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Desmos l\u00e0 g\u00ec?<\/b><\/h1>\n
Desmos l\u00e0 m\u1ed9t m\u00e1y t\u00ednh \u0111\u1ed3 th\u1ecb (graphing calculator) ch\u1ea1y tr\u00ean n\u1ec1n web. Kh\u00e1c v\u1edbi m\u00e1y t\u00ednh c\u1ea7m tay ch\u1ec9 tr\u1ea3 v\u1ec1 m\u1ed9t con s\u1ed1, Desmos v\u1ebd ngay \u0111\u1ed3 th\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c \u0111\u01b0\u1ee3c g\u00f5 v\u00e0o, \u0111\u00e1nh d\u1ea5u \u0111i\u1ec3m c\u1eaft tr\u1ee5c, \u0111i\u1ec3m giao v\u00e0 \u0111\u1ec9nh, \u0111\u1ed3ng th\u1eddi cho ph\u00e9p t\u1ea1o b\u1ea3ng gi\u00e1 tr\u1ecb hay thanh tr\u01b0\u1ee3t \u0111\u1ec3 thay \u0111\u1ed5i tham s\u1ed1.<\/span><\/p>\n Desmos c\u00f3 b\u1ea3n mi\u1ec5n ph\u00ed t\u1ea1i desmos.com, d\u00f9ng \u0111\u01b0\u1ee3c tr\u00ean m\u00e1y t\u00ednh v\u00e0 \u0111i\u1ec7n tho\u1ea1i. Phi\u00ean b\u1ea3n trong Bluebook l\u00e0 b\u1ea3n r\u00fat g\u1ecdn d\u00e0nh cho ph\u00f2ng thi. C\u00e1c ch\u1ee9c n\u0103ng c\u1ed1t l\u00f5i v\u1eabn gi\u1ed1ng b\u1ea3n web, n\u00ean\u00a0 ho\u00e0n to\u00e0n c\u00f3 th\u1ec3 luy\u1ec7n \u1edf nh\u00e0 tr\u00ean desmos.com r\u1ed3i v\u00e0o ph\u00f2ng thi d\u00f9ng y nh\u01b0 v\u1eady.<\/span><\/p>\n Theo ch\u00ednh s\u00e1ch c\u1ee7a College Board, Desmos \u0111\u01b0\u1ee3c t\u00edch h\u1ee3p tr\u1ef1c ti\u1ebfp v\u00e0o Bluebook v\u00e0 c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng trong to\u00e0n b\u1ed9 ph\u1ea7n Digital SAT Math, g\u1ed3m 2 module v\u1edbi t\u1ed5ng th\u1eddi gian 70 ph\u00fat cho 44 c\u00e2u h\u1ecfi. Th\u00ed sinh c\u1ea7n l\u01b0u \u00fd m\u1ed9t s\u1ed1 quy \u0111\u1ecbnh quan tr\u1ecdng:<\/span><\/p>\n Trong v\u00f9ng \u0111\u1ed3 th\u1ecb c\u1ee7a Desmos, n\u00fat c\u1edd l\u00ea (Graph Settings) cho ph\u00e9p \u0111i\u1ec1u ch\u1ec9nh ph\u1ea1m vi hi\u1ec3n th\u1ecb c\u1ee7a hai tr\u1ee5c <\/span>x<\/span> and <\/span>y<\/span>, trong khi n\u00fat h\u00ecnh ng\u00f4i nh\u00e0 gi\u00fap \u0111\u01b0a \u0111\u1ed3 th\u1ecb tr\u1edf v\u1ec1 khung nh\u00ecn m\u1eb7c \u0111\u1ecbnh. N\u1ebfu \u0111\u1ed3 th\u1ecb \u0111\u1ed9t nhi\u00ean bi\u1ebfn m\u1ea5t, nguy\u00ean nh\u00e2n th\u01b0\u1eddng l\u00e0 khung nh\u00ecn hi\u1ec7n t\u1ea1i kh\u00f4ng hi\u1ec3n th\u1ecb \u0111\u00fang v\u00f9ng ch\u1ee9a \u0111\u1ed3 th\u1ecb. V\u00ec v\u1eady, h\u00e3y th\u1eed nh\u1ea5n n\u00fat ng\u00f4i nh\u00e0 ho\u1eb7c thu nh\u1ecf ph\u1ea1m vi hi\u1ec3n th\u1ecb tr\u01b0\u1edbc khi ki\u1ec3m tra l\u1ea1i bi\u1ec3u th\u1ee9c \u0111\u00e3 nh\u1eadp. <\/span><\/p>\n Nh\u1eadp sai c\u00fa ph\u00e1p l\u00e0 m\u1ed9t trong nh\u1eefng l\u1ed7i th\u01b0\u1eddng g\u1eb7p nh\u1ea5t khi ng\u01b0\u1eddi m\u1edbi s\u1eed d\u1ee5ng Desmos. B\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y t\u1ed5ng h\u1ee3p c\u00e1c c\u00fa ph\u00e1p quan tr\u1ecdng v\u00e0 th\u01b0\u1eddng d\u00f9ng trong ph\u1ea7n SAT Math, gi\u00fap b\u1ea1n nh\u1eadp bi\u1ec3u th\u1ee9c ch\u00ednh x\u00e1c v\u00e0 thao t\u00e1c thu\u1eadn ti\u1ec7n h\u01a1n.<\/span><\/p>\n M\u1eb9o nh\u1ecf: Desmos hi\u1ec3u <\/span>2x<\/span> To be <\/span>2<\/span>x<\/span>, nh\u01b0ng bi\u1ec3u th\u1ee9c <\/span>xy<\/span> c\u00f3 th\u1ec3 g\u00e2y nh\u1ea7m l\u1eabn t\u00f9y theo c\u00e1ch nh\u1eadp v\u00e0 ng\u1eef c\u1ea3nh. V\u1edbi nh\u1eefng bi\u1ec3u th\u1ee9c ph\u1ee9c t\u1ea1p, b\u1ea1n n\u00ean ch\u1ee7 \u0111\u1ed9ng th\u00eam d\u1ea5u nh\u00e2n (*) gi\u1eefa c\u00e1c th\u1eeba s\u1ed1 \u0111\u1ec3 h\u1ea1n ch\u1ebf l\u1ed7i c\u00fa ph\u00e1p v\u00e0 gi\u00fap bi\u1ec3u th\u1ee9c d\u1ec5 \u0111\u1ecdc h\u01a1n.<\/span><\/p>\n Qu\u00ean ngo\u1eb7c \u1edf t\u1eed: g\u00f5 x+1\/x-2 th\u00ec Desmos ch\u1ec9 l\u1ea5y s\u1ed1 1 l\u00e0m t\u1eed, c\u00f2n x \u2212 2 g\u00f5 ti\u1ebfp b\u1ecb \u0111\u01b0a xu\u1ed1ng m\u1eabu, k\u1ebft qu\u1ea3 l\u00e0 x + 1\/(x \u2212 2), kh\u00e1c h\u1eb3n (x + 1)\/(x \u2212 2). G\u00f5 (x+1)\/ tr\u01b0\u1edbc, nh\u1eadp m\u1eabu, r\u1ed3i b\u1ea5m m\u0169i t\u00ean ph\u1ea3i \u0111\u1ec3 tho\u00e1t kh\u1ecfi m\u1eabu.<\/span><\/p>\n \u0110\u1ecdc to\u1ea1 \u0111\u1ed9 g\u1ea7n \u0111\u00fang: Desmos hi\u1ec3n th\u1ecb s\u1ed1 th\u1eadp ph\u00e2n l\u00e0m tr\u00f2n. N\u1ebfu th\u1ea5y 0.333 th\u00ec \u0111\u00e1p \u00e1n c\u00f3 th\u1ec3 l\u00e0 1\/3. V\u1edbi c\u00e2u t\u1ef1 \u0111i\u1ec1n \u0111\u00e1p \u00e1n, h\u00e3y \u0111\u1ed5i v\u1ec1 ph\u00e2n s\u1ed1 tr\u01b0\u1edbc khi nh\u1eadp.<\/span><\/p>\n Kh\u00f4ng ki\u1ec3m tra khung nh\u00ecn: giao \u0111i\u1ec3m n\u1eb1m ngo\u00e0i m\u00e0n h\u00ecnh s\u1ebd kh\u00f4ng hi\u1ec7n. Thu nh\u1ecf tr\u01b0\u1edbc khi k\u1ebft lu\u1eadn “kh\u00f4ng c\u00f3 nghi\u1ec7m”.<\/span><\/p>\n D\u00f9ng Desmos cho c\u00e2u t\u00ednh nh\u1ea9m: m\u1edf m\u00e1y, g\u00f5 bi\u1ec3u th\u1ee9c cho ph\u00e9p 3 \u00d7 15 t\u1ed1n nhi\u1ec1u th\u1eddi gian h\u01a1n t\u00ednh nh\u1ea9m.<\/span><\/p>\n – T\u00f4i c\u00f3 x\u00e1c \u0111\u1ecbnh \u0111\u00fang d\u1ea1ng b\u00e0i tr\u01b0\u1edbc khi ch\u1ecdn c\u00f4ng th\u1ee9c ho\u1eb7c c\u00f4ng c\u1ee5 kh\u00f4ng?<\/span><\/p>\n – T\u00f4i c\u00f3 th\u1ec3 gi\u1ea3i th\u00edch v\u00ec sao t\u1eebng b\u01b0\u1edbc bi\u1ebfn \u0111\u1ed5i l\u00e0 h\u1ee3p l\u1ec7 kh\u00f4ng?<\/span><\/p>\n – T\u00f4i \u0111\u00e3 ki\u1ec3m tra l\u1ea1i d\u1ea5u, \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh ho\u1eb7c m\u1ee5c ti\u00eau c\u1ee7a c\u00e2u h\u1ecfi ch\u01b0a?<\/span><\/p>\n – Sau khi l\u00e0m sai, t\u00f4i c\u00f3 ghi r\u00f5 l\u1ed7i n\u1eb1m \u1edf ki\u1ebfn th\u1ee9c, thao t\u00e1c hay c\u00e1ch \u0111\u1ecdc \u0111\u1ec1 kh\u00f4ng?<\/span><\/p>\n \u0110\u1ec1 b\u00e0i: T\u00ecm nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh:\u00a0<\/span><\/p>\n <\/p>\n x<\/span>2<\/span>-5x+6=0<\/span><\/p>\n L\u1eddi gi\u1ea3i b\u1eb1ng \u0111\u1ea1i s\u1ed1<\/span><\/p>\n Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed:<\/span><\/p>\n x<\/span>2<\/span>-5x+6=(x-2)(x-3)=0<\/span><\/p>\n \u0110\u00e1p \u00e1n \u0111\u00fang: B.\u00a0<\/span><\/p>\n C\u00e1ch gi\u1ea3i b\u1eb1ng Desmos\u00a0<\/span><\/p>\n Khi n\u00e0o n\u00ean d\u00f9ng Desmos? Khi ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nhi\u1ec1u b\u01b0\u1edbc bi\u1ebfn \u0111\u1ed5i ho\u1eb7c c\u1ea7n ki\u1ec3m tra nhanh nghi\u1ec7m. V\u1edbi ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01a1n gi\u1ea3n, ph\u00e2n t\u00edch th\u00e0nh nh\u00e2n t\u1eed c\u00f3 th\u1ec3 nhanh h\u01a1n.<\/span><\/p>\n B\u00e0i 2. T\u00ecm nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng c\u00e1ch t\u00ecm giao \u0111i\u1ec3m hai \u0111\u1ed3 th\u1ecb\u00a0<\/b><\/p>\n \u0110\u1ec1 b\u00e0i: Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 nghi\u1ec7m d\u01b0\u01a1ng b\u1eb1ng <\/span>4<\/span>?<\/span><\/p>\n x<\/b>2<\/b>-2x=8<\/b><\/p>\n L\u1eddi gi\u1ea3i b\u1eb1ng \u0111\u1ea1i s\u1ed1<\/span><\/p>\n Chuy\u1ec3n t\u1ea5t c\u1ea3 c\u00e1c h\u1ea1ng t\u1eed v\u1ec1 m\u1ed9t v\u1ebf:<\/span><\/p>\n x<\/b>2<\/b>-2x-8=0<\/b><\/p>\n Ph\u00e2n t\u00edch th\u00e0nh nh\u00e2n t\u1eed:<\/span><\/p>\n (x-4)(x+2)=0<\/b><\/p>\n Suy ra:<\/span><\/p>\n x=4 ho\u1eb7c x=-2<\/b><\/p>\n Nghi\u1ec7m d\u01b0\u01a1ng l\u00e0 <\/span>x=4<\/span>.<\/span><\/p>\n \u0110\u00e1p \u00e1n \u0111\u00fang: C.<\/span><\/p>\n C\u00e1ch gi\u1ea3i b\u1eb1ng Desmos\u00a0<\/span><\/p>\n Nh\u1eadp <\/span>y=<\/span>x<\/span>2<\/span>-2x<\/span>.<\/span><\/p>\n Nh\u1eadp th\u00eam <\/span>y=8<\/span>.<\/span><\/p>\n Quan s\u00e1t hai giao \u0111i\u1ec3m c\u1ee7a parabol v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng ngang.<\/span><\/p>\n \u0110\u1ecdc ho\u00e0nh \u0111\u1ed9 hai giao \u0111i\u1ec3m l\u00e0 <\/span>x=-2<\/span> and <\/span>x=4<\/span>, sau \u0111\u00f3 ch\u1ecdn nghi\u1ec7m d\u01b0\u01a1ng.<\/span><\/p>\n Khi m\u1edbi l\u00e0m quen v\u1edbi Desmos, b\u1ea1n kh\u00f4ng n\u00ean s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5 n\u00e0y cho m\u1ecdi c\u00e2u h\u1ecfi. Thay v\u00e0o \u0111\u00f3, h\u00e3y b\u1eaft \u0111\u1ea7u v\u1edbi m\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n ti\u00eau bi\u1ec3u trong SAT Math nh\u01b0 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai, h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh hai \u1ea9n v\u00e0 b\u00e0i to\u00e1n t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t ho\u1eb7c nh\u1ecf nh\u1ea5t. H\u00e3y t\u1ef1 gi\u1ea3i b\u00e0i b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u00f4ng th\u01b0\u1eddng tr\u01b0\u1edbc, sau \u0111\u00f3 s\u1eed d\u1ee5ng Desmos \u0111\u1ec3 ki\u1ec3m tra giao \u0111i\u1ec3m, x\u00e1c \u0111\u1ecbnh \u0111\u1ec9nh parabol ho\u1eb7c \u0111\u1ed1i chi\u1ebfu k\u1ebft qu\u1ea3.<\/span><\/p>\n Sau m\u1ed9t v\u00e0i bu\u1ed5i luy\u1ec7n t\u1eadp, b\u1ea1n n\u00ean b\u1eaft \u0111\u1ea7u b\u1ea5m gi\u1edd \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 t\u1ed1c \u0111\u1ed9 m\u1edf c\u00f4ng c\u1ee5 v\u00e0 nh\u1eadp bi\u1ec3u th\u1ee9c. N\u1ebfu th\u1eddi gian thao t\u00e1c tr\u00ean Desmos l\u00e2u h\u01a1n so v\u1edbi t\u00ednh to\u00e1n tr\u1ef1c ti\u1ebfp, h\u00e3y \u01b0u ti\u00ean r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng nh\u1eadp c\u00f4ng th\u1ee9c v\u00e0 s\u1eed d\u1ee5ng c\u00e1c ch\u1ee9c n\u0103ng c\u01a1 b\u1ea3n tr\u01b0\u1edbc khi \u00e1p d\u1ee5ng c\u00f4ng c\u1ee5 v\u00e0o b\u00e0i thi ho\u00e0n ch\u1ec9nh. M\u1ee5c ti\u00eau kh\u00f4ng ch\u1ec9 l\u00e0 s\u1eed d\u1ee5ng th\u00e0nh th\u1ea1o Desmos, m\u00e0 c\u00f2n bi\u1ebft khi n\u00e0o n\u00ean d\u00f9ng c\u00f4ng c\u1ee5 \u0111\u1ec3 ti\u1ebft ki\u1ec7m th\u1eddi gian v\u00e0 n\u00e2ng cao hi\u1ec7u qu\u1ea3 l\u00e0m b\u00e0i.<\/span><\/p>\n In <\/span>ETEST<\/span><\/a>, h\u1ecdc vi\u00ean \u0111\u01b0\u1ee3c h\u01b0\u1edbng d\u1eabn x\u00e2y d\u1ef1ng chi\u1ebfn l\u01b0\u1ee3c \u00f4n luy\u1ec7n <\/span>Digital SAT<\/span><\/a> b\u00e0i b\u1ea3n, t\u1eeb c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c SAT Math \u0111\u1ebfn s\u1eed d\u1ee5ng Desmos hi\u1ec7u qu\u1ea3 trong t\u1eebng d\u1ea1ng b\u00e0i. V\u1edbi l\u1ed9 tr\u00ecnh h\u1ecdc c\u00e1 nh\u00e2n h\u00f3a, <\/span>\u0111\u1ed9i ng\u0169 gi\u00e1o vi\u00ean gi\u00e0u kinh nghi\u1ec7m <\/span><\/a>and <\/span>ph\u01b0\u01a1ng ph\u00e1p luy\u1ec7n t\u1eadp s\u00e1t c\u1ea5u tr\u00fac \u0111\u1ec1 thi<\/span><\/a>, ETEST gi\u00fap h\u1ecdc sinh ph\u00e1t tri\u1ec3n t\u01b0 duy to\u00e1n h\u1ecdc, n\u00e2ng cao t\u1ed1c \u0111\u1ed9 x\u1eed l\u00fd c\u00e2u h\u1ecfi v\u00e0 t\u1ed1i \u01b0u h\u00f3a \u0111i\u1ec3m s\u1ed1 SAT. <\/span>\u0110\u0103ng k\u00fd ki\u1ec3m tra tr\u00ecnh \u0111\u1ed9 t\u1ea1i ETEST<\/span><\/a> ngay h\u00f4m nay \u0111\u1ec3 \u0111\u01b0\u1ee3c t\u01b0 v\u1ea5n l\u1ed9 tr\u00ecnh \u00f4n luy\u1ec7n ph\u00f9 h\u1ee3p v\u1edbi m\u1ee5c ti\u00eau du h\u1ecdc v\u00e0 s\u0103n h\u1ecdc b\u1ed5ng qu\u1ed1c t\u1ebf.\u00a0<\/span><\/p>\n C\u00f3. Desmos c\u00f3 b\u1ea3n web mi\u1ec5n ph\u00ed; trong b\u00e0i thi Digital SAT, c\u00f4ng c\u1ee5 n\u00e0y \u0111\u01b0\u1ee3c t\u00edch h\u1ee3p trong Bluebook \u1edf ph\u1ea7n Math.<\/span><\/p>\n Kh\u00f4ng. Desmos h\u1ed7 tr\u1ee3 r\u1ea5t t\u1ed1t cho \u0111\u1ed3 th\u1ecb, ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, nh\u01b0ng h\u1ecdc sinh v\u1eabn ph\u1ea3i \u0111\u1ecdc \u0111\u1ec1, l\u1eadp bi\u1ec3u th\u1ee9c v\u00e0 ki\u1ec3m tra t\u00ednh h\u1ee3p l\u00fd c\u1ee7a \u0111\u00e1p \u00e1n.<\/span><\/p>\n \u0110i\u1ec3m s\u1ed1 c\u1ee7a m\u1ed9t b\u00e0i luy\u1ec7n ch\u01b0a n\u00f3i h\u1ebft m\u1ee9c \u0111\u1ed9 ti\u1ebfn b\u1ed9. H\u00e3y theo d\u00f5i xem h\u1ecdc sinh c\u00f3 nh\u1eadn ra d\u1ea1ng b\u00e0i nhanh h\u01a1n, \u00edt l\u1eb7p l\u1ea1i c\u00f9ng m\u1ed9t l\u1ed7i h\u01a1n v\u00e0 c\u00f3 th\u1ec3 gi\u1ea3i th\u00edch c\u00e1ch l\u00e0m r\u00f5 r\u00e0ng h\u01a1n hay kh\u00f4ng. \u0110\u00f3 l\u00e0 nh\u1eefng d\u1ea5u hi\u1ec7u cho th\u1ea5y n\u1ec1n t\u1ea3ng \u0111ang v\u1eefng d\u1ea7n.<\/span><\/p>\n ETEST c\u00f3 th\u1ec3 gi\u00fap h\u1ecdc sinh luy\u1ec7n Desmos song song v\u1edbi k\u1ef9 n\u0103ng gi\u1ea3i tay, \u0111\u1ec3 bi\u1ebft l\u00fac n\u00e0o m\u1edf m\u00e1y s\u1ebd nhanh h\u01a1n v\u00e0 l\u00fac n\u00e0o kh\u00f4ng c\u1ea7n d\u00f9ng.<\/span><\/p>\n\n\nDesmos trong Digital SAT: nh\u1eefng \u0111i\u1ec1u c\u1ea7n bi\u1ebft<\/b><\/h1>\n
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Giao di\u1ec7n Desmos g\u1ed3m nh\u1eefng ph\u1ea7n n\u00e0o?<\/b><\/h1>\n
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C\u00fa ph\u00e1p g\u00f5 c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n<\/b><\/h1>\n
Nh\u1eefng l\u1ed7i th\u01b0\u1eddng g\u1eb7p khi m\u1edbi d\u00f9ng Desmos<\/b><\/h1>\n
C\u00e1ch t\u1ef1 ki\u1ec3m tra khi luy\u1ec7n<\/b><\/h1>\n
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B\u00e0i t\u1eadp minh h\u1ecda Desmos trong SAT Math k\u00e8m l\u1eddi gi\u1ea3i<\/b><\/h1>\n
B\u00e0i 1. Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai b\u1eb1ng \u0111\u1ed3 th\u1ecb<\/b><\/h2>\n
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C\u00e1ch luy\u1ec7n \u0111\u1ec3 ki\u1ebfn th\u1ee9c d\u00f9ng \u0111\u01b0\u1ee3c trong ph\u00f2ng thi<\/b><\/h1>\n
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C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 SAT Math Desmos:<\/b><\/h1>\n
Desmos c\u00f3 mi\u1ec5n ph\u00ed kh\u00f4ng?<\/b><\/h2>\n
Desmos c\u00f3 gi\u1ea3i \u0111\u01b0\u1ee3c m\u1ecdi c\u00e2u SAT Math kh\u00f4ng?<\/b><\/h2>\n
\u0110i\u1ec1u h\u1ecdc sinh v\u00e0 ph\u1ee5 huynh n\u00ean theo d\u00f5i<\/b><\/h1>\n