{"id":462,"date":"2026-05-05T04:47:05","date_gmt":"2026-05-05T04:47:05","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/10-de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gddt-bac-giang\/"},"modified":"2026-05-05T07:20:06","modified_gmt":"2026-05-05T07:20:06","slug":"10-de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gddt-bac-giang","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/10-de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gddt-bac-giang\/","title":{"rendered":"10 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 s\u1edf GD&#038;\u0110T B\u1eafc Giang"},"content":{"rendered":"<p>T\u1eadp <strong>10 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 s\u1edf GD&amp;\u0110T B\u1eafc Giang<\/strong> l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u \u0111\u1eafc l\u1ef1c h\u1ed7 tr\u1ee3 c\u00e1c b\u1ea1n h\u1ecdc sinh 12 chu\u1ea9n b\u1ecb ki\u1ebfn th\u1ee9c v\u00e0 k\u0129 n\u0103ng cho k\u00ec thi t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n s\u1eafp t\u1edbi. B\u1ed9 \u0111\u1ec1 thi th\u1eed n\u00e0y \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n v\u00f4 c\u00f9ng chi ti\u1ebft, kh\u00e1ch quan t\u1eebng ph\u1ea7n v\u00e0 c\u00f3 k\u00e8m \u0111\u00e1p \u00e1n l\u1eddi gi\u1ea3i chi ti\u1ebft m\u1ed7i \u0111\u1ec1. Do \u0111\u00f3, c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c \u00f4n t\u1eadp. C\u00f9ng xem qua n\u1ed9i dung b\u1ed9 \u0111\u1ec1 thi n\u00e0y v\u1edbi <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\">T\u00e0i li\u1ec7u \u00d4n Thi<\/a><\/strong> n\u00e0o.<\/p>\n<h2><strong>N\u1ed9i dung 10 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 s\u1edf GD&amp;\u0110T B\u1eafc Giang<\/strong><\/h2>\n<p>B\u1ed9 <strong>10 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 s\u1edf GD&amp;\u0110T B\u1eafc Giang<\/strong> v\u1edbi nhi\u1ec1u d\u1ea1ng \u0111\u1ec1 kh\u00e1c nhau \u0111\u01b0\u1ee3c th\u1ea7y c\u00f4 bi\u00ean so\u1ea1n theo c\u1ea5u tr\u00fac chu\u1ea9n c\u1ee7a \u0111\u1ec1 thi ch\u00ednh th\u1ee9c. M\u1ed7i \u0111\u1ec1 thi c\u00f3 t\u1ea5t c\u1ea3 22 c\u00e2u \u0111\u01b0\u1ee3c chia theo 3 ph\u1ea7n v\u00e0 th\u1eddi gian l\u00e0m b\u00e0i g\u00f3i g\u1ecdn trong 90 ph\u00fat.<\/p>\n<p><strong><span>Ph\u1ea7n I \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m<\/span><\/strong><\/p>\n<p>Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 12. M\u1ed7i c\u00e2u h\u1ecfi th\u00ed sinh ch\u1ec9 \u0111\u01b0\u1ee3c ch\u1ecdn m\u1ed9t ph\u01b0\u01a1ng \u00e1n duy nh\u1ea5t.<\/p>\n<p>C\u00e2u 1. Nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1  f(x) = 4^x  l\u00e0:<\/p>\n<p>A.  (4^x+1)\/(x+1) + C \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.  (4^x)\/(2 ln 2) + C \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  (4^x)\/(x) + C \u00a0 \u00a0 \u00a0 \u00a0 D.  x \u00b7 4^x-1 + C <\/p>\n<p>C\u00e2u 2. X\u00e9t h\u00ecnh ph\u1eb3ng  (H)  gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1  y = x\u00b2 &#8211; 4x + 4 , tr\u1ee5c tung, tr\u1ee5c ho\u00e0nh v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng  x = 3 . T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay khi quay h\u00ecnh  (H)  quanh tr\u1ee5c  Ox .<br \/>\nA.  33 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.  33\/5 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.  33\u03c0\/5 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.  33\u03c0 <\/p>\n<p><span><strong>Ph\u1ea7n II \u2013 C\u00e2u h\u1ecfi \u0111\u00fang sai<\/strong><\/span><\/p>\n<p>Th\u00ed sinh tr\u1ea3 l\u1eddi t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 4. Trong m\u1ed7i \u00fd a), b), c), d), \u1edf m\u1ed7i c\u00e2u th\u00ed sinh c\u1ea7n ch\u1ecdn m\u1ec7nh \u0111\u1ec1 \u0111\u00fang hay sai. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi c\u1ee7a ph\u1ea7n 2 nh\u01b0 sau:<\/p>\n<p>C\u00e2u 1. Cho h\u00e0m s\u1ed1  f(x) = 2cos x &#8211; x + \u03c0 .<\/p>\n<p>a)  f(\u03c0) = -2 .<\/p>\n<p>b) \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0  f'(x) = 2sin x &#8211; 1.\n<\/p>\n<p>c) S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh  f'(x) = 0  tr\u00ean \u0111o\u1ea1n  [ -\u03c0\/2, \u03c0\/2 ] l\u00e0 2.<\/p>\n<p>d) Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a  f(x)  tr\u00ean \u0111o\u1ea1n  [ -\u03c0\/2, \u03c0\/2 ] l\u00e0  \u03c0\/2 .<\/p>\n<p>C\u00e2u 2. M\u1ed9t ng\u01b0\u1eddi \u0111i\u1ec1u khi\u1ec3n \u00f4 t\u00f4 \u0111ang \u1edf \u0111\u01b0\u1eddng d\u1eabn mu\u1ed1n nh\u1eadp l\u00e0n v\u00e0o \u0111\u01b0\u1eddng cao t\u1ed1c. Khi \u00f4 t\u00f4 c\u00e1ch \u0111i\u1ec3m nh\u1eadp l\u00e0n 240 m, t\u1ed1c \u0111\u1ed9 c\u1ee7a \u00f4 t\u00f4 l\u00e0 28,8 km\/h. B\u1ed1n gi\u00e2y sau \u0111\u00f3, \u00f4 t\u00f4 b\u1eaft \u0111\u1ea7u t\u0103ng t\u1ed1c v\u1edbi t\u1ed1c \u0111\u1ed9  v(t) = at + b (m\/s), (a, b in mathbbR, a &gt; 0),<br \/>\ntrong \u0111\u00f3  t  l\u00e0 th\u1eddi gian t\u00ednh b\u1eb1ng gi\u00e2y k\u1ec3 t\u1eeb khi b\u1eaft \u0111\u1ea7u t\u0103ng t\u1ed1c. Bi\u1ebft r\u1eb1ng \u00f4 t\u00f4 nh\u1eadp l\u00e0n cao t\u1ed1c sau 16 gi\u00e2y v\u00e0 duy tr\u00ec s\u1ef1 t\u0103ng t\u1ed1c trong 30 gi\u00e2y k\u1ec3 t\u1eeb khi b\u1eaft \u0111\u1ea7u t\u0103ng t\u1ed1c.<\/p>\n<p>a) Qu\u00e3ng \u0111\u01b0\u1eddng \u00f4 t\u00f4 \u0111i \u0111\u01b0\u1ee3c t\u1eeb khi b\u1eaft \u0111\u1ea7u t\u0103ng t\u1ed1c \u0111\u1ebfn khi nh\u1eadp l\u00e0n l\u00e0 208 m.<\/p>\n<p>b) Gi\u00e1 tr\u1ecb c\u1ee7a  b  l\u00e0 8.<\/p>\n<p>c) Qu\u00e3ng \u0111\u01b0\u1eddng  S(t) (\u0111\u01a1n v\u1ecb: m\u00e9t) m\u00e0 \u00f4 t\u00f4 \u0111i \u0111\u01b0\u1ee3c trong th\u1eddi gian  t  gi\u00e2y  (0 \u2264 t \u2264 30)  k\u1ec3 t\u1eeb khi t\u0103ng t\u1ed1c \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c  S(t) = int\u2080^t v(t) dt.\n<\/p>\n<p>d) Sau 30 gi\u00e2y k\u1ec3 t\u1eeb khi t\u0103ng t\u1ed1c, t\u1ed1c \u0111\u1ed9 c\u1ee7a \u00f4 t\u00f4 c\u00f3 th\u1ec3 v\u01b0\u1ee3t qu\u00e1 t\u1ed1c \u0111\u1ed9 t\u1ed1i \u0111a cho ph\u00e9p l\u00e0 100 km\/h.<\/p>\n<p><strong><span>Ph\u1ea7n III \u2013 C\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn<\/span><\/strong><\/p>\n<p>Ph\u1ea7n n\u00e0y s\u1ebd c\u00f3 6 c\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn, th\u00ed sinh n\u00ean \u0111\u1ecdc th\u1eadt k\u0129 \u0111\u1ec1 v\u00e0 t\u01b0 duy gi\u1ea3i \u0111\u1ec1 ch\u00ednh x\u00e1c nh\u1ea5t nh\u00e9. C\u00f9ng \u00d4n Thi l\u00e0m quen v\u1edbi c\u00e1c d\u1ea1ng c\u00e2u h\u1ecfi n\u00e0y trong <span data-sheets-root=\"1\"><a href=\"https:\/\/tailieuonthi.edu.vn\/de-thi-thu-thpt\/de-thi-thu-thpt-mon-toan\/\" rel=\"noopener\" target=\"_blank\">\u0111\u1ec1 thi th\u1eed thpt qu\u1ed1c gia m\u00f4n to\u00e1n 2025<\/a> sau \u0111\u00e2y:<\/span><\/p>\n<p>C\u00e2u 1. Cho h\u00ecnh ch\u00f3p tam gi\u00e1c  S.ABC  c\u00f3  SA, AB, AC  \u0111\u00f4i m\u1ed9t vu\u00f4ng g\u00f3c. Bi\u1ebft r\u1eb1ng  SA = 5, AB = 3, AC = 4. Kho\u1ea3ng c\u00e1ch gi\u1eefa  SA  v\u00e0  BC  l\u00e0 bao nhi\u00eau?<\/p>\n<p>C\u00e2u 2. Cho t\u1ee9 di\u1ec7n  ABCD , m\u1ed9t con b\u1ecd \u0111ang \u0111\u1eadu \u1edf \u0111\u1ec9nh  A  c\u1ee7a t\u1ee9 di\u1ec7n. M\u1ed7i l\u1ea7n nghe m\u1ed9t ti\u1ebfng tr\u1ed1ng th\u00ec n\u00f3 nh\u1ea3y sang m\u1ed9t \u0111\u1ec9nh b\u1ea5t k\u00ec c\u1ee7a t\u1ee9 di\u1ec7n  ABCD  m\u00e0 k\u1ec1 v\u1edbi \u0111\u1ec9nh n\u00f3 \u0111ang \u0111\u1eadu. H\u1ecfi sau 4 ti\u1ebfng tr\u1ed1ng n\u00f3 c\u00f3 bao nhi\u00eau c\u00e1ch tr\u1edf v\u1ec1 \u0111\u1ec9nh  A ?<\/p>\n<h2><strong>T\u1ea3i 10 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 s\u1edf GD&amp;\u0110T B\u1eafc Giang<\/strong><\/h2>\n<p>T\u1eadp t\u00e0i li\u1ec7u <strong>10 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 s\u1edf GD&amp;\u0110T B\u1eafc Giang<\/strong> c\u00f3 \u0111\u1ea7y \u0111\u1ee7 c\u00e1c d\u1ea1ng d\u1ec1 t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ebfn n\u00e2ng cao. M\u1ed7i \u0111\u1ec1 s\u1ebd c\u00f3 \u0111\u00e1p \u00e1n v\u00e0 l\u1eddi gi\u1ea3i chi ti\u1ebft gi\u00fap h\u1ecdc sinh chu\u1ea9n b\u1ecb m\u1ed9t l\u1ed9 tr\u00ecnh \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 v\u00e0 h\u1ec7 th\u1ed1ng ki\u1ebfn th\u1ee9c m\u1ed9t c\u00e1ch ch\u1eafc ch\u1eafn nh\u1ea5t. Qu\u00fd th\u1ea7y c\u00f4 v\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh t\u1ea3i ngay <strong>10 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 s\u1edf GD&amp;\u0110T B\u1eafc Giang<\/strong> qua \u0111\u01b0\u1eddng link sau \u0111\u00e2y \u0111\u1ec3 luy\u1ec7n t\u1eadp nh\u00e9.<\/p>\n<p><iframe height=\"480\" loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1Eg6gf8Un54kFaW5mjc6_R01xjDSRgxvK\/preview\" width=\"640\"><\/iframe><br \/><a class=\"migration-iframe-fallback\" href=\"https:\/\/drive.google.com\/file\/d\/1Eg6gf8Un54kFaW5mjc6_R01xjDSRgxvK\/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><strong><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1Eg6gf8Un54kFaW5mjc6_R01xjDSRgxvK\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i 10 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 s\u1edf GD&amp;\u0110T B\u1eafc Giang <\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u1eadp 10 \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 s\u1edf GD&amp;\u0110T B\u1eafc Giang l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u \u0111\u1eafc l\u1ef1c h\u1ed7 tr\u1ee3 c\u00e1c b\u1ea1n h\u1ecdc sinh 12 chu\u1ea9n b\u1ecb ki\u1ebfn th\u1ee9c v\u00e0 k\u0129 n\u0103ng cho k\u00ec thi t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n s\u1eafp t\u1edbi. B\u1ed9 \u0111\u1ec1 thi th\u1eed n\u00e0y \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n [&#8230;]\n","protected":false},"author":1,"featured_media":1661,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[8],"class_list":["post-462","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-de-thi-thu-thpt-mon-toan","tag-de-thi-thu-thpt-mon-toan"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/462","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=462"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/462\/revisions"}],"predecessor-version":[{"id":1662,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/462\/revisions\/1662"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1661"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=462"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=462"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=462"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}