{"id":1886,"date":"2020-05-28T04:10:00","date_gmt":"2020-05-28T04:10:00","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&#038;p=1886"},"modified":"2020-07-15T04:42:17","modified_gmt":"2020-07-15T04:42:17","slug":"practice-questions-application-of-derivatives","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/applications-of-differentiation\/practice-questions-application-of-derivatives\/","title":{"rendered":"Practice Questions &#8211; Application of derivatives"},"content":{"rendered":"<p>Q1. [ Non calculator]<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1887\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-10.jpg\" alt=\"\" width=\"996\" height=\"1333\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-10.jpg 996w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-10-224x300.jpg 224w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-10-765x1024.jpg 765w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-10-768x1028.jpg 768w\" sizes=\"auto, (max-width: 996px) 100vw, 996px\" \/><\/p>\r\n<div id=\"link1-link-1886\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 1886, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-1886\">Solution<\/span><\/a><\/div><div id=\"link1-content-1886\" 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-1888\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-11.jpg\" alt=\"\" width=\"479\" height=\"857\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-11.jpg 479w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-11-168x300.jpg 168w\" sizes=\"auto, (max-width: 479px) 100vw, 479px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p>2. An engineer has designed a lifting device. The handle turns a screw which shortens the horizontal length and increases the vertical height.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-1935\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-4-300x246.png\" alt=\"\" width=\"300\" height=\"246\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-4-300x246.png 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-4.png 469w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\r\n<p>The device is modelled by a rhombus, with each side 25 cm.<br \/>\r\nThe horizontal length is\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n cm, and the vertical height is\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><\/math>\r\n cm as shown.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-1936\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-14-300x195.jpg\" alt=\"\" width=\"300\" height=\"195\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-14-300x195.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-14.jpg 529w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\r\n<p>(a) Show that\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><mo>=<\/mo><msqrt><mn>2500<\/mn><mo>&#8211;<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/msqrt><\/math>\r\n .\u00a0 \u00a0 [1 mark]<br \/>\r\n(b) The horizontal length decreases at a rate of 0\u00b73 cm per second as the handle is turned.<br \/>\r\nFind the rate of change of the vertical height when\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo>=<\/mo><mn>30<\/mn><\/math>\r\n .\u00a0 \u00a0[5 marks]<\/p>\r\n<div id=\"link2-link-1886\" class=\"sh-link link2-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link2', 1886, 'Solution2', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link2-toggle-1886\">Solution2<\/span><\/a><\/div><div id=\"link2-content-1886\" class=\"sh-content link2-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-1937\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-5-187x300.png\" alt=\"\" width=\"187\" height=\"300\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-5-187x300.png 187w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-5.png 360w\" sizes=\"auto, (max-width: 187px) 100vw, 187px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p>3.\u00a0<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2095\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-16.jpg\" alt=\"\" width=\"967\" height=\"647\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-16.jpg 967w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-16-300x201.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-16-768x514.jpg 768w\" sizes=\"auto, (max-width: 967px) 100vw, 967px\" \/><\/p>\r\n<div id=\"link3-link-1886\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 1886, 'Solution3', 'Hide Solution3'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-1886\">Solution3<\/span><\/a><\/div><div id=\"link3-content-1886\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-2096\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-17-181x300.jpg\" alt=\"\" width=\"181\" height=\"300\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-17-181x300.jpg 181w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/05\/1-17.jpg 347w\" sizes=\"auto, (max-width: 181px) 100vw, 181px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"Q1. [ Non calculator] 2. An engineer has designed a lifting device. The handle turns a screw which shortens the horizontal length and increases the vertical height. The device is modelled by a rhombus, with each side 25 cm. The horizontal length is\u00a0 x cm, and the vertical height is\u00a0 h cm as shown. (a) [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1886","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-applications-of-differentiation","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1886","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\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1886"}],"version-history":[{"count":10,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1886\/revisions"}],"predecessor-version":[{"id":2121,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1886\/revisions\/2121"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1886"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}