B\u01b0\u1edbc ch\u00e2n v\u00e0o l\u1edbp 6, h\u1ecdc sinh ch\u00ednh th\u1ee9c chuy\u1ec3n c\u1ea5p l\u00ean b\u1eadc THCS v\u1edbi m\u00f4i tr\u01b0\u1eddng h\u1ecdc t\u1eadp, ph\u01b0\u01a1ng ph\u00e1p t\u01b0 duy v\u00e0 c\u00e1ch ra \u0111\u1ec1 ho\u00e0n to\u00e0n m\u1edbi m\u1ebb. S\u1ef1 thay \u0111\u1ed5i \u0111\u1ed9t ng\u1ed9t n\u00e0y d\u1ec5 khi\u1ebfn c\u00e1c em r\u01a1i v\u00e0o tr\u1ea1ng th\u00e1i b\u1ee1 ng\u1ee1, \u0111\u1eb7c bi\u1ec7t l\u00e0 khi \u0111\u1ed1i di\u1ec7n v\u1edbi nh\u1eefng c\u00fa s\u1ed1c \u0111\u1ea7u c\u1ea5p khi l\u00ean l\u1edbp 6<\/a> xoay quanh c\u00e1c ch\u1ee7 \u0111\u1ec1 tr\u1eebu t\u01b0\u1ee3ng nh\u01b0 t\u1eadp h\u1ee3p, l\u0169y th\u1eeba, \u01afCLN \u2013 BCNN, b\u00e0i to\u00e1n th\u1ef1c t\u1ebf ph\u1ee9c t\u1ea1p v\u00e0 h\u00ecnh h\u1ecdc tr\u1ef1c quan.<\/p>\n \u0110\u1ec3 gi\u00fap c\u00e1c s\u0129 t\u1eed gi\u1ea3i t\u1ecfa \u00e1p l\u1ef1c v\u00e0 n\u1eafm ch\u1eafc n\u1ec1n t\u1ea3ng, NaviEdu bi\u00ean so\u1ea1n tr\u1ecdn b\u1ed9 \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 to\u00e1n 6<\/strong> theo chu\u1ea9n Th\u00f4ng t\u01b0 22<\/a>: t\u1ed5ng h\u1ee3p l\u00fd thuy\u1ebft c\u1ed1t l\u00f5i, ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i chi ti\u1ebft, l\u1ecbch \u00f4n 7 ng\u00e0y khoa h\u1ecdc k\u00e8m \u0111\u1ec1 thi m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n!<\/p>\n<\/div>\n <\/p>\n M\u1ee5c l\u1ee5c \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 6<\/p>\n <\/p>\n Theo quy \u0111\u1ecbnh \u0111\u00e1nh gi\u00e1 h\u1ecdc sinh c\u1ea5p THCS t\u1ea1i Th\u00f4ng t\u01b0 22\/2021\/TT-BGD\u0110T, b\u00e0i ki\u1ec3m tra \u0111\u1ecbnh k\u00ec gi\u1eefa h\u1ecdc k\u00ec 1 m\u00f4n To\u00e1n l\u1edbp 6 th\u01b0\u1eddng \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n trong th\u1eddi gian 90 ph\u00fat<\/strong>. V\u00ec ma tr\u1eadn, b\u1ea3n \u0111\u1eb7c t\u1ea3 v\u00e0 \u0111\u1ec1 thi ch\u00ednh th\u1ee9c \u0111\u1ec1u do t\u1ed5 chuy\u00ean m\u00f4n c\u1ee7a t\u1eebng tr\u01b0\u1eddng THCS t\u1ef1 x\u00e2y d\u1ef1ng d\u1ef1a tr\u00ean khung ch\u01b0\u01a1ng tr\u00ecnh c\u1ee7a B\u1ed9 GD&\u0110T, n\u00ean c\u1ea5u tr\u00fac d\u01b0\u1edbi \u0111\u00e2y ch\u1ec9 l\u00e0 m\u1eabu tham kh\u1ea3o ph\u1ed5 bi\u1ebfn v\u00e0 s\u00e1t th\u1ef1c t\u1ebf nh\u1ea5t:<\/p>\n <\/p>\n \ud83d\udca1 L\u01b0u \u00fd quan tr\u1ecdng cho ba m\u1eb9 v\u00e0 h\u1ecdc sinh:<\/strong> C\u1ea5u tr\u00fac \u0111\u1ec1 ki\u1ec3m tra c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u0111i\u1ec1u ch\u1ec9nh t\u00f9y theo y\u00eau c\u1ea7u c\u1ee7a t\u1eebng tr\u01b0\u1eddng THCS. Do \u0111\u00f3, ba m\u1eb9 n\u00ean tham kh\u1ea3o k\u1ef9 \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp do gi\u00e1o vi\u00ean b\u1ed9 m\u00f4n t\u1ea1i tr\u01b0\u1eddng ph\u00e1t ra \u0111\u1ec3 n\u1eafm ch\u00ednh x\u00e1c ph\u1ea1m vi ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 h\u00ecnh th\u1ee9c ra \u0111\u1ec1 c\u1ee7a con.<\/p>\n<\/div>\n<\/div>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n S\u1ed1 t\u1ef1 nhi\u00ean v\u00e0 c\u00e1c ph\u00e9p t\u00ednh l\u00e0 ph\u1ea7n chi\u1ebfm nhi\u1ec1u \u0111i\u1ec3m nh\u1ea5t, v\u00ec v\u1eady \u0111\u00e2y l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 6<\/strong>. Con c\u1ea7n \u0111i l\u1ea7n l\u01b0\u1ee3t t\u1eeb t\u1eadp h\u1ee3p, l\u0169y th\u1eeba \u0111\u1ebfn t\u00ednh chia h\u1ebft, \u01afCLN v\u00e0 BCNN.<\/p>\n <\/p>\n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 t\u1eadp h\u1ee3p:<\/p>\n <\/p>\n V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Vi\u1ebft t\u1eadp h\u1ee3p<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> Cho t\u1eadp h\u1ee3p A c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn h\u01a1n 3 v\u00e0 nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng 7. L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong> <\/p>\n <\/p>\n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi vi\u1ebft s\u1ed1 La M\u00e3:<\/p>\n <\/p>\n V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: \u0110\u1ecdc v\u00e0 vi\u1ebft s\u1ed1 La M\u00e3<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> a) Vi\u1ebft s\u1ed1 19 v\u00e0 24 b\u1eb1ng s\u1ed1 La M\u00e3. L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong> <\/p>\n <\/p>\n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh:<\/p>\n <\/p>\n V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c 2 b\u01b0\u1edbc<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong> <\/p>\n <\/p>\n \u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi t\u00ednh l\u0169y th\u1eeba:<\/p>\n <\/p>\n V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Vi\u1ebft g\u1ecdn v\u00e0 t\u00ednh l\u0169y th\u1eeba<\/p>\n \u0110\u1ec1 b\u00e0i:<\/strong> a) Vi\u1ebft g\u1ecdn t\u00edch sau d\u01b0\u1edbi d\u1ea1ng l\u0169y th\u1eeba: L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong>![\"\u0110\u1ec1](\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-6-tom-tat.png\")
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C\u1ea5u tr\u00fac \u0111\u1ec1 thi gi\u1eefa k\u00ec 1 To\u00e1n 6 theo Th\u00f4ng t\u01b0 22<\/h2>\n
![\"T\u00ecm](\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-6-1024x640.png\")
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B\u1ea3ng ma tr\u1eadn tham kh\u1ea3o ph\u00e2n b\u1ed5 n\u1ed9i dung v\u00e0 m\u1ee9c \u0111\u1ed9 nh\u1eadn th\u1ee9c<\/h3>\n
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\n \nM\u1ea1ch ki\u1ebfn th\u1ee9c<\/th>\n Nh\u1eadn bi\u1ebft<\/th>\n Th\u00f4ng hi\u1ec3u<\/th>\n V\u1eadn d\u1ee5ng<\/th>\n V\u1eadn d\u1ee5ng cao<\/th>\n T\u1ed5ng \u0111i\u1ec3m<\/th>\n<\/tr>\n<\/thead>\n \n T\u1eadp h\u1ee3p, ph\u00e9p t\u00ednh, l\u0169y th\u1eeba, th\u1ee9 t\u1ef1 th\u1ef1c hi\u1ec7n<\/td>\n 1,0 \u0111i\u1ec3m<\/td>\n 1,0 \u0111i\u1ec3m<\/td>\n 1,0 \u0111i\u1ec3m<\/td>\n 0,0 \u0111i\u1ec3m<\/td>\n 3,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n \n T\u00ednh chia h\u1ebft, s\u1ed1 nguy\u00ean t\u1ed1, \u01afCLN – BCNN<\/td>\n 1,0 \u0111i\u1ec3m<\/td>\n 1,5 \u0111i\u1ec3m<\/td>\n 1,0 \u0111i\u1ec3m<\/td>\n 0,5 \u0111i\u1ec3m<\/td>\n 4,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n \n H\u00ecnh h\u1ecdc tr\u1ef1c quan – C\u00e1c h\u00ecnh ph\u1eb3ng<\/td>\n 2,0 \u0111i\u1ec3m<\/td>\n 0,5 \u0111i\u1ec3m<\/td>\n 0,0 \u0111i\u1ec3m<\/td>\n 0,5 \u0111i\u1ec3m<\/td>\n 3,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n \n T\u1ed4NG \u0110I\u1ec2M & T\u1ef6 L\u1ec6<\/td>\n 4,0 \u0111i\u1ec3m (40%)<\/td>\n 3,0 \u0111i\u1ec3m (30%)<\/td>\n 2,0 \u0111i\u1ec3m (20%)<\/td>\n 1,0 \u0111i\u1ec3m (10%)<\/td>\n 10,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n Ph\u1ea7n I: S\u1ed1 v\u00e0 Ph\u00e9p T\u00ednh v\u1edbi S\u1ed1 T\u1ef1 Nhi\u00ean<\/h2>\n<\/div>\n
T\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean<\/h2>\n
K\u00fd hi\u1ec7u, ph\u1ea7n t\u1eed v\u00e0 c\u00e1ch vi\u1ebft t\u1eadp h\u1ee3p<\/h3>\n
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\u2208<\/code> d\u00f9ng \u0111\u1ec3 ch\u1ec9 ph\u1ea7n t\u1eed thu\u1ed9c t\u1eadp h\u1ee3p v\u00e0 \u2209<\/code> ch\u1ec9 ph\u1ea7n t\u1eed kh\u00f4ng thu\u1ed9c t\u1eadp h\u1ee3p.<\/li>\n\n
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N = {0, 1, 2, 3, 4, ...}<\/code>.<\/li>\nN* = {1, 2, 3, 4, ...}<\/code>.<\/li>\n<\/ul>\n<\/li>\n\n
\na) Vi\u1ebft t\u1eadp h\u1ee3p A b\u1eb1ng c\u00e1ch li\u1ec7t k\u00ea c\u00e1c ph\u1ea7n t\u1eed.
\nb) \u0110i\u1ec1n k\u00fd hi\u1ec7u th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng: 3 ... A<\/code> ; 5 ... A<\/code>.<\/p>\n
\n\u2022 C\u00e2u a:<\/strong> C\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn h\u01a1n 3 v\u00e0 nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng 7 l\u00e0 4, 5, 6, 7. Vi\u1ebft t\u1eadp h\u1ee3p: A = {4, 5, 6, 7}<\/code>.
\n\u2022 C\u00e2u b:<\/strong> V\u00ec s\u1ed1 3 kh\u00f4ng n\u1eb1m trong t\u1eadp h\u1ee3p A n\u00ean 3 \u2209 A<\/code>; s\u1ed1 5 n\u1eb1m trong t\u1eadp h\u1ee3p A n\u00ean 5 \u2208 A<\/code>.<\/p>\n<\/div>\nS\u1ed1 La M\u00e3<\/h2>\n
K\u00fd t\u1ef1 c\u01a1 b\u1ea3n v\u00e0 quy t\u1eafc \u0111\u1ecdc vi\u1ebft<\/h3>\n
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I<\/code> \u1ee9ng v\u1edbi s\u1ed1 1<\/li>\nV<\/code> \u1ee9ng v\u1edbi s\u1ed1 5<\/li>\nX<\/code> \u1ee9ng v\u1edbi s\u1ed1 10<\/li>\n<\/ul>\n<\/li>\n\n
VI = 6<\/code>, XI = 11<\/code>, XII = 12<\/code>).<\/li>\nIV = 4<\/code>, IX = 9<\/code>, XIV = 14<\/code>, XIX = 19<\/code>).<\/li>\n<\/ul>\n<\/li>\n\n
IIII<\/code> thay v\u00ec IV<\/code>) ho\u1eb7c \u0111\u1eb7t sai v\u1ecb tr\u00ed tr\u1eeb b\u00ean tr\u00e1i (v\u00ed d\u1ee5 vi\u1ebft s\u1ed1 9 th\u00e0nh VX<\/code> thay v\u00ec IX<\/code>).<\/li>\n<\/ul>\n<\/div>\n
\nb) \u0110\u1ecdc c\u00e1c s\u1ed1 La M\u00e3 sau: XXVI<\/code> ; XXIX<\/code>.<\/p>\n
\n\u2022 C\u00e2u a:<\/strong> S\u1ed1 19 vi\u1ebft th\u00e0nh XIX<\/code> (10 + 9); s\u1ed1 24 vi\u1ebft th\u00e0nh XXIV<\/code> (20 + 4).
\n\u2022 C\u00e2u b:<\/strong> XXVI<\/code> \u0111\u1ecdc l\u00e0 hai m\u01b0\u01a1i s\u00e1u (26); XXIX<\/code> \u0111\u1ecdc l\u00e0 hai m\u01b0\u01a1i ch\u00edn (29).<\/p>\n<\/div>\nTh\u1ee9 t\u1ef1 th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh<\/h2>\n
Quy t\u1eafc t\u00ednh to\u00e1n trong bi\u1ec3u th\u1ee9c<\/h3>\n
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\nL\u0169y th\u1eeba \u2192 Nh\u00e2n v\u00e0 chia \u2192 C\u1ed9ng v\u00e0 tr\u1eeb<\/code> (t\u00ednh t\u1eeb tr\u00e1i sang ph\u1ea3i).<\/li>\n
\nNgo\u1eb7c tr\u00f2n ( ) \u2192 Ngo\u1eb7c vu\u00f4ng [ ] \u2192 Ngo\u1eb7c nh\u1ecdn { }<\/code>.<\/li>\n<\/ul>\n\n
50 - [30 - (6 - 2)2<\/sup>]<\/code><\/p>\n
\n\u2022 B\u01b0\u1edbc 1 (T\u00ednh trong ngo\u1eb7c tr\u00f2n tr\u01b0\u1edbc, k\u00e8m l\u0169y th\u1eeba): (6 - 2)2<\/sup> = 42<\/sup> = 16<\/code>.
\n\u2022 B\u01b0\u1edbc 2 (T\u00ednh trong ngo\u1eb7c vu\u00f4ng): 30 - 16 = 14<\/code>.
\n\u2022 B\u01b0\u1edbc 3 (Th\u1ef1c hi\u1ec7n ph\u00e9p tr\u1eeb c\u00f2n l\u1ea1i): 50 - 14 = 36<\/strong><\/code>.<\/p>\n<\/div>\nL\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 t\u1ef1 nhi\u00ean<\/h2>\n
\u0110\u1ecbnh ngh\u0129a v\u00e0 c\u00e1c quy t\u1eafc nh\u00e2n chia l\u0169y th\u1eeba<\/h3>\n
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an<\/sup> = a \u00b7 a \u00b7 ... \u00b7 a<\/code> (v\u1edbi n \u2260 0). Trong \u0111\u00f3 a g\u1ecdi l\u00e0 c\u01a1 s\u1ed1<\/strong>, n g\u1ecdi l\u00e0 s\u1ed1 m\u0169<\/strong>.<\/li>\na1<\/sup> = a<\/code> v\u00e0 a0<\/sup> = 1<\/code> (v\u1edbi a \u2260 0).<\/li>\n\n
23<\/sup><\/code> th\u00e0nh 2 \u00b7 3 = 6<\/code> thay v\u00ec \u0111\u00fang b\u1ea3n ch\u1ea5t l\u00e0 2 \u00b7 2 \u00b7 2 = 8<\/code>); ho\u1eb7c khi nh\u00e2n chia l\u0169y th\u1eeba l\u1ea1i \u0111em nh\u00e2n\/chia c\u1ea3 s\u1ed1 m\u0169 v\u1edbi nhau.<\/li>\n<\/ul>\n<\/div>\n5 \u00b7 5 \u00b7 5 \u00b7 5<\/code>.
\nb) Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh: 34<\/sup> \u00b7 32<\/sup><\/code> v\u00e0 75<\/sup> : 73<\/sup><\/code>.<\/p>\n
\n\u2022 C\u00e2u a:<\/strong> T\u00edch c\u1ee7a 4 th\u1eeba s\u1ed1 5 vi\u1ebft g\u1ecdn th\u00e0nh 54<\/sup><\/code>.
\n\u2022 C\u00e2u b:<\/strong>
\n– 34<\/sup> \u00b7 32<\/sup> = 34 + 2<\/sup> = 36<\/sup> = 729<\/code>.
\n– 75<\/sup> : 73<\/sup> = 75 - 3<\/sup> = 72<\/sup> = 49<\/code>.<\/p>\n<\/div>\n<\/div>\n