收录高三寒假作业6题

工具v2/文本文件/新题收录列表.txt

@@ -13,3 +13,6 @@
 20240124-163621
 023674:023676
 
+20240124-194256
+023677:023682
+

题库0.3/Problems.json

@@ -69644,7 +69644,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023678"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -591967,7 +591969,9 @@
             "20230209\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023677"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -639753,6 +639757,130 @@
         "space": "4em",
         "unrelated": []
     },
+    "023677": {
+        "id": "023677",
+        "content": "若直线 $l$ 过点 $A(2,-1)$、$B(1,2)$, 则直线 $l$ 的两点式方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "021939"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023678": {
+        "id": "023678",
+        "content": "若直线 $3 x+2 y+5=0$ 的一个法向量为 $(a, a-2)$, 则 $a$ 的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "002141"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023679": {
+        "id": "023679",
+        "content": "有一直线与 $y$ 轴交于 $(0,-2)$, 若其倾斜角的正弦满足方程 $6 x^2+x-1=0$, 则此直线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023680": {
+        "id": "023680",
+        "content": "(1) 经过点 $M(2,-1)$, 倾斜角为直线 $4 x+3 y-1=0$ 的倾斜角的一半的直线方程是\\blank{50}.\\\\\n(2) 经过点 $P(3,-4)$, 且在坐标轴上的横截距和纵截距相等的直线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023681": {
+        "id": "023681",
+        "content": "(1) 若过点 $M(-2,3)$ 引一直线, 使它夹在两坐标轴间的线段被 $M$ 平分, 则该直线方程为\\blank{50}.\\\\\n(2) 若将直线 $x+2 y-4=0$ 绕着它与 $x$ 轴的交点按逆时针方向旋转 $\\dfrac{\\pi}{4}$, 旋转后所得直线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023682": {
+        "id": "023682",
+        "content": "已知三角形的一个顶点 $A(-4,2)$, 两条中线所在直线方程分别为 $3 x-2 y+2=0$ 和 $3 x+5 y-12=0$, 求三角形各边所在直线方程.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "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.",