{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho 3 ch\u1eef s\u1ed1 a, b, c kh\u00e1c nhau v\u00e0 kh\u00e1c 0. T\u1eadp h\u1ee3p A g\u1ed3m c\u00e1c s\u1ed1 c\u00f3 3 ch\u1eef s\u1ed1 g\u1ed3m \u0111\u1ee7 3 ch\u1eef s\u1ed1 tr\u00ean l\u00e0: ","select":["A. $A = \\left\\{ \\overline{abc}; \\overline{acb}; \\overline{aab}; \\overline{ccb}; \\overline{aaa}; \\overline{bbb} \\right\\}$ ","B. $A = \\left\\{ \\overline{abc}; \\overline{acb}; \\overline{bac}; \\overline{bca}; \\overline{cba}; \\overline{cab} \\right\\} $","C. $A = \\left\\{ \\overline{aaa}; \\overline{bbb}; \\overline{ccc}; \\overline{abc}; \\overline{cba}; \\overline{bca} \\right\\} $","D. $A = \\left\\{ \\overline{bba}; \\overline{ccb}; \\overline{aab}; \\overline{abc}; \\overline{aac}; \\overline{cca} \\right\\}$ "],"hint":"","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> T\u1eadp h\u1ee3p A g\u1ed3m c\u00e1c s\u1ed1 c\u00f3 \u0111\u1ee7 3 ch\u1eef s\u1ed1 a, b, c l\u00e0: <br\/> $A = \\left\\{ \\overline{abc}; \\overline{acb}; \\overline{bac}; \\overline{bca}; \\overline{cba}; \\overline{cab} \\right\\}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B <\/span> ","column":2}]}],"id_ques":1751},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"\u01afCLN(24; 54) = ? ","select":["A. 12","B. 24","C. 8","D. 6 "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Ph\u00e2n t\u00edch 24; 54 ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 <br\/><b> B\u01b0\u1edbc 2: <\/b> Ch\u1ecdn ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 chung <br\/> <b> B\u01b0\u1edbc 3: <\/b> L\u1eadp t\u00edch c\u00e1c th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 chung, m\u1ed7i th\u1eeba s\u1ed1 l\u1ea5y v\u1edbi s\u1ed1 m\u0169 nh\u1ecf nh\u1ea5t c\u1ee7a n\u00f3 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: $24 = 2^3 . 3$; $54 = 2 . 3^3$ <br\/> \u01afCLN(24; 54) = 2 . 3 = 6 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. 6 <\/span> ","column":2}]}],"id_ques":1752},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"BCNN(40; 168 ) = ? ","select":["A. 168","B. 280","C. 720","D. 840 "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Ph\u00e2n t\u00edch 40; 168 ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 <br\/><b> B\u01b0\u1edbc 2: <\/b> Ch\u1ecdn ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 chung v\u00e0 ri\u00eang <br\/> <b> B\u01b0\u1edbc 3: <\/b> L\u1eadp t\u00edch c\u00e1c th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 chung v\u00e0 ri\u00eang, m\u1ed7i th\u1eeba s\u1ed1 l\u1ea5y v\u1edbi s\u1ed1 m\u0169 l\u1edbn nh\u1ea5t c\u1ee7a n\u00f3 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: $40 = 2^3 . 5$; $168 = 2^3 . 3 . 7$ <br\/> $BCNN(40; 168) = 2^3 . 3 . 5 . 7 = 840$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. 840 <\/span> ","column":2}]}],"id_ques":1753},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ednh. <br\/> $(5^3 + 475 : 19) : (3 . 5^2)$ = _input_ ","hint":"T\u00ednh c\u00e1c l\u0169y th\u1eeba tr\u01b0\u1edbc","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh $5^3$ v\u00e0 $5^2$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh gi\u00e1 tr\u1ecb c\u00e1c bi\u1ec3u th\u1ee9c trong () tr\u01b0\u1edbc, ngo\u00e0i ngo\u1eb7c sau <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $ \\begin{align*} & (5^3 + 475 : 19) : (3 . 5^2) \\\\ &= (125 + 475 : 19) : (3 . 25) \\\\ &= (125 + 25) : 75 \\\\ &= 150 : 75 \\\\ &= 2 \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 2 <\/span> "}]}],"id_ques":1754},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Kh\u00f4ng th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh h\u00e3y cho bi\u1ebft kh\u1eb3ng \u0111\u1ecbnh sau <b> \u0111\u00fang <\/b> hay <b> sai <\/b>. <br\/> $81^7 - 27^9 - 9^{13}$ chia h\u1ebft cho 9.","select":["A. \u0110\u00daNG","B. SAI"],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t chia h\u1ebft c\u1ee7a m\u1ed9t hi\u1ec7u <br\/> X\u00e9t xem c\u00e1c s\u1ed1 h\u1ea1ng tr\u00ean c\u00f3 chia h\u1ebft cho 9 kh\u00f4ng <br\/> N\u1ebfu t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 \u0111\u1ec1u chia h\u1ebft cho 9 th\u00ec hi\u1ec7u tr\u00ean chia h\u1ebft cho 9 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> X\u00e9t hi\u1ec7u $81^7 - 27^9 - 9^{13}$ <br\/> C\u00f3 81 $\\vdots$ 9 n\u00ean $81^7$ $\\vdots$ 9 <br\/> V\u00ec 27 $\\vdots$ 9 n\u00ean $27^9$ $\\vdots$ 9 <br\/> V\u00ec 9 $\\vdots$ 9 n\u00ean $9^{13}$ $\\vdots$ 9 <br\/> $\\Rightarrow$ $(81^7 - 27^9 - 9^{13})$ $\\vdots$ 9 <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 <span class='basic_pink'> \u0110\u00daNG <\/span> ","column":2}]}],"id_ques":1755},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c $N = 20 - 5|x - 3|$ l\u00e0:","select":["A. 15","B. 20","C. 14","D. 100"],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t: V\u1edbi m\u1ecdi $a \\in \\mathbb{Z}$ th\u00ec: <br\/> $|a| \\geq 0; -|a| \\leq ; a^2 \\geq 0; -a^2 \\leq 0$ <br\/> D\u1ea5u b\u1eb1ng x\u1ea3y ra khi v\u00e0 ch\u1ec9 khi a = 0 ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> X\u00e9t bi\u1ec3u th\u1ee9c $|x - 3|$ sau \u0111\u00f3 x\u00e9t bi\u1ec3u th\u1ee9c $-5|x - 3|$ <br\/> \u0110\u1ec3 N \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t th\u00ec $-5|x - 3|$ nh\u1ecf nh\u1ea5t t\u1eeb \u0111\u00f3 ta t\u00ecm x \u0111\u1ec3 $-5|x - 3|$ nh\u1ecf nh\u1ea5t sau \u0111\u00f3 t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a N <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: $|x - 3| \\geq 0$ v\u1edbi m\u1ecdi x <br\/> $\\Rightarrow$ $-5|x - 3| \\leq 0$ ($-5|x - 3| = 0$ khi x - 3 = 0 hay x = 3) <br\/> $\\Rightarrow$ $20 - 5|x - 3| \\leq 20$ <br\/> Do \u0111\u00f3 max N = 20 khi x = 3 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. 20 <\/span> ","column":2}]}],"id_ques":1756},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"T\u00ecm x bi\u1ebft: <br\/> (19 - 51) - (x - 23) = 6","select":["A. x = -15","B. x = 15","C. x = -49","D. x = 61"],"hint":"D\u1ef1a v\u00e0o quy t\u1eafc chuy\u1ec3n v\u1ebf, quy t\u1eafc d\u1ea5u ngo\u1eb7c ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> B\u1ecf ngo\u1eb7c (l\u01b0u \u00fd \u0111\u1eb1ng tr\u01b0\u1edbc d\u1ea5u ngo\u1eb7c c\u00f3 d\u1ea5u (-) khi b\u1ecf ngo\u1eb7c ta ph\u1ea3i \u0111\u1ed5i d\u1ea5u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng trong ngo\u1eb7c) <br\/> <b> B\u01b0\u1edbc 2: <\/b> Chuy\u1ec3n c\u00e1c s\u1ed1 h\u1ea1ng kh\u00f4ng ch\u1ee9a x sang v\u1ebf ph\u1ea3i <br\/> Khi chuy\u1ec3n v\u1ebf ph\u1ea3i \u0111\u1ed5i d\u1ea5u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} (19 - 51) - (x - 23) &= 6 \\\\ 19 - 51 - x + 23 &= 6 \\\\ -x &= 6 - 19 + 51 - 23 \\\\ -x &= 15 \\\\ x &= -15 \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. x = -15 <\/span> ","column":2}]}],"id_ques":1757},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"T\u00ecm x bi\u1ebft: <br\/> [(6x - 39) : 3] . 28 = 4956","select":["A. x = 95","B. x = 82","C. x = -90","D. x = 90"],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Coi bi\u1ec3u th\u1ee9c trong [] l\u00e0 th\u1eeba s\u1ed1 ch\u01b0a bi\u1ebft <br\/> Mu\u1ed1n t\u00ecm th\u1eeba s\u1ed1 ch\u01b0a bi\u1ebft l\u1ea5y t\u00edch chia cho th\u1eeba s\u1ed1 \u0111\u00e3 bi\u1ebft <br\/> <b> B\u01b0\u1edbc 2: <\/b> Coi bi\u1ec3u th\u1ee9c trong () l\u00e0 s\u1ed1 b\u1ecb chia ch\u01b0a bi\u1ebft <br\/> Mu\u1ed1n t\u00ecm s\u1ed1 b\u1ecb chia l\u1ea5y th\u01b0\u01a1ng nh\u00e2n v\u1edbi s\u1ed1 chia <br\/> <b> B\u01b0\u1edbc 3: <\/b> Chuy\u1ec3n -39 sang v\u1ebf ph\u1ea3i (l\u01b0u \u00fd khi chuy\u1ec3n v\u1ebf ph\u1ea3i \u0111\u1ed5i d\u1ea5u ph\u00e9p t\u00ednh) r\u1ed3i t\u00ecm x <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} [(6x - 39) : 3] . 28 &= 4956 \\\\ (6x - 39) : 3 &= 4956 : 28 \\\\ (6x - 39) : 3 &= 177 \\\\ 6x - 39 &= 177 . 3 \\\\ 6x - 39 &= 531 \\\\ 6x &= 531 + 39 \\\\ 6x &= 570 \\\\ x &= 570 : 6 \\\\ x &= 95 \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. x = 95 <\/span> ","column":2}]}],"id_ques":1758},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"C\u00e1c ph\u00e2n s\u1ed1 $\\dfrac{5}{9}; \\dfrac{6}{10}$ v\u00e0 $\\dfrac{4}{11}$ \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo th\u1ee9 t\u1ef1 t\u1eeb nh\u1ecf \u0111\u1ebfn l\u1edbn l\u00e0: ","select":["A. $\\dfrac{4}{11}; \\dfrac{5}{9}; \\dfrac{6}{10}$ ","B. $\\dfrac{5}{9}; \\dfrac{6}{10}; \\dfrac{4}{11}$ ","C. $\\dfrac{6}{10}; \\dfrac{5}{9}; \\dfrac{4}{11}$ ","D. $\\dfrac{6}{10}; \\dfrac{4}{11}; \\dfrac{5}{9}$ "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> So s\u00e1nh $\\dfrac{5}{9}$ v\u1edbi $\\dfrac{4}{11}$ b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng ph\u00e2n s\u1ed1 trung gian l\u00e0 $\\dfrac{4}{9}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh $\\dfrac{5}{9}$ v\u1edbi $\\dfrac{6}{10}$ Ph\u00e2n s\u1ed1 $\\dfrac{6}{10} = \\dfrac{5 + 1}{9 + 1}$ v\u00ec v\u1edbi a < b th\u00ec $\\dfrac{a}{b} < \\dfrac{a + 1}{b + 1}$ n\u00ean.... <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: <br\/> $\\dfrac{4}{9} > \\dfrac{4}{11}$ m\u00e0 $\\dfrac{4}{9} < \\dfrac{5}{9}$ $\\Rightarrow$ $\\dfrac{4}{11} < \\dfrac{5}{9}$ <br\/> X\u00e9t ph\u00e2n s\u1ed1 $\\dfrac{5}{9}$ v\u00e0 $\\dfrac{6}{10}$ <br\/> $\\dfrac{6}{10} = \\dfrac{5 + 1}{9 + 1}$ \u00e1p d\u1ee5ng b\u00e0i to\u00e1n $\\dfrac{a}{b} < \\dfrac{a + 1}{b + 1}$ $\\Rightarrow$ $\\dfrac{5}{9} < \\dfrac{6}{10}$ <br\/> $\\Rightarrow$ $\\dfrac{4}{11} < \\dfrac{5}{9} < \\dfrac{6}{10}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A <\/span> <br\/> <span class='basic_green'> <i> B\u00e0i to\u00e1n: Cho 0 < a < b so s\u00e1nh $\\dfrac{a}{b}$ v\u00e0 $\\dfrac{a + 1}{b + 1}$ <br\/>Gi\u1ea3i: <br\/> Quy \u0111\u1ed3ng m\u1eabu hai ph\u00e2n s\u1ed1 ta \u0111\u01b0\u1ee3c: <br\/> $\\dfrac{a}{b} = \\dfrac{a . (b + 1)}{b . (b + 1)} = \\dfrac{ab + a}{b . (b + 1)}$ <br\/> $\\dfrac{a + 1}{b + 1} = \\dfrac{b . (a + 1)}{b . (b + 1)} = \\dfrac{ab + b}{b . (b + 1)}$ <br\/> V\u00ec 0 < a < b n\u00ean ab + a < ab + b <br\/> Do \u0111\u00f3: $\\dfrac{ab + a}{a. (b + 1)} < \\dfrac{ab + b}{b . (b + 1)}$ hay $\\dfrac{a}{b} < \\dfrac{a + 1}{b + 1}$ <i> <\/span> ","column":2}]}],"id_ques":1759},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7"],["20"]]],"list":[{"point":5,"width":50,"type_input":"","input_hint":["frac"],"ques":"T\u00ednh. <br\/> $A = 3,2 . \\dfrac{15}{64} - \\left( \\dfrac{4}{5} + \\dfrac{2}{3} \\right) : 3\\dfrac{2}{3}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Vi\u1ebft c\u00e1c h\u1ed7n s\u1ed1 v\u00e0 s\u1ed1 th\u1eadp ph\u00e2n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $\\begin{align*} A &= 3,2 . \\dfrac{15}{64} - \\left( \\dfrac{4}{5} + \\dfrac{2}{3} \\right) : 3\\dfrac{2}{3} \\\\ &= \\dfrac{32}{10} . \\dfrac{15}{64} - \\left( \\dfrac{12}{15} + \\dfrac{10}{15} \\right) : \\dfrac{11}{3} \\\\ &= \\dfrac{16}{5} . \\dfrac{15}{64} - \\dfrac{22}{15} . \\dfrac{3}{11} \\\\ &= \\dfrac{3}{4} - \\dfrac{2}{5} \\\\ &= \\dfrac{7}{20} \\end{align*} $"}]}],"id_ques":1760},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-37"],["50"]]],"list":[{"point":5,"width":50,"ques":"T\u00ednh. <br\/> $D = -2\\dfrac{2}{5} . 35\\% - \\left( \\dfrac{-2}{5} \\right) . \\dfrac{1}{4} $ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Vi\u1ebft c\u00e1c h\u1ed7n s\u1ed1 v\u00e0 % d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 r\u1ed3i t\u00ednh <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $\\begin{align*} D &= -2\\dfrac{2}{5} . 35\\% - \\left( \\dfrac{-2}{5} \\right) . \\dfrac{1}{4} \\\\ &= \\dfrac{-12}{5} . \\dfrac{35}{100} + \\dfrac{2}{5} . \\dfrac{1}{4} \\\\ &= \\dfrac{-21}{25} + \\dfrac{1}{10} \\\\ &= \\dfrac{-37}{50} \\end{align*} $ <br\/>"}]}],"id_ques":1761},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":5,"width":50,"type_input":"","input_hint":["frac"],"ques":"Hai ng\u01b0\u1eddi c\u00f9ng l\u00e0m chung m\u1ed9t c\u00f4ng vi\u1ec7c. N\u1ebfu l\u00e0m m\u1ed9t m\u00ecnh ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t ph\u1ea3i l\u00e0m trong 6 gi\u1edd; ng\u01b0\u1eddi th\u1ee9 hai ph\u1ea3i l\u00e0m trong 3 gi\u1edd. H\u1ecfi hai ng\u01b0\u1eddi c\u00f9ng l\u00e0m trong bao l\u00e2u s\u1ebd xong? <br\/> \u0110\u00e1p s\u1ed1: _input_ gi\u1edd ","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m trong 1 gi\u1edd, ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m trong 1 gi\u1edd <br\/> <b>B\u01b0\u1edbc 2: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c c\u1ea3 hai ng\u01b0\u1eddi l\u00e0m trong 1 gi\u1edd <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh th\u1eddi gian hai ng\u01b0\u1eddi c\u00f9ng l\u00e0m \u0111\u1ec3 ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh \u0111\u01b0\u1ee3c: $\\dfrac{1}{6}$ c\u00f4ng vi\u1ec7c <br\/> Ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m m\u1ed9t m\u00ecnh \u0111\u01b0\u1ee3c: $\\dfrac{1}{3}$ c\u00f4ng vi\u1ec7c <br\/> Hai ng\u01b0\u1eddi l\u00e0m m\u1ed9t gi\u1edd \u0111\u01b0\u1ee3c: <br\/> $\\dfrac{1}{6} + \\dfrac{1}{3} = \\dfrac{1}{2}$ (c\u00f4ng vi\u1ec7c) <br\/> Th\u1eddi gian hai ng\u01b0\u1eddi c\u00f9ng l\u00e0m \u0111\u1ec3 ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c l\u00e0: <br\/> $1 : \\dfrac{1}{2} = 2$ (gi\u1edd) <br\/> \u0110\u00e1p s\u1ed1: 2 gi\u1edd <br\/>"}]}],"id_ques":1762},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["479"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"S\u1ed1 h\u1ecdc sinh kh\u1ed1i 6 c\u1ee7a m\u1ed9t tr\u01b0\u1eddng kho\u1ea3ng 400 - 500 h\u1ecdc sinh. Bi\u1ebft r\u1eb1ng n\u1ebfu x\u1ebfp h\u00e0ng 5, h\u00e0ng 8, h\u00e0ng 12 \u0111\u1ec1u thi\u1ebfu 1. T\u00ednh s\u1ed1 h\u1ecdc sinh kh\u1ed1i 6. <br\/> \u0110\u00e1p s\u1ed1 l\u00e0: _input_ h\u1ecdc sinh","hint":"B\u00e0i to\u00e1n t\u00ecm b\u1ed9i chung nh\u1ecf nh\u1ea5t","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>N\u1ebfu g\u1ecdi s\u1ed1 h\u1ecdc sinh c\u1ea7n t\u00ecm l\u00e0 x (400 < x < 500) <br\/> V\u00ec s\u1ed1 h\u1ecdc sinh khi x\u1ebfp h\u00e0ng 5, h\u00e0ng 8, h\u00e0ng 12 \u0111\u1ec1u thi\u1ebfu 1 n\u00ean <br\/> x + 1 chia h\u1ebft cho 5; 8 v\u00e0 11 <br\/> N\u00ean x + 1 thu\u1ed9c BC(5; 8; 11) <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi s\u1ed1 h\u1ecdc sinh kh\u1ed1i 6 c\u1ee7a tr\u01b0\u1eddng l\u00e0 x (400 < x < 500) <br\/> V\u00ec khi x\u1ebfp h\u00e0ng 5, h\u00e0ng 8, h\u00e0ng 12 \u0111\u1ec1u thi\u1ebfu 1 n\u00ean (x + 1) chia h\u1ebft cho 5, 8, 12 <br\/> Ta c\u00f3: BCNN(5, 8, 12) = 120 <br\/> BC(5, 8, 12) = B(120) <br\/> $\\Rightarrow$ x + 1 $\\in$ {0; 120; 240; 360; 480; 600;...} <br\/> V\u00ec s\u1ed1 h\u1ecdc sinh t\u1eeb 400 - 500 h\u1ecdc sinh n\u00ean x + 1 = 480 $\\Rightarrow$ x = 479 <br\/> V\u1eady s\u1ed1 h\u1ecdc sinh c\u1ee7a tr\u01b0\u1eddng l\u00e0: <span class='basic_pink'> 479 <\/span> "}]}],"id_ques":1763},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho E = {1; 3; 5; 7; 9}; F = {1; 2; 3; 4; 5}. <br\/> Kh\u1eb3ng \u0111\u1ecbnh E l\u00e0 t\u1eadp h\u1ee3p con c\u1ee7a F. <b> \u0111\u00fang <\/b> hay <b> sai <\/b>? ","select":["A. \u0110\u00daNG","B. SAI"],"hint":"T\u1eadp h\u1ee3p E l\u00e0 t\u1eadp h\u1ee3p con c\u1ee7a t\u1eadp h\u1ee3p F n\u1ebfu m\u1ecdi ph\u1ea7n t\u1eed c\u1ee7a E \u0111\u1ec1u thu\u1ed9c F","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> X\u00e9t t\u1eadp h\u1ee3p E = {1; 3; 5; 7; 9} <br\/> V\u00ec 7 $\\in$ E nh\u01b0ng 7 $\\notin$ F v\u00e0 9 $\\in$ E nh\u01b0ng 9 $\\notin$ F <br\/> N\u00ean t\u1eadp h\u1ee3p E kh\u00f4ng ph\u1ea3i l\u00e0 t\u1eadp h\u1ee3p con c\u1ee7a t\u1eadp h\u1ee3p F <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0: <span class='basic_pink'> SAI <\/span> ","column":2}]}],"id_ques":1764},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["24"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u1eadp h\u1ee3p c\u00e1c \u01b0\u1edbc c\u1ee7a s\u1ed1 1428 c\u00f3: _input_ ph\u1ea7n t\u1eed ","hint":"Ph\u00e2n t\u00edch 1428 ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 r\u1ed3i t\u00ecm s\u1ed1 \u01b0\u1edbc","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> N\u1ebfu s\u1ed1 a \u0111\u01b0\u1ee3c ph\u00e2n t\u00edch ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1: <br\/> $a = x^m . y^n....$ <br\/> S\u1ed1 \u01b0\u1edbc c\u1ee7a a = (m + 1) . (n + 1) . ... <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ph\u00e2n t\u00edch s\u1ed1 1428 ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 ta \u0111\u01b0\u1ee3c: <br\/> $1428 = 2^2 . 3 . 7 . 17$ <br\/> S\u1ed1 \u01b0\u1edbc c\u1ee7a 1428 = (2 + 1) . (1 + 1) . (1 + 1) . (1 + 1) = 24 \u01b0\u1edbc <br\/> N\u00ean t\u1eadp h\u1ee3p c\u00e1c \u01b0\u1edbc c\u1ee7a s\u1ed1 1428 c\u00f3 24 ph\u1ea7n t\u1eed <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 24 <\/span> "}]}],"id_ques":1765},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["5"]]],"list":[{"point":5,"width":50,"type_input":"","input_hint":["frac"],"ques":"T\u1ec9 s\u1ed1 c\u1ee7a 16kg v\u00e0 0,8 t\u1ea1 l\u00e0: <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"\u0110\u1ed5i ra c\u00f9ng m\u1ed9t \u0111\u01a1n v\u1ecb r\u1ed3i t\u00ecm t\u1ec9 s\u1ed1","explain":" <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> \u0110\u1ed5i: 0,8 t\u1ea1 = 80kg <br\/> T\u1ec9 s\u1ed1 gi\u1eefa 16kg v\u00e0 80kg l\u00e0: $16 : 80 = \\dfrac{16}{80} = \\dfrac{1}{5}$ "}]}],"id_ques":1766},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"T\u00ecm ph\u00e2n s\u1ed1 c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng $\\dfrac{12}{30}$ v\u00e0 c\u00f3 t\u1ed5ng t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 l\u00e0 70. <br\/> \u0110\u00e1p \u00e1n l\u00e0: ","select":["A. $\\dfrac{20}{50}$ ","B. $\\dfrac{25}{35}$","C. $\\dfrac{14}{56}$","D. $\\dfrac{32}{38}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> R\u00fat g\u1ecdn ph\u00e2n s\u1ed1 $\\dfrac{12}{30} = \\dfrac{a}{b}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> Theo t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n s\u1ed1 ta c\u00f3: <br\/> $\\dfrac{a}{b} = \\dfrac{a . n}{b . n}$ v\u00ec t\u1ed5ng c\u1ee7a t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 b\u1eb1ng 70 <br\/> N\u00ean a . n + b . n = 70 t\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c n <br\/> <b> B\u01b0\u1edbc 3: <\/b> Thay n v\u00e0o $\\dfrac{a . n}{b . n}$ \u0111\u1ec3 t\u00ecm ph\u00e2n s\u1ed1 \u0111\u00f3 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: $\\dfrac{12}{30} = \\dfrac{2}{5} = \\dfrac{2 . n}{5 . n}$ $(n \\in \\mathbb{Z}, n \\neq 0)$ <br\/> Theo \u0111\u1ec1 b\u00e0i: 2n + 5n = 70 hay 7n = 70, suy ra n = 10 <br\/> Do \u0111\u00f3 ph\u00e2n s\u1ed1 ph\u1ea3i t\u00ecm l\u00e0: $\\dfrac{2 . n}{5 . n} = \\dfrac{2 . 10}{5 . 10} = \\dfrac{20}{50}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. $\\dfrac{20}{50}$ <\/span> ","column":2}]}],"id_ques":1767},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":" 60% c\u1ee7a $4\\dfrac{1}{5}$ l\u00e0: ","select":["A. $\\dfrac{1}{7}$ ","B. $\\dfrac{252}{5}$","C. $3\\dfrac{2}{25}$","D. $2\\dfrac{13}{25}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Vi\u1ebft $4\\dfrac{1}{5}$ d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1; 60% d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh 60% c\u1ee7a $4\\dfrac{1}{5}$ b\u1eb1ng c\u00e1ch l\u1ea5y 2 k\u1ebft qu\u1ea3 v\u1eeba vi\u1ebft \u1edf b\u01b0\u1edbc 1 nh\u00e2n v\u1edbi nhau <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> 60% c\u1ee7a $4\\dfrac{1}{5}$ l\u00e0: $60\\% . 4\\dfrac{1}{5} = \\dfrac{60}{100} . \\dfrac{21}{5} = \\dfrac{63}{25} = 2\\dfrac{13}{25}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. $2\\dfrac{13}{25}$ <\/span> ","column":2}]}],"id_ques":1768},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" Bi\u1ebft $\\dfrac{2}{7}$ c\u1ee7a m\u1ed9t s\u1ed1 l\u00e0 124. S\u1ed1 \u0111\u00f3 l\u00e0: ","select":["A. 434 ","B. 35","C. 824","D. 321"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Bi\u1ebft $\\dfrac{m}{n}$ c\u1ee7a m\u1ed9t s\u1ed1 b\u1eb1ng a <br\/> S\u1ed1 \u0111\u00f3 l\u00e0: $a : \\dfrac{m}{n}$ <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\dfrac{2}{7}$ c\u1ee7a m\u1ed9t s\u1ed1 b\u1eb1ng 124 n\u00ean s\u1ed1 \u0111\u00f3 l\u00e0: <br\/> $124 : \\dfrac{2}{7} = 434$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. 434 <\/span> ","column":2}]}],"id_ques":1769},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["80"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"L\u1edbp 6A c\u00f3 45 h\u1ecdc sinh. Trong \u0111\u00f3 c\u00f3 $\\dfrac{5}{9}$ s\u1ed1 h\u1ecdc sinh l\u00e0 n\u1eef. T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m gi\u1eefa h\u1ecdc sinh nam so v\u1edbi h\u1ecdc sinh n\u1eef l\u00e0 bao nhi\u00eau? <br\/> \u0110\u00e1p \u00e1n l\u00e0: _input_ %","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh s\u1ed1 h\u1ecdc sinh nam c\u1ee7a l\u1edbp v\u00e0 s\u1ed1 h\u1ecdc sinh n\u1eef c\u1ee7a l\u1edbp <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ecm t\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m c\u1ee7a s\u1ed1 h\u1ecdc sinh nam so v\u1edbi s\u1ed1 h\u1ecdc sinh n\u1eef <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> S\u1ed1 h\u1ecdc sinh n\u1eef c\u1ee7a l\u1edbp 6A l\u00e0: <br\/> $45 . \\dfrac{5}{9} = 25$ (h\u1ecdc sinh) <br\/> S\u1ed1 h\u1ecdc sinh nam c\u1ee7a l\u1edbp l\u00e0: <br\/> 45 - 25 = 20 (h\u1ecdc sinh) <br\/> T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m gi\u1eefa h\u1ecdc sinh nam v\u00e0 h\u1ecdc sinh n\u1eef l\u00e0: <br\/> $\\dfrac{20}{25} . 100 = 80\\%$ <br\/> \u0110\u00e1p s\u1ed1: 80% <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 80<\/span> "}]}],"id_ques":1770}],"lesson":{"save":0,"level":1}}