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It also includes modelling problems involving cylinder volume and water usage, plus a tiling/applied equations task using tile counts and side lengths. Time allowed is one hour 15 minutes, with full working required for scoring.",{"@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/lyceum-mathematics-entrance-test-july-2016-1-hour-15-minutes/144032/",{"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/lyceum-mathematics-entrance-test-july-2016-1-hour-15-minutes/144032.png","ImageObject",300,407,{"name":92,"@type":93},"Seraphina","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","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},"What materials are allowed during the Lyceum mathematics entrance test?","Question",{"text":113,"@type":114},"No books, notes, calculators, or any assisting material are allowed.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are marks awarded for answers?",{"text":118,"@type":114},"Answers must show all work on the same page as the question; answers without evidence of calculations score no marks.",{"name":120,"@type":111,"acceptedAnswer":121},"How much time is given to complete the test?",{"text":122,"@type":114},"The time allowed is one hour 15 minutes.","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},144032,1787698030,{"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":52,"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":144},962075114101,"https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165","ENTRANCE TEST  \nLYCEUM  \nMATHEMATICS  \nJuly 2016  \nTime allowed: One hour 15 minutes  \nANSWER ALL QUESTIONS IN DETAIL, SHOWING ALL YOUR WORK ON THE SAME PAGE AS THE QUESTION. ANSWERS WITH NO EVIDENCE OF CALCULATIONS WILL NOT SCORE ANY MARKS.  \nNO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE ALLOWED.  \nQuestion 1  \nSolve the simultaneous equations:  \ny-2x = 1  \ny2 = 2x2 + x  \nAnswer    \nTotal for page 5 marks  \nQuestion 2  \nWrite the number  \na) 2. (816) in the simplest form of  \n􀯫􀯬 where x and y are integers and y ≠ 0  \nAnswer    \nb) Simplify the expression 33222233  \nWrite your answer in its simplest form of a + b√􀜿  \nAnswer    \nTotal for page 5 marks  \nQuestion 3  \nFor the geometric series  \na + ar + ar2 +    \nthe sum of the first two terms is 24 and the sum to infinity is 27.  \nShow that r = ± 13  \nAnswer    \nTotal for page 5 marks  \nQuestion 4  \nGiven that f(x) = 2x3 + 3x2-5x-6 and (x+1) is a factor, factorise fully the polynomial f(x) . State the set of values of x for which f(x) ≤ 0  \nAnswer    \nTotal for page 5 marks  \nQuestion 5  \nOn the grid below  \na) draw the circle with equation 􀝔 2 + 􀝕 2 = 25  \nb) draw the line with equation y = 2x + 1  \nEstimate the points of intersection to one decimal place.  \nEstimated points of intersection    \n……………………….  \nTotal for page 5 marks  \nQuestion 6  \nIn the diagram below AB is parallel to DE.  \na) Prove that triangle ABC is similar to triangle DEC.  \nAnswer    \nb) Work out the value of x in the diagram below.  \nAll values are in cms.  \nGive your answer to 2 decimal places.  \nAnswer    \nTotal for page 5 marks  \nQuestion 7  \nA water tank has a radius of 80cm and a length of 200cm. It is half filled with water.  \n120 litres per day is used to water a garden.  \nFor how many days can the garden be watered from the tank?  \nUse 3.14 for the value of 􀟨  \nGive your answer to the nearest whole day. The volume of cylinder = 􀟨􀝎2 􀝈  \n1cm3 = 1 millilitre  \nAnswer    \nTotal for page 5 marks  \nQuestion 8  \nA bathroom floor is being tiled.  \nOne size of square tile will cover the floor with 200 tiles.  \nAnother square tile, with sides 2 cm less, will use 250 tiles to cover the same area. Find the size of the larger tiles to the nearest cm.  \nAnswer    \nTotal for page 5 marks  \nEND OF TEST  \nTOTAL FOR TEST 40 MARKS  \nUSE THIS PAGE FOR DRAFTS  \n10  \nTelegram: @FRstudy","cbCaigfc55P56mvg","https://ap.wps.com/l/cbCaigfc55P56mvg","pdf",144864,"English","# Question 1 - Simultaneous equations\n# Question 2 - Surds and number simplification\n# Question 3 - Geometric series and solving for r\n# Question 4 - Polynomial factorisation and inequality\n# Question 5 - Circle and line intersections\n# Question 6 - Triangle similarity and parallel lines\n# Question 7 - Cylinder volume and water days\n# Question 8 - Tile sizing using area equations","[{\"question\":\"What materials are allowed during the Lyceum mathematics entrance test?\",\"answer\":\"No books, notes, calculators, or any assisting material are allowed.\"},{\"question\":\"How are marks awarded for answers?\",\"answer\":\"Answers must show all work on the same page as the question; answers without evidence of calculations score no marks.\"},{\"question\":\"How much time is given to complete the test?\",\"answer\":\"The time allowed is one hour 15 minutes.\"}]","Lyceum Mathematics Entrance Test - July 2016 - 1 hour 15 minutes | PDF",25]