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The paper requires answers to multiple algebra, arithmetic, geometry, and graph-plotting questions without calculators. Students must present rough calculations as evidence for scoring. Tasks include solving equations and systems, simplifying algebraic expressions, summing arithmetic progressions, working with digit properties, determining areas enclosed by lines, and geometry problems such as fencing and inscribed shapes. A sample-use academic-purpose notice is included.",{"@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/wiut-2011-mathematics-entrance-test-sample-exam/143981/",{"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-2011-mathematics-entrance-test-sample-exam/143981.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":105},"InteractionCounter",{"@type":104},"ViewAction",22,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Are calculators allowed in the Mathematics entrance test sample?","Question",{"text":113,"@type":114},"No calculators are allowed.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the required exam duration?",{"text":118,"@type":114},"The time allowed is one hour ten minutes.",{"name":120,"@type":111,"acceptedAnswer":121},"Why must rough calculations be presented?",{"text":122,"@type":114},"Answers without evidence of calculations do not score any marks.","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},143981,1787697817,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145},962075114765,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Entrance test  \nMathematics  \nJanuary 2011  \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  \nQuestion 1  \nIshmael thought of a number between 1 and 10, added 5 to it, then squared the result and then subtracted seven times the original number. He then doubled the result and took away one to end up with 225. What was the number he started with?  \nAnswer: The number is  \nQuestion 2  \nA biscuit recipe uses flour, butter, sugar and almonds at a ratio, by weight, of 9:6:3:2 . If flour costs £1.50 per kilogram (one and half pounds per kg), butter £2.20 per kg, sugar £3.40 per kg and nuts £11.05 per kg, how much does it cost to make a mixture of 15kg of these ingredients?  \nAnswer: The cost is  \nQuestion 3  \nA farmer has 70 metres of fencing available and wants to enclose a rectangle area of 300 square metres. What measurements will his rectangle have?  \nAnswer:  \nQuestion 4  \nDraw the lines 3x =y+6 and 3x+4y+9 = 0, clearly showing the point where they meet each other and the axes. What is the area enclosed by the lines and the x-axis?  \nAnswer: Area is  \nQuestion 5  \nTake all the numbers between 1 and 999 that are NOT divisible by 5 and add them up. What is the result?  \nAnswer:  \nQuestion 6  \nIn the rectangle ABCD, EFA=HGC=900, AF=4m, EF=GH=3m, FG=2m. Find ED, DC and the area EFCD.  \nAnswer: ED= m, and EFCD area is m2  \nEntrance test  \nMathematics  \nMarch 2011  \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.  \nThe sum of n terms of the arithmetic progression a, a+d, a+2d, a+3d…is  \nS = ~~ ~~n2 [ 2a + (n −1)d]  \nTHIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES  \nQuestion 1 If x = 1 − 5 is a root of equation ( x − 3)2 + ( p + 6)x −13 = 0 , find p and then find the  \nsecond root of the equation  \nQuestion 2  \n 12   \nSimplify A = and B =  \n 1   \n7 +  \n7 + 1 1 +  \n3 − 7  \np q ~~ ~~ + ~~  ~~p + q p − q  p   q − p − q p + q  \nAnswer: p= and theotherroot is x=  \n.  \nAnswer: A= B=  \nQuestion 3  \nThe sum of the digits of a two figure number is 10. If the two digits are written in reverse order, the number increases by 18. What is the original number?  \nAnswer: The number is  \nQuestion 4 Draw the graphs of 3(x+4)=5(y+1) and 3(x+1)+y=14, showing clearly the points where they meet. What is the area of the triangle formed by these two lines and the x-axis.  \nX=1, y = 5  \nAnswer: T~~he~~ a~~re~~a of the triangle is .  \nQuestion 5 When Ishmael wrote down the sum 1+2+3+…+NofN  consecutive integers, he  \ncalculated the sum was equal to 3240. What is the value of N and (for this N) what is the value of the product P = 􀀋􀀈􀀍1 + ~~ ~~12~~ ~~ 􀀉􀀎􀀌􀀋􀀈􀀍1 + ~~ ~~13􀀉􀀎􀀌 ⋅ ... ⋅ 􀀋􀀈􀀍1 + ~~ ~~N~~ ~~1􀀉􀀎􀀌􀀋􀀈􀀍1 + ~~ ~~1N~~ ~~ 􀀉􀀎􀀌 ?   \nAnswer: N= and P=  \nQuestion 6  \nA square is inscribed inside a semicircle of radius 5cm, as shown. What is the area of square?  \nAnswer: The area of the square is  \nEntrance test  \nMathematics  \nApril 2011  \nTime allowed: One hour ten minutes  \nAnswer all questions.  \nIt is advised that you work quickly and that you leave behind ","cbCaibtuO7wwY9C3","https://ap.wps.com/l/cbCaibtuO7wwY9C3","pdf",3978815,18,"English","# Entrance test\n## Mathematics (January 2011)\n## Mathematics (March 2011)\n## Mathematics (April 2011)","[{\"question\":\"Are calculators allowed in the Mathematics entrance test sample?\",\"answer\":\"No calculators are allowed.\"},{\"question\":\"What is the required exam duration?\",\"answer\":\"The time allowed is one hour ten minutes.\"},{\"question\":\"Why must rough calculations be presented?\",\"answer\":\"Answers without evidence of calculations do not score any marks.\"}]","WIUT 2011 Mathematics Entrance Test - Sample Exam | PDF",45]