线$y=\\dfrac{1}{2}$与曲线$y=f(x)$的两个交点, 若$|AB|=\\dfrac{\\pi}{6}$, 则$f(\\pi)=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -0.5:2.5, samples = 100] plot (\\x,{sin(4*\\x/pi*180-120)});\n\\filldraw ({2*pi/3},0) circle (0.03) node [below right] {$\\dfrac{2\\pi}{3}$};\n\\draw (-1,0.5) -- (3,0.5);\n\\filldraw ({5*pi/24},0.5) circle (0.03) node [above left] {$A$};\n\\filldraw ({3*pi/8},0.5) circle (0.03) node [above right] {$B$};\n\\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题16",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"018098": {
|
||||
"id": "018098",
|
||||
"content": "记$\\triangle ABC$的内角$A, B, C$的对边分别为$a, b, c$, 已知三角形$\\triangle ABC$的面积为$\\sqrt{3}$, 点$D$为$BC$的中点, 且$AD=1$.\\\\\n(1) 若$\\angle ADC=\\dfrac{\\pi}{3}$, 求$\\tan B$;\\\\\n(2) 若$b^2+c^2=8$, 求$b$和$c$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题17",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"018099": {
|
||||
"id": "018099",
|
||||
"content": "$\\{a_n\\}$为等差数列, $b_n=\\begin{cases}a_n-6, & n \\text{为奇数},\\\\ 2 a_n, & n \\text{为偶数}.\\end{cases}$ 记$S_n, T_n$为$\\{a_n\\},\\{b_n\\}$的前$n$项和, $S_4=32$, $T_3=16$.\\\\\n(1) 求$\\{a_n\\}$的通项公式;\\\\\n(2) 证明: 当$n>5$时, $T_n>S_n$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题18",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"018100": {
|
||||
"id": "018100",
|
||||
"content": "某研究小组经过研究发现某种疾病的患病者与未患病者的某项医学指标有明显差异, 经过大量调查, 得到如下的患病者和未患病者该指标的频率分布直方图:\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.13, yscale = 130]\n\\draw [->] (90,0) -- (91,0) -- (91.5,0.001) -- (92.5,-0.001) -- (93,0) -- (135,0) node [below] {指标};\n\\draw [->] (90,0) -- (90,0.045) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\foreach \\i/\\j in {95/0.002,100/0.012,105/0.034,110/0.036,115/0.04,120/0.04,125/0.036}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (5,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {95/0.002,100/0.012,105/0.034,115/0.04,125/0.036}\n{\\draw [dashed] (\\i,\\j) -- (90,\\j) node [left] {$\\k$};};\n\\draw (130,0) node [below] {$130$};\n\\draw (112.5,-0.004) node [below] {患病者};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex, xscale = 0.13, yscale = 130]\n\\draw [->] (65,0) -- (66,0) -- (66.5,0.001) -- (67.5,-0.001) -- (68,0) -- (110,0) node [below] {指标};\n\\draw [->] (65,0) -- (65,0.045) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\foreach \\i/\\j in {70/0.038,75/0.04,80/0.04,85/0.036,90/0.034,95/0.01,100/0.002}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (5,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {70/0.038,75/0.04,85/0.036,90/0.034,95/0.01,100/0.002}\n{\\draw [dashed] (\\i,\\j) -- (65,\\j) node [left] {$\\k$};};\n\\draw (105,0) node [below] {$130$};\n\\draw (87.5,-0.004) node [below] {未患病者};\n\\end{tikzpicture}\n\\end{center}\n利用该指标制定一个检测标准, 需要确定临界值$c$, 将该指标大于$c$的人判定为阳性, 小于或等于$c$的人判定为阴性, 此检测标准的漏诊率是将患病者判为阴性的概率, 记为$p(c)$; 误诊率是将未患病者判定为阳性的概率, 记为$q(c)$. 假设数据在组内平均分布, 以事件发生的频率作为相应事件发生的概率.\\\\\n(1) 当$p(c)=0.5 \\%$时, 求临界值$c$和误诊率$q(c)$;\\\\\n(2) 设函数$f(c)=p(c)+q(c)$, 当$c \\in[95,105]$时, 求$f(c)$的解析式, 并求$f(c)$在区间$[95,105]$的最小值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题19",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"018101": {
|
||||
"id": "018101",
|
||||
"content": "在三棱锥$A-BCD$中, $DA=DB=DC$, $BD \\perp CD$, $\\angle ADB=\\angle ADC=60^{\\circ}$, 已知$E$为$BC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$D$} coordinate (D);\n\\draw (0,0,-2) node [below] {$C$} coordinate (C);\n\\draw (2,0,0) node [right] {$B$} coordinate (B);\n\\draw ($(B)!0.5!(C)$) node [above] {$E$} coordinate (E);\n\\draw (E) ++ (0,{sqrt(2)},0) node [above] {$A$} coordinate (A);\n\\draw ($(A)+(E)-(D)$) node [right] {$F$} coordinate (F);\n\\draw (A)--(D)--(B)--(F)--cycle(A)--(B);\n\\draw [dashed] (D)--(C)--(B)(C)--(A)(E)--(F);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $BC \\perp DA$;\\\\\n(2) 点$F$满足$\\overrightarrow{EF}=\\overrightarrow{DA}$, 求二面角$D-AB-F$的正弦值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题20",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"018102": {
|
||||
"id": "018102",
|
||||
"content": "双曲线$C$中心为坐标原点, 左焦点$F_1(-2 \\sqrt{5}, 0)$, 离心率为$\\sqrt{5}$.\\\\\n(1) 求$C$的方程;\\\\\n(2) 记$C$的左、右顶点分别为$A_1, A_2$, 过点$B(-4,0)$的直线与$C$的左支交于$M, N$两点, $M$在第二象限, 直线$MA_1$与$NA_2$交于点$P$, 证明: $P$在定直线上.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题21",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"018103": {
|
||||
"id": "018103",
|
||||
"content": "(1) 证明: 当$0<x<1$时, $x-x^2<\\sin x<x$;\\\\\n(2) 已知函数$f(x)=\\cos a x-\\ln (1-x^2)$, 若$x=0$是$f(x)$的极大值点, 求$a$的取值范围.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届全国高考新高考II卷试题22",
|
||||
"edit": [
|
||||
"20230610\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"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