{"id":528,"date":"2026-05-05T04:50:32","date_gmt":"2026-05-05T04:50:32","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-tam-dao-ii-vinh-phuc\/"},"modified":"2026-05-05T07:23:53","modified_gmt":"2026-05-05T07:23:53","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-tam-dao-ii-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-tam-dao-ii-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 Tam \u0110\u1ea3o II 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 Tam \u0110\u1ea3o II V\u0129nh Ph\u00fac <\/strong>c\u00f3 n\u1ed9i dung b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh SGK, k\u1ebft h\u1ee3p v\u1edbi b\u00e0i to\u00e1n th\u1ef1c ti\u1ec5n hi\u1ec7n \u0111\u1ea1i. V\u00ec v\u1eady \u0111\u1ec1 thi c\u00f3 th\u1ec3 \u0111\u00e1nh gi\u00e1 ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n v\u00e0 ph\u00e1t tri\u1ec3n t\u01b0 duy \u1ee9ng d\u1ee5ng cho h\u1ecdc sinh. C\u00f9ng T\u00e0i Li\u1ec7u \u00d4n Thi<\/strong><\/a> t\u00ecm hi\u1ec3u v\u1ec1 \u0111i thi th\u1eed 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 Tam \u0110\u1ea3o II 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 Tam \u0110\u1ea3o II V\u0129nh Ph\u00fac<\/strong> g\u1ed3m <\/span>ba ph\u1ea7n t\u1eeb tr\u1eafc nghi\u1ec7m \u0111\u1ebfn t\u1ef1 lu\u1eadn ng\u1eafn, bao qu\u00e1t c\u00e1c l\u0129nh v\u1ef1c ki\u1ebfn th\u1ee9c t\u1eeb gi\u1ea3i t\u00edch, \u0111\u1ea1i s\u1ed1 \u0111\u1ebfn h\u00ecnh h\u1ecdc kh\u00f4ng gian v\u00e0 x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea nh\u01b0 \u0111\u01b0\u1ee3c th\u1ec3 hi\u1ec7n qua c\u00e1c c\u00e2u h\u1ecfi ti\u00eau bi\u1ec3u sau \u0111\u00e2y.<\/p>\n

PH\u1ea6N I: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn (12 c\u00e2u)<\/strong><\/span><\/p>\n

C\u00e2u 1:<\/strong> H\u00e0m s\u1ed1 $y = x^3 \u2013 3x^2 \u2013 9x + 7$ \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o sau \u0111\u00e2y?<\/p>\n

A. $(1; +\\infty)$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. $(-5; -2)$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. $(-\\infty; 1)$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. $(-1; 3)$<\/p>\n

C\u00e2u 2:<\/strong> Cho h\u00e0m s\u1ed1 $f(x)$ li\u00ean t\u1ee5c tr\u00ean $[-1;5]$ v\u00e0 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean d\u01b0\u1edbi. G\u1ecdi $M$ v\u00e0 $m$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho tr\u00ean $[-1;5]$. Gi\u00e1 tr\u1ecb c\u1ee7a $M \u2013 m$ b\u1eb1ng:<\/p>\n

\"\"<\/p>\n

A. $1$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. $6$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. $5$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. $4$<\/p>\n

PH\u1ea6N II: C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai (4 c\u00e2u)<\/strong><\/span><\/p>\n

C\u00e2u 1:<\/strong> Cho h\u00e0m s\u1ed1 $y = f(x)$ x\u00e1c \u0111\u1ecbnh tr\u00ean $\\mathbb{R}$ v\u00e0 c\u00f3 \u0111\u1ea1o h\u00e0m $f'(x) = 3x^2 \u2013 3x^2, \\forall x \\in \\mathbb{R}$. X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau:<\/p>\n

a) H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng $(1;+\\infty)$<\/p>\n

b) H\u00e0m s\u1ed1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb<\/p>\n

c) Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean \u0111o\u1ea1n $[0;3]$ \u0111\u1ea1t t\u1ea1i $x = 0$<\/p>\n

d) $f(2) > f(3)$<\/p>\n

C\u00e2u 2:<\/strong> Cho h\u00e0m s\u1ed1 $f(x)=\\begin{cases}
\n3x^2-2x+m & \\text{khi } x \\geq 1 \\\\
\n1-4x & \\text{khi } x < 1
\n\\end{cases}$ $(m \\text{ l\u00e0 tham s\u1ed1 th\u1ef1c})$ li\u00ean t\u1ee5c tr\u00ean $\\mathbb{R}$. Bi\u1ebft r\u1eb1ng $f(x)$ c\u00f3 nguy\u00ean h\u00e0m tr\u00ean $\\mathbb{R}$ l\u00e0 $F(x)$ l\u00e0 h\u00e0m li\u00ean t\u1ee5c tr\u00ean $\\mathbb{R}$ v\u00e0 th\u1ecfa m\u00e3n $F(-2)=-6$.<\/p>\n

a) $m = -4$<\/p>\n

b) $F(x)=\\begin{cases}
\nx^3-x^2-4x+7 & \\text{khi } x \\geq 1 \\\\
\nx-2x^2+4 & \\text{khi } x < 1
\n\\end{cases}$<\/p>\n

c) $\\int_{-1}^{5} f(x)dx = 108$<\/p>\n

d) $\\int_{1}^{e^2} f(\\ln x)\\frac{1}{x}dx = 3$<\/p>\n

PH\u1ea6N III: C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u)<\/span><\/strong><\/p>\n

C\u00e2u 1:<\/strong> Ch\u1ecb H\u00e0 d\u1ef1 \u0111\u1ecbnh s\u1eed d\u1ee5ng h\u1ebft $4m^2$ k\u00ednh \u0111\u1ec3 l\u00e0m m\u1ed9t b\u1ec3 c\u00e1 b\u1eb1ng k\u00ednh c\u00f3 d\u1ea1ng h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt kh\u00f4ng n\u1eafp, chi\u1ec1u d\u00e0i g\u1ea5p \u0111\u00f4i chi\u1ec1u r\u1ed9ng (c\u00e1c m\u1ed1i gh\u00e9p c\u00f3 k\u00edch th\u01b0\u1edbc kh\u00f4ng \u0111\u00e1ng k\u1ec3). B\u1ec3 c\u00e1 c\u00f3 dung t\u00edch l\u1edbn nh\u1ea5t b\u1eb1ng bao nhi\u00eau m\u00e9t kh\u1ed1i (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m)?<\/p>\n

C\u00e2u 2:<\/strong> M\u1ed9t th\u00f9ng \u0111\u1ef1ng Bia h\u01a1i (c\u00f3 d\u1ea1ng nh\u01b0 h\u00ecnh v\u1ebd) c\u00f3 \u0111\u01b0\u1eddng k\u00ednh \u0111\u00e1y l\u00e0 $30cm$, \u0111\u01b0\u1eddng k\u00ednh l\u1edbn nh\u1ea5t c\u1ee7a th\u00e2n th\u00f9ng l\u00e0 $40cm$, chi\u1ec1u cao th\u00f9ng l\u00e0 $60 cm$, c\u1ea1nh b\u00ean h\u00f4ng c\u1ee7a th\u00f9ng c\u00f3 h\u00ecnh d\u1ea1ng c\u1ee7a m\u1ed9t parabol. T\u00ednh th\u1ec3 t\u00edch c\u1ee7a th\u00f9ng Bia h\u01a1i (gi\u1ea3 s\u1eed \u0111\u1ed9 d\u00e0y v\u1ecf kh\u00f4ng \u0111\u00e1ng k\u1ec3 v\u00e0 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c).<\/p>\n

\"\"<\/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 Tam \u0110\u1ea3o II 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 Tam \u0110\u1ea3o II V\u0129nh Ph\u00fac<\/strong> s\u1ebd gi\u00fap h\u1ecdc sinh r\u00e8n luy\u1ec7n \u0111\u01b0\u1ee3c kh\u1ea3 n\u0103ng v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c to\u00e1n h\u1ecdc v\u00e0o gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n th\u1ef1c ti\u1ec5n, \u0111\u1ed3ng th\u1eddi c\u00f3 chi\u1ebfn l\u01b0\u1ee3c \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 cho k\u1ef3 thi quan tr\u1ecdng s\u1eafp t\u1edbi. C\u00e1c em h\u00e3y t\u1ea3i b\u1ea3n \u0111\u1ea7y \u0111\u1ee7 c\u1ee7a \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p thpt m\u00f4n to\u00e1n<\/a> v\u00e0 \u0111\u00e1p \u00e1n chi ti\u1ebft \u0111\u1ec3 luy\u1ec7n gi\u1ea3i, t\u1eeb \u0111\u00f3 x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c nh\u1eefng \u0111i\u1ec3m m\u1ea1nh, \u0111i\u1ec3m y\u1ebfu c\u1ee7a b\u1ea3n th\u00e2n v\u00e0 c\u00f3 k\u1ebf ho\u1ea1ch \u00f4n t\u1eadp ph\u00f9 h\u1ee3p.<\/p>\n