收录W20250405新题

2024-03-22 12:33:12 +08:00 · 2024-03-22 12:33:12 +08:00 · f0fbe0c1d2
parent d17e854682
commit f0fbe0c1d2
2 changed files with 217 additions and 8 deletions
--- a/工具v2/文本文件/新题收录列表.txt
+++ b/工具v2/文本文件/新题收录列表.txt
@ -457,3 +457,6 @@
 20240321-183625 高三下学期测验卷02 E20240603(没有错因为有月考)
 032159:032179

+20240322-123120 高二下学期周末卷05
+002112,002409,041079:041080,041088,003441,002417,041089:041091,023320,041092,023327,023321,004479,041093:041096
+
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@ -78096,7 +78096,8 @@
        "same": [],
        "related": [
            "024124",
-            "041013"
+            "041013",
+            "041090"
        ],
        "remark": "",
        "space": "",
@ -108786,7 +108787,9 @@
            "20220701\t王伟叶"
        ],
        "same": [],
-        "related": [],
+        "related": [
+            "041090"
+        ],
        "remark": "",
        "space": "",
        "unrelated": []
@ -260192,7 +260195,9 @@
            "20220726\t王伟叶"
        ],
        "same": [],
-        "related": [],
+        "related": [
+            "041094"
+        ],
        "remark": "",
        "space": "4em",
        "unrelated": []
@ -375619,7 +375624,9 @@
            "20230118\t王伟叶"
        ],
        "same": [],
-        "related": [],
+        "related": [
+            "041090"
+        ],
        "remark": "",
        "space": "",
        "unrelated": []
@ -425045,7 +425052,9 @@
            "20230411\t王伟叶"
        ],
        "same": [],
-        "related": [],
+        "related": [
+            "041090"
+        ],
        "remark": "",
        "space": "",
        "unrelated": []
@ -672195,7 +672204,9 @@
            "20240125\t毛培菁"
        ],
        "same": [],
-        "related": [],
+        "related": [
+            "041089"
+        ],
        "remark": "",
        "space": "",
        "unrelated": []
@ -751476,7 +751487,9 @@
            "20230302\t王伟叶"
        ],
        "same": [],
-        "related": [],
+        "related": [
+            "041088"
+        ],
        "remark": "",
        "space": "",
        "unrelated": []
@ -774255,7 +774268,8 @@
        ],
        "same": [],
        "related": [
-            "002402"
+            "002402",
+            "041090"
        ],
        "remark": "",
        "space": "4em",
@ -776193,5 +776207,197 @@
        "remark": "",
        "space": "4em",
        "unrelated": []
+    },
+    "041088": {
+        "id": "041088",
+        "content": "过抛物线 $y^2=4 x$ 的焦点作一条直线与抛物线相交于 $A, B$ 两点, 它们的横坐标之和为 5 , 则这样的直线方程是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240322\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [
+            "040155"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "041089": {
+        "id": "041089",
+        "content": "过点 $P(1,0)$ 的直线 $l$ 与抛物线 $y^2=2 x$ 交于两点 $M, N, O$ 为原点, 若直线 $OM$ 与直线 $ON$ 的斜率之和为 1 , 则直线 $l$ 的方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240322\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [
+            "024139"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "041090": {
+        "id": "041090",
+        "content": "若点 $A$ 的坐标为 $(3,2), F$ 为抛物线 $y^2=2 x$ 的焦点, 点 $P$ 是抛物线上的动点. 当 $|PA|+|PF|$ 取到最小值时,点 $P$ 的坐标为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240322\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [
+            "002402",
+            "014892",
+            "003440",
+            "041013",
+            "013120"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "041091": {
+        "id": "041091",
+        "content": "已知直线 $l: 4 x-3 y+6=0$. 抛物线 $C: y^2=4 x$ 上的一个动点 $P$ 到直线 $l$ 与 $y$ 轴的距离之和的最小值为\\blank{50}, 取到最小值时, 点 $P$ 的坐标为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240322\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "041092": {
+        "id": "041092",
+        "content": "在一次为期 30 天的博览会上, 主办方统计了每天的参观人数 (单位: 千人), 得到样本的茎叶图 (如右图), 则该样本的第 70 百分位数是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{c|ccccccccc}\n2&1 &1&3&6&8\\\\\n3&0&2&2&4&7&8&8&9 \\\\\n4&1&1&1&3&3&6&7&7&9 \\\\\n5&0&0&1&2&2&2&3&5 \n\\end{tabular}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240322\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "041093": {
+        "id": "041093",
+        "content": "空气质量指数 AQI 是反映空气质量状况的指数, 其对应关系如下表:\\\\\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|}\n\\hline$AQI$ 指数值 & $0 \\sim 50$ & $51 \\sim 100$ & $101 \\sim 150$ & $151 \\sim 200$ & $201 \\sim 300$ & $>300$ \\\\\n\\hline 空气质量 & 优 & 良 & 轻度污染 & 中度污染 & 重度污染 & 严重污染 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n为监测某化工厂排放废气对周边空气质量指数的影响, 某科学兴趣小组在工厂附近某处测得 10 月 1 日至 20 日 AQI 的数据并绘成折线图如下:\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.5, yscale = 0.015]\n\\draw [->] (0,0) -- (21,0) node [below right] {日期};\n\\draw [->] (0,0) -- (0,350) node [left] {AQI};\n\\foreach \\i in {50,100,...,300}\n{\\draw (20,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\foreach \\i in {1,2,...,20}\n{\\draw (\\i,5) -- (\\i,0) node [below] {$\\i$};};\n\\draw (0,0) node [left] {$0$};\n\\filldraw (1,141) circle (0.06 and 2) coordinate (P); \n\\foreach \\i/\\j in {2/135,3/63,4/29,5/38,6/35,7/61,8/63,9/93,10/133,11/165,12/136,13/209,14/237,15/279,16/125,17/163,18/75,19/27,20/40}\n{\\draw (P) -- (\\i,\\j) coordinate (P);\n\\filldraw (P) circle (0.06 and 2);};\n\\end{tikzpicture}\n\\end{center}\n下列叙述正确的是\\bracket{20}.\n\\onech{这 20 天中 AQI 的中位数略大于 150}{10 月 4 日到 10 月 11 日, 空气质量越来越好}{这 20 天中的空气质量为优的天数占 $25 \\%$}{10 月上旬 AQI 的极差大于中旬 AQI 的极差}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240322\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "041094": {
+        "id": "041094",
+        "content": "如图, 直线 $y=\\dfrac{1}{2}x$ 与抛物线 $y=\\dfrac{1}{8}x^2-4$ 交于 $A, B$ 两点, 线段 $AB$ 的垂直平分线与直线 $y=-5$ 交于 $Q$ 点, $O$是原点. 当 $P$ 为抛物线上位于线段 $AB$ 下方(含 $A, B$ )的动点时, 求三角形 $OPQ$ 的面积 $S$ 的最大值.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.2]\n\\draw [->] (-10,0) -- (10,0) node [below] {$x$};\n\\draw [->] (0,-10) -- (0,10) node [left] {$y$};\n\\draw (0,0) node [above left] {$O$};\n\\draw [name path = line, domain = -8:10] plot (\\x,{\\x/2});\n\\draw [name path = para, domain = -9:9] plot (\\x,{pow(\\x,2)/8-4});\n\\draw (-10,-5) -- (10,-5);\n\\draw (0,-5) node [below left] {$-5$};\n\\draw (-4,-2) node [below] {$A$} coordinate (A);\n\\draw (8,4) node [below right] {$B$} coordinate (B);\n\\filldraw (6,{36/8-4}) circle (0.1) node [right] {$P$};\n\\draw (-2,9) coordinate (T) -- (6,-7) (5,-5) node [below left] {$Q$};\n\\draw (2,1) coordinate (V);\n\\draw (V) pic [draw, scale = 0.3] {right angle = B--V--T};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240322\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [
+            "009110"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "041095": {
+        "id": "041095",
+        "content": "抛物线 $y^2=16 x$ 上有三点 $A(1,4), B(x_B, y_B)$ 和 $C(x_C, y_C)$, 其中 $x_B<x_C$, 且三角形 $ABC$ 的重心是焦点 $F$.\\\\\n(1) 求 $x_B+x_C$ 与 $y_B+y_C$;\\\\\n(2) 求直线 $BC$ 的方程;\\\\\n(3) 求点 $B, C$ 的坐标.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240322\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "041096": {
+        "id": "041096",
+        "content": "设 $C_1$ 是以 $F$ 为焦点的抛物线 $y^2=2 p x(p>0), C_2$ 是以直线 $2 x-\\sqrt{3}y=0$ 与 $2 x+\\sqrt{3}y=0$ 为渐近线, 以 $(0, \\sqrt{7})$ 为一个焦点的双曲线.\\\\\n(1) 写出双曲线 $C_2$ 的标准方程;\\\\\n(2) 若 $C_1$ 与 $C_2$ 在第一象限内有两个不同的公共点 $A$ 和 $B$, 求 $p$ 的取值范围, 并求 $\\overrightarrow{FA}\\cdot \\overrightarrow{FB}$ 的最大值;\\\\\n(3) 条件同(2), 若三角形 $FAB$ 的面积 $S$ 满足 $S=\\dfrac{2}{3}\\overrightarrow{FA}\\cdot \\overrightarrow{FB}$, 求 $p$ 的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240322\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
    }
 }