收录高三寒假作业26新题

工具v2/文本文件/新题收录列表.txt

@@ -76,3 +76,6 @@
 20240125-111402
 023818:023827
 
+20240125-111717
+023828:023834
+

题库0.3/Problems.json

@@ -237499,7 +237499,8 @@
         ],
         "same": [],
         "related": [
-            "003166"
+            "003166",
+            "023828"
         ],
         "remark": "",
         "space": "",
@@ -443643,7 +443644,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023830"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -643048,6 +643051,151 @@
         "space": "4em",
         "unrelated": []
     },
+    "023828": {
+        "id": "023828",
+        "content": "函数 $y=\\sin (2 x+\\dfrac{\\pi}{4})$ 的对称轴方程为\\blank{50}, 对称中心为\\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": [
+            "008354"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023829": {
+        "id": "023829",
+        "content": "若函数 $f(x)=\\sin (\\omega x+\\dfrac{\\pi}{6})$($\\omega>0$) 的最小正周期为 $\\pi$, 则 $f(\\dfrac{\\pi}{3})$ 的值是\\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": []
+    },
+    "023830": {
+        "id": "023830",
+        "content": "把函数 $y=\\cos x-\\sqrt{3}\\sin x$ 的图像向左平移 $m$($m>0$) 个单位所得图像关于 $y$ 轴对称, 则实数 $m$ 的最小值是\\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": [
+            "030014",
+            "016090"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023831": {
+        "id": "023831",
+        "content": "电流强度 $I$(A) 随时间 $t$(s) 变化的函数 $I=A \\sin (\\omega t+\\varphi) $($A>0$, $\\omega>0$, $0<\\varphi<\\dfrac{\\pi}{2}$) 的部分图像如图所示, 则当 $t=\\dfrac{1}{100}$s时, 电流强度是\\blank{50}A.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 1.5, yscale = 0.1]\n\\draw [->] (0,0) -- ({7/3},0) node [below] {$x$};\n\\draw [->] (0,-15) -- (0,15) node [left] {$y$};\n\\draw (0,0) node [left] {$O$};\n\\draw [domain = 0:{11/6}, samples = 100] plot (\\x,{10*sin(180*\\x+30)});\n\\foreach \\i in {-10,-5,5,10}\n{\\draw (0.04,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\draw [dashed] ({4/3},0) --++ (0,-10) -- (0,-10) ({1/3},0)--++ (0,10) -- (0,10);\n\\draw ({1/3},0) node [below] {$\\dfrac{1}{300}$};\n\\draw ({4/3},0) node [above] {$\\dfrac{4}{300}$};\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": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023832": {
+        "id": "023832",
+        "content": "若函数 $f(x)=A \\sin (\\omega x+\\varphi)+k$($A>0$, $\\omega>0$, $|\\varphi|<\\dfrac{\\pi}{2}$)的图像如图所示, 则 $f(x)$ 的表达式是 $f(x)=$\\blank{50}.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [above left] {$O$};\n\\draw [domain = -1.5:2.5, samples = 100] plot (\\x,{1.5*sin(\\x*360/pi+60)+1});\n\\draw [dashed] ({7*pi/12},0) --++ (0,-0.5) -- (0,-0.5);\n\\draw [dashed] ({pi/12},0) --++ (0,2.5) -- (0,2.5);\n\\draw (0,-0.5) node [left] {$-\\frac{1}{2}$} (0,2.5) node [left] {$\\frac{5}{2}$};\n\\draw ({pi/12},0) node [below] {$\\frac{\\pi}{12}$} ({7*pi/12},0) node [above] {$\\frac{7\\pi}{12}$};\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": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023833": {
+        "id": "023833",
+        "content": "若函数 $f(x)=2 \\sin (\\dfrac{\\pi}{3}x+\\varphi)$($|\\varphi|<\\dfrac{\\pi}{2}$) 的图像经过点 $(0,1)$, 则其最小正周期 $T=$\\blank{50}, 初始相位 $\\varphi=$\\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": []
+    },
+    "023834": {
+        "id": "023834",
+        "content": "设 $\\omega \\in \\mathbf{R}$. 已知向量 $\\overrightarrow{m}=(\\cos \\omega x, \\sin \\omega x)$, $\\overrightarrow{n}=(\\cos \\omega x, \\sqrt{3}\\cos \\omega x)$, 函数 $y=f(x)$, 其中 $f(x)=\\overrightarrow{m}\\cdot \\overrightarrow{n}$.\\\\\n(1) 若 $f(x)$ 的最小正周期是 $2 \\pi$, 求 $f(x)$ 的单调增区间;\\\\\n(2) 若 $f(x)$ 的图像的一条对称轴是 $x=\\dfrac{\\pi}{6}$($0<\\omega<2$), 求 $f(x)$ 的最小正周期和值域.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\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.",
@@ -643454,7 +643602,9 @@
         "same": [
             "010931"
         ],
-        "related": [],
+        "related": [
+            "023830"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []