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The exam specifies a one hour ten minutes time limit, requires all rough calculations to be shown, disallows calculators, and instructs candidates to write answers neatly under each question. Questions cover algebraic solving and evaluation, logarithms, coordinate and graph geometry, angles in circle and diagram problems, area relationships in composite shapes, and percentage/average grade word problems.",{"@graph":69,"@context":122},[70,84,105],{"@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/wiut-2013-entrance-test-mathematics/143983/",{"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/wiut-2013-entrance-test-mathematics/143983.png","ImageObject",300,407,{"name":92,"@type":93},"Quinn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-22","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":46},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Are calculators allowed in this mathematics entrance test?","Question",{"text":112,"@type":113},"No. The paper explicitly states that calculators are not allowed.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is required when doing rough work and calculations?",{"text":117,"@type":113},"Rough calculations must be presented, using the blank pages of the exam paper, and answers must be written neatly under the corresponding question.",{"name":119,"@type":110,"acceptedAnswer":120},"What topics appear across the questions?",{"text":121,"@type":113},"The questions include algebraic equations and evaluations, logarithm computations, geometry with angles and circles/diagrams, area comparisons, and percentage/average grade word problems.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},143983,1787697825,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":46,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":129,"read_time":144},962075114765,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Entrance test  \nMathematics  \nJanuary 30, 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, THEN write your answer neatly under the question. Answers that are not written under the question neatly may not get marked.  \nNothing should be removed from the exam room.  \nlog 5 a = b ⇒ a = 5 b  \nlog 5 ab = blog 5 a  \nTHIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES  \nJanuary 2013  \nQuestion 1 Find x when xx22~~ ~~~~ ~~3x3x~~ ~~~~ ~~55 = ~~ ~~2x2x22~~ ~~~~ ~~xx~~ ~~~~ ~~33 .  \nAnswer: x = or or  \nQuestion 2 a) Find x andy when 2 x−y = 8 and 3 x −y = 1  \n2 1 1 2 1 1  \nb) Find A = (a  3 − a  3 b 3 + b  3 )(a  3 + b  3 ) when a = 1456 and b = 557  \nAnswer: a) b) A =  \nQuestion 3 In the figure below, ∠ ABC = ∠ BCD = ∠ CDA = ∠ DAB = ∠ BFG = 90O, ∠ ABG =∠ GBF, AB = 5cm and BC = 3cm. Find a) DF and b) AG  \nA B  \nG  \nD F C  \nAnswer: DF = and AG =  \nQuestion 4 The line y = 2(1-x) meets the curve y = (x-1)(x-2) at two points. a) Find these two points and b) draw the curve and the line for -0.5\u003Cx\u003C2.5, clearly showing the two points and the curve’s turning point.  \nQuestion 5 In a class of 50 students the boys obtained an average grade of 80 points for the Maths test and the girls obtained an average grade of 90 points for the same test. If the boys had scored 5% more on average and the girls had scored 10% more on average, then the whole class would have got 350 extra points. How many boys are there in this class?  \nAnswer: There are boys in the class  \nQuestion 6 Find the value of log5625 + log56252 + log56253 +…+ log5625n when n = 30  \nAnswer: The value is  \nEntrance 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  \nA = 2a  \na 2  \n3  \na  \nEvaluate C = 3A + B when  \na 3 + b3  \n+ 6a + 9 ⎛ (a − 3)2 ⎞ a b + 27 ⎜⎝ 1 + 3a ⎠⎟ and B = +a2 −  \n+ 2abb 2  \n+  \n2b 3ab  \n−  \na + b a 2 −b2  \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 g","cbCaiqpiyAy6yM13","https://ap.wps.com/l/cbCaiqpiyAy6yM13","pdf",1089335,18,"English","# Entrance test Mathematics\n## Examination instructions\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5\n## Question 6\n# March 2013 Entrance test Mathematics\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5\n## Question 6\n# April 2013 Entrance test Mathematics\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5","[{\"question\":\"Are calculators allowed in this mathematics entrance test?\",\"answer\":\"No. The paper explicitly states that calculators are not allowed.\"},{\"question\":\"What is required when doing rough work and calculations?\",\"answer\":\"Rough calculations must be presented, using the blank pages of the exam paper, and answers must be written neatly under the corresponding question.\"},{\"question\":\"What topics appear across the questions?\",\"answer\":\"The questions include algebraic equations and evaluations, logarithm computations, geometry with angles and circles/diagrams, area comparisons, and percentage/average grade word problems.\"}]","WIUT 2013 - Entrance Test Mathematics | PDF",45]