{"id":442,"date":"2025-07-22T08:01:21","date_gmt":"2025-07-22T08:01:21","guid":{"rendered":"https:\/\/giapsgk.com\/chuyen-de\/?p=442"},"modified":"2025-07-22T08:01:21","modified_gmt":"2025-07-22T08:01:21","slug":"tong-hop-cac-cong-thuc-toan-10-ket-noi-tri-thuc-hoc-ki-1-va-hoc-ki-2","status":"publish","type":"post","link":"https:\/\/giapsgk.com\/chuyen-de\/tong-hop-cac-cong-thuc-toan-10-ket-noi-tri-thuc-hoc-ki-1-va-hoc-ki-2\/","title":{"rendered":"T\u1ed5ng h\u1ee3p c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n 10 K\u1ebft N\u1ed1i Tri Th\u1ee9c h\u1ecdc k\u00ec 1 v\u00e0 h\u1ecdc k\u00ec 2"},"content":{"rendered":"<p data-start=\"511\" data-end=\"842\">Trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 10 theo b\u1ed9 s\u00e1ch <strong data-start=\"555\" data-end=\"589\">K\u1ebft N\u1ed1i Tri Th\u1ee9c v\u1edbi Cu\u1ed9c S\u1ed1ng<\/strong>, vi\u1ec7c ghi nh\u1edb v\u00e0 v\u1eadn d\u1ee5ng \u0111\u00fang <strong data-start=\"621\" data-end=\"647\">c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc<\/strong> l\u00e0 y\u1ebfu t\u1ed1 then ch\u1ed1t \u0111\u1ec3 l\u00e0m t\u1ed1t c\u00e1c b\u00e0i ki\u1ec3m tra v\u00e0 k\u1ef3 thi h\u1ecdc k\u1ef3. Th\u1ea7y \u0111\u00e3 h\u1ec7 th\u1ed1ng l\u1ea1i to\u00e0n b\u1ed9 <strong data-start=\"743\" data-end=\"764\">c\u00f4ng th\u1ee9c To\u00e1n 10<\/strong> m\u1ed9t c\u00e1ch <em data-start=\"774\" data-end=\"796\">khoa h\u1ecdc, d\u1ec5 tra c\u1ee9u<\/em>, b\u00e1m s\u00e1t n\u1ed9i dung SGK t\u1eeb \u0111\u1ea1i s\u1ed1 \u0111\u1ebfn h\u00ecnh h\u1ecdc.<\/p>\n<p data-start=\"844\" data-end=\"1120\">B\u00e0i vi\u1ebft n\u00e0y kh\u00f4ng ch\u1ec9 gi\u00fap c\u00e1c em <strong data-start=\"879\" data-end=\"924\">n\u1eafm v\u1eefng \u0111\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c quan tr\u1ecdng<\/strong> m\u00e0 c\u00f2n h\u01b0\u1edbng d\u1eabn c\u00e1ch \u00e1p d\u1ee5ng trong t\u1eebng d\u1ea1ng b\u00e0i c\u1ee5 th\u1ec3. D\u00f9 em \u0111ang \u00f4n t\u1eadp gi\u1eefa k\u1ef3, cu\u1ed1i k\u1ef3 hay luy\u1ec7n \u0111\u1ec1 thi h\u1ecdc sinh gi\u1ecfi, \u0111\u00e2y s\u1ebd l\u00e0 t\u00e0i li\u1ec7u n\u1ec1n t\u1ea3ng, d\u1ec5 hi\u1ec3u v\u00e0 \u0111\u00e1ng tin c\u1eady nh\u1ea5t d\u00e0nh cho em.<\/p>\n<p data-start=\"1122\" data-end=\"1178\">H\u00e3y c\u00f9ng th\u1ea7y b\u1eaft \u0111\u1ea7u \u00f4n t\u1eadp nghi\u00eam t\u00fac v\u00e0 hi\u1ec7u qu\u1ea3 nh\u00e9!<\/p>\n<h2><strong>Ch\u01b0\u01a1ng I. M\u1ec7nh \u0111\u1ec1 v\u00e0 t\u1eadp h\u1ee3p<\/strong><\/h2>\n<h3><strong>1. M\u1ec7nh \u0111\u1ec1<\/strong><\/h3>\n<ul>\n<li><strong>Kh\u00e1i ni\u1ec7m:<\/strong> M\u1ec7nh \u0111\u1ec1 l\u00e0 c\u00e2u kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang ho\u1eb7c sai.<\/li>\n<li><strong>Ph\u1ee7 \u0111\u1ecbnh:<\/strong> P l\u00e0 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a m\u1ec7nh \u0111\u1ec1 P.<\/li>\n<li><strong>M\u1ec7nh \u0111\u1ec1 k\u00e9o theo:<\/strong> P \u21d2 Q \u0111\u00fang khi P \u0111\u00fang k\u00e9o theo Q \u0111\u00fang.<\/li>\n<\/ul>\n<h3><strong>2 T\u1eadp h\u1ee3p v\u00e0 c\u00e1c ph\u00e9p to\u00e1n tr\u00ean t\u1eadp h\u1ee3p<\/strong><\/h3>\n<p><strong>Kh\u00e1i ni\u1ec7m:<\/strong> T\u1eadp h\u1ee3p l\u00e0 m\u1ed9t nh\u00f3m c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh r\u00f5 r\u00e0ng.<\/p>\n<p>C\u00e1c ph\u00e9p to\u00e1n:<\/p>\n<ul>\n<li><strong>H\u1ee3p:<\/strong> $A \\cup B$<\/li>\n<li><strong>Giao:<\/strong> $A \\cap B$<\/li>\n<li><strong>Hi\u1ec7u:<\/strong> $A \\setminus B$<\/li>\n<li><strong>Ph\u1ea7n b\u00f9:<\/strong> $A&#8217;$<\/li>\n<\/ul>\n<h2><strong>Ch\u01b0\u01a1ng II. B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/strong><\/h2>\n<h3><strong>3. B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/strong><\/h3>\n<ul>\n<li><strong>D\u1ea1ng t\u1ed5ng qu\u00e1t:<\/strong> $ax + by &lt; c$, $\\leq, &gt;, \\geq$<\/li>\n<li><strong>Bi\u1ec3u di\u1ec5n:<\/strong> N\u1eeda m\u1eb7t ph\u1eb3ng tr\u00ean h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9.<\/li>\n<\/ul>\n<h3><strong>4. H\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/strong><\/h3>\n<ul>\n<li><strong>Kh\u00e1i ni\u1ec7m:<\/strong> G\u1ed3m nhi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh c\u00f9ng hai \u1ea9n.<\/li>\n<li><strong>Bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc:<\/strong> Giao c\u00e1c mi\u1ec1n nghi\u1ec7m c\u1ee7a t\u1eebng b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh.<\/li>\n<\/ul>\n<h2><strong>Ch\u01b0\u01a1ng III. H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c<\/strong><\/h2>\n<h3><strong>5. Gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0<\/strong><\/h3>\n<p>C\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c: sin, cos, tan, cot.<\/p>\n<p>Quan h\u1ec7:<\/p>\n<ul>\n<li>$\\sin^2 \\alpha + \\cos^2 \\alpha = 1$<\/li>\n<li>$\\tan \\alpha = \\frac{\\sin \\alpha}{\\cos \\alpha}$<\/li>\n<\/ul>\n<h3><strong>6. H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c<\/strong><\/h3>\n<ul>\n<li><strong>\u0110\u1ecbnh l\u00fd cosin:<\/strong> $c^2 = a^2 + b^2 &#8211; 2ab\\cos C$<\/li>\n<li><strong>\u0110\u1ecbnh l\u00fd sin: <\/strong>$\\frac{a}{\\sin A} = \\frac{b}{\\sin B} = \\frac{c}{\\sin C}$<\/li>\n<li><strong>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch:\u00a0<\/strong>$S = \\frac{1}{2} ab\\sin C$<\/li>\n<\/ul>\n<h2><strong>Ch\u01b0\u01a1ng IV. Vect\u01a1<\/strong><\/h2>\n<h3><strong>7. C\u00e1c kh\u00e1i ni\u1ec7m, ph\u00e9p to\u00e1n v\u00e0 t\u00edch v\u00f4 h\u01b0\u1edbng<\/strong><\/h3>\n<ul>\n<li><strong>Vect\u01a1:<\/strong> C\u00f3 \u0111\u1ed9 d\u00e0i, h\u01b0\u1edbng.<\/li>\n<li><strong>T\u1ed5ng vect\u01a1:<\/strong> $\\vec{u} + \\vec{v}$<\/li>\n<li><strong>Hi\u1ec7u vect\u01a1:<\/strong> $\\vec{u} &#8211; \\vec{v}$<\/li>\n<li><strong>T\u00edch v\u1edbi s\u1ed1:<\/strong> $k\\vec{u}$<\/li>\n<li><strong>Vect\u01a1 t\u1ecda \u0111\u1ed9:<\/strong> $\\vec{u} = (x, y)$<\/li>\n<li><strong>T\u00edch v\u00f4 h\u01b0\u1edbng:<\/strong> $\\vec{u} \\cdot \\vec{v} = x_1x_2 + y_1y_2 = |\\vec{u}||\\vec{v}|\\cos \\theta$<\/li>\n<\/ul>\n<h2><strong>Ch\u01b0\u01a1ng V. C\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u kh\u00f4ng gh\u00e9p nh\u00f3m<\/strong><\/h2>\n<h3><strong>8. S\u1ed1 g\u1ea7n \u0111\u00fang v\u00e0 sai s\u1ed1<\/strong><\/h3>\n<ul>\n<li><strong>S\u1ed1 g\u1ea7n \u0111\u00fang:<\/strong> G\u1ed3m c\u00e1c ch\u1eef s\u1ed1 \u0111\u00e1ng tin v\u00e0 m\u1ed9t ch\u1eef s\u1ed1 \u01b0\u1edbc l\u01b0\u1ee3ng.<\/li>\n<li><strong>Sai s\u1ed1 tuy\u1ec7t \u0111\u1ed1i:<\/strong> $\\Delta = |x &#8211; x_0|$<\/li>\n<\/ul>\n<h3><strong>9. \u0110o xu th\u1ebf trung t\u00e2m<\/strong><\/h3>\n<ul>\n<li><strong>Trung b\u00ecnh c\u1ed9ng:<\/strong> $\\bar{x} = \\frac{x_1 + x_2 + \\cdots + x_n}{n}$<\/li>\n<li>Trung v\u1ecb, m\u1ed1t<\/li>\n<\/ul>\n<h3><strong>10. \u0110o \u0111\u1ed9 ph\u00e2n t\u00e1n<\/strong><\/h3>\n<ul>\n<li>Ph\u01b0\u01a1ng sai: $\\sigma^2 = \\frac{1}{n} \\sum (x_i &#8211; \\bar{x})^2$<\/li>\n<li>\u0110\u1ed9 l\u1ec7ch chu\u1ea9n: $\\sigma = \\sqrt{\\sigma^2}$<\/li>\n<\/ul>\n<h2><strong>Ch\u01b0\u01a1ng VI. H\u00e0m s\u1ed1, \u0111\u1ed3 th\u1ecb v\u00e0 \u1ee9ng d\u1ee5ng<\/strong><\/h2>\n<h3><strong>11. H\u00e0m s\u1ed1<\/strong><\/h3>\n<ul>\n<li><strong>Kh\u00e1i ni\u1ec7m:<\/strong> G\u00e1n m\u1ed7i gi\u00e1 tr\u1ecb $x$ m\u1ed9t gi\u00e1 tr\u1ecb $y$ duy nh\u1ea5t.<\/li>\n<li><strong>T\u00ednh \u0111\u1ed3ng bi\u1ebfn\/ngh\u1ecbch bi\u1ebfn: <\/strong>\u0110\u1ed3ng bi\u1ebfn n\u1ebfu $x_1 &lt; x_2 \\Rightarrow f(x_1) &lt; f(x_2)$<\/li>\n<\/ul>\n<h3><strong>12. H\u00e0m b\u1eadc hai<\/strong><\/h3>\n<ul>\n<li><strong>D\u1ea1ng t\u1ed5ng qu\u00e1t:<\/strong> $y = ax^2 + bx + c$<\/li>\n<li><strong>\u0110\u1ec9nh parabol:<\/strong> $x = -\\frac{b}{2a}$<\/li>\n<li><strong>Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng:<\/strong> $x = -\\frac{b}{2a}$<\/li>\n<\/ul>\n<h3><strong>13. D\u1ea5u tam th\u1ee9c b\u1eadc hai<\/strong><\/h3>\n<p>X\u00e9t d\u1ea5u b\u1eb1ng b\u1ea3ng x\u00e9t d\u1ea5u tam th\u1ee9c $ax^2 + bx + c$<\/p>\n<h3><strong>14. Ph\u01b0\u01a1ng tr\u00ecnh quy v\u1ec1 b\u1eadc hai<\/strong><\/h3>\n<p><strong>Bi\u1ebfn \u0111\u1ed5i:<\/strong> S\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c, \u1ea9n ph\u1ee5 \u0111\u1ec3 \u0111\u01b0a v\u1ec1 b\u1eadc hai.<\/p>\n<h2><strong>Ch\u01b0\u01a1ng VII. Ph\u01b0\u01a1ng ph\u00e1p t\u1ecda \u0111\u1ed9 trong m\u1eb7t ph\u1eb3ng<\/strong><\/h2>\n<h3><strong>15. Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng<\/strong><\/h3>\n<p>D\u1ea1ng t\u1ed5ng qu\u00e1t: $Ax + By + C = 0$<\/p>\n<p>D\u1ea1ng tham s\u1ed1, \u0111o\u1ea1n ch\u1eafn.<\/p>\n<h3><strong>16. V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i, g\u00f3c v\u00e0 kho\u1ea3ng c\u00e1ch<\/strong><\/h3>\n<p><strong>G\u00f3c gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng:<\/strong> $\\tan \\theta = \\left| \\frac{a_1b_2 &#8211; a_2b_1}{a_1a_2 + b_1b_2} \\right|$<\/p>\n<p><strong>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng:<\/strong> $d = \\frac{|Ax + By + C|}{\\sqrt{A^2 + B^2}}$<\/p>\n<h3><strong>17. \u0110\u01b0\u1eddng tr\u00f2n trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9<\/strong><\/h3>\n<p>D\u1ea1ng: $(x &#8211; a)^2 + (y &#8211; b)^2 = R^2$<\/p>\n<h3><strong>18. Ba \u0111\u01b0\u1eddng conic<\/strong><\/h3>\n<p>\u0110\u01b0\u1eddng tr\u00f2n, elip, parabol, hyperbol (gi\u1edbi thi\u1ec7u c\u01a1 b\u1ea3n)<\/p>\n<h3><strong>Ch\u01b0\u01a1ng VIII. \u0110\u1ea1i s\u1ed1 t\u1ed5 h\u1ee3p<\/strong><\/h3>\n<h3><strong>19. Quy t\u1eafc \u0111\u1ebfm<\/strong><\/h3>\n<p><strong>C\u1ed9ng:<\/strong> N\u1ebfu c\u00f3 $m$ c\u00e1ch + $n$ c\u00e1ch \u2192 t\u1ed5ng: $m + n$<\/p>\n<p><strong>Nh\u00e2n:<\/strong> $m \\times n$<\/p>\n<h3><strong>20. Ho\u00e1n v\u1ecb, ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p<\/strong><\/h3>\n<p><strong>Ho\u00e1n v\u1ecb:<\/strong>$P_n = n!$<\/p>\n<p><strong>Ch\u1ec9nh h\u1ee3p:<\/strong> $A_n^k = \\frac{n!}{(n-k)!}$<\/p>\n<p><strong>T\u1ed5 h\u1ee3p:<\/strong> $C_n^k = \\frac{n!}{k!(n-k)!}$<\/p>\n<h3><strong>21. Nh\u1ecb th\u1ee9c Newton<\/strong><\/h3>\n<p>Khai tri\u1ec3n: $(a + b)^n = \\sum_{k=0}^{n} C_n^k a^{n-k} b^k$<\/p>\n<h2><strong>Ch\u01b0\u01a1ng IX. T\u00ednh x\u00e1c su\u1ea5t theo \u0111\u1ecbnh ngh\u0129a c\u1ed5 \u0111i\u1ec3n<\/strong><\/h2>\n<h3><strong>22. Bi\u1ebfn c\u1ed1 v\u00e0 x\u00e1c su\u1ea5t c\u1ed5 \u0111i\u1ec3n<\/strong><\/h3>\n<p>X\u00e1c su\u1ea5t:\u00a0$P(A) = \\frac{\\text{s\u1ed1 ph\u1ea7n t\u1eed c\u1ee7a A}}{\\text{s\u1ed1 ph\u1ea7n t\u1eed kh\u00f4ng gian m\u1eabu}}$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 10 theo b\u1ed9 s\u00e1ch K\u1ebft N\u1ed1i Tri Th\u1ee9c v\u1edbi Cu\u1ed9c S\u1ed1ng, vi\u1ec7c ghi nh\u1edb v\u00e0 v\u1eadn d\u1ee5ng \u0111\u00fang c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc l\u00e0 y\u1ebfu t\u1ed1 then ch\u1ed1t \u0111\u1ec3 l\u00e0m t\u1ed1t c\u00e1c b\u00e0i ki\u1ec3m tra v\u00e0 k\u1ef3 thi h\u1ecdc k\u1ef3. Th\u1ea7y \u0111\u00e3 h\u1ec7 th\u1ed1ng l\u1ea1i to\u00e0n b\u1ed9 c\u00f4ng th\u1ee9c To\u00e1n &#8230; <a title=\"T\u1ed5ng h\u1ee3p c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n 10 K\u1ebft N\u1ed1i Tri Th\u1ee9c h\u1ecdc k\u00ec 1 v\u00e0 h\u1ecdc k\u00ec 2\" class=\"read-more\" href=\"https:\/\/giapsgk.com\/chuyen-de\/tong-hop-cac-cong-thuc-toan-10-ket-noi-tri-thuc-hoc-ki-1-va-hoc-ki-2\/\" aria-label=\"\u0110\u1ecdc th\u00eam v\u1ec1 T\u1ed5ng h\u1ee3p c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n 10 K\u1ebft N\u1ed1i Tri Th\u1ee9c h\u1ecdc k\u00ec 1 v\u00e0 h\u1ecdc k\u00ec 2\">\u0110\u1ecdc ti\u1ebfp<\/a><\/p>\n","protected":false},"author":1,"featured_media":455,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-442","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ly-thuyet"],"_links":{"self":[{"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/posts\/442","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/comments?post=442"}],"version-history":[{"count":6,"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/posts\/442\/revisions"}],"predecessor-version":[{"id":457,"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/posts\/442\/revisions\/457"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/media\/455"}],"wp:attachment":[{"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/media?parent=442"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/categories?post=442"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/giapsgk.com\/chuyen-de\/wp-json\/wp\/v2\/tags?post=442"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}