{"id":2330,"date":"2026-04-25T02:41:47","date_gmt":"2026-04-25T02:41:47","guid":{"rendered":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/dap-an-de-thi-mon-toan-tot-nghiep-thpt-2025\/"},"modified":"2026-04-25T02:41:47","modified_gmt":"2026-04-25T02:41:47","slug":"dap-an-de-thi-mon-toan-tot-nghiep-thpt-2025","status":"publish","type":"post","link":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/dap-an-de-thi-mon-toan-tot-nghiep-thpt-2025\/","title":{"rendered":"\u0110\u00e1p \u00e1n \u0111\u1ec1 thi m\u00f4n To\u00e1n t\u1ed1t nghi\u1ec7p THPT 2025 (\u0111\u1ec1 ch\u00ednh th\u1ee9c)"},"content":{"rendered":"
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\u0110\u00e1p \u00e1n \u0111\u1ec1 thi m\u00f4n To\u00e1n t\u1ed1t nghi\u1ec7p THPT 2025 (\u0111\u1ec1 ch\u00ednh th\u1ee9c) \u0111\u01b0\u1ee3c c\u1eadp nh\u1eadt nhanh v\u00e0 ch\u00ednh x\u00e1c nh\u1ea5t t\u1ea1i Tailieuonthi.org.<\/p>\n

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N\u0103m 2025 l\u00e0 n\u0103m \u0111\u1ea7u ti\u00ean th\u1ef1c hi\u1ec7n thi t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n v\u00e0 c\u00e1c m\u00f4n h\u1ecdc kh\u00e1c theo Ch\u01b0\u01a1ng tr\u00ecnh Gi\u00e1o d\u1ee5c ph\u1ed5 th\u00f4ng 2018 m\u1edbi. N\u1ed9i dung thi t\u1ed1t nghi\u1ec7p THPT ch\u1ee7 y\u1ebfu \u1edf ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 12, nh\u01b0ng c\u0169ng c\u00f3 th\u1ec3 c\u00f3 ph\u1ea7n ki\u1ebfn th\u1ee9c thu\u1ed9c l\u1edbp 10 v\u00e0 11.<\/p>\n

M\u00f4n To\u00e1n thi t\u1ed1t nghi\u1ec7p THPT \u0111\u01b0\u1ee3c l\u00e0m b\u00e0i trong 90 ph\u00fat, theo h\u00ecnh th\u1ee9c tr\u1eafc nghi\u1ec7m.\u00a0<\/p>\n

<\/span>\u0110\u1ec1 thi m\u00f4n To\u00e1n t\u1ed1t nghi\u1ec7p THPT 2025<\/span><\/h2>\n

D\u01b0\u1edbi \u0111\u00e2y l\u00e0 t\u1ed5ng h\u1ee3p \u0111\u1ec1 thi TN THPT 2025 m\u00f4n To\u00e1n m\u00e0 ch\u00fang m\u00ecnh s\u01b0u t\u1ea7m \u0111\u01b0\u1ee3c. C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 xem ho\u1eb7c t\u1ea3i v\u1ec1 nh\u00e9.<\/p>\n

M\u00c3 \u0110\u1ec0 120<\/strong><\/p>\n

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<\/span>\u0110\u00e1p \u00e1n tham kh\u1ea3o \u0111\u1ec1 thi m\u00f4n To\u00e1n t\u1ed1t nghi\u1ec7p THPT 2025<\/span><\/h2>\n

D\u01b0\u1edbi \u0111\u00e2y l\u00e0 \u0111\u00e1p \u00e1n chi ti\u1ebft c\u1ee7a m\u1ed9t s\u1ed1 th\u1ea7y c\u00f4 c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o nh\u00e9<\/p>\n

Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c \u2013 M\u00e3 120<\/strong><\/p>\n

PH\u1ea6N TR\u1eaeC NGHI\u1ec6M 4 PH\u01af\u01a0NG \u00c1N L\u1ef0A CH\u1eccN<\/p>\n

12 c\u00e2u \u0111\u1ea7u v\u1eabn theo chu\u1ea9n c\u1ea5u tr\u00fac c\u1ee7a \u0111\u1ec1 tham kh\u1ea3o, v\u1edbi m\u1ee5c ti\u00eau x\u00e9t t\u1ed1t nghi\u1ec7p, c\u00e1c em s\u1ebd kh\u00f4ng g\u1eb7p kh\u00f3 kh\u0103n \u0111\u1ec3 gi\u1ea3i h\u1ebft<\/p>\n

PH\u1ea6N TR\u1eaeC NGHI\u1ec6M \u0110\u00daNG SAI (x\u00e9t theo m\u1ee9c t\u1eeb d\u1ec5 \u0111\u1ebfn kh\u00f3)<\/p>\n

C\u00e2u 1. H\u00e0m s\u1ed1 \u2013 C\u00e2u n\u00e0y r\u1ea5t d\u1ec5 v\u00e0 ch\u1eafc ch\u1eafn c\u00e1c em s\u1ebd l\u00e0m t\u1ed1t<\/p>\n

C\u00e2u 2. X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n \u2013 \u0110\u00e2y l\u00e0 d\u1ea1ng to\u00e1n d\u1ec5 c\u1ee7a x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n, th\u00f4ng th\u01b0\u1eddng c\u00e1c em ch\u1ec9 c\u1ea7n v\u1ebd m\u1ed9t s\u01a1 \u0111\u1ed3 c\u00e2y l\u00e0 xong. Ph\u1ea7n n\u00e0y c\u00e1c em c\u0169ng \u0111\u01b0\u1ee3c luy\u1ec7n kh\u00e1 nhi\u1ec1u n\u00ean ch\u1eafc ch\u1eafn b\u00e0i n\u00e0y kh\u00f4ng l\u00e0m kh\u00f3 kh\u0103n cho c\u00e1c em \u0111\u01b0\u1ee3c<\/p>\n

C\u00e2u 3. (nu\u00f4i tr\u1ed3ng th\u1ee7y s\u1ea3n) \u2013 B\u00e0i to\u00e1n th\u1ef1c t\u1ebf n\u00e0y b\u1ea3n ch\u1ea5t l\u00e0 x\u00e9t 1 h\u00e0m s\u1ed1, ch\u1ee7 y\u1ebfu em c\u1ea7n \u0111\u1ecdc \u0111\u1ec1 \u0111\u1ec3 hi\u1ec3u r\u00f5 m\u1ed1i quan h\u1ec7 gi\u1eefa y(t) v\u00e0 g(t), t\u1eeb \u0111\u00f3 thay s\u1ed1 v\u00e0o<\/p>\n

C\u00e2u 4. (Oxyz \u2013 c\u00f3 l\u1ed3ng gh\u00e9p v\u00e0o b\u00e0i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng) \u2013 Ch\u1ee7 y\u1ebfu b\u00e0i to\u00e1n n\u00e0y em c\u1ea7n \u0111\u1ecdc hi\u1ec3u t\u1eebng d\u1eef ki\u1ec7n v\u00e0 x\u1eed l\u00fd. X\u00e9t 1 c\u00e1ch c\u00f4ng b\u1eb1ng th\u00ec \u0111\u00e2y v\u1eabn l\u00e0 1 b\u00e0i to\u00e1n nh\u1eb9 nh\u00e0ng, ch\u1ee7 y\u1ebfu r\u00e8n luy\u1ec7n b\u1ea3n l\u0129nh ph\u00f2ng thi v\u00ec \u0111\u1ec1 d\u00e0i l\u00e0m cho ta \u0111\u1ecdc \u0111\u1ec1 s\u1ebd c\u1ea3m th\u1ea5y h\u01a1i cu\u1ed1ng<\/p>\n

PH\u1ea6N TR\u1eaeC NGHI\u1ec6M TR\u1ea2 L\u1edcI NG\u1eaeN<\/p>\n

C\u00e2u 1. H\u00e0m s\u1ed1 \u2013 (kinh t\u1ebf) \u2013 B\u00e0i to\u00e1n kh\u00e1 \u0111\u01a1n gi\u1ea3n, ch\u1ec9 c\u1ea7n n\u1eafm \u0111\u01b0\u1ee3c l\u1ee3i nhu\u1eadn b\u1eb1ng doanh thu tr\u1eeb chi ph\u00ed.<\/p>\n

C\u00e2u 2. Quy ho\u1ea1ch tuy\u1ebfn t\u00ednh \u2013 Th\u1ef1c s\u1ef1 h\u1ecdc sinh \u0111\u00e3 \u0111\u01b0\u1ee3c luy\u1ec7n t\u1eeb n\u0103m l\u1edbp 10, v\u00e0 n\u0103m nay th\u1ea7y lu\u00f4n nh\u1ea5n m\u1ea1nh em c\u1ea7n l\u01b0u \u00fd ph\u1ea7n quy ho\u1ea1ch tuy\u1ebfn t\u00ednh. Th\u1ea7y ngh\u0129 c\u00e2u n\u00e0y \u0111a s\u1ed1 c\u00e1c em quen thu\u1ed9c v\u00e0 l\u00e0m t\u1ed1t.<\/p>\n

C\u00e2u 3. H\u00ecnh h\u1ecdc kh\u00f4ng gian \u2013 B\u00e0i to\u00e1n n\u00e0y c\u00f3 kh\u00e1 nhi\u1ec1u c\u00e1ch, k\u1ec3 c\u1ea3 gh\u00e9p h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz c\u0169ng \u0111\u01b0\u1ee3c. Trong ph\u00f2ng thi em c\u00f3 th\u1ec3 d\u00f9ng \u0110KH, ho\u1eb7c l\u00e0m tr\u1ef1c ti\u1ebfp t\u1ea1o m\u1eb7t ph\u1eb3ng song song, ho\u1eb7c t\u1ea1o \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c chung\u2026<\/p>\n

C\u00e2u 4. \u1ee8ng d\u1ee5ng t\u00edch ph\u00e2n \u2013 B\u00e0i to\u00e1n n\u00e0y b\u1ea3n ch\u1ea5t l\u00e0 t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p c\u1ee5t tr\u1eeb th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay c\u1eaft ra t\u1eeb m\u1eb7t c\u1ea7u. Ch\u1ee7 y\u1ebfu em c\u1ea7n hi\u1ec3u r\u00f5 \u0111\u1ec1 n\u00f3i c\u00e1i g\u00ec, c\u00f2n ph\u1ea7n t\u00ednh to\u00e1n kh\u00e1 quen thu\u1ed9c<\/p>\n

C\u00e2u 5. X\u00e1c su\u1ea5t k\u1ec7 s\u00e1ch \u2013 \u0110\u00e2y l\u00e0 1 b\u00e0i to\u00e1n hay, b\u00e0i to\u00e1n n\u00e0y n\u1ebfu em n\u00e0o \u0111\u00e3 h\u1ecdc nh\u1eefng b\u00e0i to\u00e1n \u0111\u1ebfm, nh\u01b0 v\u00e1ch ng\u1eafn, ho\u1eb7c l\u00e0 \u0111\u00e3 h\u1ecdc b\u00e0i to\u00e1n chia k\u1eb9o Euler th\u00ec c\u00f3 th\u1ec3 t\u01b0 duy nhanh \u0111\u01b0\u1ee3c. Tuy nhi\u00ean ch\u1eafc ch\u1eafn b\u00e0i n\u00e0y c\u0169ng s\u1ebd g\u00e2y nhi\u1ec1u kh\u00f3 kh\u0103n cho h\u1ea7u h\u1ebft c\u00e1c b\u1ea1n, v\u00ec b\u1ea3n ch\u1ea5t h\u1ecdc sinh th\u01b0\u1eddng hay s\u1ee3 x\u00e1c su\u1ea5t, v\u00e0 c\u00f2n t\u00e2m l\u00fd ph\u00f2ng thi n\u1eefa.<\/p>\n

C\u00e2u 6. X\u00e1c su\u1ea5t gi\u1ea3i m\u1eadt m\u00e3 c\u1ea5p s\u1ed1 c\u1ed9ng \u2013 \u0110\u00e2y l\u00e0 c\u00e2u kh\u00f3 nh\u1ea5t \u0111\u1ec1 v\u00e0 s\u1ebd l\u00e0 c\u00e2u ph\u00e2n lo\u1ea1i trong k\u00ec thi n\u0103m nay. Ch\u1ee7 y\u1ebfu n\u00f3 d\u1ec5 khi\u1ebfn cho h\u1ecdc sinh nh\u1ea7m v\u00e0 gi\u1ea3i sai.<\/p>\n

\u2014<\/p>\n

\u0110\u00e1nh gi\u00e1 chung: V\u1edbi n\u0103m \u0111\u1ea7u ti\u00ean thi theo ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi, th\u1ea7y \u0110\u1ee9c ngh\u0129 \u0111\u1ec1 thi nh\u01b0 v\u1eady l\u00e0 hay, ph\u00f9 h\u1ee3p ki\u1ebfn th\u1ee9c v\u00e0 c\u00f3 t\u00ednh ph\u00e2n lo\u1ea1i. \u0110\u1ec1 n\u00e0y ch\u1eafc ch\u1eafn s\u1ebd kh\u00f4ng d\u1ec5 d\u00e0ng \u0111\u01b0\u1ee3c \u0111i\u1ec3m cao v\u00ec c\u00f2n t\u00e2m l\u00fd ph\u00f2ng thi, \u0111\u1eb7c bi\u1ec7t l\u00e0 trong ph\u00f2ng thi \u00e1p l\u1ef1c, em g\u1eb7p nh\u1eefng b\u00e0i to\u00e1n th\u1ef1c t\u1ebf c\u1ea7n \u0111\u1ecdc hi\u1ec3u c\u0169ng l\u00e0 1 ph\u1ea7n g\u00e2y kh\u00f3 kh\u0103n cho c\u00e1c em.<\/p>\n

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Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c \u2013 M\u00e3 120<\/strong><\/p>\n

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\u0110\u00e1p \u00e1n \u0111\u1ec1 thi m\u00f4n To\u00e1n t\u1ed1t nghi\u1ec7p THPT 2025 (\u0111\u1ec1 ch\u00ednh th\u1ee9c) \u0111\u01b0\u1ee3c c\u1eadp nh\u1eadt nhanh v\u00e0 ch\u00ednh x\u00e1c nh\u1ea5t t\u1ea1i Tailieuonthi.org. N\u0103m 2025 l\u00e0 n\u0103m \u0111\u1ea7u ti\u00ean th\u1ef1c hi\u1ec7n thi t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n v\u00e0 c\u00e1c m\u00f4n h\u1ecdc kh\u00e1c theo Ch\u01b0\u01a1ng tr\u00ecnh Gi\u00e1o d\u1ee5c ph\u1ed5 th\u00f4ng 2018 m\u1edbi. N\u1ed9i dung thi t\u1ed1t […]\n","protected":false},"author":1,"featured_media":2309,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27,23],"tags":[],"class_list":["post-2330","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-de-tn-thpt-toan","category-tai-lieu-toan"],"_links":{"self":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2330","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=2330"}],"version-history":[{"count":0,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2330\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/2309"}],"wp:attachment":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=2330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=2330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=2330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}