{"id":716,"date":"2026-05-05T05:01:00","date_gmt":"2026-05-05T05:01:00","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/tong-on-toan-dien-toan-11-hoc-ki-2-pdf-anh-giao-kid\/"},"modified":"2026-05-05T07:35:43","modified_gmt":"2026-05-05T07:35:43","slug":"tong-on-toan-dien-toan-11-hoc-ki-2-pdf-anh-giao-kid","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/tong-on-toan-dien-toan-11-hoc-ki-2-pdf-anh-giao-kid\/","title":{"rendered":"T\u1ed5ng \u00f4n to\u00e0n di\u1ec7n To\u00e1n 11 h\u1ecdc k\u00ec 2 PDF Anh Gi\u00e1o Kid"},"content":{"rendered":"<p><strong>T\u1ed5ng \u00f4n to\u00e0n di\u1ec7n To\u00e1n 11 h\u1ecdc k\u00ec 2 PDF<\/strong> Anh Gi\u00e1o Kid k\u1ebft h\u1ee3p gi\u1eefa l\u00fd thuy\u1ebft tr\u1ecdng t\u00e2m l\u1edbp 11, c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp ti\u00eau bi\u1ec3u v\u00e0 h\u1ec7 th\u1ed1ng \u0111\u1ec1 \u00f4n t\u1eadp s\u00e1t s\u01b0\u1eddn. T\u00e0i li\u1ec7u n\u00e0y s\u1ebd gi\u00fap b\u1ea1n b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1, t\u1ef1 tin v\u1ec1 \u0111\u00edch v\u1edbi k\u1ebft qu\u1ea3 cao nh\u1ea5t. H\u00e3y c\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u \u00d4n Thi<\/strong><\/a> kh\u00e1m ph\u00e1 nh\u1eefng ki\u1ebfn th\u1ee9c c\u1ed1t l\u00f5i v\u00e0 ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i nhanh hi\u1ec7u qu\u1ea3 \u0111\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c m\u1ee5c ti\u00eau h\u1ecdc t\u1eadp c\u1ee7a m\u00ecnh!<\/p>\n<h2><strong>N\u1ed9i dung T\u1ed5ng \u00f4n to\u00e0n di\u1ec7n To\u00e1n 11 h\u1ecdc k\u00ec 2 PDF Anh Gi\u00e1o Kid<\/strong><\/h2>\n<p>T\u00e0i li\u1ec7u <strong>T\u1ed5ng \u00f4n to\u00e0n di\u1ec7n To\u00e1n 11 h\u1ecdc k\u00ec 2 PDF<\/strong> bao g\u1ed3m c\u00e1c ch\u1ee7 \u0111\u1ec1 v\u00e0 ph\u1ea7n \u00f4n t\u1eadp ch\u00ednh sau:<\/p>\n<ul>\n<li><strong>Ch\u1ee7 \u0111\u1ec1 1:<\/strong> H\u00e0m s\u1ed1 m\u0169 v\u00e0 logarit<\/li>\n<li><strong>Ch\u1ee7 \u0111\u1ec1 2: <\/strong>\u0110\u1ea1o h\u00e0m<\/li>\n<li><strong>Ch\u1ee7 \u0111\u1ec1 3: <\/strong>X\u00e1c su\u1ea5t<\/li>\n<li><strong>Ch\u1ee7 \u0111\u1ec1 4: <\/strong>Quan h\u1ec7 vu\u00f4ng g\u00f3c trong kh\u00f4ng gian<\/li>\n<li><strong>Ch\u1ee7 \u0111\u1ec1 5: <\/strong>M\u1ed9t s\u1ed1 b\u00e0i to\u00e1n th\u1ef1c t\u1ebf h\u1ecdc k\u00ec 2<\/li>\n<li><strong>10 \u0111\u1ec1 \u00f4n t\u1eadp tr\u00fang t\u1ee7 h\u1ecdc k\u00ec II<\/strong><\/li>\n<\/ul>\n<p>Ngo\u00e0i ra, t\u00e0i li\u1ec7u c\u00f2n cung c\u1ea5p c\u00e1c c\u00f4ng th\u1ee9c, v\u00ed d\u1ee5 minh h\u1ecda v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng cho t\u1eebng ch\u1ee7 \u0111\u1ec1, c\u00f9ng l\u1eddi gi\u1ea3i chi ti\u1ebft.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi tham kh\u1ea3o trong \u0111\u1ec1 thi \u00f4n t\u1eadp s\u1ed1 01:<\/p>\n<p><strong>PH\u1ea6N I: C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/p>\n<p><strong>C\u00e2u 1.<\/strong> [KID] V\u1edbi $a$ l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, $\\log_{5}(25a)$ b\u1eb1ng:<\/p>\n<p>A. $1+\\log_{5}a$.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. $5+\\log_{5}a$.<br \/>\nC. $5-\\log_{5}a$.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. $2+\\log_{5}a$.<\/p>\n<p><strong>C\u00e2u 2.<\/strong>\u00a0[KID] Ch\u1ecdn ng\u1eabu nhi\u00ean m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb 1 \u0111\u1ebfn 20. X\u00e9t c\u00e1c bi\u1ebfn c\u1ed1 $A$: \u201cS\u1ed1 \u0111\u01b0\u1ee3c ch\u1ecdn chia h\u1ebft cho 3\u201d; $B$: \u201cS\u1ed1 \u0111\u01b0\u1ee3c ch\u1ecdn chia h\u1ebft cho 4\u201d. Khi \u0111\u00f3 bi\u1ebfn c\u1ed1 $A \\cap B$ l\u00e0:<\/p>\n<p>A. $\\{3;4;12\\}$.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. $\\{3;4;6;8;9;12;15;16;18;20\\}$.<br \/>\nC. $\\{12\\}$.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. $\\{3;6;9;12;15;18\\}$.<\/p>\n<p><strong>PH\u1ea6N 2: C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/p>\n<p><strong>C\u00e2u 1.<\/strong> [KID] M\u1ed9t ch\u1ea5t \u0111i\u1ec3m r\u01a1i t\u1ef1 do v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh chuy\u1ec3n \u0111\u1ed9ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi h\u00e0m s\u1ed1 $S(t) = \\frac{1}{2}gt^{2}$ (v\u1edbi $g=10m\/s^2$) \u1edf \u0111\u1ed9 cao $125m$. C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n<p>a) V\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m t\u1ea1i th\u1eddi \u0111i\u1ec3m $t = \\frac{1}{2}$ gi\u00e2y l\u00e0 $S\u2019\\left(\\frac{1}{2}\\right) = \\lim_{t \\to \\frac{1}{2}} \\frac{\\frac{1}{2}gt^{2} \u2013 \\frac{1}{8}g}{t \u2013 \\frac{1}{2}}$.<br \/>\nb) N\u1ebfu $\\lim_{t \\to 2} \\frac{\\frac{1}{2}gt^{2} \u2013 2g}{t \u2013 2} = 2g$ th\u00ec ch\u1ea5t \u0111i\u1ec3m \u0111\u1ea1t v\u1eadn t\u1ed1c l\u00e0 $2m\/s$.<br \/>\nc) V\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi c\u00f4ng th\u1ee9c $v(t) = gt$.<br \/>\nd) Khi ch\u1ea1m \u0111\u1ea5t th\u00ec ch\u1ea5t \u0111i\u1ec3m \u0111\u1ea1t v\u1eadn t\u1ed1c $v = 40m\/s$.<\/p>\n<p><strong>C\u00e2u 2.<\/strong> [KID] Cho h\u00ecnh ch\u00f3p $S.ABCD$ c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh $2a$, $SA \\perp (ABCD)$, $SA = 2\\sqrt{2}a$ (tham kh\u1ea3o h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y). C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n<p><img loading=\"lazy\" alt=\"T\u1ed5ng \u00f4n to\u00e0n di\u1ec7n To\u00e1n 11 h\u1ecdc k\u00ec 2 PDF\" class=\"wp-image-3849 size-full aligncenter\" decoding=\"async\" height=\"307\" sizes=\"auto, (max-width: 310px) 100vw, 310px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/tong-on-toan-dien-toan-11-hoc-ki-2-pdf-anh-giao-kid-1.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/tong-on-toan-dien-toan-11-hoc-ki-2-pdf-anh-giao-kid-1.jpg 310w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/tong-on-toan-dien-toan-11-hoc-ki-2-pdf-anh-giao-kid-1-300x297.jpg 300w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/tong-on-toan-dien-toan-11-hoc-ki-2-pdf-anh-giao-kid-1-150x150.jpg 150w\" width=\"310\"\/><\/p>\n<p>a) $BC \\perp (SAB)$.<br \/>\nb) G\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng $SD$ v\u00e0 $(ABCD)$ l\u00e0 $\\widehat{SDA}$.<br \/>\nc) G\u00f3c c\u1ee7a $(SBC)$ v\u00e0 $(ABCD)$ b\u1eb1ng $30^{\\circ}$.<br \/>\nd) G\u1ecdi $H,K,I$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a \u0111i\u1ec3m $A$ tr\u00ean c\u00e1c c\u1ea1nh $SB,SD$ v\u00e0 $SC$. Khi \u0111\u00f3 $HK \\perp AI$.<\/p>\n<p><strong>PH\u1ea6N 3: C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/p>\n<p><strong>C\u00e2u 1.<\/strong> [KID] M\u1ed9t n\u1ed3i c\u01a1m \u0111i\u1ec7n g\u1ed3m hai van b\u1ea3o hi\u1ec3m ho\u1ea1t \u0111\u1ed9ng \u0111\u1ed9c l\u1eadp. X\u00e1c su\u1ea5t ho\u1ea1t \u0111\u1ed9ng t\u1ed1t c\u1ee7a van I v\u00e0 van II l\u1ea7n l\u01b0\u1ee3t l\u00e0 $0,8$ v\u00e0 $0,6$. N\u1ed3i c\u01a1m \u0111i\u1ec7n ho\u1ea1t \u0111\u1ed9ng an to\u00e0n khi c\u00f3 \u00edt nh\u1ea5t m\u1ed9t van ho\u1ea1t \u0111\u1ed9ng t\u1ed1t. T\u00ednh x\u00e1c su\u1ea5t n\u1ed3i c\u01a1m \u0111i\u1ec7n ho\u1ea1t \u0111\u1ed9ng an to\u00e0n.<\/p>\n<p><strong>C\u00e2u 2.<\/strong> [KID] Ph\u01b0\u01a1ng tr\u00ecnh chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a m\u1ed9t h\u1ea1t \u0111\u01b0\u1ee3c cho b\u1edfi $s(t) = 10 + 0,5\\sin\\left(2\\pi t + \\frac{\\pi}{5}\\right)$, trong \u0111\u00f3 $s$ t\u00ednh b\u1eb1ng centim\u00e9t v\u00e0 $t$ t\u00ednh b\u1eb1ng gi\u00e2y. T\u00ednh gia t\u1ed1c c\u1ee7a h\u1ea1t t\u1ea1i th\u1eddi \u0111i\u1ec3m $t=5$ gi\u00e2y (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t).<\/p>\n<p><strong>PH\u1ea6N 4: T\u1ef1 lu\u1eadn<\/strong><\/p>\n<p><strong>C\u00e2u 1.<\/strong> [KID] Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $\\log_{2}(x-2) \u2013 \\log_{2}(8-x) &lt; 0$.<\/p>\n<p><strong>C\u00e2u 2.<\/strong> [KID] Ba x\u1ea1 th\u1ee7 $A_{1}, A_{2}, A_{3}$ \u0111\u1ed9c l\u1eadp v\u1edbi nhau c\u00f9ng n\u1ed5 s\u00fang b\u1eafn v\u00e0o m\u1ee5c ti\u00eau. Bi\u1ebft r\u1eb1ng x\u00e1c su\u1ea5t b\u1eafn tr\u00fang m\u1ee5c ti\u00eau c\u1ee7a $A_{1}, A_{2}, A_{3}$ t\u01b0\u01a1ng \u1ee9ng l\u00e0 $0,7; 0,6$ v\u00e0 $0,5$. T\u00ednh x\u00e1c su\u1ea5t \u0111\u1ec3 c\u00f3 \u00edt nh\u1ea5t m\u1ed9t x\u1ea1 th\u1ee7 b\u1eafn tr\u00fang.<\/p>\n<h2><strong>T\u1ea3i T\u1ed5ng \u00f4n to\u00e0n di\u1ec7n To\u00e1n 11 h\u1ecdc k\u00ec 2 PDF Anh Gi\u00e1o Kid<\/strong><\/h2>\n<p>C\u00e1c \u0111\u1ec1 \u00f4n t\u1eadp trong <strong><a href=\"https:\/\/tailieuonthi.edu.vn\/lop-11\/toan-11\/\" rel=\"noopener\" target=\"_blank\">t\u00e0i li\u1ec7u to\u00e1n 11<\/a><\/strong>\u00a0n\u00e0y c\u00f3 th\u1ec3 b\u1ea1n c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c, l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi, v\u00e0 t\u1ed1i \u01b0u h\u00f3a chi\u1ebfn l\u01b0\u1ee3c l\u00e0m b\u00e0i, t\u1eeb \u0111\u00f3 t\u1ef1 tin \u0111\u1ea1t \u0111i\u1ec3m cao trong k\u1ef3 thi cu\u1ed1i k\u1ef3. H\u00e3y t\u1ea3i ngay file <strong>T\u1ed5ng \u00f4n to\u00e0n di\u1ec7n To\u00e1n 11 h\u1ecdc k\u00ec 2 PDF<\/strong> \u0111\u1ec3 b\u1eaft \u0111\u1ea7u luy\u1ec7n t\u1eadp v\u00e0 b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1 c\u1ee7a m\u00ecnh!<\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1VPf3nvoa_Ef6z4nGeulskN9bEmfyF0QC\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i T\u1ed5ng \u00f4n to\u00e0n di\u1ec7n To\u00e1n 11 h\u1ecdc k\u00ec 2 PDF Anh Gi\u00e1o Kid<\/a><\/p>\n<p>\u0110\u00e2y l\u00e0 b\u1ea3n PDF \u0111\u00f4i khi s\u1ebd c\u00f3 sai s\u00f3t. N\u1ebfu c\u00f3 \u0111i\u1ec1u ki\u1ec7n, c\u00e1c b\u1ea1n n\u00ean mua b\u1ea3n g\u1ed1c \u0111\u1ec3 c\u00f3 tr\u1ea3i nghi\u1ec7m t\u1ed1t nh\u1ea5t v\u00e0 \u1ee7ng h\u1ed9 t\u00e1c gi\u1ea3 nh\u00e9.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u1ed5ng \u00f4n to\u00e0n di\u1ec7n To\u00e1n 11 h\u1ecdc k\u00ec 2 PDF Anh Gi\u00e1o Kid k\u1ebft h\u1ee3p gi\u1eefa l\u00fd thuy\u1ebft tr\u1ecdng t\u00e2m l\u1edbp 11, c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp ti\u00eau bi\u1ec3u v\u00e0 h\u1ec7 th\u1ed1ng \u0111\u1ec1 \u00f4n t\u1eadp s\u00e1t s\u01b0\u1eddn. T\u00e0i li\u1ec7u n\u00e0y s\u1ebd gi\u00fap b\u1ea1n b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1, t\u1ef1 tin v\u1ec1 \u0111\u00edch v\u1edbi k\u1ebft qu\u1ea3 cao nh\u1ea5t. [&#8230;]\n","protected":false},"author":1,"featured_media":1914,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[78,77,16],"class_list":["post-716","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-toan-11","tag-anh-giao-kid","tag-flash-study","tag-toan-11"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/716","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=716"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/716\/revisions"}],"predecessor-version":[{"id":1915,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/716\/revisions\/1915"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1914"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=716"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=716"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}