{"id":60109,"date":"2021-07-07T21:15:32","date_gmt":"2021-07-07T14:15:32","guid":{"rendered":"https:\/\/scholarshipplanet.info\/vi?p=60109&#038;preview_id=60109"},"modified":"2021-07-07T21:15:35","modified_gmt":"2021-07-08T04:15:35","slug":"tu-luyen-thi-gre-p1-mot-so-meo-va-kinh-nghiem-cho-phan-quantitative-reasoning-nippon-kiyoshi-blog","status":"publish","type":"post","link":"https:\/\/scholarshipplanet.info\/vi\/tu-luyen-thi-gre-p1-mot-so-meo-va-kinh-nghiem-cho-phan-quantitative-reasoning-nippon-kiyoshi-blog\/","title":{"rendered":"T\u1ef1 luy\u1ec7n thi GRE (P1): M\u1ed9t s\u1ed1 m\u1eb9o v\u00e0 kinh nghi\u1ec7m cho ph\u1ea7n Quantitative Reasoning \u2013 Nippon Kiyoshi Blog"},"content":{"rendered":"\n<p>G\u1ea7n \u0111\u00e2y m\u00ecnh kh\u00f4ng vi\u1ebft m\u1ea5y v\u1ec1 ti\u1ebfng Nh\u1eadt n\u1eefa, v\u00ec th\u1eadt ra nh\u1eefng g\u00ec n\u00ean vi\u1ebft nh\u1ea5t v\u1ec1 ti\u1ebfng Nh\u1eadt th\u00ec m\u00ecnh \u0111\u1ec1u vi\u1ebft c\u1ea3 r\u1ed3i. Th\u1eddi gian qua c\u0169ng c\u00f3 \u00f4n luy\u1ec7n thi GRE (Graduate Record Examinations) \u0111\u1ec3 app v\u00e0o Grad School. N\u1ebfu nh\u1eefng ai quan t\u00e2m \u0111\u1ebfn vi\u1ec7c du h\u1ecdc b\u1eadc sau \u0111\u1ea1i h\u1ecdc, h\u1ecdc ch\u01b0\u01a1ng tr\u00ecnh ti\u1ebfng Anh (v\u1ec1 Econs, CS, STEM) th\u00ec ch\u1eafc \u0111\u1ec1u bi\u1ebft \u0111\u1ebfn k\u1ef3 thi n\u00e0y. T\u1ea1i Nh\u1eadt B\u1ea3n, c\u00e1c ch\u01b0\u01a1ng tr\u00ecnh cao h\u1ecdc b\u1eb1ng ti\u1ebfng Anh t\u1ea1i c\u00e1c tr\u01b0\u1eddng top \u0111\u1ec1u y\u00eau c\u1ea7u GRE l\u00e0m c\u01a1 s\u1edf \u0111\u00e1nh gi\u00e1 (nh\u01b0 Tokyo, Tohoku, \u2026), c\u00f2n n\u1ebfu mu\u1ed1n sang \u00c2u M\u1ef9 th\u00ec g\u1ea7n nh\u01b0 l\u00e0 b\u1eaft bu\u1ed9c (b\u00ean c\u1ea1nh TOEFL\/IELTS). G\u1ea7n \u0111\u00e2y th\u00ec k\u1ef3 thi n\u00e0y ng\u00e0y c\u00e0ng tr\u1edf n\u00ean c\u1ea1nh tranh, v\u00ec c\u00e0ng c\u00f3 nhi\u1ec1u ng\u01b0\u1eddi gi\u1ecfi tham gia, khi\u1ebfn cho vi\u1ec7c leo rank percentile c\u0169ng tr\u1edf n\u00ean kh\u1ed1c li\u1ec7t h\u01a1n. Sau m\u1ed9t th\u1eddi gian \u00f4n v\u00e0 thi th\u00ec \u0111\u00e2y l\u00e0 nh\u1eefng kinh nghi\u1ec7m \u0111\u00fac k\u1ebft \u0111\u01b0\u1ee3c cho ph\u1ea7n Quantitative Reasoning (General) m\u00e0 m\u00ecnh th\u1ea5y r\u1ea5t h\u1eefu \u00edch n\u1ebfu mu\u1ed1n \u0111\u01b0\u1ee3c \u0111i\u1ec3m cao. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Tips chung<\/h3>\n\n\n\n<p>Nh\u00ecn chung th\u00ec l\u00e0m b\u00e0i Quant. ph\u1ea3i \u0111\u1ecdc R\u1ea4T R\u1ea4T k\u1ef9.<\/p>\n\n\n\n<p>GRE r\u1ea5t hay l\u1eeba b\u1eb1ng 1 trong s\u1ed1 ho\u1eb7c t\u1ea5t c\u1ea3 c\u00e1c c\u00e1ch sau:<\/p>\n\n\n\n<p>+ c\u1ed1 t\u00ecnh d\u00f9ng ch\u1eef thay v\u00ec d\u00f9ng s\u1ed1. Ki\u1ec3u nh\u01b0 thay v\u00ec vi\u1ebft \u2018the 6th number\u2019 th\u00ec h\u1ecd vi\u1ebft \u2018the sixth number\u2019 nh\u1eb1m l\u00e0m ta b\u1ecb r\u1ed1i.<br>+ c\u1ed1 t\u00ecnh ch\u00e8n \u0111\u00e1p \u00e1n trung gian. Ki\u1ec3u nh\u01b0 \u0111\u1ec3 ra \u0111\u01b0\u1ee3c \u0111\u00fang \u0111\u00e1p s\u1ed1, c\u00e1c b\u1ea1n ph\u1ea3i t\u00ednh to\u00e1n k\u1ebft qu\u1ea3 b\u01b0\u1edbc 1, d\u00f9ng b\u01b0\u1edbc 1 \u0111\u1ec3 t\u00ednh b\u01b0\u1edbc 2. L\u1ebd ra n\u00ean khoanh k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng \u1edf b\u01b0\u1edbc 2 th\u00ec nhi\u1ec1u khi ta nh\u00ecn nh\u1ea7m ho\u1eb7c r\u1ed1i lo\u1ea1n n\u00ean khoanh k\u1ebft qu\u1ea3 c\u1ee7a b\u01b0\u1edbc 1.<br>V\u00ed d\u1ee5:<br>H\u1ecfi b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n th\u00ec l\u1ea1i t\u00ednh \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng k\u00ednh nh\u01b0ng qu\u00ean chia 2<br>H\u1ecfi di\u1ec7n t\u00edch h\u00ecnh tam gi\u00e1c th\u00ec t\u00ednh \u0111\u01b0\u1ee3c t\u00edch a.h r\u1ed3i nh\u01b0ng qu\u00ean chia 2<br>H\u1ecfi 3 l\u1ea7n x th\u00ec t\u00ednh \u0111\u01b0\u1ee3c x r\u1ed3i xong qu\u00ean nh\u00e2n 3 \u2026<br>+ c\u1ed1 t\u00ecnh n\u00f3i sai \u0111\u01a1n v\u1ecb t\u00ednh. Nh\u01b0 ki\u1ec3u h\u1ecfi v\u1eadn t\u1ed1c km\/h nh\u01b0ng \u0111\u1ec1 b\u00e0i ch\u1ec9 c\u00f3 m\/s, c\u00e1c b\u1ea1n ph\u1ea3i t\u1ef1 \u0111\u1ed5i. Ho\u1eb7c m\u1ed7i \u0111\u1ec1 b\u00e0i d\u00f9ng \u0111\u01a1n v\u1ecb l\u00e0 Tu\u1ea7n nh\u01b0ng c\u00e2u h\u1ecfi l\u00e0 h\u1ecfi v\u1ec1 Ng\u00e0y, n\u00ean mu\u1ed1n ra \u0111\u00e1p s\u1ed1 \u0111\u00fang ph\u1ea3i x7 ch\u1eb3ng h\u1ea1n. N\u1ebfu kh\u00f4ng tinh \u00fd th\u00ec d\u1ec5 khoanh sai.<\/p>\n\n\n\n<p>=&gt; N\u1ebfu kh\u00f4ng c\u1ea9n th\u1eadn th\u00ec s\u1ebd r\u1ea5t d\u1ec5 m\u1ea5t \u0111i\u1ec3m. Nh\u1edb r\u1eb1ng, 1 \u0111i\u1ec3m \u0111\u1ea1t \u0111\u01b0\u1ee3c trong GRE ph\u1ea7n Quant. c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 3 PERCENTILE RANK!!<\/p>\n\n\n\n<p>Do \u0111\u00f3, kh\u00f4ng c\u00f3 ch\u1ed7 cho nh\u1eefng sai l\u1ea7m ng\u1edb ng\u1ea9n.<\/p>\n\n\n\n<p><strong>M\u1ed9t s\u1ed1 l\u1eddi khuy\u00ean:<\/strong><\/p>\n\n\n\n<p>+ D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p substitute \u0111\u1ec3 th\u1eed ho\u1eb7c t\u00ednh nhanh. N\u1ebfu nh\u01b0 h\u1ecd b\u1ea3o so s\u00e1nh A v\u00e0 B m\u00e0 c\u00f3 \u1ea9n, c\u00f3 th\u1ec3 thay \u1ea9n \u0111\u00f3 b\u1eb1ng 1 s\u1ed1 c\u1ee5 th\u1ec3 n\u00e0o \u0111\u00f3 \u0111\u1ec3 th\u1eed (th\u01b0\u1eddng l\u00e0 <strong>1<\/strong>). \u0110\u1eb7c bi\u1ec7t trong c\u00e1c ph\u1ea7n b\u00e0i v\u1ec1 t\u00ednh ph\u1ea7n tr\u0103m, nhi\u1ec1u khi s\u1ed1 g\u1ed1c r\u1ea5t to v\u00e0 kh\u00f3 t\u00ednh, ch\u00fang ta c\u00f3 th\u1ec3 normalize n\u00f3 v\u1ec1 s\u1ed1 nh\u1ecf h\u01a1n cho d\u1ec5 t\u00ednh.<br>+ N\u1ebfu g\u1eb7p m\u1ed9t b\u00e0i t\u00ecm x, lu\u00f4n ki\u1ec3m tra xem x l\u00e0 s\u1ed1 NGUY\u00caN (integer) hay kh\u00f4ng? (ki\u1ec3u nh\u01b0 n\u00f3 c\u00f3 th\u1ec3 l\u00e0 1\/3, 2\/7, \u2026 kh\u00f4ng). V\u00e0 mi\u1ec1n gi\u00e1 tr\u1ecb c\u1ee7a x (&gt;0, &lt;0, \u22650, \u22640, \u2026)<br>+ Sau khi ch\u1ecdn xong \u0111\u00e1p \u00e1n, lu\u00f4n lu\u00f4n \u0111\u1ecdc l\u1ea1i c\u00e2u h\u1ecfi v\u00e0 th\u1eed l\u1ea1i \u0111\u1ec3 ch\u1eafc ch\u1eafn l\u00e0 kh\u00f4ng b\u1ecb sai \u2018ng\u1edb ng\u1ea9n\u2019.<br>+ Sau khi thi xong, khi c\u00f3 \u0111i\u1ec3m, ph\u1ea3i nh\u1edb check Diagnostics.<br>+ N\u1ebfu c\u00e1c b\u1ea1n d\u00f9ng s\u00e1ch 5lbs c\u1ee7a Manhattan, kh\u00f4ng \u0111\u01b0\u1ee3c ph\u00e9p b\u1ecf s\u00f3t b\u1ea5t c\u1ee9 b\u00e0i n\u00e0o trong Advanced Quant.<br><\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Ph\u1ea7n arithmatic, albegra v\u00e0 number properties<\/strong><\/h3>\n\n\n\n<p>M\u1ee5c n\u00e0y l\u00e0 c\u00e1c ph\u00e9p to\u00e1n ch\u00fang ta ch\u1eafc ai c\u0169ng \u0111\u1ec1u bi\u1ebft t\u1eeb h\u1ed3i ti\u1ec3u h\u1ecdc. G\u1ea7n nh\u01b0 ch\u1eb3ng bao gi\u1edd d\u00f9ng \u0111\u1ebfn, nh\u1ea5t l\u00e0 \u1edf b\u1eadc graduate, \u1ea5y v\u1eady m\u00e0 trong GRE c\u00f3 kh\u00e1 nhi\u1ec1u. \u0110i\u1ec3n h\u00ecnh nh\u01b0:<\/p>\n\n\n\n<p><strong><em>+ Cho m\u1ed9t d\u00e3y s\u1ed1, t\u00ecm s\u1ed1 h\u1ea1ng th\u1ee9 n c\u1ee7a d\u00e3y:<\/em><\/strong><\/p>\n\n\n\n<p>=&gt; V\u1edbi d\u1ea1ng b\u00e0i n\u00e0y, th\u00f4ng th\u01b0\u1eddng ph\u1ea3i \u0111\u1ebfm s\u1ed1 \u2018jumps\u2018.<\/p>\n\n\n\n<p>V\u00ed d\u1ee5: If each number in a sequence is three more than the previous number, and the sixth number is 32, what is the 100th number?<\/p>\n\n\n\n<p>A. 312<br>B. 313<br>C. 314<br>D. 315<br>E. 316<\/p>\n\n\n\n<p>=&gt; Mu\u1ed1n gi\u1ea3i \u0111\u01b0\u1ee3c th\u00ec c\u1ea7n x\u00e1c \u0111\u1ecbnh s\u1ed1 jumps c\u1ee7a n\u00f3. Trong b\u00e0i n\u00e0y, m\u1ed7i jump l\u00e0 b\u1eb1ng 3. S\u1ed1 th\u1ee9 6th l\u00e0 32, nh\u01b0 v\u1eady t\u1eeb s\u1ed1 n\u00e0y \u0111\u1ebfn s\u1ed1 th\u1ee9 100th c\u1ee7a d\u00e3y, c\u00f3 94 jumps of 3, v\u00e0 nh\u01b0 v\u1eady s\u1ed1 th\u1ee9 100th s\u1ebd nhi\u1ec1u h\u01a1n s\u1ed1 th\u1ee9 6th 94\u00d73=282 \u0111\u01a1n v\u1ecb, v\u00e0 nh\u01b0 v\u1eady, s\u1ed1 h\u1ea1ng th\u1ee9 100th l\u00e0 32+282 = 314.<\/p>\n\n\n\n<p><strong>T\u1ed5ng qu\u00e1t:<\/strong><\/p>\n\n\n\n<p>N\u1ebfu d\u00e3y l\u00e0 arithmetic sequence (kho\u1ea3ng c\u00e1ch gi\u1eefa c\u00e1c s\u1ed1 li\u00ean ti\u1ebfp l\u00e0 b\u1eb1ng nhau)<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=a_1%2C+a_2%2C+...%2C+a_n&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"a_1, a_2, ..., a_n\" title=\"\"><\/figure>\n\n\n\n<p>D\u00e3y  (n s\u1ed1 h\u1ea1ng)<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=d&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"d\" title=\"\"><\/figure>\n\n\n\n<p>Common difference (kho\u1ea3ng c\u00e1ch gi\u1eefa c\u00e1c s\u1ed1 li\u00ean ti\u1ebfp) l\u00e0 <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=a_n+%3D+a_1+%2B+%28n+-+1%29d&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"a_n = a_1 + (n - 1)d\" title=\"\"><\/figure>\n\n\n\n<p>Th\u00ec: <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=S_n+%3D+%5Cfrac%7Bn%7D%7B2%7D%28a_1+%2B+a_n%29&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"S_n = frac{n}{2}(a_1 + a_n)\" title=\"\"><\/figure>\n\n\n\n<p>T\u1ed5ng c\u1ee7a d\u00e3y: <\/p>\n\n\n\n<p>N\u1ebfu d\u00e3y l\u00e0 geometric sequence (t\u1ef7 l\u1ec7 gi\u1eefa c\u00e1c s\u1ed1 li\u00ean ti\u1ebfp l\u00e0 b\u1eb1ng nhau)<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=a_1%2C+a_2%2C+...%2C+a_n&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"a_1, a_2, ..., a_n\" title=\"\"><\/figure>\n\n\n\n<p>D\u00e3y  (n s\u1ed1 h\u1ea1ng)<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=r&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"r\" title=\"\"><\/figure>\n\n\n\n<p>Common ratio (t\u1ef7 l\u1ec7 gi\u1eefa c\u00e1c s\u1ed1 li\u00ean ti\u1ebfp) l\u00e0 <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=a_n+%3D+a_1+%5C+r%5E%7Bn+-+1%7D&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"a_n = a_1  r^{n - 1}\" title=\"\"><\/figure>\n\n\n\n<p>Th\u00ec: <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=S_n+%3D+a_1%281+%2B+r+%2B+r%5E2+%2B+...+%2B+r%5E%7Bn-1%7D%29+%3D+a_1+%5Cfrac%7B1-r%5En%7D%7B1-r%7D&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"S_n = a_1(1 + r + r^2 + ... + r^{n-1}) = a_1 frac{1-r^n}{1-r}\" title=\"\"><\/figure>\n\n\n\n<p>T\u1ed5ng c\u1ee7a d\u00e3y: <\/p>\n\n\n\n<p><strong><em>+ H\u1ecfi s\u1ed1 h\u1ea1ng h\u00e0ng \u0111\u01a1n v\u1ecb:<\/em><\/strong><\/p>\n\n\n\n<p>M\u1ed9t b\u00e0i to\u00e1n ti\u1ec3u h\u1ecdc t\u01b0\u1edfng nh\u01b0 ngon \u0103n nh\u01b0ng nhi\u1ec1u khi \u0103n kh\u00f4ng h\u1ec1 ngon t\u00ed n\u00e0o.<\/p>\n\n\n\n<p>Trong ti\u1ebfng Anh, s\u1ed1 h\u1ea1ng h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 <strong>units digit<\/strong>, h\u00e0ng ch\u1ee5c l\u00e0 <strong>tens digit<\/strong>.<\/p>\n\n\n\n<p>=&gt; V\u1edbi d\u1ea1ng n\u00e0y th\u00ec ph\u1ea3i t\u00ecm quy lu\u1eadt.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=S_n+%3D+3%5En&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"S_n = 3^n\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=S_%7B65%7D+&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"S_{65} \" title=\"\"><\/figure>\n\n\n\n<p>V\u00ed d\u1ee5: if , what is the unit digit of  ?<\/p>\n\n\n\n<p>=&gt; N\u1ebfu ch\u01b0a ph\u00e1t hi\u1ec7n ra ngay quy lu\u1eadt th\u00ec ch\u00fang ta c\u1ee9 vi\u1ebft ra v\u00e0 t\u00ednh. L\u01b0u \u00fd l\u00e0 kh\u00f4ng c\u1ea7n ph\u1ea3i t\u00ednh ra \u0111\u00e1p s\u1ed1, ch\u1ec9 c\u1ea7n bi\u1ebft h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 bao nhi\u00eau l\u00e0 \u0111\u01b0\u1ee3c.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=3%5E1+%3D+3&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"3^1 = 3\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=3%5E2+%3D+9&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"3^2 = 9\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=3%5E3+%3D+27&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"3^3 = 27\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=3%5E4+%3D+81&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"3^4 = 81\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=3%5E5+%3D+..3&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"3^5 = ..3\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=3%5E6+%3D+..9&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"3^6 = ..9\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=3%5E7+%3D+..7&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"3^7 = ..7\" title=\"\"><\/figure>\n\n\n\n<p>Nh\u01b0 v\u1eady, quy lu\u1eadt l\u00e0 1 -&gt; 3 -&gt; 9 -&gt; 7 r\u1ed3i l\u1eb7p l\u1ea1i, t\u1ee9c l\u00e0 quy lu\u1eadt l\u1eb7p l\u1ea1i sau m\u1ed7i \u20184 terms\u2019, tu\u1ef3 v\u00e0o n t\u01b0\u01a1ng \u1ee9ng. N\u00ean c\u00e1c b\u1ea1n l\u1ea5y n, chia cho 4, \u0111\u1ebfm s\u1ed1 d\u01b0.<\/p>\n\n\n\n<p>N\u1ebfu d\u01b0 1 th\u00ec theo quy lu\u1eadt, h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 1<br>N\u1ebfu d\u01b0 2 th\u00ec theo quy lu\u1eadt, h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 3<br>N\u1ebfu d\u01b0 3 th\u00ec theo quy lu\u1eadt, h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 9<br>N\u1ebfu d\u01b0 0 th\u00ec theo quy lu\u1eadt, h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 7<\/p>\n\n\n\n<p>65\/4 d\u01b0 1, v\u1eady unit digit=3. B\u00e0i n\u00e0y ph\u1ea3i c\u1ea9n th\u1eadn v\u00ec n\u1ebfu nh\u01b0 n chia h\u1ebft cho s\u1ed1 term th\u00ec unit digit l\u00e0 7 (term cu\u1ed1i) ch\u1ee9 kh\u00f4ng ph\u1ea3i l\u00e0 1 (term \u0111\u1ea7u ti\u00ean).<\/p>\n\n\n\n<p><strong><em>+ H\u1ecfi v\u1ec1 t\u00ednh chia h\u1ebft:<\/em><\/strong><\/p>\n\n\n\n<p>M\u1ea5y c\u00e1i \u0111\u01a1n gi\u1ea3n nh\u01b0 chia h\u1ebft cho 2,3,5,10 th\u00ec kh\u00f4ng n\u00f3i.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"777\" height=\"386\" src=\"https:\/\/scholarshipplanet.info\/vi\/wp-content\/uploads\/2021\/07\/Noname.png\" alt=\"\" class=\"wp-image-60116\" title=\"\" srcset=\"https:\/\/scholarshipplanet.info\/vi\/wp-content\/uploads\/2021\/07\/Noname.png 777w, https:\/\/scholarshipplanet.info\/vi\/wp-content\/uploads\/2021\/07\/Noname-486x241.png 486w, https:\/\/scholarshipplanet.info\/vi\/wp-content\/uploads\/2021\/07\/Noname-300x149.png 300w, https:\/\/scholarshipplanet.info\/vi\/wp-content\/uploads\/2021\/07\/Noname-768x382.png 768w\" sizes=\"(max-width: 777px) 100vw, 777px\" \/><\/figure>\n\n\n\n<p><strong><em>+ V\u1ec1 d\u00e3y s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp<\/em><\/strong><\/p>\n\n\n\n<p>C\u00f3 m\u1ed9t s\u1ed1 quy lu\u1eadt c\u00e1c b\u1ea1n n\u00ean nh\u1edb \u0111\u1ec3 l\u00e0m b\u00e0i cho nhanh.<\/p>\n\n\n\n<p>Li\u00ean quan \u0111\u1ebfn t\u00ednh chia h\u1ebft<\/p>\n\n\n\n<ul><li>N\u1ebfu s\u1ed1 s\u1ed1 h\u1ea1ng li\u00ean ti\u1ebfp l\u00e0 l\u1ebb th\u00ec<br>T\u1ed5ng c\u00e1c s\u1ed1 h\u1ea1ng lu\u00f4n  s\u1ed1 s\u1ed1 h\u1ea1ng<br>V\u00ed d\u1ee5: 1,2,3,4,5 c\u00f3 s\u1ed1 s\u1ed1 h\u1ea1ng l\u00e0 5 (m\u1ed9t s\u1ed1 l\u1ebb) =&gt; T\u1ed5ng 1+2+3+4+5 = 15  5<\/li><li>N\u1ebfu s\u1ed1 s\u1ed1 h\u1ea1ng li\u00ean ti\u1ebfp l\u00e0 ch\u1eb5n th\u00ec<br>T\u1ed5ng c\u00e1c s\u1ed1 h\u1ea1ng s\u1ebd <strong>kh\u00f4ng<\/strong>  s\u1ed1 s\u1ed1 h\u1ea1ng<br>V\u00ed d\u1ee5: 1,2,3,4 c\u00f3 s\u1ed1 s\u1ed1 h\u1ea1ng l\u00e0 4 (m\u1ed9t s\u1ed1 ch\u1eb5n) =&gt; T\u1ed5ng 1+2+3+4 = 10  4<\/li><\/ul>\n\n\n\n<p>Li\u00ean quan \u0111\u1ebfn t\u1ed5ng<\/p>\n\n\n\n<ul><li>T\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp t\u1eeb 1 \u0111\u1ebfn n:<\/li><li>\n\n<\/li><li>T\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp t\u1eeb m \u0111\u1ebfn n.<br>Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y th\u00ec t\u00ednh t\u1ed5ng t\u1eeb 1 \u0111\u1ebfn n, r\u1ed3i tr\u1eeb \u0111i t\u1ed5ng t\u1eeb 1 \u0111\u1ebfn (m-1)<\/li><li>\nSuy ra t\u1eeb t\u1ed5ng t\u1eeb m -&gt; n s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp:<br>\n<\/li><li>T\u1ed5ng c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean ch\u1eb5n, v\u00ed d\u1ee5 t\u1eeb 1 \u0111\u1ebfn 100 th\u00ec n\u00ean t\u00e1ch ra v\u00e0 n\u00f3 s\u1ebd tr\u1edf th\u00e0nh:<\/li><li>\n\n<\/li><\/ul>\n\n\n\n<p><strong><em>+ H\u1ecfi s\u1ed1 factors (th\u1eeba s\u1ed1) c\u1ee7a m\u1ed9t s\u1ed1:<\/em><\/strong><\/p>\n\n\n\n<p>L\u1ea1i m\u1ed9t b\u00e0i to\u00e1n ti\u1ec3u h\u1ecdc nh\u01b0ng c\u0169ng g\u00e2y nhi\u1ec1u hoang mang. M\u00ecnh kh\u00f4ng r\u00f5 c\u00f3 c\u00e1ch n\u00e0o hay h\u01a1n c\u00e1ch n\u00e0y kh\u00f4ng, nh\u01b0ng \u0111\u00e2y l\u00e0 c\u00e1ch \u0111\u1ec3 c\u00e1c b\u1ea1n \u201c\u0111\u1ebfm\u201d s\u1ed1 th\u1eeba s\u1ed1 m\u00e0 kh\u00f4ng b\u1ecb s\u00f3t m\u00e0 Manhattan d\u1ea1y)<\/p>\n\n\n\n<p><strong>B1:<\/strong> ph\u00e2n t\u00edch th\u00e0nh th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1.<\/p>\n\n\n\n<p><strong>B2:<\/strong> l\u1eadp b\u1ea3ng factor pairs (c\u1eb7p th\u1eeba s\u1ed1)<\/p>\n\n\n\n<p><strong>B3:<\/strong> \u0111\u1ebfm (nh\u1edb \u0111\u1ebfm 1 v\u00e0 ch\u00ednh n\u00f3)<\/p>\n\n\n\n<p>V\u00ed d\u1ee5 t\u00ecm all factors c\u1ee7a 60.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=60+%3D+2+%5Ctimes+2+%5Ctimes+3+%5Ctimes+5+%3D+2%5E2+%5Ctimes+3+%5Ctimes+5&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"60 = 2 times 2 times 3 times 5 = 2^2 times 3 times 5\" title=\"\"><\/figure>\n\n\n\n<p><strong>B1:<\/strong> Ph\u00e2n t\u00edch ra th\u00ec th\u00e0nh <\/p>\n\n\n\n<p><strong>B2:<\/strong> l\u1eadp b\u1ea3ng factor pairs<\/p>\n\n\n\n<table class=\"wp-block-table\"><tbody><tr><td>no.<\/td><td>Small<\/td><td>Large<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>2x2x3x5<\/td><\/tr><tr><td>2<\/td><td>2<\/td><td>2x3x5<\/td><\/tr><tr><td>3.<\/td><td>3<\/td><td>2x2x5<\/td><\/tr><tr><td>4.<\/td><td>2\u00d72<\/td><td>3\u00d75<\/td><\/tr><tr><td>5.<\/td><td>2\u00d73<\/td><td>2\u00d75<\/td><\/tr><tr><td>6.<\/td><td>2x2x3<\/td><td>5<\/td><\/tr><\/tbody><\/table>\n\n\n\n<p>Sau h\u00e0ng th\u1ee9 6 th\u00ec n\u00f3 s\u1ebd l\u1eb7p l\u1ea1i, n\u00ean ta d\u1eebng \u1edf \u0111\u00e2y.<\/p>\n\n\n\n<p><strong>B3:<\/strong> T\u1eeb b\u1ea3ng tr\u00ean ta s\u1ebd \u0111\u1ebfm th\u1ea5y s\u1ed1 60 c\u00f3 t\u1ed5ng c\u1ed9ng 12 factors.<\/p>\n\n\n\n<p>*** M\u1eb9o nhanh h\u01a1n sau khi l\u00e0m xong B\u01b0\u1edbc 1 (t\u1eeb <a href=\"https:\/\/www.reddit.com\/r\/GRE\/comments\/dpxktg\/q_170_v_156_unofficial_sharing_some_tips_on_how\/\" rel=\"nofollow noopener\" target=\"_blank\">Reddit<\/a>), b\u1ecf qua ph\u1ea7n l\u1eadp b\u1ea3ng factor pairs.<\/p>\n\n\n\n<p><strong>B1:<\/strong> V\u1eabn ph\u00e2n t\u00edch th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 nh\u01b0 b\u00ecnh th\u01b0\u1eddng.<\/p>\n\n\n\n<p><strong>B2:<\/strong> Sau khi ph\u00e2n t\u00edch ra th\u00e0nh th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 c\u00f3 d\u1ea1ng<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=a%5Ex+b%5Ey+c%5Ez&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"a^x b^y c^z\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%28x%2B1%29%28y%2B1%29%28z%2B1%29&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"(x+1)(y+1)(z+1)\" title=\"\"><\/figure>\n\n\n\n<p> th\u00ec t\u1ed5ng s\u1ed1 factors s\u1ebd l\u00e0 <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=60+%3D+2%5E2.3%5E1.5%5E1&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"60 = 2^2.3^1.5^1\" title=\"\"><\/figure>\n\n\n\n<p>Nh\u01b0 v\u1eady, nh\u00ecn v\u00e0o s\u1ed1 60, ta th\u1ea5y n\u00f3 ph\u00e2n t\u00edch \u0111\u01b0\u1ee3c th\u00e0nh <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%282%2B1%29+%5Ctimes+%281%2B1%29+%5Ctimes+%281%2B1%29+%3D+12&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"(2+1) times (1+1) times (1+1) = 12\" title=\"\"><\/figure>\n\n\n\n<p>n\u00ean t\u1ed5ng factors s\u1ebd l\u00e0 <\/p>\n\n\n\n<p><strong><em>+ Exponents (Lu\u1ef9 th\u1eeba):<\/em><\/strong><\/p>\n\n\n\n<p>N\u1ebfu nh\u1edb \u0111\u01b0\u1ee3c c\u00e1c quy t\u1eafc sau th\u00ec c\u00f3 th\u1ec3 tr\u00e1nh \u0111\u01b0\u1ee3c c\u00e1c b\u01b0\u1edbc t\u00ednh to\u00e1n kh\u00f4ng c\u1ea7n thi\u1ebft khi so s\u00e1nh.<\/p>\n\n\n\n<ul><li>M\u1ed9t s\u1ed1 b\u1ea5t k\u1ef3 &lt;1 m\u00e0 lu\u1ef9 th\u1eeba &gt;1 s\u1ebd l\u00e0m s\u1ed1 \u0111\u00f3 nh\u1ecf \u0111i<\/li><li>\n\n<\/li><li>M\u1ed9t s\u1ed1 b\u1ea5t k\u1ef3 m\u00e0 nh\u00e2n v\u1edbi m\u1ed9t s\u1ed1 &gt;1 s\u1ebd lu\u00f4n l\u00e0m s\u1ed1 \u0111\u00f3 l\u1edbn h\u01a1n<\/li><li>\n\n<\/li><li>(Nh\u01b0 v\u1eady, <\/li><li>B\u00ecnh ph\u01b0\u01a1ng 1 fraction (ph\u00e2n s\u1ed1) trong kho\u1ea3ng 0 -&gt; 1 s\u1ebd lu\u00f4n l\u00e0m n\u00f3 nh\u1ecf \u0111i<br>L\u1ea5y c\u0103n c\u1ee7a 1 fraction c\u0169ng trong kho\u1ea3ng \u0111\u00f3 s\u1ebd lu\u00f4n l\u00e0m n\u00f3 l\u1edbn h\u01a1n<\/li><\/ul>\n\n\n\n<p>M\u1ed9t s\u1ed1 gi\u00e1 tr\u1ecb hay g\u1eb7p:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csqrt%7B2%7D+%5Capprox+1.4&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sqrt{2} approx 1.4\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csqrt%7B3%7D+%5Capprox+1.7&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sqrt{3} approx 1.7\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csqrt%7B4%7D+%3D+2&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sqrt{4} = 2\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csqrt%7B5%7D+%5Capprox+2.24&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sqrt{5} approx 2.24\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csqrt%7B6%7D+%5Capprox+2.45&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sqrt{6} approx 2.45\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csqrt%7B7%7D+%5Capprox+2.65&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sqrt{7} approx 2.65\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csqrt%7B8%7D+%5Capprox+2.83&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sqrt{8} approx 2.83\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csqrt%7B9%7D+%3D+3&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sqrt{9} = 3\" title=\"\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Ph\u1ea7n Fractions, Decimals, Division v\u00e0 Percents<\/h3>\n\n\n\n<p><strong>+ Quy t\u1eafc:<\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>(1\/x)\/y = 1\/xy<\/p><p>1\/(x\/y) = y\/x<\/p><\/blockquote>\n\n\n\n<p><strong><em>+ So s\u00e1nh:<\/em><\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Th\u00f4ng th\u01b0\u1eddng \u0111\u1ec3 so s\u00e1nh gi\u1eefa A v\u00e0 B th\u00ec c\u1ee9 l\u1ea5y A \u2013 B<br>A \u2013 B &gt; 0 th\u00ec A &gt; B<br>A \u2013 B &lt; 0 th\u00ec A &lt; B<br>A \u2013 B = 0 th\u00ec A = B <\/p><\/blockquote>\n\n\n\n<p>Trong m\u1ed9t s\u1ed1 tr\u01b0\u1eddng h\u1ee3p, ch\u00fang ta c\u00f3 th\u1ec3 d\u00f9ng benchmark \u0111\u1ec3 so s\u00e1nh cho nhanh.<\/p>\n\n\n\n<p>V\u00ed d\u1ee5: so s\u00e1nh A. <strong>127\/255<\/strong> v\u00e0 B. <strong>162\/320<\/strong>.<\/p>\n\n\n\n<p>N\u1ebfu tinh \u00fd s\u1ebd th\u1ea5y ph\u00e2n s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c d\u00f9ng l\u00e0m benchmark \u1edf \u0111\u00e2y l\u00e0 1\/2, ta th\u1ea5y A &lt; 1\/2 v\u00e0 B &gt; 1\/2 n\u00ean suy ra B &gt; A.<\/p>\n\n\n\n<p>**\u0110\u1eb7c bi\u1ec7t, v\u1edbi ph\u00e2n s\u1ed1 th\u00ec c\u00f3 1 m\u1eb9o nhanh n\u1eefa \u0111\u00f3 l\u00e0 nh\u00e2n ch\u00e9o<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=A.+%5Cfrac%7Ba%7D%7Bb%7D&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"A. frac{a}{b}\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=B.+%5Cfrac%7Bc%7D%7Bd%7D&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"B. frac{c}{d}\" title=\"\"><\/figure>\n\n\n\n<p>So s\u00e1nh  v\u00e0 <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=ad+%3E+bc&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"ad &gt; bc\" title=\"\"><\/figure>\n\n\n\n<p>N\u1ebfu  th\u00ec A &gt; B.<\/p>\n\n\n\n<p><strong><em>+ T\u0103ng gi\u1ea3m:<\/em><\/strong><\/p>\n\n\n\n<p>D\u1ea1ng n\u00e0y \u0111\u1ec1 n\u00e0o c\u0169ng c\u00f3. Ki\u1ec3u nh\u01b0 h\u1ecfi l\u00e0 \u201d X t\u0103ng l\u00ean 20% sau \u0111\u00f3 gi\u1ea3m \u0111i 5% th\u00ec cu\u1ed1i c\u00f9ng c\u00f2n l\u1ea1i bao nhi\u00eau X?\u201d<\/p>\n\n\n\n<p>D\u1ea1ng n\u00e0y c\u00f2n g\u1ecdi l\u00e0 successive percents, c\u00e1ch l\u00e0m nhanh nh\u01b0 sau:<\/p>\n\n\n\n<ul><li>t\u0103ng 20% ngh\u0129a l\u00e0 s\u1ed1 \u0111\u00f3 nh\u00e2n v\u1edbi 1.2<\/li><li>gi\u1ea3m 5% ngh\u0129a l\u00e0 s\u1ed1 \u0111\u00f3 nh\u00e2n v\u1edbi 0.95<\/li><\/ul>\n\n\n\n<p>C\u00e1ch t\u00ednh nhanh cho b\u00e0i tr\u00ean s\u1ebd l\u00e0:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Ctext%7BNew+%7D+X+%3D+X+%5Ctimes+1.2+%5Ctimes+0.95+%3D+1.14+X&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"text{New } X = X times 1.2 times 0.95 = 1.14 X\" title=\"\"><\/figure>\n\n\n\n<p>Khi b\u00e0i h\u1ecfi t\u0103ng th\u00eam bao nhi\u00eau ph\u1ea7n tr\u0103m.<\/p>\n\n\n\n<p>V\u00ed d\u1ee5: N\u0103m ngo\u00e1i c\u00f3 $1240, n\u0103m nay c\u00f3 $1960, h\u1ecfi t\u0103ng bao nhi\u00eau %.<\/p>\n\n\n\n<p>Thay v\u00ec t\u00ednh (1960-1240)\/1240 \u0111\u1ec3 ra 58%.<\/p>\n\n\n\n<p>Ta l\u1ea5y th\u1eb3ng:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>1960\/1240 = 1.58 r\u1ed3i tr\u1eeb 1 th\u1ea5y b\u1eb1ng 0.58 v\u00e0 suy ra lu\u00f4n l\u00e0 t\u0103ng th\u00eam 58%.<\/p><\/blockquote>\n\n\n\n<p>Gi\u1ea3 s\u1eed n\u1ebfu ng\u01b0\u1ee3c l\u1ea1i, n\u0103m nay l\u00e0 $1240 v\u00e0 n\u0103m ngo\u00e1i l\u00e0 $1960 th\u00ec l\u1ea5y<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>1240\/1960 = 0.63 r\u1ed3i tr\u1eeb 1 th\u1ea5y c\u00f2n -0.37, suy ra n\u00f3 gi\u1ea3m \u0111i 37%.<\/p><\/blockquote>\n\n\n\n<p>B\u1edbt th\u00eam 1 b\u01b0\u1edbc trung gian l\u00e0 ti\u1ebft ki\u1ec7m \u0111\u01b0\u1ee3c r\u1ea5t nhi\u1ec1u th\u1eddi gian b\u1ea5m m\u00e1y t\u00ednh r\u1ed3i.<\/p>\n\n\n\n<p><strong><em>+ L\u00e3i su\u1ea5t:<\/em><\/strong><\/p>\n\n\n\n<p>C\u00f3 2 d\u1ea1ng l\u00e0 simple interest rate v\u00e0 compound interest rate.<\/p>\n\n\n\n<p>C\u00f4ng th\u1ee9c: (m\u1eb7c \u0111\u1ecbnh r l\u00e0 %\/n\u0103m) v\u00e0 t l\u00e0 s\u1ed1 n\u0103m.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=V+%3D+P%281+%2B+rt%29&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"V = P(1 + rt)\" title=\"\"><\/figure>\n\n\n\n<p>L\u00e3i su\u1ea5t \u0111\u01a1n: <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=V+%3D+P%281+%2B+%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"V = P(1 + frac{r}{n})^{nt}\" title=\"\"><\/figure>\n\n\n\n<p>L\u00e3i su\u1ea5t k\u00e9p:  v\u1edbi n l\u00e0 s\u1ed1 compound frequency m\u1ed7i n\u0103m.<\/p>\n\n\n\n<p>V\u00ed d\u1ee5 1 ng\u01b0\u1eddi vay P = $2 v\u1edbi l\u00e3i su\u1ea5t l\u00e0 r = 6% \/ n\u0103m. V\u1eady sau 1 n\u0103m, ng\u01b0\u1eddi n\u00e0y ph\u1ea3i tr\u1ea3 bao nhi\u00eau?<\/p>\n\n\n\n<p>Nh\u01b0 v\u1eady, t=1<\/p>\n\n\n\n<ul><li>N\u1ebfu l\u00e0 l\u00e3i su\u1ea5t \u0111\u01a1n (simple interest rate) th\u00ec sau 1 n\u0103m ng\u01b0\u1eddi n\u00e0y ph\u1ea3i tr\u1ea3:<br><\/li><li>N\u1ebfu l\u00e0 l\u00e3i su\u1ea5t k\u00e9p (compound interest rate) v\u1edbi compound frequency l\u00e0 4 (t\u1ee9c l\u00e0 c\u1ed9ng l\u00e3i h\u1eb1ng qu\u00fd, do 1 n\u0103m c\u00f3 4 qu\u00fd) th\u00ec sau 1 n\u0103m, ng\u01b0\u1eddi n\u00e0y ph\u1ea3i tr\u1ea3:<br><\/li><li>N\u1ebfu l\u00e0 l\u00e3i su\u1ea5t k\u00e9p v\u1edbi compound frequency n=12 (t\u1ee9c l\u00e0 c\u1ed9ng l\u00e3i h\u1eb1ng th\u00e0ng) th\u00ec sau 1 n\u0103m, ng\u01b0\u1eddi n\u00e0y ph\u1ea3i tr\u1ea3:<br><\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Ph\u1ea7n h\u00ecnh h\u1ecdc<\/strong><\/h3>\n\n\n\n<p>Ph\u1ea7n n\u00e0y m\u00ecnh th\u1ea5y kh\u00f4ng kh\u00f3, c\u0169ng r\u01a1i v\u00e0o ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n th\u00f4i (c\u00f4ng th\u1ee9c t\u00ednh chu vi, di\u1ec7n t\u00edch c\u00e1c h\u00ecnh l\u00e0 g\u00ec.<\/p>\n\n\n\n<p>Quan tr\u1ecdng l\u00e0 ph\u1ea3i <strong>bi\u1ebft<\/strong> t\u1eeb v\u1ef1ng v\u00e0 nh\u1edb m\u1ed9t s\u1ed1 m\u1eb9o v\u00e0 c\u00f4ng th\u1ee9c \u0111\u1ec3 ti\u1ebft ki\u1ec7m th\u1eddi gian, b\u1edbt \u0111i c\u00e1c b\u01b0\u1edbc t\u00ednh to\u00e1n trung gian kh\u00f4ng c\u1ea7n thi\u1ebft.<\/p>\n\n\n\n<p><strong><em>+ T\u1eeb v\u1ef1ng:<\/em><\/strong><\/p>\n\n\n\n<p>Square = h\u00ecnh vu\u00f4ng<\/p>\n\n\n\n<p>Rectangle = h\u00ecnh ch\u1eef nh\u1eadt<\/p>\n\n\n\n<p>Parallelogram = h\u00ecnh b\u00ecnh th\u00e0nh<\/p>\n\n\n\n<p>Rhombus = h\u00ecnh thoi<\/p>\n\n\n\n<p>Trapezoid = h\u00ecnh thang<\/p>\n\n\n\n<p>\u2026<\/p>\n\n\n\n<p>Equilateral triangle = tam gi\u00e1c \u0111\u1ec1u<\/p>\n\n\n\n<p>Isosceles triangle = tam gi\u00e1c c\u00e2n<\/p>\n\n\n\n<p>Right triangle = tam gi\u00e1c vu\u00f4ng.<\/p>\n\n\n\n<p>Trong tam gi\u00e1c vu\u00f4ng th\u00ec Hypotenuse = c\u1ea1nh huy\u1ec1n, opposite leg = c\u1ea1nh \u0111\u1ed1i, adjacent leg = c\u1ea1nh k\u1ec1.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=a%5E2+%2B+b%5E2+%3D+c%5E2&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"a^2 + b^2 = c^2\" title=\"\"><\/figure>\n\n\n\n<p>\u0110\u1ecbnh l\u00fd Pytago: <\/p>\n\n\n\n<p>C\u00e1c b\u1ed9 hay g\u1eb7p: (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17)<\/p>\n\n\n\n<p>Trong h\u00ecnh tr\u00f2n th\u00ec arc length = chi\u1ec1u d\u00e0i d\u00e2y cung<\/p>\n\n\n\n<p>\u2026<\/p>\n\n\n\n<p>C\u00f9ng \u0111\u1ec3 ch\u1ec9 chu vi nh\u01b0ng m\u00e0<\/p>\n\n\n\n<ul><li>Perimeter l\u00e0 chu vi c\u00e1c h\u00ecnh kh\u00f4ng ph\u1ea3i h\u00ecnh tr\u00f2n<\/li><li>Circumference \u0111\u01b0\u1ee3c d\u00f9ng ri\u00eang cho h\u00ecnh tr\u00f2n<\/li><\/ul>\n\n\n\n<p>Area = di\u1ec7n t\u00edch (d\u00f9ng chung)<\/p>\n\n\n\n<p>Radius = b\u00e1n k\u00ednh, Diameter = \u0111\u01b0\u1eddng k\u00ednh<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/nipponkiyoshi.files.wordpress.com\/2021\/01\/167.png?w=660\" alt=\"\" class=\"wp-image-3053\" title=\"\"><\/figure><\/div>\n\n\n\n<p><strong><em>+ C\u00f4ng th\u1ee9c \u0111\u00e1ng nh\u1edb:<\/em><\/strong><\/p>\n\n\n\n<ul><li>V\u1edbi tam gi\u00e1c \u0111\u1ec1u th\u00ec c\u00f4ng th\u1ee9c t\u00ednh nhanh di\u1ec7n t\u00edch l\u00e0<br><\/li><li>V\u1edbi b\u1ea5t k\u1ef3 tam gi\u00e1c n\u00e0o m\u00e0 bi\u1ebft hai c\u1ea1nh a, b v\u00e0 g\u00f3c  t\u1ea1o b\u1edfi 2 c\u1ea1nh \u0111\u00f3, s\u1ebd lu\u00f4n t\u00ednh \u0111\u01b0\u1ee3c di\u1ec7n t\u00edch v\u1edbi c\u00f4ng th\u1ee9c l\u00e0:<br><\/li><li>C\u00f4ng th\u1ee9c HERON<br>T\u00ednh di\u1ec7n t\u00edch b\u1ea5t k\u1ef3 tam gi\u00e1c n\u00e0o m\u00e0 bi\u1ebft 3 c\u1ea1nh a,b,c (kh\u00f4ng c\u1ea7n bi\u1ebft g\u00f3c)<br>\u0110\u1ea7u ti\u00ean, t\u00ednh n\u1eeda chu vi (semi-perimeter) <br>=&gt; <\/li><\/ul>\n\n\n\n<p>GRE c\u0169ng hay h\u1ecfi v\u1ec1 b\u1ea5t \u0111\u1eb3ng th\u1ee9c trong tam gi\u00e1c. C\u1ee5 th\u1ec3:<\/p>\n\n\n\n<ul><li>\u0110\u1ed9 d\u00e0i m\u1ed7i c\u1ea1nh l\u1edbn h\u01a1n hi\u1ec7u \u0111\u1ed9 d\u00e0i hai c\u1ea1nh kia v\u00e0 nh\u1ecf h\u01a1n t\u1ed5ng \u0111\u1ed9 d\u00e0i c\u1ee7a ch\u00fang.<br>(Bigger side \u2013 Smaller side) &lt; x &lt; (Bigger side + Smaller side)<\/li><li>Trong m\u1ed9t tam gi\u00e1c, c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u1edbi g\u00f3c l\u1edbn h\u01a1n l\u00e0 c\u1ea1nh l\u1edbn h\u01a1n.<br>Ng\u01b0\u1ee3c l\u1ea1i, g\u00f3c \u0111\u1ed1i di\u1ec7n v\u1edbi c\u1ea1nh l\u1edbn h\u01a1n l\u00e0 g\u00f3c l\u1edbn h\u01a1n.<\/li><\/ul>\n\n\n\n<p>Ch\u00fa \u00fd l\u00e0 c\u00e1c b\u1ea1n n\u00ean \u00f4n l\u1ea1i c\u1ea3 ki\u1ebfn th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c.<\/p>\n\n\n\n<p>C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c gi\u00fap t\u00ednh ra c\u1ea1nh bi\u1ebft tr\u01b0\u1edbc g\u00f3c r\u1ea5t nhanh.<\/p>\n\n\n\n<p>V\u00ec nhi\u1ec1u b\u00e0i h\u00ecnh h\u1ecdc n\u00e2ng cao (nhi\u1ec1u \u0111i\u1ec3m) c\u00f3 li\u00ean quan \u0111\u1ebfn c\u00e1c c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c c\u01a1 b\u1ea3n (sin, cos c\u00e1c g\u00f3c \u0111\u1eb7c bi\u1ec7t). N\u1ebfu kh\u00f4ng nh\u1edb c\u00e1c g\u00f3c \u0111\u1eb7c bi\u1ec7t th\u00ec c\u1ee9 v\u1ebd \u0111\u01b0\u1eddng tr\u00f2n l\u01b0\u1ee3ng gi\u00e1c ra l\u00e0 suy ra \u0111\u01b0\u1ee3c ngay. (sin \u0111\u1ed1i\/huy\u1ec1n, cos k\u1ec1\/huy\u1ec1n)<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/nipponkiyoshi.files.wordpress.com\/2021\/01\/giatriluonggiaccuamotcung.png?w=660\" alt=\"\" class=\"wp-image-3050\" title=\"\"><\/figure><\/div>\n\n\n\n<p>M\u1ed9t s\u1ed1 gi\u00e1 tr\u1ecb hay g\u1eb7p:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csin+45+%3D+%5Ccos+45+%3D+%5Csqrt%7B2%7D%2F2+&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sin 45 = cos 45 = sqrt{2}\/2 \" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csin+30+%3D+%5Ccos+60+%3D+1%2F2+&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sin 30 = cos 60 = 1\/2 \" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csin+60+%3D+%5Ccos+30+%3D+%5Csqrt%7B3%7D%2F2+&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sin 60 = cos 30 = sqrt{3}\/2 \" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csin%5E2+%2B+%5Ccos%5E2+%3D+1&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sin^2 + cos^2 = 1\" title=\"\"><\/figure>\n\n\n\n<p><strong>+ To\u1ea1 \u0111\u1ed9<\/strong><\/p>\n\n\n\n<ul><li>Trong m\u1eb7t ph\u1eb3ng to\u1ea1 \u0111\u1ed9 0xy, cho<\/li><li>\n v\u00e0  th\u00ec<br>kho\u1ea3ng c\u00e1ch (distance) gi\u1eefa A v\u00e0 B l\u00e0<br>\n<\/li><li>kh\u00f4ng c\u1ea7n ph\u1ea3i ngh\u0129.<\/li><li>C\u0169ng trong 0xy, n\u1ebfu h\u1ecd h\u1ecfi t\u00ecm slope th\u00ec h\u00e3y nh\u1edb c\u00f4ng th\u1ee9c<\/li><li>\nslope = , d\u00e2n gian hay g\u1ecdi l\u00e0 rise\/run.\n<\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Ph\u1ea7n Statistics v\u00e0 Data Interpretation<\/strong><\/h3>\n\n\n\n<p><strong>+ Nh\u1edb kh\u00e1i ni\u1ec7m:<\/strong><\/p>\n\n\n\n<p>Mean l\u00e0 s\u1ed1 trung b\u00ecnh<\/p>\n\n\n\n<p>Median l\u00e0 s\u1ed1 ch\u00ednh gi\u1eefa (ti\u1ebfng Vi\u1ec7t c\u00f2n g\u1ecdi l\u00e0 trung v\u1ecb)<\/p>\n\n\n\n<p>Mod l\u00e0 s\u1ed1 xu\u1ea5t hi\u1ec7n nhi\u1ec1u nh\u1ea5t<\/p>\n\n\n\n<p><strong>+ Normal Distribution<\/strong><\/p>\n\n\n\n<p>Vi\u1ec7c v\u1ebd Normal Probability Distribution (trong ti\u1ebfng Vi\u1ec7t hay g\u1ecdi l\u00e0 h\u00e0m m\u1eadt \u0111\u1ed9 x\u00e1c su\u1ea5t) l\u00e0 ph\u1ea7n quan tr\u1ecdng c\u1ea7n ghi nh\u1edb nh\u1ea5t khi l\u00e0m ph\u1ea7n stats.<\/p>\n\n\n\n<p>Nhi\u1ec1u b\u00e0i t\u1eadp ch\u1ec9 c\u1ea7n v\u1ebd ra l\u00e0 t\u00ednh \u0111\u01b0\u1ee3c ngay. Theo convention th\u00ec v\u1edbi \u0111\u1ed9 tin c\u1eady kho\u1ea3ng 5%, c\u00e1c b\u1ea1n c\u1ee9 nh\u1edb<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>c\u00f4ng th\u1ee9c ma thu\u1eadt  2 | 14 | 34<\/p><\/blockquote>\n\n\n\n<p>Deviation l\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n, th\u01b0\u1eddng s\u1ebd \u0111\u01b0\u1ee3c \u0111\u1ec1 cho. C\u00f2n n\u1ebfu kh\u00f4ng th\u00ec c\u00f4ng th\u1ee9c \u1edf b\u00ean d\u01b0\u1edbi:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/nipponkiyoshi.files.wordpress.com\/2021\/01\/image620.jpg?w=660&amp;h=265\" alt=\"\" class=\"wp-image-3047\" title=\"\"><\/figure><\/div>\n\n\n\n<p>N\u1ebfu data l\u00e0 ph\u00e2n ph\u1ed1i chu\u1ea9n th\u00ec Mean x\u1ea5p x\u1ec9 = Median<\/p>\n\n\n\n<p><strong><em>+ Standard Deviation (\u0111\u1ed9 l\u1ec7ch chu\u1ea9n)<\/em><\/strong><\/p>\n\n\n\n<p>C\u00f4ng th\u1ee9c l\u00e0<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csigma+%3D+%5Csqrt%7B%5Csum%5EN_i+%28%5Cfrac%7Bx_i+-+Mean%7D%7BN%7D%29%5E2%7D&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"sigma = sqrt{sum^N_i (frac{x_i - Mean}{N})^2}\" title=\"\"><\/figure>\n\n\n\n<p><strong><em>+ Interquartile range:<\/em><\/strong><\/p>\n\n\n\n<p>Interquartile range (IQR) th\u1ef1c ch\u1ea5t ch\u00ednh l\u00e0 t\u00ecm \u2018middle fifty\u2019 c\u1ee7a data.<\/p>\n\n\n\n<p>T\u1ee9c l\u00e0 t\u00ecm Median c\u1ee7a Lower Half (Q1) v\u00e0 Median c\u1ee7a Upper Half (Q3) r\u1ed3i l\u1ea5y Q3 \u2013 Q1.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/nipponkiyoshi.files.wordpress.com\/2021\/01\/iqr_quartiles.png?w=660&amp;h=220\" alt=\"\" class=\"wp-image-3046\" title=\"\"><\/figure><\/div>\n\n\n\n<p>C\u00e1c b\u01b0\u1edbc nh\u01b0 sau:<\/p>\n\n\n\n<p><strong>B1:<\/strong> X\u1ebfp s\u1ed1 li\u1ec7u theo th\u1ee9 t\u1ef1 t\u1eeb nh\u1ecf \u0111\u1ebfn l\u1edbn<\/p>\n\n\n\n<p><strong>B2:<\/strong> T\u00ecm \u0111i\u1ec3m ch\u00ednh gi\u1eefa chia data th\u00e0nh 2 n\u1eeda b\u1eb1ng nhau.<\/p>\n\n\n\n<p><strong>B3:<\/strong> T\u00ednh Q1 = median c\u1ee7a n\u1eeda d\u01b0\u1edbi, Q3 = median c\u1ee7a n\u1eeda tr\u00ean<\/p>\n\n\n\n<p><strong>B4:<\/strong> IQR = Q3 \u2013 Q1<\/p>\n\n\n\n<p><strong>V\u00ed d\u1ee5 1. S\u00f4 ph\u1ea7n t\u1eed l\u00e0 l\u1ebb, \u0111i\u1ec3m ch\u00ednh gi\u1eefa ch\u00ednh l\u00e0 median c\u1ee7a data set:<\/strong><\/p>\n\n\n\n<p>T\u00ecm IQR c\u1ee7a {2,1,3,2,5,9,5} (s\u1ed1 ph\u1ea7n t\u1eed l\u00e0 l\u1ebb)<\/p>\n\n\n\n<p><strong>B1:<\/strong> S\u1eafp x\u1ebfp l\u1ea1i th\u00e0nh 1,2,2,<strong>3<\/strong>,5,5,9<\/p>\n\n\n\n<p><strong>B2:<\/strong> Median l\u00e0 3. T\u1eeb 3 chia data th\u00e0nh 2 n\u1eeda l\u00e0 (1,2,2),<strong>3<\/strong>,(5,5,9)<\/p>\n\n\n\n<p><strong>B3:<\/strong> Median c\u1ee7a n\u1eeda d\u01b0\u1edbi (1,<strong>2<\/strong>,2) l\u00e0 Q1 = 2, Median c\u1ee7a n\u1eeda tr\u00ean (5,<strong>5<\/strong>,9) l\u00e0 Q3 = 5<\/p>\n\n\n\n<p><strong>B4:<\/strong> Nh\u01b0 v\u1eady, IQR = Q3 \u2013 Q1 = 3<\/p>\n\n\n\n<p><strong>V\u00ed d\u1ee5 2. S\u1ed1 ph\u1ea7n t\u1eed l\u00e0 ch\u1eb5n<\/strong>:<\/p>\n\n\n\n<p>T\u00ccm IQR c\u1ee7a {2,1,3,2,5,9} (s\u1ed1 ph\u1ea7n t\u1eed l\u00e0 ch\u1eb5n)<\/p>\n\n\n\n<p><strong>B1:<\/strong> S\u1eafp x\u1ebfp l\u1ea1i th\u00e0nh 1,2,2,3,5,9<\/p>\n\n\n\n<p><strong>B2:<\/strong> Chia data set l\u00e0m 2 n\u1eeda, (1,2,2)<strong>,<\/strong>(3,5,9)<\/p>\n\n\n\n<p><strong>B3:<\/strong> Median c\u1ee7a n\u1eeda d\u01b0\u1edbi (1,<strong>2<\/strong>,2) l\u00e0 Q1 = 2, Median c\u1ee7a n\u1eeda tr\u00ean (3,<strong>5<\/strong>,9) l\u00e0 Q3 = 5<\/p>\n\n\n\n<p><strong>B4:<\/strong> Nh\u01b0 v\u1eady, IQR = Q3 \u2013 Q1 = 3<\/p>\n\n\n\n<p><strong>+ Data Interpretation:<\/strong><\/p>\n\n\n\n<p>M\u1eb9o t\u00ednh nhanh<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Total = CategoryA + CategoryB \u2013 Both + Neither<\/p><\/blockquote>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><strong>Ph\u1ea7n Word Problems<\/strong><\/p>\n\n\n\n<p><strong>+ V\u1eadn t\u1ed1c <\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=v_1&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"v_1\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=v_2&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"v_2\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=d&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"d\" title=\"\"><\/figure>\n\n\n\n<p>Hai xe \u00f4 t\u00f4 c\u00f9ng xu\u1ea5t ph\u00e1t <strong>c\u00f9ng l\u00fac<\/strong> v\u1edbi v\u1eadn t\u1ed1c l\u1ea7n l\u01b0\u1ee3t l\u00e0  v\u00e0 , qu\u00e3ng \u0111\u01b0\u1eddng l\u00e0 <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cfrac%7Bd%7D%7Bv_1+%2B+v_2%7D&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"frac{d}{v_1 + v_2}\" title=\"\"><\/figure>\n\n\n\n<p>Hai xe \u0111i ng\u01b0\u1ee3c chi\u1ec1u th\u00ec sau  s\u1ebd g\u1eb7p nhau.<\/p>\n\n\n\n<p><strong>+ S\u1ed1 c\u00e1ch ch\u1ecdn:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=rCn+%3D+%5Cfrac%7Bn%21%7D%7B%28n-r%29%21+%5C+r%21%7D&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"rCn = frac{n!}{(n-r)!  r!}\" title=\"\"><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=rPn+%3D+%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D&amp;bg=ffffff&amp;fg=444444&amp;s=0&amp;c=20201002\" alt=\"rPn = frac{n!}{(n-r)!}\" title=\"\"><\/figure>\n\n\n\n<p>Kh\u00e1c th\u1ef1 t\u1ef1 l\u00e0 c\u00f9ng ph\u1ea7n t\u1eed: <br>Kh\u00e1c th\u1ee9 t\u1ef1 l\u00e0 kh\u00e1c ph\u1ea7n t\u1eed: <\/p>\n\n\n\n<p>Nh\u1edb nhanh:<\/p>\n\n\n\n<p>3! = 6<br>4! = 24<br>5! = 120<br>6! = 720<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>K\u1ebft<\/strong><\/h3>\n\n\n\n<p>N\u1ebfu c\u00e1c b\u1ea1n c\u00f3 tips n\u00e0o hay kh\u00e1c, kinh nghi\u1ec7m g\u00ec c\u1ee7a c\u00e1c b\u1ea1n, hay c\u00f3 l\u1ed7i sai n\u00e0o c\u1ee7a m\u00ecnh \u1edf tr\u00ean th\u00ec h\u00e3y comment nh\u00e9 <\/p>\n\n\n\n<p>Khi app Ph.D. c\u1ee7a Econs, m\u00ecnh th\u1ea5y nh\u01b0 c\u00e1c tr\u01b0\u1eddng \u1edf \u0110\u1ee9c hay M\u1ef9 \u0111\u1ec1u y\u00eau c\u1ea7u \u0111i\u1ec3m Quant. ph\u1ea3i \u0111\u1ea1t \u1edf ng\u01b0\u1ee1ng 80th percentile \u0111\u1ed5 l\u00ean, t\u1ee9c l\u00e0 c\u1ea7n \u00edt nh\u1ea5t 164\/170, ngh\u0129a l\u00e0 ch\u1ec9 \u0111\u01b0\u1ee3c sai t\u1ed1i \u0111a 3 c\u00e2u \u1edf m\u1ed7i ph\u1ea7n Quant. (GRE c\u00f3 2 ph\u1ea7n Quant, l\u00e0m t\u1ed1t ph\u1ea7n 1 th\u00ec ph\u1ea7n 2 s\u1ebd kh\u00f3 h\u01a1n, \u0103n nhi\u1ec1u \u0111i\u1ec3m h\u01a1n). Do \u0111\u00f3, hi v\u1ecdng nh\u1eefng tips n\u00e0y s\u1ebd gi\u00fap \u00edch \u0111\u01b0\u1ee3c cho c\u00e1c b\u1ea1n \u0111\u1ea1t \u0111\u01b0\u1ee3c \u0111i\u1ec3m nh\u01b0 mong mu\u1ed1n.<\/p>\n\n\n\n<p>V\u1ec1 t\u00e0i li\u1ec7u \u00f4n thi GRE, m\u00ecnh s\u1ebd c\u1ed1 g\u1eafng vi\u1ebft v\u00e0o m\u1ed9t ng\u00e0y g\u1ea7n nh\u1ea5t (Ph\u1ea7n 2).<\/p>\n\n\n\n<p>Ph\u1ea7n Verbal m\u00ecnh kh\u00f4ng gi\u1ecfi l\u1eafm, nh\u01b0ng ph\u1ea7n AWA th\u00ec c\u0169ng kha kh\u00e1 (t\u1ea7m 80th percentile). N\u1ebfu c\u00f3 th\u1eddi gian c\u0169ng s\u1ebd vi\u1ebft v\u00e0 chia s\u1ebb s\u1edbm l\u00ean blog (Ph\u1ea7n 3)<\/p>\n\n\n\n<p><strong>P\/S:<\/strong> Ph\u1ea7n 1 \u0111\u1ebfn \u0111\u00e2y l\u00e0 h\u1ebft. XIn l\u1ed7i c\u00e1c b\u1ea1n n\u1ebfu c\u00e1c bi\u1ec3u th\u1ee9c to\u00e1n tr\u00f4ng kh\u00f3 nh\u00ecn. WordPress c\u00f3 h\u1ed7 tr\u1ee3 LaTeX m\u00e0 tr\u00f4ng t\u1ec7 qu\u00e1 <\/p>\n\n\n\n<p><strong>P\/S 2:<\/strong> Tr\u00ean Reddit th\u00ec \u0111\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng cheat sheet \u0111\u01b0\u1ee3c recommend nhi\u1ec1u nh\u1ea5t:<\/p>\n\n\n\n<p>LInk: <a href=\"https:\/\/drive.google.com\/file\/d\/1axrhGHoPsPD0Uw5Y4JPSD8h2Riwi-DsV\/view\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/drive.google.com\/file\/d\/1axrhGHoPsPD0Uw5Y4JPSD8h2Riwi-DsV\/view<\/a><\/p>\n\n\n\n<p><strong>P\/S 3:<\/strong> Trong qu\u00e1 tr\u00ecnh \u00f4n luy\u1ec7n m\u1ed9t m\u00ecnh, c\u00f3 b\u1ea1n c\u00f3 b\u00e8 l\u00e0 m\u1ed9t \u0111i\u1ec1u r\u1ea5t tuy\u1ec7t v\u1eddi. N\u1ebfu c\u00f3 th\u1eddi gian, h\u00e3y gh\u00e9 qua sub r\/GRE tr\u00ean Reddit. C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 \u0111\u1ecdc tips t\u1eeb nh\u1eefng test takers \u0111i tr\u01b0\u1edbc v\u00e0 c\u1ea3 t\u1eeb nh\u1eefng tutors n\u1eefa, hay n\u1ebfu c\u00f3 c\u00e2u h\u1ecfi g\u00ec th\u00ec c\u1ee9 m\u1ea1nh d\u1ea1n post v\u00e0o sub n\u00e0y.<\/p>\n\n\n\n<p>Link: <a href=\"https:\/\/www.reddit.com\/r\/GRE\/top\/?t=all\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/www.reddit.com\/r\/GRE\/top\/?t=all<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>G\u1ea7n \u0111\u00e2y m\u00ecnh kh\u00f4ng vi\u1ebft m\u1ea5y v\u1ec1 ti\u1ebfng Nh\u1eadt n\u1eefa, v\u00ec th\u1eadt ra nh\u1eefng g\u00ec n\u00ean vi\u1ebft nh\u1ea5t v\u1ec1 ti\u1ebfng Nh\u1eadt th\u00ec m\u00ecnh \u0111\u1ec1u vi\u1ebft c\u1ea3 r\u1ed3i. Th\u1eddi gian qua c\u0169ng c\u00f3 \u00f4n luy\u1ec7n thi GRE (Graduate Record Examinations) \u0111\u1ec3 app v\u00e0o Grad School. N\u1ebfu nh\u1eefng ai quan t\u00e2m \u0111\u1ebfn vi\u1ec7c du h\u1ecdc b\u1eadc sau [&hellip;]<\/p>\n","protected":false},"author":11728,"featured_media":60110,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2019],"tags":[],"_links":{"self":[{"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/posts\/60109"}],"collection":[{"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/users\/11728"}],"replies":[{"embeddable":true,"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/comments?post=60109"}],"version-history":[{"count":3,"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/posts\/60109\/revisions"}],"predecessor-version":[{"id":60117,"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/posts\/60109\/revisions\/60117"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/media\/60110"}],"wp:attachment":[{"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/media?parent=60109"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/categories?post=60109"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scholarshipplanet.info\/vi\/wp-json\/wp\/v2\/tags?post=60109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}