{"id":925,"date":"2020-06-24T02:27:55","date_gmt":"2020-06-23T18:27:55","guid":{"rendered":"https:\/\/study-together.com\/edu\/?page_id=925"},"modified":"2020-11-02T23:14:09","modified_gmt":"2020-11-02T15:14:09","slug":"algebraic-expressions-equations","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/algebraic-expressions-equations\/","title":{"rendered":"2. \u4ee3\u6578\u5f0f\u548c\u65b9\u7a0b\u5f0f (Algebraic Expressions &#038; Equations)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"925\" class=\"elementor elementor-925\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a4f1a32 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a4f1a32\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-294f86c\" data-id=\"294f86c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7ca2047 elementor-widget elementor-widget-menu-anchor\" data-id=\"7ca2047\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-menu-anchor\" id=\"algebraicExp\"><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4de7562 elementor-widget elementor-widget-text-editor\" data-id=\"4de7562\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>2.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u4ee3\u6578\u5f0f (Algebraic Expressions)<\/h2><ul><li>\u4ee3\u6578\u5f0f\u4fc2\u7531\u6578\u5b57\uff0c\u7b26\u865f\uff08\u5982\u300c+\u300d\uff09\u548c\u5b57\u6bcd\uff08\u5373\u672a\u77e5\u6578\/\u8b8a\u6578\uff0c\u5982\\(x\\)\uff09\u7b49\u7d44\u6210\u7684\u3002<br \/>\u4f8b\uff1a\\(5 + 2a &#8211; 3b + 4a\\)<br \/><br \/><\/li><li><strong>\u9805 (terms) <\/strong>\u4fc2\u4ee3\u6578\u5f0f\u4e2d\uff0c\u4ee5\u300c+\u300d\u6216\u300c\uff0d\u300d\u865f\u4f5c\u9694\u7dda\u5605\u90e8\u5206\uff08\u5305\u62ec\u300c+\u300d\u548c\u300c\uff0d\u300d\uff09\u3002<br \/>\u4f8b\uff1a\\(5 + 2a &#8211; 3b + 4a\\) \u5305\u542b\u54974\u500b\u9805\uff0c\u5206\u5225\u4fc2\\(5\uff0c2a\uff0c\uff0d3b\u540c4a\\)\u3002<br \/><br \/><\/li><li>\u5728\u4ee3\u6578\u5f0f\u4e2d\uff0c<ul><li>\u53ea\u6709\u6578\u5b57\u7684\u9805\u7a31\u70ba<strong>\u5e38\u6578\u9805<\/strong><strong> (constant term)<\/strong><\/li><li>\u6709\u76f8\u540c\u5b57\u6bcd\u7d44\u5408\u7684\u9805\u70ba<strong>\u540c\u985e\u9805<\/strong><strong> (like terms)<\/strong><\/li><li>\u5176\u4ed6\u7a31\u70ba<strong>\u7570\u985e\u9805<\/strong><strong> (unlike terms)<\/strong><\/li><\/ul><\/li><\/ul><p style=\"padding-left: 40px;\">\u4f8b: \u5728\u4ee3\u6578\u5f0f \uff1b\u67094\u9805\uff0c 5\u662f\u5e38\u6578\u9805\uff0c 2<em>a<\/em> \u548c 4<em>a<\/em> \u662f\u540c\u985e\u9805\uff0c 2<em>a<\/em>\uff0c5\uff0c\u548c(\u20133<em>b<\/em>)\u662f\u7570\u985e\u9805\u3002<\/p><ul><li>\u540c\u985e\u9805\u53ef\u4ee5\u76f8\u52a0\u6e1b\uff0c\u7570\u9805\u4e0d\u80fd\u3002<br \/>\u5982 \\(2a + 4a = 6a\\)<br \/><br \/><\/li><li>\u5728\u6bcf\u4e00\u9805\u4e2d\uff0c\u8b8a\u6578\u524d\u7684\u6578\u5b57\u7a31\u70ba<strong>\u4fc2\u6578<\/strong><strong> (coefficient)<\/strong>\u3002\u5982\u5c0d(\uff0d3<em>b<\/em>)\u4f86\u8aaa\uff0c<em>b<\/em>\u7684\u4fc2\u6578\u4fc2(\uff0d3)\u3002<\/li><\/ul><h2>2.2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u516c\u5f0f (Formulae)<\/h2><ul><li>\u516c\u5f0f\u662f\u4ee5\u7b49\u865f\u8868\u793a2\u500b\u6216\u4ee5\u4e0a\u8b8a\u6578 (variables) \u4e4b\u9593\u7684\u95dc\u4fc2\u3002<\/li><\/ul><p style=\"padding-left: 40px;\">\u4f8b\uff1a \\(P = 2 ( h + w )\\)<br \/>\u5176\u4e2dP\u4ee3\u8868\u9577\u65b9\u5f62\u7684\u5468\u754c\uff0ch\u53caw\u4ee3\u8868\u9577\u65b9\u5f62\u7684\u9ad8\u53ca\u6ff6\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f49daba elementor-widget elementor-widget-text-editor\" data-id=\"f49daba\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>2.3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u65b9\u7a0b\u5f0f (Equations)<\/h2><ul><li>\u65b9\u7a0b\u4fc2\u4e00\u500b&#8221;\u542b\u6709\u672a\u77e5\u6578(unknown)\uff0c\u4e26\u4ee5\u7b49\u865f\u300c=\u300d\u8868\u793a\u76f8\u7b49&#8221;\u5605\u95dc\u4fc2\u3002<\/li><li>\u53ea\u6709\u4e00\u500b\u672a\u77e5\u6578\u7684\u65b9\u7a0b\u7a31\u70ba\u4e00\u5143\u65b9\u7a0b(Equation in one unknown)\u3002<\/li><\/ul><h3>2.3.1\u00a0\u00a0\u00a0\u00a0 \u89e3\u65b9\u7a0b (Solving Equations)<\/h3><ul><li>\u89e3\u65b9\u7a0b\u662f\u6307<strong>\u6c42\u51fa\u8a72\u65b9\u7a0b\u4e2d\u672a\u77e5\u6578\u7684\u503c<\/strong>\u3002\u5e73\u65e5\u540c\u5b78\u4e00\u822c\u53eb\u4f9d\u500b\u503c\u505a&#8221;\u7b54\u6848&#8221;\uff0c\u4f46\u5176\u5be6\u6b63\u78ba\u61c9\u53eb\u4f5c\u65b9\u7a0b\u7684\u300c<strong>\u89e3<\/strong><strong>(solution)<\/strong>\u300d\u6216\u300c<strong>\u6839<\/strong><strong>(root)<\/strong>\u300d\u3002<\/li><li>\u89e3\u65b9\u7a0b\u6642\u7528\u5230\u5605\u4e3b\u8981\u6280\u5de7\u5305\u62ec\uff1a<ul><li>\u5728\u65b9\u7a0b\u7b49\u865f\u7684\u5169\u908a\u9032\u884c\u76f8\u540c\u7684\u904b\u7b97<\/li><li>\u79fb\u9805<\/li><\/ul><\/li><\/ul><h3>2.3.2\u00a0\u00a0\u00a0\u00a0 \u61c9\u7528\u2500\u2500\u6587\u5b57\u984c<\/h3><p>\u5927\u90e8\u4efd\u6587\u5b57\u984c\u53ef\u7d93<strong>\u5efa\u7acb\u53ca\u89e3\u4ee3\u6578\u65b9\u7a0b<\/strong>\u4f86\u89e3\u6c7a\u3002\u65b9\u6cd5\u5982\u4e0b\uff1a<\/p><ul><li>\u8a2d\u7acb\u672a\u77e5\u6578<\/li><li>\u4f9d\u64da\u984c\u76ee\u5beb\u4e0b\u672a\u77e5\u6578\u7684\u95dc\u4fc2\uff08\u5373\u65b9\u7a0b\u5f0f\uff09<\/li><\/ul><p>\u4f8b1\uff1a\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u7236\u89aa\u7684\u5e74\u9f61\u662f48\u6b72\u3002\u516d\u5e74\u5f8c\uff0c\u7236\u89aa\u7684\u5e74\u9f61\u662f\u5152\u5b50\u5e74\u9f61\u76843\u500d\u3002\u6c42\u5152\u5b50\u73fe\u5728\u7684\u5e74\u9f61\u3002<\/p><p>\u65b9\u6cd5\uff1a\u00a0\u00a0\u00a0 \u8a2d\u5152\u5b50\u73fe\u5728\u7684\u5e74\u9f61\u70ba\\(x\\)\u30026\u5e74\u5f8c\uff0c\u5152\u5b50\u7684\u5e74\u9f61\u662f\\(x+6\\)\uff0c\u7236\u89aa\u7684\u5e74\u9f61\u662f\\(48+6\\)\u6b72\u3002\u6240\u4ee5\u53ef\u5efa\u7acb\u4e00\u689d\u65b9\u7a0b \uff0c\u4e4b\u5f8c\u518d\u8a08\u500b\u89e3(\u5373\u7b54\u6848)\u3002<\/p><p style=\"text-align: center;\">\\( \\begin{align} 3 (x + 6) &amp;= 48 + 6 \\\\<br \/>3x + 18 &amp;= 54 \\\\<br \/>3x &amp; = 54 &#8211; 18 \\\\<br \/>3x &amp; = 36 \\\\<br \/>x &amp;= 12<br \/>\\end{align}\\)<\/p><p>\u7b54\uff1a\u5152\u5b50\u73fe\u572812\u6b72\u3002<\/p><p>\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-6cd35a0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6cd35a0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-483d3e4\" data-id=\"483d3e4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0836792 elementor-widget elementor-widget-text-editor\" data-id=\"0836792\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/directed-numbers\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u6709\u5411\u6578<\/a>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-d9ddb36\" data-id=\"d9ddb36\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-03ae503 elementor-widget elementor-widget-text-editor\" data-id=\"03ae503\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/laws-of-integral-indices\/\">\u6307\u6578\u53ca\u9032\u5236 <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-23c9e3a\" data-id=\"23c9e3a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bae7f63 elementor-widget elementor-widget-sidebar\" data-id=\"bae7f63\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-2 > ul > li > a, .custom-menu-widget .ocean_custom_menu-2 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-2.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e00\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-2 left dropdown-hover\"><ul id=\"menu-form1mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-928\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-928\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/directed-numbers\/\" class=\"menu-link\">1. \u6709\u5411\u6578 (Directed Numbers)<\/a><\/li>\n<li  id=\"menu-item-929\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-929\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/algebraic-expressions-equations\/\" class=\"menu-link\">2. \u4ee3\u6578\u5f0f\u548c\u65b9\u7a0b\u5f0f (Algebraic Expressions &#038; Equations)<\/a><\/li>\n<li  id=\"menu-item-995\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-995\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/laws-of-integral-indices\/\" class=\"menu-link\">3. \u6307\u6578\u53ca\u9032\u5236 (Laws of integral indices)<\/a><\/li>\n<li  id=\"menu-item-1000\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1000\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/polynomials\/\" class=\"menu-link\">4. \u591a\u9805\u5f0f (Polynomials)<\/a><\/li>\n<li  id=\"menu-item-1043\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1043\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/using-percentages\/\" class=\"menu-link\">5. \u767e\u5206\u6cd5 (Using percentages)<\/a><\/li>\n<li  id=\"menu-item-1053\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1053\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/approximate-values-estimation\/\" class=\"menu-link\">6. \u8fd1\u4f3c\u503c\u8207\u4f30\u7b97 (Approximate values &#038; estimation)<\/a><\/li>\n<li  id=\"menu-item-1071\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1071\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/introduction-to-geometry\/\" class=\"menu-link\">7. \u5e7e\u4f55\u7c21\u4ecb (Introduction to Geometry)<\/a><\/li>\n<li  id=\"menu-item-1093\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1093\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/symmetry-and-transformation\/\" class=\"menu-link\">8. \u5c0d\u7a31\u53ca\u8b8a\u63db (Symmetry and Transformation)<\/a><\/li>\n<li  id=\"menu-item-1109\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1109\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/congruence-and-similarity\/\" class=\"menu-link\">9. \u5168\u7b49\u53ca\u76f8\u4f3c (Congruence and Similarity)<\/a><\/li>\n<li  id=\"menu-item-1120\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1120\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/estimation-in-measurements\/\" class=\"menu-link\">10. \u91cf\u5ea6\u65b9\u9762\u7684\u4f30\u8a08 (Estimation in measurements)<\/a><\/li>\n<li  id=\"menu-item-1136\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1136\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/area-and-volume\/\" class=\"menu-link\">11. \u9762\u7a4d\u53ca\u9ad4\u7a4d (Area and Volume)<\/a><\/li>\n<li  id=\"menu-item-1150\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1150\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/introduction-to-coordinates\/\" class=\"menu-link\">12.   \u5750\u6a19\u7c21\u4ecb (Introduction to Coordinates)<\/a><\/li>\n<li  id=\"menu-item-1164\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1164\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/introduction-to-statistics\/\" class=\"menu-link\">13.  \u7d71\u8a08\u7c21\u4ecb (Introduction to Statistics)<\/a><\/li>\n<li  id=\"menu-item-16138\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16138\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/exam_papers\/\" class=\"menu-link\">*** \u521d\u4e2d\u8a66\u5377 \/ \u8a66\u984c\u5eab ***<\/a><\/li>\n<\/ul><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>2.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u4ee3\u6578\u5f0f (Algebraic Expressions) \u4ee3\u6578\u5f0f\u4fc2\u7531\u6578\u5b57\uff0c\u7b26\u865f\uff08\u5982\u300c+ 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