收录高二寒假作业5新题

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weiye.wang 2024-02-04 13:24:32 +08:00
parent 454f3b7a97
commit c967fcd4bf
2 changed files with 296 additions and 8 deletions

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20240204-131518 高二寒假作业4
024458:024475
20240204-132416 高二寒假作业5
024476:024478,017842,011651,024479:024483,009311,022102,009344,024484:024488

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@ -124100,7 +124100,9 @@
"20220703\t王伟叶"
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@ -216725,7 +216727,9 @@
"20220720\t王伟叶"
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@ -217335,7 +217339,9 @@
"20220720\t王伟叶"
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@ -217937,7 +217943,9 @@
"20220720\t王伟叶"
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@ -217992,7 +218000,8 @@
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"023733"
"023733",
"024484"
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@ -218073,7 +218082,8 @@
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@ -219349,7 +219359,9 @@
"20220720\t王伟叶"
],
"same": [],
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"related": [
"024485"
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@ -219374,7 +219386,9 @@
"20220720\t王伟叶"
],
"same": [],
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@ -662918,6 +662932,277 @@
"space": "4em",
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"024476": {
"id": "024476",
"content": "$(1+\\sqrt{2})^7$ 展开式中有理项的项数是\\bracket{20}.\n\\fourch{4}{5}{6}{7}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024477": {
"id": "024477",
"content": "已知 $(1+a x)(1+x)^5$ 的展开式中 $x^2$ 的系数为 5 , 则 $a=$\\bracket{20}.\n\\fourch{$-4$}{$-3$}{$-2$}{$-1$}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
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"remark": "",
"space": "",
"unrelated": []
},
"024478": {
"id": "024478",
"content": "$(1+x)^8(1+y)^4$ 的展开式中 $x^2 y^2$ 的系数是\\bracket{20}.\n\\fourch{$56$}{$84$}{$112$}{$168$}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024479": {
"id": "024479",
"content": "在 $(2 x-\\dfrac{1}{3}y)^7$ 展开式中, $x^5 y^2$ 的系数是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024480": {
"id": "024480",
"content": "$(\\sqrt[3]{5}+\\dfrac{1}{\\sqrt{5}})^{20}$ 的展开式中的有理项是展开式的第\\blank{50}项.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"007563"
],
"remark": "",
"space": "",
"unrelated": []
},
"024481": {
"id": "024481",
"content": "$(a+b)^n$ 的二项展开式中二项式系数的最大值是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
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},
"024482": {
"id": "024482",
"content": "$\\mathrm{C}_{11}^1+\\mathrm{C}_{11}^3+\\mathrm{C}_{11}^5+\\mathrm{C}_{11}^7+\\mathrm{C}_{11}^9+\\mathrm{C}_{11}^{11}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024483": {
"id": "024483",
"content": "$\\dfrac{\\mathrm{C}_{n+1}^1+\\mathrm{C}_{n+1}^2+\\cdots+\\mathrm{C}_{n+1}^n}{\\mathrm{C}_n^0+\\mathrm{C}_n^1+\\mathrm{C}_n^2+\\cdots+\\mathrm{C}_n^n}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024484": {
"id": "024484",
"content": "求 $(x^2-3 x+2)^8$ 展开式中 $x^3$ 项的系数.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"007590",
"007587"
],
"remark": "",
"space": "4em",
"unrelated": []
},
"024485": {
"id": "024485",
"content": "求 $55^{55}$ 被 8 除所得的余数.",
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"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"004028",
"007585",
"007640",
"007539",
"007639"
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"remark": "",
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},
"024486": {
"id": "024486",
"content": "求 $(\\sqrt[3]{2}+\\sqrt{3})^{12}$ 的展开式中的所有有理项的和.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
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"remark": "",
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"024487": {
"id": "024487",
"content": "数列 $\\{a_n\\}$ 的前 $n$ 项的和为 $S_n$, 且满足 $S_n=2 a_n-1$.\\\\\n(1) 求数列 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 求和: $\\mathrm{C}_n^0S_1+\\mathrm{C}_n^1S_2+\\mathrm{C}_n^2S_3+\\cdots+\\mathrm{C}_n^n S_{n+1}$.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
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"duration": -1,
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"024488": {
"id": "024488",
"content": "利用二项式定理证明:\\\\\n(1) $2^n>n^2+n+1$($n \\in N^*$, $n \\geq 5$);\\\\\n(2) $2<(1+\\dfrac{1}{n})^n<3$($n \\geq 2$, $n \\in N^*$).",
"objs": [],
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"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
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"030001": {
"id": "030001",
"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.",