{"id":496,"date":"2026-05-05T04:48:52","date_gmt":"2026-05-05T04:48:52","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-chuyen-dhkhtn-tp-hcm\/"},"modified":"2026-05-05T07:22:05","modified_gmt":"2026-05-05T07:22:05","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-chuyen-dhkhtn-tp-hcm","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-chuyen-dhkhtn-tp-hcm\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Chuy\u00ean \u0110HKHTN TP HCM"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Chuy\u00ean \u0110HKHTN TP HCM<\/strong> l\u00e0 t\u00e0i li\u1ec7u h\u1eefu \u00edch d\u00e0nh cho c\u00e1c b\u1ea1n h\u1ecdc sinh 12 trong giai \u0111o\u1ea1n chu\u1ea9n b\u1ecb \u00f4n luy\u1ec7n k\u00ec thi thpt. V\u1edbi c\u1ea5u tr\u00fac b\u00e1m s\u00e1t \u0111\u1ec1 thi th\u1eadt chu\u1ea9n quy \u0111\u1ecbnh c\u1ee7a B\u1ed9 GD&DT, gi\u00fap c\u00e1c b\u1ea1n l\u00e0m quen v\u1edbi ma tr\u1eadn \u0111\u1ec1 v\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp c\u00f3 trong \u0111\u1ec1 thi. H\u00e3y c\u00f9ng T\u00e0i li\u1ec7u \u00d4n Thi<\/a> t\u00ecm hi\u1ec3u th\u00eam n\u1ed9i dung c\u1ee7a t\u00e0i li\u1ec7u qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y.<\/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 Chuy\u00ean \u0110HKHTN TP HCM<\/strong><\/h2>\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 Chuy\u00ean \u0110HKHTN TP HCM<\/strong> t\u1eadp trung v\u00e0o n\u1ed9i dung c\u1ee7a to\u00e1n \u0111\u1ea1i s\u1ed1 \u2013 gi\u1ea3i t\u00edch, x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea, ph\u01b0\u01a1ng tr\u00ecnh logarit,.. H\u00ecnh h\u1ecdc kh\u00f4ng gian, b\u00e0i to\u00e1n v\u1eadn d\u1ee5ng cao. Ma tr\u1eadn c\u1ee7a \u0111\u1ec1 thi th\u1eed to\u00e1n thpt<\/a> n\u00e0y c\u00f3 t\u1ea5t c\u1ea3 22 c\u00e2u chia th\u00e0nh 3 ph\u1ea7n nh\u01b0 sau:<\/p>\n

PH\u1ea6N 1 \u2013 TR\u1eaeC NGHI\u1ec6M 4 PH\u01af\u01a0NG \u00c1N L\u1ef0A CH\u1eccN
\n<\/strong>
\nC\u00f3 t\u1ea5t c\u1ea3 12 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m, v\u1edbi 4 \u0111\u00e1p \u00e1n A, B, C, D. H\u1ecdc sinh ch\u1ecdn duy nh\u1ea5t m\u1ed9t \u0111\u00e1p \u00e1n ch\u00ednh x\u00e1c nh\u1ea5t. V\u00ed d\u1ee5 c\u00e1c c\u00e2u h\u1ecfi sau \u0111\u00e2y:<\/p>\n

C\u00e2u 1<\/strong>: Cho h\u00e0m s\u1ed1 f(x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau:
\n\\[
\n\\begin{array}{|c|c|c|c|c|}
\n\\hline
\nx & -\\infty & -2 & 1 & +\\infty \\\\
\n\\hline
\nf'(x) & + & 0 & \u2013 & 0 & + \\\\
\n\\hline
\nf(x) & \\nearrow & -2 & \\searrow & -2 & \\nearrow \\\\
\n\\hline
\n\\end{array}
\n\\]\n<\/p>\n

H\u00e0m s\u1ed1 \u0111\u00e3 cho ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng:
\nA. (0; 2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. (-2; 1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. (-\u221e; 0) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. (2; +\u221e) <\/p>\n

C\u00e2u 2<\/strong>: Th\u1ed1ng k\u00ea chi\u1ec1u cao (\u0111\u01a1n v\u1ecb: cm) c\u1ee7a c\u00e1c h\u1ecdc sinh trong m\u1ed9t l\u1edbp h\u1ecdc ta c\u00f3 b\u1ea3ng s\u1ed1 li\u1ec7u sau:
\n\\[
\n\\begin{array}{|c|c|c|c|c|c|c|c|}
\n\\hline
\n\\text{Chi\u1ec1u cao} & [150;155) & [155;160) & [160;165) & [165;170) & [170;175) & [175;180) \\\\
\n\\hline
\n\\text{S\u1ed1 h\u1ecdc sinh} & 1 & 4 & 10 & 9 & 4 & 2 \\\\
\n\\hline
\n\\end{array}
\n\\]\n<\/p>\n

\u0110\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u tr\u00ean b\u1ea3ng bao nhi\u00eau? (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m)<\/p>\n

A. 35,66 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. 5,87 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. 34,47 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. 5,97 <\/p>\n

PH\u1ea6N 2 \u2013 TR\u1eaeC NGHI\u1ec6M CH\u1eccN \u0110\u00daNG SAI<\/strong><\/p>\n

\u0110\u1ec3 chi\u1ebfm tr\u1ecdn s\u1ed1 \u0111i\u1ec3m c\u1ee7a 4 c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai c\u1ee7a ph\u1ea7n 2 trong \u0111\u1ec1 thi, h\u00e3y tham kh\u1ea3o v\u00e0 gi\u1ea3i ngay c\u00e1c c\u00e2u h\u1ecfi nh\u01b0 sau:<\/p>\n

C\u00e2u 1<\/strong>: Trong kh\u00f4ng gian Oxyz , cho c\u00e1c \u0111i\u1ec3m A(1;1;0) , B(5;-3;2) v\u00e0 C(0;4;-1) . X\u00e9t c\u00e1c \u0111i\u1ec3m M thay \u0111\u1ed5i trong kh\u00f4ng gian sao cho di\u1ec7n t\u00edch tam gi\u00e1c ABM b\u1eb1ng 6\u221a2 .<\/p>\n

a) \u0110o\u1ea1n th\u1eb3ng AB c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng 3 .<\/p>\n

b) \u0110\u01b0\u1eddng th\u1eb3ng AB c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0: (x – 1)\/(2) = (y – 1)\/(-1) = z\/1\n<\/p>\n

c) Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m C t\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng AB b\u1eb1ng 2\u221a2 .<\/p>\n

d) \u0110o\u1ea1n th\u1eb3ng MC c\u00f3 \u0111\u1ed9 d\u00e0i nh\u1ecf nh\u1ea5t b\u1eb1ng \u221a2 .<\/p>\n

C\u00e2u 2<\/strong>: C\u00f3 hai ph\u00e1c \u0111\u1ed3 \u0111i\u1ec1u tr\u1ecb A v\u00e0 B cho m\u1ed9t lo\u1ea1i b\u1ec7nh. Ph\u00e1c \u0111\u1ed3 A c\u00f3 x\u00e1c su\u1ea5t ch\u1eefa kh\u1ecfi b\u1ec7nh l\u00e0 60\\% v\u00e0 x\u00e1c su\u1ea5t g\u00e2y t\u00e1c d\u1ee5ng ph\u1ee5 nghi\u00eam tr\u1ecdng l\u00e0 5%. Ph\u00e1c \u0111\u1ed3 B c\u00f3 x\u00e1c su\u1ea5t ch\u1eefa kh\u1ecfi b\u1ec7nh l\u00e0 70% v\u00e0 x\u00e1c su\u1ea5t g\u00e2y t\u00e1c d\u1ee5ng ph\u1ee5 nghi\u00eam tr\u1ecdng l\u00e0 10%. M\u1ed9t b\u1ec7nh nh\u00e2n \u0111\u01b0\u1ee3c \u0111i\u1ec1u tr\u1ecb ng\u1eabu nhi\u00ean b\u1eb1ng m\u1ed9t trong hai ph\u00e1c \u0111\u1ed3 (x\u00e1c su\u1ea5t ch\u1ecdn m\u1ed7i ph\u00e1c \u0111\u1ed3 l\u00e0 50%).<\/p>\n

a) X\u00e1c su\u1ea5t b\u1ec7nh nh\u00e2n \u0111i\u1ec1u tr\u1ecb b\u1eb1ng ph\u00e1c \u0111\u1ed3 A v\u00e0 \u0111\u01b0\u1ee3c ch\u1eefa kh\u1ecfi b\u1ec7nh l\u00e0 0,6 .<\/p>\n

b) X\u00e1c su\u1ea5t \u0111\u1ec3 b\u1ec7nh nh\u00e2n b\u1ecb t\u00e1c d\u1ee5ng ph\u1ee5 nghi\u00eam tr\u1ecdng l\u00e0 0,075 .<\/p>\n

c) N\u1ebfu bi\u1ebft b\u1ec7nh nh\u00e2n n\u00e0y g\u1eb7p t\u00e1c d\u1ee5ng ph\u1ee5 nghi\u00eam tr\u1ecdng th\u00ec x\u00e1c su\u1ea5t b\u1ec7nh nh\u00e2n \u0111\u00e3 \u0111\u01b0\u1ee3c \u0111i\u1ec1u tr\u1ecb b\u1eb1ng ph\u00e1c \u0111\u1ed3 B l\u00e0 l\u1edbn h\u01a1n 0,65 .<\/p>\n

d) Bi\u1ebft r\u1eb1ng trong m\u1ed7i ph\u00e1c \u0111\u1ed3 \u0111i\u1ec1u tr\u1ecb th\u00ec bi\u1ebfn c\u1ed1 \u201cb\u1ec7nh nh\u00e2n \u0111\u01b0\u1ee3c ch\u1eefa kh\u1ecfi b\u1ec7nh\u201d v\u00e0 bi\u1ebfn c\u1ed1 \u201cb\u1ec7nh nh\u00e2n kh\u00f4ng b\u1ecb t\u00e1c d\u1ee5ng ph\u1ee5 nghi\u00eam tr\u1ecdng\u201d l\u00e0 \u0111\u1ed9c l\u1eadp v\u1edbi nhau. X\u00e1c su\u1ea5t b\u1ec7nh nh\u00e2n kh\u1ecfi b\u1ec7nh v\u00e0 kh\u00f4ng b\u1ecb t\u00e1c d\u1ee5ng ph\u1ee5 nghi\u00eam tr\u1ecdng l\u00e0 0,6 .<\/p>\n

PH\u1ea6N 3 \u2013 TR\u1eaeC NGHI\u1ec6M TR\u1ea2 L\u1edcI NG\u1eaeN<\/strong><\/p>\n

C\u00e2u h\u1ecfi trong ph\u1ea7n 3 t\u01b0\u01a1ng t\u1ef1 nh\u01b0 d\u1ea1ng c\u00e2u t\u1ef1 lu\u1eadn c\u1ee7a c\u00e1c \u0111\u1ec1 thi n\u0103m tr\u01b0\u1edbc. Nh\u01b0ng \u0111\u1ec3 l\u1ea5y \u0111\u01b0\u1ee3c \u0111i\u1ec3m s\u1ed1 cao \u1edf ph\u1ea7n tr\u1ecdng t\u00e2m n\u00e0y, h\u1ecdc sinh c\u1ea7n c\u00f3 qu\u00e1 tr\u00ecnh luy\u1ec7n t\u1eadp v\u00e0 gi\u1ea3i \u0111\u1ec1 \u0111\u1ec3 n\u00e2ng cao t\u01b0 duy khi l\u00e0m l\u00e0m. V\u00ed d\u1ee5:<\/p>\n

C\u00e2u 1<\/strong>: Gi\u1ea3 s\u1eed chi ph\u00ed \u0111\u1eb7t h\u00e0ng v\u00e0 v\u1eadn chuy\u1ec3n C (\u0111\u01a1n v\u1ecb: tri\u1ec7u \u0111\u1ed3ng) c\u1ee7a m\u1ed9t linh ki\u1ec7n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong s\u1ea3n xu\u1ea5t m\u1ed9t s\u1ea3n ph\u1ea9m \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh theo c\u00f4ng th\u1ee9c:
\n C = (19200000)\/(x\u00b2) + (27x)\/(x + 3000), x \u2265 1 . Trong \u0111\u00f3 x l\u00e0 s\u1ed1 linh ki\u1ec7n \u0111\u01b0\u1ee3c \u0111\u1eb7t h\u00e0ng v\u00e0 v\u1eadn chuy\u1ec3n. T\u00ecm x \u0111\u1ec3 chi ph\u00ed \u0111\u1eb7t h\u00e0ng v\u00e0 v\u1eadn chuy\u1ec3n cho m\u1ed7i linh ki\u1ec7n tr\u00ean l\u00e0 nh\u1ecf nh\u1ea5t.<\/p>\n

C\u00e2u 2<\/strong>: M\u1ed9t nh\u00e0 m\u00e1y c\u00f3 hai ph\u00e2n x\u01b0\u1edfng I v\u00e0 II t\u01b0\u01a1ng \u1ee9ng l\u00e0m ra 40% v\u00e0 60% s\u1ea3n ph\u1ea9m c\u1ee7a nh\u00e0 m\u00e1y. Bi\u1ebft r\u1eb1ng t\u1ec9 l\u1ec7 ph\u1ebf ph\u1ea9m c\u1ee7a hai ph\u00e2n x\u01b0\u1edfng I v\u00e0 II t\u01b0\u01a1ng \u1ee9ng l\u00e0 1% v\u00e0 2% . Ch\u1ecdn ng\u1eabu nhi\u00ean m\u1ed9t s\u1ea3n ph\u1ea9m c\u1ee7a nh\u00e0 m\u00e1y th\u00ec th\u1ea5y n\u00f3 l\u00e0 ph\u1ebf ph\u1ea9m. T\u00ednh x\u00e1c su\u1ea5t \u0111\u1ec3 s\u1ea3n ph\u1ea9m \u0111\u00f3 thu\u1ed9c ph\u00e2n x\u01b0\u1edfng I.<\/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 Chuy\u00ean \u0110HKHTN TP HCM<\/strong><\/h2>\n

T\u1ea3i ngay \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Chuy\u00ean \u0110HKHTN TP HCM <\/strong>qua \u0111\u01b0\u1eddng link sau \u0111\u1ec3 th\u1eed s\u1ee9c v\u1edbi nh\u1eefng c\u00e2u h\u1ecfi ch\u1ea5t l\u01b0\u1ee3ng, b\u00e1m s\u00e1t \u0111\u1ec1 thi th\u1eadt nh\u1ea5t. \u0110\u00e2y s\u1ebd l\u00e0 b\u01b0\u1edbc \u0111\u1ec7m quan tr\u1ecdng gi\u00fap b\u1ea1n c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c, r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng l\u00e0m b\u00e0i v\u00e0 t\u1ef1 tin b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1 trong k\u1ef3 thi quan tr\u1ecdng. Ngo\u00e0i ra, b\u1ed9 t\u00e0i li\u1ec7u c\u00f2n k\u00e8m theo \u0111\u00e1p \u00e1n v\u00e0 c\u00e1ch gi\u1ea3i, tr\u00ecnh b\u00e0y khoa h\u1ecdc gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng \u00f4n t\u1eadp h\u01a1n.<\/p>\n