{"segment":[{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u theo \u0111\u00fang th\u1ee9 t\u1ef1 c\u00e1c b\u01b0\u1edbc khi gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ","title_trans":"","temp":"sequence","correct":[[[5],[4],[1],[3],[2]]],"list":[{"point":5,"image":"","left":["Tr\u1ea3 l\u1eddi: Ki\u1ec3m tra xem trong c\u00e1c nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, nghi\u1ec7m n\u00e0o th\u00edch h\u1ee3p v\u1edbi b\u00e0i to\u00e1n v\u00e0 k\u1ebft lu\u1eadn","Gi\u1ea3i h\u1ec7 hai ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp","Ch\u1ecdn hai \u1ea9n v\u00e0 \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n th\u00edch h\u1ee3p cho ch\u00fang","L\u1eadp hai ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng","Bi\u1ec3u di\u1ec5n c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng ch\u01b0a bi\u1ebft theo c\u00e1c \u1ea9n v\u00e0 c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng \u0111\u00e3 bi\u1ebft"],"top":70,"hint":"","explain":"<span class='basic_left'> C\u00e1c b\u01b0\u1edbc gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>- Ch\u1ecdn hai \u1ea9n v\u00e0 \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n th\u00edch h\u1ee3p cho ch\u00fang<br\/>- Bi\u1ec3u di\u1ec5n c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng ch\u01b0a bi\u1ebft theo c\u00e1c \u1ea9n v\u00e0 c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng \u0111\u00e3 bi\u1ebft<br\/>- L\u1eadp hai ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 hai ph\u01b0\u01a1ng tr\u00ecnh n\u00f3i tr\u00ean<br\/>B\u01b0\u1edbc 3: Tr\u1ea3 l\u1eddi: Ki\u1ec3m tra xem trong c\u00e1c nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, nghi\u1ec7m n\u00e0o th\u00edch h\u1ee3p v\u1edbi b\u00e0i to\u00e1n v\u00e0 k\u1ebft lu\u1eadn"}]}],"id_ques":301},{"time":24,"part":[{"title":"\u0110i\u1ec1n c\u00e1c th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["25"],["9"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u1ed5ng c\u1ee7a hai s\u1ed1 b\u1eb1ng $34$. Hi\u1ec7u c\u1ee7a hai s\u1ed1 b\u1eb1ng $16$. T\u00ecm hai s\u1ed1 \u0111\u00f3.<br\/> <b> \u0110\u00e1p s\u1ed1:<\/b> Hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 _input_ v\u00e0 _input_","hint":"Gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi \u1ea9n l\u00e0 hai s\u1ed1 c\u1ea7n t\u00ecm","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>- G\u1ecdi hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $x$ v\u00e0 $y.$<br\/>- T\u1eeb gi\u1ea3 thi\u1ebft t\u1ed5ng v\u00e0 hi\u1ec7u hai s\u1ed1, ta thi\u1ebft l\u1eadp hai ph\u01b0\u01a1ng tr\u00ecnh<br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1 (ho\u1eb7c ph\u01b0\u01a1ng ph\u00e1p th\u1ebf)<br\/>B\u01b0\u1edbc 3: K\u1ebft lu\u1eadn b\u00e0i to\u00e1n<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi hai s\u1ed1 ph\u1ea3i t\u00ecm l\u00e0 $x$ v\u00e0 $y$<br\/> V\u00ec t\u1ed5ng c\u1ee7a hai s\u1ed1 b\u1eb1ng $34$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=34$ (1)<br\/>V\u00ec hi\u1ec7u c\u1ee7a hai s\u1ed1 b\u1eb1ng $16$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x-y=16$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>$\\left\\{ \\begin{align}& x+y=34 \\\\ & x-y=16 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& 2x=50 \\\\ & y=34-x \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& x=25 \\\\ & y=9 \\\\ \\end{align} \\right.$<br\/>V\u1eady hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $25$ v\u00e0 $9$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $25$ v\u00e0 $9$<\/span><\/span>"}]}],"id_ques":302},{"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":"T\u1ed5ng hai s\u1ed1 t\u1ef1 nhi\u00ean b\u1eb1ng $51$. Bi\u1ebft $\\dfrac{2}{5}$ s\u1ed1 th\u1ee9 nh\u1ea5t b\u1eb1ng $\\dfrac{1}{6}$ s\u1ed1 th\u1ee9 hai. T\u00ecm hai s\u1ed1 t\u1ef1 nhi\u00ean \u0111\u00f3.","select":["A. $14$ v\u00e0 $37$","B. $36$ v\u00e0 $15$","C. $34$ v\u00e0 $17$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>- G\u1ecdi hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $x$ v\u00e0 $y.$<br\/>- T\u1eeb gi\u1ea3 thi\u1ebft b\u00e0i to\u00e1n, ta thi\u1ebft l\u1eadp hai ph\u01b0\u01a1ng tr\u00ecnh<br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf<br\/>B\u01b0\u1edbc 3: K\u1ebft lu\u1eadn b\u00e0i to\u00e1n <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi hai s\u1ed1 ph\u1ea3i t\u00ecm l\u00e0 $x$ v\u00e0 $y$ <br\/> V\u00ec t\u1ed5ng c\u1ee7a hai s\u1ed1 b\u1eb1ng $51$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=51$ (1)<br\/>V\u00ec $\\dfrac{2}{5}$ s\u1ed1 th\u1ee9 nh\u1ea5t b\u1eb1ng $\\dfrac{1}{6}$ s\u1ed1 th\u1ee9 hai n\u00ean ta c\u00f3: $\\dfrac{2}{5}x=\\dfrac{1}{6}y\\Leftrightarrow y=\\dfrac{12}{5}x$ (2) <br\/> T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\left\\{ \\begin{aligned} & x+y=51 \\\\ & y=\\dfrac{12}{5}x \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x+\\dfrac{12}{5}x=51 \\\\ & x+y=51 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & \\dfrac{17}{5}x=51 \\\\ & x+y=51 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=15 \\\\ & 15+y=51 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=15 \\\\ & y = 36 \\\\ \\end{aligned} \\right.$ <br\/> V\u1eady hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $15$ v\u00e0 $36$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":3}]}],"id_ques":303},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"T\u00ecm hai s\u1ed1 t\u1ef1 nhi\u00ean, bi\u1ebft t\u1ed5ng c\u1ee7a ch\u00fang b\u1eb1ng $72$ v\u00e0 n\u1ebfu l\u1ea5y s\u1ed1 l\u1edbn chia s\u1ed1 nh\u1ecf th\u00ec \u0111\u01b0\u1ee3c th\u01b0\u01a1ng l\u00e0 $4$ v\u00e0 s\u1ed1 d\u01b0 l\u00e0 $2$.<br\/><b> C\u00e2u 1: <\/b> N\u1ebfu g\u1ecdi s\u1ed1 nh\u1ecf l\u00e0 $x$, s\u1ed1 l\u1edbn l\u00e0 $y$ (\u0111i\u1ec1u ki\u1ec7n $x, y \\in \\mathbb{N}$ v\u00e0 $x < y$) th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ta l\u1eadp \u0111\u01b0\u1ee3c l\u00e0:","select":["A.$\\left\\{ \\begin{align}& x+y=72 \\\\ & y=\\dfrac{x}{4}+2 \\\\ \\end{align} \\right.$","B. $\\left\\{ \\begin{align} & x+y=72 \\\\ & y=\\dfrac{x}{2}+4 \\\\ \\end{align} \\right.$ ","C. $\\left\\{ \\begin{align}& x+y=72 \\\\ & 4x-y=-2 \\\\ \\end{align} \\right.$ ","D. $\\left\\{ \\begin{align}& x+y=72 \\\\ & y=2x+4 \\\\ \\end{align} \\right.$ "],"hint":"Chia s\u1ed1 $x$ cho $y$ \u0111\u01b0\u1ee3c th\u01b0\u01a1ng l\u00e0 $q$ v\u00e0 d\u01b0 l\u00e0 $r$ th\u00ec ta c\u00f3 bi\u1ec3u di\u1ec5n $x=yq+r$","explain":"<span class='basic_left'> G\u1ecdi s\u1ed1 nh\u1ecf l\u00e0 $x$, s\u1ed1 l\u1edbn l\u00e0 $y$ (\u0111i\u1ec1u ki\u1ec7n $x, y \\in \\mathbb{N}$ v\u00e0 $x < y$) <br\/> V\u00ec t\u1ed5ng c\u1ee7a hai s\u1ed1 b\u1eb1ng $72$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=72$ (1) <br\/> V\u00ec l\u1ea5y s\u1ed1 l\u1edbn chia s\u1ed1 nh\u1ecf, ta \u0111\u01b0\u1ee3c th\u01b0\u01a1ng l\u00e0 4 v\u00e0 d\u01b0 l\u00e0 2 n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/> $y=4x+2\\Leftrightarrow 4x-y=-2$ (2) <br\/> T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) $\\left\\{ \\begin{align}& x+y=72 \\\\ & 4x-y=-2 \\\\ \\end{align} \\right.$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":304},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank_random","correct":[[["14"],["58"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>T\u00ecm hai s\u1ed1 t\u1ef1 nhi\u00ean, bi\u1ebft t\u1ed5ng c\u1ee7a ch\u00fang b\u1eb1ng $72$ v\u00e0 n\u1ebfu l\u1ea5y s\u1ed1 l\u1edbn chia s\u1ed1 nh\u1ecf th\u00ec \u0111\u01b0\u1ee3c th\u01b0\u01a1ng l\u00e0 $4$ v\u00e0 s\u1ed1 d\u01b0 l\u00e0 $2$.<br\/><b> C\u00e2u 2: <\/b> N\u1ebfu g\u1ecdi s\u1ed1 nh\u1ecf l\u00e0 $x$, s\u1ed1 l\u1edbn l\u00e0 $y$ (\u0111i\u1ec1u ki\u1ec7n $x, y \\in \\mathbb{N}$ v\u00e0 $x < y$) th\u00ec $x=$_input_ v\u00e0 $y=$_input_","hint":"","explain":"<span class='basic_left'> Theo k\u1ebft qu\u1ea3 c\u00e2u 1, ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:$\\left\\{ \\begin{align}& x+y=72 \\\\ & 4x-y=-2 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 5x=70 \\\\ & x+y=72 \\\\ \\end{aligned}\\right.\\Leftrightarrow\\left\\{ \\begin{aligned}& x=14 \\\\ & y=72-x \\\\ \\end{aligned}\\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=14 \\\\ & y=58 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/><span class='basic_pink'>V\u1eady hai s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $14$ v\u00e0 $58$<\/span><\/span>"}]}],"id_ques":305},{"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":"<span class='basic_left'>T\u1ed5ng c\u1ee7a hai s\u1ed1 b\u1eb1ng $59.$ Hai l\u1ea7n s\u1ed1 n\u00e0y b\u00e9 h\u01a1n ba l\u1ea7n s\u1ed1 kia l\u00e0 $7.$ T\u00edch c\u1ee7a hai s\u1ed1 l\u00e0: ","select":["A. $850$ ","B. $800$","C. $900$","D. $750$"],"hint":"T\u00ecm hai s\u1ed1 b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh r\u1ed3i t\u00ednh t\u00edch hai s\u1ed1 \u0111\u00f3","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 ph\u1ea3i t\u00ecm l\u00e0 $x$ v\u00e0 $y.$ <br\/>V\u00ec t\u1ed5ng c\u1ee7a hai s\u1ed1 b\u1eb1ng $59$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=59$ (1)<br\/>Ta c\u00f3 hai l\u1ea7n s\u1ed1 n\u00e0y l\u00e0 $2x$ v\u00e0 ba l\u1ea7n s\u1ed1 kia l\u00e0 $3y.$ <br\/> V\u00ec hai l\u1ea7n s\u1ed1 n\u00e0y b\u00e9 h\u01a1n ba l\u1ea7n s\u1ed1 kia l\u00e0 7 n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $3y-2x=7$ (2) <br\/> T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x+y=59 \\\\ & 3y-2x=7 \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 2y+2x=118 \\\\ & 3y-2x=7 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& 5y=125 \\\\ & x=59-y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& y=25 \\\\ & x=59-y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=34 \\\\ & y=25 \\\\ \\end{aligned} \\right.$<br\/>Suy ra t\u00edch hai s\u1ed1 l\u00e0 $x.y=34.25=850$.<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span><\/span>","column":4}]}],"id_ques":306},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["10"],["b"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Bi\u1ec3u di\u1ec5n s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 <br\/> V\u1edbi $0 < a \\le 9, 0 \\le b \\le 9$ v\u00e0 $a, b \\in \\mathbb{N}$, ta c\u00f3: $\\overline{ab}=$ _input_ $.a+$ _input_","hint":"","explain":"<span class='basic_left'> Bi\u1ec3u di\u1ec5n s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1: $\\overline{ab}=10.a+b$ <br\/> Trong \u0111\u00f3 $a$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c v\u00e0 $b$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n theo th\u1ee9 t\u1ef1 l\u00e0 $10$ v\u00e0 $b.$<\/span><\/span>"}]}],"id_ques":307},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1, bi\u1ebft r\u1eb1ng t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $6$ v\u00e0 n\u1ebfu \u0111\u1ed5i ch\u1ed7 hai ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 th\u00ec \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 nh\u1ecf h\u01a1n s\u1ed1 ban \u0111\u1ea7u $18$ \u0111\u01a1n v\u1ecb. <br\/><b> C\u00e2u 1: <\/b>G\u1ecdi ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u00e0 $a$ v\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $b$ th\u00ec $a, b$ th\u1ecfa m\u00e3n h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ","select":["A. $\\left\\{ \\begin{align}& a+b=6 \\\\ & a-2b=2 \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align}& a+b=6 \\\\ & a-b=2 \\\\ \\end{align} \\right.$","C. $\\left\\{ \\begin{align}& a+b=6 \\\\ & a-b=3 \\\\ \\end{align} \\right.$"],"hint":"S\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 c\u00f3 d\u1ea1ng $\\overline{ab}$ v\u00e0 $\\overline{ab}=10.a+b$.","explain":"<span class='basic_left'> T\u1eeb gi\u1ea3 thi\u1ebft, ta c\u00f3 s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $\\overline{ab}$ v\u1edbi $0 < a \\le 9, 0 < b \\le 9$ v\u00e0 $a, b \\in \\mathbb{N}$,<br\/> V\u00ec t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 b\u1eb1ng $6$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $a+b=6$ (1) <br\/> \u0110\u1ed5i ch\u1ed7 hai ch\u1eef s\u1ed1 c\u1ee7a $\\overline{ab}$, ta \u0111\u01b0\u1ee3c s\u1ed1 m\u1edbi l\u00e0 $\\overline{ba}$ <br\/> Do \u0111\u1ed5i ch\u1ed7 hai ch\u1eef s\u1ed1 c\u1ee7a s\u1ed1 t\u1ef1 nhi\u00ean th\u00ec \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 nh\u1ecf h\u01a1n s\u1ed1 ban \u0111\u1ea7u $18$ \u0111\u01a1n v\u1ecb n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: <br\/> $\\overline{ab}-\\overline{ba}=18\\Leftrightarrow \\left( 10a+b \\right)-\\left( 10b+a \\right)=18\\Leftrightarrow a-b=2$ (2) <br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& a+b=6 \\\\ & a-b=2 \\\\ \\end{align} \\right.$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span><br\/>V\u1edbi b\u00e0i to\u00e1n t\u00ecm m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1: Khi vi\u1ebft hai ch\u1eef s\u1ed1 \u1ea5y theo th\u1ee9 t\u1ef1 ng\u01b0\u1ee3c l\u1ea1i, ta v\u1eabn \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 c\u00f3 hai ch\u1eef s\u1ed1 n\u00ean c\u1ea3 hai ch\u1eef s\u1ed1 \u0111\u00f3 \u0111\u1ec1u ph\u1ea3i kh\u00e1c $0$.<\/span>","column":3}]}],"id_ques":308},{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["42"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"<span class='basic_left'>T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1, bi\u1ebft r\u1eb1ng t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $6$ v\u00e0 n\u1ebfu \u0111\u1ed5i ch\u1ed7 hai ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 th\u00ec \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 nh\u1ecf h\u01a1n s\u1ed1 ban \u0111\u1ea7u $18$ \u0111\u01a1n v\u1ecb. <br\/><b> C\u00e2u 2: <\/b>S\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 _input_","hint":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u00ecm \u0111\u01b0\u1ee3c \u1edf c\u00e2u 1","explain":"<span class='basic_left'>G\u1ecdi ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u00e0 $a$ v\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $b,$ v\u1edbi $0 < a \\le 9, 0 < b \\le 9$ v\u00e0 $a, b \\in \\mathbb{N}$. <br\/>Ta c\u00f3 s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $\\overline{ab}$ <br\/>Theo k\u1ebft qu\u1ea3 c\u00e2u 1, ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& a+b=6 \\\\ & a-b=2 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 2a=8 \\\\ & a-b=2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& a=4 \\\\ & b=a-2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& a=4 \\\\ & b=2 \\\\ \\end{aligned} \\right.$<br\/>V\u1eady s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $42$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $42$.<\/span><\/span>. "}]}],"id_ques":309},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'>T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1, bi\u1ebft r\u1eb1ng t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $10$ v\u00e0 n\u1ebfu vi\u1ebft hai ch\u1eef s\u1ed1 \u1ea5y theo th\u1ee9 t\u1ef1 ng\u01b0\u1ee3c l\u1ea1i th\u00ec \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 l\u1edbn h\u01a1n s\u1ed1 ban \u0111\u1ea7u $36$ \u0111\u01a1n v\u1ecb.","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[2],[7],[1],[4],[6],[5],[3]]],"list":[{"point":5,"image":"","left":["V\u00ec t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 b\u1eb1ng $10$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $a+b=10$ (1) ","V\u1eady s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $37$ ","G\u1ecdi ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u00e0 $a$ v\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $b,$ v\u1edbi $0 < a \\le 9, 0 < b \\le 9$ v\u00e0 $a, b \\in \\mathbb{N}$. Khi \u0111\u00f3 s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $\\overline{ab}$ ","$\\overline{ba}-\\overline{ab}=36\\Leftrightarrow \\left( 10b+a \\right)-\\left( 10a+b \\right)=36\\Leftrightarrow b-a=4$ (2)","Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ta t\u00ecm \u0111\u01b0\u1ee3c $a=3$ v\u00e0 $b=7$ (th\u1ecfa m\u00e3n)","T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& a+b=10 \\\\ & b-a=4 \\\\\\end{align} \\right.$","Vi\u1ebft hai ch\u1eef s\u1ed1 theo th\u1ee9 t\u1ef1 ng\u01b0\u1ee3c l\u1ea1i ta \u0111\u01b0\u1ee3c s\u1ed1 m\u1edbi l\u00e0 $\\overline{ba}$ . Theo \u0111\u1ec1 ra, ta c\u00f3 "],"top":75,"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn: <\/span><br\/>B\u01b0\u1edbc 1: Bi\u1ec3u di\u1ec5n s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1. \u0110\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho \u1ea9n<br\/>B\u01b0\u1edbc 2: Theo \u0111i\u1ec1u ki\u1ec7n b\u00e0i to\u00e1n, ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u1ea9n.T\u1eeb \u0111\u00f3 thi\u1ebft l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh. <br\/>B\u01b0\u1edbc 3: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp.<br\/>B\u01b0\u1edbc 4: Ki\u1ec3m tra nghi\u1ec7m c\u00f3 th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n kh\u00f4ng v\u00e0 k\u1ebft lu\u1eadn <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u00e0 $a$ v\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $b,$ v\u1edbi $0 < a \\le 9, 0 < b \\le 9$ v\u00e0 $a, b \\in \\mathbb{N}$.<br\/>Khi \u0111\u00f3 s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $\\overline{ab}$ <br\/> V\u00ec t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 b\u1eb1ng $10$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $a+b=10$ (1)<br\/>Vi\u1ebft hai ch\u1eef s\u1ed1 theo th\u1ee9 t\u1ef1 ng\u01b0\u1ee3c l\u1ea1i ta \u0111\u01b0\u1ee3c s\u1ed1 m\u1edbi l\u00e0 $\\overline{ba}$ . Theo \u0111\u1ec1 ra, ta c\u00f3 <br\/>$\\overline{ba}-\\overline{ab}=36\\Leftrightarrow \\left( 10b+a \\right)-\\left( 10a+b \\right)=36\\Leftrightarrow b-a=4$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& a+b=10 \\\\ & b-a=4 \\\\\\end{align} \\right.$<br\/>Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ta t\u00ecm \u0111\u01b0\u1ee3c $a=3$ v\u00e0 $b=7$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $37$ <\/span>"}]}],"id_ques":310},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7000"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"<span class='basic_left'>M\u1ed9t s\u00e2n tr\u01b0\u1eddng h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 chu vi l\u00e0 $340 m$. Ba l\u1ea7n chi\u1ec1u d\u00e0i h\u01a1n b\u1ed1n l\u1ea7n chi\u1ec1u r\u1ed9ng l\u00e0 $20 m.$ T\u00ednh di\u1ec7n t\u00edch s\u00e2n tr\u01b0\u1eddng.<br\/><b> \u0110\u00e1p s\u1ed1: <\/b>_input_ $m^2$","hint":"T\u00ednh chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt<br\/> Di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt b\u1eb1ng t\u00edch chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng<br\/>Chu vi h\u00ecnh ch\u1eef nh\u1eadt b\u1eb1ng 2 l\u1ea7n t\u1ed5ng chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng.<br\/>","explain":" <span class='basic_left'>G\u1ecdi chi\u1ec1u d\u00e0i s\u00e2n tr\u01b0\u1eddng l\u00e0 $x (m)$ ; chi\u1ec1u r\u1ed9ng l\u00e0 $y (m).$ \u0110i\u1ec1u ki\u1ec7n: $x>y>0$<br\/>Do chu vi s\u00e2n tr\u01b0\u1eddng l\u00e0 $340$ n\u00ean $2(x+y)=340$ hay $x+y=170$ (1)<br\/> Do ba l\u1ea7n chi\u1ec1u d\u00e0i l\u1edbn h\u01a1n b\u1ed1n l\u1ea7n chi\u1ec1u r\u1ed9ng l\u00e0 $20m$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $3x \u2013 4y= 20$ (2) <br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x+y=170 \\\\ & 3\\text{x}-4y=20 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 3x+3y=510 \\\\ & 3\\text{x}-4y=20 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 7y=490 \\\\ & x=170-y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& y=70 \\\\ & x=100 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n).<br\/>Suy ra chi\u1ec1u d\u00e0i s\u00e2n tr\u01b0\u1eddng l\u00e0 $100m$ v\u00e0 chi\u1ec1u r\u1ed9ng l\u00e0 $70m.$<br\/>Di\u1ec7n t\u00edch s\u00e2n tr\u01b0\u1eddng l\u00e0 $100.70=7000 (m^2)$ <br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $7000$<\/span><\/span>"}]}],"id_ques":311},{"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":"<span class='basic_left'>C\u00f3 $50$ con g\u00e0 v\u00e0 ch\u00f3. Bi\u1ebft t\u1ed5ng s\u1ed1 ch\u00e2n g\u00e0 v\u00e0 ch\u00f3 l\u00e0 $140$ ch\u00e2n. An n\u00f3i: ''S\u1ed1 g\u00e0 nhi\u1ec1u h\u01a1n s\u1ed1 ch\u00f3'' \u0111\u00fang hay sai?","select":["A. \u0110\u00fang ","B. Sai"],"hint":"T\u00ecm s\u1ed1 g\u00e0 v\u00e0 s\u1ed1 ch\u00f3, t\u1eeb \u0111\u00f3 so s\u00e1nh xem con n\u00e0o nhi\u1ec1u h\u01a1n","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 g\u00e0 l\u00e0 $x$ con, s\u1ed1 ch\u00f3 l\u00e0 $y$ con. \u0110i\u1ec1u ki\u1ec7n: $x,y$ nguy\u00ean d\u01b0\u01a1ng<br\/> V\u00ec t\u1ed5ng s\u1ed1 g\u00e0 v\u00e0 ch\u00f3 l\u00e0 $50$ con n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=50$ (1)<br\/> V\u00ec g\u00e0 c\u00f3 $2$ ch\u00e2n n\u00ean t\u1ed5ng s\u1ed1 ch\u00e2n g\u00e0 l\u00e0 $2x$ ch\u00e2n <br\/> V\u00ec ch\u00f3 c\u00f3 $4$ ch\u00e2n n\u00ean t\u1ed5ng s\u1ed1 ch\u00e2n ch\u00f3 l\u00e0 $4y$ ch\u00e2n <br\/> Do t\u1ed5ng s\u1ed1 ch\u00e2n g\u00e0 v\u00e0 ch\u00f3 l\u00e0 $140$ ch\u00e2n n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $2x+4y=140$ hay $x+2y=70$ (2) <br\/> T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x+y=50 \\\\ & x+2y=70 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& y=20 \\\\ & x=50-y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& y=20 \\\\ & x=50-20 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=30 \\\\ & y=20 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>Suy ra c\u00f3 $30$ con g\u00e0 v\u00e0 $20$ con ch\u00f3. <br\/>Do \u0111\u00f3 s\u1ed1 g\u00e0 nhi\u1ec1u h\u01a1n s\u1ed1 ch\u00f3 n\u00ean kh\u1eb3ng \u0111\u1ecbnh c\u1ee7a An \u0111\u00fang.<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":312},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>Hai xe m\u00e1y c\u00f9ng \u0111i qu\u00e3ng \u0111\u01b0\u1eddng t\u1eeb H\u00e0 N\u1ed9i \u0111\u1ebfn H\u1ea3i Ph\u00f2ng. Xe th\u1ee9 nh\u1ea5t \u0111i h\u1ebft $3$ gi\u1edd $20$ ph\u00fat, xe th\u1ee9 hai \u0111i h\u1ebft $3$ gi\u1edd $40$ ph\u00fat. Bi\u1ebft v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 nh\u1ea5t nhanh h\u01a1n v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 hai l\u00e0 $3km\/h.$<br\/><b> C\u00e2u 1: <\/b> G\u1ecdi v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 nh\u1ea5t l\u00e0 $x (km\/h)$ v\u00e0 v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 hai l\u00e0 $y(km\/h).$ Ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 nh\u1ea5t nhanh h\u01a1n v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 hai l\u00e0 3 km\/h l\u00e0<\/span>","select":["A. $y-x=3$ ","B. $y+x=3$ ","C. $x-y=3$ "],"hint":"","explain":"<span class='basic_left'>\u0110i\u1ec1u ki\u1ec7n: $x>y>3$<br\/>V\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 nh\u1ea5t nhanh h\u01a1n v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 hai l\u00e0 $3 km\/h$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: ph\u01b0\u01a1ng tr\u00ecnh<br\/> $x-y=3$ (1) <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":3}]}],"id_ques":313},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<span class='basic_left'>Hai xe m\u00e1y c\u00f9ng \u0111i qu\u00e3ng \u0111\u01b0\u1eddng t\u1eeb H\u00e0 N\u1ed9i \u0111\u1ebfn H\u1ea3i Ph\u00f2ng. Xe th\u1ee9 nh\u1ea5t \u0111i h\u1ebft $3$ gi\u1edd $20$ ph\u00fat, xe th\u1ee9 hai \u0111i h\u1ebft $3$ gi\u1edd $40$ ph\u00fat. Bi\u1ebft v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 nh\u1ea5t nhanh h\u01a1n v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 hai l\u00e0 $3km\/h.$<br\/><b> C\u00e2u 2: <\/b> G\u1ecdi v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 nh\u1ea5t l\u00e0 $x (km\/h)$ v\u00e0 v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 hai l\u00e0 $y(km\/h).$ Ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb gi\u1ea3 thi\u1ebft v\u1ec1 qu\u00e3ng \u0111\u01b0\u1eddng t\u1eeb H\u00e0 N\u1ed9i \u0111\u1ebfn H\u1ea3i Ph\u00f2ng c\u1ee7a hai xe m\u00e1y l\u00e0<\/span>","select":["A. $10x=11y$ ","B. $\\dfrac{8}{3}x=\\dfrac{11}{3}y$ ","C. $\\dfrac{10}{3}x=\\dfrac{11}{3}y$ ","D. \u0110\u00e1p \u00e1n A v\u00e0 C "],"hint":"S\u1eed d\u1ee5ng $s=vt$ trong \u0111\u00f3 $s$ l\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng, $v$ l\u00e0 v\u1eadn t\u1ed1c v\u00e0 $t$ l\u00e0 th\u1eddi gian.","explain":"<span class='basic_left'>\u0110i\u1ec1u ki\u1ec7n: $x>y>3$<br\/>\u0110\u1ed5i $3$ gi\u1edd $20$ ph\u00fat = $\\dfrac{10}{3}$ gi\u1edd; $3$ gi\u1edd $40$ ph\u00fat = $\\dfrac{11}{3}$ gi\u1edd.<br\/>Xe th\u1ee9 nh\u1ea5t \u0111i h\u1ebft $\\dfrac{10}{3}$gi\u1edd n\u00ean \u0111i qu\u00e3ng \u0111\u01b0\u1eddng l\u00e0 $\\dfrac{10}{3}x$<br\/> Xe th\u1ee9 hai \u0111i h\u1ebft $\\dfrac{11}{3}$ gi\u1edd n\u00ean \u0111i \u0111\u01b0\u1ee3c qu\u00e3ng \u0111\u01b0\u1eddng l\u00e0 $\\dfrac{11}{3}y$. <br\/>V\u00ec hai xe m\u00e1y c\u00f9ng \u0111i qu\u00e3ng \u0111\u01b0\u1eddng t\u1eeb H\u00e0 N\u1ed9i \u0111\u1ebfn H\u1ea3i ph\u00f2ng n\u00ean $\\dfrac{10}{3}x=\\dfrac{11}{3}y\\Leftrightarrow 10x=11y$ (2)<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span><br\/>Tr\u01b0\u1edbc khi gi\u1ea3i b\u00e0i to\u00e1n v\u1ec1 chuy\u1ec3n \u0111\u1ed9ng, ta c\u1ea7n \u0111\u01b0a th\u1eddi gian v\u1ec1 c\u00f9ng \u0111\u01a1n v\u1ecb.<\/span>","column":2}]}],"id_ques":314},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"fill_the_blank","correct":[[["33"],["30"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Hai xe m\u00e1y c\u00f9ng \u0111i qu\u00e3ng \u0111\u01b0\u1eddng t\u1eeb H\u00e0 N\u1ed9i \u0111\u1ebfn H\u1ea3i Ph\u00f2ng. Xe th\u1ee9 nh\u1ea5t \u0111i h\u1ebft $3$ gi\u1edd $20$ ph\u00fat, xe th\u1ee9 hai \u0111i h\u1ebft $3$ gi\u1edd $40$ ph\u00fat. Bi\u1ebft v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 nh\u1ea5t nhanh h\u01a1n v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 hai l\u00e0 $3km\/h.$<br\/><b> C\u00e2u 3: <\/b> V\u1eadn t\u1ed1c c\u1ee7a xe m\u00e1y th\u1ee9 nh\u1ea5t v\u00e0 th\u1ee9 hai l\u1ea7n l\u01b0\u1ee3t l\u00e0 _input_ $(km\/h)$; _input_ $(km\/h)$<\/span>","hint":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh thu \u0111\u01b0\u1ee3c \u1edf c\u00e2u 1 v\u00e0 c\u00e2u 2","explain":"<span class='basic_left'>G\u1ecdi v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 nh\u1ea5t l\u00e0 $x (km\/h)$ v\u00e0 v\u1eadn t\u1ed1c xe m\u00e1y th\u1ee9 hai l\u00e0 $y(km\/h).$ \u0110i\u1ec1u ki\u1ec7n: $x>y>3$<br\/>Theo k\u1ebft qu\u1ea3 c\u00e2u 1 v\u00e0 c\u00e2u 2, ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x-y=3 \\\\ & 10x=11y \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 10x-10y=30 \\\\ & 10x-11y=0 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& y=30 \\\\ & x=y+3 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=33 \\\\ & y=30 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a xe m\u00e1y th\u1ee9 nh\u1ea5t l\u00e0 $33 km\/h,$ v\u1eadn t\u1ed1c c\u1ee7a xe m\u00e1y th\u1ee9 hai l\u00e0 $30km\/h.$<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $33;30$<\/span><\/span>"}]}],"id_ques":315},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["60"],["55"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>M\u1ed9t kh\u00e1ch du l\u1ecbch \u0111i tr\u00ean \u00f4 t\u00f4 $4$ gi\u1edd, sau \u0111\u00f3 \u0111i ti\u1ebfp b\u1eb1ng t\u00e0u h\u1ecfa trong $7$ gi\u1edd \u0111\u01b0\u1ee3c qu\u00e3ng \u0111\u01b0\u1eddng d\u00e0i $640km.$ T\u00ednh v\u1eadn t\u1ed1c c\u1ee7a t\u00e0u h\u1ecfa v\u00e0 \u00f4 t\u00f4 bi\u1ebft m\u1ed7i gi\u1edd t\u00e0u h\u1ecfa \u0111i nhanh h\u01a1n \u00f4 t\u00f4 $5 km$.<br\/><b> \u0110\u00e1p s\u1ed1: <\/b>V\u1eadn t\u1ed1c c\u1ee7a t\u00e0u h\u1ecfa l\u00e0 _input_$(km\/h)$, v\u1eadn t\u1ed1c \u00f4 t\u00f4 l\u00e0 _input_ $(km\/h)$<\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u1ea3ng ph\u00e2n t\u00edch chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a kh\u00e1ch du l\u1ecbch:<br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>V\u1eadn t\u1ed1c $(km\/h)$<br><\/th><th>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>\u00d4 t\u00f4<br><\/th><td>$x$<\/td><td>$4x$<\/td><td>$4$<\/td><\/tr><tr><th>T\u00e0u h\u1ecfa<br><\/th><td>$y$<\/td><td>$7y$<\/td><td>$7$<\/td><\/tr><\/table><br\/><br\/>T\u1eeb b\u1ea3ng tr\u00ean v\u00e0 t\u1eeb gi\u1ea3 thi\u1ebft b\u00e0i to\u00e1n, ta thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb v\u1eadn t\u1ed1c c\u1ee7a hai xe v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 qu\u00e3ng \u0111\u01b0\u1eddng m\u00e0 du kh\u00e1ch \u0111i \u0111\u01b0\u1ee3c. <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 l\u00e0 $x\\, (km\/h)$ v\u00e0 v\u1eadn t\u1ed1c c\u1ee7a t\u00e0u h\u1ecfa l\u00e0 $y\\,(km\/h).$\u0110i\u1ec1u ki\u1ec7n $x,y>0$<br\/>Qu\u00e3ng \u0111\u01b0\u1eddng m\u00e0 kh\u00e1ch du l\u1ecbch \u0111i tr\u00ean \u00f4 t\u00f4 l\u00e0 $4x\\, (km)$, qu\u00e3ng \u0111\u01b0\u1eddng kh\u00e1ch du l\u1ecbch \u0111i tr\u00ean t\u00e0u h\u1ecfa l\u00e0 $7y\\, (km).$<br\/> V\u00ec t\u1ed5ng qu\u00e3ng \u0111\u01b0\u1eddng ng\u01b0\u1eddi \u0111\u00f3 \u0111i \u0111\u01b0\u1ee3c l\u00e0 $640 km$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $4x+7y=640$ (1)<br\/> V\u00ec m\u1ed7i gi\u1edd t\u00e0u h\u1ecfa \u0111i nhanh h\u01a1n \u00f4 t\u00f4 $5 km$ n\u00ean v\u1eadn t\u1ed1c c\u1ee7a t\u00e0u h\u1ecfa l\u1edbn h\u01a1n \u00f4 t\u00f4 l\u00e0 $5 (km\/h)$. <br\/> Do \u0111\u00f3 ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $y-x=5$ (2)<br\/>T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left( I \\right)\\,\\,\\left\\{ \\begin{align}& -x+y=5 \\\\ & 4x+7y=640 \\\\ \\end{align} \\right.$ <br\/> $\\Leftrightarrow \\left\\{ \\begin{aligned} & x=y-5 \\\\ & 4\\left( y-5 \\right)+7y=640 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=y-5 \\\\ & 11y=660 \\\\ \\end{aligned} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& x=y-5 \\\\ & y=60 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=55 \\\\ & y=60 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 l\u00e0 $55\\,(km\/h)$, v\u1eadn t\u1ed1c c\u1ee7a t\u00e0u h\u1ecfa l\u00e0 $60\\,(km\/h).$<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $60$ v\u00e0 $55$<\/span>"}]}],"id_ques":316},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>Hai v\u00f2i n\u01b0\u1edbc c\u00f9ng ch\u1ea3y v\u00e0o m\u1ed9t b\u1ec3 th\u00ec sau $4$ gi\u1edd $48$ ph\u00fat b\u1ec3 \u0111\u1ea7y. N\u1ebfu v\u00f2i I ch\u1ea3y trong $4$ gi\u1edd, v\u00f2i II ch\u1ea3y trong $3$ gi\u1edd th\u00ec c\u1ea3 hai v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{3}{4}$ b\u1ec3. T\u00ednh th\u1eddi gian \u0111\u1ec3 m\u1ed7i v\u00f2i ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3.<br\/>G\u1ecdi $x$ l\u00e0 s\u1ed1 gi\u1edd v\u00f2i th\u1ee9 nh\u1ea5t ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3; $y$ l\u00e0 s\u1ed1 gi\u1edd v\u00f2i th\u1ee9 hai ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3. Khi \u0111\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u1eadp \u0111\u01b0\u1ee3c l\u00e0 <\/span>","select":["A. $\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{24}{5} \\\\ & \\dfrac{4}{x}+\\dfrac{3}{y}=\\dfrac{3}{4} \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{24}{5} \\\\ & \\dfrac{3}{x}+\\dfrac{4}{y}=\\dfrac{3}{4} \\\\ \\end{align} \\right.$ ","C. $\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{5}{24} \\\\ & \\dfrac{4}{x}+\\dfrac{3}{y}=\\dfrac{3}{4} \\\\ \\end{align} \\right.$ ","D. $\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{24}{5} \\\\ & \\dfrac{3}{x}+\\dfrac{4}{y}=\\dfrac{1}{4} \\\\ \\end{align} \\right.$ "],"hint":"G\u1ecdi $x$ l\u00e0 s\u1ed1 gi\u1edd v\u00f2i th\u1ee9 nh\u1ea5t ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3; $y$ l\u00e0 s\u1ed1 gi\u1edd v\u00f2i th\u1ee9 hai ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3. <br\/>Ch\u00fa \u00fd: S\u1ed1 ph\u1ea7n b\u1ec3 m\u00e0 m\u1ed7i v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c trong m\u1ed9t gi\u1edd v\u00e0 s\u1ed1 gi\u1edd c\u1ea7n thi\u1ebft \u0111\u1ec3 v\u00f2i \u0111\u00f3 ch\u1ea3y \u0111\u1ea7y b\u1ec3 l\u00e0 hai \u0111\u1ea1i l\u01b0\u1ee3ng t\u1ec9 l\u1ec7 ngh\u1ecbch.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> + Ch\u1ecdn \u1ea9n v\u00e0 \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho \u1ea9n.<br\/>+ T\u1eeb gi\u1ea3i thi\u1ebft th\u1ee9 1, ta thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb ph\u1ea7n b\u1ec3 m\u00e0 hai v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c trong $1$ gi\u1edd.<br\/>+ T\u1eeb gi\u1ea3 thi\u1ebft th\u1ee9 hai, ta thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai. <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> \u0110\u1ed5i $4$ gi\u1edd $48$ ph\u00fat $= \\dfrac{24}{5}$ gi\u1edd<br\/>G\u1ecdi $x$ l\u00e0 s\u1ed1 gi\u1edd v\u00f2i th\u1ee9 nh\u1ea5t ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3; $y$ l\u00e0 s\u1ed1 gi\u1edd v\u00f2i th\u1ee9 hai ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3.<br\/> \u0110i\u1ec1u ki\u1ec7n: $ x, y>0 $<br\/>M\u1ed9t gi\u1edd, v\u00f2i th\u1ee9 nh\u1ea5t ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$( b\u1ec3), v\u00f2i th\u1ee9 hai ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{y}$(b\u1ec3). <br\/>Hai v\u00f2i ch\u1ea3y \u0111\u1ea7y b\u1ec3 trong $4$ gi\u1edd $48$ ph\u00fat n\u00ean m\u1ed7i gi\u1edd hai v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{5}{24}$ b\u1ec3. Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/><\/span> $\\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{5}{24}$ (1)<br\/><span class='basic_left'>V\u00f2i th\u1ee9 nh\u1ea5t ch\u1ea3y trong $4$ gi\u1edd \u0111\u01b0\u1ee3c$\\dfrac{4}{x}$ b\u1ec3, v\u00f2i th\u1ee9 hai ch\u1ea3y trong $3$ gi\u1edd \u0111\u01b0\u1ee3c $\\dfrac{3}{y}$ th\u1eeda ru\u1ed9ng. C\u1ea3 hai v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{3}{4}$ b\u1ec3 n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh<\/span><br\/> $\\dfrac{4}{x}+\\dfrac{3}{y}=\\dfrac{3}{4}$ (2)<br\/><span class='basic_left'>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/><\/span> $\\left( I \\right)\\,\\,\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{5}{24} \\\\ & \\dfrac{4}{x}+\\dfrac{3}{y}=\\dfrac{3}{4} \\\\ \\end{align} \\right.$ <br\/><span class='basic_left'><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C <\/span><\/span>","column":2}]}],"id_ques":317},{"time":24,"part":[{"time":3,"title":"Hai ng\u01b0\u1eddi th\u1ee3 l\u00e0m m\u1ed9t th\u1eeda ru\u1ed9ng trong $7$ gi\u1edd $12$ ph\u00fat th\u00ec xong. N\u1ebfu ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m trong $5$ gi\u1edd v\u00e0 ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m trong $6$ gi\u1edd th\u00ec c\u1ea3 hai ng\u01b0\u1eddi l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{3}{4}$ th\u1eeda ru\u1ed9ng. H\u1ecfi n\u1ebfu l\u00e0m m\u1ed9t m\u00ecnh th\u00ec m\u1ed7i ng\u01b0\u1eddi ho\u00e0n th\u00e0nh xong c\u00f4ng vi\u1ec7c trong bao l\u00e2u?","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[3],[6],[1],[5],[4],[2]]],"list":[{"point":5,"image":"img\/1.png","left":["Ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m trong $5$ gi\u1edd \u0111\u01b0\u1ee3c $\\dfrac{5}{x}$ th\u1eeda ru\u1ed9ng, ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m trong $6$ gi\u1edd \u0111\u01b0\u1ee3c $\\dfrac{6}{y}$ th\u1eeda ru\u1ed9ng, c\u1ea3 hai ng\u01b0\u1eddi l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{3}{4}$ th\u1eeda ru\u1ed9ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{5}{x}+\\dfrac{6}{y}=\\dfrac{3}{4}$ (2)","V\u1eady ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh trong $12$ gi\u1edd xong th\u1eeda ru\u1ed9ng, ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m trong $18$ gi\u1edd xong th\u1eeda ru\u1ed9ng.","<span class='basic_left'>G\u1ecdi $x$ l\u00e0 s\u1ed1 gi\u1edd ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh xong th\u1eeda ru\u1ed9ng; $y$ l\u00e0 s\u1ed1 gi\u1edd ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m m\u1ed9t m\u00ecnh xong th\u1eeda ru\u1ed9ng $(x,y>0).$<br\/>M\u1ed9t gi\u1edd, ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$(th\u1eeda ru\u1ed9ng), ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{y}$(th\u1eeda ru\u1ed9ng). <\/span> ","Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng c\u00e1ch \u0111\u1eb7t \u1ea9n ph\u1ee5, ta t\u00ecm \u0111\u01b0\u1ee3c $x=12$ v\u00e0 $y=18$ (th\u1ecfa m\u00e3n)","<span class='basic_left'>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{5}{36} \\\\ & \\dfrac{5}{x}+\\dfrac{6}{y}=\\dfrac{3}{4} \\\\ \\end{align} \\right.$<\/span>","Hai ng\u01b0\u1eddi th\u1ee3 l\u00e0m m\u1ed9t th\u1eeda ru\u1ed9ng trong $7$ gi\u1edd $12$ ph\u00fat, t\u1ee9c $\\dfrac{36}{5}$ gi\u1edd th\u00ec xong n\u00ean m\u1ed7i gi\u1edd hai ng\u01b0\u1eddi c\u00f9ng l\u00e0m th\u00ec \u0111\u01b0\u1ee3c $\\dfrac{5}{36}$ th\u1eeda ru\u1ed9ng. Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{5}{36}$ (1)"],"top":145,"hint":"G\u1ecdi $x$ l\u00e0 s\u1ed1 gi\u1edd ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh xong th\u1eeda ru\u1ed9ng; $y$ l\u00e0 s\u1ed1 gi\u1edd ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m m\u1ed9t m\u00ecnh xong th\u1eeda ru\u1ed9ng. <br\/>Ch\u00fa \u00fd: S\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c m\u00e0 m\u1ed7i ng\u01b0\u1eddi l\u00e0m \u0111\u01b0\u1ee3c trong m\u1ed9t gi\u1edd v\u00e0 s\u1ed1 gi\u1edd c\u1ea7n thi\u1ebft \u0111\u1ec3 ng\u01b0\u1eddi \u0111\u00f3 ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c l\u00e0 hai \u0111\u1ea1i l\u01b0\u1ee3ng t\u1ec9 l\u1ec7 ngh\u1ecbch. ","explain":"<span class='basic_left'> \u0110\u1ed5i: $7$ gi\u1edd $12$ ph\u00fat $=\\dfrac{36}{5}$gi\u1edd <br\/> G\u1ecdi $x$ l\u00e0 s\u1ed1 gi\u1edd ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh xong th\u1eeda ru\u1ed9ng; $y$ l\u00e0 s\u1ed1 gi\u1edd ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m m\u1ed9t m\u00ecnh xong th\u1eeda ru\u1ed9ng.<br\/> \u0110i\u1ec1u ki\u1ec7n: $x,y>0$<br\/>M\u1ed9t gi\u1edd, ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$(th\u1eeda ru\u1ed9ng), ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{y}$(th\u1eeda ru\u1ed9ng). <br\/>Hai ng\u01b0\u1eddi th\u1ee3 l\u00e0m m\u1ed9t th\u1eeda ru\u1ed9ng trong $\\dfrac{36}{5}$ gi\u1edd th\u00ec xong n\u00ean m\u1ed7i gi\u1edd hai ng\u01b0\u1eddi c\u00f9ng l\u00e0m th\u00ec \u0111\u01b0\u1ee3c $\\dfrac{5}{36}$ th\u1eeda ru\u1ed9ng. <br\/> Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{5}{36}$ (1)<br\/> Ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m trong $5$ gi\u1edd \u0111\u01b0\u1ee3c $\\dfrac{5}{x}$ th\u1eeda ru\u1ed9ng, ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m trong $6$ gi\u1edd \u0111\u01b0\u1ee3c $\\dfrac{6}{y}$ th\u1eeda ru\u1ed9ng <br\/> Do ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m trong $5$ gi\u1edd v\u00e0 ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m trong $6$ gi\u1edd th\u00ec c\u1ea3 hai ng\u01b0\u1eddi l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{3}{4}$ th\u1eeda ru\u1ed9ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: <br\/> $\\dfrac{5}{x}+\\dfrac{6}{y}=\\dfrac{3}{4}$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left( I \\right)\\,\\,\\left\\{ \\begin{align}& \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{5}{36} \\\\ & \\dfrac{5}{x}+\\dfrac{6}{y}=\\dfrac{3}{4} \\\\ \\end{align} \\right.$<br\/>\u0110\u1eb7t $u=\\dfrac{1}{x},v=\\dfrac{1}{y}$, h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) tr\u1edf th\u00e0nh: $\\left\\{ \\begin{aligned}& u+v=\\dfrac{5}{36} \\\\ & 5u+6v=\\dfrac{3}{4} \\\\ \\end{aligned} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 5u+5v=\\dfrac{25}{36} \\\\ & 5u+6v=\\dfrac{3}{4} \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& v=\\dfrac{1}{18} \\\\ & u=\\dfrac{5}{36}-v \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& v=\\dfrac{1}{18} \\\\ & u=\\dfrac{1}{12} \\\\ \\end{aligned} \\right.$<br\/>Suy ra $\\left\\{ \\begin{aligned}& \\dfrac{1}{x}=\\dfrac{1}{12} \\\\ & \\dfrac{1}{y}=\\dfrac{1}{18} \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=12 \\\\ & y=18 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh trong $12$ gi\u1edd xong th\u1eeda ru\u1ed9ng, ng\u01b0\u1eddi th\u1ee9 hai l\u00e0m trong $18$ gi\u1edd xong th\u1eeda ru\u1ed9ng.<\/span>"}]}],"id_ques":318},{"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":"B\u1ea1n Nam c\u00f3 $1$ tri\u1ec7u \u0111\u1ed3ng g\u1ed3m $2$ t\u1edd $500 000$ \u0111\u1ed3ng. Nam mu\u1ed1n \u0111\u1ed5i l\u1ea5y $30$ t\u1edd lo\u1ea1i $50 000$ \u0111\u1ed3ng v\u00e0 $20 000$ \u0111\u1ed3ng. H\u1ecfi Nam c\u00f3 th\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c \u00fd mu\u1ed1n hay kh\u00f4ng?","select":["A. C\u00f3 ","B. Kh\u00f4ng"],"hint":"G\u1ecdi s\u1ed1 t\u1edd lo\u1ea1i $50 000$ \u0111\u1ed3ng v\u00e0 s\u1ed1 t\u1edd $20 000$ \u0111\u1ed3ng l\u00e0 \u1ea9n. Gi\u1ea3 s\u1eed Nam \u0111\u1ea1t \u0111\u01b0\u1ee3c \u00fd mu\u1ed1n c\u1ee7a m\u00ecnh, t\u1eeb \u0111\u00f3 gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi hai \u1ea9n tr\u00ean. ","explain":"<span class='basic_left'>Gi\u1ea3 s\u1eed Nam \u0111\u1ed5i 1 tri\u1ec7u \u0111\u1ed3ng \u0111\u01b0\u1ee3c $x$ t\u1edd lo\u1ea1i $50 000$ \u0111\u1ed3ng v\u00e0 $y$ t\u1edd lo\u1ea1i $20 000$ \u0111\u1ed3ng $(x, y \\in \\mathbb{N})$ <br\/> Do t\u1ed5ng s\u1ed1 t\u1edd ti\u1ec1n m\u1ec7nh gi\u00e1 $50000$ \u0111\u1ed3ng v\u00e0 $20000$ \u0111\u1ed3ng l\u00e0 $30$ t\u1edd <br\/> N\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=30$ (1)<br\/> V\u00ec s\u1ed1 ti\u1ec1n v\u1eabn gi\u1eefa nguy\u00ean n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $50000x+20000y=1000000 $ hay $5x+2y=100$ (2) <br\/> T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x+y=30 \\\\ & 5x+2y=100 \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 2x+2y=60 \\\\ & 5x+2y=100 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 3x=40 \\\\ & y=30-x \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=\\dfrac{40}{3} \\\\ & y=\\dfrac{50}{3} \\\\ \\end{aligned} \\right.$ (kh\u00f4ng th\u1ecfa m\u00e3n) <br\/> V\u1eady b\u1ea1n Nam kh\u00f4ng th\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c \u00fd mu\u1ed1n c\u1ee7a m\u00ecnh.<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":319},{"time":24,"part":[{"time":3,"title":"Bi\u1ebft r\u1eb1ng $15$ qu\u1ea3 t\u00e1o v\u00e0 $8$ qu\u1ea3 thanh long n\u1eb7ng $7,1$ kg; $5$ qu\u1ea3 t\u00e1o n\u1eb7ng h\u01a1n $3$ qu\u1ea3 thanh long $100g$. H\u1ecfi m\u1ed7i qu\u1ea3 t\u00e1o, qu\u1ea3 thanh long n\u1eb7ng bao nhi\u00eau gam?","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[2],[6],[1],[5],[4],[3]]],"list":[{"point":5,"image":"img\/1.png","left":["Theo \u0111\u1ec1 ra, $15$ qu\u1ea3 t\u00e1o v\u00e0 $8$ qu\u1ea3 thanh long n\u1eb7ng $7,1kg$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $15x+8y=7100$ (1) ","V\u1eady m\u1ed7i qu\u1ea3 t\u00e1o n\u1eb7ng $260$ gam v\u00e0 m\u1ed7i qu\u1ea3 thanh long n\u1eb7ng $400$ gam. ","G\u1ecdi $x$ l\u00e0 s\u1ed1 gam c\u1ee7a m\u1ed7i qu\u1ea3 t\u00e1o, $y$ l\u00e0 s\u1ed1 gam c\u1ee7a m\u1ed7i qu\u1ea3 thanh long $(x, y>0)$ ","Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ta t\u00ecm \u0111\u01b0\u1ee3c $x=260$ v\u00e0 $y=400$ (th\u1ecfa m\u00e3n)","T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& 15x+8y=7100 \\\\ & 5x-3y=100 \\\\ \\end{align} \\right.$","V\u00ec $5$ qu\u1ea3 t\u00e1o n\u1eb7ng h\u01a1n $3$ qu\u1ea3 thanh long $100g$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $5x-3y=100$ (2) "],"top":75,"hint":"G\u1ecdi $x$ l\u00e0 s\u1ed1 gam c\u1ee7a m\u1ed7i qu\u1ea3 t\u00e1o, $y$ l\u00e0 s\u1ed1 gam c\u1ee7a m\u1ed7i qu\u1ea3 thanh long. T\u1eeb gi\u1ea3 thi\u1ebft b\u00e0i to\u00e1n, ta l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh hai \u1ea9n","explain":"<span class='basic_left'>G\u1ecdi $x$ l\u00e0 s\u1ed1 gam c\u1ee7a m\u1ed7i qu\u1ea3 t\u00e1o, $y$ l\u00e0 s\u1ed1 gam c\u1ee7a m\u1ed7i qu\u1ea3 thanh long $(x, y>0)$<br\/>Theo \u0111\u1ec1 ra, $15$ qu\u1ea3 t\u00e1o v\u00e0 $8$ qu\u1ea3 thanh long n\u1eb7ng $7,1kg$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $15x+8y=7100$ (1)<br\/> V\u00ec $5$ qu\u1ea3 t\u00e1o n\u1eb7ng h\u01a1n $3$ qu\u1ea3 thanh long $100g$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $5x-3y=100$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& 15x+8y=7100 \\\\ & 5x-3y=100 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 15x+8y=7100 \\\\ & 15x-9y=300 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& 17y=6800 \\\\ & 5x=100+3y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=400 \\\\ & 5x=1300 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& y=400 \\\\ & x=260 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady m\u1ed7i qu\u1ea3 t\u00e1o n\u1eb7ng $260$ gam v\u00e0 m\u1ed7i qu\u1ea3 thanh long n\u1eb7ng $400$ gam.<\/span>"}]}],"id_ques":320}],"lesson":{"save":0,"level":1}}