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The paper requires detailed working without books, notes, calculators, or other assisting materials. Topics include simplifying expressions, expanding and rewriting (3-√5)^2, factoring a cubic polynomial into linear factors, solving series problems for a given value, finding remainders via division by x-2, solving simultaneous equations using labeled axes, computing volumes from cube slices of thickness x, and working with a number chart and right-angled triangles to answer several sub-questions.",{"@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/lyceum-exam-maths-2015-test-a1-entrance-test/143184/",{"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-exam-maths-2015-test-a1-entrance-test/143184.png","ImageObject",300,407,{"name":92,"@type":93},"Lucas Martin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-03","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the allowed materials for this Lyceum Maths entrance test?","Question",{"text":112,"@type":113},"No books, notes, calculators, or any assisting materials are allowed. All answers must be shown in detail on the same page as the questions.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you handle Question 2 about (3-√5)^2?",{"text":117,"@type":113},"Rewrite (3-√5)^2 into the requested surd forms: first as m+n√5 with m and n integers, then as p+q√5 with p and q integers.",{"name":119,"@type":110,"acceptedAnswer":120},"What does Question 5 require?",{"text":121,"@type":113},"Find the coordinates of the intersection points of the equations x^2+y^2=13 and 2x+y=7, and label your axes.","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},143184,1787693576,{"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":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":52},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","ENTRANCE TEST  \nLYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENTMATHEMATICS  \nJuly 2015  \nTest A1  \nTime allowed:One hour 15 minutes  \nANSWER ALL QUESTIONS IN DETAIL,SHOWING ALL YOUR WORK ON THE SAME PAGE AS THEQUESTION.  \nNO BOOKS,NOTES,CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE ALLOWED.  \nKITOB,DAFTAR,KALKULYATOR YOKI BOSHQAYORDAMCHI MATERIALLARDANFOYDALANISH TAQIQLANADI.  \nnOnb30BAHME KHMroǔ,TETPAAbIO,KANbKyn8TOPOM MnM NIO5bIM BCnOMOrATENbHbIMMATEPWANOM3ANPE山IAETCA.  \nQuestion 1 Simplify the following  \nS严宗出品SL①50F器OT字只U山?L号a岩望望  \nt.me/ma  \nCo6cTBOHHOCTb MeAyHapoAHoro BecTMMHCTepcKoro YHMBepcMTeTa B TauKeHTe  \nCnnonb30BaHMR B HeKOMMepyecKMx uengx  \nQuestion 2  \n(a)Express(3-√5)²in the form of m+n√5,where m and n are integers(2 marks)  \nmnooeuoen noxioECnAT1H0xeNer2ecnayouet cune hia0emwi…Ps uonb30BaHMA日HeKOMMepheCKX uengX  \n(b)Express(3-√5)²in the form p+q√5,where p and qare integers1+√5  \n(3 marks)  \ncoocTeHoCTb MeAyHapoAHoro BeCTMHCTepckoro YHueepchTera B TaukeHTe  \nQuestion 3  \nThe polynomial,p(x)is given byp(x)=x³+7x²+7x-15(a)Express p(x)as the product of three linear factors(3 marks)  \nQuestion 4  \n2%,4,5Y₂,7,…………Determine the number of the term whose value is 22 in the series  \nclub  \n(b)Find the remainder when p(x)is divided by x-2  \nsternuZ  \n(2 marks)  \n0gcTBeHHO5TMeKowwepvec eunae2  \nTotal for page 5 marks  \n(08aHis BHenocoe  \nCo6cTBCHHOCTb MeAyHapoAHoro BeCTMMHCTepckoro YHMBepcMTeTa B TauKeHTe  \nQuestion 5  \nFind the co-ordinates of the points of intersection of these equations:  \nx²+y²=13  \n2x+y=7  \n(You must label your axes)  \n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\nme/ma  \nPoints of intersection…………………  \n···    ···    ···  \nTotal for page 5 marks  \n3rw ieaMeHe0Hue dredn ox0距ECnATHOcaerecneryomen caie hitp/yceum wiut uzlyceumndexphpleadmisionlenryrequiemenig  \nAng nonb3OBaHM9 B HeKOMMepyecKMx uengx  \n# Question 6\n\nA cube has edges of 10cm each.Three slices,each of thickness xcm are cut off the cube.  \n10cm  \nx cm  \nSlice A is cut off the side.Slice B is cut off the top.Slice Cis cut off the front.What is the volume of each slice in terms of x?  \nSlice A……        …………cm³Slice B……   …    …  ………cm³Slice C…………     ……………cm³  \nTotal for page 5 marks  \n9TW ak3ameHauoHHbe npnmepbI MOKHO 5ECIIATHO ckalaTb no cneayoueǔ ccbInke: htp:/yceum.wiut.uzlyceumlindex.phplen/admissionentry-requirements  \nCo6cTBeHHOCTb MeknyHapoAHoro BeCTMMHCTepckoro YHuBepcMTeTa B TaukeHTe  \nAng nonb3OBaHMR B HeKOMMepyecKMX uengX  \nCo6CTBeHHOCTb MekAyHapoAHoro BecTMMHCTepckoro YHMBepcMTeTa B TawkeHTe  \n3w ereaveHaoHue drpu Mox0 BEcATHOokavar2ocneayouen cunmce.htp/yceum wut uzlyceumindexphplenadmistonlentryrequirements  \n3rw ieaMeHe0Hu","cbCainCUmJaKthmN","https://ap.wps.com/l/cbCainCUmJaKthmN","pdf",998532,"English","# Question 1\n## Simplify the following\n# Question 2\n## Express (3-√5)^2 in the form m+n√5\n## Express (3-√5)^2 in the form p+q√5\n# Question 3\n## Factor the polynomial p(x)\n# Question 4\n## Determine the term whose value is 22 in the series\n## Find the remainder when p(x) is divided by x-2\n# Question 5\n## Points of intersection of two equations\n# Question 6\n## Volume of cube slices in terms of x\n# Question 7\n# Question 8\n## Number chart and two right-angled triangles","[{\"question\":\"What are the allowed materials for this Lyceum Maths entrance test?\",\"answer\":\"No books, notes, calculators, or any assisting materials are allowed. All answers must be shown in detail on the same page as the questions.\"},{\"question\":\"How do you handle Question 2 about (3-√5)^2?\",\"answer\":\"Rewrite (3-√5)^2 into the requested surd forms: first as m+n√5 with m and n integers, then as p+q√5 with p and q integers.\"},{\"question\":\"What does Question 5 require?\",\"answer\":\"Find the coordinates of the intersection points of the equations x^2+y^2=13 and 2x+y=7, and label your axes.\"}]","Lyceum Exam Maths 2015 - Test A1 - Entrance Test | PDF"]