收录高二寒假作业1的9-16题
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20240203-220459 高二寒假作业1(1-8题)
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024418:024422,017769,024423:024424
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20240203-221900 高二寒假作业1(9-16题)
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019519,024425:024427,031901,023142,024428:024430,022083
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"20230101\t王伟叶"
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"space": "",
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},
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"024425": {
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"id": "024425",
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"content": "$P$ 是 $\\triangle ABC$ 所在平面外一点, 且 $PA \\perp$ 平面 $ABC$, 则以下结论正确的是\\bracket{20}.\n\\twoch{$\\angle BPC<\\angle BAC$}{$\\angle BPC>\\angle BAC$}{$\\angle BPC=\\angle BAC$}{$\\angle BPC$ 与 $\\angle BAC$ 的大小关系不确定}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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],
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"same": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024426": {
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"id": "024426",
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"content": "相交成 $90^{\\circ}$ 的两条直线和一个平面所成的角分别是 $30^{\\circ}$ 和 $45^{\\circ}$, 且这两条直线在该平面内的射影所成的锐角为 $\\theta$, 则有\\bracket{20}.\n\\fourch{$\\sin \\theta=\\dfrac{\\sqrt{6}}{3}$}{$\\cos \\theta=\\dfrac{\\sqrt{6}}{3}$}{$\\tan \\theta=\\dfrac{\\sqrt{2}}{2}$}{$\\cos \\theta=-\\dfrac{\\sqrt{3}}{3}$}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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],
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"remark": "",
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"024427": {
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"id": "024427",
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"content": "不共面的四个定点到平面 $\\alpha$ 的距离都相等, 这样的平面 $\\alpha$ 共有\\blank{50}个.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"024428": {
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"id": "024428",
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"content": "四面体 $ABCD$ 中, $AC=BD$, $E, F$ 分别为 $AD, BC$ 的中点, 且 $EF=\\dfrac{\\sqrt{2}}{2}AC$, $\\angle BDC=90$, 求证: $BD \\perp$ 平面 $ACD$.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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"same": [
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"024429": {
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"id": "024429",
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"content": "已知正四棱锥 $P-ABCD, M$、$N$ 分别是 $PA$、$BD$ 上的点, 且 $PM: MA=BN: ND$, 求证: 直线 $MN \\parallel $ 平面 $PBC$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-1,0,1) node [below] {$A$} coordinate (A);\n\\draw (1,0,1) node [below] {$B$} coordinate (B);\n\\draw (1,0,-1) node [right] {$C$} coordinate (C);\n\\draw (-1,0,-1) node [left] {$D$} coordinate (D);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\filldraw ($(P)!0.4!(A)$) circle (0.03) node [left] {$M$} coordinate (M);\n\\filldraw ($(B)!0.4!(D)$) circle (0.03) node [above] {$N$} coordinate (N);\n\\draw (P)--(A)--(B)--(C)--cycle(B)--(P);\n\\draw [dashed] (P)--(D)--(A)(D)--(C)(D)--(B)(M)--(N);\n\\end{tikzpicture}\n\\end{center}",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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"same": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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"024430": {
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"id": "024430",
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"content": "已知空间一个平面与一个正方体的 12 条棱的所成的角都等于 $\\alpha$, 则 $\\cos \\alpha=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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"same": [],
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},
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"030001": {
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"id": "030001",
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"content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
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