{"id":1467,"date":"2020-07-20T23:19:24","date_gmt":"2020-07-20T15:19:24","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1467"},"modified":"2020-11-02T23:18:01","modified_gmt":"2020-11-02T15:18:01","slug":"inequalities","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/inequalities\/","title":{"rendered":"1. \u4e0d\u7b49\u5f0f (Inequalities)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1467\" class=\"elementor elementor-1467\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b139dad elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b139dad\" 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-6130808\" data-id=\"6130808\" 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-72ccb9c elementor-widget elementor-widget-text-editor\" data-id=\"72ccb9c\" 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>1.1\u00a0 \u4e0d\u7b49\u5f0f\u7684\u610f\u7fa9<\/h2><p>\u7c21\u55ae\u4f86\u8aaa\uff0c\u4e0d\u7b49\u5f0f\u662f\u4e00\u500b\u8868\u793a\u201c\u4e0d\u76f8\u7b49\u95dc\u4fc2\u201d\u7684\u6578\u5f0f\u3002<\/p><p>\u5176\u5be6\u65e5\u5e38\u751f\u6d3b\u4e2d\u90fd\u6709\u597d\u591a\u4e0d\u76f8\u7b49\u95dc\u4fc2\u7684\u4f8b\u5b50\uff1a<\/p><ul><li>4\u4eba\u7684\u58eb\u8f09\u4e58\u5ba2\u7684\u6578\u91cf\u7d30\u904e4<\/li><li>\u7238\u7238\u548c\u5abd\u5abd\u7684\u5e74\u9f61\u76f8\u52a0\u5927\u904e100<\/li><li>\u65c5\u884c\u793e\u8209\u8fa6\u65c5\u884c\u5718\u6642\uff0c\u53c3\u52a0\u4eba\u6578\u5fc5\u9808\u5927\u65bc10\u4eba\u624d\u300c\u6210\u884c\u300d<\/li><\/ul>\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-83837da elementor-widget elementor-widget-text-editor\" data-id=\"83837da\" 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>1.2\u00a0 \u4e0d\u7b49\u865f<\/h2><p>\u8003\u616ex\u548cy\u5169\u8b8a\u6578\uff0c\u201cx\u4e0d\u76f8\u7b49y\u201d\u6709\u56db\u7a2e\u60c5\u6cc1\uff0c\u53ef\u80fd\u4ee5\u4e0b\u56db\u500b\u4e0d\u7b49\u865f\u569f\u8868\u793a\uff1a<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\\(x &gt; y\u00a0 \\quad \\quad x\u5927\u65bcy\\)<\/li><li>\\(x \\geqslant y\u00a0 \\quad \\quad x\u5927\u65bc\u6216\u7b49\u65bcy\\)<\/li><li>\\(x &lt; y\u00a0 \\quad \\quad x\u5c0f\u65bcy\\)<\/li><li>\\(x \\leqslant y\u00a0 \\quad \\quad x\u5c0f\u65bc\u6216\u7b49\u65bcy\\)<\/li><\/ul><\/li><\/ul><p>\u7559\u610f:<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\\(x &gt; y\u00a0 \\quad \u540c\\quad y\u00a0 &lt; x quad \u5605\u610f\u601d\u4fc2\u4e00\u6a23\u7684\u3002\\)<ul><li>\u56e0\u70ba \u300cx\u5927\u904ey\u300d\u5373\u300cy\u7d30\u904ex\u300d<\/li><\/ul><\/li><\/ul><\/li><\/ul>\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-1488e7f elementor-widget elementor-widget-text-editor\" data-id=\"1488e7f\" 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>1.3\u00a0 \u65bc\u6578\u7dda\u4e0a\u7528\u5716\u50cf\u8868\u793a\u4e0d\u7b49\u5f0f<\/h2><p>\u7576\u6211\u5730\u8b1b\u300cx \u5927\u904e3\u300d\u5605\u6642\u5019\uff0c\u5481x\u53ef\u4ee5\u4fc2\u5e7e\u591a\u5462?\u53ef\u4ee5\u4fc24, 5, 5.3, 1000, 999, 9999\uff0c\u7e3d\u4e4bx\u5605\u503c\u4fc2\u55ba\u300c\u5927\u904e3\u5605\u7bc4\u570d\u300d\u5165\u9762\u90fd\u53ef\u4ee5\u3002<\/p><p>\u70ba\u5497\u66f4\u5bb9\u6613\u5730\u8868\u9039x\u53ef\u4ee5\u9078\u53d6\u5605\u7bc4\u570d\uff0c\u6211\u5730\u6709\u6642\u6703\u55ba\u6578\u7dda\u4e0a\u7528\u5716\u50cf\u569f\u8868\u793a\u53ef\u9078\u53d6\u5605\u7bc4\u570d\u3002<\/p><p style=\"padding-left: 40px;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-medium wp-image-1547\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_ineqalities_01-300x267.jpg\" alt=\"\u65bc\u6578\u7dda\u4e0a\u8868\u793a\u4e0d\u7b49\u5f0f\" width=\"300\" height=\"267\" srcset=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_ineqalities_01-300x267.jpg 300w, https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_ineqalities_01.jpg 378w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>\u5f9e\u4e0a\u9762\u5605\u5716\u50cf\u4e2d\uff0c\u5927\u5bb6\u61c9\u4e0d\u96e3\u767c\u73fe<\/p><ul><li>\u7576\u4e0d\u7b49\u5f0f\u7b26\u865f\u6c92\u6709\u201c\u7b49\u65bc\u201d\u5605\u90e8\u4efd\uff0c\u6211\u5011\u8981\u4f7f\u7528\u7a7a\u5fc3\u5713\u3002<\/li><li>\u7576\u4e0d\u7b49\u5f0f\u662f\u201c\u5927\u65bc\u201d\u6642\uff0c\u7bad\u5480\u6307\u5411\u53f3\u908a\u3002\u5481\u4fc2\u56e0\u70ba\u6578\u7dda\u4e0a\uff0c\ud85f\uded7\u5411\u53f3\u6578\u503c\u5c31\ud85f\uded7\u5927\u3002<ul><li>\u76f8\u53cd\uff0c\u7576\u4e0d\u7b49\u5f0f\u662f\u201c\u5927\u65bc\u201d\u6642\uff0c\u7bad\u5480\u6307\u5411\u5de6\u908a\uff08\uff0d\uff13\u53f3\u908a\u7684\u6578\u6bd4\uff0d\uff13\u5927\uff09\u3002<\/li><\/ul><\/li><\/ul>\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-de3fee4 elementor-widget elementor-widget-text-editor\" data-id=\"de3fee4\" 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>1.4\u00a0 \u4e0d\u7b49\u5f0f\u7684\u57fa\u672c\u6027\u8cea<\/h2><ul><li>\u50b3\u905e\u6027\u8cea\uff08Transitive Property\uff09<ul><li>\u5982\u679c a &gt; b \u53ca b &gt; c\uff0c\u5247 a &gt; c \u3002<\/li><\/ul><\/li><\/ul><ul><li>\u52a0\u6cd5\u6027\u8cea\uff08Additive Property\uff09<ul><li>\u5982\u679c a &gt; b \uff0c\u5247 a + c &gt; b + c \u3002<\/li><\/ul><\/li><li>\u4e58\u6cd5\u6027\u8cea\uff08Multiplicative Property\uff09<ul><li>\u5982\u679c a &gt; b \u53ca c &gt; 0\uff0c\u5247 ac &gt; bc \u3002<\/li><li>\u5982\u679c a &gt; b \u53ca c &lt; 0\uff0c\u5247 ac &lt; bc \u3002<br \/>\u7c21\u55ae\u569f\u8b1b\uff0c\u5927\u5bb6\u53ea\u8981\u8a18\u4f4f\u300c<span style=\"color: #ff0000;\"><strong>\u7576\u5c0d\u4e0d\u7b49\u5f0f\u5de6\u53f3\u540c\u6642\u4e58\u6216\u9664\u4e00\u500b\u8ca0\u6578\u5b57\uff0c\u500b\u4e0d\u7b49\u5f0f\u7b26\u865f\u8981\u5012\u8f49<\/strong><\/span>\u300d\u5c31\u53ef\u4ee5\u4e86\u3002<\/li><\/ul><\/li><li>\u5012\u6578\u6027\u8cea\uff08Reciprocal Property\uff09<ul><li>\u5982\u679c a &gt; b \u4e14 a\u3001b\u5747\u662f\u6b63\u6578\uff0c\u5247 \\(\\dfrac{1}{a} &lt; \\dfrac{1}{b}\\)<\/li><li>\u5982\u679c\u5176\u4e2d\u4e00\u500b\u4fc2\u8ca0\u6578\uff0c\u5247\u5de6\u53f3\u651e\u5012\u6578\u5f8c\u500b\u7b26\u865f\u4e0d\u8b8a\u3002<br \/>** \u5012\u6578\u6027\u8cea\u55ba\u521d\u4e2d\u5605\u6642\u5019\u5927\u5bb6\u5514\u592a\u660e\u90fd\u5514\u7dca\u8981\u3002\u7576\u51fa\u73fe\u5012\u6578\u6642\uff0c\u5927\u5bb6\u7528\u6578\u5b57\u53bb\u60f3\u4e00\u60f3\u5c31\u53ef\u4ee5\u4e86\u3002<ul><li>\u4f8b\u5982\u00a0 -2 &lt; 5\u3002<br \/>\u651e\u5012\u6578\u5f8c\u4fc2\u00a0 \\(1\\dfrac{1}{2} \u540c \\dfrac{1}{5}\\)\u3002\u56e0\u70ba\u8ca0\u6578\u9ede\u90fd\u4fc2\u7d30\u904e\u6b63\u6578\uff0c\u6240\u4ee5 \\(1\\dfrac{1}{2} &lt; \\dfrac{1}{5}\\)\u3002<\/li><\/ul><\/li><\/ul><\/li><\/ul>\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-af1f221 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"af1f221\" 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-33 elementor-inner-column elementor-element elementor-element-e950a0a\" data-id=\"e950a0a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6eb9043\" data-id=\"6eb9043\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-e91318a\" data-id=\"e91318a\" 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-f17abb8 elementor-widget elementor-widget-text-editor\" data-id=\"f17abb8\" 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\/form3_maths\/indices\/\">\u6307\u6578 <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-700acbc\" data-id=\"700acbc\" 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-69cc6ed elementor-widget elementor-widget-sidebar\" data-id=\"69cc6ed\" 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-4 > ul > li > a, .custom-menu-widget .ocean_custom_menu-4 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-4.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e09\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-4 left dropdown-hover\"><ul id=\"menu-form3mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1543\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1543\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/inequalities\/\" class=\"menu-link\">1. \u4e0d\u7b49\u5f0f (Inequalities)<\/a><\/li>\n<li  id=\"menu-item-1542\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1542\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/indices\/\" class=\"menu-link\">2. \u6307\u6578 (Indices)<\/a><\/li>\n<li  id=\"menu-item-1541\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1541\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/use-of-percentage\/\" class=\"menu-link\">3. \u767e\u4efd\u6cd5  (Use of Percentage)<\/a><\/li>\n<li  id=\"menu-item-1540\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1540\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/rational-irrational-numbers\/\" class=\"menu-link\">4. \u6709\u7406\u6578\u53ca\u7121\u7406\u6578 (Rational &#038; Irrational Numbers)<\/a><\/li>\n<li  id=\"menu-item-1539\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1539\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/deductive-geometry\/\" class=\"menu-link\">5. \u6f14\u7e79\u5e7e\u4f55 (Deductive Geometry)<\/a><\/li>\n<li  id=\"menu-item-1538\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1538\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/quadrilateral\/\" class=\"menu-link\">6. \u56db\u908a\u5f62 (Quadrilateral)<\/a><\/li>\n<li  id=\"menu-item-1537\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1537\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/area-volume\/\" class=\"menu-link\">7. \u9762\u7a4d\u8207\u9ad4\u7a4d (Area &#038; Volume)<\/a><\/li>\n<li  id=\"menu-item-1536\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1536\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/coordinate-geometry\/\" class=\"menu-link\">8. \u5750\u6a19\u5e7e\u4f55 (Coordinate Geometry)<\/a><\/li>\n<li  id=\"menu-item-1535\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1535\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/trigonometry\/\" class=\"menu-link\">9. \u4e09\u89d2\u5b78 (Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1534\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1534\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/applications-of-trigonometry\/\" class=\"menu-link\">10. \u4e09\u89d2\u6bd4\u7684\u61c9\u7528 (Applications of Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1533\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1533\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/probability\/\" class=\"menu-link\">11. \u6982\u7387 (Probability)<\/a><\/li>\n<li  id=\"menu-item-1532\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1532\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/statistics-measure-of-central-tendency\/\" class=\"menu-link\">12. \u7d71\u8a08 \u2013 \u96c6\u4e2d\u8da8\u52e2\u7684\u91cf\u5ea6 (Measure of Central Tendency)<\/a><\/li>\n<li  id=\"menu-item-1625\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1625\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/centers-of-triangles\/\" class=\"menu-link\">13. \u4e09\u89d2\u5f62\u7684\u5fc3 (Centers of Triangles)<\/a><\/li>\n<li  id=\"menu-item-16136\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16136\"><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>1.1\u00a0 \u4e0d\u7b49\u5f0f\u7684\u610f\u7fa9 \u7c21\u55ae\u4f86\u8aaa\uff0c\u4e0d\u7b49\u5f0f\u662f\u4e00\u500b\u8868\u793a\u201c\u4e0d\u76f8\u7b49\u95dc\u4fc2\u201d\u7684\u6578\u5f0f\u3002 \u5176\u5be6\u65e5\u5e38\u751f\u6d3b\u4e2d\u90fd\u6709\u597d\u591a\u4e0d\u76f8\u7b49\u95dc\u4fc2\u7684\u4f8b 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