{"id":492,"date":"2026-05-05T04:48:40","date_gmt":"2026-05-05T04:48:40","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-doi-can-vinh-phuc\/"},"modified":"2026-05-05T07:21:53","modified_gmt":"2026-05-05T07:21:53","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-doi-can-vinh-phuc","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-doi-can-vinh-phuc\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed9i C\u1ea5n V\u0129nh Ph\u00fac"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed9i C\u1ea5n V\u0129nh Ph\u00fac<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u00e1m s\u00e1t c\u1ea5u tr\u00fac \u0111\u1ec1 thi minh h\u1ecda c\u1ee7a B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o. \u0110\u1ec1 thi g\u1ed3m c\u00e1c c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m, bao qu\u00e1t nhi\u1ec1u ch\u1ee7 \u0111\u1ec1 trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 12 nh\u01b0 \u0111\u1ea1i s\u1ed1, gi\u1ea3i t\u00edch, h\u00ecnh h\u1ecdc kh\u00f4ng gian v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf. C\u00f9ng T\u00e0i Li\u1ec7u Mi\u1ec5n Ph\u00ed<\/strong><\/a> t\u00ecm hi\u1ec3u c\u00e1c c\u00e2u h\u1ecfi c\u00f3 trong b\u00e0i vi\u1ebft n\u00e0y.<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed9i C\u1ea5n V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed9i C\u1ea5n V\u0129nh Ph\u00fac<\/strong> bao g\u1ed3m 6 trang v\u1edbi t\u1ed5ng c\u1ed9ng 22 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u01b0\u1ee3c chia th\u00e0nh nhi\u1ec1u d\u1ea1ng b\u00e0i kh\u00e1c nhau, t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. \u0110\u1ec1 thi th\u1eed to\u00e1n<\/a> k\u00e8m theo \u0111\u00e1p \u00e1n chi ti\u1ebft, gi\u00fap h\u1ecdc sinh d\u1ec5 d\u00e0ng t\u1ef1 ki\u1ec3m tra v\u00e0 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c.<\/p>\n

Ph\u1ea7n I: C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n ch\u1ecdn<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Cho A v\u00e0 overlineA l\u00e0 hai bi\u1ebfn c\u1ed1 \u0111\u1ed1i nhau. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o d\u01b0\u1edbi \u0111\u00e2y lu\u00f4n \u0111\u00fang?<\/p>\n

A. P(A) = 1 + P(overlineA) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. P(A) = P(overlineA) \u00a0 \u00a0 \u00a0 \u00a0 C. P(A) = 1 – P(overlineA) \u00a0 \u00a0 \u00a0 \u00a0 D. P(A) + P(overlineA) = 0 <\/p>\n

C\u00e2u 2.<\/strong> S\u1ed1 d\u00e2n c\u1ee7a m\u1ed9t th\u1ecb tr\u1ea5n sau t n\u0103m k\u1ec3 t\u1eeb n\u0103m 2022 \u0111\u01b0\u1ee3c \u01b0\u1edbc t\u00ednh b\u1edfi c\u00f4ng th\u1ee9c f(t) = (26t + 10)\/(t + 5) ( f(t) \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng ngh\u00ecn ng\u01b0\u1eddi). H\u1ecfi trong kho\u1ea3ng th\u1eddi gian t\u1eeb n\u0103m 2022 \u0111\u1ebfn n\u0103m 2032 , d\u00e2n s\u1ed1 c\u1ee7a th\u1ecb tr\u1ea5n \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t b\u1eb1ng bao nhi\u00eau?<\/p>\n

A. 6 ngh\u00ecn ng\u01b0\u1eddi. \u00a0 \u00a0 \u00a0 \u00a0 B. 18 ngh\u00ecn ng\u01b0\u1eddi. \u00a0 \u00a0 \u00a0 \u00a0 C. 2 ngh\u00ecn ng\u01b0\u1eddi. \u00a0 \u00a0 \u00a0 \u00a0 D. 18,5 ngh\u00ecn ng\u01b0\u1eddi.<\/p>\n

Ph\u1ea7n II: C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 f(x) = (-x\u00b2 + 2x – 4)\/(x – 2) . X\u00e9t t\u00ednh c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau:<\/p>\n

a) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = 2 .<\/p>\n

b) Ph\u01b0\u01a1ng tr\u00ecnh f'(x) = 0 c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t l\u00e0 0 v\u00e0 3 suy ra h\u00e0m s\u1ed1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>\n

c) B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 l\u00e0<\/p>\n

\"\"<\/p>\n

d) H\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 sau<\/p>\n

\"\"<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt ABCD.EFGH c\u00f3 AB = AE = 2 , AD = 3 v\u00e0 \u0111\u1eb7t a = AB, b = AD, c = AE . L\u1ea5y hai \u0111i\u1ec3m M, N th\u1ecfa m\u00e3n AM\/AD = 1\/5, EN\/EC = 2\/5 , (tham kh\u1ea3o h\u00ecnh v\u1ebd).<\/p>\n

\"\"<\/p>\n

X\u00e9t c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau:<\/p>\n

a) MA\u20d7 = -1\/5 b\u20d7 .<\/p>\n

b) EN\u20d7 = 2\/5 (a\u20d7 – b\u20d7 + c\u20d7) .<\/p>\n

c) | ma\u20d7 + nb\u20d7 + pc\u20d7 |\u00b2 = m\u00b2 | a\u20d7 |\u00b2 + n\u00b2 | b\u20d7 |\u00b2 + p\u00b2 | c\u20d7 |\u00b2 v\u1edbi m, n, p l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c. <\/p>\n

d) MN = (\u221a61)\/(5) .<\/p>\n

Ph\u1ea7n III: C\u00e2u tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/p>\n

C\u00e2u 1.<\/strong> M\u1ed9t ng\u1ecdn h\u1ea3i \u0111\u0103ng \u0111\u1eb7t t\u1ea1i v\u1ecb tr\u00ed A c\u00e1ch b\u1edd bi\u1ec3n m\u1ed9t kho\u1ea3ng AB = 4 (km) . Tr\u00ean b\u1edd bi\u1ec3n c\u00f3 m\u1ed9t c\u00e1i kho \u1edf v\u1ecb tr\u00ed C c\u00e1ch B m\u1ed9t kho\u1ea3ng BC = 7 (km) . Ng\u01b0\u1eddi canh h\u1ea3i \u0111\u0103ng ph\u1ea3i ch\u00e8o thuy\u1ec1n t\u1eeb v\u1ecb tr\u00ed A \u0111\u1ebfn v\u1ecb tr\u00ed M tr\u00ean b\u1edd bi\u1ec3n v\u1edbi v\u1eadn t\u1ed1c 6 (km\/h) r\u1ed3i \u0111i xe \u0111\u1ea1p t\u1eeb M \u0111\u1ebfn C v\u1edbi v\u1eadn t\u1ed1c 10 (km\/h) (h\u00ecnh v\u1ebd b\u00ean). X\u00e1c \u0111\u1ecbnh kho\u1ea3ng c\u00e1ch t\u1eeb M \u0111\u1ebfn C \u0111\u1ec3 ng\u01b0\u1eddi \u0111\u00f3 \u0111i t\u1eeb A \u0111\u1ebfn C l\u00e0 nhanh nh\u1ea5t.<\/p>\n

\"\"<\/p>\n

C\u00e2u 2.<\/strong> Ng\u01b0\u1eddi ta tr\u1ed3ng 15050 c\u00e2y theo d\u1ea1ng m\u1ed9t h\u00ecnh tam gi\u00e1c b\u1eadc thang nh\u01b0 sau: H\u00e0ng th\u1ee9 nh\u1ea5t tr\u1ed3ng 2 c\u00e2y, h\u00e0ng th\u1ee9 hai tr\u1ed3ng 5 c\u00e2y, h\u00e0ng th\u1ee9 ba tr\u1ed3ng 8 c\u00e2y,\u2026, c\u1ee9 ti\u1ebfp t\u1ee5c tr\u1ed3ng cho \u0111\u1ebfn khi h\u1ebft s\u1ed1 c\u00e2y v\u00e0 h\u00e0ng cu\u1ed1i c\u00f9ng c\u00f3 \u0111\u1ee7 s\u1ed1 c\u00e2y theo quy lu\u1eadt n\u00e0y. T\u00ednh s\u1ed1 h\u00e0ng c\u00e2y \u0111\u01b0\u1ee3c tr\u1ed3ng.<\/p>\n

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed9i C\u1ea5n V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT \u0110\u1ed9i C\u1ea5n V\u0129nh Ph\u00fac<\/strong> c\u00f3 \u0111\u00e1p \u00e1n chi ti\u1ebft k\u00e8m l\u1eddi gi\u1ea3i, gi\u00fap h\u1ecdc sinh t\u1ef1 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c v\u00e0 r\u00fat kinh nghi\u1ec7m trong qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp. C\u00e1c c\u00e2u h\u1ecfi \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, ph\u00f9 h\u1ee3p v\u1edbi nhi\u1ec1u m\u1ee9c \u0111\u1ed9 h\u1ecdc sinh. H\u00e3y t\u1ea3i ngay file \u0111\u1ec1 thi \u0111\u1ec3 b\u1eaft \u0111\u1ea7u \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3!<\/p>\n