\u0110\u1ec1 To\u00e1n v\u00e0o \u0110H Y H\u00e0 N\u1ed9i n\u0103m 2000 to\u00e0n c\u00e2u trong s\u00e1ch gi\u00e1o khoa, mang t\u00ednh l\u00fd thuy\u1ebft, nh\u01b0ng \u0111\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c th\u00ed sinh c\u1ea7n hi\u1ec3u s\u00e2u ki\u1ebfn th\u1ee9c.<\/strong><\/em><\/p>\n

Th\u1ea7y gi\u00e1o Ph\u1ea1m Xu\u00e2n Anh chia s\u1ebb quan \u0111i\u1ec3m v\u1ec1 vi\u1ec7c ra \u0111\u1ec1 thi THPT qu\u1ed1c gia.<\/em><\/p>\n

V\u1edbi t\u01b0 c\u00e1ch l\u00e0 m\u1ed9t gi\u00e1o vi\u00ean m\u00f4n To\u00e1n THPT, qua \u0111\u1ec1 thi m\u00f4n To\u00e1n THPT qu\u1ed1c gia v\u1eeba r\u1ed3i, t\u00f4i xin \u0111\u01b0a ra th\u00eam m\u1ed9t g\u00f3c nh\u00ecn v\u1ec1 chuy\u1ec7n ra \u0111\u1ec1 thi. \u0110\u1ec3 n\u00f3i v\u1ec1 vi\u1ec7c ra \u0111\u1ec1 thi, \u1edf \u0111\u00e2y minh h\u1ecda b\u1eb1ng \u0111\u1ec1 thi m\u00f4n To\u00e1n, t\u00f4i xin k\u1ec3 hai c\u00e2u chuy\u1ec7n:<\/p>\n

N\u0103m th\u1ee9 nh\u1ea5t c\u1ee7a sinh vi\u00ean Khoa To\u00e1n, \u0110\u1ea1i h\u1ecdc Khoa h\u1ecdc t\u1ef1 nhi\u00ean (\u0110\u1ea1i h\u1ecdc Qu\u1ed1c gia H\u00e0 N\u1ed9i) c\u00f3 m\u00f4n \u0110\u1ea1i s\u1ed1 \u0111\u1ea1i c\u01b0\u01a1ng. \u0110\u00e2y l\u00e0 m\u00f4n h\u1ecdc kh\u00f3 v\u00ec r\u1ea5t tr\u1eebu t\u01b0\u1ee3ng. N\u0103m \u0111\u00f3 th\u1ea7y d\u1ea1y l\u1edbp ch\u00fang t\u00f4i l\u00e0 m\u1ed9t gi\u00e1o s\u01b0 To\u00e1n n\u1ed5i ti\u1ebfng. Ngo\u00e0i vi\u1ec7c gi\u1ea3ng d\u1ea1y \u1edf Vi\u1ec7t Nam, th\u1ea7y c\u00f2n tham gia gi\u1ea3ng d\u1ea1y t\u1ea1i m\u1ed9t tr\u01b0\u1eddng \u0111\u1ea1i h\u1ecdc l\u1edbn t\u1ea1i Nh\u1eadt B\u1ea3n. Khi h\u1ecdc r\u1ea5t kh\u00f3 nh\u01b0ng khi th\u1ea7y ra \u0111\u1ec1 thi th\u00ec l\u1ea1i c\u00f3 v\u1ebb… \u0111\u01a1n gi\u1ea3n: to\u00e0n n\u00eau \u0111\u1ecbnh ngh\u0129a, ch\u1ee9ng minh \u0111\u1ecbnh l\u00fd r\u1ed3i \u00e1p d\u1ee5ng \u0111\u1ec3 gi\u1ea3i b\u00e0i t\u1eadp.<\/p>\n

<\/p>\n

Tuy nhi\u00ean, v\u1ea5n \u0111\u1ec1 ch\u00ednh l\u1ea1i \u1edf \u0111\u00f3. Mu\u1ed1n l\u00e0m \u0111\u01b0\u1ee3c b\u00e0i, sinh vi\u00ean ph\u1ea3i hi\u1ec3u s\u00e2u v\u1ea5n \u0111\u1ec1. N\u1ebfu h\u1ecdc g\u1ea1o, h\u1ecdc m\u00ec \u0103n li\u1ec1n, ch\u1ec9 c\u1ea7n nh\u1edb c\u00f4ng th\u1ee9c r\u1ed3i \u00e1p d\u1ee5ng v\u00e0o gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp th\u00ec s\u1ebd kh\u00f4ng th\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c, ngh\u0129a l\u00e0 \u0111\u1ec1 thi ki\u1ec3u n\u00e0y ho\u00e0n to\u00e0n kh\u00f4ng h\u1ec1 \u0111\u01a1n gi\u1ea3n. Trong \u0111\u1ec1 thi c\u00f3 c\u00e2u, \u0111\u1ea1i \u00fd: “H\u00e3y \u0111\u1ecbnh ngh\u0129a ph\u1ea7n t\u1eed trung h\u00f2a c\u1ee7a m\u1ed9t kh\u00f4ng gian to\u00e1n E. K\u00fd hi\u1ec7u ph\u1ea7n t\u1eed trung h\u00f2a l\u00e0 0, d\u00f9ng \u0111\u1ecbnh ngh\u0129a \u0111\u1ec3 ch\u1ee9ng minh r\u1eb1ng a*0 = 0; a + 0 = a v\u1edbi a thu\u1ed9c E”.<\/p>\n

\u1ede \u0111\u00e2y c\u00f3 m\u1ed9t ch\u00fat v\u1ec1 chuy\u00ean m\u00f4n nghe c\u00f3 v\u1ebb kh\u00f3 hi\u1ec3u, nh\u01b0ng th\u1ef1c t\u1ebf c\u0169ng kh\u00f4ng \u0111\u1ebfn n\u1ed7i kh\u00f3 hi\u1ec3u l\u1eafm. S\u1ed1 0 ch\u1eb3ng h\u1ea1n, ch\u00fang ta v\u1eabn d\u00f9ng m\u1ed9t c\u00e1ch t\u1ef1 nhi\u00ean, nh\u01b0ng v\u1edbi nh\u1eefng ng\u01b0\u1eddi nghi\u00ean c\u1ee9u To\u00e1n th\u00ec c\u1ea7n ph\u1ea3i \u0111\u1ecbnh ngh\u0129a r\u1ed3i m\u1edbi \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng. V\u00ed d\u1ee5, c\u1ee5 th\u1ec3 \u0111\u1ec3 minh h\u1ecda cho \u0111i\u1ec1u n\u00e0y th\u00ec s\u1ed1 0 l\u00e0 m\u1ed9t ph\u1ea7n t\u1eed trung h\u00f2a tr\u00ean t\u1eadp h\u1ee3p s\u1ed1 t\u1ef1 nhi\u00ean, hi\u1ec3n nhi\u00ean a + 0 = a; a * 0 = 0 v\u1edbi b\u1ea5t c\u1ee9 s\u1ed1 t\u1ef1 nhi\u00ean a n\u00e0o.<\/p>\n

C\u00e2u h\u1ecfi n\u00e0y nghe th\u00ec \u0111\u01a1n gi\u1ea3n nh\u01b0ng l\u1ea1i r\u1ea5t b\u1ea5t ng\u1edd v\u00e0 kh\u00f3 v\u1edbi \u0111a s\u1ed1 sinh vi\u00ean l\u1edbp ch\u00fang t\u00f4i. N\u1ebfu nh\u01b0 \u00e1p d\u1ee5ng ngay c\u00f4ng th\u1ee9c th\u00ec s\u1ebd c\u00f3 ngay k\u1ebft qu\u1ea3 a + 0 = a; a * 0 = 0. Tuy nhi\u00ean, \u0111\u1ec3 x\u00e2y d\u1ef1ng c\u00f4ng th\u1ee9c n\u00e0y, t\u1ee9c l\u00e0 hi\u1ec3u th\u1eadt s\u00e2u v\u1ea5n \u0111\u1ec1 th\u00ec kh\u00f4ng h\u1ec1 \u0111\u01a1n gi\u1ea3n.<\/p>\n

Trong \u0111\u1ec1 thi c\u00f2n nhi\u1ec1u c\u00e2u kh\u00e1c ho\u00e0n to\u00e0n trong nh\u1eefng ph\u1ea7n \u0111\u00e3 h\u1ecdc, kh\u00f4ng \u0111\u00e1nh \u0111\u1ed1. Nh\u01b0ng nh\u01b0 \u0111\u00e3 n\u00f3i \u1edf tr\u00ean, \u0111\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c th\u00ec sinh vi\u00ean ph\u1ea3i hi\u1ec3u r\u1ea5t s\u00e2u v\u1ea5n \u0111\u1ec1, t\u1ee9c l\u00e0 ph\u1ea3i ch\u1ecbu h\u1ecdc, ch\u1ecbu kh\u00f3 t\u00ecm t\u00f2i. K\u1ebft qu\u1ea3 l\u00e0 s\u1ed1 sinh vi\u00ean l\u1edbp ch\u00fang t\u00f4i b\u1ecb r\u1edbt m\u00f4n n\u00e0y r\u1ea5t cao, chi\u1ebfm \u0111\u1ebfn 2 ph\u1ea7n 3.<\/p>\n

Qua th\u1eddi gian ch\u00fang t\u00f4i nh\u1eadn th\u1ea5y r\u1eb1ng nh\u1eefng ng\u01b0\u1eddi \u0111i\u1ec3m t\u1ed1t m\u00f4n n\u00e0y l\u00e0 nh\u1eefng ng\u01b0\u1eddi th\u00e0nh c\u00f4ng trong cu\u1ed9c s\u1ed1ng sau n\u00e0y: \u1edf n\u01b0\u1edbc ngo\u00e0i nhi\u1ec1u ng\u01b0\u1eddi l\u00e0 gi\u00e1o s\u01b0, ti\u1ebfn s\u0129 t\u1ea1i nh\u1eefng tr\u01b0\u1eddng \u0111\u1ea1i h\u1ecdc h\u00e0ng \u0111\u1ea7u c\u1ee7a M\u1ef9, Ph\u00e1p, Nh\u1eadt; \u1edf trong n\u01b0\u1edbc th\u00ec c\u00f3 ng\u01b0\u1eddi l\u00e0m ch\u1ee7 doanh nghi\u1ec7p, c\u00f3 t\u00e0i s\u1ea3n r\u1ea5t l\u1edbn d\u00f9 tu\u1ed5i \u0111\u1eddi c\u00f2n tr\u1ebb.<\/p>\n

C\u00e2u chuy\u1ec7n th\u1ee9 hai l\u00e0 nh\u1eefng n\u0103m tr\u01b0\u1edbc khi c\u00e1c tr\u01b0\u1eddng \u0111\u1ea1i h\u1ecdc t\u1ed5 ch\u1ee9c \u0111\u1ec1 thi ri\u00eang bi\u1ec7t th\u00ec \u0111\u1ec1 thi c\u1ee7a \u0110\u1ea1i h\u1ecdc Y H\u00e0 N\u1ed9i l\u00e0 m\u1ed9t trong nh\u1eefng \u0111\u1ec1 thi kh\u00f3 nh\u1ea5t. \u0110\u1ec1 thi To\u00e1n n\u0103m 2000 c\u1ee7a tr\u01b0\u1eddng n\u00e0y to\u00e0n l\u00e0 nh\u1eefng c\u00e2u trong s\u00e1ch gi\u00e1o khoa, mang t\u00ednh l\u00fd thuy\u1ebft. Tuy v\u1eady \u0111\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c th\u00ed sinh c\u1ea7n hi\u1ec3u r\u1ea5t s\u00e2u ki\u1ebfn th\u1ee9c. Trong \u0111\u1ec1 thi c\u00f3 c\u00e2u: “H\u00e3y t\u00ednh \u0111\u1ea1o h\u00e0m theo \u0111\u1ecbnh ngh\u0129a c\u1ee7a h\u00e0m s\u1ed1 y = 2000 m\u0169 x”, hi\u1ec3n nhi\u00ean l\u00e0 ho\u00e0n to\u00e0n trong s\u00e1ch gi\u00e1o khoa, kh\u00f4ng \u0111\u00e1nh \u0111\u1ed1, kh\u00f4ng c\u1ea7n… \u0111i h\u1ecdc th\u00eam v\u1eabn c\u00f3 th\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c.<\/p>\n

Tuy nhi\u00ean l\u1ea1i kh\u00f4ng h\u1ec1 \u0111\u01a1n gi\u1ea3n nh\u01b0 v\u1eady. N\u1ebfu \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c th\u00ec ch\u1ec9 \u0111\u00fang m\u1ed9t d\u00f2ng. Nh\u01b0ng \u1edf \u0111\u00e2y kh\u00f4ng \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng m\u00e0 ph\u1ea3i x\u00e2y d\u1ef1ng c\u00f4ng th\u1ee9c \u0111\u00f3, t\u1ee9c l\u00e0 c\u1ea7n hi\u1ec3u r\u1ea5t s\u00e2u v\u1ea5n \u0111\u1ec1. V\u00e0 ch\u1ec9 nh\u1eefng th\u00ed sinh v\u1edbi t\u01b0 duy s\u00e2u s\u1eafc, suy lu\u1eadn logic… m\u1edbi c\u00f3 th\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c. K\u1ebft qu\u1ea3 l\u00e0 sinh vi\u00ean Y H\u00e0 N\u1ed9i th\u01b0\u1eddng l\u00e0 nh\u1eefng th\u00ed sinh gi\u1ecfi nh\u1ea5t nh\u01b0 ch\u00fang ta th\u1ea5y.<\/p>\n

Tr\u1edf l\u1ea1i v\u1ea5n \u0111\u1ec1 v\u1ec1 \u0111\u1ec1 thi To\u00e1n THPT qu\u1ed1c gia n\u0103m h\u1ecdc 2018-2019 v\u1eeba qua, d\u00f9 k\u1ef3 thi \u0111\u00e3 di\u1ec5n ra \u0111\u01b0\u1ee3c m\u1ea5y th\u00e1ng nh\u01b0ng d\u01b0 \u00e2m v\u1ec1 \u0111\u1ed9 kh\u00f3, nhi\u1ec1u c\u00e2u mang t\u00ednh \u0111\u00e1nh \u0111\u1ed1 c\u1ee7a \u0111\u1ec1 thi m\u00f4n To\u00e1n v\u1eabn c\u00f2n n\u00f3ng.<\/p>\n

Qua hai c\u00e2u chuy\u1ec7n tr\u00ean, t\u00f4i mu\u1ed1n \u0111\u01b0a ra m\u1ed9t g\u00f3c nh\u00ecn c\u1ee7a m\u00ecnh v\u1ec1 chuy\u1ec7n ra \u0111\u1ec1 thi. Kh\u00f4ng c\u1ea7n ph\u1ea3i \u0111\u00e1nh \u0111\u1ed1, kh\u00f4ng c\u1ea7n cao si\u00eau, ch\u1ec9 c\u1ea7n trong s\u00e1ch gi\u00e1o khoa v\u1edbi nh\u1eefng c\u00e2u h\u1ecfi ki\u1ec3u: ch\u1ee9ng minh l\u1ea1i \u0111\u1ecbnh l\u00fd; gi\u1ea3i b\u00e0i to\u00e1n theo \u0111\u1ecbnh ngh\u0129a, gi\u1ea3i b\u00e0i t\u1eadp trong b\u00e0i \u0111\u1ecdc th\u00eam… th\u00ec ch\u00fang ta v\u1eabn c\u00f3 th\u1ec3 tuy\u1ec3n ch\u1ecdn \u0111\u01b0\u1ee3c nh\u1eefng th\u00ed sinh c\u00f3 l\u1ef1c h\u1ecdc t\u1ed1t, \u0111\u1ed3ng th\u1eddi v\u1eabn c\u00f3 th\u1ec3 ph\u00e2n lo\u1ea1i th\u00ed sinh \u0111\u01b0\u1ee3c v\u00ec ng\u01b0\u1eddi gi\u1ecfi th\u1ef1c s\u1ef1 c\u1ea7n ph\u1ea3i hi\u1ec3u s\u00e2u s\u1eafc v\u1ea5n \u0111\u1ec1. \u1ede Khoa To\u00e1n, \u0110\u1ea1i h\u1ecdc Khoa h\u1ecdc T\u1ef1 nhi\u00ean (\u0110\u1ea1i h\u1ecdc Qu\u1ed1c gia H\u00e0 N\u1ed9i), nh\u1eefng ng\u01b0\u1eddi d\u1ea1y l\u00fd thuy\u1ebft To\u00e1n \u0111\u1ec1u l\u00e0 nh\u1eefng gi\u00e1o s\u01b0, ti\u1ebfn s\u0129 To\u00e1n n\u1ed5i ti\u1ebfng, d\u1ea1y b\u00e0i t\u1eadp th\u01b0\u1eddng l\u00e0 nh\u1eefng tr\u1ee3 gi\u1ea3ng.<\/p>\n

V\u1edbi \u0111\u1ec1 thi ho\u00e0n to\u00e0n trong s\u00e1ch gi\u00e1o khoa th\u00ec t\u00ecnh tr\u1ea1ng h\u1ecdc th\u00eam, d\u1ea1y th\u00eam s\u1ebd h\u1ea1n ch\u1ebf r\u1ea5t nhi\u1ec1u (m\u00e0 n\u1ebfu c\u00f3 th\u00ec h\u1ecdc sinh s\u1ebd \u0111\u01b0\u1ee3c h\u1ecdc k\u1ef9 v\u1ec1 \u0111\u1ecbnh ngh\u0129a, \u0111\u1ecbnh l\u00fd trong s\u00e1ch gi\u00e1o khoa, t\u1ee9c l\u00e0 s\u1ebd hi\u1ec3u s\u00e2u ki\u1ebfn th\u1ee9c g\u1ed1c ch\u1eb3ng ph\u1ea3i l\u00e0 t\u1ed1t l\u1eafm sao). \u0110i\u1ec1u quan tr\u1ecdng h\u01a1n l\u00e0 gi\u00fap h\u1ecdc sinh ch\u00fang ta ph\u1ea3i hi\u1ec3u s\u00e2u ki\u1ebfn th\u1ee9c To\u00e1n ph\u1ed5 th\u00f4ng, g\u1ed1c c\u1ee7a m\u1ee5c \u0111\u00edch gi\u1ea3ng d\u1ea1y m\u00f4n To\u00e1n cho h\u1ecdc sinh ph\u1ed5 th\u00f4ng.<\/p>\n

Khi hi\u1ec3u s\u00e2u s\u1eafc ki\u1ebfn th\u1ee9c To\u00e1n ph\u1ed5 th\u00f4ng, h\u1ecdc sinh s\u1ebd c\u00f3 t\u01b0 duy logic, suy lu\u1eadn s\u1eafc b\u00e9n, gi\u00fap c\u00e1c em c\u00f3 n\u1ec1n t\u1ea3ng, k\u1ef9 n\u0103ng t\u1ed1t \u0111\u1ec3 b\u01b0\u1edbc v\u00e0o \u0111\u1eddi. Ngo\u00e0i chuy\u1ec7n ra \u0111\u1ec1 thi qu\u1ed1c gia th\u00ec c\u00f2n c\u00f3 nh\u1eefng \u0111\u1ec1 15 ph\u00fat, m\u1ed9t ti\u1ebft, h\u1ecdc k\u1ef3…, vi\u1ec7c ra \u0111\u1ec1 thi ho\u00e0n to\u00e0n trong s\u00e1ch gi\u00e1o khoa \u0111\u1ec3 v\u1eeba gi\u00fap h\u1ecdc sinh hi\u1ec3u s\u00e2u v\u1ea5n \u0111\u1ec1, v\u1eeba c\u00f3 th\u1ec3 ph\u00e2n lo\u1ea1i h\u1ecdc sinh l\u00e0 ho\u00e0n to\u00e0n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c. \u0110i\u1ec1u n\u00e0y kh\u00f4ng ch\u1ec9 \u0111\u00fang v\u1edbi ri\u00eang m\u00f4n To\u00e1n m\u00e0 c\u00e1c m\u00f4n kh\u00e1c c\u0169ng v\u1eady!<\/p>\n

Theo VNE<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0110\u1ec1 To\u00e1n v\u00e0o \u0110H Y H\u00e0 N\u1ed9i n\u0103m 2000 to\u00e0n c\u00e2u trong s\u00e1ch gi\u00e1o khoa, mang t\u00ednh l\u00fd thuy\u1ebft, nh\u01b0ng \u0111\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c th\u00ed sinh c\u1ea7n hi\u1ec3u s\u00e2u ki\u1ebfn th\u1ee9c. Th\u1ea7y gi\u00e1o Ph\u1ea1m Xu\u00e2n Anh chia s\u1ebb quan \u0111i\u1ec3m v\u1ec1 vi\u1ec7c ra \u0111\u1ec1 thi THPT qu\u1ed1c gia. V\u1edbi t\u01b0 c\u00e1ch l\u00e0 m\u1ed9t gi\u00e1o vi\u00ean m\u00f4n […]<\/p>\n","protected":false},"author":3,"featured_media":35479,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[19],"tags":[],"yoast_head":"\n