B\u00e0i Test Tr\u1eafc Nghi\u1ec7m<\/title>\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Alegreya:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\n \n \n \n \n\t<link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.21\/dist\/katex.min.css\" integrity=\"sha384-zh0CIslj+VczCZtlzBcjt5ppRcsAmDnRem7ESsYwWwg3m\/OaJ2l4x7YBZl9Kxxib\" crossorigin=\"anonymous\">\n\n \n <script defer src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.21\/dist\/katex.min.js\" integrity=\"sha384-Rma6DA2IPUwhNxmrB\/7S3Tno0YY7sFu9WSYMCuulLhIqYSGZ2gKCJWIqhBWqMQfh\" crossorigin=\"anonymous\"><\/script>\n\n \n <script defer src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.21\/dist\/contrib\/auto-render.min.js\" integrity=\"sha384-hCXGrW6PitJEwbkoStFjeJxv+fSOOQKOPbJxSfM6G5sWZjAyWhXiTIIAmQqnlLlh\" crossorigin=\"anonymous\"\n onload=\"renderMathInElement(document.body);\"><\/script> \n \n <style> \n body {\n font-family: 'Alegreya', serif;\n line-height: 1.5;\n font-size: 17px;\n } \n .question {\n font-family: \"Times New Roman\", Times, Georgia, \"Noto Serif\", serif;\n counter-increment: question;\n \t\t \/* border: 2px solid #4CAF50; \u0110\u01b0\u1eddng vi\u1ec1n m\u00e0u xanh l\u00e1 c\u00e2y *\/\n background-color: #ebfab4; \/* M\u00e0u n\u1ec1n nh\u1ea1t *\/\n padding: 5px; \/* Kho\u1ea3ng c\u00e1ch b\u00ean trong *\/\n margin: 10px 0; \/* Kho\u1ea3ng c\u00e1ch b\u00ean ngo\u00e0i *\/\n border-radius: 8px; \/* Bo g\u00f3c cho \u0111\u01b0\u1eddng vi\u1ec1n *\/\n }\n .question::before {font-family: 'time new roman';\n content: \"C\u00e2u \" counter(question) \". \";\n font-weight: bold;\n display: inline;\n }\n h2 {font-family: 'Alegreya';\n font-size: 17px;\n font-weight: normal;\n margin-bottom: 0;\n display: inline;\n }\n .options {\n color: #000 ;\n font-family: 'Alegreya';\n display: block;\n margin: 3px 0;\n font-size: 17px;\n font-weight: normal;\n width: 95%;\n \n }\n\n .options label {\n display: block;\n break-inside: avoid; \/* tr\u00e1nh c\u1eaft label gi\u1eefa c\u1ed9t *\/\n -webkit-column-break-inside: avoid;\n -moz-column-break-inside: avoid;\n margin-bottom: 6px;\n}\n \n .column-1 .options {\n display: block;\n }\n .column-2 .options {\n column-count: 2;\n column-gap: 8px;\n }\n .column-4 .options {\n column-count: 4;\n column-gap: 8px;\n } \n \n input[type=\"radio\"] {\n appearance: none;\n width: 15px;\n height: 15px;\n border: 2px solid #333;\n border-radius: 50%;\n background-color: white;\n cursor: pointer;\n outline: none; \n \n \n }\n input[type=\"checkbox\"] {\n appearance: none;\n width: 20px;\n height: 20px;\n border: 2px solid #333;\n border-radius: 30%;\n background-color: white;\n cursor: pointer;\n outline: none;\n }\n input[type=\"radio\"]:checked {background-color: #99ce34; border-color:#99ce34}\n input[type=\"checkbox\"]:checked{background-color: #CC9900;border-color: #CC9933;}\n \n \n .blank-container {\n display: inline-flex;\n align-items: center;\n margin-left: 10px;\n}\n\n.blank {\n border-bottom: 1px solid #333;\n width: 100px;\n max-width: 150px;\n text-align: center;\n outline: none;\n padding: 2px 4px;\n box-sizing: border-box;\n}\n.preview {\n text-align: center; \/* C\u0103n gi\u1eefa n\u1ed9i dung preview *\/\n margin-top: 8px;\n font-size: 1.1em; \/* K\u00edch th\u01b0\u1edbc ch\u1eef preview *\/\n color: #444; \/* M\u00e0u ch\u1eef preview *\/\n min-height: 30px; \/* \u0110\u1ea3m b\u1ea3o c\u00f3 kho\u1ea3ng tr\u1ed1ng khi ch\u01b0a nh\u1eadp *\/\n}\n #result {\n margin-top: 20px;\n font-weight: bold;\n }\n .katex { \n \n font-size: 17px; \/* \u0110i\u1ec1u ch\u1ec9nh gi\u00e1 tr\u1ecb n\u00e0y \u0111\u1ec3 t\u0103ng\/gi\u1ea3m k\u00edch th\u01b0\u1edbc c\u00f4ng th\u1ee9c *\/\n ; \/* Thay \u0111\u1ed5i font ch\u1eef \u1edf \u0111\u00e2y *\/ \n }\n \n <\/style>\n<\/head>\n<body>\n\n\n\n<div id=\"timer\" style=\"font-size: 24px; text-align: center; margin-bottom: 20px;\"><\/div> \n\n<form id=\"quiz-form\">\n\n<h1 font-size: 15px; font-weight: bold; color: #333> 1. Ph\u1ea7n tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn <\/h1> \n<div class=\"section\" id=\"section-1\">\n <div class=\"question column-2\">\n <h2> Trong kh\u00f4ng gian $Oxyz$, ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a m\u1eb7t ph\u1eb3ng $(P)$ \u0111i qua \u0111i\u1ec3m $B(2;1;-3)$, \u0111\u1ed3ng th\u1eddi vu\u00f4ng g\u00f3c v\u1edbi hai m\u1eb7t ph\u1eb3ng $(Q)\\colon x + y + 3z = 0$, $(R)\\colon 2x – y + z = 0$ l\u00e0 <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question1\"> $2x + y – 3z – 14 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question1\"> $4x – 5y – 3z – 12 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question1\"> $4x + 5y – 3z + 22 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question1\"> $4x + 5y – 3z – 22 = 0$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Cho h\u00e0m s\u1ed1 $y = f(x)$ li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n $[a;b]$. G\u1ecdi $D$ l\u00e0 h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n v\u1edbi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y = f(x)$, tr\u1ee5c ho\u00e0nh v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng $x=a$, $x=b$, $ (a < b) $. Th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh khi quay $D$ quanh tr\u1ee5c ho\u00e0nh l\u00e0 <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question2\"> $V = 2\\pi \\int\\limits_a^b \\left[ f(x) \\right]^2 dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question2\"> $V = \\pi^2 \\int\\limits_a^b f(x) dx$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question2\"> $V = \\pi \\int\\limits_a^b \\left[ f(x) \\right]^2 dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question2\"> $V = \\pi^2 \\int\\limits_a^b \\left[ f(x) \\right]^2 dx$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Cho hai h\u00e0m s\u1ed1 $y = f(x)$ v\u00e0 $y = g(x)$ li\u00ean t\u1ee5c tr\u00ean $\\mathbb{R}$. M\u1ec7nh \u0111\u1ec1 n\u00e0o sau \u0111\u00e2y sai? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question3\"> $\\int k f(x)dx = k \\int f(x)dx$ v\u1edbi m\u1ecdi h\u1eb1ng s\u1ed1 $k \\in \\mathbb{R} \\setminus \\{0\\}$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question3\"> $\\int f(x) \\cdot g(x)dx = \\int f(x)dx \\cdot \\int g(x)dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question3\"> $\\int [f(x)+g(x)]dx = \\int f(x)dx + \\int g(x)dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question3\"> $\\int [f(x)-g(x)]dx = \\int f(x)dx – \\int g(x)dx$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-4\">\n <h2> Bi\u1ebft $\\int\\limits_0^2 f(x)dx = -2$ v\u00e0 $\\int\\limits_2^5 f(x)dx = -4$. T\u00ednh $\\int\\limits_0^5 f(x)dx$ <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question4\"> $6$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question4\"> $-2$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question4\"> $-6$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question4\"> $2$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-2\">\n <h2> Cho $f(x)$ l\u00e0 h\u00e0m s\u1ed1 li\u00ean t\u1ee5c tr\u00ean $[a;b]$ v\u00e0 $F(x)$ l\u00e0 nguy\u00ean h\u00e0m c\u1ee7a $f(x)$. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 sai? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question5\"> $\\int\\limits_a^b f(x)dx = F(x) \\big|_a^b = F(b) – F(a)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question5\"> $\\int\\limits_a^b f(x)dx = -\\int\\limits_b^a f(t) dt$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question5\"> $\\int\\limits_a^a f(x)dx = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question5\"> $\\int\\limits_a^b f(x)dx = f'(x) \\big|_a^b = f'(b) – f'(a)$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-4\">\n <h2> H\u1ecd nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $f(x) = x^3$ l\u00e0 <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question6\"> $3x^2 + C$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question6\"> $4x^4 + C$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question6\"> $x^4 + C$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question6\"> $\\frac{1}{4}x^4 + C$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-2\">\n <h2> H\u00e0m s\u1ed1 $F(x)$ l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $f(x)$ tr\u00ean kho\u1ea3ng $K$ n\u1ebfu <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"true\" name=\"question7\"> $F'(x) = f(x), \\forall x \\in K$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question7\"> $f'(x) = F(x), \\forall x \\in K$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question7\"> $f'(x) = -F(x), \\forall x \\in K$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question7\"> $F'(x)=-f(x), \\forall x \\in K$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-4\">\n <h2> \u0110\u00e2u l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $f(x)=2\\sin 2x+2x$? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question8\"> $4\\cos 2x+2$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question8\"> $-\\cos 2x+x^2$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question8\"> $\\cos 2x+x^2$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question8\"> $\\sin 2x+x^2$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Trong kh\u00f4ng gian $Oxyz$, m\u1eb7t ph\u1eb3ng $(\\alpha)\\colon x – 2y + z – 4 = 0$ \u0111i qua \u0111i\u1ec3m n\u00e0o sau \u0111\u00e2y? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question9\"> $N(0;2;0)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question9\"> $M(1;0;0)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question9\"> $P(0;0;-4)$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question9\"> $Q(1;-1;1)$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-2\">\n <h2> Trong kh\u00f4ng gian $Oxyz$, vect\u01a1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 gi\u00e1 vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng $(\\alpha)\\colon 2x – 3y + 1 = 0$? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"true\" name=\"question10\"> $\\overrightarrow{c} = (2;-3;0)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question10\"> $\\overrightarrow{b} = (2;1;-3)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question10\"> $\\overrightarrow{d} = (3;2;0)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question10\"> $\\overrightarrow{a} = (2;-3;1)$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 $Oxyz$, ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng \u0111i qua \u0111i\u1ec3m $A(1;2;-3)$ c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn $\\overrightarrow{n} = (2;-1;3)$ l\u00e0 <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question11\"> $x – 2y – 4 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question11\"> $2x – y + 3z – 4 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question11\"> $2x – y + 3z + 4 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question11\"> $2x – y + 3z + 9 = 0$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> G\u1ecdi $S$ l\u00e0 di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi c\u00e1c \u0111\u01b0\u1eddng $y = 2^x$, $y = 0$, $x = 0$, $x = 2$. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question12\"> $S = \\int\\limits_0^2 2^{2x} dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question12\"> $S = \\pi \\int\\limits_0^2 2^x dx$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question12\"> $S = \\int\\limits_0^2 2^x dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question12\"> $S = \\pi \\int\\limits_0^2 2^{2x} dx$ <\/label>\n <\/div>\n <\/div>\n \n<\/div>\n\n\n \n<h1 font-size: 15px; font-weight: bold; color: #333>2. Ph\u1ea7n tr\u1eafc nghi\u1ec7m \u0111\u00fang sai <\/h1> \n<div class=\"section\" id=\"section-2\">\n <div class=\"question\">\n <h2> \u0110\u1ed1i v\u1edbi c\u00e1c d\u1ef1 \u00e1n x\u00e2y d\u1ef1ng, chi ph\u00ed nh\u00e2n c\u00f4ng lao \u0111\u1ed9ng \u0111\u01b0\u1ee3c t\u00ednh theo s\u1ed1 ng\u00e0y c\u00f4ng. \nG\u1ecdi $m(t)$ l\u00e0 s\u1ed1 l\u01b0\u1ee3ng c\u00f4ng nh\u00e2n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u1edf ng\u00e0y th\u1ee9 $t$ (k\u1ec3 t\u1eeb khi kh\u1edfi c\u00f4ng d\u1ef1 \u00e1n). \nG\u1ecdi $M(t)$ l\u00e0 s\u1ed1 ng\u00e0y c\u00f4ng \u0111\u01b0\u1ee3c t\u00ednh \u0111\u1ebfn h\u1ebft ng\u00e0y th\u1ee9 $t$ (k\u1ec3 t\u1eeb khi kh\u1edfi c\u00f4ng d\u1ef1 \u00e1n). \nTrong kinh t\u1ebf x\u00e2y d\u1ef1ng, ng\u01b0\u1eddi ta \u0111\u00e3 bi\u1ebft r\u1eb1ng $M'(t) = m(t)$. \n\nM\u1ed9t c\u00f4ng tr\u00ecnh x\u00e2y d\u1ef1ng d\u1ef1 ki\u1ebfn ho\u00e0n th\u00e0nh trong 400 ng\u00e0y. \nS\u1ed1 l\u01b0\u1ee3ng c\u00f4ng nh\u00e2n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng cho m\u1ed7i ng\u00e0y \u0111\u01b0\u1ee3c cho b\u1edfi h\u00e0m s\u1ed1 $m(t) =\\dfrac{-t^2}{100}+4t+400$, \ntrong \u0111\u00f3 $t$ t\u00ednh theo ng\u00e0y $(0 \\leq t \\leq 400)$, $m(t)$ t\u00ednh theo ng\u01b0\u1eddi. \n\u0110\u01a1n gi\u00e1 cho m\u1ed9t ng\u00e0y c\u00f4ng lao \u0111\u1ed9ng l\u00e0 400 000 \u0111\u1ed3ng. <\/h2>\n <div class=\"options\">\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question13\"> $M(t)$ l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $m(t)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question13\"> $M(100)$ c\u00f3 ph\u1ea7n nguy\u00ean b\u1eb1ng $56666$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question13\"> Trong kho\u1ea3ng th\u1eddi gian t\u1eeb $0$ \u0111\u1ebfn $400$ ng\u00e0y, $m(t)$ c\u00f3 xu h\u01b0\u1edbng t\u0103ng d\u1ea7n r\u1ed3i gi\u1ea3m d\u1ea7n v\u1ec1 $0$ <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question13\"> Chi ph\u00ed (t\u1ef7 \u0111\u1ed3ng) nh\u00e2n c\u00f4ng lao \u0111\u1ed9ng c\u1ee7a c\u00f4ng tr\u00ecnh \u0111\u00f3 cho \u0111\u1ebfn l\u00fac ho\u00e0n th\u00e0nh (c\u00f3 ph\u1ea7n nguy\u00ean) l\u00e0 $107$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Cho m\u1eb7t ph\u1eb3ng $(P)\\colon 2x+y+3z-6=0$ v\u00e0 c\u00e1c \u0111i\u1ec3m $A(-1;3;2)$, $B(-4;6;3)$, $C(1;4;5)$ <\/h2>\n <div class=\"options\">\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question14\"> $\\overrightarrow{n}=(2;1;-3)$ l\u00e0 ph\u00e1p tuy\u1ebfn c\u1ee7a $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question14\"> $AC$ song song v\u1edbi $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question14\"> $AB$ vu\u00f4ng g\u00f3c v\u1edbi $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question14\"> $BC$ n\u1eb1m trong $(P)$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Cho \u0111i\u1ec3m $I(-3; 0; 1)$ v\u00e0 m\u1eb7t ph\u1eb3ng $(P)\\colon x – 3y – 4z + 1 = 0$. <\/h2>\n <div class=\"options\">\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question15\"> \u0110i\u1ec3m $I(-3; 0; 1)$ kh\u00f4ng thu\u1ed9c m\u1eb7t ph\u1eb3ng $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question15\"> $(1; -3; 4)$ kh\u00f4ng ph\u1ea3i t\u1ecda \u0111\u1ed9 c\u1ee7a ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question15\"> N\u1ebfu m\u1eb7t ph\u1eb3ng $(Q)$ song song v\u1edbi m\u1eb7t ph\u1eb3ng $(P)$ th\u00ec vector $\\overrightarrow{n} = (1; -3; 4)$ l\u00e0 m\u1ed9t vector ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng $(Q)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question15\"> M\u1eb7t ph\u1eb3ng $(R)$ \u0111i qua \u0111i\u1ec3m $I$ v\u00e0 song song v\u1edbi $(P)$ c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $x – 3y – 4z – 7 = 0$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> M\u1ed9t v\u01b0\u1eddn \u01b0\u01a1m c\u00e2y c\u1ea3nh b\u00e1n m\u1ed9t c\u00e2y sau 6 n\u0103m tr\u1ed3ng v\u00e0 u\u1ed1n t\u1ea1o d\u00e1ng. \nT\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng c\u1ee7a c\u00e2y \u0111\u00f3 trong su\u1ed1t 6 n\u0103m \u0111\u01b0\u1ee3c t\u00ednh x\u1ea5p x\u1ec9 b\u1edfi c\u00f4ng th\u1ee9c \n$h'(t) = 1.5t + 5$, trong \u0111\u00f3 $h(t)$ (cm) l\u00e0 chi\u1ec1u cao c\u1ee7a c\u00e2y sau $t$ (n\u0103m). \nC\u00e2y con khi \u0111\u01b0\u1ee3c tr\u1ed3ng cao 12 cm. <\/h2>\n <div class=\"options\">\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question16\"> $h(t)$ l\u00e0 h\u1ecd nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $h'(t) = 1.5t + 5$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question16\"> $h(t) = \\dfrac{3}{2} t^2 + 5t + C$ v\u1edbi $C$ l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1 n\u00e0o \u0111\u00f3 <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question16\"> Sau n\u0103m \u0111\u1ea7u ti\u00ean tr\u1ed3ng c\u00e2y cao th\u00eam $5{,}75$ cm <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question16\"> Chi\u1ec1u cao c\u1ee7a c\u00e2y \u0111\u00f3 khi \u0111\u01b0\u1ee3c b\u00e1n l\u00e0 69 cm <\/label>\n <\/div>\n <\/div>\n \n<\/div>\n\n\n \n<h1 font-size: 15px; ; color: #333> 3. Ph\u1ea7n tr\u1eafc nghi\u1ec7m \u0111i\u1ec1n khuy\u1ebft <\/h1> \n<div class=\"section\" id=\"section-3\">\n <div class=\"question\">\n <h2> M\u1ed9t b\u1ec3 n\u01b0\u1edbc c\u00f3 d\u1ea1ng h\u00ecnh b\u00e1n c\u1ea7u b\u00e1n k\u00ednh $R = 3$ m\u00e9t, \u0111\u01b0\u1ee3c \u0111\u1ed5 \u0111\u1ea7y n\u01b0\u1edbc. Ta c\u1ea7n b\u01a1m to\u00e0n b\u1ed9 n\u01b0\u1edbc trong b\u1ec3 ra ngo\u00e0i qua m\u1ed9t \u1ed1ng \u0111\u1eb7t \u1edf mi\u1ec7ng b\u1ec3, \u0111\u1ea7u h\u00fat n\u01b0\u1edbc c\u1ee7a \u1ed1ng \u0111\u1eb7t \u1edf \u0111\u00e1y b\u1ec3 (xem h\u00ecnh minh h\u1ecda). C\u00f4ng $A$ (\u0111\u01a1n v\u1ecb Jun) \u0111\u1ec3 b\u01a1m h\u1ebft l\u01b0\u1ee3ng n\u01b0\u1edbc trong b\u1ec3 ra ngo\u00e0i \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c \\<p class=\"ql-center-displayed-equation\" style=\"line-height: 68px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-61a4b7401c2762dfb4b9f515b4b63f19_l3.svg\" height=\"68\" width=\"152\" class=\"ql-img-displayed-equation \" alt=\"\[A=9{,}8 \int\limits_0^R x S(x) \dif x,\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p> v\u1edbi $S(x)$ l\u00e0 di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t n\u01b0\u1edbc \u1edf \u0111\u1ed9 s\u00e2u $x$ m\u00e9t.\nH\u00e3y t\u00ednh c\u00f4ng \u0111\u1ec3 b\u01a1m n\u01b0\u1edbc kh\u1ecfi b\u1ec3. <div class=\"quicklatex\" style=\"display: flex; justify-content: center; margin: 15px 0;\">\n <p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-399082550bd1cf189c3ff930d82c1d95_l3.svg\" height=\"174\" width=\"309\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n <\/div>\n \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"$123$\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-1\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> M\u1ed9t v\u1eadt chuy\u1ec3n \u0111\u1ed9ng tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 t\u1ed1c \u0111\u1ed9 $v(t)=\\dfrac{1}{3}t^3-3t^2+5t+9 $ (\u0111\u01a1n v\u1ecb t\u00ednh b\u1eb1ng m\/s) v\u1edbi $0\\leq t\\leq 8$. H\u00e3y x\u00e1c \u0111\u1ecbnh qu\u00e3ng \u0111\u01b0\u1eddng (t\u00ednh b\u1eb1ng m\u00e9t) v\u1eadt di chuy\u1ec3n \u0111\u01b0\u1ee3c t\u1eeb l\u00fac $t=0$ \u0111\u1ebfn th\u1eddi \u0111i\u1ec3m m\u00e0 t\u1ed1c d\u1ed9 c\u1ee7a v\u1eadt l\u1edbn nh\u1ea5t (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb) \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"$35$\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-2\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> \u0110\u1ec3 chu\u1ea9n b\u1ecb cho h\u1ed9i tr\u1ea1i do \u0110o\u00e0n tr\u01b0\u1eddng t\u1ed5 ch\u1ee9c, l\u1edbp d\u1ef1 \u0111\u1ecbnh d\u1ef1ng m\u1ed9t c\u00e1i l\u1ec1u tr\u1ea1i c\u00f3 h\u00ecnh d\u1ea1ng m\u1eaft c\u1eaft ngang l\u00e0 m\u1ed9t parabol nh\u01b0 h\u00ecnh v\u1ebd. N\u1ec1n c\u1ee7a l\u1ec1u tr\u1ea1i l\u00e0 m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc b\u1ec1 ngang 3 m\u00e9t, chi\u1ec1u d\u00e0i 6 m\u00e9t, \u0111\u1ec9nh tr\u1ea1i c\u00e1ch n\u1ec1n 3 m\u00e9t. T\u00ednh th\u1ec3 t\u00edch (\u0111\u01a1n v\u1ecb m$^3$) ph\u1ea7n kh\u00f4ng gian b\u00ean trong tr\u1ea1i.\n <div class=\"quicklatex\" style=\"display: flex; justify-content: center; margin: 0px 0;\">\n <p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-9851a39be6070f747c6766ee93348314_l3.svg\" height=\"227\" width=\"271\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n <\/div>\n \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"$36$\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-3\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> M\u1ed9t v\u1eadn \u0111\u1ed9ng vi\u00ean b\u00f3ng chuy\u1ec1n khi ph\u00e1t b\u00f3ng, b\u00f3ng di chuy\u1ec3n theo m\u1ed9t \u0111\u01b0\u1eddng cong tr\u00ean\\m\u1eb7t ph\u1eb3n ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t s\u00e2n v\u00e0 r\u01a1i \u1edf v\u1ecb tr\u00ed c\u00e1ch\n v\u1eadn \u0111\u1ed9ng vi\u00ean 10 m\u00e9t v\u00e0 l\u1ec7ch v\u1ec1 h\u01b0\u1edbng tay ph\u1ea3i c\u1ee7a v\u1eadn \u0111\u1ed9ng vi\u00ean \u0111\u00f3 6 m\u00e9t. Ng\u01b0\u1eddi ta minh h\u1ecda l\u1ea1i v\u1ecb tr\u00ed c\u1ee7a v\u1eadn \u0111\u1ed9ng vi\u00ean tr\u00ean s\u00e2n v\u00e0 k\u00edch th\u01b0\u1edbc c\u1ee7a s\u00e2n trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy nh\u01b0 h\u00ecnh d\u01b0\u1edbi. N\u1ebfu ch\u1ecdn tr\u1ee5c Oz h\u01b0\u1edbng th\u1eb3ng \u0111\u1ee9ng h\u01b0\u1edbng t\u1eeb d\u01b0\u1edbi \u0111\u1ea5t l\u00ean tr\u00ean th\u00ec m\u1eb7t ph\u1eb3ng ch\u1ee9a \u0111\u01b0\u1eddng \u0111i c\u1ee7a qu\u1ea3 b\u00f3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh d\u1ea1ng $ax+by+cz-1=0$. Gi\u00e1 tr\u1ecb c\u1ee7a a+b+c l\u00e0 bao nhi\u00eau. <div class=\"quicklatex\" style=\"display: flex; justify-content: center; margin: 15px 0;\">\n <p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-ecac14f4e1faad612cacecbe3b0511f2_l3.svg\" height=\"190\" width=\"360\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n <\/div>\n \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"1\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-4\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> Trong kh\u00f4ng ph\u1eadn, c\u00f3 m\u1ed9t v\u00f9ng c\u1ea5m bay \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi hai m\u1eb7t ph\u1eb3ng song song, t\u1ea1o th\u00e0nh m\u1ed9t d\u1ea3i kh\u00f4ng gian m\u00e0 m\u00e1y bay kh\u00f4ng \u0111\u01b0\u1ee3c ph\u00e9p \u0111i v\u00e0o. Ta c\u00f3 th\u1ec3 hi\u1ec3u, v\u00f9ng c\u1ea5m bay ch\u00ednh l\u00e0 t\u1eadp c\u00e1c \u0111i\u1ec3m $M$ trong kh\u00f4ng gian gi\u1edbi h\u1ea1n b\u1edfi hai m\u1eb7t $(P)$ v\u00e0 $(Q)$ (bao g\u1ed3m c\u1ea3 $(P)$ v\u00e0 $(Q)$). \u0110\u1ec3 \u0111\u1ea3m b\u1ea3o an to\u00e0n, l\u1ed9 tr\u00ecnh bay c\u1ea7n \u0111\u01b0\u1ee3c thi\u1ebft l\u1eadp sao cho lu\u00f4n n\u1eb1m ngo\u00e0i v\u00f9ng c\u1ea5m n\u00e0y. G\u1ecdi $d_1,d_2$ t\u01b0\u01a1ng \u1ee9ng l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb M \u0111\u1ebfn $(P)$ v\u00e0 $(Q)$; $d$ l\u00e0 kho\u1ea3ng c\u00e1ch gi\u1eefa $(P)$ v\u00e0 $(Q)$.\n<ul style= \"margin-bottom: 0em;padding-left: 20px\">\n <li>N\u1ebfu \u0111i\u1ec3m $M$ n\u1eb1m trong v\u00f9ng c\u1ea5m bay $S$, ta n\u00f3i kho\u1ea3ng c\u00e1ch t\u1eeb $M$ \u0111\u1ebfn $S$ b\u1eb1ng $0$.<\/li>\n <li>N\u1ebfu \u0111i\u1ec3m $M$ n\u1eb1m ngo\u00e0i v\u00f9ng c\u1ea5m bay $S$, ta n\u00f3i kho\u1ea3ng c\u00e1ch t\u1eeb $M$ \u0111\u1ebfn $S$ b\u1eb1ng gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $d_1$ v\u00e0 $d_2$<\/li>\n<\/ul>\nTrong kh\u00f4ng gian $Oxyz$, v\u00f9ng c\u1ea5m bay \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi hai m\u1eb7t ph\u1eb3ng $(P)\\colon x + 4y – 2z + 7 = 0$ v\u00e0 $(Q)\\colon x + 4y – 2z + 12 = 0$. Khi m\u00e1y bay \u1edf v\u1ecb tr\u00ed $M(3;1;3)$ th\u00ec kho\u1ea3ng c\u00e1ch t\u1eeb m\u00e1y bay \u0111\u1ebfn v\u00f9ng c\u1ea5m $S$ l\u00e0 bao nhi\u00eau \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"0\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-5\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> Cho hai m\u1eb7t ph\u1ea3ng c\u1eaft nhau $(P)\\colon x+y+2z-12=0$ v\u00e0 $(Q)\\colon 2x-y+z-3=0$. X\u00e9t g\u00f3c g\u00f3c nh\u1ecb di\u1ec7n $\\alpha$ t\u1ea1o b\u1edfi $(P)$ v\u00e0 $(Q)$ sao cho kh\u00f4ng gian b\u1ecb gi\u1edbi h\u1ea1n b\u1edfi $\\alpha$ ch\u1ee9a $M(4;8;6)$. H\u00e3y x\u00e1c \u0111\u1ecbnh s\u1ed1 \u0111o c\u1ee7a g\u00f3c $\\alpha$ (t\u00ednh b\u1eb1ng \u0111\u1ed9 v\u00e0 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb). \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"$120$\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-6\"> \n <\/span> \n <\/div>\n \n<\/div>\n\n\n<form id=\"scoreForm\">\n <label for=\"name\">T\u00ean:<\/label>\n <input type=\"text\" id=\"name\" name=\"name\" required><br><br> \n<\/form>\n\n<\/form>\n<button type=\"button\" id=\"submit-button\">N\u1ed9p b\u00e0i<\/button>\n<div id=\"result\"><\/div>\n\n<script>\ndocument.addEventListener(\"DOMContentLoaded\", function () {\n \/\/ T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c div ch\u1ee9a class=\"quicklatex\" \u0111\u1ec3 b\u1ecf qua khi render KaTeX\n const quicklatexElements = document.querySelectorAll('div.quicklatex');\n\n \/\/ KaTeX render c\u00f4ng th\u1ee9c b\u00ecnh th\u01b0\u1eddng cho to\u00e0n b\u1ed9 trang, ngo\u1ea1i tr\u1eeb c\u00e1c div.quicklatex\n renderMathInElement(document.body, {\n delimiters: [\n {left: '<p class=\"ql-center-displayed-equation\" style=\"line-height: 20px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-77baa04537073105b02318b995c7964b_l3.svg\" height=\"20\" width=\"70\" class=\"ql-img-displayed-equation \" alt=\"\[', right: '\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>', display: true},\n {left: '$', right: '$', display: false}\n ],\n ignoredElements: ['div.quicklatex'] \/\/ B\u1ecf qua div.quicklatex khi render KaTeX\n });\n\n \/\/ Sau khi KaTeX render xong, QuickLaTeX x\u1eed l\u00fd c\u00e1c c\u00f4ng th\u1ee9c trong div.quicklatex\n quicklatexElements.forEach(function(element) {\n const latex = element.innerText; \/\/ L\u1ea5y n\u1ed9i dung latex trong div.quicklatex\n QuickLaTeX.render(latex, element); \/\/ D\u00f9ng QuickLaTeX \u0111\u1ec3 render c\u00f4ng th\u1ee9c\n });\n});\n\n<\/script>\n\n\n<script>\n\/\/ Move this outside of calculateScore\n \n\n function updatePreview(input) {\n const previewElement = input.closest('.blank-container').nextElementSibling;\n \n let userAnswer = input.value.trim();\n\n if (!userAnswer) {\n previewElement.style.display = 'none'; \/\/ \u1ea8n khi kh\u00f4ng c\u00f3 n\u1ed9i dung\n previewElement.innerHTML = '';\n return;\n }\n\n previewElement.style.display = 'block'; \/\/ Hi\u1ec3n th\u1ecb khi c\u00f3 n\u1ed9i dung\n\n try {\n katex.render(userAnswer, previewElement, {\n throwOnError: false \/\/ Kh\u00f4ng b\u00e1o l\u1ed7i khi c\u00fa ph\u00e1p LaTeX sai\n });\n } catch (err) {\n previewElement.innerHTML = 'L\u1ed7i c\u00f4ng th\u1ee9c LaTeX!';\n }\n }\n\nfunction normalizeLatex(latex) {\n latex = latex.replace(\/\\s+\/g, ' ').trim();\n latex = latex.replace(\/\\\\dfrac{([^}]*)}{([^}]*)}\/g, (match, num, denom) => {\n return `\\\\dfrac{${num.trim()}}{${denom.trim()}}`;\n });\n latex = latex.replace(\/\\\\pm\/g, '\u00b1')\n .replace(\/\\\\sqrt{([^}]*)}\/g, '\u221a($1)')\n .replace(\/\\\\frac{([^}]*)}{([^}]*)}\/g, '($1)\/($2)')\n .replace(\/\\\\dfrac{([^}]*)}{([^}]*)}\/g, '($1)\/($2)');\n return latex;\n}\n\n<\/script>\n<script>\nlet totalScore = 0;\n\nfunction calculateScore() {\n totalScore = 0; \/\/ \u0110\u1eb7t l\u1ea1i \u0111i\u1ec3m tr\u01b0\u1edbc khi t\u00ednh to\u00e1n\n const sections = document.querySelectorAll('.section');\n\n \/\/ Part 1: Multiple Choice\n const question1 = sections[0].querySelectorAll('.question');\n question1.forEach(question => {\n const selectedRadio = question.querySelector('input[type=\"radio\"]:checked');\n if (selectedRadio && selectedRadio.dataset.value === \"true\") {\n totalScore+=2.5; \/\/ 2.5 point for each correct answer\n }\n });\n\n \/\/ Part 2: True\/False\n const question2 = sections[1].querySelectorAll('.question');\n question2.forEach(question => {\n let reasonableCount = 0;\n const checkboxes = question.querySelectorAll('input[type=\"checkbox\"]');\n checkboxes.forEach(checkbox => {\n const isChecked = checkbox.checked;\n const isTrueValue = checkbox.dataset.value === \"true\";\n if (isChecked && isTrueValue || !isChecked && !isTrueValue) {\n reasonableCount++;\n }\n });\n\t\tfunction calculatePoints(reasonableCount) {\n switch (reasonableCount) {\n case 1: return 1;\n case 2: return 2.5;\n case 3: return 5;\n case 4: return 10;\n default: return 0;\n }\n } \n totalScore += calculatePoints(reasonableCount);\n });\n\n \/\/ Part 3: Fill in the blanks\n const question3 = sections[2].querySelectorAll('.question');\n question3.forEach(question => {\n const blank = question.querySelector('input[type=\"text\"]');\n const userAnswer = normalizeLatex(blank.value.trim());\n const correctAnswer = normalizeLatex(blank.dataset.value.trim());\n if (userAnswer === correctAnswer) {\n totalScore += 5; \/\/ 5 points for each correct answer\n }\n });\n\n const maxScore = question1.length*2.5 + question2.length*10 + question3.length*5 ;\n document.getElementById('result').innerText = `T\u1ed5ng \u0111i\u1ec3m: ${totalScore} \/ ${maxScore}`;\n}\n\n\t\/\/ Attach event listener correctly\ndocument.getElementById('submit-button').addEventListener('click', function() {\n calculateScore(); \/\/ T\u00ednh \u0111i\u1ec3m\n\n const name = document.getElementById('name').value;\n\n \/\/ Ki\u1ec3m tra xem t\u00ean c\u00f3 \u0111\u01b0\u1ee3c nh\u1eadp v\u00e0 \u0111i\u1ec3m c\u00f3 h\u1ee3p l\u1ec7\n if (!name || totalScore === 0) {\n alert('Vui l\u00f2ng nh\u1eadp t\u00ean v\u00e0 ch\u1eafc ch\u1eafn r\u1eb1ng b\u1ea1n \u0111\u00e3 l\u00e0m b\u00e0i.');\n return; \/\/ Ng\u1eebng n\u1ebfu kh\u00f4ng h\u1ee3p l\u1ec7\n }\n\n \/\/ G\u1eedi d\u1eef li\u1ec7u \u0111\u1ebfn server\n fetch('https:\/\/script.google.com\/macros\/s\/AKfycbzHg2x_X-slmAnt2W8uyaDLz6dPr1o96E73Xc8MTlcz6N-uHLJ65DFTGwPI_MuU9X1-\/exec', {\n method: 'POST',\n headers: {\n 'Content-Type': 'application\/x-www-form-urlencoded',\n },\n body: `name=${encodeURIComponent(name)}&score=${encodeURIComponent(totalScore)}`\n })\n .then(response => response.text())\n .then(data => {\n alert('G\u1eedi th\u00e0nh c\u00f4ng!');\n document.getElementById('scoreForm').reset(); \/\/ \u0110\u1eb7t l\u1ea1i form sau khi g\u1eedi\n totalScore = 0; \/\/ \u0110\u1eb7t l\u1ea1i \u0111i\u1ec3m sau khi g\u1eedi\n document.getElementById('result').innerText = ''; \/\/ X\u00f3a k\u1ebft qu\u1ea3\n })\n .catch(error => console.error('L\u1ed7i:', error));\n});\t\n\n\n \/\/ \u0110\u1ebfm s\u1ed1 c\u00e2u h\u1ecfi trong t\u1eebng section\n const section1Count = document.querySelectorAll('#section-1 .question').length;\n const section2Count = document.querySelectorAll('#section-2 .question').length;\n const section3Count = document.querySelectorAll('#section-3 .question').length;\n\n \n \/\/ C\u1eadp nh\u1eadt counter-reset cho t\u1eebng section\n document.getElementById('section-2').style.setProperty('counter-reset', `question ${section1Count}`);\n document.getElementById('section-3').style.setProperty('counter-reset', `question ${section1Count + section2Count}`); \n\n \/\/ Thay \u0111\u1ed5i s\u1ed1 gi\u00e2y theo y\u00eau c\u1ea7u c\u1ee7a b\u1ea1n\n const totalTime = 5460; \/\/ Th\u1eddi gian t\u1ed5ng c\u1ed9ng cho b\u00e0i test (600 gi\u00e2y = 10 ph\u00fat)\n let timeLeft = totalTime;\n\n const timerElement = document.getElementById('timer');\n\n function updateTimer() {\n const minutes = Math.floor(timeLeft \/ 60);\n const seconds = timeLeft % 60;\n timerElement.innerText = `Th\u1eddi gian c\u00f2n l\u1ea1i: ${minutes}:${seconds < 91 ? '' : '0'}${seconds}`;\n \n if (timeLeft > 0) {\n timeLeft--;\n } else {\n clearInterval(timerInterval);\n alert(\"Th\u1eddi gian \u0111\u00e3 h\u1ebft! B\u00e0i test s\u1ebd t\u1ef1 \u0111\u1ed9ng n\u1ed9p.\");\n document.getElementById('quiz-form').submit(); \/\/ T\u1ef1 \u0111\u1ed9ng n\u1ed9p b\u00e0i test\n }\n }\n\n const timerInterval = setInterval(updateTimer, 1000); \/\/ C\u1eadp nh\u1eadt m\u1ed7i gi\u00e2y\n\n<\/script> \n <\/body>\n <\/html>\n","protected":false},"excerpt":{"rendered":"<p>B\u00e0i Test Tr\u1eafc Nghi\u1ec7m 1. Ph\u1ea7n tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn Trong kh\u00f4ng gian $Oxyz$, ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a m\u1eb7t ph\u1eb3ng $(P)$ \u0111i qua \u0111i\u1ec3m $B(2;1;-3)$, \u0111\u1ed3ng th\u1eddi vu\u00f4ng g\u00f3c v\u1edbi hai m\u1eb7t ph\u1eb3ng $(Q)\\colon x + y + 3z = 0$, $(R)\\colon 2x – y + z = 0$ l\u00e0 $2x + y – 3z […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1290","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/posts\/1290","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1290"}],"version-history":[{"count":95,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/posts\/1290\/revisions"}],"predecessor-version":[{"id":1393,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/posts\/1290\/revisions\/1393"}],"wp:attachment":[{"href":"https:\/\/sunflower-math.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1290"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1290"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":1290,"date":"2025-03-29T15:13:41","date_gmt":"2025-03-29T08:13:41","guid":{"rendered":"https:\/\/sunflower-math.com\/?p=1290"},"modified":"2025-10-12T12:29:56","modified_gmt":"2025-10-12T05:29:56","slug":"121","status":"publish","type":"post","link":"https:\/\/sunflower-math.com\/?p=1290","title":{"rendered":"121"},"content":{"rendered":"\n\n\n\n \n \n B\u00e0i Test Tr\u1eafc Nghi\u1ec7m<\/title>\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Alegreya:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\n \n \n \n \n\t<link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.21\/dist\/katex.min.css\" integrity=\"sha384-zh0CIslj+VczCZtlzBcjt5ppRcsAmDnRem7ESsYwWwg3m\/OaJ2l4x7YBZl9Kxxib\" crossorigin=\"anonymous\">\n\n \n <script defer src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.21\/dist\/katex.min.js\" integrity=\"sha384-Rma6DA2IPUwhNxmrB\/7S3Tno0YY7sFu9WSYMCuulLhIqYSGZ2gKCJWIqhBWqMQfh\" crossorigin=\"anonymous\"><\/script>\n\n \n <script defer src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.21\/dist\/contrib\/auto-render.min.js\" integrity=\"sha384-hCXGrW6PitJEwbkoStFjeJxv+fSOOQKOPbJxSfM6G5sWZjAyWhXiTIIAmQqnlLlh\" crossorigin=\"anonymous\"\n onload=\"renderMathInElement(document.body);\"><\/script> \n \n <style> \n body {\n font-family: 'Alegreya', serif;\n line-height: 1.5;\n font-size: 17px;\n } \n .question {\n font-family: \"Times New Roman\", Times, Georgia, \"Noto Serif\", serif;\n counter-increment: question;\n \t\t \/* border: 2px solid #4CAF50; \u0110\u01b0\u1eddng vi\u1ec1n m\u00e0u xanh l\u00e1 c\u00e2y *\/\n background-color: #ebfab4; \/* M\u00e0u n\u1ec1n nh\u1ea1t *\/\n padding: 5px; \/* Kho\u1ea3ng c\u00e1ch b\u00ean trong *\/\n margin: 10px 0; \/* Kho\u1ea3ng c\u00e1ch b\u00ean ngo\u00e0i *\/\n border-radius: 8px; \/* Bo g\u00f3c cho \u0111\u01b0\u1eddng vi\u1ec1n *\/\n }\n .question::before {font-family: 'time new roman';\n content: \"C\u00e2u \" counter(question) \". \";\n font-weight: bold;\n display: inline;\n }\n h2 {font-family: 'Alegreya';\n font-size: 17px;\n font-weight: normal;\n margin-bottom: 0;\n display: inline;\n }\n .options {\n color: #000 ;\n font-family: 'Alegreya';\n display: block;\n margin: 3px 0;\n font-size: 17px;\n font-weight: normal;\n width: 95%;\n \n }\n\n .options label {\n display: block;\n break-inside: avoid; \/* tr\u00e1nh c\u1eaft label gi\u1eefa c\u1ed9t *\/\n -webkit-column-break-inside: avoid;\n -moz-column-break-inside: avoid;\n margin-bottom: 6px;\n}\n \n .column-1 .options {\n display: block;\n }\n .column-2 .options {\n column-count: 2;\n column-gap: 8px;\n }\n .column-4 .options {\n column-count: 4;\n column-gap: 8px;\n } \n \n input[type=\"radio\"] {\n appearance: none;\n width: 15px;\n height: 15px;\n border: 2px solid #333;\n border-radius: 50%;\n background-color: white;\n cursor: pointer;\n outline: none; \n \n \n }\n input[type=\"checkbox\"] {\n appearance: none;\n width: 20px;\n height: 20px;\n border: 2px solid #333;\n border-radius: 30%;\n background-color: white;\n cursor: pointer;\n outline: none;\n }\n input[type=\"radio\"]:checked {background-color: #99ce34; border-color:#99ce34}\n input[type=\"checkbox\"]:checked{background-color: #CC9900;border-color: #CC9933;}\n \n \n .blank-container {\n display: inline-flex;\n align-items: center;\n margin-left: 10px;\n}\n\n.blank {\n border-bottom: 1px solid #333;\n width: 100px;\n max-width: 150px;\n text-align: center;\n outline: none;\n padding: 2px 4px;\n box-sizing: border-box;\n}\n.preview {\n text-align: center; \/* C\u0103n gi\u1eefa n\u1ed9i dung preview *\/\n margin-top: 8px;\n font-size: 1.1em; \/* K\u00edch th\u01b0\u1edbc ch\u1eef preview *\/\n color: #444; \/* M\u00e0u ch\u1eef preview *\/\n min-height: 30px; \/* \u0110\u1ea3m b\u1ea3o c\u00f3 kho\u1ea3ng tr\u1ed1ng khi ch\u01b0a nh\u1eadp *\/\n}\n #result {\n margin-top: 20px;\n font-weight: bold;\n }\n .katex { \n \n font-size: 17px; \/* \u0110i\u1ec1u ch\u1ec9nh gi\u00e1 tr\u1ecb n\u00e0y \u0111\u1ec3 t\u0103ng\/gi\u1ea3m k\u00edch th\u01b0\u1edbc c\u00f4ng th\u1ee9c *\/\n ; \/* Thay \u0111\u1ed5i font ch\u1eef \u1edf \u0111\u00e2y *\/ \n }\n \n <\/style>\n<\/head>\n<body>\n\n\n\n<div id=\"timer\" style=\"font-size: 24px; text-align: center; margin-bottom: 20px;\"><\/div> \n\n<form id=\"quiz-form\">\n\n<h1 font-size: 15px; font-weight: bold; color: #333> 1. Ph\u1ea7n tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn <\/h1> \n<div class=\"section\" id=\"section-1\">\n <div class=\"question column-2\">\n <h2> Trong kh\u00f4ng gian $Oxyz$, ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a m\u1eb7t ph\u1eb3ng $(P)$ \u0111i qua \u0111i\u1ec3m $B(2;1;-3)$, \u0111\u1ed3ng th\u1eddi vu\u00f4ng g\u00f3c v\u1edbi hai m\u1eb7t ph\u1eb3ng $(Q)\\colon x + y + 3z = 0$, $(R)\\colon 2x – y + z = 0$ l\u00e0 <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question1\"> $2x + y – 3z – 14 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question1\"> $4x – 5y – 3z – 12 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question1\"> $4x + 5y – 3z + 22 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question1\"> $4x + 5y – 3z – 22 = 0$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Cho h\u00e0m s\u1ed1 $y = f(x)$ li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n $[a;b]$. G\u1ecdi $D$ l\u00e0 h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n v\u1edbi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y = f(x)$, tr\u1ee5c ho\u00e0nh v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng $x=a$, $x=b$, $ (a < b) $. Th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh khi quay $D$ quanh tr\u1ee5c ho\u00e0nh l\u00e0 <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question2\"> $V = 2\\pi \\int\\limits_a^b \\left[ f(x) \\right]^2 dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question2\"> $V = \\pi^2 \\int\\limits_a^b f(x) dx$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question2\"> $V = \\pi \\int\\limits_a^b \\left[ f(x) \\right]^2 dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question2\"> $V = \\pi^2 \\int\\limits_a^b \\left[ f(x) \\right]^2 dx$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Cho hai h\u00e0m s\u1ed1 $y = f(x)$ v\u00e0 $y = g(x)$ li\u00ean t\u1ee5c tr\u00ean $\\mathbb{R}$. M\u1ec7nh \u0111\u1ec1 n\u00e0o sau \u0111\u00e2y sai? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question3\"> $\\int k f(x)dx = k \\int f(x)dx$ v\u1edbi m\u1ecdi h\u1eb1ng s\u1ed1 $k \\in \\mathbb{R} \\setminus \\{0\\}$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question3\"> $\\int f(x) \\cdot g(x)dx = \\int f(x)dx \\cdot \\int g(x)dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question3\"> $\\int [f(x)+g(x)]dx = \\int f(x)dx + \\int g(x)dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question3\"> $\\int [f(x)-g(x)]dx = \\int f(x)dx – \\int g(x)dx$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-4\">\n <h2> Bi\u1ebft $\\int\\limits_0^2 f(x)dx = -2$ v\u00e0 $\\int\\limits_2^5 f(x)dx = -4$. T\u00ednh $\\int\\limits_0^5 f(x)dx$ <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question4\"> $6$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question4\"> $-2$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question4\"> $-6$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question4\"> $2$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-2\">\n <h2> Cho $f(x)$ l\u00e0 h\u00e0m s\u1ed1 li\u00ean t\u1ee5c tr\u00ean $[a;b]$ v\u00e0 $F(x)$ l\u00e0 nguy\u00ean h\u00e0m c\u1ee7a $f(x)$. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 sai? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question5\"> $\\int\\limits_a^b f(x)dx = F(x) \\big|_a^b = F(b) – F(a)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question5\"> $\\int\\limits_a^b f(x)dx = -\\int\\limits_b^a f(t) dt$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question5\"> $\\int\\limits_a^a f(x)dx = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question5\"> $\\int\\limits_a^b f(x)dx = f'(x) \\big|_a^b = f'(b) – f'(a)$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-4\">\n <h2> H\u1ecd nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $f(x) = x^3$ l\u00e0 <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question6\"> $3x^2 + C$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question6\"> $4x^4 + C$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question6\"> $x^4 + C$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question6\"> $\\frac{1}{4}x^4 + C$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-2\">\n <h2> H\u00e0m s\u1ed1 $F(x)$ l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $f(x)$ tr\u00ean kho\u1ea3ng $K$ n\u1ebfu <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"true\" name=\"question7\"> $F'(x) = f(x), \\forall x \\in K$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question7\"> $f'(x) = F(x), \\forall x \\in K$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question7\"> $f'(x) = -F(x), \\forall x \\in K$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question7\"> $F'(x)=-f(x), \\forall x \\in K$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-4\">\n <h2> \u0110\u00e2u l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $f(x)=2\\sin 2x+2x$? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question8\"> $4\\cos 2x+2$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question8\"> $-\\cos 2x+x^2$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question8\"> $\\cos 2x+x^2$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question8\"> $\\sin 2x+x^2$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Trong kh\u00f4ng gian $Oxyz$, m\u1eb7t ph\u1eb3ng $(\\alpha)\\colon x – 2y + z – 4 = 0$ \u0111i qua \u0111i\u1ec3m n\u00e0o sau \u0111\u00e2y? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question9\"> $N(0;2;0)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question9\"> $M(1;0;0)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question9\"> $P(0;0;-4)$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question9\"> $Q(1;-1;1)$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question column-2\">\n <h2> Trong kh\u00f4ng gian $Oxyz$, vect\u01a1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 gi\u00e1 vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng $(\\alpha)\\colon 2x – 3y + 1 = 0$? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"true\" name=\"question10\"> $\\overrightarrow{c} = (2;-3;0)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question10\"> $\\overrightarrow{b} = (2;1;-3)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question10\"> $\\overrightarrow{d} = (3;2;0)$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question10\"> $\\overrightarrow{a} = (2;-3;1)$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 $Oxyz$, ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng \u0111i qua \u0111i\u1ec3m $A(1;2;-3)$ c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn $\\overrightarrow{n} = (2;-1;3)$ l\u00e0 <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question11\"> $x – 2y – 4 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question11\"> $2x – y + 3z – 4 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question11\"> $2x – y + 3z + 4 = 0$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question11\"> $2x – y + 3z + 9 = 0$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> G\u1ecdi $S$ l\u00e0 di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi c\u00e1c \u0111\u01b0\u1eddng $y = 2^x$, $y = 0$, $x = 0$, $x = 2$. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? <\/h2>\n <div class=\"options\">\n <label><input type=\"radio\" data-value=\"false\" name=\"question12\"> $S = \\int\\limits_0^2 2^{2x} dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question12\"> $S = \\pi \\int\\limits_0^2 2^x dx$ <\/label>\n <label><input type=\"radio\" data-value=\"true\" name=\"question12\"> $S = \\int\\limits_0^2 2^x dx$ <\/label>\n <label><input type=\"radio\" data-value=\"false\" name=\"question12\"> $S = \\pi \\int\\limits_0^2 2^{2x} dx$ <\/label>\n <\/div>\n <\/div>\n \n<\/div>\n\n\n \n<h1 font-size: 15px; font-weight: bold; color: #333>2. Ph\u1ea7n tr\u1eafc nghi\u1ec7m \u0111\u00fang sai <\/h1> \n<div class=\"section\" id=\"section-2\">\n <div class=\"question\">\n <h2> \u0110\u1ed1i v\u1edbi c\u00e1c d\u1ef1 \u00e1n x\u00e2y d\u1ef1ng, chi ph\u00ed nh\u00e2n c\u00f4ng lao \u0111\u1ed9ng \u0111\u01b0\u1ee3c t\u00ednh theo s\u1ed1 ng\u00e0y c\u00f4ng. \nG\u1ecdi $m(t)$ l\u00e0 s\u1ed1 l\u01b0\u1ee3ng c\u00f4ng nh\u00e2n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u1edf ng\u00e0y th\u1ee9 $t$ (k\u1ec3 t\u1eeb khi kh\u1edfi c\u00f4ng d\u1ef1 \u00e1n). \nG\u1ecdi $M(t)$ l\u00e0 s\u1ed1 ng\u00e0y c\u00f4ng \u0111\u01b0\u1ee3c t\u00ednh \u0111\u1ebfn h\u1ebft ng\u00e0y th\u1ee9 $t$ (k\u1ec3 t\u1eeb khi kh\u1edfi c\u00f4ng d\u1ef1 \u00e1n). \nTrong kinh t\u1ebf x\u00e2y d\u1ef1ng, ng\u01b0\u1eddi ta \u0111\u00e3 bi\u1ebft r\u1eb1ng $M'(t) = m(t)$. \n\nM\u1ed9t c\u00f4ng tr\u00ecnh x\u00e2y d\u1ef1ng d\u1ef1 ki\u1ebfn ho\u00e0n th\u00e0nh trong 400 ng\u00e0y. \nS\u1ed1 l\u01b0\u1ee3ng c\u00f4ng nh\u00e2n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng cho m\u1ed7i ng\u00e0y \u0111\u01b0\u1ee3c cho b\u1edfi h\u00e0m s\u1ed1 $m(t) =\\dfrac{-t^2}{100}+4t+400$, \ntrong \u0111\u00f3 $t$ t\u00ednh theo ng\u00e0y $(0 \\leq t \\leq 400)$, $m(t)$ t\u00ednh theo ng\u01b0\u1eddi. \n\u0110\u01a1n gi\u00e1 cho m\u1ed9t ng\u00e0y c\u00f4ng lao \u0111\u1ed9ng l\u00e0 400 000 \u0111\u1ed3ng. <\/h2>\n <div class=\"options\">\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question13\"> $M(t)$ l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $m(t)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question13\"> $M(100)$ c\u00f3 ph\u1ea7n nguy\u00ean b\u1eb1ng $56666$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question13\"> Trong kho\u1ea3ng th\u1eddi gian t\u1eeb $0$ \u0111\u1ebfn $400$ ng\u00e0y, $m(t)$ c\u00f3 xu h\u01b0\u1edbng t\u0103ng d\u1ea7n r\u1ed3i gi\u1ea3m d\u1ea7n v\u1ec1 $0$ <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question13\"> Chi ph\u00ed (t\u1ef7 \u0111\u1ed3ng) nh\u00e2n c\u00f4ng lao \u0111\u1ed9ng c\u1ee7a c\u00f4ng tr\u00ecnh \u0111\u00f3 cho \u0111\u1ebfn l\u00fac ho\u00e0n th\u00e0nh (c\u00f3 ph\u1ea7n nguy\u00ean) l\u00e0 $107$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Cho m\u1eb7t ph\u1eb3ng $(P)\\colon 2x+y+3z-6=0$ v\u00e0 c\u00e1c \u0111i\u1ec3m $A(-1;3;2)$, $B(-4;6;3)$, $C(1;4;5)$ <\/h2>\n <div class=\"options\">\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question14\"> $\\overrightarrow{n}=(2;1;-3)$ l\u00e0 ph\u00e1p tuy\u1ebfn c\u1ee7a $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question14\"> $AC$ song song v\u1edbi $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question14\"> $AB$ vu\u00f4ng g\u00f3c v\u1edbi $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question14\"> $BC$ n\u1eb1m trong $(P)$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> Cho \u0111i\u1ec3m $I(-3; 0; 1)$ v\u00e0 m\u1eb7t ph\u1eb3ng $(P)\\colon x – 3y – 4z + 1 = 0$. <\/h2>\n <div class=\"options\">\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question15\"> \u0110i\u1ec3m $I(-3; 0; 1)$ kh\u00f4ng thu\u1ed9c m\u1eb7t ph\u1eb3ng $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question15\"> $(1; -3; 4)$ kh\u00f4ng ph\u1ea3i t\u1ecda \u0111\u1ed9 c\u1ee7a ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng $(P)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question15\"> N\u1ebfu m\u1eb7t ph\u1eb3ng $(Q)$ song song v\u1edbi m\u1eb7t ph\u1eb3ng $(P)$ th\u00ec vector $\\overrightarrow{n} = (1; -3; 4)$ l\u00e0 m\u1ed9t vector ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng $(Q)$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question15\"> M\u1eb7t ph\u1eb3ng $(R)$ \u0111i qua \u0111i\u1ec3m $I$ v\u00e0 song song v\u1edbi $(P)$ c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $x – 3y – 4z – 7 = 0$ <\/label>\n <\/div>\n <\/div>\n \n <div class=\"question\">\n <h2> M\u1ed9t v\u01b0\u1eddn \u01b0\u01a1m c\u00e2y c\u1ea3nh b\u00e1n m\u1ed9t c\u00e2y sau 6 n\u0103m tr\u1ed3ng v\u00e0 u\u1ed1n t\u1ea1o d\u00e1ng. \nT\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng c\u1ee7a c\u00e2y \u0111\u00f3 trong su\u1ed1t 6 n\u0103m \u0111\u01b0\u1ee3c t\u00ednh x\u1ea5p x\u1ec9 b\u1edfi c\u00f4ng th\u1ee9c \n$h'(t) = 1.5t + 5$, trong \u0111\u00f3 $h(t)$ (cm) l\u00e0 chi\u1ec1u cao c\u1ee7a c\u00e2y sau $t$ (n\u0103m). \nC\u00e2y con khi \u0111\u01b0\u1ee3c tr\u1ed3ng cao 12 cm. <\/h2>\n <div class=\"options\">\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question16\"> $h(t)$ l\u00e0 h\u1ecd nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 $h'(t) = 1.5t + 5$ <\/label>\n <label><input type=\"checkbox\" data-value=\"false\" name=\"question16\"> $h(t) = \\dfrac{3}{2} t^2 + 5t + C$ v\u1edbi $C$ l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1 n\u00e0o \u0111\u00f3 <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question16\"> Sau n\u0103m \u0111\u1ea7u ti\u00ean tr\u1ed3ng c\u00e2y cao th\u00eam $5{,}75$ cm <\/label>\n <label><input type=\"checkbox\" data-value=\"true\" name=\"question16\"> Chi\u1ec1u cao c\u1ee7a c\u00e2y \u0111\u00f3 khi \u0111\u01b0\u1ee3c b\u00e1n l\u00e0 69 cm <\/label>\n <\/div>\n <\/div>\n \n<\/div>\n\n\n \n<h1 font-size: 15px; ; color: #333> 3. Ph\u1ea7n tr\u1eafc nghi\u1ec7m \u0111i\u1ec1n khuy\u1ebft <\/h1> \n<div class=\"section\" id=\"section-3\">\n <div class=\"question\">\n <h2> M\u1ed9t b\u1ec3 n\u01b0\u1edbc c\u00f3 d\u1ea1ng h\u00ecnh b\u00e1n c\u1ea7u b\u00e1n k\u00ednh $R = 3$ m\u00e9t, \u0111\u01b0\u1ee3c \u0111\u1ed5 \u0111\u1ea7y n\u01b0\u1edbc. Ta c\u1ea7n b\u01a1m to\u00e0n b\u1ed9 n\u01b0\u1edbc trong b\u1ec3 ra ngo\u00e0i qua m\u1ed9t \u1ed1ng \u0111\u1eb7t \u1edf mi\u1ec7ng b\u1ec3, \u0111\u1ea7u h\u00fat n\u01b0\u1edbc c\u1ee7a \u1ed1ng \u0111\u1eb7t \u1edf \u0111\u00e1y b\u1ec3 (xem h\u00ecnh minh h\u1ecda). C\u00f4ng $A$ (\u0111\u01a1n v\u1ecb Jun) \u0111\u1ec3 b\u01a1m h\u1ebft l\u01b0\u1ee3ng n\u01b0\u1edbc trong b\u1ec3 ra ngo\u00e0i \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c \\<p class=\"ql-center-displayed-equation\" style=\"line-height: 68px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-61a4b7401c2762dfb4b9f515b4b63f19_l3.svg\" height=\"68\" width=\"152\" class=\"ql-img-displayed-equation \" alt=\"\[A=9{,}8 \int\limits_0^R x S(x) \dif x,\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p> v\u1edbi $S(x)$ l\u00e0 di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t n\u01b0\u1edbc \u1edf \u0111\u1ed9 s\u00e2u $x$ m\u00e9t.\nH\u00e3y t\u00ednh c\u00f4ng \u0111\u1ec3 b\u01a1m n\u01b0\u1edbc kh\u1ecfi b\u1ec3. <div class=\"quicklatex\" style=\"display: flex; justify-content: center; margin: 15px 0;\">\n <p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-399082550bd1cf189c3ff930d82c1d95_l3.svg\" height=\"174\" width=\"309\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n <\/div>\n \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"$123$\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-1\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> M\u1ed9t v\u1eadt chuy\u1ec3n \u0111\u1ed9ng tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 t\u1ed1c \u0111\u1ed9 $v(t)=\\dfrac{1}{3}t^3-3t^2+5t+9 $ (\u0111\u01a1n v\u1ecb t\u00ednh b\u1eb1ng m\/s) v\u1edbi $0\\leq t\\leq 8$. H\u00e3y x\u00e1c \u0111\u1ecbnh qu\u00e3ng \u0111\u01b0\u1eddng (t\u00ednh b\u1eb1ng m\u00e9t) v\u1eadt di chuy\u1ec3n \u0111\u01b0\u1ee3c t\u1eeb l\u00fac $t=0$ \u0111\u1ebfn th\u1eddi \u0111i\u1ec3m m\u00e0 t\u1ed1c d\u1ed9 c\u1ee7a v\u1eadt l\u1edbn nh\u1ea5t (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb) \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"$35$\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-2\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> \u0110\u1ec3 chu\u1ea9n b\u1ecb cho h\u1ed9i tr\u1ea1i do \u0110o\u00e0n tr\u01b0\u1eddng t\u1ed5 ch\u1ee9c, l\u1edbp d\u1ef1 \u0111\u1ecbnh d\u1ef1ng m\u1ed9t c\u00e1i l\u1ec1u tr\u1ea1i c\u00f3 h\u00ecnh d\u1ea1ng m\u1eaft c\u1eaft ngang l\u00e0 m\u1ed9t parabol nh\u01b0 h\u00ecnh v\u1ebd. N\u1ec1n c\u1ee7a l\u1ec1u tr\u1ea1i l\u00e0 m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc b\u1ec1 ngang 3 m\u00e9t, chi\u1ec1u d\u00e0i 6 m\u00e9t, \u0111\u1ec9nh tr\u1ea1i c\u00e1ch n\u1ec1n 3 m\u00e9t. T\u00ednh th\u1ec3 t\u00edch (\u0111\u01a1n v\u1ecb m$^3$) ph\u1ea7n kh\u00f4ng gian b\u00ean trong tr\u1ea1i.\n <div class=\"quicklatex\" style=\"display: flex; justify-content: center; margin: 0px 0;\">\n <p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-9851a39be6070f747c6766ee93348314_l3.svg\" height=\"227\" width=\"271\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n <\/div>\n \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"$36$\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-3\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> M\u1ed9t v\u1eadn \u0111\u1ed9ng vi\u00ean b\u00f3ng chuy\u1ec1n khi ph\u00e1t b\u00f3ng, b\u00f3ng di chuy\u1ec3n theo m\u1ed9t \u0111\u01b0\u1eddng cong tr\u00ean\\m\u1eb7t ph\u1eb3n ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t s\u00e2n v\u00e0 r\u01a1i \u1edf v\u1ecb tr\u00ed c\u00e1ch\n v\u1eadn \u0111\u1ed9ng vi\u00ean 10 m\u00e9t v\u00e0 l\u1ec7ch v\u1ec1 h\u01b0\u1edbng tay ph\u1ea3i c\u1ee7a v\u1eadn \u0111\u1ed9ng vi\u00ean \u0111\u00f3 6 m\u00e9t. Ng\u01b0\u1eddi ta minh h\u1ecda l\u1ea1i v\u1ecb tr\u00ed c\u1ee7a v\u1eadn \u0111\u1ed9ng vi\u00ean tr\u00ean s\u00e2n v\u00e0 k\u00edch th\u01b0\u1edbc c\u1ee7a s\u00e2n trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy nh\u01b0 h\u00ecnh d\u01b0\u1edbi. N\u1ebfu ch\u1ecdn tr\u1ee5c Oz h\u01b0\u1edbng th\u1eb3ng \u0111\u1ee9ng h\u01b0\u1edbng t\u1eeb d\u01b0\u1edbi \u0111\u1ea5t l\u00ean tr\u00ean th\u00ec m\u1eb7t ph\u1eb3ng ch\u1ee9a \u0111\u01b0\u1eddng \u0111i c\u1ee7a qu\u1ea3 b\u00f3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh d\u1ea1ng $ax+by+cz-1=0$. Gi\u00e1 tr\u1ecb c\u1ee7a a+b+c l\u00e0 bao nhi\u00eau. <div class=\"quicklatex\" style=\"display: flex; justify-content: center; margin: 15px 0;\">\n <p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-ecac14f4e1faad612cacecbe3b0511f2_l3.svg\" height=\"190\" width=\"360\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n <\/div>\n \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"1\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-4\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> Trong kh\u00f4ng ph\u1eadn, c\u00f3 m\u1ed9t v\u00f9ng c\u1ea5m bay \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi hai m\u1eb7t ph\u1eb3ng song song, t\u1ea1o th\u00e0nh m\u1ed9t d\u1ea3i kh\u00f4ng gian m\u00e0 m\u00e1y bay kh\u00f4ng \u0111\u01b0\u1ee3c ph\u00e9p \u0111i v\u00e0o. Ta c\u00f3 th\u1ec3 hi\u1ec3u, v\u00f9ng c\u1ea5m bay ch\u00ednh l\u00e0 t\u1eadp c\u00e1c \u0111i\u1ec3m $M$ trong kh\u00f4ng gian gi\u1edbi h\u1ea1n b\u1edfi hai m\u1eb7t $(P)$ v\u00e0 $(Q)$ (bao g\u1ed3m c\u1ea3 $(P)$ v\u00e0 $(Q)$). \u0110\u1ec3 \u0111\u1ea3m b\u1ea3o an to\u00e0n, l\u1ed9 tr\u00ecnh bay c\u1ea7n \u0111\u01b0\u1ee3c thi\u1ebft l\u1eadp sao cho lu\u00f4n n\u1eb1m ngo\u00e0i v\u00f9ng c\u1ea5m n\u00e0y. G\u1ecdi $d_1,d_2$ t\u01b0\u01a1ng \u1ee9ng l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb M \u0111\u1ebfn $(P)$ v\u00e0 $(Q)$; $d$ l\u00e0 kho\u1ea3ng c\u00e1ch gi\u1eefa $(P)$ v\u00e0 $(Q)$.\n<ul style= \"margin-bottom: 0em;padding-left: 20px\">\n <li>N\u1ebfu \u0111i\u1ec3m $M$ n\u1eb1m trong v\u00f9ng c\u1ea5m bay $S$, ta n\u00f3i kho\u1ea3ng c\u00e1ch t\u1eeb $M$ \u0111\u1ebfn $S$ b\u1eb1ng $0$.<\/li>\n <li>N\u1ebfu \u0111i\u1ec3m $M$ n\u1eb1m ngo\u00e0i v\u00f9ng c\u1ea5m bay $S$, ta n\u00f3i kho\u1ea3ng c\u00e1ch t\u1eeb $M$ \u0111\u1ebfn $S$ b\u1eb1ng gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $d_1$ v\u00e0 $d_2$<\/li>\n<\/ul>\nTrong kh\u00f4ng gian $Oxyz$, v\u00f9ng c\u1ea5m bay \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi hai m\u1eb7t ph\u1eb3ng $(P)\\colon x + 4y – 2z + 7 = 0$ v\u00e0 $(Q)\\colon x + 4y – 2z + 12 = 0$. Khi m\u00e1y bay \u1edf v\u1ecb tr\u00ed $M(3;1;3)$ th\u00ec kho\u1ea3ng c\u00e1ch t\u1eeb m\u00e1y bay \u0111\u1ebfn v\u00f9ng c\u1ea5m $S$ l\u00e0 bao nhi\u00eau \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"0\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-5\"> \n <\/span> \n <\/div>\n \n <div class=\"question\">\n <h2> Cho hai m\u1eb7t ph\u1ea3ng c\u1eaft nhau $(P)\\colon x+y+2z-12=0$ v\u00e0 $(Q)\\colon 2x-y+z-3=0$. X\u00e9t g\u00f3c g\u00f3c nh\u1ecb di\u1ec7n $\\alpha$ t\u1ea1o b\u1edfi $(P)$ v\u00e0 $(Q)$ sao cho kh\u00f4ng gian b\u1ecb gi\u1edbi h\u1ea1n b\u1edfi $\\alpha$ ch\u1ee9a $M(4;8;6)$. H\u00e3y x\u00e1c \u0111\u1ecbnh s\u1ed1 \u0111o c\u1ee7a g\u00f3c $\\alpha$ (t\u00ednh b\u1eb1ng \u0111\u1ed9 v\u00e0 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng \u0111\u01a1n v\u1ecb). \n <\/h2>\n <span class=\"blank-container\"> \n <input type=\"text\" class=\"blank\" data-value=\"$120$\" placeholder=\"\u0110i\u1ec1n v\u00e0o \u0111\u00e2y\" oninput=\"updatePreview(this)\"> \n <\/span> \n <span class=\"preview\" id=\"preview-6\"> \n <\/span> \n <\/div>\n \n<\/div>\n\n\n<form id=\"scoreForm\">\n <label for=\"name\">T\u00ean:<\/label>\n <input type=\"text\" id=\"name\" name=\"name\" required><br><br> \n<\/form>\n\n<\/form>\n<button type=\"button\" id=\"submit-button\">N\u1ed9p b\u00e0i<\/button>\n<div id=\"result\"><\/div>\n\n<script>\ndocument.addEventListener(\"DOMContentLoaded\", function () {\n \/\/ T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c div ch\u1ee9a class=\"quicklatex\" \u0111\u1ec3 b\u1ecf qua khi render KaTeX\n const quicklatexElements = document.querySelectorAll('div.quicklatex');\n\n \/\/ KaTeX render c\u00f4ng th\u1ee9c b\u00ecnh th\u01b0\u1eddng cho to\u00e0n b\u1ed9 trang, ngo\u1ea1i tr\u1eeb c\u00e1c div.quicklatex\n renderMathInElement(document.body, {\n delimiters: [\n {left: '<p class=\"ql-center-displayed-equation\" style=\"line-height: 20px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sunflower-math.com\/wp-content\/ql-cache\/quicklatex.com-77baa04537073105b02318b995c7964b_l3.svg\" height=\"20\" width=\"70\" class=\"ql-img-displayed-equation \" alt=\"\[', right: '\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>', display: true},\n {left: '$', right: '$', display: false}\n ],\n ignoredElements: ['div.quicklatex'] \/\/ B\u1ecf qua div.quicklatex khi render KaTeX\n });\n\n \/\/ Sau khi KaTeX render xong, QuickLaTeX x\u1eed l\u00fd c\u00e1c c\u00f4ng th\u1ee9c trong div.quicklatex\n quicklatexElements.forEach(function(element) {\n const latex = element.innerText; \/\/ L\u1ea5y n\u1ed9i dung latex trong div.quicklatex\n QuickLaTeX.render(latex, element); \/\/ D\u00f9ng QuickLaTeX \u0111\u1ec3 render c\u00f4ng th\u1ee9c\n });\n});\n\n<\/script>\n\n\n<script>\n\/\/ Move this outside of calculateScore\n \n\n function updatePreview(input) {\n const previewElement = input.closest('.blank-container').nextElementSibling;\n \n let userAnswer = input.value.trim();\n\n if (!userAnswer) {\n previewElement.style.display = 'none'; \/\/ \u1ea8n khi kh\u00f4ng c\u00f3 n\u1ed9i dung\n previewElement.innerHTML = '';\n return;\n }\n\n previewElement.style.display = 'block'; \/\/ Hi\u1ec3n th\u1ecb khi c\u00f3 n\u1ed9i dung\n\n try {\n katex.render(userAnswer, previewElement, {\n throwOnError: false \/\/ Kh\u00f4ng b\u00e1o l\u1ed7i khi c\u00fa ph\u00e1p LaTeX sai\n });\n } catch (err) {\n previewElement.innerHTML = 'L\u1ed7i c\u00f4ng th\u1ee9c LaTeX!';\n }\n }\n\nfunction normalizeLatex(latex) {\n latex = latex.replace(\/\\s+\/g, ' ').trim();\n latex = latex.replace(\/\\\\dfrac{([^}]*)}{([^}]*)}\/g, (match, num, denom) => {\n return `\\\\dfrac{${num.trim()}}{${denom.trim()}}`;\n });\n latex = latex.replace(\/\\\\pm\/g, '\u00b1')\n .replace(\/\\\\sqrt{([^}]*)}\/g, '\u221a($1)')\n .replace(\/\\\\frac{([^}]*)}{([^}]*)}\/g, '($1)\/($2)')\n .replace(\/\\\\dfrac{([^}]*)}{([^}]*)}\/g, '($1)\/($2)');\n return latex;\n}\n\n<\/script>\n<script>\nlet totalScore = 0;\n\nfunction calculateScore() {\n totalScore = 0; \/\/ \u0110\u1eb7t l\u1ea1i \u0111i\u1ec3m tr\u01b0\u1edbc khi t\u00ednh to\u00e1n\n const sections = document.querySelectorAll('.section');\n\n \/\/ Part 1: Multiple Choice\n const question1 = sections[0].querySelectorAll('.question');\n question1.forEach(question => {\n const selectedRadio = question.querySelector('input[type=\"radio\"]:checked');\n if (selectedRadio && selectedRadio.dataset.value === \"true\") {\n totalScore+=2.5; \/\/ 2.5 point for each correct answer\n }\n });\n\n \/\/ Part 2: True\/False\n const question2 = sections[1].querySelectorAll('.question');\n question2.forEach(question => {\n let reasonableCount = 0;\n const checkboxes = question.querySelectorAll('input[type=\"checkbox\"]');\n checkboxes.forEach(checkbox => {\n const isChecked = checkbox.checked;\n const isTrueValue = checkbox.dataset.value === \"true\";\n if (isChecked && isTrueValue || !isChecked && !isTrueValue) {\n reasonableCount++;\n }\n });\n\t\tfunction calculatePoints(reasonableCount) {\n switch (reasonableCount) {\n case 1: return 1;\n case 2: return 2.5;\n case 3: return 5;\n case 4: return 10;\n default: return 0;\n }\n } \n totalScore += calculatePoints(reasonableCount);\n });\n\n \/\/ Part 3: Fill in the blanks\n const question3 = sections[2].querySelectorAll('.question');\n question3.forEach(question => {\n const blank = question.querySelector('input[type=\"text\"]');\n const userAnswer = normalizeLatex(blank.value.trim());\n const correctAnswer = normalizeLatex(blank.dataset.value.trim());\n if (userAnswer === correctAnswer) {\n totalScore += 5; \/\/ 5 points for each correct answer\n }\n });\n\n const maxScore = question1.length*2.5 + question2.length*10 + question3.length*5 ;\n document.getElementById('result').innerText = `T\u1ed5ng \u0111i\u1ec3m: ${totalScore} \/ ${maxScore}`;\n}\n\n\t\/\/ Attach event listener correctly\ndocument.getElementById('submit-button').addEventListener('click', function() {\n calculateScore(); \/\/ T\u00ednh \u0111i\u1ec3m\n\n const name = document.getElementById('name').value;\n\n \/\/ Ki\u1ec3m tra xem t\u00ean c\u00f3 \u0111\u01b0\u1ee3c nh\u1eadp v\u00e0 \u0111i\u1ec3m c\u00f3 h\u1ee3p l\u1ec7\n if (!name || totalScore === 0) {\n alert('Vui l\u00f2ng nh\u1eadp t\u00ean v\u00e0 ch\u1eafc ch\u1eafn r\u1eb1ng b\u1ea1n \u0111\u00e3 l\u00e0m b\u00e0i.');\n return; \/\/ Ng\u1eebng n\u1ebfu kh\u00f4ng h\u1ee3p l\u1ec7\n }\n\n \/\/ G\u1eedi d\u1eef li\u1ec7u \u0111\u1ebfn server\n fetch('https:\/\/script.google.com\/macros\/s\/AKfycbzHg2x_X-slmAnt2W8uyaDLz6dPr1o96E73Xc8MTlcz6N-uHLJ65DFTGwPI_MuU9X1-\/exec', {\n method: 'POST',\n headers: {\n 'Content-Type': 'application\/x-www-form-urlencoded',\n },\n body: `name=${encodeURIComponent(name)}&score=${encodeURIComponent(totalScore)}`\n })\n .then(response => response.text())\n .then(data => {\n alert('G\u1eedi th\u00e0nh c\u00f4ng!');\n document.getElementById('scoreForm').reset(); \/\/ \u0110\u1eb7t l\u1ea1i form sau khi g\u1eedi\n totalScore = 0; \/\/ \u0110\u1eb7t l\u1ea1i \u0111i\u1ec3m sau khi g\u1eedi\n document.getElementById('result').innerText = ''; \/\/ X\u00f3a k\u1ebft qu\u1ea3\n })\n .catch(error => console.error('L\u1ed7i:', error));\n});\t\n\n\n \/\/ \u0110\u1ebfm s\u1ed1 c\u00e2u h\u1ecfi trong t\u1eebng section\n const section1Count = document.querySelectorAll('#section-1 .question').length;\n const section2Count = document.querySelectorAll('#section-2 .question').length;\n const section3Count = document.querySelectorAll('#section-3 .question').length;\n\n \n \/\/ C\u1eadp nh\u1eadt counter-reset cho t\u1eebng section\n document.getElementById('section-2').style.setProperty('counter-reset', `question ${section1Count}`);\n document.getElementById('section-3').style.setProperty('counter-reset', `question ${section1Count + section2Count}`); \n\n \/\/ Thay \u0111\u1ed5i s\u1ed1 gi\u00e2y theo y\u00eau c\u1ea7u c\u1ee7a b\u1ea1n\n const totalTime = 5460; \/\/ Th\u1eddi gian t\u1ed5ng c\u1ed9ng cho b\u00e0i test (600 gi\u00e2y = 10 ph\u00fat)\n let timeLeft = totalTime;\n\n const timerElement = document.getElementById('timer');\n\n function updateTimer() {\n const minutes = Math.floor(timeLeft \/ 60);\n const seconds = timeLeft % 60;\n timerElement.innerText = `Th\u1eddi gian c\u00f2n l\u1ea1i: ${minutes}:${seconds < 91 ? '' : '0'}${seconds}`;\n \n if (timeLeft > 0) {\n timeLeft--;\n } else {\n clearInterval(timerInterval);\n alert(\"Th\u1eddi gian \u0111\u00e3 h\u1ebft! B\u00e0i test s\u1ebd t\u1ef1 \u0111\u1ed9ng n\u1ed9p.\");\n document.getElementById('quiz-form').submit(); \/\/ T\u1ef1 \u0111\u1ed9ng n\u1ed9p b\u00e0i test\n }\n }\n\n const timerInterval = setInterval(updateTimer, 1000); \/\/ C\u1eadp nh\u1eadt m\u1ed7i gi\u00e2y\n\n<\/script> \n <\/body>\n <\/html>\n","protected":false},"excerpt":{"rendered":"<p>B\u00e0i Test Tr\u1eafc Nghi\u1ec7m 1. Ph\u1ea7n tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn Trong kh\u00f4ng gian $Oxyz$, ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a m\u1eb7t ph\u1eb3ng $(P)$ \u0111i qua \u0111i\u1ec3m $B(2;1;-3)$, \u0111\u1ed3ng th\u1eddi vu\u00f4ng g\u00f3c v\u1edbi hai m\u1eb7t ph\u1eb3ng $(Q)\\colon x + y + 3z = 0$, $(R)\\colon 2x – y + z = 0$ l\u00e0 $2x + y – 3z […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1290","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/posts\/1290","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1290"}],"version-history":[{"count":95,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/posts\/1290\/revisions"}],"predecessor-version":[{"id":1393,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=\/wp\/v2\/posts\/1290\/revisions\/1393"}],"wp:attachment":[{"href":"https:\/\/sunflower-math.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1290"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1290"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sunflower-math.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}