{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" <span class='basic_left'> <i>Vi\u1ebft bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 bi\u1ec3u th\u1ecb di\u1ec5n \u0111\u1ea1t sau: <\/i> N\u1eeda t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai s\u1ed1 $a$ v\u00e0 $b$ <\/span>","select":["A. $\\dfrac{(a+b)^2}{2}$","B. $\\dfrac{a^2+b^2}{2}$","C. $(a+b)^2$","D. $a^2+b^2$"],"explain":"<span class='basic_left'>Ta di\u1ec5n \u0111\u1ea1t c\u00e1c bi\u1ec3u th\u1ee9c \u1edf t\u1eebng \u0111\u00e1p \u00e1n: <br\/> $\\dfrac{(a+b)^2}{2}$ l\u00e0 ''n\u1eeda b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a t\u1ed5ng hai s\u1ed1 $a$ v\u00e0 $b$'' <br\/> $\\dfrac{a^2+b^2}{2}$ l\u00e0 ''n\u1eeda t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai s\u1ed1 $a$ v\u00e0 $b$'' <br\/> $(a+b)^2$ l\u00e0 ''b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a t\u1ed5ng hai s\u1ed1 $a$ v\u00e0 $b$'' <br\/> $a^2+b^2$ l\u00e0 ''t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai s\u1ed1 $a$ v\u00e0 $b$'' <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span><\/span>","column":2}]}],"id_ques":1071},{"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":" <span class='basic_left'> Bi\u1ec3u th\u1ee9c n\u00e0o sau \u0111\u00e2y bi\u1ec3u th\u1ecb chu vi h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 hai c\u1ea1nh d\u00e0i $x$ v\u00e0 $y:$ <\/span>","select":["A. $xy$","B. $4xy$","C. $2xy$","D. $2(x+y)$"],"hint":"Chu vi h\u00ecnh ch\u1eef nh\u1eadt b\u1eb1ng hai l\u1ea7n t\u1ed5ng chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng c\u1ee7a n\u00f3","explain":"<span class='basic_left'>Chu vi h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 hai c\u1ea1nh l\u00e0 $x$ v\u00e0 $y$ vi\u1ebft th\u00e0nh bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 l\u00e0: $2(x+y)$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span><\/span>","column":4}]}],"id_ques":1072},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0111\u00e2y \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Bi\u1ec3u th\u1ee9c $5a-6b$ di\u1ec5n \u0111\u1ea1t b\u1eb1ng l\u1eddi l\u00e0: <b> Hi\u1ec7u c\u1ee7a $5$ l\u1ea7n $a$ v\u1edbi $6$ l\u1ea7n $b$ <\/b> <\/span>","select":["\u0110\u00fang","Sai "],"explain":"<span class='basic_left'> Kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0111\u00fang. <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span><\/span>","column":2}]}],"id_ques":1073},{"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":" <span class='basic_left'> Bi\u1ec3u th\u1ee9c $\\dfrac{x+y}{x-y}$ di\u1ec5n \u0111\u1ea1t b\u1eb1ng l\u1eddi l\u00e0: <\/span>","select":["A. T\u00edch c\u1ee7a t\u1ed5ng hai s\u1ed1 $x$ v\u00e0 $y$ v\u1edbi hi\u1ec7u c\u1ee7a ch\u00fang","B. Th\u01b0\u01a1ng c\u1ee7a t\u1ed5ng hai s\u1ed1 $x$ v\u00e0 $y$ v\u1edbi hi\u1ec7u c\u1ee7a ch\u00fang","C. Th\u01b0\u01a1ng c\u1ee7a t\u00edch hai s\u1ed1 $x$ v\u00e0 $y$ v\u1edbi hi\u1ec7u c\u1ee7a ch\u00fang","D. T\u00edch c\u1ee7a th\u01b0\u01a1ng hai s\u1ed1 $x$ v\u00e0 $y$ v\u1edbi hi\u1ec7u c\u1ee7a ch\u00fang"],"explain":"<span class='basic_left'> Bi\u1ec3u th\u1ee9c $\\dfrac{x+y}{x-y}$ di\u1ec5n \u0111\u1ea1t b\u1eb1ng l\u1eddi l\u00e0: <b> Th\u01b0\u01a1ng c\u1ee7a t\u1ed5ng hai s\u1ed1 $x$ v\u00e0 $y$ v\u1edbi hi\u1ec7u c\u1ee7a ch\u00fang <\/b> <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span><\/span>","column":1}]}],"id_ques":1074},{"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":" <span class='basic_left'> Bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 bi\u1ec3u th\u1ecb <i>''T\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng hai s\u1ed1 l\u1ebb li\u00ean ti\u1ebfp''<\/i> l\u00e0: <\/span>","select":["A. $(k+1)^2+(k+2)^2$ v\u1edbi $k\\in \\mathbb{Z}$","B. $(2k+1)^2+(2k+2)^2$ v\u1edbi $k\\in \\mathbb{Z}$","C. $(k+1)^2+(k+3)^2$ v\u1edbi $k\\in \\mathbb{Z}$","D. $(2k+1)^2+(2k+3)^2$ v\u1edbi $k\\in \\mathbb{Z}$"],"explain":"<span class='basic_left'> V\u1edbi $k\\in \\mathbb{Z}$ th\u00ec hai s\u1ed1 l\u1ebb li\u00ean ti\u1ebfp c\u00f3 d\u1ea1ng: $2k+1$ v\u00e0 $2k+3$ <br\/> Bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 bi\u1ec3u th\u1ecb <i>''T\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng hai s\u1ed1 l\u1ebb li\u00ean ti\u1ebfp''<\/i> l\u00e0: $(2k+1)^2+(2k+3)^2$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span><\/span>","column":2}]}],"id_ques":1075},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","f","t"]],"list":[{"point":5,"image":"","col_name":["Kh\u1eb3ng \u0111\u1ecbnh","\u0110\u00fang","Sai"],"arr_ques":[" Bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 bi\u1ec3u th\u1ecb <i> ''T\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng hai s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp''<\/i> l\u00e0: $n^2+(n+1)^2$ v\u1edbi $n\\in \\mathbb{N}$ ","Bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 bi\u1ec3u th\u1ecb <i> ''M\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean chia cho $3$ d\u01b0 $1$''<\/i> l\u00e0: $n:3+1$ v\u1edbi $n\\in \\mathbb{N}$","Bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 bi\u1ec3u th\u1ecb <i> ''T\u00edch hai s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp''<\/i> l\u00e0: $n(n+1)$ v\u1edbi $n\\in \\mathbb{N}$"],"hint":"","explain":[" <span class='basic_left'>\u0110\u00fang, v\u00ec: G\u1ecdi hai s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp l\u00e0 $n$ v\u00e0 $n+1$ v\u1edbi $n\\in \\mathbb{N}$ <br\/> Do \u0111\u00f3, t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng hai s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp l\u00e0 $n^2+(n+1)^2$<\/span>"," <br\/> <span class='basic_left'>Sai, v\u00ec: Bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 bi\u1ec3u th\u1ecb <i> ''M\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean chia cho $3$ d\u01b0 $1$''<\/i> l\u00e0: $n=3k+1$ v\u1edbi $k\\in \\mathbb{N}$<\/span> ","<br\/> <span class='basic_left'>\u0110\u00fang, v\u00ec: G\u1ecdi hai s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp l\u00e0 $n$ v\u00e0 $n+1$ v\u1edbi $n\\in \\mathbb{N}$ <br\/> Do \u0111\u00f3, t\u00edch hai s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp l\u00e0 $n(n+1)$<\/span>"]}]}],"id_ques":1076},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $B=\\dfrac{{{x}^{2}}+2xy+{{y}^{2}}}{x-y}$ t\u1ea1i $x=3;y=-1$ l\u00e0 _input_ <\/span>","hint":" Thay gi\u00e1 tr\u1ecb c\u1ee7a $x;y$ v\u00e0o bi\u1ec3u th\u1ee9c $B$ r\u1ed3i t\u00ednh.","explain":"<span class='basic_left'> Thay $x=3;y=-1$ v\u00e0o bi\u1ec3u th\u1ee9c $B$ ta \u0111\u01b0\u1ee3c: <br\/> $\\begin{align} & B\\,=\\dfrac{{{3}^{2}}+2.3.\\left( -1 \\right)+{{\\left( -1 \\right)}^{2}}}{3-\\left( -1 \\right)} \\\\ & \\,\\,\\,\\,\\,=\\dfrac{9-6+1}{3+1} \\\\ & \\,\\,\\,\\,\\,=1 \\\\ \\end{align}$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $1$<\/span><\/span>"}]}],"id_ques":1077},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-17"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $C=x^2+xy-yz$ t\u1ea1i $x=-2;y=3;z=5$ l\u00e0 _input_ <\/span>","hint":" Thay gi\u00e1 tr\u1ecb c\u1ee7a $x;y;z$ v\u00e0o bi\u1ec3u th\u1ee9c $C$ r\u1ed3i t\u00ednh.","explain":"<span class='basic_left'> Thay $x=-2;y=3;z=5$ v\u00e0o bi\u1ec3u th\u1ee9c $C$ ta \u0111\u01b0\u1ee3c: <br\/> $C=(-2)^2+(-2).3-3.5=4-6-15=-17$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-17$<\/span><\/span>"}]}],"id_ques":1078},{"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'> Bi\u1ebft $x;y$ th\u1ecfa m\u00e3n $(x-2)^2+|y-1|=0$ <br\/> Khi \u0111\u00f3 gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $D=2x+\\dfrac{x-y}{x+2y}$ l\u00e0: <\/span>","select":["A. $4\\dfrac{1}{4}$","B. $4\\dfrac{3}{4}$","C. $4$","D. $0$"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a $x;y$ t\u1eeb bi\u1ec3u th\u1ee9c $(x-2)^2+|y-1|=0$ <br\/> Thay gi\u00e1 tr\u1ecb c\u1ee7a $x;y$ v\u1eeba t\u00ecm \u0111\u01b0\u1ee3c v\u00e0o $D$ r\u1ed3i t\u00ednh.<br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $(x-2)^2\\ge 0\\,; \\,|y-1|\\ge 0$ v\u1edbi m\u1ecdi $x,y$ <br\/> $\\Rightarrow (x-2)^2+|y-1|=0$ x\u1ea3y ra khi v\u00e0 ch\u1ec9 khi $\\left\\{ \\begin{aligned} & x-2=0 \\\\ & y-1=0 \\\\ \\end{aligned} \\right.\\Rightarrow \\left\\{ \\begin{aligned} & x=2 \\\\ & y=1 \\\\ \\end{aligned} \\right.$ <br\/> Thay $x=2;y=1$ v\u00e0o bi\u1ec3u th\u1ee9c $D$ ta \u0111\u01b0\u1ee3c: <br\/> $D=2.2+\\dfrac{2-1}{2+2.1}=4\\dfrac{1}{4}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span><\/span>","column":2}]}],"id_ques":1079},{"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'> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $P=\\dfrac{2x-3y}{2x+3y}$ bi\u1ebft $\\dfrac{x}{18}=\\dfrac{y}{9}$ <\/span>","select":["A. $P=2$","B. $P=3$","C. $P=\\dfrac{1}{7}$","D. $P=\\dfrac{2}{3}$"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> T\u1eeb $\\dfrac{x}{18}=\\dfrac{y}{9}$ r\u00fat $x$ theo $y$ <br\/> Thay $x$ v\u1eeba t\u00ednh \u0111\u01b0\u1ee3c v\u00e0o $P$ v\u00e0 bi\u1ebfn \u0111\u1ed5i \u0111\u1ec3 t\u00ecm $y$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> T\u1eeb $\\dfrac{x}{18}=\\dfrac{y}{9} \\Rightarrow x=2y$ <br\/> Ta c\u00f3: <br\/> $P=\\dfrac{2x-3y}{2x+3y}=\\dfrac{2.2y-3y}{2.2y+3y}=\\dfrac{y}{7y}=\\dfrac{1}{7}\\,\\,\\left( y\\ne 0 \\right)$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span><\/span>","column":2}]}],"id_ques":1080},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"],["-3"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> T\u00ecm c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn \u0111\u1ec3 bi\u1ec3u th\u1ee9c $(x-2)^2+(y+3)^2$ c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng $0$ <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $\\left\\{ \\begin{align} & x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ & y=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ \\end{align} \\right.$ <\/span>","explain":"<span class='basic_left'> Ta c\u00f3: $(x-2)^2\\ge 0\\,;\\,(y+3)^2\\ge 0$ v\u1edbi m\u1ecdi $x,y$ <br\/> $\\Rightarrow (x-2)^2+(y+3)^2 =0$ khi v\u00e0 ch\u1ec9 khi $\\left\\{ \\begin{aligned} & x-2=0 \\\\ & y+3=0 \\\\ \\end{aligned} \\right.\\Rightarrow \\left\\{ \\begin{aligned} & x=2 \\\\ & y=-3 \\\\ \\end{aligned} \\right.$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $2;-3$ <\/span><\/span>"}]}],"id_ques":1081},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c sau, bi\u1ebft $x+y=0$ <br\/> $M=x^4-xy^3+x^3y-y^4-1$ <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $M=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>T\u1eeb $x+y=0$ r\u00fat $x$ theo $y$ ho\u1eb7c $y$ theo $x$ <br\/> Thay $x$ ho\u1eb7c $y$ v\u1eeba t\u00ecm \u1edf tr\u00ean v\u00e0o $M$ r\u1ed3i bi\u1ebfn \u0111\u1ed5i \u0111\u1ec3 t\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c $M$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> T\u1eeb $x+y=0$ ta suy ra $y=-x$ <br\/> $\\Rightarrow y^3=-x^3;\\,y^4=x^4$ <br\/> Do \u0111\u00f3 bi\u1ec3u th\u1ee9c $M$ tr\u1edf th\u00e0nh: <br\/> $M=x^4-x.(-x)^3+x^3.(-x)-x^4-1$ <br\/> $M=x^4+x^4-x^4-x^4-1$ <br\/> $M=-1$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1$ <\/span><\/span>"}]}],"id_ques":1082},{"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":" <span class='basic_left'> M\u1ed9t b\u1ec3 \u0111ang ch\u1ee9a $480$ l\u00edt n\u01b0\u1edbc, c\u00f3 m\u1ed9t v\u00f2i ch\u1ea3y v\u00e0o m\u1ed7i ph\u00fat ch\u1ea3y \u0111\u01b0\u1ee3c $x$ (l\u00edt). C\u00f9ng l\u00fac \u0111\u00f3 m\u1ed9t v\u00f2i kh\u00e1c ch\u1ea3y t\u1eeb b\u1ec3 ra. M\u1ed7i ph\u00fat l\u01b0\u1ee3ng n\u01b0\u1edbc ch\u1ea3y ra b\u1eb1ng $\\dfrac{1}{4}$ l\u01b0\u1ee3ng n\u01b0\u1edbc ch\u1ea3y v\u00e0o. H\u00e3y bi\u1ec3u th\u1ecb l\u01b0\u1ee3ng n\u01b0\u1edbc trong b\u1ec3 sau khi \u0111\u1ed3ng th\u1eddi m\u1edf c\u1ea3 hai v\u00f2i tr\u00ean sau $a$ ph\u00fat. <\/span>","select":["A. $\\dfrac{3ax}{4}$ (l\u00edt)","B. $480+\\dfrac{3ax}{4}$ (l\u00edt)","C. $480-\\dfrac{ax}{4}$ (l\u00edt)","D. $\\dfrac{ax}{4}$ (l\u00edt)"],"hint":"T\u00ednh l\u01b0\u1ee3ng n\u01b0\u1edbc ch\u1ea3y v\u00e0o t\u1eeb v\u00f2i $1$ v\u00e0 l\u01b0\u1ee3ng n\u01b0\u1edbc ch\u1ea3y ra t\u1eeb v\u00f2i $2$ trong $a$ ph\u00fat.","explain":"<span class='basic_left'> M\u1edf v\u00f2i $1$ trong $a$ ph\u00fat th\u00ec l\u01b0\u1ee3ng n\u01b0\u1edbc ch\u1ea3y v\u00e0o b\u1ec3 l\u00e0: $ax$ (l\u00edt) <br\/> M\u1edf v\u00f2i $2$ trong $a$ ph\u00fat th\u00ec l\u01b0\u1ee3ng n\u01b0\u1edbc ch\u1ea3y ra t\u1eeb b\u1ec3 l\u00e0: $\\dfrac{ax}{4}$ (l\u00edt)<br\/> Bi\u1ec3u th\u1ee9c bi\u1ec3u th\u1ecb l\u01b0\u1ee3ng n\u01b0\u1edbc trong b\u1ec3 sau khi \u0111\u1ed3ng th\u1eddi m\u1edf c\u1ea3 hai v\u00f2i tr\u00ean sau $a$ ph\u00fat l\u00e0: <br\/> $480+ax-\\dfrac{ax}{4}=480+\\dfrac{3ax}{4}$ (l\u00edt)<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span><\/span>","column":2}]}],"id_ques":1083},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["-1"],["1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn \u0111\u1ec3 bi\u1ec3u th\u1ee9c $(x+1)(x-1)(x^2+1)+1$ c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng $1.$<br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $\\left[ \\begin{align} & x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ & x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\\\ \\end{align} \\right.$ <\/span>","hint":"Cho bi\u1ec3u th\u1ee9c b\u1eb1ng $1$ r\u1ed3i bi\u1ebfn \u0111\u1ed5i t\u00ecm $x$","explain":"<span class='basic_left'> Cho bi\u1ec3u th\u1ee9c b\u1eb1ng $1$ ta c\u00f3: <br\/> $\\begin{aligned} & \\left( x+1 \\right)\\left( x-1 \\right)\\left( {{x}^{2}}+1 \\right)+1=1 \\\\ & \\left( x+1 \\right)\\left( x-1 \\right)\\left( {{x}^{2}}+1 \\right)=1-1 \\\\ & \\left( x+1 \\right)\\left( x-1 \\right)\\left( {{x}^{2}}+1 \\right)=0 \\\\ & Do\\,\\,\\,{{x}^{2}}+1\\,\\,\\ge \\,\\,1\\,\\,\\forall\\,x\\,\\text{n\u00ean} \\\\ & \\left( x+1 \\right)\\left( x-1 \\right)\\left( {{x}^{2}}+1 \\right)=0 \\\\ & \\Rightarrow \\left[ \\begin{aligned} & x+1=0 \\\\ & x-1=0 \\\\ \\end{aligned} \\right.\\Rightarrow \\left[ \\begin{aligned} & x=-1 \\\\ & x=1 \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng l\u00e0 $-1;1$ <\/span><\/span>"}]}],"id_ques":1084},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0111\u00e2y \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $\\dfrac{100}{y^2+5}$ lu\u00f4n d\u01b0\u01a1ng v\u1edbi $\\forall y \\in \\mathbb{Q}$ <\/span>","select":["\u0110\u00fang","Sai"],"hint":"Nh\u1eadn \u0111\u1ecbnh v\u1ec1 gi\u00e1 tr\u1ecb c\u1ee7a $y^2+5$","explain":"<span class='basic_left'> Ta c\u00f3: $y^2\\ge 0$ v\u1edbi $ \\forall y \\in \\mathbb{Q}$ <br\/> $\\Rightarrow y^2+5\\ge 5 > 0$ <br\/> $\\Rightarrow \\dfrac{100}{y^2+5} > 0$ v\u1edbi $\\forall y \\in \\mathbb{Q}$ <br\/> Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $\\dfrac{100}{y^2+5}$ lu\u00f4n d\u01b0\u01a1ng v\u1edbi $\\forall y \\in \\mathbb{Q}$ l\u00e0 \u0111\u00fang. <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span><\/span>","column":2}]}],"id_ques":1085},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["9"],["3"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c $A=(x-3)^2+9.$ Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t \u0111\u00f3 \u0111\u1ea1t \u0111\u01b0\u1ee3c khi n\u00e0o? <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $Min\\,A=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ khi $x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u0110\u00e1nh gi\u00e1 v\u00e0 nh\u1eadn \u0111\u1ecbnh $A\\ge m$ v\u1edbi $m$ l\u00e0 h\u1eb1ng s\u1ed1. <br\/> Khi \u0111\u00f3 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $m$ <br\/> T\u00ecm \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 $A=m$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $(x-3)^2 \\ge 0$ v\u1edbi $\\forall x$ <br\/> $\\Rightarrow A=(x-3)^2+9 \\ge 9$ v\u1edbi $\\forall x$ <br\/> $\\Rightarrow Min\\,A=9$ <br\/> D\u1ea5u ''='' x\u1ea3y ra khi $x=3$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $9;3$ <\/span><\/span>"}]}],"id_ques":1086},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["-6"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c $B=-2(x+6)^2+5.$ Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t \u0111\u00f3 \u0111\u1ea1t \u0111\u01b0\u1ee3c khi n\u00e0o? <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $Max\\,B=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ khi $x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u0110\u00e1nh gi\u00e1 v\u00e0 nh\u1eadn \u0111\u1ecbnh $B\\le m$ v\u1edbi $m$ l\u00e0 h\u1eb1ng s\u1ed1. <br\/> Khi \u0111\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $B$ l\u00e0 $m$ <br\/> T\u00ecm \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 $B=m$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $(x+6)^2 \\ge 0 \\Rightarrow -2(x+6)^2 \\le 0$ v\u1edbi $\\forall x$ <br\/> $\\Rightarrow B=-2(x+6)^2+5 \\le 5$ v\u1edbi $\\forall x$ <br\/> $\\Rightarrow Max\\,B=5$ <br\/> D\u1ea5u ''='' x\u1ea3y ra khi $x+6=0 \\Rightarrow x=-6$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $5;-6$ <\/span><\/span>"}]}],"id_ques":1087},{"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'> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $E=\\dfrac{3a+2b}{4a-3b}$ v\u1edbi $\\dfrac{a}{b}=\\dfrac{1}{3}$ <\/span>","select":["A. $E=\\dfrac{2}{3}$","B. $E=\\dfrac{4}{5}$","C. $E=-\\dfrac{9}{5}$","D. $E=-\\dfrac{7}{3}$"],"hint":"T\u1eeb $\\dfrac{a}{b}=\\dfrac{1}{3}$ r\u00fat $b$ theo $a$ r\u1ed3i thay v\u00e0o $E$","explain":"<span class='basic_left'> T\u1eeb $\\dfrac{a}{b}=\\dfrac{1}{3}$ $\\Rightarrow b=3a$ <br\/> Thay $b=3a$ v\u00e0o bi\u1ec3u th\u1ee9c $E$ ta \u0111\u01b0\u1ee3c: <br\/> $E=\\dfrac{3a+2.3a}{4a-3.3a}=\\dfrac{9a}{-5a}=-\\dfrac{9}{5}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span><\/span>","column":4}]}],"id_ques":1088},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["21"],["14"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","input_hint":["frac"],"ques":" <span class='basic_left'> T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c $Q=\\dfrac{5}{{{\\left( x-14 \\right)}^{2}}+21}$ <br\/> Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t \u0111\u00f3 \u0111\u1ea1t \u0111\u01b0\u1ee3c khi n\u00e0o?<\/span><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $Max\\,Q=$ <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div> khi $x=$ _input_","hint":"V\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $A(x)$ l\u00e0 bi\u1ec3u th\u1ee9c theo bi\u1ebfn $x$ th\u00ec $\\dfrac{a}{A(x)}$ l\u1edbn nh\u1ea5t n\u1ebfu $A(x)$ nh\u1ecf nh\u1ea5t.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u0110\u00e1nh gi\u00e1 v\u00e0 nh\u1eadn \u0111\u1ecbnh $Q\\le m$ v\u1edbi $m$ l\u00e0 h\u1eb1ng s\u1ed1. <br\/> Khi \u0111\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $Q$ l\u00e0 $m$ <br\/> T\u00ecm \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 $Q=m$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $(x-14)^2 \\ge 0 \\Rightarrow (x-14)^2+21 \\ge 21$ <br\/> $\\Rightarrow Q=\\dfrac{5}{{{\\left( x-14 \\right)}^{2}}+21} \\le \\dfrac{5}{21}$ <br\/> $\\Rightarrow Max\\,Q=\\dfrac{5}{21}$ <br\/> D\u1ea5u ''='' x\u1ea3y ra khi $(x-14)^2+21=21 \\Rightarrow x-14=0 \\Rightarrow x=14$<\/span>"}]}],"id_ques":1089},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"],["4"],["5"],["7"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> X\u00e1c \u0111\u1ecbnh $x;y;z;t$ bi\u1ebft r\u1eb1ng $y+t=11;\\,y+z=9;\\,x+y=6;\\,z+t=12.$ <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $\\left\\{ \\begin{align} & x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ & y= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ & z= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ & t= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ \\end{align} \\right.$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> C\u1ed9ng t\u1eebng v\u1ebf c\u1ee7a $y+t=11$ v\u00e0 $y+z=9$ v\u1edbi nhau r\u1ed3i bi\u1ebfn \u0111\u1ed5i suy ra gi\u00e1 tr\u1ecb c\u1ee7a $y$ <br\/> T\u1eeb c\u00e1c d\u1eef ki\u1ec7n c\u1ee7a b\u00e0i to\u00e1n t\u00ecm ra gi\u00e1 tr\u1ecb c\u1ee7a $x;z;t$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: <br\/> $y+t=11\\,\\,\\,(1)$ <br\/> $y+z=9\\,\\,\\,(2)$ <br\/> $x+y=6\\,\\,\\,(3)$ <br\/> $z+t=12\\,\\,\\,(4)$ <br\/> C\u1ed9ng t\u1eebng v\u1ebf c\u1ee7a (1) v\u00e0 (2) v\u1edbi nhau ta \u0111\u01b0\u1ee3c: $2y+z+t=11+9=20$ <br\/> V\u00ec $z+t=12$ (theo (4)) n\u00ean $2y+12=20 \\Rightarrow 2y=8 \\Rightarrow y=4$ <br\/> Theo (1) suy ra $t=11-y=11-4=7$ <br\/> Theo (2) suy ra $z=9-y=9-4=5$ <br\/> Theo (3) suy ra $x=6-y=6-4=2$ <br\/> V\u1eady $x=2;y=4;z=5;t=7$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $2;4;5;7$ <\/span><\/span>"}]}],"id_ques":1090}],"lesson":{"save":0,"level":2}}