[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-144050-105":59,"doc-detail-144050-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","mathematics-entrance-test-march-2012","Mathematics Entrance Test - March 2012","","Mathematics entrance test for March 2012 with a total duration of one hour ten minutes. Covers six question sets across algebra, sequences/arithmetic progressions, geometry of isosceles and square-based figures, and coordinate geometry involving straight lines and parallel lines through the origin. Requires full working and rough calculations to be shown because answers without evidence receive no marks; no calculators are allowed, and only writing materials may be used.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/mathematics-entrance-test-march-2012/144050/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/mathematics-entrance-test-march-2012/144050.png","ImageObject",300,407,{"name":92,"@type":93},"Seraphina","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-26","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How long is the Mathematics entrance test and what materials are allowed?","Question",{"text":113,"@type":114},"The test duration is one hour ten minutes. Only writing materials such as pens, pencils, erasers, and rulers may be brought in.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Are calculators permitted, and how are rough calculations graded?",{"text":118,"@type":114},"Calculators are not allowed. Rough calculations must be presented, and answers without evidence of calculations do not receive marks.",{"name":120,"@type":111,"acceptedAnswer":121},"What topics are included across the questions?",{"text":122,"@type":114},"The paper includes solving systems of equations, working with algebraic expressions, triangle geometry (including an isosceles triangle), coordinate geometry for lines, arithmetic progressions, and angle/area calculations involving a square and an equilateral triangle.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},144050,1787698099,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":39},962075114101,"https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165","Entrance test  \nMathematics  \nMarch 2012  \nTime allowed: One hour ten minutes  \nAnswer all questions.  \nIt is advised that you work quickly and that you leave behind questions that are taking you too long to answer.  \nYou should only bring in writing material (pens, pencils, erasers, rulers).  \nNo calculators are allowed.  \nAll your rough calculations have to be presented. Answers with no evidence of calculations will not score any marks.  \nUse the blank pages of the exam paper to do your rough work.  \nNothing should be removed from the exam room.  \nTHIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES  \nMarch 2012  \nQuestion 1  \nThe numbers P and Q satisfy the system of equations  1  +  1  =  7  and  1  −  1  =  1  .  \nP Q 12 P Q 12  \na) without solving the system find the value of ~~ ~~12~~ ~~ −~~ ~~12~~ ~~ . Then P Q  \nb) Find the values of P and Q by solving the system.  \nAnswer: a) 1 − 1 = b) P= and Q= . P2 Q 2  \nQuestion 2  \na) Find A = s(s − a)(s − b)(s − c) when s = 1 (a + b + c) and a=13, b=14, and c=15 2  \nb) Simplify as much as possible the expression  \nB = (x − y )3 + (y − z)3 + (z − x)3 − 3(x − y)(y − z)(z − x)  \nAnswer: a) A= b) B=  \nQuestion 3  \nIn an isosceles triangle, the base is 20% larger than one of the equal sides. If the sum of the sides equals 32 metres, find the length of the base and the area of the triangle.  \nNote: isosceles=two sides equal  \nAnswer: The base is metres and the area is square metres  \nQuestion 4  \nThe line y=ax+b passes through (2,11) and (1,4)  \na) Find a and b and draw the line for 0 ≤ x ≤ 1  \nb) Find the equation of the straight line which passes through the origin (0,0) and is parallel to the given line  \nQuestion 5  \nIf N is an integer, find in terms of N  \nThe sum of the first 4N terms of the arithmetic progression 1,2,3 ... and  \nThe sum of the first 3N terms of the arithmetic progression 1,3,5 ... If the two sums found in a) and b) are equal, find N  \nAnswer: N=  \nQuestion 6  \nLet ABCD be a square of side 4m. We draw an equilateral triangle ABE, where E is a point outside the square. Calculate the angle ∠ECB , and the area of the triangle ECB  \nNote: equilateral= all sides are equal  \nAnswer: a) Angle ECB= the area is m2","cbCaireoF253S0Sw","https://ap.wps.com/l/cbCaireoF253S0Sw","pdf",403352,"English","# Question 1\n## System of equations for P and Q\n# Question 2\n## Expression for A and simplification of B\n# Question 3\n## Isosceles triangle base and area\n# Question 4\n## Line y=ax+b and parallel line through origin\n# Question 5\n## Arithmetic progression sums and solving for N\n# Question 6\n## Square and equilateral triangle geometry calculations","[{\"question\":\"How long is the Mathematics entrance test and what materials are allowed?\",\"answer\":\"The test duration is one hour ten minutes. Only writing materials such as pens, pencils, erasers, and rulers may be brought in.\"},{\"question\":\"Are calculators permitted, and how are rough calculations graded?\",\"answer\":\"Calculators are not allowed. Rough calculations must be presented, and answers without evidence of calculations do not receive marks.\"},{\"question\":\"What topics are included across the questions?\",\"answer\":\"The paper includes solving systems of equations, working with algebraic expressions, triangle geometry (including an isosceles triangle), coordinate geometry for lines, arithmetic progressions, and angle/area calculations involving a square and an equilateral triangle.\"}]","Mathematics Entrance Test - March 2012 | PDF"]