{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"width":50,"type_input":"","point":5,"ques":"Cho M = $4 - |5x + 3| $ T\u00ednh gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a M <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> max M = _input_","hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t $|A| \\geq 0; -|A| \\leq 0 $ ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t $|A| \\geq 0; -|A| \\leq 0 $ <br\/> D\u1ea5u ''='' x\u1ea9y ra khi v\u00e0 ch\u1ec9 khi A = 0. <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3 $|5x + 3| \\geq 0 $ <br\/> Suy ra $ 4 - |5x + 3| \\leq 4$ <br\/> V\u1eady gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a M l\u00e0 4 khi $5x + 3 = 0 \\Leftrightarrow x = \\dfrac{-3}{5} $ <br\/> <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 4 <\/span><\/span>"}]}],"id_ques":521},{"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":" S\u1ed1 h\u1ecdc sinh 3 l\u1edbp 7A, 7B, 7C c\u1ee7a m\u1ed9t tr\u01b0\u1eddng t\u1ec9 l\u1ec7 v\u1edbi 10; 9; 8. S\u1ed1 h\u1ecdc sinh l\u1edbp 7A nhi\u1ec1u h\u01a1n s\u1ed1 h\u1ecdc sinh l\u1edbp 7C l\u00e0 10 h\u1ecdc sinh. S\u1ed1 h\u1ecdc sinh c\u1ee7a l\u1edbp 7C l\u00e0: ","select":["A. 50 h\u1ecdc sinh","B. 45 h\u1ecdc sinh ","C. 40 h\u1ecdc sinh ","D. 55 h\u1ecdc sinh "],"hint":" \u0110\u1eb7t \u1ea9n r\u1ed3i gi\u1ea3i b\u00e0i to\u00e1n. ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng, hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i><u> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <\/u> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c}$ v\u00e0 $x - z = M$ <br\/> th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c} = \\dfrac{x-z}{a-c} = \\dfrac{M}{a-c}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y, z$ <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi s\u1ed1 h\u1ecdc sinh c\u1ee7a 3 l\u1edbp 7A, 7B, 7C l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x, y, z$ (h\u1ecdc sinh) ($x, y, z$ nguy\u00ean d\u01b0\u01a1ng) <br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: $ \\dfrac{x}{10} = \\dfrac{y}{9} = \\dfrac{z}{8}$ v\u00e0 $x - z = 10$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{x}{10} = \\dfrac{y}{9} = \\dfrac{z}{8} = \\dfrac{x-z}{10-8} = \\dfrac{10}{2} = 5 $ <br\/> Suy ra $ \\dfrac{z}{8} = 5 \\Rightarrow z = 8.5 = 40 $ <br\/> V\u1eady s\u1ed1 h\u1ecdc sinh l\u1edbp 7C l\u00e0 40 (h\u1ecdc sinh) . <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span>","column":2}]}],"id_ques":522},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["40"],["28"],["48"]]],"list":[{"width":50,"type_input":"","point":5,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/2.jpg'\/><\/center> T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $ 42x = 60y = 35z $ v\u00e0 $x - y + z = 60 $ <br\/><br\/>$x = $ _input_;$y =$ _input_; $z=$_input_","hint":" T\u1eeb: $42x = 60y = 35z $ ta chia cho BCNN[42; 60; 35] = 420, ta \u0111\u01b0\u1ee3c: <br\/> $ \\dfrac{x}{10} = \\dfrac{y}{7} = \\dfrac{z}{12} $","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng, hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i><u> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <\/u> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c}$ v\u00e0 $x - y + z = M$ <br\/> th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c} = \\dfrac{x-y+z}{a-b+c} = \\dfrac{M}{a-b+c}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y, z$ <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> T\u1eeb: $42x = 60y = 35z $ ta chia cho BCNN[42; 60; 35] = 420, ta \u0111\u01b0\u1ee3c: <br\/> $ \\dfrac{42x}{420} = \\dfrac{60y}{420} = \\dfrac{35z}{420} $ hay $ \\dfrac{x}{10} = \\dfrac{y}{7} = \\dfrac{z}{12} $ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{x}{10} = \\dfrac{y}{7} = \\dfrac{z}{12} = \\dfrac{x-y+z}{10-7+12} = \\dfrac{60}{15} = 4 $ <br\/> Suy ra $ \\dfrac{x}{10} = 4 \\Rightarrow x = 10.4 = 40 \\\\ \\dfrac{y}{7} = 4 \\Rightarrow y = 7.4 = 28 \\\\ \\dfrac{z}{12} = 4 \\Rightarrow z = 12.4 = 48 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 40; 28; 48 <\/span><\/span>"}]}],"id_ques":523},{"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 t\u1ec9 l\u1ec7 th\u1ee9c $\\dfrac{a}{b} = \\dfrac{c}{d} (a, b, c, d \\neq 0; a \\neq b; c \\neq d).$ Ta c\u00f3 th\u1ec3 suy ra \u0111\u01b0\u1ee3c: <br\/> (I) $\\dfrac{a-b}{b} = \\dfrac{d}{c-d}; $ (II) $ \\dfrac{a+b}{a} = \\dfrac{c+d}{c} $ <br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o trong c\u00e1c kh\u1eb3ng \u0111\u1ecbnh tr\u00ean \u0111\u00fang? ","select":["A. Ch\u1ec9 c\u00f3 (I) \u0111\u00fang. ","B. Ch\u1ec9 c\u00f3 (II) \u0111\u00fang. ","C. C\u1ea3 (I) v\u00e0 (II) \u0111\u1ec1u \u0111\u00fang. ","D. C\u1ea3 (I) v\u00e0 (II) \u0111\u1ec1u sai. "],"hint":" T\u1eeb $\\dfrac{a}{b} = \\dfrac{c}{d}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i. ","explain":" (I) T\u1eeb $\\dfrac{a}{b} = \\dfrac{c}{d} \\Rightarrow \\dfrac{a}{b} - 1 = \\dfrac{c}{d} - 1 \\Rightarrow \\dfrac{a-b}{b} = \\dfrac{c-d}{d}$ <br\/> (II) T\u1eeb $\\dfrac{a}{b} = \\dfrac{c}{d} \\Rightarrow \\dfrac{a}{c} = \\dfrac{b}{d} = \\dfrac{a+b}{c+d} $ <br\/> T\u1eeb $\\dfrac{a+b}{c+d} = \\dfrac{a}{c} \\Rightarrow \\dfrac{a+b}{a} = \\dfrac{c+d}{c} $ <br\/> V\u1eady ch\u1ec9 c\u00f3 (II) \u0111\u00fang. <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":524},{"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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/2.jpg'\/><\/center> T\u00ecm c\u00e1c s\u1ed1 nguy\u00ean $n$ bi\u1ebft: <br\/> $ 3^{4} < \\dfrac{1}{9}.27^{n} < 3^{10} $ ","select":["A. $ n \\in \\{ 2; 3; 4 \\} $ ","B. $ n \\in \\{2; 3 \\}$ ","C. $ n \\in \\{ 3; 4 \\}$","D. $n = 3$"],"hint":"\u0110\u01b0a t\u1ea5t c\u1ea3 v\u1ec1 l\u0169y th\u1eeba c\u01a1 s\u1ed1 3.","explain":" Ta c\u00f3: $ 3^{4} < \\dfrac{1}{9}.27^{n} < 3^{10} (n \\in \\mathbb{Z})$ <br\/> Suy ra: $ 3^{4} < 3^{-2}.(3^{3})^{n} < 3^{10} \\\\ \\Rightarrow 3^{4} < 3^{-2+3n} < 3^{10} \\\\ \\Rightarrow 4 < -2 + 3n < 10 \\\\ \\Rightarrow 6 < 3n < 12 \\\\ \\Rightarrow 2 < n < 4$ <br\/> M\u00e0 $n \\in \\mathbb{Z} $ do \u0111\u00f3 n = 3. <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":2}]}],"id_ques":525},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["77"]]],"list":[{"width":50,"type_input":"","input_hint":["sqrt","frac"],"point":5,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/2.jpg'\/><\/center> T\u00ecm $x$ bi\u1ebft: <br\/> $ 5^{2}.7^{3}.11^{2}.x - 5^{3}.7^{2}.11 = 0 $ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $ x$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"\u0110\u1eb7t nh\u00e2n t\u1eed chung ra ngo\u00e0i.","explain":" Ta c\u00f3: $ 5^{2}.7^{3}.11^{2}.x - 5^{3}.7^{2}.11 = 0 \\\\ \\Leftrightarrow 5^{2}.7^{2}.11(7.11.x - 5) = 0 $<br\/> $ \\Leftrightarrow 77x - 5 = 0 $ (do $5^{2}.7^{2}.11 \\neq 0 $)<br\/> $ \\Leftrightarrow x = \\dfrac{5}{77}$<\/span>"}]}],"id_ques":526},{"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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/4.jpg'\/><\/center> So s\u00e1nh hai bi\u1ec3u th\u1ee9c <br\/> $\\sqrt{13+17}$ v\u00e0 $\\sqrt{13} + \\sqrt{17} $ ta \u0111\u01b0\u1ee3c: ","select":["A. $\\sqrt{13+17}$ < $\\sqrt{13} + \\sqrt{17} $ ","B. $\\sqrt{13+17}$ = $\\sqrt{13} + \\sqrt{17} $ ","C. $\\sqrt{13+17}$ > $\\sqrt{13} + \\sqrt{17} $ "],"hint":"So s\u00e1nh $\\sqrt{13+17}$ v\u1edbi 6. <br\/> So s\u00e1nh hai bi\u1ec3u th\u1ee9c sau $\\sqrt{13} + \\sqrt{17}$ v\u1edbi 7 ","explain":" <span class='basic_left'> $\\sqrt{13+17}$ v\u00e0 $\\sqrt{13} + \\sqrt{17} $ <br\/> C\u00f3: $\\sqrt{13+17} = \\sqrt{30} < \\sqrt{36} = 6 $ <br\/> $\\sqrt{13} + \\sqrt{17} > \\sqrt{9} + \\sqrt{16} = 3 + 4 = 7 $ <br\/> Suy ra $\\sqrt{13+17} < \\sqrt{13} + \\sqrt{17} $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A <\/span><\/span> ","column":1}]}],"id_ques":527},{"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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/4.jpg'\/><\/center> T\u00ecm $x$ bi\u1ebft: <br\/> $|2x - 1| - x = 1$ ","select":["A. $x = 0$ ho\u1eb7c $x = 2$ ","B. $x = 0$ ","C. $x = 2$","D. Kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a $x$ th\u1ecfa m\u00e3n."],"hint":"X\u00e9t hai tr\u01b0\u1eddng h\u1ee3p: <br\/> $|2x - 1| \\geq 0 $ v\u00e0 $|2x - 1| < 0$","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> - X\u00e9t d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i, t\u00ecm \u0111i\u1ec1u ki\u1ec7n c\u1ee7a $x$ <br\/> - T\u00ecm x v\u1edbi \u0111i\u1ec1u ki\u1ec7n b\u00ean tr\u00ean. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> * N\u1ebfu $|2x - 1| \\geq 0 \\Leftrightarrow x \\geq \\dfrac{1}{2}$ th\u00ec ta c\u00f3: <br\/> $2x - 1 - x = 1 $ <br\/> $\\Rightarrow x = 2$ (th\u1ecfa m\u00e3n $x \\geq \\dfrac{1}{2}$) <br\/> * N\u1ebfu $|2x - 1| < 0 \\Leftrightarrow x < \\dfrac{1}{2}$ th\u00ec ta c\u00f3: <br\/> $-2x + 1 - x = 1 $ <br\/> $ \\Rightarrow x = 0 $ (th\u1ecfa m\u00e3n $x < \\dfrac{1}{2}$ ) <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0 $x = 2$ ho\u1eb7c $x = 0$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":2}]}],"id_ques":528},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["12"],["7"]]],"list":[{"width":50,"type_input":"","input_hint":["sqrt","frac"],"point":5,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/4.jpg'\/><\/center> T\u00ecm $x$ bi\u1ebft: <br\/> $\\left( \\dfrac{4}{7} - \\dfrac{1}{2}x\\right)^{3} = \\dfrac{-8}{343} $ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"\u0110\u01b0a $\\dfrac{-8}{343} $ v\u1ec1 c\u01a1 s\u1ed1 l\u0169y th\u1eeba 3 ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> V\u1edbi $a \\neq 0; a \\neq \\pm 1$, n\u1ebfu $a^{m} = a^{n}$ th\u00ec $m = n$ <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $\\left( \\dfrac{4}{7} - \\dfrac{1}{2}x\\right)^{3} = \\dfrac{-8}{343} \\\\ \\Leftrightarrow \\left( \\dfrac{4}{7} - \\dfrac{1}{2}x\\right)^{3} = \\left(\\dfrac{-2}{7}\\right)^{3} \\\\ \\Leftrightarrow \\dfrac{4}{7} - \\dfrac{1}{2}x = \\dfrac{-2}{7} \\\\ \\Leftrightarrow \\dfrac{1}{2}x = \\dfrac{4}{7} + \\dfrac{2}{7} = \\dfrac{6}{7} \\\\ \\Leftrightarrow x = \\dfrac{6}{7} : \\dfrac{1}{2} \\\\ \\Leftrightarrow x = \\dfrac{12}{7} $ <\/span>"}]}],"id_ques":529},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"width":50,"type_input":"","point":5,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/4.jpg'\/><\/center> T\u00ecm $x$ bi\u1ebft: <br\/> $\\sqrt{\\dfrac{0,09}{25}} = \\dfrac{-4,7}{5} + x $ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x$ = _input_","explain":" Ta c\u00f3: $\\sqrt{\\dfrac{0,09}{25}} = \\dfrac{-4,7}{5} + x \\\\ \\Rightarrow \\dfrac{0,3}{5} = \\dfrac{-4,7}{5} + x \\\\ \\Rightarrow x = \\dfrac{0,3}{5} + \\dfrac{4,7}{5} \\\\ \\Rightarrow x = \\dfrac{0,3+4,7}{5} \\\\ \\Rightarrow x = \\dfrac{5}{5} \\\\ \\Rightarrow x = 1 $<\/span>"}]}],"id_ques":530},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["80"]]],"list":[{"width":50,"type_input":"","input_hint":["sqrt","frac"],"point":5,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/10.jpg'\/><\/center> Gi\u00e1 tr\u1ecb c\u1ee7a $\\dfrac{(0,8)^{5}}{(0,4)^{6}} = $ _input_","explain":" Ta c\u00f3: $ \\dfrac{(0,8)^{5}}{(0,4)^{6}} = \\dfrac{(2.0,4)^{5}}{(0,4)^{6}} $$= \\dfrac{2^{5}.(0,4)^{5}}{(0,4)^{6}} = \\dfrac{2^{5}}{0,4} = \\dfrac{32}{0,4} = 80 $<\/span>"}]}],"id_ques":531},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["16"]]],"list":[{"width":50,"type_input":"","point":5,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/10.jpg'\/><\/center> $ 18^{16} = 2^{x} . 3^{32} $ <br\/> $x$ =_input_","explain":" <span class='basic_left'> Ta c\u00f3: $18^{16} = 2^{x}.3^{32} \\\\ \\Rightarrow (9.2)^{16} = 2^{x}.3^{32} \\\\ \\Rightarrow (3^{2}.2)^{16} = 2^{x}.3^{32} \\\\ \\Rightarrow (3^{2})^{16}.2^{16} = 2^{x}.3^{32} \\\\ \\Rightarrow 3^{32}.2^{16} = 2^{x}.3^{32} \\\\ \\Rightarrow x = 16 $ <br\/> <br\/> <span class='basic_pink'> K\u1ebft qu\u1ea3 l\u00e0 16. <\/span><\/span>"}]}],"id_ques":532},{"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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/10.jpg'\/><\/center> Khi $x = \\dfrac{-1}{2}$ th\u00ec bi\u1ec3u th\u1ee9c $A = |x + 1| + |x + 2| + |x|$ c\u00f3 gi\u00e1 tr\u1ecb l\u00e0: ","select":["A. $3\\dfrac{1}{2}$ ","B. $1\\dfrac{3}{4}$","C. $2\\dfrac{3}{4}$","D. $2\\dfrac{1}{2}$"],"hint":"Thay $x = \\dfrac{-1}{2}$ v\u00e0o A r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh.","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> Ta c\u00f3: $ \\mid x \\mid = \\begin{cases} x \\text { n\u1ebfu } x \\geq 0 \\\\ -x \\text { n\u1ebfu } x < 0. \\end{cases} $ <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Thay $x = \\dfrac{-1}{2}$ v\u00e0o bi\u1ec3u th\u1ee9c A ta \u0111\u01b0\u1ee3c: <br\/> $A = \\left| \\dfrac{-1}{2} + 1\\right| + \\left| \\dfrac{-1}{2} + 2\\right| + \\left| \\dfrac{-1}{2} \\right| \\\\ = \\left| \\dfrac{1}{2} \\right| + \\left| \\dfrac{3}{2} \\right| + \\left| \\dfrac{-1}{2} \\right| \\\\ = \\dfrac{1}{2} + \\dfrac{3}{2} + \\dfrac{1}{2} \\\\ = \\dfrac{5}{2} = 2\\dfrac{1}{2} $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":4}]}],"id_ques":533},{"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":" S\u1ed1 h\u1ecdc sinh Gi\u1ecfi, Kh\u00e1, Trung b\u00ecnh c\u1ee7a kh\u1ed1i 7 \u1edf m\u1ed9t tr\u01b0\u1eddng t\u1ec9 l\u1ec7 v\u1edbi 2; 5; 3. Bi\u1ebft r\u1eb1ng s\u1ed1 h\u1ecdc sinh Kh\u00e1 nhi\u1ec1u h\u01a1n s\u1ed1 h\u1ecdc sinh Gi\u1ecfi l\u00e0 45 b\u1ea1n. T\u00ednh s\u1ed1 h\u1ecdc sinh c\u1ea3 kh\u1ed1i 7. ","select":["A. 90 h\u1ecdc sinh ","B. 225 h\u1ecdc sinh ","C. 135 h\u1ecdc sinh ","D. 150 h\u1ecdc sinh "],"hint":"D\u00f9ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau.","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> T\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau. <\/b> <br\/> T\u1eeb d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau $\\dfrac{a}{m} = \\dfrac{b}{n} = \\dfrac{c}{t}$ ta suy ra: <br\/> $\\dfrac{a}{m} = \\dfrac{b}{n} = \\dfrac{c}{t} = \\dfrac{b-a}{n-m}$ <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi s\u1ed1 h\u1ecdc sinh Gi\u1ecfi, Kh\u00e1, Trung b\u00ecnh l\u1ea7n l\u01b0\u1ee3t l\u00e0 a, b, c. ($a, b, c \\in \\mathbb{N^{*}}$ v\u00e0 b > a) <br\/> Theo b\u00e0i ta c\u00f3: <br\/> $\\dfrac{a}{2} = \\dfrac{b}{5} = \\dfrac{c}{3}$ v\u00e0 $b - a = 45$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta \u0111\u01b0\u1ee3c: <br\/> $\\dfrac{a}{2} = \\dfrac{b}{5} = \\dfrac{c}{3} = \\dfrac{b-a}{5-2} = \\dfrac{45}{3} = 15 $ <br\/> Suy ra: $ \\begin{cases} \\dfrac{a}{2} = 15 \\Rightarrow a = 2.15 = 30 \\\\ \\dfrac{b}{5} = 15 \\Rightarrow b = 15.5 = 75 \\\\ \\dfrac{c}{3} = 15 \\Rightarrow c = 15.3 = 45 \\end{cases} $ <br\/> V\u1eady s\u1ed1 h\u1ecdc sinh c\u1ee7a c\u1ea3 kh\u1ed1i 7 l\u00e0: 30 + 75 + 45 = 150 (h\u1ecdc sinh) <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":2}]}],"id_ques":534},{"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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/10.jpg'\/><\/center> Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh: <br\/> $M = 1\\dfrac{1}{23} + \\dfrac{2}{21} - \\dfrac{1}{23} + \\dfrac{19}{21} + 2017^{0} $ ","select":["A. 0 ","B. 1","C. 2","D. 3 "],"hint":" <br\/> - Nh\u00f3m s\u1ed1 h\u1ea1ng th\u00edch h\u1ee3p r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh. <br\/> - Nh\u1edb: $a^{0} = 1$","explain":" Ta c\u00f3: $M = 1\\dfrac{1}{23} + \\dfrac{2}{21} - \\dfrac{1}{23} + \\dfrac{19}{21} + 2017^{0} \\\\ = \\dfrac{24}{23} + \\dfrac{2}{21} - \\dfrac{1}{23} + \\dfrac{19}{21} + 1 \\\\ = \\left( \\dfrac{24}{23} - \\dfrac{1}{23} \\right) + \\left( \\dfrac{2}{21} + \\dfrac{19}{21} \\right) + 1 \\\\ = 1 + 1 + 1 \\\\ = 3 $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":4}]}],"id_ques":535},{"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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/10.jpg'\/><\/center> T\u00ecm $x$ bi\u1ebft: <br\/> $3^{x+1} = 9^{x}$ ","select":["A. $x = 9 $ ","B. $x = 3 $","C. $x = 6 $","D. $x = 1 $"],"hint":"\u0110\u01b0a v\u1ec1 hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 3.","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> C\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00e1c t\u00ednh ch\u1ea5t \u0111\u01b0\u1ee3c th\u1eeba nh\u1eadn d\u01b0\u1edbi \u0111\u00e2y: <br\/> <br\/> $(x^{m})^{n} = x^{m.n}$ <br\/> V\u1edbi $a \\neq 0; a \\neq \\pm 1,$ n\u1ebfu $a^{m} = a^{n}$ th\u00ec $m = n.$ <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $3^{x+1} = 9^{x} \\\\ \\Rightarrow 3^{x+1} = (3^{2})^{x} \\\\ \\Rightarrow 3^{x+1} = 3^{2x} \\\\ \\Rightarrow x + 1 = 2x \\\\ \\Rightarrow x = 1 $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":2}]}],"id_ques":536},{"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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/10.jpg'\/><\/center> T\u00ecm $x$ bi\u1ebft: <br\/> $\\dfrac{2}{3} + \\dfrac{1}{3} : x = -1\\dfrac{1}{3}$ ","select":["A. $x = \\dfrac{1}{6} $ ","B. $x = \\dfrac{-1}{6} $","C. $x = \\dfrac{-2}{3} $","D. $x = \\dfrac{2}{3} $"],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> B\u00e0i to\u00e1n t\u00ecm $x$ <\/b> <br\/> - Chuy\u1ec3n c\u00e1c h\u1ea1ng t\u1eed ch\u1ee9a $x$ sang m\u1ed9t v\u1ebf, c\u00e1c h\u1eb1ng s\u1ed1 sang v\u1ebf kia. <br\/> - Thu g\u1ecdn v\u00e0 t\u00ecm $x$ <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $\\dfrac{2}{3} + \\dfrac{1}{3} : x = -1\\dfrac{1}{3} \\\\ \\Rightarrow \\dfrac{1}{3} : x = -1\\dfrac{1}{3} - \\dfrac{2}{3} = -2 \\\\ \\Rightarrow x = \\dfrac{1}{3} : (-2) = \\dfrac{-1}{6} $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":537},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"],["25"]]],"list":[{"width":50,"type_input":"","point":5,"ques":" T\u00ecm $x \\in \\mathbb{Q}$ bi\u1ebft: $ \\dfrac{25}{12}.x + \\dfrac{11}{15} = \\dfrac{9}{10} $ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x $= <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u00e0i to\u00e1n t\u00ecm $x$ <\/b> <br\/> - Chuy\u1ec3n c\u00e1c h\u1ea1ng t\u1eed ch\u1ee9a $x$ sang m\u1ed9t v\u1ebf, c\u00e1c h\u1eb1ng s\u1ed1 sang v\u1ebf kia. <br\/> - Thu g\u1ecdn v\u00e0 t\u00ecm $x$ <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $\\dfrac{25}{12}.x + \\dfrac{11}{15} = \\dfrac{9}{10} \\\\ \\Rightarrow \\dfrac{25}{12}.x = \\dfrac{9}{10} - \\dfrac{11}{15} = \\dfrac{1}{6} \\\\ \\Rightarrow x = \\dfrac{1}{6} : \\dfrac{25}{12} \\\\ \\Rightarrow x = \\dfrac{2}{25}$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0: $x = \\dfrac{2}{25}$ <\/span><\/span>"}]}],"id_ques":538},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ( >, =, <)","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"width":50,"type_input":"","point":5,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/10.jpg'\/><\/center> So s\u00e1nh hai l\u0169y th\u1eeba sau: <br\/> $3^{2^{3}} $_input_$(3^{2})^{3}$","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u00c1p d\u1ee5ng: $(x^{m})^{n} = x^{m.n}$ <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $3^{2^{3}} = 3^{8} \\\\ (3^{2})^{3} = 3^{2.3} = 3^{6} $ <br\/> M\u00e0 $3^{8} > 3^{6} $ <br\/> Suy ra $3^{2^{3}} > (3^{2})^{3}$ <br\/> <br\/> <span class='basic_pink'> D\u1ea5u so s\u00e1nh l\u00e0 '' > '' <\/span><\/span>"}]}],"id_ques":539},{"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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai11/lv2/img\/10.jpg'\/><\/center> So s\u00e1nh hai bi\u1ec3u th\u1ee9c sau: <br\/> $4 - \\sqrt{29}$ v\u00e0 $\\sqrt{15} - \\sqrt{30}$ ","select":["A. $4 - \\sqrt{29}$ > $\\sqrt{15} - \\sqrt{30}$ ","B. $4 - \\sqrt{29}$ = $\\sqrt{15} - \\sqrt{30}$ ","C. $4 - \\sqrt{29}$ < $\\sqrt{15} - \\sqrt{30}$ "],"explain":" <span class='basic_left'> Ta c\u00f3: $4 - \\sqrt{29} = \\sqrt{16} - \\sqrt{29}$ <br\/> M\u00e0 $\\sqrt{16} > \\sqrt{15} \\\\ \\sqrt{29} < \\sqrt{30} \\Rightarrow -\\sqrt{29} > -\\sqrt{30}$ <br\/> Suy ra $\\sqrt{16} - \\sqrt{29} > \\sqrt{15} - \\sqrt{30}$ <br\/> Hay $ 4 - \\sqrt{29} > \\sqrt{15} - \\sqrt{30} $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A <\/span><\/span> ","column":1}]}],"id_ques":540}],"lesson":{"save":0,"level":2}}