{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 c\u1ee7a B v\u00e0o \u00f4 tr\u1ed1ng <br\/> $ B = \\left( \\dfrac{3}{25} - 1,12 \\right) : \\dfrac{3}{7} : \\left[ \\left( 3\\dfrac{1}{2} - 3\\dfrac{2}{3} \\right) : \\dfrac{1}{14} \\right] = $ _input_","hint":" Th\u1ef1c hi\u1ec7n trong ngo\u1eb7c tr\u01b0\u1edbc ngo\u00e0i ngo\u1eb7c sau","explain":" Ta c\u00f3: $ B = \\left( \\dfrac{3}{25} - 1,12 \\right) : \\dfrac{3}{7} : \\left[ \\left( 3\\dfrac{1}{2} - 3\\dfrac{2}{3} \\right) : \\dfrac{1}{14} \\right] \\\\ = \\left( \\dfrac{3}{25} - \\dfrac{28}{25} \\right) : \\dfrac{3}{7} : \\left[ \\left( \\dfrac{7}{2} - \\dfrac{11}{3} \\right) : \\dfrac{1}{14} \\right] \\\\ = \\dfrac{-25}{25} : \\dfrac{3}{7} : \\left( \\dfrac{21-22}{6} : \\dfrac{1}{14} \\right) \\\\ = -1 . \\dfrac{7}{3} : \\left( \\dfrac{-1}{6} . 14 \\right) \\\\ = \\dfrac{-7}{3} : \\dfrac{-7}{3} \\\\ = 1 $ <br\/> <br\/> <span class='basic_pink'> Gi\u00e1 tr\u1ecb c\u1ea7n \u0111i\u1ec1n l\u00e0 $1$.<\/span><\/span> <br\/>"}]}],"id_ques":141},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" T\u00ecm th\u01b0\u01a1ng trong ph\u00e9p chia s\u1ed1 h\u1eefu t\u1ec9 \u00e2m nh\u1ecf nh\u1ea5t vi\u1ebft b\u1edfi ba ch\u1eef s\u1ed1 1 cho s\u1ed1 h\u1eefu t\u1ec9 \u00e2m l\u1edbn nh\u1ea5t vi\u1ebft b\u1edfi ba ch\u1eef s\u1ed1 1 ","select":["A. $ 100 $","B. $1221$","C. $ 10 $ ","D. $ 1 $ "],"hint":" T\u00ecm s\u1ed1 h\u1eefu t\u1ec9 \u00e2m nh\u1ecf nh\u1ea5t v\u00e0 l\u1edbn nh\u1ea5t r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p to\u00e1n","explain":" Ta c\u00f3: S\u1ed1 h\u1eefu t\u1ec9 \u00e2m nh\u1ecf nh\u1ea5t vi\u1ebft b\u1edfi ba ch\u1eef s\u1ed1 $1$ l\u00e0 $-111$. <br> $\\qquad$ S\u1ed1 h\u1eefu t\u1ec9 \u00e2m l\u1edbn nh\u1ea5t vi\u1ebft b\u1edfi ba ch\u1eef s\u1ed1 $1$ l\u00e0 $\\dfrac{-1}{11}$ <br\/> Suy ra : $-111 : \\dfrac{-1}{11} = -111 . (-11) = 1221$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span><\/span> <br\/>","column":2}]}],"id_ques":142},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" V\u1edbi gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a x th\u00ec $A = \\left( x - \\dfrac{3}{4} \\right) \\left( x + \\dfrac{1}{2} \\right)$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng?","select":["A. $ \\dfrac{-1}{2} < x < \\dfrac{3}{4} $","B. $x > \\dfrac{3}{4}$","C. $x > \\dfrac{3}{4}$ ho\u1eb7c $x < - \\dfrac{1}{2}$","D. $x > \\dfrac{-1}{2} $ "],"hint":" $ab > 0$ khi hai th\u1eeba s\u1ed1 c\u00f9ng d\u1ea5u. ","explain":" Ta c\u00f3: $A = \\left( x - \\dfrac{3}{4} \\right) \\left( x + \\dfrac{1}{2} \\right) > 0 $ khi hai th\u1eeba s\u1ed1 c\u00f9ng d\u1ea5u. <br\/> Tr\u01b0\u1eddng h\u1ee3p 1: $\\left[ \\begin{array}{} x - \\dfrac{3}{4} > 0 \\\\ x + \\dfrac{1}{2} > 0 \\end{array} \\right.$ $\\Rightarrow\\left[ \\begin{array}{} x > \\dfrac{3}{4} \\\\ x > -\\dfrac{1}{2} \\end{array} \\right.$ $ \\Rightarrow x > \\dfrac{3}{4}$ <br\/> <br\/> Tr\u01b0\u1eddng h\u1ee3p 2: $\\left[ \\begin{array}{} x - \\dfrac{3}{4} < 0 \\\\ x + \\dfrac{1}{2} < 0 \\end{array} \\right.$ $\\Rightarrow \\left[ \\begin{array}{} x < \\dfrac{3}{4} \\\\ x < -\\dfrac{1}{2} \\end{array} \\right.$ $\\Rightarrow x < \\dfrac{-1}{2}$ <br\/> \u0110\u00e1p s\u1ed1: $x > \\dfrac{3}{4}$ ho\u1eb7c $x < - \\dfrac{1}{2}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C.<\/span><\/span> <br\/>","column":2}]}],"id_ques":143},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" T\u00ecm $x \\in \\mathbb{Q}$ bi\u1ebft: <br\/> $ x - 128 = \\left( 4\\dfrac{20}{21} - 5 \\right) : \\left( \\dfrac{4141}{4242} - 1 \\right) : \\left( \\dfrac{636363}{646464} - 1 \\right) $ ","select":["A. $ x = 128 $","B. $ x = 0 $","C. $ x = \\dfrac{1}{128} $","D. $ x = \\dfrac{-1}{21}$ "],"hint":" Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c b\u00ean ph\u1ea3i r\u1ed3i t\u00ecm x. ","explain":" Ta c\u00f3: $ x - 128 = \\left( 4\\dfrac{20}{21} - 5 \\right) : \\left( \\dfrac{4141}{4242} - 1 \\right) : \\left( \\dfrac{636363}{646464} - 1 \\right) \\\\ x - 128 = \\left( 4 + \\dfrac{20}{21} - 5 \\right) : \\left( \\dfrac{41.101}{42.101} - 1 \\right) : \\left( \\dfrac{63.10101}{64.10101} - 1 \\right)\\\\ x - 128 = \\left(\\dfrac{20}{21} - 1 \\right) : \\left( \\dfrac{41}{42} - 1 \\right) : \\left( \\dfrac{63}{64} - 1 \\right) \\\\ x - 128 = \\left( \\dfrac{20-21}{21} \\right) : \\left( \\dfrac{41-42}{42} \\right) : \\left( \\dfrac{63-64}{64} \\right) \\\\ x -128 = \\left( \\dfrac{-1}{21} \\right) : \\left( \\dfrac{-1}{42} \\right) : \\left( \\dfrac{-1}{64} \\right) \\\\ x - 128 = \\left( \\dfrac{-1}{21} \\right) . (-42) . (-64) \\\\ x - 128 = -128 \\\\ \\Rightarrow x = 0 $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span><\/span> <br\/>","column":2}]}],"id_ques":144},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" C\u00f3 m\u1ea5y gi\u00e1 tr\u1ecb c\u1ee7a $x \\in \\mathbb{Z}$ th\u1ecfa m\u00e3n : <br\/> $ -4\\dfrac{3}{5} . 2\\dfrac{4}{23} \\leqslant x \\leqslant -2\\dfrac{3}{5} . 1\\dfrac{6}{15} $ ","select":["A. $ 5 $","B. $ 6 $ ","C. $ 7 $","D. $ 8 $ "],"hint":" Bi\u1ebfn \u0111\u1ed5i c\u1ea3 2 v\u1ebf r\u1ed3i t\u00ecm k\u1ebft qu\u1ea3. ","explain":" Ta c\u00f3: $ -4\\dfrac{3}{5} . 2\\dfrac{4}{23} \\leqslant x \\leqslant -2\\dfrac{3}{5} . 1\\dfrac{6}{15} \\\\ \\Rightarrow \\dfrac{-23}{5} . \\dfrac{50}{23} \\leqslant x \\leqslant \\dfrac{-13}{5} . \\dfrac{21}{15} \\\\ \\Rightarrow -10 \\leqslant x \\leqslant -3\\dfrac{16}{25}$ <br\/> m\u00e0 $x \\in \\mathbb{Z}$ n\u00ean $ x \\in \\{ -10; -9; -8; -7; -6; -5; -4 \\}$ <br\/> V\u1eady c\u00f3 7 gi\u00e1 tr\u1ecb c\u1ee7a x th\u1ecfa m\u00e3n. <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C.<\/span><\/span> <br\/>","column":2}]}],"id_ques":145},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" C\u00f3 m\u1ea5y gi\u00e1 tr\u1ecb c\u1ee7a $x \\in \\mathbb{Z}$ \u0111\u1ec3 $ F = \\dfrac{3x-2}{x+3}$ l\u00e0 s\u1ed1 nguy\u00ean?","select":["A. $ 3 $","B. $ 4 $ ","C. $ 5 $","D. $ 6 $ "],"hint":" S\u1ed1 h\u1eefu t\u1ec9 $ \\dfrac{a}{b}$ l\u00e0 s\u1ed1 nguy\u00ean khi $b$ l\u00e0 \u01b0\u1edbc c\u1ee7a $a$. ","explain":" Ta c\u00f3: $ F = \\dfrac{3x-2}{x+3} \\\\ = \\dfrac{3x+9-11}{x+3} = \\dfrac{3(x+3)-11}{x+3} = 3 - \\dfrac{11}{x+3}$<br\/> \u0110\u1ec3 $F \\in \\mathbb{Z} $ th\u00ec $\\dfrac{11}{x+3} \\in \\mathbb{Z}$ hay $(x + 3)$ l\u00e0 \u01b0\u1edbc c\u1ee7a $11$. <br\/> $\u01af(11) = ( \\pm 1; \\pm 11)$. Ta c\u00f3 b\u1ea3ng sau :<br\/> <table><tr><td>$x+3$<\/td><td>$-11$<\/td><td>$-1$<\/td><td>$1$<\/td><td>$11$<\/td><\/tr><tr><td>x<\/td><td>$-14$<\/td><td>$-4$<\/td><td>$-2$<\/td><td>$8$<\/td><\/tr><\/table> <br\/> V\u1eady c\u00f3 4 gi\u00e1 tr\u1ecb c\u1ee7a x th\u1ecfa m\u00e3n l\u00e0 $ -14; -4; -2; 8$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span><\/span> <br\/>","column":2}]}],"id_ques":146},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":" T\u00ecm $x \\in \\mathbb{Q}$ bi\u1ebft: <br\/> $ \\left( -0,75x + \\dfrac{5}{2} \\right) . \\dfrac{4}{7} - \\dfrac{-1}{3} = \\dfrac{-5}{6}$ ","select":["A. $ x = 6\\dfrac{1}{18}$","B. $x = \\dfrac{-109}{18}$","C. $x = -4\\dfrac{1}{2}$","D. $ x = 2\\dfrac{1}{6} $"],"hint":" \u00c1p d\u1ee5ng quy t\u1eafc nh\u00e2n, chia s\u1ed1 h\u1eefu t\u1ec9. Quy t\u1eafc chuy\u1ec3n v\u1ebf.","explain":" Ta c\u00f3: $ \\left( -0,75x + \\dfrac{5}{2} \\right) . \\dfrac{4}{7} - \\dfrac{-1}{3} = \\dfrac{-5}{6} $ <br\/> $ \\Rightarrow \\left( \\dfrac{-3}{4}x + \\dfrac{5}{2} \\right) . \\dfrac{4}{7} = \\dfrac{-5}{6} - \\dfrac{1}{3}$ <br\/> $ \\Rightarrow \\left( \\dfrac{-3}{4}x + \\dfrac{5}{2} \\right) . \\dfrac{4}{7} = \\dfrac{-7}{6} $ <br\/> $ \\Rightarrow \\dfrac{-3}{4}x + \\dfrac{5}{2} = \\dfrac{-7}{6} : \\dfrac{4}{7}$ <br\/> $ \\Rightarrow \\dfrac{-3}{4}x + \\dfrac{5}{2} = \\dfrac{-49}{24} $ <br\/> $ \\Rightarrow \\dfrac{-3}{4}x = \\dfrac{-49}{24} - \\dfrac{5}{2}$ <br\/> $ \\Rightarrow \\dfrac{-3}{4}x = \\dfrac{-109}{24}$ <br\/> $ \\Rightarrow x = \\dfrac{-109}{24} : \\dfrac{-3}{4} $ <br\/> $ \\Rightarrow x = \\dfrac{109}{18} = 6\\dfrac{1}{18}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span><\/span> <br\/>","column":2}]}],"id_ques":147},{"time":14,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"],["13"]]],"list":[{"point":10,"width":50,"type_input":"","input_hint":["frac"],"ques":" T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: <br\/> $H = \\dfrac{\\dfrac{3}{4}-\\dfrac{3}{5}+\\dfrac{3}{7}+\\dfrac{3}{11}}{\\dfrac{13}{4}-\\dfrac{13}{5}+\\dfrac{13}{7}+\\dfrac{13}{11}}$ <br\/> <br\/>\u0110\u00e1p s\u1ed1: H = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","explain":"Ta c\u00f3: $H = \\dfrac{\\dfrac{3}{4}-\\dfrac{3}{5}+\\dfrac{3}{7}+\\dfrac{3}{11}}{\\dfrac{13}{4}-\\dfrac{13}{5}+\\dfrac{13}{7}+\\dfrac{13}{11}} \\\\ = \\dfrac{3.\\left( \\dfrac{1}{4}-\\dfrac{1}{5}+\\dfrac{1}{7}+\\dfrac{1}{11} \\right)}{13.\\left( \\dfrac{1}{4}-\\dfrac{1}{5}+\\dfrac{1}{7}+\\dfrac{1}{11} \\right)} \\\\ = \\dfrac{3}{13} $"}]}],"id_ques":148},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $ F = \\left( \\dfrac{112}{13.20} + \\dfrac{112}{20.27} + \\dfrac{112}{27.34} + ... + \\dfrac{112}{62.69} \\right) : \\left( - \\dfrac{5}{9.13} - \\dfrac{7}{9.25} - \\dfrac{13}{19.25} - \\dfrac{31}{19.69} \\right)$ l\u00e0:","select":["A. $\\dfrac{1}{12}$","B. $\\dfrac{-1}{8}$","C. $-8$","D. $-1$"],"hint":"\u0110\u1eb7t F = P : Q. Sau \u0111\u00f3 \u0111\u1eb7t th\u1eeba s\u1ed1 chung r\u1ed3i r\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c. ","explain":" <span class='basic_left'> \u0110\u1eb7t F = P : Q <br\/> C\u00f3 $P = \\left( \\dfrac{112}{13.20} + \\dfrac{112}{20.27} + \\dfrac{112}{27.34} + ... + \\dfrac{112}{62.69} \\right) \\\\ = 16.\\left( \\dfrac{7}{13.20} + \\dfrac{7}{20.27} + \\dfrac{7}{27.34} + ... + \\dfrac{7}{62.69} \\right) \\\\ = 16.\\left( \\dfrac{1}{13} - \\dfrac{1}{20} + \\dfrac{1}{20} - \\dfrac{1}{27} + \\dfrac{1}{27} - \\dfrac{1}{34} + ... + \\dfrac{1}{62} - \\dfrac{1}{69} \\right) \\\\ = 16. \\left(\\dfrac{1}{13} - \\dfrac{1}{69} \\right) $ <br\/> C\u00f3 $ Q = -\\left( \\dfrac{5}{9.13} + \\dfrac{7}{9.25} + \\dfrac{13}{19.25} + \\dfrac{31}{19.69} \\right) \\\\ = -\\dfrac{1}{9} . \\left( \\dfrac{5}{13} + \\dfrac{7}{25} \\right) - \\dfrac{1}{19} . \\left( \\dfrac{13}{25} + \\dfrac{31}{69} \\right) \\\\ = -\\dfrac{1}{9} . \\dfrac{125+91}{13.25} - \\dfrac{1}{19} . \\dfrac{897+775}{25.69} \\\\ = -\\dfrac{24}{13.25} - \\dfrac{88}{25.69} \\\\ = -2 . \\left( \\dfrac{1}{13} - \\dfrac{1}{25} + \\dfrac{1}{25} - \\dfrac{1}{69} \\right) \\\\ = -2 . \\left( \\dfrac{1}{13} - \\dfrac{1}{69} \\right)$ <br\/>Suy ra $ F = P : Q = 16 : (-2) = -8$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C.<\/span><\/span> <br\/>","column":2}]}],"id_ques":149},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["5"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":" \u0110i\u1ec1n k\u1ebft qu\u1ea3 c\u1ee7a v\u00e0o \u00f4 tr\u1ed1ng <br\/> $ G = \\left( -0,75 - \\dfrac{1}{4} \\right) : (-5) + \\dfrac{1}{15} - \\left(\\dfrac{-1}{5} \\right) : (-3) $= <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":" \u00c1p d\u1ee5ng qui t\u1eafc chia hai s\u1ed1 h\u1eefu t\u1ec9.","explain":" Ta c\u00f3: $ G = \\left( -0,75 - \\dfrac{1}{4} \\right) : (-5) + \\dfrac{1}{15} - \\left(\\dfrac{-1}{5} \\right) : (-3) \\\\ = \\left( \\dfrac{-3}{4} - \\dfrac{1}{4} \\right) : (-5) + \\dfrac{1}{15} - \\left( \\dfrac{-1}{5} . \\dfrac{1}{-3} \\right) \\\\ = \\left( (-1):(-5) \\right) + \\dfrac{1}{15} - \\dfrac{1}{15} \\\\ = \\dfrac{1}{5} $ <br\/> <br\/> <span class='basic_pink'> Gi\u00e1 tr\u1ecb c\u1ee7a G l\u00e0 $\\dfrac{1}{5}$.<\/span><\/span> <br\/>"}]}],"id_ques":150}],"lesson":{"save":0,"level":3}}