{"id":561,"date":"2020-01-26T15:06:42","date_gmt":"2020-01-26T15:06:42","guid":{"rendered":"http:\/\/localhost\/?post_type=knowledgebase&#038;p=561"},"modified":"2020-03-24T07:54:05","modified_gmt":"2020-03-24T07:54:05","slug":"past-year-exam-questions-quadratics","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/quadratics\/past-year-exam-questions-quadratics\/","title":{"rendered":"IBDP Past year exam questions -Quadratics"},"content":{"rendered":"<p><strong>1.\u00a0 [M18\/P1\/TZ1]<\/strong><\/p>\r\n<p>Solve\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mfenced><mrow><mi>ln<\/mi><mi>x<\/mi><\/mrow><\/mfenced><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mfenced><mrow><mi>ln<\/mi><mn>2<\/mn><\/mrow><\/mfenced><mfenced><mrow><mi>ln<\/mi><mi>x<\/mi><\/mrow><\/mfenced><mo>&#60;<\/mo><mn>2<\/mn><msup><mfenced><mrow><mi>ln<\/mi><mn>2<\/mn><\/mrow><\/mfenced><mn>2<\/mn><\/msup><\/math>\r\n .\u00a0 \u00a0[6 marks]<\/p>\r\n<div id=\"link1-link-561\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 561, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-561\">Solution<\/span><\/a><\/div><div id=\"link1-content-561\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1408\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1.jpg\" alt=\"\" width=\"1029\" height=\"702\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1.jpg 1029w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1-300x205.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1-1024x699.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1-768x524.jpg 768w\" sizes=\"auto, (max-width: 1029px) 100vw, 1029px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>2.\u00a0 [M18\/P2\/TZ2]\u00a0<\/strong><\/p>\r\n<p>Given\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mfenced><mi>t<\/mi><\/mfenced><mo>=<\/mo><msup><mfenced><mfrac><mrow><mn>1<\/mn><mo>+<\/mo><mi>t<\/mi><\/mrow><mrow><mn>1<\/mn><mo>&#8211;<\/mo><mi>t<\/mi><\/mrow><\/mfrac><\/mfenced><mn>2<\/mn><\/msup><\/math>\r\n . Let\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><mo>&#160;<\/mo><mo>,<\/mo><mo>&#160;<\/mo><mi>&#946;<\/mi><\/math>\r\n be the roots of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mfenced><mi>t<\/mi><\/mfenced><mo>=<\/mo><mi>k<\/mi><\/math>\r\n , where\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>0<\/mn><mo>&#60;<\/mo><mi>k<\/mi><mo>&#60;<\/mo><mn>1<\/mn><\/math>\r\n .<\/p>\r\n<p>(i)\u00a0 \u00a0Find\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><\/math>\r\n and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#946;<\/mi><\/math>\r\n in terms of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math>\r\n .<\/p>\r\n<p>(ii)\u00a0 \u00a0Show that\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><mo>+<\/mo><mi>&#946;<\/mi><mo>&#60;<\/mo><mo>&#8211;<\/mo><mn>2<\/mn><\/math>\r\n .\u00a0 \u00a0[7 marks]<\/p>\r\n<div id=\"link2-link-561\" class=\"sh-link link2-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link2', 561, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link2-toggle-561\">Solution<\/span><\/a><\/div><div id=\"link2-content-561\" class=\"sh-content link2-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1410\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/2.jpg\" alt=\"\" width=\"939\" height=\"962\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/2.jpg 939w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/2-293x300.jpg 293w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/2-768x787.jpg 768w\" sizes=\"auto, (max-width: 939px) 100vw, 939px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>3.\u00a0 [N17\/P2\/TZ0]\u00a0<\/strong><\/p>\r\n<p>In the quadratic equation \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>7<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>8<\/mn><mi>x<\/mi><mo>+<\/mo><mi>p<\/mi><mo>=<\/mo><mn>0<\/mn><\/math>\r\n, \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>p<\/mi><mo>&#8712;<\/mo><mi mathvariant=\"normal\">&#8474;<\/mi><\/mrow><\/mfenced><\/math>\r\n, one root is three times the other root. Find the value of <em>\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>p<\/mi><\/math>\r\n<\/em>.<\/p>\r\n<div id=\"link3-link-561\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 561, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-561\">Solution<\/span><\/a><\/div><div id=\"link3-content-561\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1423\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/3.jpg\" alt=\"\" width=\"1035\" height=\"1180\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/3.jpg 1035w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/3-263x300.jpg 263w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/3-898x1024.jpg 898w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/3-768x876.jpg 768w\" sizes=\"auto, (max-width: 1035px) 100vw, 1035px\" \/><\/p>\r\n<p>\u00a0<\/div><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"1.\u00a0 [M18\/P1\/TZ1] Solve\u00a0 lnx2&#8211;ln2lnx&#60;2ln22 .\u00a0 \u00a0[6 marks] 2.\u00a0 [M18\/P2\/TZ2]\u00a0 Given\u00a0 gt=1+t1&#8211;t2 . Let\u00a0 &#945;&#160;,&#160;&#946; be the roots of\u00a0 gt=k , where\u00a0 0&#60;k&#60;1 . (i)\u00a0 \u00a0Find\u00a0 &#945; and\u00a0 &#946; in terms of\u00a0 k . (ii)\u00a0 \u00a0Show that\u00a0 &#945;+&#946;&#60;&#8211;2 .\u00a0 \u00a0[7 marks] 3.\u00a0 [N17\/P2\/TZ0]\u00a0 In the quadratic equation 7&#215;2&#8211;8x+p=0 , p&#8712;&#8474; , one root is three times [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-561","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-quadratics","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/561","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=561"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/561\/revisions"}],"predecessor-version":[{"id":1424,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/561\/revisions\/1424"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=561"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}