{"id":536,"date":"2026-05-05T04:50:57","date_gmt":"2026-05-05T04:50:57","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-tuyen-quang\/"},"modified":"2026-05-05T07:24:23","modified_gmt":"2026-05-05T07:24:23","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-tuyen-quang","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-so-gd-dt-tuyen-quang\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Tuy\u00ean Quang"},"content":{"rendered":"

C\u00e1c b\u1ea1n h\u1ecdc sinh 12 \u00f4n luy\u1ec7n \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Tuy\u00ean Quang<\/strong> cho k\u00ec thi thpt m\u00f4n to\u00e1n s\u1eafp t\u1edbi ch\u01b0a. \u0110\u00e2y ch\u00ednh l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u v\u00f4 c\u00f9ng h\u1eefu \u00edch gi\u00fap c\u00e1c b\u1ea1n l\u00e0m quen m\u1edbi ma tr\u1eadn \u0111\u1ec1 thi v\u00e0 r\u00fat ra nhi\u1ec1u kinh nghi\u1ec7m cho b\u00e0i thi th\u1eadt. H\u00e3y c\u00f9ng ch\u00fang t\u00f4i t\u00ecm hi\u1ec3u qua n\u1ed9i dung v\u00e0 \u00d4n Thi<\/a> ngay nh\u00e9.<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Tuy\u00ean Quang<\/strong><\/h2>\n

Ma tr\u1eadn \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Tuy\u00ean Quang<\/strong> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n theo c\u1ea5u tr\u00fac chung c\u1ee7a b\u1ed9 v\u1edbi quy \u0111\u1ecbnh m\u1edbi nh\u1ea5t. C\u00f3 nhi\u1ec1u c\u1ea3i ti\u1ebfn v\u1ec1 ch\u1ea5t l\u01b0\u1ee3ng c\u00e2u h\u1ecfi c\u0169ng nh\u01b0 quy \u0111\u1ecbnh c\u00e1ch tr\u00ecnh b\u00e0y trong \u0111\u1ec1 thi. Chi ti\u1ebft n\u1ed9i dung trong \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p thpt m\u00f4n to\u00e1n nh\u01b0 sau:<\/p>\n

Ph\u1ea7n 1 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/p>\n

Th\u00ed sinh ch\u1ec9 c\u1ea7n ch\u1ecdn m\u1ed9t \u0111\u00e1p \u00e1n ch\u00ednh x\u00e1c trong 4 \u0111\u00e1p \u00e1n A, B, C, D.<\/p>\n

C\u00e2u 1:<\/strong> Cho h\u00ecnh l\u1eadp ph\u01b0\u01a1ng ABCD.EFGH c\u1ea1nh b\u1eb1ng a . Gi\u00e1 tr\u1ecb c\u1ee7a AC\u20d7 \u00b7 EG\u20d7 b\u1eb1ng:<\/p>\n

A. -a\u00b2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. a\u00b2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. -2a\u00b2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. 2a\u00b2 <\/p>\n

C\u00e2u 2:<\/strong> T\u1eadp nghi\u1ec7m S c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 2^x\u00b2 + 7x + 10 = 1 l\u00e0<\/p>\n

A. S = 2; 5 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. S = -5; -2 <\/p>\n

C. S = -5; 2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. S = (-7 – \u221a13)\/(2), (-7 + \u221a13)\/(2) <\/p>\n

Ph\u1ea7n 2 \u2013 C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai
\n<\/strong>
\nC\u00f3 t\u1ea5t c\u1ea3 4 c\u00e2u h\u1ecfi ph\u00e2n b\u1ed5 \u0111\u1ec1u c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 h\u00ecnh h\u1ecdc kh\u00f4ng gian, ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1, x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea,\u2026Xem qua c\u00e1c v\u00ed d\u1ee5 sau:<\/p>\n

C\u00e2u 1:<\/strong> M\u1ed9t trang s\u00e1ch c\u00f3 d\u1ea1ng h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 di\u1ec7n t\u00edch 486 cm\u00b2 . Gi\u1ea3 s\u1eed trang s\u00e1ch \u0111\u01b0\u1ee3c \u0111\u1eb7t d\u1ecdc tr\u00ean m\u1eb7t b\u00e0n v\u00e0 l\u1ec1 tr\u00ean, l\u1ec1 d\u01b0\u1edbi \u0111\u1ec1u \u0111\u1ec3 3 cm; l\u1ec1 tr\u00e1i v\u00e0 l\u1ec1 ph\u1ea3i \u0111\u1ec1u \u0111\u1ec3 2 cm; ph\u1ea7n c\u00f2n l\u1ea1i c\u1ee7a trang s\u00e1ch \u0111\u01b0\u1ee3c in ch\u1eef. G\u1ecdi x l\u00e0 chi\u1ec1u r\u1ed9ng c\u1ee7a trang s\u00e1ch.<\/p>\n

a) Chi\u1ec1u d\u00e0i c\u1ee7a trang s\u00e1ch khi \u0111\u00f3 l\u00e0 486\/x (cm)<\/p>\n

b) Ph\u1ea7n in ch\u1eef c\u1ee7a trang s\u00e1ch c\u00f3 di\u1ec7n t\u00edch l\u1edbn nh\u1ea5t khi x = 18 (cm) <\/p>\n

c) Ph\u1ea7n in ch\u1eef c\u1ee7a trang s\u00e1ch c\u00f3 di\u1ec7n t\u00edch l\u1edbn nh\u1ea5t l\u00e0 276 cm\u00b2 <\/p>\n

d) Ph\u1ea7n di\u1ec7n t\u00edch l\u1ec1 \u0111\u1ec3 tr\u1ed1ng l\u00e0 210 cm\u00b2 <\/p>\n

C\u00e2u 2:<\/strong> Trong kh\u00f4ng gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz cho tam gi\u00e1c ABC v\u1edbi A(4;0;2), B(1;-4;-2), C(2;1;1) <\/p>\n

a) T\u1ecda \u0111\u1ed9 tr\u1ecdng t\u00e2m tam gi\u00e1c ABC l\u00e0 G(7\/3; -1; 1\/3) <\/p>\n

b) Di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c ABC b\u1eb1ng (\u221a210)\/(2) <\/p>\n

c) T\u1ecda \u0111\u1ed9 \u0111i\u1ec3m D th\u1ecfa m\u00e3n ABCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 D(5;5;5) <\/p>\n

d) G\u1ecdi \u0111i\u1ec3m E(a; b; c) l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng BC v\u1edbi m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 (Oxz) khi \u0111\u00f3 2a\/c + b = 9\/2\n<\/p>\n

Ph\u1ea7n 3 \u2013 Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/p>\n

C\u00e1c c\u00e2u h\u1ecfi ph\u1ea7n 3 c\u00f3 \u0111\u1ed9 kh\u00f3 t\u0103ng theo t\u1eebng b\u1eadc, th\u00ed sinh c\u1ea7n ph\u1ea3i n\u1eafm v\u1eefng l\u00fd thuy\u1ebft v\u00e0 bi\u1ebft v\u1eadn d\u1ee5ng \u0111\u1ec3 gi\u1ea3i \u0111\u1ec1. Ngo\u00e0i ra, c\u00e1ch tr\u00ecnh b\u00e0y t\u1ed1t v\u00e0 r\u00e0nh m\u1ea1ch s\u1ebd \u0111\u01b0\u1ee3c \u0111i\u1ec3m c\u1ed9ng cao. V\u00ed d\u1ee5:<\/p>\n

C\u00e2u 1:<\/strong> M\u1ed9t c\u00e1i ao c\u00f3 h\u00ecnh ABCDE tham kh\u1ea3o h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y, \u1edf gi\u1eefa ao c\u00f3 m\u1ed9t m\u1ea3nh v\u01b0\u1eddn tr\u1ed3ng hoa h\u00ecnh tr\u00f2n b\u00e1n k\u00ednh 9 m ng\u01b0\u1eddi ta mu\u1ed1n b\u1eafc m\u1ed9t c\u00e2y c\u1ea7u t\u1eeb b\u1edd AB c\u1ee7a ao \u0111\u1ebfn v\u01b0\u1eddn. Hai b\u1edd AE v\u00e0 BC n\u1eb1m tr\u00ean hai \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi nhau, hai \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y c\u1eaft nhau t\u1ea1i \u0111i\u1ec3m O . B\u1edd AB l\u00e0 m\u1ed9t ph\u1ea7n c\u1ee7a parabol c\u00f3 \u0111\u1ec9nh l\u00e0 \u0111i\u1ec3m A v\u00e0 c\u00f3 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng OA . \u0110\u1ed9 d\u00e0i \u0111o\u1ea1n OA v\u00e0 OB l\u1ea7n l\u01b0\u1ee3t l\u00e0 48 m v\u00e0 20 m, t\u00e2m I c\u1ee7a m\u1ea3nh v\u01b0\u1eddn c\u00e1ch \u0111\u01b0\u1eddng th\u1eb3ng AE v\u00e0 BC l\u1ea7n l\u01b0\u1ee3t l\u00e0 48 m v\u00e0 30 m. \u0110\u1ed9 d\u00e0i ng\u1eafn nh\u1ea5t c\u00f3 th\u1ec3 c\u1ee7a c\u00e2y c\u1ea7u l\u00e0 bao nhi\u00eau m\u00e9t (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n ch\u1ee5c)?<\/p>\n

C\u00e2u 2:<\/strong> Hai chi\u1ebfc m\u00e1y bay kh\u00f4ng ng\u01b0\u1eddi l\u00e1i c\u00f9ng bay l\u00ean t\u1eeb m\u1ed9t \u0111\u1ecba \u0111i\u1ec3m. Sau m\u1ed9t gi\u1edd bay, chi\u1ebfc th\u1ee9 nh\u1ea5t c\u00e1ch \u0111i\u1ec3m xu\u1ea5t ph\u00e1t v\u1ec1 ph\u00eda b\u1eafc 23 km v\u00e0 v\u1ec1 ph\u00eda t\u00e2y 18 km, \u0111\u1ed3ng th\u1eddi c\u00e1ch m\u1eb7t \u0111\u1ea5t 2 km. Chi\u1ebfc th\u1ee9 hai c\u00e1ch \u0111i\u1ec3m xu\u1ea5t ph\u00e1t v\u1ec1 ph\u00eda \u0111\u00f4ng 22 km v\u00e0 v\u1ec1 ph\u00eda nam 27 km, \u0111\u1ed3ng th\u1eddi c\u00e1ch m\u1eb7t \u0111\u1ea5t 3 km.<\/p>\n

Ch\u1ecdn h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz v\u1edbi g\u1ed1c O \u0111\u1eb7t t\u1ea1i \u0111i\u1ec3m xu\u1ea5t ph\u00e1t c\u1ee7a hai chi\u1ebfc m\u00e1y bay, m\u1eb7t ph\u1eb3ng (Oxy) tr\u00f9ng v\u1edbi m\u1eb7t \u0111\u1ea5t sao cho tr\u1ee5c Ox h\u01b0\u1edbng v\u1ec1 ph\u00eda b\u1eafc, tr\u1ee5c Oy h\u01b0\u1edbng v\u1ec1 ph\u00eda t\u00e2y v\u00e0 tr\u1ee5c Oz h\u01b0\u1edbng th\u1eb3ng \u0111\u1ee9ng l\u00ean tr\u1eddi, \u0111\u01a1n v\u1ecb \u0111o l\u1ea5y theo kil\u00f4m\u00e9t. Sau \u0111\u00fang m\u1ed9t gi\u1edd bay, hai m\u00e1y bay \u0111\u00f3 c\u00f9ng b\u1eafn m\u1ed9t m\u1ee5c ti\u00eau di \u0111\u1ed9ng tr\u00ean m\u1eb7t \u0111\u1ea5t. Bi\u1ebft t\u1ed5ng kho\u1ea3ng c\u00e1ch t\u1eeb m\u1ed7i m\u00e1y bay \u0111\u1ebfn m\u1ee5c ti\u00eau l\u00e0 nh\u1ecf nh\u1ea5t, l\u00fac \u0111\u00f3 m\u1ee5c ti\u00eau c\u1ea7n \u0111i\u1ec3m xu\u1ea5t ph\u00e1t c\u1ee7a hai m\u00e1y bay bao nhi\u00eau kil\u00f4m\u00e9t (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng ph\u1ea7n tr\u0103m)?<\/p>\n

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Tuy\u00ean Quang<\/strong><\/h2>\n

C\u00e1c b\u1ea1n h\u1ecdc sinh 12 chu\u1ea9n b\u1ecb l\u1ed9 tr\u00ecnh \u00f4n luy\u1ec7n b\u1eb1ng c\u00e1ch gi\u1ea3i th\u1eadt nhi\u1ec1u \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p thpt m\u00f4n to\u00e1n<\/a>. T\u1ea3i ngay \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 S\u1edf GD & \u0110T Tuy\u00ean Quang<\/strong> qua \u0111\u01b0\u1eddng link sau \u0111\u00e2y v\u00e0 luy\u1ec7n t\u1eadp t\u1eeb h\u00f4m nay nh\u00e9. Ch\u1eafc h\u1eb3n, \u0111\u00e2y s\u1ebd l\u00e0 ch\u00eca kh\u00f3a gi\u00fap b\u1ea1n n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c v\u00e0 chinh ph\u1ee5c th\u00e0nh t\u00edch cao.<\/p>\n