\nS\u1ed1 v\u00e0 ph\u00e9p t\u00ednh
\n(S\u1ed1 c\u00f3 nhi\u1ec1u ch\u1eef s\u1ed1, h\u00e0ng l\u1edbp, so s\u00e1nh, l\u00e0m tr\u00f2n, d\u00e3y s\u1ed1, t\u00ednh ch\u1ea5t ph\u00e9p c\u1ed9ng, bi\u1ec3u th\u1ee9c ch\u1ee9a ch\u1eef, trung b\u00ecnh c\u1ed9ng)<\/span><\/td>\n | Nh\u1eadn di\u1ec7n h\u00e0ng v\u00e0 l\u1edbp; \u0111\u1ecdc vi\u1ebft s\u1ed1; so s\u00e1nh s\u1ed1 (2,0 \u0111i\u1ec3m)<\/td>\n | L\u00e0m tr\u00f2n s\u1ed1; t\u00ednh nhanh b\u1eb1ng t\u00ednh ch\u1ea5t giao ho\u00e1n, k\u1ebft h\u1ee3p; t\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c (2,0 \u0111i\u1ec3m)<\/td>\n | Gi\u1ea3i b\u00e0i to\u00e1n c\u00f3 l\u1eddi v\u0103n v\u1ec1 s\u1ed1 trung b\u00ecnh c\u1ed9ng v\u00e0 d\u00e3y s\u1ed1 (1,5 \u0111i\u1ec3m)<\/td>\n | 5,5 \u0111i\u1ec3m<\/td>\n<\/tr>\n |
\n\u0110o l\u01b0\u1eddng
\n(Y\u1ebfn, t\u1ea1, t\u1ea5n; Gi\u00e2y, th\u1ebf k\u1ec9)<\/span><\/td>\n | Nh\u1eadn bi\u1ebft c\u00e1c \u0111\u01a1n v\u1ecb \u0111o kh\u1ed1i l\u01b0\u1ee3ng v\u00e0 th\u1eddi gian (0,5 \u0111i\u1ec3m)<\/td>\n | \u0110\u1ed5i \u0111\u01a1n v\u1ecb \u0111o t\u1eeb l\u1edbn ra b\u00e9 v\u00e0 ng\u01b0\u1ee3c l\u1ea1i; \u0111\u1ed5i th\u1ebf k\u1ec9 ra n\u0103m (1,5 \u0111i\u1ec3m)<\/td>\n | –<\/td>\n | 2,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n |
\nH\u00ecnh h\u1ecdc
\n(G\u00f3c nh\u1ecdn, g\u00f3c t\u00f9, g\u00f3c b\u1eb9t; \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c, song song)<\/span><\/td>\n | Nh\u1eadn bi\u1ebft g\u00f3c nh\u1ecdn, g\u00f3c t\u00f9, g\u00f3c b\u1eb9t b\u1eb1ng \u00ea-ke (1,0 \u0111i\u1ec3m)<\/td>\n | X\u00e1c \u0111\u1ecbnh hai \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c ho\u1eb7c song song trong h\u00ecnh v\u1ebd (1,5 \u0111i\u1ec3m)<\/td>\n | –<\/td>\n | 2,5 \u0111i\u1ec3m<\/td>\n<\/tr>\n |
\n| T\u1ed4NG T\u1ef6 L\u1ec6 \/ \u0110I\u1ec2M S\u1ed0<\/td>\n | 4,0 \u0111i\u1ec3m (40%)<\/td>\n | 4,0 \u0111i\u1ec3m (40%)<\/td>\n | 2,0 \u0111i\u1ec3m (20%)<\/td>\n | 10,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n <\/p>\n <\/p>\n \n <\/p>\n \n Ph\u1ea7n I: S\u1ed1 v\u00e0 Ph\u00e9p T\u00ednh<\/h2>\n<\/div>\n<\/p>\n S\u1ed1 v\u00e0 ph\u00e9p t\u00ednh l\u00e0 m\u1ea1ch ki\u1ebfn th\u1ee9c chi\u1ebfm nhi\u1ec1u \u0111i\u1ec3m nh\u1ea5t, v\u00ec v\u1eady \u0111\u00e2y l\u00e0 ph\u1ea7n tr\u1ecdng t\u00e2m c\u1ee7a \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 4<\/strong>. Con c\u1ea7n n\u1eafm ch\u1eafc c\u00e1c ch\u1ee7 \u0111\u1ec1 d\u01b0\u1edbi \u0111\u00e2y, t\u1eeb \u0111\u1ecdc, vi\u1ebft s\u1ed1 c\u00f3 nhi\u1ec1u ch\u1eef s\u1ed1 \u0111\u1ebfn s\u1ed1 trung b\u00ecnh c\u1ed9ng.<\/p>\nS\u1ed1 c\u00f3 nhi\u1ec1u ch\u1eef s\u1ed1<\/h2>\n\u0110\u1ecdc v\u00e0 vi\u1ebft s\u1ed1 \u0111\u1ebfn l\u1edbp tri\u1ec7u<\/h3>\n\n- Quy t\u1eafc \u0111\u1ecdc s\u1ed1:<\/strong> \u0110\u1ecdc t\u1eeb tr\u00e1i sang ph\u1ea3i, t\u00e1ch theo t\u1eebng l\u1edbp t\u1eeb l\u1edbp cao xu\u1ed1ng l\u1edbp th\u1ea5p (l\u1edbp tri\u1ec7u \u2192 l\u1edbp ngh\u00ecn \u2192 l\u1edbp \u0111\u01a1n v\u1ecb). \u1ede m\u1ed7i l\u1edbp, \u0111\u1ecdc nh\u01b0 \u0111\u1ecdc c\u00e1c s\u1ed1 c\u00f3 t\u1edbi ba ch\u1eef s\u1ed1 k\u00e8m theo t\u00ean l\u1edbp \u0111\u00f3 (tr\u1eeb l\u1edbp \u0111\u01a1n v\u1ecb kh\u00f4ng \u0111\u1ecdc t\u00ean l\u1edbp).<\/li>\n
- Quy t\u1eafc vi\u1ebft s\u1ed1:<\/strong> Vi\u1ebft t\u1eeb tr\u00e1i sang ph\u1ea3i, vi\u1ebft theo th\u1ee9 t\u1ef1 t\u1eeb l\u1edbp cao \u0111\u1ebfn l\u1edbp th\u1ea5p. Ch\u00fa \u00fd n\u1ebfu l\u1edbp n\u00e0o thi\u1ebfu ch\u1eef s\u1ed1 \u1edf h\u00e0ng n\u00e0o th\u00ec h\u00e0ng \u0111\u00f3 ph\u1ea3i vi\u1ebft ch\u1eef s\u1ed1
0<\/code>.<\/li>\n<\/ul>\n<\/p>\n \n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi \u0111\u1ecdc\/vi\u1ebft s\u1ed1:<\/p>\n \n- H\u1ecdc sinh th\u01b0\u1eddng \u0111\u1ecdc thi\u1ebfu ch\u1eef s\u1ed1
0<\/code> \u1edf h\u00e0ng ch\u1ee5c ho\u1eb7c h\u00e0ng tr\u0103m khi s\u1ed1 c\u00f3 ch\u1eef s\u1ed1 0<\/code> \u1edf gi\u1eefa (V\u00ed d\u1ee5: s\u1ed1 4005020<\/code> \u0111\u1ecdc nh\u1ea7m th\u00e0nh “b\u1ed1n tri\u1ec7u n\u0103m ngh\u00ecn hai m\u01b0\u01a1i” thay v\u00ec “b\u1ed1n tri\u1ec7u linh n\u0103m ngh\u00ecn kh\u00f4ng tr\u0103m hai m\u01b0\u01a1i”).<\/li>\n<\/ul>\n<\/div>\n<\/p>\n \n V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: \u0110\u1ecdc v\u00e0 vi\u1ebft s\u1ed1<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> a) Vi\u1ebft s\u1ed1: Ba m\u01b0\u01a1i l\u0103m tri\u1ec7u b\u1ed1n tr\u0103m linh hai ngh\u00ecn t\u00e1m tr\u0103m m\u01b0\u1eddi.
\nb) \u0110\u1ecdc s\u1ed1: 80204050<\/code>.<\/p>\nL\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong>
\n\u2022 C\u00e2u a:<\/strong> L\u1edbp tri\u1ec7u l\u00e0 35<\/code>, l\u1edbp ngh\u00ecn l\u00e0 402<\/code>, l\u1edbp \u0111\u01a1n v\u1ecb l\u00e0 810<\/code>. Vi\u1ebft th\u00e0nh s\u1ed1: 35402810<\/strong>.
\n\u2022 C\u00e2u b:<\/strong> T\u00e1ch c\u00e1c l\u1edbp t\u1eeb ph\u1ea3i sang tr\u00e1i (m\u1ed7i l\u1edbp 3 ch\u1eef s\u1ed1): 80<\/code> (tri\u1ec7u) 204<\/code> (ngh\u00ecn) 050<\/code> (\u0111\u01a1n v\u1ecb). \u0110\u1ecdc l\u00e0: T\u00e1m m\u01b0\u01a1i tri\u1ec7u hai tr\u0103m linh b\u1ed1n ngh\u00ecn kh\u00f4ng tr\u0103m n\u0103m m\u01b0\u01a1i<\/strong>.<\/p>\n<\/div>\n<\/p>\n H\u00e0ng v\u00e0 l\u1edbp c\u1ee7a s\u1ed1 t\u1ef1 nhi\u00ean<\/h2>\nC\u1ea5u tr\u00fac b\u1ea3ng h\u00e0ng v\u00e0 l\u1edbp<\/h3>\nC\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean \u0111\u01b0\u1ee3c c\u1ea5u t\u1ea1o t\u1eeb c\u00e1c h\u00e0ng v\u00e0 nh\u00f3m l\u1ea1i th\u00e0nh c\u00e1c l\u1edbp theo th\u1ee9 t\u1ef1 t\u1eeb ph\u1ea3i sang tr\u00e1i:<\/p>\n \n- L\u1edbp \u0111\u01a1n v\u1ecb:<\/strong> G\u1ed3m h\u00e0ng \u0111\u01a1n v\u1ecb, h\u00e0ng ch\u1ee5c, h\u00e0ng tr\u0103m.<\/li>\n
- L\u1edbp ngh\u00ecn:<\/strong> G\u1ed3m h\u00e0ng ngh\u00ecn, h\u00e0ng ch\u1ee5c ngh\u00ecn, h\u00e0ng tr\u0103m ngh\u00ecn.<\/li>\n
- L\u1edbp tri\u1ec7u:<\/strong> G\u1ed3m h\u00e0ng tri\u1ec7u, h\u00e0ng ch\u1ee5c tri\u1ec7u, h\u00e0ng tr\u0103m tri\u1ec7u.<\/li>\n<\/ul>\n
M\u1ed7i \u0111\u01a1n v\u1ecb \u1edf m\u1ed9t h\u00e0ng li\u1ec1n tr\u01b0\u1edbc l\u1ea1i g\u1ea5p 10 l\u1ea7n \u0111\u01a1n v\u1ecb \u1edf h\u00e0ng li\u1ec1n sau.<\/p>\n <\/p>\n \n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi vi\u1ebft s\u1ed1 th\u00e0nh t\u1ed5ng:<\/p>\n \n- Khi ph\u00e2n t\u00edch s\u1ed1 th\u00e0nh t\u1ed5ng theo h\u00e0ng v\u00e0 l\u1edbp, h\u1ecdc sinh hay qu\u00ean b\u1ecf qua c\u00e1c h\u00e0ng c\u00f3 ch\u1eef s\u1ed1
0<\/code> ho\u1eb7c nh\u1ea7m l\u1eabn gi\u00e1 tr\u1ecb h\u00e0ng ch\u1ee5c ngh\u00ecn v\u1edbi h\u00e0ng tr\u0103m ngh\u00ecn.<\/li>\n<\/ul>\n<\/div>\n<\/p>\n \n V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: X\u00e1c \u0111\u1ecbnh h\u00e0ng, l\u1edbp v\u00e0 vi\u1ebft th\u00e0nh t\u1ed5ng<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> Cho s\u1ed1 4826305<\/code>. N\u00eau ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c ngh\u00ecn v\u00e0 vi\u1ebft s\u1ed1 \u0111\u00f3 th\u00e0nh t\u1ed5ng theo c\u00e1c h\u00e0ng.<\/p>\nL\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong>
\n\u2022 S\u1ed1 4826305<\/code> c\u00f3 ch\u1eef s\u1ed1 \u1edf h\u00e0ng ch\u1ee5c ngh\u00ecn l\u00e0 ch\u1eef s\u1ed1 2<\/strong> (thu\u1ed9c l\u1edbp ngh\u00ecn, gi\u00e1 tr\u1ecb l\u00e0 20 000).
\n\u2022 Vi\u1ebft th\u00e0nh t\u1ed5ng: 4826305 = 4 000 000 + 800 000 + 20 000 + 6 000 + 300 + 5<\/code>.<\/p>\n<\/div>\n<\/p>\n So s\u00e1nh c\u00e1c s\u1ed1 c\u00f3 nhi\u1ec1u ch\u1eef s\u1ed1<\/h2>\nQuy t\u1eafc so s\u00e1nh 2 b\u01b0\u1edbc<\/h3>\n\n- B\u01b0\u1edbc 1 (So s\u00e1nh s\u1ed1 ch\u1eef s\u1ed1):<\/strong> S\u1ed1 n\u00e0o c\u00f3 nhi\u1ec1u ch\u1eef s\u1ed1 h\u01a1n th\u00ec s\u1ed1 \u0111\u00f3 l\u1edbn h\u01a1n. S\u1ed1 n\u00e0o c\u00f3 \u00edt ch\u1eef s\u1ed1 h\u01a1n th\u00ec s\u1ed1 \u0111\u00f3 b\u00e9 h\u01a1n.<\/li>\n
- B\u01b0\u1edbc 2 (So s\u00e1nh t\u1eebng c\u1eb7p ch\u1eef s\u1ed1):<\/strong> N\u1ebfu hai s\u1ed1 c\u00f3 s\u1ed1 ch\u1eef s\u1ed1 b\u1eb1ng nhau, ta l\u1ea7n l\u01b0\u1ee3t so s\u00e1nh c\u00e1c c\u1eb7p ch\u1eef s\u1ed1 \u1edf c\u00f9ng m\u1ed9t h\u00e0ng k\u1ec3 t\u1eeb tr\u00e1i sang ph\u1ea3i (t\u1eeb h\u00e0ng cao \u0111\u1ebfn h\u00e0ng th\u1ea5p). Ch\u1eef s\u1ed1 \u1edf h\u00e0ng n\u00e0o l\u1edbn h\u01a1n th\u00ec s\u1ed1 \u0111\u00f3 l\u1edbn h\u01a1n.<\/li>\n<\/ul>\n
<\/p>\n \n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi so s\u00e1nh:<\/p>\n \n- Qu\u00ean \u0111\u1ebfm s\u1ed1 ch\u1eef s\u1ed1 m\u00e0 v\u1ed9i v\u00e0ng so s\u00e1nh ch\u1eef s\u1ed1 \u0111\u1ea7u ti\u00ean b\u00ean tr\u00e1i (d\u1eabn \u0111\u1ebfn sai l\u1ea7m khi so s\u00e1nh hai s\u1ed1 c\u00f3 s\u1ed1 l\u01b0\u1ee3ng ch\u1eef s\u1ed1 kh\u00e1c nhau).<\/li>\n<\/ul>\n<\/div>\n
<\/p>\n \n V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: S\u1eafp x\u1ebfp th\u1ee9 t\u1ef1 s\u1ed1<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> S\u1eafp x\u1ebfp c\u00e1c s\u1ed1 sau theo th\u1ee9 t\u1ef1 t\u1eeb b\u00e9 \u0111\u1ebfn l\u1edbn: 987654<\/code> ; 1000000<\/code> ; 98999<\/code> ; 987645<\/code>.<\/p>\nL\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong>
\n\u2022 B\u01b0\u1edbc 1: X\u00e9t s\u1ed1 ch\u1eef s\u1ed1 c\u1ee7a c\u00e1c s\u1ed1:
\n– S\u1ed1 98999<\/code> c\u00f3 5 ch\u1eef s\u1ed1 (b\u00e9 nh\u1ea5t).
\n– S\u1ed1 1000000<\/code> c\u00f3 7 ch\u1eef s\u1ed1 (l\u1edbn nh\u1ea5t).
\n– Hai s\u1ed1 987654<\/code> v\u00e0 987645<\/code> \u0111\u1ec1u c\u00f3 6 ch\u1eef s\u1ed1.
\n\u2022 B\u01b0\u1edbc 2: So s\u00e1nh hai s\u1ed1 c\u00f3 6 ch\u1eef s\u1ed1 t\u1eeb tr\u00e1i sang ph\u1ea3i: h\u00e0ng tr\u0103m ngh\u00ecn (9=9), h\u00e0ng ch\u1ee5c ngh\u00ecn (8=8), h\u00e0ng ngh\u00ecn (7=7), h\u00e0ng tr\u0103m (6=6), h\u00e0ng ch\u1ee5c (5 > 4). Suy ra 987645 < 987654<\/code>.
\n\u2022 Th\u1ee9 t\u1ef1 t\u1eeb b\u00e9 \u0111\u1ebfn l\u1edbn l\u00e0: 98999 ; 987645 ; 987654 ; 1000000<\/strong>.<\/p>\n<\/div>\n<\/p>\n L\u00e0m tr\u00f2n s\u1ed1<\/h2>\nQuy t\u1eafc l\u00e0m tr\u00f2n s\u1ed1 t\u1ef1 nhi\u00ean<\/h3>\n\n- X\u00e1c \u0111\u1ecbnh h\u00e0ng c\u1ea7n l\u00e0m tr\u00f2n<\/strong> (h\u00e0ng ch\u1ee5c, h\u00e0ng tr\u0103m, h\u00e0ng ngh\u00ecn, h\u00e0ng ch\u1ee5c ngh\u00ecn, tr\u0103m ngh\u00ecn…).<\/li>\n
- Nh\u00ecn sang ch\u1eef s\u1ed1 ngay b\u00ean ph\u1ea3i<\/strong> (ch\u1eef s\u1ed1 thu\u1ed9c h\u00e0ng th\u1ea5p h\u01a1n li\u1ec1n k\u1ec1):\n
\n- N\u1ebfu ch\u1eef s\u1ed1 \u0111\u00f3 l\u00e0
0, 1, 2, 3, 4<\/code> (nh\u1ecf h\u01a1n 5): Gi\u1eef nguy\u00ean ch\u1eef s\u1ed1 \u1edf h\u00e0ng l\u00e0m tr\u00f2n v\u00e0 thay th\u1ebf t\u1ea5t c\u1ea3 c\u00e1c ch\u1eef s\u1ed1 \u1edf b\u00ean ph\u1ea3i b\u1eb1ng ch\u1eef s\u1ed1 0<\/code>.<\/li>\n- N\u1ebfu ch\u1eef s\u1ed1 \u0111\u00f3 l\u00e0
5, 6, 7, 8, 9<\/code> (l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 5): Th\u00eam 1<\/code> v\u00e0o ch\u1eef s\u1ed1 \u1edf h\u00e0ng l\u00e0m tr\u00f2n v\u00e0 thay th\u1ebf t\u1ea5t c\u1ea3 c\u00e1c ch\u1eef s\u1ed1 \u1edf b\u00ean ph\u1ea3i b\u1eb1ng ch\u1eef s\u1ed1 0<\/code>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/p>\n \n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi l\u00e0m tr\u00f2n s\u1ed1:<\/p>\n \n- Qu\u00ean thay th\u1ebf c\u00e1c ch\u1eef s\u1ed1 \u1edf b\u00ean ph\u1ea3i th\u00e0nh ch\u1eef s\u1ed1
0<\/code> ho\u1eb7c nh\u1ea7m l\u1eabn khi x\u00e9t ch\u1eef s\u1ed1 b\u00ean ph\u1ea3i (v\u00ed d\u1ee5: l\u00e0m tr\u00f2n s\u1ed1 43820<\/code> \u0111\u1ebfn h\u00e0ng ngh\u00ecn, x\u00e9t s\u1ed1 8 \u1edf h\u00e0ng tr\u0103m l\u00e0 \u2265 5$ n\u00ean ph\u1ea3i l\u00e0m tr\u00f2n th\u00e0nh 44000<\/code>, nh\u01b0ng h\u1ecdc sinh hay qu\u00ean t\u0103ng 1 \u1edf h\u00e0ng ngh\u00ecn).<\/li>\n<\/ul>\n<\/div>\n<\/p>\n \n V\u00ed d\u1ee5 m\u1eabu th\u1ef1c t\u1ebf: L\u00e0m tr\u00f2n s\u1ed1 d\u00e2n v\u00e0 gi\u00e1 ti\u1ec1n<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> a) L\u00e0m tr\u00f2n s\u1ed1 d\u00e2n 486253<\/code> ng\u01b0\u1eddi \u0111\u1ebfn h\u00e0ng ngh\u00ecn.
\nb) L\u00e0m tr\u00f2n gi\u00e1 ti\u1ec1n 874500<\/code> \u0111\u1ed3ng \u0111\u1ebfn h\u00e0ng ch\u1ee5c ngh\u00ecn.<\/p>\nL\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong>
\n\u2022 C\u00e2u a:<\/strong> H\u00e0ng ngh\u00ecn l\u00e0 ch\u1eef s\u1ed1 6<\/code>. Ch\u1eef s\u1ed1 ngay b\u00ean ph\u1ea3i l\u00e0 ch\u1eef s\u1ed1 2<\/code> (nh\u1ecf h\u01a1n 5). Gi\u1eef nguy\u00ean ch\u1eef s\u1ed1 6, \u0111\u1ed5i c\u00e1c ch\u1eef s\u1ed1 b\u00ean ph\u1ea3i th\u00e0nh 0. K\u1ebft qu\u1ea3: 486000<\/strong> ng\u01b0\u1eddi.
\n\u2022 C\u00e2u b:<\/strong> H\u00e0ng ch\u1ee5c ngh\u00ecn l\u00e0 ch\u1eef s\u1ed1 7<\/code>. Ch\u1eef s\u1ed1 ngay b\u00ean ph\u1ea3i l\u00e0 ch\u1eef s\u1ed1 4<\/code> (nh\u1ecf h\u01a1n 5). Gi\u1eef nguy\u00ean ch\u1eef s\u1ed1 7, \u0111\u1ed5i c\u00e1c ch\u1eef s\u1ed1 b\u00ean ph\u1ea3i th\u00e0nh 0. K\u1ebft qu\u1ea3: 870000<\/strong> \u0111\u1ed3ng.<\/p>\n<\/div>\n<\/div>\n<\/p>\n <\/p>\n \n <\/p>\n D\u00e3y s\u1ed1 t\u1ef1 nhi\u00ean<\/h2>\n\u0110\u1eb7c \u0111i\u1ec3m v\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp c\u01a1 b\u1ea3n<\/h3>\n\n- \u0110\u1eb7c \u0111i\u1ec3m c\u1ee7a d\u00e3y s\u1ed1 t\u1ef1 nhi\u00ean:<\/strong>\n
\n- D\u00e3y s\u1ed1 t\u1ef1 nhi\u00ean b\u1eaft \u0111\u1ea7u t\u1eeb s\u1ed1
0<\/code> (0, 1, 2, 3, 4, 5,…).<\/li>\n- Hai s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp th\u00ec h\u01a1n k\u00e9m nhau \u0111\u00fang
1 \u0111\u01a1n v\u1ecb<\/code> (s\u1ed1 li\u1ec1n tr\u01b0\u1edbc k\u00e9m s\u1ed1 li\u1ec1n sau 1 \u0111\u01a1n v\u1ecb, s\u1ed1 li\u1ec1n sau h\u01a1n s\u1ed1 li\u1ec1n tr\u01b0\u1edbc 1 \u0111\u01a1n v\u1ecb).<\/li>\n- D\u00e3y s\u1ed1 t\u1ef1 nhi\u00ean k\u00e9o d\u00e0i v\u00f4 t\u1eadn, do \u0111\u00f3 kh\u00f4ng c\u00f3 s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn nh\u1ea5t<\/strong>.<\/li>\n
- S\u1ed1
0<\/code> l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean b\u00e9 nh\u1ea5t.<\/li>\n<\/ul>\n<\/li>\n- S\u1ed1 ch\u1eb5n v\u00e0 s\u1ed1 l\u1ebb:<\/strong>\n
\n- S\u1ed1 ch\u1eb5n l\u00e0 s\u1ed1 c\u00f3 t\u1eadn c\u00f9ng l\u00e0
0, 2, 4, 6, 8<\/code>. Hai s\u1ed1 ch\u1eb5n li\u00ean ti\u1ebfp h\u01a1n k\u00e9m nhau 2 \u0111\u01a1n v\u1ecb<\/code>.<\/li>\n- S\u1ed1 l\u1ebb l\u00e0 s\u1ed1 c\u00f3 t\u1eadn c\u00f9ng l\u00e0
1, 3, 5, 7, 9<\/code>. Hai s\u1ed1 l\u1ebb li\u00ean ti\u1ebfp h\u01a1n k\u00e9m nhau 2 \u0111\u01a1n v\u1ecb<\/code>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/p>\n \n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng \u0433\u0440\u0430\u0444 khi t\u00ecm s\u1ed1 li\u1ec1n tr\u01b0\u1edbc\/li\u1ec1n sau:<\/p>\n \n- Khi t\u00ecm s\u1ed1 li\u1ec1n tr\u01b0\u1edbc c\u1ee7a s\u1ed1
0<\/code>, h\u1ecdc sinh hay nh\u1ea7m l\u1eabn (s\u1ed1 0 l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean b\u00e9 nh\u1ea5t n\u00ean kh\u00f4ng c\u00f3 s\u1ed1 t\u1ef1 nhi\u00ean li\u1ec1n tr\u01b0\u1edbc n\u00f3). Ho\u1eb7c khi t\u00ecm s\u1ed1 ch\u1eb5n\/l\u1ebb li\u00ean ti\u1ebfp, c\u00e1c con hay c\u1ed9ng tr\u1eeb nh\u1ea7m 1 \u0111\u01a1n v\u1ecb thay v\u00ec 2 \u0111\u01a1n v\u1ecb.<\/li>\n<\/ul>\n<\/div>\n<\/p>\n \n V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ecm s\u1ed1 li\u1ec1n tr\u01b0\u1edbc, li\u1ec1n sau v\u00e0 \u0111i\u1ec1n s\u1ed1 v\u00e0o d\u00e3y<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> a) Vi\u1ebft s\u1ed1 li\u1ec1n tr\u01b0\u1edbc v\u00e0 s\u1ed1 li\u1ec1n sau c\u1ee7a s\u1ed1 9999<\/code>.
\nb) \u0110i\u1ec1n ti\u1ebfp 2 s\u1ed1 v\u00e0o d\u00e3y s\u1ed1 sau: 2, 4, 6, 8, 10, ...<\/code><\/p>\nL\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong>
\n\u2022 C\u00e2u a:<\/strong> S\u1ed1 li\u1ec1n tr\u01b0\u1edbc c\u1ee7a 9999<\/code> l\u00e0 9998<\/code>; s\u1ed1 li\u1ec1n sau c\u1ee7a 9999<\/code> l\u00e0 10000<\/code>.
\n\u2022 C\u00e2u b:<\/strong> Nh\u1eadn x\u00e9t d\u00e3y s\u1ed1 l\u00e0 c\u00e1c s\u1ed1 ch\u1eb5n t\u0103ng d\u1ea7n, hai s\u1ed1 li\u00ean ti\u1ebfp h\u01a1n k\u00e9m nhau 2 \u0111\u01a1n v\u1ecb. Hai s\u1ed1 ti\u1ebfp theo c\u1ea7n \u0111i\u1ec1n l\u00e0: 12, 14<\/strong>.<\/p>\n<\/div>\n<\/p>\n T\u00ednh ch\u1ea5t giao ho\u00e1n, k\u1ebft h\u1ee3p c\u1ee7a ph\u00e9p c\u1ed9ng<\/h2>\nC\u00f4ng th\u1ee9c v\u00e0 b\u1ea3n ch\u1ea5t t\u00ednh ch\u1ea5t<\/h3>\n\n- T\u00ednh ch\u1ea5t giao ho\u00e1n:<\/strong> Khi \u0111\u1ed5i ch\u1ed7 c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t t\u1ed5ng th\u00ec t\u1ed5ng \u0111\u00f3 kh\u00f4ng thay \u0111\u1ed5i.\n
a + b = b + a<\/div>\n<\/li>\n - T\u00ednh ch\u1ea5t k\u1ebft h\u1ee3p:<\/strong> Khi c\u1ed9ng m\u1ed9t t\u1ed5ng hai s\u1ed1 v\u1edbi s\u1ed1 th\u1ee9 ba, ta c\u00f3 th\u1ec3 c\u1ed9ng s\u1ed1 th\u1ee9 nh\u1ea5t v\u1edbi t\u1ed5ng c\u1ee7a s\u1ed1 th\u1ee9 hai v\u00e0 s\u1ed1 th\u1ee9 ba.\n
(a + b) + c = a + (b + c)<\/div>\n<\/li>\n - \u1ee8ng d\u1ee5ng t\u00ednh nhanh:<\/strong> D\u00f9ng \u0111\u1ec3 nh\u00f3m c\u00e1c s\u1ed1 h\u1ea1ng c\u00f3 t\u1ed5ng l\u00e0 s\u1ed1 tr\u00f2n ch\u1ee5c, tr\u00f2n tr\u0103m, tr\u00f2n ngh\u00ecn l\u1ea1i v\u1edbi nhau \u0111\u1ec3 t\u00ednh to\u00e1n thu\u1eadn ti\u1ec7n nh\u1ea5t.<\/li>\n<\/ul>\n
<\/p>\n \n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi t\u00ednh nhanh:<\/p>\n \n- Nh\u00f3m nh\u1ea7m d\u1ea5u (\u0111\u01b0a s\u1ed1 h\u1ea1ng \u0111i nh\u01b0ng qu\u00ean mang theo d\u1ea5u ph\u00e9p t\u00ednh ph\u00eda tr\u01b0\u1edbc n\u00f3) ho\u1eb7c t\u00ednh nh\u1ea9m sai t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 tr\u00f2n ch\u1ee5c, tr\u00f2n tr\u0103m.<\/li>\n<\/ul>\n<\/div>\n
<\/p>\n \n V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh b\u1eb1ng c\u00e1ch thu\u1eadn ti\u1ec7n nh\u1ea5t<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> T\u00ednh nhanh: 38 + 25 + 62 + 75<\/code><\/p>\nL\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong>
\n\u2022 Nh\u1eadn x\u00e9t: 38 + 62 = 100<\/code> (tr\u00f2n tr\u0103m) v\u00e0 25 + 75 = 100<\/code> (tr\u00f2n tr\u0103m).
\n\u2022 \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t giao ho\u00e1n v\u00e0 k\u1ebft h\u1ee3p \u0111\u1ec3 nh\u00f3m s\u1ed1:
\n38 + 25 + 62 + 75 = (38 + 62) + (25 + 75)<\/code>
\n= 100 + 100 = 200<\/strong><\/code>.<\/p>\n<\/div>\n<\/p>\n Bi\u1ec3u th\u1ee9c c\u00f3 ch\u1ee9a ch\u1eef<\/h2>\nKh\u00e1i ni\u1ec7m v\u00e0 c\u00e1ch t\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c<\/h3>\n |
![\"\u0110\u1ec1](\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-4-tom-tat.png\")
![\"T\u00ecm](\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-4-300x188.png\")