10 b\u00ed quy\u1ebft \u0111\u1ec3 l\u00e0m b\u00e0i thi m\u00f4n To\u00e1n THPT qu\u1ed1c gia 2016 hi\u1ec7u qu\u1ea3 nh\u1ea5t<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/10-bi-quyet-de-lam-bai-thi-mon-toan-thpt-quoc-gia-2016-hieu-qua-nhat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"10 b\u00ed quy\u1ebft \u0111\u1ec3 l\u00e0m b\u00e0i thi m\u00f4n To\u00e1n THPT qu\u1ed1c gia 2016 hi\u1ec7u qu\u1ea3 nh\u1ea5t\" \/>\n<meta property=\"og:description\" content=\"S\u1ed1 h\u1ecdc sinh \u0111\u1ea1t \u0111i\u1ec3m t\u1ed1i \u0111a m\u00f4n To\u00e1n trong k\u00ec thi THPT qu\u1ed1c gia c\u00f2n r\u1ea5t \u00edt, b\u1edfi c\u00e1c em th\u01b0\u1eddng m\u1eafc ph\u1ea3i nh\u1eefng sai s\u00f3t r\u1ea5t \u0111\u00e1ng ti\u1ebfc khi l\u00e0m b\u00e0i. \u0110\u1ec3 gi\u00fap c\u00e1c em c\u00f3 th\u1ec3 h\u1ea1n ch\u1ebf v\u00e0 kh\u1eafc ph\u1ee5c c\u00e1c sai s\u00f3t, ThS Ng\u00f4 Thanh S\u01a1n, t\u1ed5 tr\u01b0\u1edfng t\u1ed5 To\u00e1n […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lop12.edu.vn\/10-bi-quyet-de-lam-bai-thi-mon-toan-thpt-quoc-gia-2016-hieu-qua-nhat\/\" \/>\n<meta property=\"og:site_name\" content=\"Lop12.edu.vn - 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{"id":505,"date":"2016-03-02T18:06:12","date_gmt":"2016-03-02T18:06:12","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=505"},"modified":"2016-03-02T18:06:12","modified_gmt":"2016-03-02T18:06:12","slug":"10-bi-quyet-de-lam-bai-thi-mon-toan-thpt-quoc-gia-2016-hieu-qua-nhat","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/10-bi-quyet-de-lam-bai-thi-mon-toan-thpt-quoc-gia-2016-hieu-qua-nhat\/","title":{"rendered":"10 b\u00ed quy\u1ebft \u0111\u1ec3 l\u00e0m b\u00e0i thi m\u00f4n To\u00e1n THPT qu\u1ed1c gia 2016 hi\u1ec7u qu\u1ea3 nh\u1ea5t"},"content":{"rendered":"

Kh\u00f4ng n\u00ean th\u1ee9c qu\u00e1 khuya<\/strong><\/p>\n

Trong nh\u1eefng ng\u00e0y g\u1ea7n thi do t\u00e2m l\u00fd qu\u00e1 lo l\u1eafng n\u00ean m\u1ed9t s\u1ed1 em ti\u1ebfp t\u1ee5c \u00f4n thi r\u1ea5t c\u0103ng th\u1eb3ng: th\u1ee9c qu\u00e1 khuya, s\u01b0u t\u1ea7m th\u00eam b\u00e0i t\u1eadp l\u1ea1 v\u00e0 kh\u00f3 \u0111\u1ec3 gi\u1ea3i. Th\u1eadt ra \u0111i\u1ec1u n\u00e0y l\u00e0 kh\u00f4ng n\u00ean v\u00ec ch\u1ec9 khi\u1ebfn c\u00e1c em m\u1ea5t s\u1ee9c kh\u1ecfe, th\u1eddi gian v\u00e0 s\u1ef1 t\u1ef1 tin.<\/p>\n

C\u00e1c em n\u00ean \u00f4n t\u1eadp m\u1ed9t c\u00e1ch nh\u1eb9 nh\u00e0ng b\u1eb1ng c\u00e1ch xem l\u1ea1i c\u00e1c b\u00e0i t\u1eadp v\u00e0 c\u00e1c c\u00f4ng th\u1ee9c \u0111\u00e3 \u0111\u01b0\u1ee3c h\u1ecdc trong n\u0103m. C\u1ed1 g\u1eafng \u0111\u1ec3 khi v\u00e0o ph\u00f2ng thi, c\u00e1c em c\u00f3 \u0111\u01b0\u1ee3c m\u1ed9t s\u1ee9c kh\u1ecfe t\u1ed1t, m\u1ed9t t\u00e2m l\u00fd tho\u1ea3i m\u00e1i \u0111\u1ec3 c\u00f3 th\u1ec3 l\u00e0m b\u00e0i thi \u0111\u00fang nh\u01b0 s\u1ee9c h\u1ecdc b\u00ecnh th\u01b0\u1eddng c\u1ee7a m\u00ecnh. \u0110a s\u1ed1 h\u1ecdc sinh v\u00e0o ph\u00f2ng thi \u0111\u1ec1u l\u00e0m b\u00e0i k\u00e9m h\u01a1n l\u00fac b\u00ecnh th\u01b0\u1eddng.<\/p>\n

L\u01b0u \u00fd \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho b\u00e0i to\u00e1n c\u00f3 ngh\u0129a<\/strong><\/p>\n

Ph\u1ea3i \u0111\u1ecdc \u0111\u1ec1 k\u1ef9 tr\u01b0\u1edbc khi b\u1eaft \u0111\u1ea7u l\u00e0m b\u00e0i, tuy\u1ec7t \u0111\u1ed1i tr\u00e1nh t\u00ecnh tr\u1ea1ng hi\u1ec3u sai \u0111\u1ec1. L\u00e0m b\u00e0i theo nguy\u00ean t\u1eafc: ch\u1ecdn nh\u1eefng c\u00e2u d\u1ec5 \u0111\u1ec3 l\u00e0m tr\u01b0\u1edbc, c\u00e2u kh\u00f3 l\u00e0m sau. C\u00e1c em kh\u00f4ng \u0111\u01b0\u1ee3c l\u00e0m t\u1eaft, n\u00ean th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p bi\u1ebfn \u0111\u1ed5i m\u1ed9t c\u00e1ch c\u1ea9n th\u1eadn v\u00e0 ch\u1eadm r\u00e3i ngay trong b\u00e0i thi n\u1ebfu b\u00e0i to\u00e1n \u0111\u00e3 c\u00f3 h\u01b0\u1edbng gi\u1ea3i quy\u1ebft \u0111\u00fang. C\u00e1c em c\u1ea7n l\u01b0u \u00fd \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho b\u00e0i to\u00e1n c\u00f3 ngh\u0129a, sau khi gi\u1ea3i xong ph\u1ea3i ki\u1ec3m tra l\u1ea1i k\u1ebft qu\u1ea3, th\u1eed l\u1ea1i c\u00e1c nghi\u1ec7m xem c\u00f3 th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n hay kh\u00f4ng.<\/p>\n

N\u00ean l\u00e0m b\u00e0i ngay v\u00e0o gi\u1ea5y thi, gi\u1ea5y nh\u00e1p ch\u1ec9 d\u00f9ng \u0111\u1ec3 th\u1eed v\u00e0 t\u00ecm ra c\u00e1c ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i khi ch\u01b0a bi\u1ebft ch\u1eafc c\u00e1ch gi\u1ea3i \u0111\u00f3 c\u00f3 \u0111i \u0111\u1ebfn k\u1ebft qu\u1ea3 hay kh\u00f4ng. Trong khi l\u00e0m b\u00e0i, c\u00e1c em ph\u1ea3i t\u1eadp trung to\u00e0n b\u1ed9 t\u00e2m tr\u00ed v\u00e0o c\u00f4ng vi\u1ec7c c\u1ee7a m\u00ecnh, \u0111\u1eebng ngh\u0129 \u0111\u1ebfn \u0111\u1eadu hay r\u1edbt, \u0111i\u1ec3m cao hay \u0111i\u1ec3m th\u1ea5p v\u00ec b\u1ea5t c\u1ee9 \u00fd ngh\u0129 (kh\u00f4ng \u0111\u00fang l\u00fac) n\u00e0o c\u0169ng l\u00e0m t\u1ed1n n\u0103ng l\u01b0\u1ee3ng v\u00e0 ph\u00e2n t\u00e2m.<\/p>\n

\u0110\u1ed1i v\u1edbi b\u00e0i thi m\u00f4n to\u00e1n, theo c\u1ea5u tr\u00fac \u0111\u1ec1 thi c\u1ee7a b\u1ed9 \u0111\u01b0a ra trong k\u00ec thi THPT Qu\u1ed1c gia n\u0103m 2015, \u0111\u1ec1 ngh\u1ecb c\u00e1c em n\u00ean l\u01b0u \u00fd nh\u1eefng \u0111i\u1ec1u sau \u0111\u00e2y:<\/em><\/p>\n

C\u00e2u 1:<\/strong><\/u>\u00a0Vi\u1ec7c kh\u1ea3o s\u00e1t h\u00e0m s\u1ed1 v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb, c\u00e1c em h\u1ebft s\u1ee9c l\u01b0u \u00fd vi\u1ec7c t\u00ednh \u0111\u00fang \u0111\u1ea1o h\u00e0m. B\u1edfi v\u00ec n\u1ebfu t\u00ednh sai th\u00ec \u0111i\u1ec3m t\u1ed1i \u0111a c\u00e1c em c\u00f3 th\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c cho c\u00e2u n\u00e0y ch\u1ec9 l\u00e0 0.25\u0111. Th\u00f4ng th\u01b0\u1eddng vi\u1ec7c v\u1ebd \u0111\u1ed3 th\u1ecb ch\u1ee7 y\u1ebfu d\u1ef1a v\u00e0o c\u00e1c \u0111i\u1ec3m \u0111\u1eb7c bi\u1ec7t, \u0111\u1ed9c l\u1eadp v\u1edbi \u0111\u1ea1o h\u00e0m v\u00e0 b\u1ea3ng bi\u1ebfn thi\u00ean n\u00ean c\u00f3 th\u1ec3 d\u00f9ng d\u00e1ng \u0111i\u1ec7u (\u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn) c\u1ee7a \u0111\u1ed3 th\u1ecb \u0111\u00e3 v\u1ebd \u0111\u1ec3 ki\u1ec3m tra l\u1ea1i d\u1ea5u c\u1ee7a \u0111\u1ea1o h\u00e0m v\u00e0 b\u1ea3ng bi\u1ebfn thi\u00ean c\u00f3 ph\u00f9 h\u1ee3p v\u1edbi \u0111\u1ed3 th\u1ecb hay kh\u00f4ng? N\u00ean v\u1ebd \u0111\u1ed3 th\u1ecb v\u1eeba ph\u1ea3i, kh\u00f4ng n\u00ean qu\u00e1 to (s\u1ebd kh\u00f3 v\u1ebd).<\/p>\n

Kh\u00f4ng \u0111\u01b0\u1ee3c v\u1ebd \u0111\u1ed3 th\u1ecb b\u1eb1ng vi\u1ebft ch\u00ec, n\u1ebfu kh\u00f4ng b\u00e0i thi s\u1ebd b\u1ecb ch\u1ea5m t\u1eadp th\u1ec3 trong h\u1ed9i \u0111\u1ed3ng ch\u1ea5m thi. \u0110\u00e2y c\u0169ng l\u00e0 quy \u0111\u1ecbnh chung v\u1edbi c\u00e1c c\u00e2u c\u00f3 h\u00ecnh v\u1ebd, tr\u1eeb khi v\u1ebd h\u00ecnh b\u1eb1ng compa.<\/p>\n

C\u00e2u 2:\u00a0<\/strong><\/u>\u0110\u00e2y l\u00e0 c\u00e2u t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean m\u1ed9t \u0111o\u1ea1n [a; b]; ho\u1eb7c m\u1ed9t c\u00e2u h\u1ecfi ph\u1ee5 c\u1ee7a ph\u1ea7n kh\u1ea3o s\u00e1t h\u00e0m s\u1ed1 (g\u1ed3m c\u00e1c d\u1ea1ng to\u00e1n: s\u1ef1 \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1, c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1, s\u1ef1 t\u01b0\u01a1ng giao c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng, ti\u1ebfp tuy\u1ebfn, t\u00ecm \u0111i\u1ec3m th\u1ecfa \u0111i\u1ec1u ki\u1ec7n cho tr\u01b0\u1edbc). V\u1edbi d\u1ea1ng b\u00e0i t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean m\u1ed9t \u0111o\u1ea1n, c\u1ea7n ch\u00fa \u00fd \u0111\u1ebfn vi\u1ec7c h\u00e0m s\u1ed1 ph\u1ea3i x\u00e1c \u0111\u1ecbnh v\u00e0 li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n \u0111\u00f3. N\u1ebfu \u0111\u1ec1 ch\u01b0a cho \u0111o\u1ea1n [a; b] th\u00ec ta ph\u1ea3i t\u1ef1 x\u00e1c \u0111\u1ecbnh [a; b] b\u1eb1ng c\u00e1ch \u0111i t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, c\u0169ng c\u00f3 th\u1ec3 t\u00ecm [a; b] n\u1ebfu ta \u0111\u1ed5i bi\u1ebfn khi g\u1eb7p h\u00e0m l\u01b0\u1ee3ng gi\u00e1c (v\u00ed d\u1ee5 khi \u0111\u1eb7t t = sinx ho\u1eb7c t = cosx th\u00ec t thu\u1ed9c \u0111o\u1ea1n [\u20131; 1]).<\/p>\n

C\u00e2u 3:<\/strong><\/u>\u00a0\u0110\u1ec1 th\u01b0\u1eddng ra 2 \u00fd: c\u00e1c d\u1ea1ng to\u00e1n v\u1ec1 s\u1ed1 ph\u1ee9c v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh\/ b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh m\u0169 \u2013 logarit. \u0110\u00e2y l\u00e0 m\u1ed9t c\u00e2u t\u01b0\u01a1ng \u0111\u1ed1i d\u1ec5 trong \u0111\u1ec1 thi \u0111\u1ea1i h\u1ecdc c\u00e1c n\u0103m g\u1ea7n \u0111\u00e2y. V\u1ec1 s\u1ed1 ph\u1ee9c c\u00e1c em ch\u1ec9 c\u1ea7n bi\u1ebft c\u00e1c c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n, c\u00e1c thao t\u00e1c t\u00ednh to\u00e1n \u0111\u01a1n gi\u1ea3n l\u00e0 c\u00f3 th\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c. C\u1ea7n bi\u1ebft c\u00e1ch s\u1eed d\u1ee5ng m\u00e1y t\u00ednh c\u1ea7m tay \u0111\u1ec3 c\u00f3 th\u1ec3 ki\u1ec3m tra b\u00e0i l\u00e0m c\u1ee7a m\u00ecnh.<\/p>\n

\u1ede c\u00e2u ph\u01b0\u01a1ng tr\u00ecnh ho\u1eb7c b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh m\u0169 \u2013 logarit, ta ch\u1ec9 c\u1ea7n n\u1eafm v\u1eefng c\u00e1c d\u1ea1ng to\u00e1n c\u01a1 b\u1ea3n: ph\u01b0\u01a1ng ph\u00e1p l\u1ea5y logarit 2 v\u1ebf, \u0111\u01b0a v\u1ec1 c\u00f9ng c\u01a1 s\u1ed1, \u0111\u1eb7t \u1ea9n s\u1ed1 ph\u1ee5 l\u00e0 c\u00f3 th\u1ec3 gi\u1ea3i tr\u1ecdn v\u1eb9n c\u00e2u n\u00e0y. C\u00e1c em c\u00f3 th\u1ec3 b\u1ecf qua ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i b\u1eb1ng c\u00e1c d\u1ef1a v\u00e0o t\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 c\u0169ng c\u00e1c b\u00e0i to\u00e1n m\u00e0 trong c\u01a1 s\u1ed1 c\u00f3 ch\u1ee9a x v\u00ec kh\u00f4ng ph\u00f9 h\u1ee3p v\u1edbi tinh th\u1ea7n \u0111\u1ec1 thi hi\u1ec7n nay. Ph\u1ea3i nh\u1edb \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho c\u00e1c bi\u1ec3u th\u1ee9c logarit, c\u0169ng nh\u01b0 \u0111i\u1ec1u ki\u1ec7n khi s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7t \u1ea9n s\u1ed1 ph\u1ee5.<\/p>\n

C\u00e2u 4:<\/strong><\/u>\u00a0V\u1edbi b\u00e0i to\u00e1n t\u00edch ph\u00e2n, c\u00e1c em n\u00ean ch\u00fa \u00fd \u0111\u1ebfn ph\u01b0\u01a1ng ph\u00e1p t\u00edch ph\u00e2n t\u1eebng ph\u1ea7n v\u00e0 ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ed5i bi\u1ebfn. \u0110\u00e2y l\u00e0 c\u00e2u h\u1ecfi d\u1ec5 v\u00e0 c\u00f3 th\u1ec3 v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c \u0111\u1ec3 gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n trong \u0111\u1eddi s\u1ed1ng th\u1ef1c ti\u1ec5n n\u00ean c\u00e1c em c\u1ea7n hi\u1ec3u r\u00f5 \u1ee9ng d\u1ee5ng c\u1ee7a t\u00edch ph\u00e2n \u0111\u1ec3 t\u00ednh di\u1ec7n t\u00edch v\u00e0 th\u1ec3 t\u00edch.<\/p>\n

Ph\u1ea7n \u0111\u1ed5i bi\u1ebfn d\u1ea1ng l\u01b0\u1ee3ng gi\u00e1c (x = asint, x = atant\u2026) c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c l\u01b0\u1ee3c b\u1ecf v\u00ec hi\u1ec7n nay c\u00e2u t\u00edch ph\u00e2n l\u00e0 c\u00e2u d\u00e0nh cho \u0111\u1ed1i t\u01b0\u1ee3ng h\u1ecdc sinh trung b\u00ecnh c\u0169ng c\u00f3 th\u1ec3 l\u1ea5y \u0111i\u1ec3m tr\u1ecdn v\u1eb9n.<\/p>\n

C\u00e2u 5:<\/strong><\/u>\u00a0L\u00e0 m\u1ed9t b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc gi\u1ea3i t\u00edch trong kh\u00f4ng gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz. C\u00e2u n\u00e0y l\u00e0 m\u1ed9t c\u00e2u d\u1ec5, n\u1ebfu thu\u1ed9c l\u00fd thuy\u1ebft v\u00e0 bi\u1ebft v\u1eadn d\u1ee5ng m\u1ed9t c\u00e1ch th\u00edch h\u1ee3p, c\u00e1c em c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng. C\u1ea7n r\u00e8n luy\u1ec7n c\u00e1ch t\u00ednh c\u00e1c ph\u00e9p to\u00e1n trong h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz b\u1eb1ng m\u00e1y t\u00ednh nh\u1eb1m c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng ki\u1ec3m tra k\u1ebft qu\u1ea3.<\/p>\n

H\u1ecdc sinh n\u00ean ch\u1ecdn mua lo\u1ea1i m\u00e1y t\u00ednh c\u1ea7m tay c\u00f3 th\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c h\u1ec7 g\u1ed3m 4 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t 4 \u1ea9n, \u0111i\u1ec1u n\u00e0y s\u1ebd gi\u00fap ti\u1ebft ki\u1ec7m th\u1eddi gian r\u1ea5t nhi\u1ec1u trong b\u00e0i to\u00e1n t\u00ecm ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t c\u1ea7u.<\/p>\n

C\u00e2u 6<\/strong><\/u>: \u0110\u1ec3 gi\u1ea3i t\u1ed1t b\u00e0i to\u00e1n ph\u01b0\u01a1ng tr\u00ecnh l\u01b0\u1ee3ng gi\u00e1c, ngo\u00e0i vi\u1ec7c thu\u1ed9c nhu\u1ea7n nhuy\u1ec5n c\u00e1c c\u00f4ng th\u1ee9c, bi\u1ebft c\u00e1ch bi\u1ebfn \u0111\u1ed5i v\u00e0 v\u1eadn d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c, c\u00e1c em c\u1ea7n ngh\u0129 \u0111\u1ebfn 2 ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i ch\u1ee7 y\u1ebfu l\u00e0: \u0111\u1eb7t nh\u00e2n t\u1eed chung v\u00e0 \u0111\u1eb7t \u1ea9n ph\u1ee5.<\/p>\n

C\u0169ng c\u1ea7n ph\u1ea3i ch\u00fa \u00fd th\u00eam \u0111\u1ebfn d\u1ea1ng to\u00e1n t\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c \u0111\u00e3 xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi minh h\u1ecda, \u0111\u1ec1 thi ch\u00ednh th\u1ee9c c\u1ee7a B\u1ed9 gi\u00e1o d\u1ee5c trong n\u0103m 2015 c\u0169ng nh\u01b0 trong c\u00e1c \u0111\u1ec1 thi th\u1eed c\u1ee7a c\u00e1c tr\u01b0\u1eddng tr\u00ean to\u00e0n qu\u1ed1c.<\/p>\n

V\u1ec1 ph\u1ea7n t\u1ed5 h\u1ee3p c\u00e1c em ph\u1ea3i n\u1eafm v\u1eefng qui t\u1eafc \u0111\u1ebfm, ho\u00e1n v\u1ecb, t\u1ed5 h\u1ee3p v\u00e0 ch\u1ec9nh h\u1ee3p, bi\u1ebft khai tri\u1ec3n nh\u1ecb th\u1ee9c Newton \u1edf m\u1ee9c \u0111\u1ed9 c\u01a1 b\u1ea3n. Ph\u1ea7n x\u00e1c su\u1ea5t ch\u1ee7 y\u1ebfu t\u1eadp trung v\u00e0o c\u00f4ng th\u1ee9c t\u00ednh x\u00e1c su\u1ea5t c\u1ed5 \u0111i\u1ec3n (t\u1ee9c l\u00e0 t\u00ednh s\u1ed1 ph\u1ea7n t\u1eed c\u1ee7a kh\u00f4ng gian m\u1eabu v\u00e0 c\u1ee7a bi\u1ebfn c\u1ed1), nh\u01b0ng c\u1ea7n n\u00f3i r\u00f5 ra kh\u00f4ng gian m\u1eabu v\u00e0 ph\u1ea3i g\u1ecdi t\u00ean bi\u1ebfn c\u1ed1.<\/p>\n

C\u00e2u 7:<\/strong><\/u>\u00a0V\u1edbi b\u00e0i to\u00e1n H\u00ecnh h\u1ecdc kh\u00f4ng gian n\u1ebfu kh\u00f4ng gi\u1ea3i \u0111\u01b0\u1ee3c b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p h\u00ecnh h\u1ecdc thu\u1ea7n t\u00fay th\u00ec c\u00e1c em n\u00ean t\u00ecm c\u00e1ch \u0111\u01b0a h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 v\u00e0o \u0111\u1ec3 chuy\u1ec3n th\u00e0nh b\u00e0i to\u00e1n h\u00ecnh gi\u1ea3i t\u00edch trong kh\u00f4ng gian. Th\u01b0\u1eddng l\u00e0 nh\u1eefng c\u00e2u h\u1ecfi v\u1ec1 kho\u1ea3ng c\u00e1ch v\u00e0 th\u1ec3 t\u00edch. Th\u00f4ng th\u01b0\u1eddng \u0111\u00e2y l\u00e0 m\u1ed9t c\u00e2u t\u01b0\u01a1ng \u0111\u1ed1i d\u1ec5, nh\u01b0ng l\u00e0 ph\u1ea7n ki\u1ebfn th\u1ee9c m\u00e0 \u0111a s\u1ed1 h\u1ecdc sinh \u0111\u1ec1u s\u1ee3, v\u00ec \u0111\u00e3 kh\u00f4ng n\u1eafm v\u1eefng c\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n \u0111\u00e3 \u0111\u01b0\u1ee3c h\u1ecdc \u1edf l\u1edbp 11.<\/p>\n

C\u00e2u 8:\u00a0<\/u><\/strong>L\u00e0 m\u1ed9t b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc gi\u1ea3i t\u00edch trong trong m\u1eb7t ph\u1eb3ng v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxy. C\u00e1c em n\u00ean \u00f4n l\u1ea1i nh\u1eefng ki\u1ebfn th\u1ee9c h\u00ecnh h\u1ecdc c\u1ee7a l\u1edbp 9 v\u00e0 l\u1edbp 10 \u0111\u1ec3 c\u00f3 th\u1ec3 nh\u1eadn ra c\u00e1c t\u00ednh ch\u1ea5t h\u00ecnh h\u1ecdc c\u1ee7a b\u00e0i to\u00e1n. \u0110\u00e2y l\u00e0 m\u1ed9t c\u00e2u kh\u00f3 v\u00ec \u0111\u00f2i h\u1ecfi th\u00ed sinh ph\u1ea3i nh\u1edb v\u00e0 bi\u1ebft s\u1eed d\u1ee5ng ki\u1ebfn th\u1ee9c c\u1ee7a c\u00e1c l\u1edbp d\u01b0\u1edbi.<\/p>\n

\u0110\u1ec3 c\u00f3 th\u1ec3 nh\u1eadn ra \u0111\u01b0\u1ee3c c\u00e1c t\u00ednh ch\u1ea5t h\u00ecnh h\u1ecdc n\u00e0y, vi\u1ec7c v\u1ebd h\u00ecnh m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c d\u1ef1a v\u00e0o d\u1eef ki\u1ec7n c\u1ee7a \u0111\u1ec1 b\u00e0i l\u00e0 r\u1ea5t quan tr\u1ecdng. Tuy nhi\u00ean, h\u1ecdc sinh ph\u1ea3i lu\u00f4n nh\u1edb r\u1eb1ng, \u1edf c\u00e2u n\u00e0y y\u1ebfu t\u1ed1 \u201cgi\u1ea3i t\u00edch\u201d v\u1eabn \u0111\u01b0\u1ee3c xem trong, v\u00ec v\u1eady kh\u00f4ng n\u00ean sa \u0111\u00e0 v\u00e0o vi\u1ec7c gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp qu\u00e1 \u0111\u1eb7t n\u1eb7ng v\u1ec1 t\u00ednh ch\u1ea5t h\u00ecnh h\u1ecdc ph\u1eb3ng.<\/p>\n

C\u00e2u 9:\u00a0<\/strong><\/u>L\u00e0 m\u1ed9t c\u00e2u v\u1ec1 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ho\u1eb7c b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 ch\u1ee9a c\u0103n th\u1ee9c. Th\u01b0\u1eddng \u0111\u00e2y l\u00e0 m\u1ed9t c\u00e2u kh\u00f3 th\u1ee9 nh\u00ec (sau c\u00e2u 10). C\u00e1c ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i quan tr\u1ecdng nh\u01b0 \u0111\u1eb7t \u1ea9n ph\u1ee5, li\u00ean h\u1ee3p, d\u00f9ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 c\u1ea7n \u0111\u01b0\u1ee3c k\u1ebft h\u1ee3p nhu\u1ea7n nhuy\u1ec5n v\u1edbi nhau khi gi\u1ea3i. C\u00e1c em ph\u1ea3i bi\u1ebft c\u00e1ch s\u1eed d\u1ee5ng hi\u1ec7u qu\u1ea3 m\u00e1y t\u00ednh c\u1ea7m tay \u0111\u1ec3 gi\u1ea3m nh\u1eb9 kh\u1ed1i l\u01b0\u1ee3ng t\u00ednh to\u00e1n, \u0111\u1ed3ng th\u1eddi h\u1ed7 tr\u1ee3 cho m\u00ecnh trong qu\u00e1 tr\u00ecnh ph\u00e2n t\u00edch nh\u00e2n t\u1eed, c\u0169ng nh\u01b0 d\u1ef1 \u0111o\u00e1n nghi\u1ec7m.<\/p>\n

M\u1ed9t s\u1ed1 l\u1edbn c\u00e1c b\u00e0i to\u00e1n c\u00f3 th\u1ec3 gi\u1ea3i kh\u00e1 hi\u1ec7u qu\u1ea3 v\u1edbi s\u1ef1 h\u1ed7 tr\u1ee3 c\u1ee7a m\u00e1y t\u00ednh c\u1ea7m tay. H\u1ecdc sinh c\u0169ng c\u1ea7n nghi\u00ean c\u1ee9u th\u00eam c\u00e1c b\u00e0i to\u00e1n g\u00e2y nhi\u1ec1u kh\u00f3 kh\u0103n cho vi\u1ec7c gi\u1ea3i b\u1eb1ng m\u00e1y t\u00ednh, \u0111\u00f3 l\u00e0 nh\u1eefng b\u00e0i to\u00e1n s\u1eed d\u1ee5ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 bi\u1ec3u th\u1ee9c. Ph\u1ea3i n\u1eafm v\u1eefng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i v\u00e0 ch\u1ecbu kh\u00f3 r\u00e8n luy\u1ec7n th\u00eam c\u00e1c b\u00e0i n\u00e2ng cao trong su\u1ed1t qu\u00e1 tr\u00ecnh h\u1ecdc m\u1edbi c\u00f3 th\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c c\u00e2u n\u00e0y trong m\u1ed9t th\u1eddi gian ng\u1eafn.<\/p>\n

C\u00e2u 10:\u00a0<\/strong><\/u>\u0110\u00e2y l\u00e0 c\u00e2u kh\u00f3 nh\u1ea5t d\u00f9ng \u0111\u1ec3 ph\u00e2n lo\u1ea1i th\u00ed sinh, th\u01b0\u1eddng l\u00e0 c\u00e2u b\u1ea5t \u0111\u1eb3ng th\u1ee9c ho\u1eb7c t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t hay gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t. \u0110\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c c\u00e2u n\u00e0y \u0111\u00f2i h\u1ecfi th\u00ed sinh ph\u1ea3i c\u00f3 kh\u1ea3 n\u0103ng t\u01b0 duy \u0111\u1ed9c l\u1eadp, c\u00f3 \u00f3c ch\u1ee7 \u0111\u1ed9ng s\u00e1ng t\u1ea1o, c\u00f3 kh\u1ea3 n\u0103ng v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c t\u1ed5ng h\u1ee3p v\u00e0o gi\u1ea3i quy\u1ebft m\u1ed9t v\u1ea5n \u0111\u1ec1, kh\u00f4ng l\u00e0m theo khu\u00f4n m\u1eabu.<\/p>\n

Ph\u01b0\u01a1ng ph\u00e1p \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng ph\u1ed5 bi\u1ebfn trong c\u00e1c \u0111\u1ec1 thi c\u1ee7a B\u1ed9 gi\u00e1o d\u1ee5c trong su\u1ed1t nh\u1eefng n\u0103m g\u1ea7n \u0111\u00e2y l\u00e0 \u0111\u01b0a b\u00e0i to\u00e1n 3 bi\u1ebfn x, y, z v\u1ec1 b\u00e0i to\u00e1n 1 bi\u1ebfn n\u00e0o \u0111\u00f3 r\u1ed3i kh\u1ea3o s\u00e1t h\u00e0m m\u1ed9t bi\u1ebfn \u0111\u00f3 \u0111\u1ec3 \u0111i \u0111\u1ebfn k\u1ebft lu\u1eadn. Th\u01b0\u1eddng th\u00ec ta s\u1ebd d\u1ed3n v\u1ec1 bi\u1ebfn c\u00f3 vai tr\u00f2 kh\u00f4ng \u0111\u1ed1i x\u1ee9ng. Su\u1ed1t qu\u00e1 tr\u00ecnh \u0111\u00e1nh gi\u00e1 b\u00e0i to\u00e1n, ta ph\u1ea3i \u0111\u1ea3m b\u1ea3o \u0111\u01b0\u1ee3c d\u1ea5u \u201c=\u201d x\u1ea3y ra.<\/p>\n

N\u1ebfu c\u00e1c em kh\u00f4ng th\u1eadt s\u1ef1 t\u1ef1 tin \u0111\u1ec3 gi\u1ea3i th\u00ec n\u00ean b\u1ecf qua, s\u1ebd quay l\u1ea1i b\u00e0i n\u00e0y sau khi \u0111\u00e3 gi\u1ea3i quy\u1ebft nh\u1eefng b\u00e0i to\u00e1n kh\u00e1c v\u00e0 c\u00f2n th\u1eddi gian. \u0110\u1ec3 \u0111\u1eadu \u0111\u1ea1i h\u1ecdc, kh\u00f4ng c\u1ea7n t\u1edbi \u0111i\u1ec3m 10, n\u00ean d\u00e0nh th\u1eddi gian ch\u0103m ch\u00fat 9 \u0111i\u1ec3m c\u00f2n l\u1ea1i.<\/p>\n

V\u1edbi ch\u1ee7 tr\u01b0\u01a1ng c\u1ee7a B\u1ed9 gi\u00e1o d\u1ee5c l\u00e0 ra \u0111\u1ec1 ch\u1ee7 y\u1ebfu n\u1eb1m trong ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 12, c\u0169ng nh\u01b0 t\u1ec9 l\u1ec7 \u0111i\u1ec3m d\u00e0nh cho m\u1ee9c \u0111\u1ed9 c\u01a1 b\u1ea3n chi\u1ebfm kho\u1ea3ng 60% th\u00ec c\u00e1c c\u00e2u t\u1eeb c\u00e2u 1 \u0111\u1ebfn c\u00e2u 6 s\u1ebd c\u00f3 \u0111\u1ed9 kh\u00f3 kh\u00f4ng ch\u00eanh l\u1ec7ch v\u1edbi \u0111\u1ec1 thi THPT Qu\u1ed1c gia n\u0103m 2015.<\/p>\n

Vi\u1ec7c cho c\u00e2u 8 \u2013 9 qu\u00e1 d\u1ec5 nh\u01b0 n\u0103m 2015 \u0111\u00e3 d\u1eabn \u0111\u1ebfn vi\u1ec7c ch\u1ec9 ph\u00e2n lo\u1ea1i \u0111\u01b0\u1ee3c h\u1ecdc sinh trung b\u00ecnh kh\u00e1 v\u00e0 h\u1ecdc sinh gi\u1ecfi, ch\u1ee9 ch\u01b0a th\u1ec3 ph\u00e2n lo\u1ea1i \u0111\u01b0\u1ee3c h\u1ecdc sinh kh\u00e1. V\u00ec v\u1eady c\u00e1c c\u00e2u 7 \u2013 8 \u2013 9 s\u1ebd \u0111\u01b0\u1ee3c n\u00e2ng d\u1ea7n \u0111\u1ed9 kh\u00f3, \u00edt nh\u1ea5t l\u00e0 b\u1eb1ng v\u1edbi m\u1ee9c \u0111\u1ed9 c\u1ee7a \u0111\u1ec1 thi \u0111\u1ea1i h\u1ecdc \u1edf c\u00e1c n\u0103m tr\u01b0\u1edbc.<\/p>\n

Cu\u1ed1i c\u00f9ng, \u0111\u1ed1i v\u1edbi c\u00e1c th\u00ed sinh, m\u1ecdi chi ti\u1ebft v\u1ec1 c\u00e1c ch\u1ee7 \u0111\u1ec1 tr\u00ean \u0111\u1ec1u quan tr\u1ecdng, nh\u01b0ng quan tr\u1ecdng nh\u1ea5t, \u0111\u00f3 l\u00e0 c\u00e1c em ph\u1ea3i t\u1ef1 trang b\u1ecb cho m\u00ecnh \u0111\u1ea7y \u0111\u1ee7 ki\u1ebfn th\u1ee9c v\u00e0 s\u1ef1 b\u00ecnh t\u0129nh, t\u1ef1 tin trong l\u00fac l\u00e0m b\u00e0i thi. Ch\u00fac c\u00e1c em c\u00f3 m\u1ed9t m\u00f9a thi may m\u1eafn v\u00e0 th\u00e0nh c\u00f4ng.<\/p>\n","protected":false},"excerpt":{"rendered":"

S\u1ed1 h\u1ecdc sinh \u0111\u1ea1t \u0111i\u1ec3m t\u1ed1i \u0111a m\u00f4n To\u00e1n trong k\u00ec thi THPT qu\u1ed1c gia c\u00f2n r\u1ea5t \u00edt, b\u1edfi c\u00e1c em th\u01b0\u1eddng m\u1eafc ph\u1ea3i nh\u1eefng sai s\u00f3t r\u1ea5t \u0111\u00e1ng ti\u1ebfc khi l\u00e0m b\u00e0i. \u0110\u1ec3 gi\u00fap c\u00e1c em c\u00f3 th\u1ec3 h\u1ea1n ch\u1ebf v\u00e0 kh\u1eafc ph\u1ee5c c\u00e1c sai s\u00f3t, ThS Ng\u00f4 Thanh S\u01a1n, t\u1ed5 tr\u01b0\u1edfng t\u1ed5 To\u00e1n […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[17],"tags":[],"yoast_head":"\n10 b\u00ed quy\u1ebft \u0111\u1ec3 l\u00e0m b\u00e0i thi m\u00f4n To\u00e1n THPT qu\u1ed1c gia 2016 hi\u1ec7u qu\u1ea3 nh\u1ea5t<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/10-bi-quyet-de-lam-bai-thi-mon-toan-thpt-quoc-gia-2016-hieu-qua-nhat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"10 b\u00ed quy\u1ebft \u0111\u1ec3 l\u00e0m b\u00e0i thi m\u00f4n To\u00e1n THPT qu\u1ed1c gia 2016 hi\u1ec7u qu\u1ea3 nh\u1ea5t\" \/>\n<meta property=\"og:description\" content=\"S\u1ed1 h\u1ecdc sinh \u0111\u1ea1t \u0111i\u1ec3m t\u1ed1i \u0111a m\u00f4n To\u00e1n trong k\u00ec thi THPT qu\u1ed1c gia c\u00f2n r\u1ea5t \u00edt, b\u1edfi c\u00e1c em th\u01b0\u1eddng m\u1eafc ph\u1ea3i nh\u1eefng sai s\u00f3t r\u1ea5t \u0111\u00e1ng ti\u1ebfc khi l\u00e0m b\u00e0i. \u0110\u1ec3 gi\u00fap c\u00e1c em c\u00f3 th\u1ec3 h\u1ea1n ch\u1ebf v\u00e0 kh\u1eafc ph\u1ee5c c\u00e1c sai s\u00f3t, ThS Ng\u00f4 Thanh S\u01a1n, t\u1ed5 tr\u01b0\u1edfng t\u1ed5 To\u00e1n […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lop12.edu.vn\/10-bi-quyet-de-lam-bai-thi-mon-toan-thpt-quoc-gia-2016-hieu-qua-nhat\/\" \/>\n<meta property=\"og:site_name\" content=\"Lop12.edu.vn - 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