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The problems cover evaluating expressions, solving equations and inequalities, circle geometry using perpendicular chords/diameters, coordinate geometry with trapezium and triangle area relationships, algebraic evaluation with parameterized expressions, and a class-average word problem comparing boys and girls under percentage grade changes.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/mathematics-entrance-test-march-2013-exam-practice/144034/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/mathematics-entrance-test-march-2013-exam-practice/144034.png","ImageObject",300,407,{"name":42,"@type":43},"Seraphina","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-08-25",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",15,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"Are calculators allowed in this March 2013 mathematics entrance test?","Question",{"text":63,"@type":64},"No calculators are allowed.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What is required to receive marks for answers?",{"text":68,"@type":64},"All rough calculations must be presented, and answers without evidence of calculations will not score marks.",{"name":70,"@type":61,"acceptedAnswer":71},"What is the time allowed for completing the exam?",{"text":72,"@type":64},"The time allowed is one hour ten minutes.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},144034,1787698034,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":111},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 2013  \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 2013  \nQuestion 1 Evaluate A where  \nA =  1 + ⎛⎜ 1 +  2  ⎞⎟ + ⎛⎜ 1 +  2 +  3  ⎞⎟ + ⎜⎛ 1 +  2 +  3 +  4  ⎞⎟ + + ⎛⎜ 1  + 2  + +  99 ⎞⎟  \n2 ⎝ 3 3 ⎠ ⎝ 4 4 4 ⎠ ⎝ 5 5 5 5 ⎠ ... ⎝ 100 100 ... 100 ⎠  \nAnswer: A =  \nQuestion 2 Solve a) 2(x-8)(x-4) = 0.125 and b)  y + 2 > y > 0 .  \nAnswer: a) and b)  \nQuestion 3 In the diagram below ADC is a diameter of the circle and BD is perpendicular to AC (BD ⊥ AC) . If AB = 2√5 and AD = 2 a) find the radius R of the circle and b) show that BC = 2AB  \nAnswer: R =  \nQuestion 4 The lines y = 0, y = 2x – 2, y = 4 and x + y = 10 form a trapezium with a triangle above it (the triangle is formed by the last three of these lines) . Draw all the lines and show that the area of the trapezium is eight times the area of the triangle above it. Make sure that all the points of intersection are clearly shown on your graph. Choose the origin close to the bottom left of the grid to make the trapezium and the triangle as big as possible.  \nQuestion 5 Evaluate C = 3A + B when  \nA = aa23  6a27 ⎛⎜⎝⎜1 + ~~ ~~(a~~ ~~−3a3)2~~ ~~⎟ and B =  ~~ ~~a3a~~ ~~bb2 +b22ab + ~~ ~~ab − ~~ ~~a~~ ~~32bb2~~ ~~  \nAnswer: C =  \nQuestion 6. In a test the average grade of each boy is 60 points and the average grade of each girl is 80 points. The total number of points of the class is 580. If each boy had a 10% higher grade and each girl had a 10% lower grade then the whole class would have a total which is 32 points less than before. How many are the boys in this class?  \nAnswer: The boys are","cbCait0X50yvkDz7","https://ap.wps.com/l/cbCait0X50yvkDz7","pdf",198742,"English","# Question 1\n## Evaluate A where A is a large summation-style expression\n# Question 2\n## Solve a) 2(x-8)(x-4)=0.125 and b) y+2>y>0\n# Question 3\n## Circle geometry with ADC as a diameter and BD ⟂ AC\n# Question 4\n## Coordinate geometry: trapezium vs triangle areas\n# Question 5\n## Evaluate C=3A+B with given algebraic A and B\n# Question 6\n## Average grades word problem for boys and girls","[{\"question\":\"Are calculators allowed in this March 2013 mathematics entrance test?\",\"answer\":\"No calculators are allowed.\"},{\"question\":\"What is required to receive marks for answers?\",\"answer\":\"All rough calculations must be presented, and answers without evidence of calculations will not score marks.\"},{\"question\":\"What is the time allowed for completing the exam?\",\"answer\":\"The time allowed is one hour ten minutes.\"}]","Mathematics Entrance Test - March 2013 - exam practice | PDF"]