收录高三寒假作业43新题

工具v2/文本文件/新题收录列表.txt

@@ -127,3 +127,6 @@
 20240125-122636
 023943:023949
 
+20240125-122954
+004230,023950:023953,011258
+

题库0.3/Problems.json

@@ -119860,7 +119860,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023951"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -147447,7 +147449,9 @@
             "20220712\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023952"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -645656,6 +645660,90 @@
         "space": "4em",
         "unrelated": []
     },
+    "023950": {
+        "id": "023950",
+        "content": "若一个圆柱和一个圆锥的轴截面分别是边长为 $a$ 的正方形和正三角形, 则它们的表面积之比为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023951": {
+        "id": "023951",
+        "content": "若在长方体 $ABCD-A_1B_1C_1D_1$ 中, $A_1D$ 和 $CD_1$ 与底面所成的角分别为 $30^{\\circ}$ 和 $45^{\\circ}$, 则异面直线 $A_1D$ 和 $CD_1$ 所成角的余弦值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "003875"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023952": {
+        "id": "023952",
+        "content": "如图, $S$ 是圆锥的顶点, $O$ 是底面圆的圆心, $AB$、$CD$ 是底面圆的两条直径. 若 $AB \\perp CD$, $SO=4$, $OB=2, P$ 为 $SB$ 的中点, 则点 $S$ 到平面 $PCD$ 的距离为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw (-2,0) node [left] {$A$} coordinate (A);\n\\draw (2,0) node [right] {$B$} coordinate (B);\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (0,4) node [above] {$S$} coordinate (S);\n\\draw ($(S)!0.5!(B)$) node [above right] {$P$} coordinate (P);\n\\draw (120:2 and 0.5) node [above] {$C$} coordinate (C);\n\\draw (-60:2 and 0.5) node [below] {$D$} coordinate (D);\n\\draw (A)--(S)--(B)(A) arc (180:360:2 and 0.5);\n\\draw [dashed] (A) arc (180:0:2 and 0.5);\n\\draw [dashed] (A)--(B)(C)--(D)(C)--(P)--(D)(O)--(S);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "004761"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023953": {
+        "id": "023953",
+        "content": "若正四棱柱 $ABCD-A_1B_1C_1D_1$ 中, $BE=\\dfrac{1}{4}BB_1=2$, $4AB=3AA_1$,\n则该四棱柱被过点 $A_1, C, E$ 的平面截得的截面面积为\\bracket{20}.\n\\fourch{$24 \\sqrt{2}$}{$36$}{$12 \\sqrt{19}$}{$6 \\sqrt{95}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
     "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.",