{"segment":[{"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"Cho t\u1eadp h\u1ee3p X = {2; 4; 7; 1}. T\u1eadp h\u1ee3p n\u00e0o sau \u0111\u00e2y l\u00e0 t\u1eadp h\u1ee3p con c\u1ee7a t\u1eadp h\u1ee3p X.","select":["A. {1; 7}","B. {1; 5} ","C. {2; 5}","D. {3; 7} "],"hint":"","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> T\u1eadp h\u1ee3p {1; 7} c\u00f3 1 $\\in$ X v\u00e0 7 $\\in$ X n\u00ean {1; 7} l\u00e0 t\u1eadp h\u1ee3p con c\u1ee7a t\u1eadp h\u1ee3p X <br\/> T\u1eadp h\u1ee3p {1; 5} c\u00f3 5 $\\notin$ X n\u00ean {1; 5} kh\u00f4ng ph\u1ea3i l\u00e0 t\u1eadp h\u1ee3p con c\u1ee7a t\u1eadp h\u1ee3p X <br\/> T\u1eadp h\u1ee3p {2; 5} c\u00f3 5 $\\notin$ X n\u00ean {2; 5} kh\u00f4ng ph\u1ea3i l\u00e0 t\u1eadp h\u1ee3p con c\u1ee7a t\u1eadp h\u1ee3p X <br\/> T\u1eadp h\u1ee3p {3; 7} c\u00f3 3 $\\notin$ X n\u00ean {3; 7} kh\u00f4ng ph\u1ea3i t\u1eadp h\u1ee3p con c\u1ee7a t\u1eadp h\u1ee3p X <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A <\/span> ","column":2}],"id_ques":851},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"Cho t\u1eadp h\u1ee3p $Y = \\left\\{ x \\in \\mathbb{N} | x \\leq 9 \\right\\}$. S\u1ed1 ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p Y l\u00e0: ","select":["A. 7","B. 8 ","C. 9","D. 10 "],"hint":"","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: $Y = \\left\\{ x \\in \\mathbb{N} | x \\leq 9 \\right\\}$ <br\/> N\u00ean: Y = {0; 1; 2; 3; 4; 5; 6; 7; 8; 9} <br\/> V\u1eady t\u1eadp h\u1ee3p Y c\u00f3 10 ph\u1ea7n t\u1eed <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}],"id_ques":852},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["297"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"T\u00ednh. <br\/> $490 -\\left\\{ [(128 + 22) : 3 . 2^2] - 7 \\right\\}$ = _input_ ","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 bi\u1ec3u th\u1ee9c trong ngo\u1eb7c () <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c trong ngo\u1eb7c [] <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c trong {} <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $\\begin{align*}& 490 -\\left\\{ [(128 + 22) : 3 . 2^2] - 7 \\right\\} \\\\ &= 490 - \\left\\{[150 : 3 . 4] - 7\\right\\} \\\\ &= 490 - \\left\\{ 50 . 4 - 7\\right\\} \\\\ &= 490 - \\left\\{200 - 7 \\right\\} \\\\ &= 490 - 193 \\\\ &= 297 \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 297 <\/span>"}],"id_ques":853},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang. ","select":["A. $80 \\in BC(20, 30)$","B. $36 \\in BC(4; 6; 8)$ ","C. $12 \\in BC(4; 6; 8)$","D. $24 \\in BC(4; 6; 8)$ "],"hint":"","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: <br\/> V\u00ec 80 $\\vdots$ 20 nh\u01b0ng 80 $\\not \\vdots$ 30 n\u00ean 80 $\\notin$ BC(20, 30) <b> (lo\u1ea1i) <\/b> <br\/> V\u00ec 30 $\\vdots$ 4; 36 $\\vdots$ 6 nh\u01b0ng 36 $\\not \\vdots$ 8 n\u00ean 36 $\\notin$ BC(4, 6, 8) <b> (lo\u1ea1i) <\/b> <br\/> V\u00ec 12 $\\vdots$ 4; 12 $\\vdots$ 6 nh\u01b0ng 12 $\\not \\vdots$ 8 n\u00ean 12 $\\notin$ BC(4; 6; 8) <b> (lo\u1ea1i) <\/b> <br\/> V\u00ec 24 $\\vdots$ 4; 24 $\\vdots$ 6 v\u00e0 24 $\\vdots$ 8 n\u00ean 24 $\\in$ BC(4; 6; 8) <b> (th\u1ecfa m\u00e3n) <\/b> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}],"id_ques":854},{"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 nh\u1ecf nh\u1ea5t bi\u1ebft x $\\vdots$ 2; x $\\vdots$ 3; x $\\vdots$ 4. \u0110\u00e1p \u00e1n l\u00e0: ","select":["A. x = 8","B. x = 12 ","C. x = 10","D. x = 24 "],"hint":"","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> V\u00ec x $\\vdots$ 2 n\u00ean x $\\in$ B(2); x $\\vdots$ 3 n\u00ean x $\\in$ B(3); x $\\vdots$ 4 n\u00ean x $\\in$ B(4) <br\/> $\\Rightarrow$ x $\\in$ BC(2; 3; 4) <br\/> V\u00ec x l\u00e0 nh\u1ecf nh\u1ea5t n\u00ean x = BCNN(2, 3, 4) = 12 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. x = 12 <\/span> ","column":2}],"id_ques":855},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"Thay * b\u1eb1ng ch\u1eef s\u1ed1 th\u00edch h\u1ee3p \u0111\u1ec3 $\\overline{94*21}$ chia h\u1ebft cho 2 v\u00e0 3. <br\/> \u0110\u00e1p \u00e1n l\u00e0: ","select":["A. * = 2","B. * = 5 ","C. * = 8","D. Kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb n\u00e0o th\u1ecfa m\u00e3n"],"hint":"","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> V\u00ec $\\overline{94*21}$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 1 n\u00ean $\\overline{94*21}$ $\\not \\vdots$ 2 <br\/> N\u00ean kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a * th\u1ecfa m\u00e3n \u0111\u1ec3 $\\overline{94*21}$ chia h\u1ebft cho 2 v\u00e0 3 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}],"id_ques":856},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["40"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"Ng\u01b0\u1eddi ta mu\u1ed1n chia 200 b\u00fat bi, 240 b\u00fat ch\u00ec, 320 c\u1ee5c t\u1ea9y th\u00e0nh m\u1ed9t s\u1ed1 ph\u1ea7n th\u01b0\u1edfng nh\u01b0 nhau. H\u1ecfi c\u00f3 th\u1ec3 chia \u0111\u01b0\u1ee3c nhi\u1ec1u nh\u1ea5t bao nhi\u00eau ph\u1ea7n th\u01b0\u1edfng. <br\/> \u0110\u00e1p \u00e1n l\u00e0: _input_ ph\u1ea7n th\u01b0\u1edfng","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> N\u1ebfu s\u1ed1 ph\u00e2n th\u01b0\u1edfng l\u00e0 x th\u00ec 200 $\\vdots$ x; 240 $\\vdots$ x v\u00e0 320 $\\vdots$ x <br\/> <b> B\u01b0\u1edbc 1: <\/b> Ph\u00e2n t\u00edch 200; 240; 320 ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 <br\/> <b> B\u01b0\u1edbc 2: <\/b> L\u1eadp t\u00edch c\u00e1c th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 chung, m\u1ed7i th\u1eeba s\u1ed1 l\u1ea5y v\u1edbi s\u1ed1 m\u0169 nh\u1ecf nh\u1ea5t <br\/> <b> B\u01b0\u1edbc 3: <\/b> S\u1ed1 ph\u1ea7n th\u01b0\u1edfng l\u1edbn nh\u1ea5t c\u00f3 th\u1ec3 = \u01afCLN(200; 240; 320) <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> G\u1ecdi s\u1ed1 ph\u1ea7n th\u01b0\u1edfng nhi\u1ec1u nh\u1ea5t c\u00f3 th\u1ec3 chia l\u00e0 x (x > 0) <br\/> Khi \u0111\u00f3: 200 $\\vdots$ x; 240 $\\vdots$ x v\u00e0 320 $\\vdots$ x <br\/> V\u00ec x l\u00e0 l\u1edbn nh\u1ea5t n\u00ean x = \u01afCLN(200; 240; 320) <br\/> C\u00f3: $200 = 2^3 . 5^2$; $240 = 2^4 . 3 . 5$; $320 = 2^6 . 5$ <br\/> $x = \u01afCLN(200; 240; 320) = 2^3 . 5 = 40$ <br\/> V\u1eady s\u1ed1 ph\u00e2n th\u01b0\u1edfng nhi\u1ec1u nh\u1ea5t c\u00f3 th\u1ec3 chia l\u00e0 40 (ph\u1ea7n th\u01b0\u1edfng) <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 40 <\/span>"}],"id_ques":857},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"H\u00e3y ch\u1ecdn d\u1ea5u th\u00edch h\u1ee3p thay cho d\u1ea5u <span class='basic_hoi_black'>?<\/span> <br\/> $3^{500}$ <span class='basic_hoi_black'>?<\/span> $7^{300}$ ","select":["A. > ","B. < ","C. ="],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u0110\u01b0a $3^{500}$ v\u00e0 $7^{300}$ v\u1ec1 c\u00f9ng s\u1ed1 m\u0169 100 r\u1ed3i so s\u00e1nh hai l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: $3^{500} = 3^{5 . 100} = (3^5)^{100} = 243^{100}$ <br\/> $7^{300} = (7^3)^{100} = 343^{100}$ <br\/> V\u00ec $243^{100} < 343^{100}$ n\u00ean $3^{500} < 7^{300}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: < <\/span> ","column":3}],"id_ques":858},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["18"],["24"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean a, b bi\u1ebft a < b; a + b = 42 v\u00e0 BCNN(a, b) = 72 <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\/> G\u1ecdi \u01afCLN(a, b) = d ta \u0111i t\u00ecm d $\\in$ \u01afC(a + b, BCNN(a, b)) <br\/> Thay d v\u00e0o c\u00f4ng th\u1ee9c a . b = \u01afCLN(a, b) . BCNN(a, b) k\u1ebft h\u1ee3p \u0111i\u1ec1u ki\u1ec7n a + b = 42 \u0111\u1ec3 t\u00ecm a, b<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi \u01afCLN(a, b) = d khi \u0111\u00f3: a = dm, b = dn; (m, n) = 1 <br\/> a + b = 42 = dm + dn = d(m + n) $\\Rightarrow$ m + n = $\\dfrac{42}{d}$ <br\/> $\\Rightarrow$ d $\\in$ \u01af(a + b) hay d $\\in$ \u01af(42) (1) <br\/> V\u00ec BCNN(a, b) = 72 = d . m . n $\\Rightarrow$ m . n = $\\dfrac{72}{d}$ <br\/> $\\Rightarrow$ d $\\in$ \u01af(72) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ d $\\in$ \u01afC(42; 72) m\u00e0 \u01afCLN(42; 72) = 2 . 3 = 6 $\\Rightarrow$ d $\\in$ \u01afC(42, 72) = {1; 2; 3; 6} <br\/> V\u00ec a . b = \u01afCLN(a, b) . BCNN(a, b)<br\/> d . 72 = 1 . 72 = 2 . 36 = 3 . 24 = 6 . 12 <br\/> Th\u1eed l\u1ea7n l\u01b0\u1ee3t c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a d ta \u0111\u01b0\u1ee3c: <br\/> * V\u1edbi d = 1 $\\Rightarrow \\begin{cases}m + n = 42 \\\\ m . n = 72 \\end{cases}$ <br\/> $\\Rightarrow$ m = 1, n = 72 <br\/> $\\Rightarrow$ m + n = 73 <b> (kh\u00f4ng th\u1ecfa m\u00e3n) <\/b> <br\/> * V\u1edbi d = 2 $\\Rightarrow \\begin{cases}m + n = 21 \\\\ m . n = 36 \\end{cases}$ <br\/> $\\Rightarrow$ m = 1, n = 36 <br\/> $\\Rightarrow$ m + n = 37 <b> (kh\u00f4ng th\u1ecfa m\u00e3n) <\/b> <br\/> Ho\u1eb7c m = 4, n = 9 $\\Rightarrow$ m + n = 13 <b> (kh\u00f4ng th\u1ecfa m\u00e3n) <\/b> <br\/> * V\u1edbi d = 3 $\\Rightarrow \\begin{cases}m + n = 14 \\\\ m . n = 24 \\end{cases}$ <br\/> $\\Rightarrow$ m = 1, n = 24 <br\/> $\\Rightarrow$ m + n = 25 <b> (kh\u00f4ng th\u1ecfa m\u00e3n) <\/b> <br\/> Ho\u1eb7c m = 3, n = 8 $\\Rightarrow$ m + n = 11 <b> (kh\u00f4ng th\u1ecfa m\u00e3n) <\/b> <br\/> * V\u1edbi d = 6 $\\Rightarrow \\begin{cases}m + n = 7 \\\\ m . n = 12 \\end{cases}$ <br\/> $\\Rightarrow$ m = 1, n = 12 $\\Rightarrow$ m + n = 13 <b> (kh\u00f4ng th\u1ecfa m\u00e3n) <\/b> <br\/> Ho\u1eb7c m = 3, n = 4 $\\Rightarrow$ m + n = 7 <b> (th\u1ecfa m\u00e3n) <\/b> <br\/> $\\Rightarrow$ a = 3 . 6 = 18; b = 6 . 4 = 24 <br\/> <span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: a = 18; b = 24 <\/span> "}],"id_ques":859},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"T\u00ecm ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a s\u1ed1 $2003^{15}$ <br\/> Ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0: _input_ ","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Ta \u0111i t\u00ecm ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 $3^{15}$ <br\/> Ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $2003^{15}$ ch\u00ednh l\u00e0 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $3^{15}$ <\/span> <br\/><br\/> <span class='basic_green'> B\u00e0i gi\u1ea3i:<\/span><br\/> $2003^{15}$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $3^{15}$ <br\/> Ta c\u00f3: $3^4 = 81$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 1 <br\/> M\u00e0 $3^{15} = 3^{12} . 3^3$ <br\/> $3^{12} = (3^4)^3$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 1 <br\/> $3^{3} = 27$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 7 <br\/> N\u00ean $3^{15}$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 1 . 7 = 7 <br\/> $\\Rightarrow$ $2003^{15}$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 7 <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 7 <\/span> "}],"id_ques":860}],"id_ques":0}],"lesson":{"save":1,"level":3,"time":44}}