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3
工具v2/文本文件/新题收录列表.txt
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@ -412,3 +412,6 @@
20240307-162342 高一下学期统考复习卷03
024660:024678
20240307-163014 高一下学期统考复习卷04
024679:024697

506
题库0.3/Problems.json
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@ -21482,7 +21482,8 @@
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"space": "4em",
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"024679": {
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"content": "若点 $(\\dfrac{\\sqrt{3}}{3}, \\dfrac{\\sqrt{3}}{9})$ 在一个幂函数图像上, 则这个幂函数的表达式是\\blank{50}.",
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"024680": {
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"content": "函数 $y=\\lg (3-\\dfrac{1}{x})$ 的定义域是\\blank{50}.",
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"024681": {
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"content": "若函数 $y=(m+1)^x$ 在 $\\mathbf{R}$ 上是严格增函数, 则实数 $m$ 的取值范围是\\blank{50}.",
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"024682": {
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"content": "若函数 $y=a+\\dfrac{1}{4^x-1}$ 的图像关于原点成中心对称, 则实数 $a$ 的值为\\blank{50}.",
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"content": "若 $2^{2 x}-2^5=2^{x+2}$, 则 $\\lg (x^2+1)=$\\blank{50}.",
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"content": "若实数 $x$ 满足不等式 $\\log _2(x^2-2 x)>\\log _2(x+4)$, 则实数 $x$ 的取值范围是\\blank{50}.",
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"content": "若函数 $y=\\lg (x^2-2 a x+2 a+3)$ 的值域是 $\\mathbf{R}$, 则实数 $a$ 的取值范围是\\blank{50}.",
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"024686": {
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"content": "若直线 $y=a$ 与函数 $y=|2^x-1|$ 的图像有两个公共点, 则 $a$ 的取值范围是\\blank{50}.",
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"content": "无论 $a$ 为何值, 函数 $y=(a-1) 2^x-\\dfrac{a}{2}$ 恒过一定点, 这个定点的坐标是\\blank{50}.",
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"024688": {
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"content": "若函数 $y=\\begin{cases}a^x, & x<0,\\\\(a-3) x+4 a,& x \\geq 0\\end{cases}$ 在 $x \\in (-\\infty, +\\infty)$ 上严格减,则实数 $a$ 的取值范围是\\blank{50}.",
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"024689": {
"id": "024689",
"content": "函数 $y=2+\\log _2 x$($x \\geq 1$) 的值域为\\bracket{20}.\n\\fourch{$(2,+\\infty)$}{$(-\\infty, 2)$}{$[2,+\\infty)$}{$[3,+\\infty)$}",
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"024690": {
"id": "024690",
"content": "方程 $\\lg (x+2)=(\\dfrac{1}{2})^x$ 解的情况为\\bracket{20}.\n\\fourch{两个正根}{一个正根一个负根}{一个正根}{无实数根}",
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"origin": "导学先锋必修第四章测验试题12",
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"024691": {
"id": "024691",
"content": "不等式 $\\log _{a-1}(2 x-1)>\\log _{a-1}(x-1)$ 成立的充要条件是\\bracket{20}.\n\\fourch{$x>0$}{$x>0$ 且 $a>2$}{$x>1$ 且 $a>1$}{$x>1$ 且 $a>2$}",
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"024692": {
"id": "024692",
"content": "若函数 $y=\\log _2(x^2-2 x+17)$ 的值域为 $[m,+\\infty)$, 当正数 $a$、$b$满足 $\\dfrac{2}{3 a+b}+\\dfrac{1}{a+2 b}=m$ 时, 则 $7 a+4 b$ 的最小值为\\bracket{20}.\n\\fourch{$\\dfrac{9}{4}$}{1}{$\\dfrac{5+2 \\sqrt{2}}{4}$}{2}",
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"origin": "导学先锋必修第四章测验试题14",
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"024693": {
"id": "024693",
"content": "已知 $m \\in \\mathbf{Z}$, 函数 $y=x^{m^2-8 m}$ 的图像关于原点对称, 且与 $x$ 轴、 $y$轴均无交点, 求 $m$ 的值.",
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"024694": {
"id": "024694",
"content": "求 $y=\\dfrac{1}{2^x-1}$ 的值域.",
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"genre": "解答题",
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"solution": "",
"duration": -1,
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"024695": {
"id": "024695",
"content": "银行一年定期储蓄年利率为 $2.25 \\%$, 若存款到期不取继续留存于银行,银行自动将本金及 $80 \\%$ 的利息 ($20 \\%$ 交纳利息税)转存一年定期储蓄.某人于年初存人银行 5 万元.\\\\\n(1) 至少存几年,才可以得到大于 2500 元的利息?\\\\\n(2) 若此人改为按三年定期储蓄存人银行 5 万元 (三年定期储蓄的年利率为 $3.24 \\%$ ), 三年后一次取出全部本息 (利息按 $20 \\%$ 交税), 问按哪一种方式能获得更多的利息? 利息差是多少? (保留 2 位小数)",
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"024696": {
"id": "024696",
"content": "已知关于 $x$ 的方程 $9^x+(a+4) \\cdot 3^x+4=0$ 有实数解, 求实数 $a$的取值范围.",
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"024697": {
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"content": "已知 $x$ 满足 $\\log _2^2 x-5 \\log _2 x+6 \\leq 0$, 求函数 $y=\\log _2(\\dfrac{x}{2}) \\log _{\\frac{1}{2}}(\\dfrac{4}{x})$ 的最大值和最小值.",
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"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.",
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