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The paper includes algebra tasks involving solving for p, simplification of expressions, age modeling with equations, graphing quadratic functions and estimating intersection distance, pattern-based area calculations on a chessboard-colored stair-like figure, and a geometry problem involving right-angled triangles to justify an angle relationship and compute total area.",{"@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/wiut-maths-mathematics-entrance-test-august-2012/144040/",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/wiut-maths-mathematics-entrance-test-august-2012/144040.png","ImageObject",300,407,{"name":42,"@type":43},"Seraphina","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-23","2026-08-25",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",19,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What are the key exam rules for answering questions?","Question",{"text":63,"@type":64},"Answer all questions and work quickly. 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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  \nAugust 2012  \nQuestion 1 Find the value(s) of p if the equation [(x2– 15)p2 + (x + 1)p]2 = 36 has x = 4 as a root.  \nAnswer: p = or or or  \nQuestion 2  \nSimplify as much as possible the expression  \nE = ⎝⎛⎜ ~~ ~~a4+b~~6~~b4~~ ~~⎟⎜ ~~ ~~a~~ ~~~~ ~~b − ~~ ~~a~~ ~~~~ ~~b − ~~ ~~a2b2~~ ~~ − ~~ ~~a443b4~~ ~~⎟ .  \nAnswer: E =  \nQuestion 3  \nThe ages of an elephant and a lion add up to 60. In 12 years time the age of the elephant will be three times as much as the age of the lion. In how many years will the age of the elephant be four times the age of the lion?  \nAnswer: In   years time.  \nQuestion 4  \nDraw the graphs of y = x2 – 2x + 1 and y = 2x – x2 for 0 ≤ x ≤ 2 showing clearly the turning points. For your graphs use the grid below taking 20 grid lines as the unit, as shown. Also, from your graph estimate roughly the distance between the two points where the graphs meet.  \nAnswer: Distance between meeting points is approximately units  \nQuestion 5 A stair-like figure has side of length n and is composed of unit squares. Also, the squares are painted alternately black and white (as on a chess board) starting with the bottom left square which is painted black. The figure bellow is a diagram for the case n = 5. If n = 1000 find a) the area of the figure, b) the total area of squares that are painted black.  \nAnswer: a) Area =  \nQuestion 6 The diagram below is a rough  \nB C  \nsq. units. b) Total area of black squares = sq. units sketch of a garden. Triangle ABC is a right angled triangle with B = 900 and AB = 3m. Triangle ACD is also a right angled triangle with C = 900 , AD = 13mand CD = 12m. a) Give a reason (without measuring with an instrument) why angle DAC is larger than angle CAB and b) Find the area of the garden, in square meters.  \nAnswer: The area is m2","cbCaieMtvG4TBKqA","https://ap.wps.com/l/cbCaieMtvG4TBKqA","pdf",403584,"English","# Question 1\n# Question 2\n# Question 3\n# Question 4\n# Question 5\n# Question 6","[{\"question\":\"What are the key exam rules for answering questions?\",\"answer\":\"Answer all questions and work quickly. Only writing materials are allowed. Calculators are not allowed, and rough calculations must be presented because answers without evidence do not score marks.\"},{\"question\":\"How is Question 1 set up?\",\"answer\":\"Question 1 asks for the value(s) of p given that a specified equation has x = 4 as a root.\"},{\"question\":\"What does Question 6 require?\",\"answer\":\"Question 6 includes a justification about comparing angles without using instruments, and it asks for the area of the garden in square meters using the given right-angled triangle dimensions.\"}]","WIUT maths - Mathematics Entrance Test - August 2012 | PDF"]