{"id":135,"date":"2006-10-13T15:14:08","date_gmt":"2006-10-13T15:14:08","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=135"},"modified":"2007-10-31T14:34:00","modified_gmt":"2007-10-31T14:34:00","slug":"stretching-question-2","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=135","title":{"rendered":"Stretching Question 2"},"content":{"rendered":"<p>In <a href=\"http:\/\/www.sixthform.info\/maths\/index.php?m=200606#120\" target=\"_blank\">Stretching Question<\/a> I wondered how students would cope with a type of question they wouldn&#8217;t have seen before:<\/p>\n<ul>If <img src='\/maths\/latexrender\/pictures\/ab3d544a0c2e3877c3a054b8136d6ea1.gif' title='M=\\begin{pmatrix}&#10;\\frac{1}{\\sqrt{2}} &amp; \\frac{1}{\\sqrt{2}} \\\\ \\vspace{-2mm} \\\\&#10;-\\frac{1}{\\sqrt{2}} &amp; \\frac{1}{\\sqrt{2}}&#10;\\end{pmatrix}' alt='M=\\begin{pmatrix}&#10;\\frac{1}{\\sqrt{2}} &amp; \\frac{1}{\\sqrt{2}} \\\\ \\vspace{-2mm} \\\\&#10;-\\frac{1}{\\sqrt{2}} &amp; \\frac{1}{\\sqrt{2}}&#10;\\end{pmatrix}' align=absmiddle> calculate <img src='\/maths\/latexrender\/pictures\/7fd72b492702502c3161375fc217ffd1.gif' title='M^2,\\,M^4' alt='M^2,\\,M^4' align=absmiddle> and <img src='\/maths\/latexrender\/pictures\/f3f06d7fc7ba40b616a673f7b3b835df.gif' title='M^{2006}' alt='M^{2006}' align=absmiddle><\/ul>\n<p>The examiners&#8217; report is now out and it says <small>(edited to show context)<\/small> <\/p>\n<ul><i>Attempts at calculating <img src='\/maths\/latexrender\/pictures\/f3f06d7fc7ba40b616a673f7b3b835df.gif' title='M^{2006}' alt='M^{2006}' align=absmiddle> were rarely completely successful. Many candidates found that <img src='\/maths\/latexrender\/pictures\/b812582002814df8010b8818e6143086.gif' title='M^8' alt='M^8' align=absmiddle> was the identity matrix but then went on to say that <img src='\/maths\/latexrender\/pictures\/f3f06d7fc7ba40b616a673f7b3b835df.gif' title='M^{2006}' alt='M^{2006}' align=absmiddle> must also be the identity matrix. Others gave the value of <img src='\/maths\/latexrender\/pictures\/c9a13a1909260a233dab3c6420bdc77b.gif' title='M^2' alt='M^2' align=absmiddle> or gave the correct answer without any indication as to their reason for doing so, or with incomplete reasoning.<\/i><\/ul>\n<p>How disappointing that so few managed to complete the question successfully. The lack of reasoning doesn&#8217;t tell us whether students guessed or found it too easy to bother putting down the working. It might have helped if students were taught that if <img src='\/maths\/latexrender\/pictures\/0cc175b9c0f1b6a831c399e269772661.gif' title='a' alt='a' align=absmiddle> and <img src='\/maths\/latexrender\/pictures\/92eb5ffee6ae2fec3ad71c777531578f.gif' title='b' alt='b' align=absmiddle> are integers then there exist integers <img src='\/maths\/latexrender\/pictures\/7694f4a66316e53c8cdd9d9954bd611d.gif' title='q' alt='q' align=absmiddle> and <img src='\/maths\/latexrender\/pictures\/4b43b0aee35624cd95b910189b3dc231.gif' title='r' alt='r' align=absmiddle> with <img src='\/maths\/latexrender\/pictures\/2a215312db6b822ce2a44bab0e7c3bcf.gif' title='0 \\leq r&lt;b ' alt='0 \\leq r&lt;b ' align=absmiddle> such that <img src='\/maths\/latexrender\/pictures\/d7643484420495caaa61afbac1ace760.gif' title='a=qb+r' alt='a=qb+r' align=absmiddle> but these fundamental ideas seemed to have been lost to A level.\n\n\nIn the first AS exam the examiners comment that \n\n<ul><i>When asked to use the Factor Theorem or Remainder Theorem, no marks can be earned for using long division.<\/i><\/ul>\n<p>which means <\/p>\n<ul><i>British students haven&#8217;t a clue how to do long division of polynomials so we&#8217;ve made it easier for you, so don&#8217;t try and pretend you know best. (See <a href=\"http:\/\/www.sixthform.info\/maths\/index.php?m=200604#117\" target=\"_blank\">A Level Exam Questions<\/a>).<\/i><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In Stretching Question I wondered how students would cope with a type of question they wouldn&#8217;t have seen before: If calculate and The examiners&#8217; report is now out and it says (edited to show context) Attempts at calculating were rarely completely successful. Many candidates found that was the identity matrix but then went on to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-135","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=135"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/135\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}