收录高一周末卷15及小测

工具/批量收录题目.py

@@ -1,8 +1,8 @@
 #修改起始id,出处,文件名
-starting_id = 40753
+starting_id = 40772
 raworigin = ""
 filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目13.tex"
-editor = "20230520\t王伟叶"
+editor = "20230526\t王伟叶"
 indexed = False
 IndexDescription = "试题"
 

工具/文本文件/批量题目分类号记录.txt

@@ -216,6 +216,8 @@ problems_dict =  {
 "2025届高一下学期周末卷10与11小测":"40707:40715",
 "2025届高一下学期周末卷13":"40716:40737",
 "2025届高一下学期周末卷14":"40753:40771",
+"2025届高一下学期周末卷15":"40772:40790",
+"2025届高一下学期周末卷15小测":"40791:40798",
 "2025届高一下学期期中复习一(集合逻辑不等式)":"40283:40298",
 "2025届高一下学期期中复习二(幂指对函数)":"40368:40386",
 "2025届高一下学期测验01":"40336:40349",

题库0.3/Problems.json

@@ -550252,5 +550252,545 @@
         "remark": "",
         "space": "4em",
         "unrelated": []
+    },
+    "040772": {
+        "id": "040772",
+        "content": "关于$x$的方程$|\\overline {x}|-2 x=2-4 \\mathrm{i}$的解是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040773": {
+        "id": "040773",
+        "content": "关于复数$z$的方程$|z|+z=1-3 \\mathrm{i}$的解集是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040774": {
+        "id": "040774",
+        "content": "若复数$z$满足方程$z^2+2=0$, 则$z^3=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040775": {
+        "id": "040775",
+        "content": "已知复数$z=x+y \\mathrm{i}$($x, y \\in \\mathbf{R}$), 若$|z-4 \\mathrm{i}|=|z+2|$, 则$2^x+4^y$的最小值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040776": {
+        "id": "040776",
+        "content": "已知常数$a, b \\in \\mathbf{R}$, 实系数一元二次方程$x^2+p x+q=0$的两个根为$2+a \\mathrm{i}$与$b+\\mathrm{i}$, 那么$p^3+q$的值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040777": {
+        "id": "040777",
+        "content": "若$2+\\mathrm{i}$是关于$x$的复系数方程$x^2-2 k x+1=0$的一个根, 则$k=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040778": {
+        "id": "040778",
+        "content": "复数$\\sin 10^{\\circ}-\\mathrm{i} \\cdot \\cos 10^{\\circ}$的三角形式(用辐角主值)是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040779": {
+        "id": "040779",
+        "content": "已知复数$z=(a+\\mathrm{i})^2$, $\\arg z=\\dfrac{7}{4} \\pi$, 则实数$a$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040780": {
+        "id": "040780",
+        "content": "计算: $\\dfrac{(\\dfrac{\\sqrt{2}}{2}-\\dfrac{\\sqrt{2}}{2} \\mathrm{i})^8 \\cdot(1+\\sqrt{3} \\mathrm{i})^6}{(1+\\mathrm{i})^6 \\cdot(-\\dfrac{\\sqrt{3}}{2}+\\dfrac{1}{2} \\mathrm{i})^5}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040781": {
+        "id": "040781",
+        "content": "若$z=\\cos \\theta+\\mathrm{i} \\sin \\theta$($\\mathrm{i}$为虚数单位), 则使$z^2=-1$的$\\theta$值可能是\\bracket{20}.\n\\fourch{$\\dfrac{\\pi}{6}$}{$\\dfrac{\\pi}{4}$}{$\\dfrac{\\pi}{3}$}{$\\dfrac{\\pi}{2}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040782": {
+        "id": "040782",
+        "content": "设复数$z=(a+\\mathrm{i})^2$的辐角是$\\dfrac{3 \\pi}{2}$, 则实数$a$的值为\\bracket{20}.\n\\fourch{$1$}{$-1$}{$-\\sqrt{2}$}{$-\\sqrt{3}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040783": {
+        "id": "040783",
+        "content": "设$\\arg (3+4 \\mathrm{i})=\\theta$, 则$\\arg (8-6 \\mathrm{i})=$\\bracket{20}.\n\\fourch{$\\dfrac{3 \\pi}{2}+\\theta$}{$\\dfrac{3 \\pi}{2}-\\theta$}{$\\dfrac{\\pi}{2}+\\theta$}{$\\dfrac{\\pi}{2}-\\theta$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040784": {
+        "id": "040784",
+        "content": "设$z=\\cos \\dfrac{\\pi}{4}+\\mathrm{i} \\sin \\dfrac{\\pi}{4}$, 若$z^n=\\overline {z}$($n \\in \\mathbf{N}$, $n\\ge 1$), 则$n$的最小值为\\bracket{20}.\n\\fourch{$7$}{$8$}{$9$}{$10$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040785": {
+        "id": "040785",
+        "content": "求下列复数的辐角主值:\\\\\n(1) $-\\sin 100^{\\circ}+\\mathrm{i} \\cos 100^{\\circ}$;\\\\\n(2) $-\\sin \\theta+\\mathrm{i} \\cos \\theta$($\\dfrac{3 \\pi}{2}<\\theta<2 \\pi$);\\\\\n(3) $3-\\sqrt{3} \\mathrm{i}$;\\\\\n(4) $-5-4 \\mathrm{i}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040786": {
+        "id": "040786",
+        "content": "求$-1$的$6$次方根.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040787": {
+        "id": "040787",
+        "content": "若实系数一元二次方程$x^2-2 x+p=0$的两根在复平面上所对应的点之间的距离为$\\sqrt{3}$, 求$p$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040788": {
+        "id": "040788",
+        "content": "已知$-\\dfrac{1}{2}+\\dfrac{\\sqrt{3}}{2} \\mathrm{i}$是方程$x^2+k x+2=0$($k \\in \\mathbf{C}$)的一个根, 求$k$的值, 并解此方程.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040789": {
+        "id": "040789",
+        "content": "设$m \\in \\mathbf{R}$. 关于$x$的方程$x^2-6 x+m=0$的两根分别为$\\alpha, \\beta$, 求$|\\alpha|+|\\beta|$关于$m$的表达式$g(m)$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040790": {
+        "id": "040790",
+        "content": "若关于$x$的方程$x^2+a x+a^2+2 a=0$至少有一个模为$2$的根, 求实数$a$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040791": {
+        "id": "040791",
+        "content": "已知$3 \\mathrm{i}-2$是关于$x$的方程$2 x^2+p x+q=0$($p, q \\in \\mathbf{R}$)的一个根, 则$p=$\\blank{50}, $q=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15小测",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040792": {
+        "id": "040792",
+        "content": "若复数$z$满足$|z-\\mathrm{i}|=2$, 则$z$在复平面内所对应的点构成的轨迹的长度为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15小测",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040793": {
+        "id": "040793",
+        "content": "将$2(\\cos \\dfrac{\\pi}{9}+\\mathrm{i} \\sin \\dfrac{\\pi}{9}) \\cdot 3(\\cos \\dfrac{\\pi}{18}+\\mathrm{i} \\sin \\dfrac{\\pi}{18})$化为复数的代数形式: \\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15小测",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040794": {
+        "id": "040794",
+        "content": "设$z_1=-2+\\mathrm{i}$, $z_2=-1-3 \\mathrm{i}$, 则$\\arg z_1+\\arg z_2=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15小测",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040795": {
+        "id": "040795",
+        "content": "设$\\arg (1+\\mathrm{i})<\\arg z<\\arg \\mathrm{i}$, 则复数$-\\dfrac{1}{z^2}$的对应点位于\\bracket{20}.\n\\fourch{第一象限}{第二象限}{第三象限}{第四象限}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15小测",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040796": {
+        "id": "040796",
+        "content": "已知关于$x$的方程$x^2+(4+\\mathrm{i}) x+3+p \\mathrm{i}=0$($p \\in R$)有实数根, 求$p$的值, 并解这个方程.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15小测",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040797": {
+        "id": "040797",
+        "content": "已知关于$x$的方程$3 x^2-6(m-1) x+m^2+1=0$的两根为$\\alpha, \\beta$, 若$|\\alpha|+|\\beta|=2$, 求实数$m$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15小测",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040798": {
+        "id": "040798",
+        "content": "已知$z=\\dfrac{1-\\sin \\alpha+\\mathrm{i} \\cos \\alpha}{1-\\sin \\alpha-\\mathrm{i} \\cos \\alpha}$.\\\\\n(1) 把$z$化成三角形式;\\\\\n(2) 当$\\alpha \\in[\\dfrac{3 \\pi}{2}, 2 \\pi]$时, 求$\\arg z$;\\\\\n(3) 若$\\alpha=\\dfrac{\\pi}{5}$, 求使$z^n$为实数的最小正整数$n$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷15小测",
+        "edit": [
+            "20230526\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
     }
 }