{"id":522,"date":"2026-05-05T04:50:13","date_gmt":"2026-05-05T04:50:13","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh\/"},"modified":"2026-05-05T07:23:33","modified_gmt":"2026-05-05T07:23:33","slug":"de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh\/","title":{"rendered":"\u0110\u1ec1 ki\u1ec3m tra ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Qu\u1ebf V\u00f5 1 B\u1eafc Ninh"},"content":{"rendered":"<p><strong>\u0110\u1ec1 ki\u1ec3m tra ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Qu\u1ebf V\u00f5 1 B\u1eafc Ninh <\/strong>l\u00e0 t\u00e0i li\u1ec7u gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng v\u00e0 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c tr\u01b0\u1edbc k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT. \u0110\u1ec1 thi bao g\u1ed3m 22 c\u00e2u h\u1ecfi \u0111a d\u1ea1ng, t\u1eeb b\u00e0i t\u1eadp c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, ki\u1ec3m tra to\u00e0n di\u1ec7n ki\u1ebfn th\u1ee9c \u0110\u1ea1i s\u1ed1 v\u00e0 H\u00ecnh h\u1ecdc kh\u00f4ng gian. C\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u Mi\u1ec5n Ph\u00ed<\/strong><\/a> t\u00ecm hi\u1ec3u chi ti\u1ebft v\u1ec1 \u0111\u1ec1 thi n\u00e0y.<\/p>\n<h2><strong>N\u1ed9i dung <span data-sheets-root=\"1\">\u0110\u1ec1 ki\u1ec3m tra ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Qu\u1ebf V\u00f5 1 B\u1eafc Ninh<\/span><\/strong><\/h2>\n<h3><strong>Th\u00f4ng tin \u0111\u1ec1 thi<\/strong><\/h3>\n<p><strong>Th\u1eddi gian l\u00e0m b\u00e0i:<\/strong> 50 ph\u00fat (kh\u00f4ng k\u1ec3 th\u1eddi gian ph\u00e1t \u0111\u1ec1)<\/p>\n<p><strong>C\u1ea5u tr\u00fac \u0111\u1ec1 thi:<\/strong> G\u1ed3m 3 ph\u1ea7n v\u1edbi t\u1ed5ng c\u1ed9ng 22 c\u00e2u h\u1ecfi<\/p>\n<ul>\n<li><strong>Ph\u1ea7n I:<\/strong> 12 c\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/li>\n<li><strong>Ph\u1ea7n II:<\/strong> 4 c\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/li>\n<li><strong>Ph\u1ea7n III:<\/strong> 6 c\u00e2u h\u1ecfi tr\u1ea3 l\u1eddi ng\u1eafn<\/li>\n<\/ul>\n<h3><strong>N\u1ed9i dung \u0111\u1ec1 thi<\/strong><\/h3>\n<p><a href=\"https:\/\/tailieuonthi.edu.vn\/de-khao-sat-chat-luong-toan-12\/\" rel=\"noopener\" target=\"_blank\">\u0110\u1ec1 kh\u1ea3o s\u00e1t ch\u1ea5t l\u01b0\u1ee3ng to\u00e1n 12<\/a> bao g\u1ed3m nhi\u1ec1u d\u1ea1ng b\u00e0i t\u1eadp ti\u00eau bi\u1ec3u t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao nh\u01b0:<\/p>\n<p><span><strong>Ph\u1ea7n I: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (12 c\u00e2u)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 $y = f(x)$ c\u00f3 b\u1ea3ng x\u00e9t d\u1ea5u \u0111\u1ea1o h\u00e0m nh\u01b0 sau:<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter wp-image-2688 size-full\" decoding=\"async\" height=\"65\" sizes=\"auto, (max-width: 605px) 100vw, 605px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh-1.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh-1.jpg 605w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh-1-300x32.jpg 300w\" width=\"605\"\/><\/p>\n<p>M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y <strong>\u0111\u00fang<\/strong>?<\/p>\n<p>A. H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng $(-\\infty;-2)$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng $(-2;0)$<br \/>\nC. H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng $(-\\infty;0)$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng $(0;2)$<\/p>\n<p><strong>C\u00e2u 2.<\/strong> \u0110\u1ed3 th\u1ecb b\u00ean d\u01b0\u1edbi l\u00e0 t\u1ed1c \u0111\u1ed9 c\u1ee7a m\u1ed9t chi\u1ebfc xe \u0111ua tr\u00ean \u0111o\u1ea1n \u0111\u01b0\u1eddng \u0111ua b\u1eb1ng ph\u1eb3ng d\u00e0i 3 km.<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter wp-image-2689 size-full\" decoding=\"async\" height=\"241\" sizes=\"auto, (max-width: 383px) 100vw, 383px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh-2.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh-2.jpg 383w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh-2-300x189.jpg 300w\" width=\"383\"\/><\/p>\n<p>T\u1ed1c \u0111\u1ed9 nh\u1ecf nh\u1ea5t c\u1ee7a xe \u0111ua tr\u00ean \u0111o\u1ea1n \u0111\u01b0\u1eddng n\u00e0y b\u1eb1ng:<\/p>\n<p>A. $3 km\/h$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. $160 km\/h$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. $130 km\/h$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. $70 km\/h$<\/p>\n<p><span><strong>Ph\u1ea7n II: Tr\u1eafc nghi\u1ec7m \u0111\u00fang sai (4 c\u00e2u)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 $y = f(x) = \\frac{x^2 + 2x \u2013 2}{x \u2013 1}$ c\u00f3 \u0111\u1ed3 th\u1ecb $(C)$. C\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau \u0111\u00e2y \u0111\u00fang hay sai?<\/p>\n<p>a) H\u00e0m s\u1ed1 \u0111\u00e3 cho ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng $(0;2)$<br \/>\nb) \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a $(C)$ c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $y = x + 3$<br \/>\nc) Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 $y = f(x)$ tr\u00ean \u0111o\u1ea1n $[2;4]$ b\u1eb1ng $\\frac{13}{2}$<br \/>\nd) C\u00f3 3 s\u1ed1 nguy\u00ean d\u01b0\u01a1ng $m$ \u0111\u1ec3 h\u00e0m s\u1ed1 $y = \\frac{x^2 + 2x \u2013 m}{x \u2013 1}$ c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb<\/p>\n<p><strong>C\u00e2u 2.<\/strong> Trong bu\u1ed5i sinh ho\u1ea1t nh\u00f3m c\u1ee7a l\u1edbp, t\u1ed5 m\u1ed9t c\u00f3 12 h\u1ecdc sinh g\u1ed3m 4 h\u1ecdc sinh n\u1eef trong \u0111\u00f3 c\u00f3 B\u00ed th\u01b0 v\u00e0 8 h\u1ecdc sinh nam trong \u0111\u00f3 c\u00f3 L\u1edbp tr\u01b0\u1edfng. Chia t\u1ed5 th\u00e0nh 3 nh\u00f3m, m\u1ed7i nh\u00f3m g\u1ed3m 4 h\u1ecdc sinh v\u00e0 ph\u1ea3i c\u00f3 \u00edt nh\u1ea5t 1 h\u1ecdc sinh n\u1eef. G\u1ecdi $A$ l\u00e0 bi\u1ebfn c\u1ed1: \u201cL\u1edbp tr\u01b0\u1edfng v\u00e0 B\u00ed th\u01b0 \u0111\u01b0\u1ee3c chia c\u00f9ng m\u1ed9t nh\u00f3m\u201d. C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n<p>a) Nh\u00f3m nhi\u1ec1u nh\u1ea5t c\u00f3 2 h\u1ecdc sinh n\u1eef<br \/>\nb) S\u1ed1 ph\u1ea7n t\u1eed c\u1ee7a kh\u00f4ng gian m\u1eabu l\u00e0 $n(\\Omega) = 6720$<br \/>\nc) S\u1ed1 ph\u1ea7n t\u1eed c\u1ee7a bi\u1ebfn c\u1ed1 $A$ l\u00e0 $n(A) = 2100$<br \/>\nd) X\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 $A$ l\u00e0 $\\frac{7}{32}$<\/p>\n<p><span><strong>Ph\u1ea7n III: C\u00e2u h\u1ecfi tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u)<\/strong><\/span><\/p>\n<p><strong>C\u00e2u 1.<\/strong> G\u1ecdi $M, m$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 $y = \\frac{3\\sin x + 2}{\\sin x + 1}$ tr\u00ean \u0111o\u1ea1n $[0; \\frac{\\pi}{2}]$. Khi \u0111\u00f3 gi\u00e1 tr\u1ecb c\u1ee7a $M^2 + m^2 = \\frac{b}{c}$, t\u00ednh $T = b \u2013 c$.<\/p>\n<p><strong>C\u00e2u 2.<\/strong> M\u1ed9t t\u00ean l\u1eeda bay v\u00e0o kh\u00f4ng trung v\u1edbi qu\u00e3ng \u0111\u01b0\u1eddng \u0111i \u0111\u01b0\u1ee3c l\u00e0 $s(t)(km)$ l\u00e0 h\u00e0m ph\u1ee5 thu\u1ed9c theo bi\u1ebfn $t$ (gi\u00e2y), tu\u00e2n theo bi\u1ec3u th\u1ee9c sau: $s(t) = e^{t^2+3} + 2te^{t+1} (km)$. H\u1ecfi v\u1eadn t\u1ed1c c\u1ee7a t\u00ean l\u1eeda sau 1 gi\u00e2y l\u00e0 bao nhi\u00eau (bi\u1ebft h\u00e0m bi\u1ec3u th\u1ecb v\u1eadn t\u1ed1c l\u00e0 \u0111\u1ea1o h\u00e0m c\u1ea5p m\u1ed9t c\u1ee7a h\u00e0m bi\u1ec3u th\u1ecb qu\u00e3ng \u0111\u01b0\u1eddng theo th\u1eddi gian) $ae^b (km\/s)$. T\u00ednh $a + 2b$.<\/p>\n<p><strong>C\u00e2u 3.<\/strong> M\u1ed9t t\u1ea5m v\u1ea3i h\u00ecnh ch\u1eef nh\u1eadt $ABCD$ \u0111\u01b0\u1ee3c d\u00f9ng l\u00e0m m\u1eb7t ph\u1eb3ng nghi\u00eang \u0111\u1ec3 k\u00e9o m\u1ed9t v\u1eadt l\u00ean kh\u1ecfi h\u1ed1 s\u00e2u $2m$. Cho bi\u1ebft $AB = 1m, AD = 3,5m$. T\u00ednh g\u00f3c (theo \u0111\u01a1n v\u1ecb \u0111\u1ed9) gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng $BD$ v\u00e0 \u0111\u00e1y h\u1ed1 (l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n m\u01b0\u1eddi).<\/p>\n<p><img alt=\"\" class=\"aligncenter wp-image-2690 size-full\" decoding=\"async\" height=\"207\" loading=\"lazy\" sizes=\"auto, (max-width: 625px) 100vw, 625px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh-3.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh-3.jpg 625w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/04\/de-kiem-tra-chat-luong-mon-toan-12-nam-2024-2025-truong-thpt-que-vo-1-bac-ninh-3-300x99.jpg 300w\" width=\"625\"\/><\/p>\n<h2><strong>T\u1ea3i <span data-sheets-root=\"1\">\u0110\u1ec1 ki\u1ec3m tra ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Qu\u1ebf V\u00f5 1 B\u1eafc Ninh<\/span><\/strong><\/h2>\n<p><strong>\u0110\u1ec1 ki\u1ec3m tra ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Qu\u1ebf V\u00f5 1 B\u1eafc Ninh<\/strong> \u0111i k\u00e8m \u0111\u00e1p \u00e1n v\u00e0 h\u01b0\u1edbng d\u1eabn gi\u1ea3i chi ti\u1ebft gi\u00fap h\u1ecdc sinh t\u1ef1 luy\u1ec7n t\u1eadp v\u00e0 chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t cho k\u1ef3 thi s\u1eafp t\u1edbi. T\u1ea3i ngay \u0111\u1ec1 thi n\u00e0y \u0111\u1ec3 luy\u1ec7n t\u1eadp!<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1FLgge4ocyeH6jZb_0CzTgfx_pFp7jZqO\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1FLgge4ocyeH6jZb_0CzTgfx_pFp7jZqO\/view\" rel=\"nofollow noopener\" target=\"_blank\">M\u1edf t\u00e0i li\u1ec7u n\u1ebfu khung xem tr\u01b0\u1edbc kh\u00f4ng hi\u1ec3n th\u1ecb<\/a><\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1FLgge4ocyeH6jZb_0CzTgfx_pFp7jZqO\/view\" rel=\"noopener nofollow\" target=\"_blank\">T\u1ea3i \u0110\u1ec1 ki\u1ec3m tra ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Qu\u1ebf V\u00f5 1 B\u1eafc Ninh<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 ki\u1ec3m tra ch\u1ea5t l\u01b0\u1ee3ng m\u00f4n To\u00e1n 12 n\u0103m 2024 \u2013 2025 tr\u01b0\u1eddng THPT Qu\u1ebf V\u00f5 1 B\u1eafc Ninh l\u00e0 t\u00e0i li\u1ec7u gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng v\u00e0 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c tr\u01b0\u1edbc k\u1ef3 thi t\u1ed1t nghi\u1ec7p THPT. \u0110\u1ec1 thi bao g\u1ed3m 22 c\u00e2u h\u1ecfi \u0111a d\u1ea1ng, t\u1eeb b\u00e0i t\u1eadp c\u01a1 b\u1ea3n \u0111\u1ebfn [&#8230;]\n","protected":false},"author":1,"featured_media":1721,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60],"tags":[61],"class_list":["post-522","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tong-hop","tag-tong-hop"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/522","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=522"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/522\/revisions"}],"predecessor-version":[{"id":1722,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/522\/revisions\/1722"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1721"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=522"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=522"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}