{"segment":[{"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y sai.","select":["A. $|x| = 0$ th\u00ec $x = 0$","B. $|x| = 1\\dfrac{1}{3}$ th\u00ec $x = 1$","C. $|x| = 1,5$ th\u00ec $x = \\pm 1,5$","D. $|x| = 0,4$ th\u00ec $x = \\pm 0,4$"],"hint":"D\u1ef1a v\u00e0o \u0111\u1ecbnh ngh\u0129a gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh tr\u1ecb tuy\u1ec7t \u0111\u1ed1i \u0111\u1ec3 t\u00ecm x.","explain":" <span class='basic_left'> Theo \u0111\u1ecbnh ngh\u0129a gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i ta c\u00f3: <br\/> $ \\begin{align} |x| = 0 \\Leftrightarrow x = 0 \\end{align}$ <br\/> $\\begin{align} |x| = 1\\dfrac{1}{3} \\Leftrightarrow \\left[ \\begin{array}{I} x = 1\\dfrac{1}{3} \\\\ x = -1\\dfrac{1}{3} \\end{array} \\right. \\end{align}$ <br\/> $\\begin{align} |x| = 1,5 \\Leftrightarrow \\left[ \\begin{array}{I} x = 1,5 \\\\ x = -1,5 \\end{array} \\right. \\end{align}$ <br\/> $\\begin{align} |x| = 0,4 \\Leftrightarrow \\left[ \\begin{array}{I} x = 0,4 \\\\ x = -0,4 \\end{array} \\right. \\end{align}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n sai l\u00e0: B<\/span> ","column":2}],"id_ques":871},{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["4"],["-5"]]],"list":[{"point":5,"width":20,"type_input":"","input_hint":[""],"ques":"T\u00ecm $x$ bi\u1ebft: $|x + 0,5| - 4 = \\dfrac{1}{2}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0: $\\left[ \\begin{array}{I} x = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ x = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\end{array} \\right.$ ","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c $|x| = x$ n\u1ebfu $x \\geq 0$ ho\u1eb7c $|x| = -x$ n\u1ebfu $x < 0$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $|x + 0,5| - 4 = \\dfrac{1}{2} \\\\ \\Leftrightarrow |x + 0,5| = \\dfrac{1}{2} + 4 \\\\ \\Leftrightarrow |x + \\dfrac{1}{2}| = \\dfrac{9}{2} \\\\ \\Leftrightarrow \\left[\\begin{array}{I} x + \\dfrac{1}{2} = \\dfrac{9}{2} \\\\ x + \\dfrac{1}{2} = -\\dfrac{9}{2} \\end{array}\\right.$ <br\/> $\\Leftrightarrow \\left[ \\begin{array}{I} x = 4 \\\\ x = -5 \\end{array} \\right.$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0: $4; -5$ <\/span> "}],"id_ques":872},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"\u0110i\u1ec3m $A(3; -9)$ kh\u00f4ng thu\u1ed9c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 n\u00e0o sau \u0111\u00e2y?","select":["A. $y = -x - 6$","B. $y = 3x - 18$","C. $y = x^2 - 18$","D. $y = -3x - 2$"],"hint":"Thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $A$ v\u00e0o c\u00e1c h\u00e0m s\u1ed1 tr\u00ean","explain":" <span class='basic_left'> Thay $A(3; -9)$ v\u00e0o h\u00e0m s\u1ed1 $y = -x - 6$ ta \u0111\u01b0\u1ee3c: <br\/> $-9 = -3 - 6$ <b> (th\u1ecfa m\u00e3n), suy ra $A$ thu\u1ed9c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y = -x - 6$ <\/b> <br\/> Thay $A(3; -9)$ v\u00e0o h\u00e0m s\u1ed1 $y = 3x - 18$ ta \u0111\u01b0\u1ee3c: <br\/> $-9 = 3 . 3 - 18$ <b> (th\u1ecfa m\u00e3n), suy ra $A$ thu\u1ed9c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y = 3x - 18$ <\/b> <br\/> Thay $A(3; -9)$ v\u00e0o h\u00e0m s\u1ed1 $y = x^2 - 18$ ta \u0111\u01b0\u1ee3c: <br\/> $-9 = 3^2 - 18 = 9 - 18$ <b> (th\u1ecfa m\u00e3n), suy ra $A$ thu\u1ed9c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y = x^2 - 18$ <\/b> <br\/> Thay $A(3; -9)$ v\u00e0o h\u00e0m s\u1ed1 $y = -3x - 2$ ta \u0111\u01b0\u1ee3c: <br\/> $-9 = -3.3 - 2 = -11$ <b> (v\u00f4 l\u00fd) <\/b> <br\/> V\u1eady \u0111i\u1ec3m $A(3; -9)$ kh\u00f4ng thu\u1ed9c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y = -3x - 2$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> <br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: <\/span> Ngo\u00e0i c\u00e1ch thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $A$ v\u00e0o t\u1eebng h\u00e0m s\u1ed1 nh\u01b0 tr\u00ean ta c\u0169ng c\u00f3 th\u1ec3 l\u00e0m theo c\u00e1ch v\u1ebd \u0111\u1ed3 th\u1ecb c\u00e1c h\u00e0m s\u1ed1 \u0111\u00f3 xem ch\u00fang c\u00f3 \u0111i qua \u0111i\u1ec3m $A$ kh\u00f4ng? <\/i> ","column":2}],"id_ques":873},{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["-2"]]],"list":[{"point":5,"width":20,"type_input":"","input_hint":[],"ques":" Cho h\u00e0m s\u1ed1 $y = f(x) = ax + b$. Bi\u1ebft $f(0) = -2$ v\u00e0 $f(3) = 1$. T\u00ecm c\u00e1c h\u1ec7 s\u1ed1 $a, b$.<br\/> \u0110\u00e1p \u00e1n l\u00e0: $a$ = _input_ ; $b$ = _input_ ","hint":"","explain":" <span class='basic_left'> <span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Thay $x = 0; y = -2$ v\u00e0o $f(x)$ \u0111\u1ec3 t\u00ecm $b$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> Thay $x = 3; y = 1$ v\u00e0o $f(x)$ \u0111\u1ec3 t\u00ecm m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa $a$ v\u00e0 $b$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> Thay $b$ v\u00e0o bi\u1ec3u th\u1ee9c \u1edf b\u01b0\u1edbc 2 \u0111\u1ec3 t\u00ecm $a$. <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec $f(0) = -2$ n\u00ean ta c\u00f3: $-2 = a . 0 + b$ $\\Rightarrow b = -2$ <br\/> V\u00ec $f(3) = 1$ n\u00ean ta c\u00f3: $1 = a . 3 + b$ (*) <br\/> Thay $b = -2$ v\u00e0o (*), ta \u0111\u01b0\u1ee3c: <br\/> $\\begin{align} 1 - 3a &= -2 \\\\ 3a &= 1 - (-2) \\\\ 3a &= 3 \\\\ a & = 1 \\end{align}$ <br\/> H\u00e0m s\u1ed1 c\u1ea7n t\u00ecm l\u00e0: $y = x - 2$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0: $1; -2$ <\/span> "}],"id_ques":874},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Cho h\u00e0m s\u1ed1 $y = f(x) = ax^2$. Bi\u1ebft $f(\\dfrac{1}{2}) = 1$. T\u00ednh $f(\\dfrac{2}{3})$. <br\/> \u0110\u00e1p \u00e1n l\u00e0: ","select":["A. $1\\dfrac{7}{9}$","B. $\\dfrac{4}{9}$","C. $\\dfrac{2}{9}$","D. $4\\dfrac{1}{9}$"],"hint":"T\u00ecm $a$ r\u1ed3i t\u00ednh $f(\\dfrac{2}{3})$","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b>Thay $x = \\dfrac{1}{2}; y = 1$ v\u00e0o $f(x)$ \u0111\u1ec3 t\u00ecm $a$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh $f(\\dfrac{2}{3})$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> V\u00ec $f(\\dfrac{1}{2}) = 1$ n\u00ean ta c\u00f3: $1 = a . \\left( \\dfrac{1}{2} \\right)^2$ $\\Rightarrow a = 4$ <br\/> Khi \u0111\u00f3 ta c\u00f3 h\u00e0m s\u1ed1 $f(x) = 4x^2$ <br\/> $f(\\dfrac{2}{3}) = 4 . \\left(\\dfrac{2}{3} \\right)^2 = 4 . \\dfrac{4}{9} = \\dfrac{16}{9} = 1\\dfrac{7}{9}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. $1\\dfrac{7}{9}$<\/span> ","column":2}],"id_ques":875},{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"]]],"list":[{"point":5,"width":50,"type_input":"","input_hint":["frac"],"ques":"T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c. <br\/> $\\dfrac{27}{49} . \\left[ \\left( -\\dfrac{25}{27} \\right) - \\left( \\dfrac{1}{3} + \\dfrac{5}{9} \\right) \\right]$ = _input_ ","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh trong ngo\u1eb7c tr\u01b0\u1edbc, ngo\u00e0i ngo\u1eb7c sau <br\/> Trong ngo\u1eb7c th\u1ef1c hi\u1ec7n theo th\u1ee9 t\u1ef1: ( ) --&gt; [ ] <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align} & \\dfrac{27}{49} . \\left[ \\left( -\\dfrac{25}{27} \\right) - \\left( \\dfrac{1}{3} + \\dfrac{5}{9} \\right) \\right] \\\\ &= \\dfrac{27}{49} . \\left[ \\left( -\\dfrac{25}{27} \\right) - \\left( \\dfrac{3}{9} + \\dfrac{5}{9} \\right) \\right] \\\\ &= \\dfrac{27}{49} . \\left( \\dfrac{-25}{27} - \\dfrac{8}{9} \\right) \\\\ &= \\dfrac{27}{49} . \\left( \\dfrac{-25}{27} - \\dfrac{24}{27} \\right) \\\\ &= \\dfrac{27}{49} . \\dfrac{-49}{27} \\\\ &= -1 \\end{align}$"}],"id_ques":876},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"N\u1ebfu $\\left[ \\left( \\dfrac{-2}{5} \\right)^6 \\right]^2 = \\left( \\dfrac{-2}{5} \\right)^x$ th\u00ec $x$ b\u1eb1ng: ","select":["A. $8$","B. $3$","C. $12$","D. $4$"],"hint":"D\u1ef1a v\u00e0o c\u00f4ng th\u1ee9c $a^x = a^y \\Leftrightarrow x = y$ $(a \\neq 0; 1)$ ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> D\u1ef1a v\u00e0o c\u00f4ng th\u1ee9c $(a^m)^n = a^{m.n}$ \u0111\u1ec3 r\u00fat g\u1ecdn v\u1ebf tr\u00e1i <br\/> <b> B\u01b0\u1edbc 2: <\/b> V\u00ec v\u1ebf tr\u00e1i v\u00e0 v\u1ebf ph\u1ea3i l\u00e0 hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 n\u00ean VT = VP khi v\u00e0 ch\u1ec9 khi s\u1ed1 m\u0169 b\u1eb1ng nhau <br\/> Cho hai s\u1ed1 m\u0169 b\u1eb1ng nhau \u0111\u1ec3 t\u00ecm $x$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> Ta c\u00f3: <br\/> $\\left[ \\left( \\dfrac{-2}{5} \\right)^6 \\right]^2 = \\left( \\dfrac{-2}{5} \\right)^{6 . 2} = \\left( \\dfrac{-2}{5} \\right)^{12}$ <br\/> V\u00ec $\\left[ \\left( \\dfrac{-2}{5} \\right)^6 \\right]^2 = \\left( \\dfrac{-2}{5} \\right)^x$ <br\/> $\\Rightarrow \\left( \\dfrac{-2}{5} \\right)^{12} = \\left( \\dfrac{-2}{5} \\right)^x$ <br\/> $\\Leftrightarrow x = 12$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. $12$<\/span> ","column":2}],"id_ques":877},{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["12"]]],"list":[{"point":5,"width":50,"type_input":"","input_hint":["frac"],"ques":"T\u00ecm $x$ bi\u1ebft: <br\/> $\\dfrac{2}{3} - \\left( \\dfrac{3}{4} - x \\right) = \\sqrt{\\dfrac{1}{9}}$ <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> $x = $ <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"Khai c\u0103n v\u1ebf ph\u1ea3i r\u1ed3i t\u00ecm $x$","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Khai c\u0103n v\u1ebf ph\u1ea3i <br\/> <b> B\u01b0\u1edbc 2: <\/b> B\u1ecf ng\u1eb7c \u1edf v\u1ebf tr\u00e1i (l\u01b0u \u00fd \u0111\u1ed5i d\u1ea5u c\u00e1c h\u1ea1ng t\u1eed trong ngo\u1eb7c v\u00ec tr\u01b0\u1edbc d\u1ea5u ngo\u1eb7c l\u00e0 d\u1ea5u (-)) <br\/> <b> B\u01b0\u1edbc 3: <\/b> Th\u1ef1c hi\u1ec7n bi\u1ebfn \u0111\u1ed5i v\u00e0 t\u00ecm $x$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align} & \\dfrac{2}{3} - \\left( \\dfrac{3}{4} - x \\right) = \\sqrt{\\frac{1}{9}} \\\\ & \\Leftrightarrow \\dfrac{2}{3} - \\left( \\dfrac{3}{4} - x \\right) = \\dfrac{1}{3} \\\\ & \\Leftrightarrow \\dfrac{2}{3} - \\dfrac{3}{4} + x = \\dfrac{1}{3} \\\\ &\\Leftrightarrow x - \\dfrac{1}{12} = \\dfrac{1}{3} \\\\ &\\Leftrightarrow x = \\dfrac{1}{3} + \\dfrac{1}{12} \\\\ &\\Leftrightarrow x = \\dfrac{5}{12} \\end{align}$"}],"id_ques":878},{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-59479"],["2565"]]],"list":[{"point":5,"width":70,"type_input":"","input_hint":["frac"],"ques":"T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: <br\/> $\\dfrac{\\left( 1\\dfrac{2}{3} - 2\\dfrac{3}{4} - 3\\dfrac{4}{5} \\right). \\left( -4\\dfrac{5}{6} \\right)}{5\\dfrac{6}{7} - 6\\dfrac{7}{8}}$ <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"\u0110\u1ed5i c\u00e1c h\u1ed7n s\u1ed1 ra ph\u00e2n s\u1ed1 sau \u0111\u00f3 quy \u0111\u1ed3ng v\u00e0 th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u1ed5i c\u00e1c h\u1ed7n s\u1ed1 ra ph\u00e2n s\u1ed1 <br\/> <b> B\u01b0\u1edbc 2: <\/b> Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 c\u00e1c ph\u00e2n s\u1ed1 <br\/> <b> B\u01b0\u1edbc 3: <\/b> Bi\u1ebfn \u0111\u1ed5i v\u00e0 t\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align} & \\dfrac{\\left( 1\\dfrac{2}{3} - 2\\dfrac{3}{4} - 3\\dfrac{4}{5} \\right). \\left( -4\\dfrac{5}{6} \\right)}{5\\dfrac{6}{7} - 6\\dfrac{7}{8}} \\\\ &= \\dfrac{\\left( \\dfrac{5}{3} - \\dfrac{11}{4} - \\dfrac{19}{5} \\right). \\left( \\dfrac{-29}{6} \\right)}{\\dfrac{41}{7} - \\dfrac{55}{8}} \\\\ &= \\dfrac{\\dfrac{5 . 4 . 5 - 11 . 3 . 5 - 19 . 3 . 4}{3 . 4 . 5} . \\dfrac{-29}{6}}{\\dfrac{41 . 8 - 55 . 7}{7 . 8}} \\\\ &= \\dfrac{-293}{60} . \\dfrac{-29}{6} : \\dfrac{-57}{56} \\\\ &= \\dfrac{-293}{60} . \\dfrac{-29}{6} . \\dfrac{56}{-57} \\\\ &= \\dfrac{-293}{15} . \\dfrac{-29}{3} . \\dfrac{7}{-57} \\\\ &= \\dfrac{-59479}{2565} \\end{align}$"}],"id_ques":879},{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-6"],["-8"]]],"list":[{"point":5,"width":20,"type_input":"","input_hint":[],"ques":"T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$, bi\u1ebft: <br\/> $\\dfrac{x}{y} = \\dfrac{3}{4}$ v\u00e0 $x + y = -14$ <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> $x = $ _input_ ; $y =$ _input_","hint":"S\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c v\u00e0 d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau","explain":" Ta c\u00f3: <br\/> $\\dfrac{x}{y} = \\dfrac{3}{4}$ $\\Rightarrow$ $\\dfrac{x}{3} = \\dfrac{y}{4}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{x}{3} = \\dfrac{y}{4} = \\dfrac{x + y}{3 + 4} = \\dfrac{-14}{7} = -2$ <br\/> $\\Rightarrow$ $x = -2 . 3 = -6$; $y = -2 . 4 = -8$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0: $-6; -8$ <\/span> "}],"id_ques":880},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho ba s\u1ed1 $x,y,z$ bi\u1ebft r\u1eb1ng ch\u00fang t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi $3; 5; 7$ v\u00e0 $y\u2212x = 10$. T\u00ecm ba s\u1ed1 \u0111\u00f3? ","select":["A. $15; 21; 28$","B. $15; 25; 35$","C. $17; 27; 37$","D. $17; 25; 32$"],"hint":"\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c v\u00e0 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> B\u01b0\u1edbc 1: <\/b> Vi\u1ebft t\u1ec9 l\u1ec7 th\u1ee9c c\u1ee7a $x, y, z$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, k\u1ebft h\u1ee3p \u0111i\u1ec1u ki\u1ec7n $y - x = 10$ \u0111\u1ec3 t\u00ecm $x, y, z$ <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> V\u00ec ba s\u1ed1 $x, y, z$ t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi $3; 5; 7$ n\u00ean ta c\u00f3: $\\dfrac{x}{3} = \\dfrac{y}{5} = \\dfrac{z}{7}$ <br\/> Theo b\u00e0i ra ta c\u00f3: $y - x = 10$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{x}{3} = \\dfrac{y}{5} = \\dfrac{z}{7} = \\dfrac{y - x}{5 - 3} = \\dfrac{10}{2} = 5$ <br\/> $\\Rightarrow$ $\\begin{cases} x = 3 . 5 = 15 \\\\ y = 5 . 5 = 25 \\\\ z = 7 . 5 = 35 \\end{cases}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. $15; 25; 35$<\/span> ","column":2}],"id_ques":881},{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"],["8"]]],"list":[{"point":5,"width":20,"type_input":"","input_hint":[],"ques":"T\u00ecm hai s\u1ed1 d\u01b0\u01a1ng $x$, $y$, bi\u1ebft: <br\/> $4x = 3y$ v\u00e0 $x^2 + y^2 = 100$ <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> $x = $ _input_ ; $y =$ _input_","hint":"S\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c v\u00e0 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> B\u01b0\u1edbc 1: <\/b> T\u1eeb \u0111\u1eb3ng th\u1ee9c $4x = 3y$ ta r\u00fat ra t\u1ec9 l\u1ec7 th\u1ee9c c\u1ee7a $x$ v\u00e0 $y$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> B\u00ecnh ph\u01b0\u01a1ng hai v\u1ebf c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c <br\/> <b> B\u01b0\u1edbc 3: <\/b> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau t\u00ecm h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 sau \u0111\u00f3 t\u00ecm $x$ v\u00e0 $y$ <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $4x = 3y$ $\\Rightarrow$ $\\dfrac{x}{3} = \\dfrac{y}{4}$ $\\Rightarrow$ $\\dfrac{x^2}{9} = \\dfrac{y^2}{16}$ (b\u00ecnh ph\u01b0\u01a1ng hai v\u1ebf) <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{x^2}{9} = \\dfrac{y^2}{16} = \\dfrac{x^2 + y^2}{9 + 16} = \\dfrac{100}{25} = 4$ <br\/> $\\Rightarrow$ $x^2 = 9 . 4 = 36$ $\\Leftrightarrow x = \\pm 6$ <br\/> $y^2 = 16 . 4 = 64 \\Leftrightarrow y = \\pm 8$ <br\/> Gi\u00e1 tr\u1ecb d\u01b0\u01a1ng c\u1ee7a $x$ v\u00e0 $y$ c\u1ea7n t\u00ecm l\u00e0 $x = 6$; $y = 8$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0: $6; 8$ <\/span> "}],"id_ques":882},{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["140"]]],"list":[{"point":5,"width":20,"type_input":"","input_hint":[],"ques":" Hai \u00f4 t\u00f4 c\u00f9ng kh\u1edfi h\u00e0nh t\u1eeb \u0111i\u1ec3m A v\u00e0 B. Xe th\u1ee9 nh\u1ea5t \u0111i t\u1eeb A \u0111\u1ebfn B h\u1ebft $8$ gi\u1edd, xe th\u1ee9 hai \u0111i t\u1eeb B \u0111\u1ebfn A m\u1ea5t $6$ gi\u1edd. Khi g\u1eb7p nhau xe th\u1ee9 hai \u0111i \u0111\u01b0\u1ee3c qu\u00e3ng \u0111\u01b0\u1eddng d\u00e0i h\u01a1n xe th\u1ee9 nh\u1ea5t 20km. T\u00ednh chi\u1ec1u d\u00e0i qu\u00e3ng \u0111\u01b0\u1eddng AB. <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> _input_ km ","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> G\u1ecdi qu\u00e3ng \u0111\u01b0\u1eddng m\u1ed7i xe \u0111i \u0111\u01b0\u1ee3c \u0111\u1ebfn khi g\u1eb7p nhau l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x$, $y$ v\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng AB l\u00e0 S <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh v\u1eadn t\u1ed1c m\u1ed7i xe theo S <br\/> <b> B\u01b0\u1edbc 3: <\/b> Do hai xe c\u00f9ng xu\u1ea5t ph\u00e1t n\u00ean th\u1eddi gian m\u1ed7i xe \u0111i \u0111\u1ebfn khi g\u1eb7p nhau l\u00e0 b\u1eb1ng nhau t\u1eeb \u0111\u00f3 ta c\u00f3 t\u1ec9 l\u1ec7 th\u1ee9c <br\/> <b> B\u01b0\u1edbc 4: <\/b> T\u00ecm m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa $x$ v\u00e0 $y$ d\u1ef1a v\u00e0o \u0111i\u1ec1u ki\u1ec7n b\u00e0i cho, k\u1ebft h\u1ee3p v\u1edbi t\u1ec9 l\u1ec7 th\u1ee9c \u1edf tr\u00ean \u0111\u1ec3 t\u00ecm $x$ v\u00e0 $y$ t\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c qu\u00e3ng \u0111\u01b0\u1eddng AB <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi $x$ v\u00e0 $y$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng m\u1ed7i xe \u0111i \u0111\u01b0\u1ee3c khi g\u1eb7p nhau ($x > 0, y > 20$) <br\/> G\u1ecdi S l\u00e0 \u0111\u1ed9 d\u00e0i qu\u00e3ng \u0111\u01b0\u1eddng AB <br\/> Khi \u0111\u00f3, v\u1eadn t\u1ed1c c\u1ee7a xe th\u1ee9 nh\u1ea5t l\u00e0: $\\dfrac{S}{8}$ <br\/> V\u1eadn t\u1ed1c c\u1ee7a xe th\u1ee9 hai l\u00e0: $\\dfrac{S}{6}$ <br\/> Do hai xe c\u00f9ng xu\u1ea5t ph\u00e1t n\u00ean \u0111\u1ebfn khi g\u1eb7p nhau th\u00ec th\u1eddi gian m\u1ed7i xe \u0111i l\u00e0 nh\u01b0 nhau n\u00ean ta c\u00f3: <br\/> $\\dfrac{x}{\\dfrac{S}{8}} = \\dfrac{y}{\\dfrac{S}{6}}$ do \u0111\u00f3 $8x = 6y$ <br\/> V\u00ec xe th\u1ee9 hai \u0111i \u0111\u01b0\u1ee3c qu\u00e3ng \u0111\u01b0\u1eddng d\u00e0i h\u01a1n xe th\u1ee9 nh\u1ea5t $20$km n\u00ean ta c\u00f3: $y - x = 20$ $\\Rightarrow$ $y = x + 20$ <br\/> $\\Rightarrow$ $8x = 6 . (x + 20)$ $\\Rightarrow$ $2x = 120$ $\\Rightarrow$ $x = 60$ <br\/> $\\Rightarrow$ $y = 60 + 20 = 80$ $\\Rightarrow$ S $= 60 + 80 = 140$(km) <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0: $140$ <\/span> "}],"id_ques":883},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Cho bi\u1ebft $y$ t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi $x$ theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 l\u00e0 $0,8$ v\u00e0 $x$ t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi $z$ theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 l\u00e0 $0,5$. Khi \u0111\u00f3, $y$ t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi $z$ theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 l\u00e0: ","select":["A. $0,625$","B. $1,3$","C. $0,4$","D. $1,6$"],"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 bi\u1ec3u th\u1ee9c th\u1ec3 hi\u1ec7n m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa $y$ v\u00e0 $x$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> Vi\u1ebft bi\u1ec3u th\u1ee9c th\u1ec3 hi\u1ec7n m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa $x$ v\u00e0 $z$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u1eeb hai bi\u1ec3u th\u1ee9c tr\u00ean vi\u1ebft bi\u1ec3u th\u1ee9c th\u1ec3 hi\u1ec7n m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa $y$ v\u00e0 $z$ <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> V\u00ec $y$ t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi $x$ theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 l\u00e0 $0,8$ n\u00ean ta c\u00f3: $xy = 0,8$ hay $y = \\dfrac{0,8}{x}$ (1) <br\/> $x$ t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi $z$ theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 l\u00e0 $0,5$ n\u00ean ta c\u00f3: $xz = 0,5$ hay $x = \\dfrac{0,5}{z}$ (2) <br\/> Thay (2) v\u00e0o (1) ta \u0111\u01b0\u1ee3c: $y = \\dfrac{0,8}{\\dfrac{0,5}{z}} = \\dfrac{0,8.z}{0,5} = 1,6z $ <br\/> N\u00ean $y$ t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi $z$ theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 l\u00e0 $1,6$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. $1,6$<\/span> ","column":2}],"id_ques":884},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Trong c\u00e1c ph\u00e2n s\u1ed1 sau, ph\u00e2n s\u1ed1 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n l\u00e0: ","select":["A. $\\dfrac{34}{240}$","B. $\\dfrac{15}{260}$","C. $\\dfrac{24}{300}$","D. $\\dfrac{6}{180}$"],"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 c\u00e1c ph\u00e2n s\u1ed1 tr\u00ean v\u1ec1 ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n <br\/> <b> B\u01b0\u1edbc 2: <\/b> Ph\u00e2n t\u00edch m\u1eabu s\u1ed1 c\u1ee7a c\u00e1c ph\u00e2n s\u1ed1 (sau khi r\u00fat g\u1ecdn) th\u00e0nh t\u00edch c\u00e1c th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 <br\/> <b> B\u01b0\u1edbc 3: <\/b> X\u00e9t m\u1eabu s\u1ed1 c\u1ee7a c\u00e1c ph\u00e2n s\u1ed1 \u0111\u00f3 <br\/> N\u1ebfu m\u1eabu d\u01b0\u01a1ng v\u00e0 kh\u00f4ng c\u00f3 \u01b0\u1edbc nguy\u00ean t\u1ed1 kh\u00e1c $2$ v\u00e0 $5$ th\u00ec ph\u00e2n s\u1ed1 \u0111\u00f3 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n <br\/> N\u1ebfu m\u1eabu s\u1ed1 d\u01b0\u01a1ng c\u00f3 \u01b0\u1edbc nguy\u00ean t\u1ed1 kh\u00e1c $2$ v\u00e0 $5$ th\u00ec ph\u00e2n s\u1ed1 \u0111\u00f3 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> X\u00e9t ph\u00e2n s\u1ed1 $\\dfrac{34}{240} = \\dfrac{17}{120}$ v\u00ec $120 = 2^3 . 3 . 5$, m\u1eabu l\u00e0 $120$ c\u00f3 m\u1ed9t \u01b0\u1edbc nguy\u00ean t\u1ed1 l\u00e0 $3$ kh\u00e1c $2$ v\u00e0 $5$ <br\/> N\u00ean ph\u00e2n s\u1ed1 $\\dfrac{17}{20}$ vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n <br\/> $\\dfrac{15}{260} = \\dfrac{3}{52}$ v\u00ec $52 = 2^2 . 13$, m\u1eabu l\u00e0 $52$ c\u00f3 m\u1ed9t \u01b0\u1edbc nguy\u00ean t\u1ed1 l\u00e0 $13$ kh\u00e1c $2$ v\u00e0 $5$ n\u00ean <br\/> N\u00ean ph\u00e2n s\u1ed1 $\\dfrac{3}{52}$ vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n <br\/> $\\dfrac{24}{300} = \\dfrac{2}{25}$, v\u00ec $25 = 5^2$ ch\u1ec9 c\u00f3 \u01b0\u1edbc nguy\u00ean t\u1ed1 l\u00e0 $5$ <br\/> N\u00ean ph\u00e2n s\u1ed1 \u0111\u00e3 cho vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n <br\/> $\\dfrac{6}{180} = \\dfrac{1}{30}$, v\u00ec m\u1eabu $30 = 2 . 3 . 5$ c\u00f3 m\u1ed9t \u01b0\u1edbc nguy\u00ean t\u1ed1 l\u00e0 $3$ kh\u00e1c $2$ v\u00e0 $5$ <br\/> N\u00ean ph\u00e2n s\u1ed1 $\\dfrac{1}{30}$ vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. $\\dfrac{24}{300}$<\/span> ","column":2}],"id_ques":885},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y, bi\u1ebft $xx' \/\/ yy'$, $\\widehat{zBy'} = 115^{o}$. Khi \u0111\u00f3 s\u1ed1 \u0111o $\\widehat{BAx}$ b\u1eb1ng: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/D7kiemtrahocki1/lv3/img\/H7kiemtrahocki1_01.png' \/><\/center> ","select":["A. $115^{o}$","B. $65^{o}$","C. $25^{o}$","D. $75^{o}$"],"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 \u0111o g\u00f3c $yBz'$ t\u00ednh ch\u1ea5t hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh s\u1ed1 \u0111o g\u00f3c $BAx$ d\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t hai g\u00f3c trong c\u00f9ng ph\u00eda <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> Ta c\u00f3: <br\/> $\\widehat{yBz'} = \\widehat{zBy'} = 115^{o}$ (\u0111\u1ed1i \u0111\u1ec9nh) <br\/> $\\widehat{BAx} + \\widehat{yBz'} = 180^{o}$ (hai g\u00f3c trong c\u00f9ng ph\u00eda) <br\/> $\\begin{align} \\Rightarrow \\widehat{BAx} & = 180^{o} - \\widehat{yBz'} \\\\ &= 180^{o} - 115^{o} \\\\ &= 65^{o} \\end{align}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. $65^{o}$<\/span> ","column":2}],"id_ques":886},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y, bi\u1ebft $a \/\/ b$. S\u1ed1 \u0111o c\u1ee7a g\u00f3c $\\widehat{B_{1}}$ b\u1eb1ng: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/D7kiemtrahocki1/lv3/img\/H7kiemtrahocki1_02.png' \/><\/center> ","select":["A. $140^{o}$","B. $50^{o}$","C. $130^{o}$","D. $75^{o}$"],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> Qua $H$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng $cc'$ song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng $a$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh s\u1ed1 \u0111o g\u00f3c $\\widehat{AHc}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh s\u1ed1 \u0111o g\u00f3c $\\widehat{B_{1}}$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/D7kiemtrahocki1/lv3/img\/H7kiemtrahocki1_02a.png' \/><\/center> <br\/> Qua $H$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng $cc'$ song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng a. <br\/> V\u00ec $a \/\/ b $ v\u00e0 $a \/\/ cc'$ $\\Rightarrow$ $b \/\/ cc'$ <br\/> $\\Rightarrow$ $\\widehat{cHA} = \\widehat{HAa} = 40^{o}$ (so le trong) <br\/> $\\widehat{cHB} = \\widehat{B_{1}}$ (so le trong) (1) <br\/> M\u1eb7t kh\u00e1c ta c\u00f3: $\\widehat{cHA} + \\widehat{cHB} = \\widehat{AHB} = 90^{o}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\begin{align} \\Rightarrow \\widehat{cHB} &= 90^{o} - \\widehat{cHA} \\\\ & = 90^{o} - 40^{o} \\\\ &= 50^{o} (2) \\end{align}$ <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\widehat{B_{1}} = 50^{o}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. $50^{o}$<\/span> ","column":2}],"id_ques":887},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"M\u1ed9t tam gi\u00e1c c\u00e2n c\u00f3 g\u00f3c \u1edf \u0111\u00e1y b\u1eb1ng $62^{o}$. G\u00f3c \u1edf \u0111\u1ec9nh s\u1ebd c\u00f3 s\u1ed1 \u0111o l\u00e0: ","select":["A. $62^{o}$","B. $118^{o}$","C. $28^{o}$","D. $56^{o}$"],"hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c","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 \u0111o g\u00f3c \u1edf \u0111\u00e1y c\u00f2n l\u1ea1i <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh s\u1ed1 \u0111o g\u00f3c \u1edf \u0111\u1ec9nh d\u1ef1a v\u00e0o \u0111\u1ecbnh l\u00fd t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/D7kiemtrahocki1/lv3/img\/H7kiemtrahocki1_03.png' \/><\/center> <br\/> V\u00ec tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A$ v\u00e0 c\u00f3 $\\widehat{B} = 62^{o}$ <br\/> $\\Rightarrow \\widehat{C} = \\widehat{B} = 62^{o}$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> Theo \u0111\u1ecbnh l\u00fd t\u1ed5ng 3 g\u00f3c trong m\u1ed9t tam gi\u00e1c ta c\u00f3: <br\/> $ \\widehat{A} + \\widehat{B} + \\widehat{C} = 180^{o}$ <br\/> $\\begin{align} \\Rightarrow \\widehat{A} & = 180^{o} - \\widehat{B} - \\widehat{C} \\\\ &= 180^{o} - 62^{o} - 62^{o} \\\\ &= 56^{o} \\end{align}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. $56^{o}$<\/span> ","column":2}],"id_ques":888},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Gi\u1ea3 thi\u1ebft n\u00e0o d\u01b0\u1edbi \u0111\u00e2y suy ra \u0111\u01b0\u1ee3c $\\triangle{MNP} = \\triangle{ABC}$.","select":["A. $\\widehat{M} = \\widehat{A}; \\widehat{N} = \\widehat{B}; \\widehat{P} = \\widehat{C}$","B. $\\widehat{M} = \\widehat{A}; MP=AB ; NP=BC $","C. $\\widehat{M} = \\widehat{A}; MN =AB; MP = AC$","D. $\\widehat{M} = \\widehat{A}; MN =AB; NP = BC$"],"hint":"D\u1ef1a v\u00e0o tr\u01b0\u1eddng h\u1ee3p b\u1eb1ng nhau th\u1ee9 hai c\u1ee7a tam gi\u00e1c","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> V\u1ebd h\u00ecnh minh h\u1ecda cho t\u1eebng tr\u01b0\u1eddng h\u1ee3p <br\/> <b> B\u01b0\u1edbc 2: <\/b> D\u1ef1a v\u00e0o tr\u01b0\u1eddng h\u1ee3p b\u1eb1ng nhau th\u1ee9 hai c\u1ee7a tam gi\u00e1c \u0111\u1ec3 ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> \u0110\u00e1p \u00e1n A sai v\u00ec: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/D7kiemtrahocki1/lv3/img\/H7kiemtrahocki1_04.png' \/><\/center> <br\/> \u0110\u00e1p \u00e1n B sai v\u00ec theo tr\u01b0\u1eddng h\u1ee3p b\u1eb1ng nhau th\u1ee9 hai c\u1ee7a hai tam gi\u00e1c th\u00ec: N\u1ebfu hai c\u1ea1nh v\u00e0 m\u1ed9t g\u00f3c xen gi\u1eefa c\u1ee7a tam gi\u00e1c n\u00e0y l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa c\u1ee7a tam gi\u00e1c kia th\u00ec hai tam gi\u00e1c b\u1eb1ng nhau (b\u00e0i n\u00e0y g\u00f3c $A$ v\u00e0 g\u00f3c $M$ kh\u00f4ng ph\u1ea3i l\u00e0 g\u00f3c xen gi\u1eefa) <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/D7kiemtrahocki1/lv3/img\/H7kiemtrahocki1_05.png' \/><\/center> <br\/> \u0110\u00e1p \u00e1n C \u0111\u00fang v\u00ec: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/D7kiemtrahocki1/lv3/img\/H7kiemtrahocki1_06.png' \/><\/center> <br\/> X\u00e9t $\\triangle{ABC}$ v\u00e0 $\\triangle{MNP}$ c\u00f3: <br\/> $\\begin{cases} \\widehat{A} = \\widehat{M} (gt) \\\\ MN = AB(gt) \\\\ MP = AC (gt) \\end{cases}$ <br\/> $\\Rightarrow \\triangle{ABC} = \\triangle{MNP}$ (c.g.c) <br\/> \u0110\u00e1p \u00e1n D sai v\u00ec theo tr\u01b0\u1eddng h\u1ee3p b\u1eb1ng nhau th\u1ee9 hai c\u1ee7a hai tam gi\u00e1c (\u1edf b\u00e0i n\u00e0y g\u00f3c $A$ v\u00e0 g\u00f3c $M$ kh\u00f4ng ph\u1ea3i l\u00e0 g\u00f3c xen gi\u1eefa) <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/D7kiemtrahocki1/lv3/img\/H7kiemtrahocki1_07.png' \/><\/center> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C <\/span> ","column":2}],"id_ques":889},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A$. Tr\u00ean c\u1ea1nh $AB$ l\u1ea5y \u0111i\u1ec3m $D$, tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $CA$ l\u1ea5y \u0111i\u1ec3m $E$ sao cho $BD = CE$. K\u1ebb $DH$ vu\u00f4ng g\u00f3c v\u1edbi $BC$ t\u1ea1i $H$, $EK$ vu\u00f4ng g\u00f3c v\u1edbi $BC$ t\u1ea1i $K$. G\u1ecdi $I$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $DE$ v\u00e0 $BC$. Khi \u0111\u00f3 $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $DE$ <b> \u0111\u00fang <\/b> hay <b> sai <\/b>?","select":["A. \u0110\u00fang","B. Sai"],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> Ph\u00e2n t\u00edch b\u00e0i to\u00e1n: <\/b> <br\/> \u0110\u1ec3 c\u00f3 I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $DE$ ta c\u1ea7n ch\u1ee9ng minh $ID = IE$ $\\Rightarrow$ c\u1ea7n ch\u1ee9ng minh $\\triangle{HDI} = \\triangle{KEI}$ $\\Rightarrow$ c\u1ea7n ch\u1ee9ng minh $DH = EK$ $\\Rightarrow$ c\u1ea7n ch\u1ee9ng minh $\\triangle{HBD} = \\triangle{KCE}$ $\\Rightarrow$ c\u1ea7n ch\u1ee9ng minh $\\widehat{ABC} = \\widehat{ECK}$ <br\/> <b> B\u01b0\u1edbc 1: <\/b> Ch\u1ee9ng minh $DH = EK$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> Ch\u1ee9ng minh $\\triangle{HDI} = \\triangle{KEI}$ $\\Rightarrow DI = IE$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i: <\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/D7kiemtrahocki1/lv3/img\/H7kiemtrahocki1_08.png' \/><\/center> <br\/> Ta c\u00f3: <br\/> $\\triangle{ABC}$ c\u00e2n t\u1ea1i $A$ $\\Rightarrow \\widehat{ABC} = \\widehat{ACB}$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) (1) <br\/> M\u00e0 $\\widehat{ACB} = \\widehat{ECK}$ (\u0111\u1ed1i \u0111\u1ec9nh) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\widehat{ABC} = \\widehat{ECK}$ <br\/> X\u00e9t $\\triangle{HBD}$ v\u00e0 $\\triangle{KCE}$ c\u00f3: <br\/> $\\begin{cases} BD = CE (gt) \\\\ \\widehat{ABC} = \\widehat{ECK} (cmt) \\\\ \\widehat{BHD} = \\widehat{EKC} = 90^{o} (gt) \\end{cases}$ <br\/> $\\Rightarrow \\triangle{HBD} = \\triangle{KCE}$ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow DH = EK$ (c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> X\u00e9t hai tam gi\u00e1c vu\u00f4ng $HDI$ v\u00e0 $KEI$ c\u00f3: <br\/> $ DH = EK (cmt)$ <br\/> $\\widehat{HID} = \\widehat{KIE} (\\text{\u0111\u1ed1i} \\hspace{0,2cm} \\text{\u0111\u1ec9nh}) $ <br\/> $\\Rightarrow$ $\\widehat{HDI} = \\widehat{KEI}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{HID}$) <br\/> $\\Rightarrow$ $\\triangle{HDI} = \\triangle{KEI}$ (c\u1ea1nh g\u00f3c vu\u00f4ng - g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow DI = EI$ hay $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $DE$ <br\/> <span class='basic_pink'> V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0110\u00daNG <\/span> ","column":1}],"id_ques":890}],"id_ques":0}],"lesson":{"save":1,"level":3,"time":44}}