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Questions include working with infinite geometric series and arithmetic series links, factoring a cubic polynomial, proving a right angle in a coordinate triangle, and expressing surds in required integer-coefficient forms. Additional tasks require plotting curves/lines on a grid, analyzing repeated bounce height ratios, finding intersection points, and solving cuboid ratio and paint-mixing mixture proportion 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to perpendicular lines (product of gradients equals -1), then state the reasoning explicitly.",{"name":124,"@type":111,"acceptedAnswer":125},"What is the key idea for Question 8 about mixing Sea Green and Azure Blue paints?",{"text":126,"@type":114},"Convert each paint color into its yellow/blue ratio composition, combine them, then determine the extra yellow needed so the final mixture matches the Sea Green ratio again.","https://schema.org",{"og:url":83,"og:type":129,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":131,"canonical":83},"index,follow",{"doc_id":133,"site_id":62},143242,1787693867,{"code":4,"msg":5,"data":136},{"doc_id":133,"user_id":137,"nickname":92,"user_avatar":138,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":139,"file_id":140,"file_url":141,"file_type":142,"file_size":143,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":144,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":145,"faqs":146,"seo_title":147,"seo_description":67,"update_tm":134,"read_time":52},1649267921044,"https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1786009248482753345","3w eewere0ie uoedu woBECnATHO ceverecneayouerocue. hitpr/yoeumwiut uzlyoceumindexphpleadmisionentryrequiements  \nENTRANCE TEST  \nLYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT  \nMATHEMATIC5  \nJuly 2015  \nTest B1  \n# Question 1\n\nAn infinite geometric series has a common ratio,r.  \nThe first term of the series is 10 and the sum to infinity is 50.  \n(a)Show that the common ratio is 4/5(1 mark)  \n(b)Find the second term of the series(1 mark)  \nCo6cTBeHHOCT Me*AyHapo4HOro BecTMMHCTepCKoro yHMBepcTera B TauKeHTe  \n(c)The first and second terms of the geometric series in part(a)have thesame values as the 4and 8\"terms respectively,in an arithmetic series.Find the common difference of the arithmetic series.(3 marks)  \nTotal for page 5 marks  \nFor model  \nAng nonb30BaHMR B HeKOMMepyeCKMx uengx  \n8uoeuoemooooEcmr7ocernearoues cume iaMemwiatevcuminoe phoentamnsonesntvteemoi  \n# Question 2\n\nThe polynomial p(x)=x³-13x-12Express p(x)as the product of three inear factors  \nclub  \nsternuZ  \nCo6CTBeHHOCTb Me*AYHapoAHoro BecTMMHCTepcKoro YHMBepcMTeTa B TauKeHTe  \nAng nonb30BaHM9 B HeKOMMepyecKMX uenX  \n3rw ieaMeHe0Hue dredn ox0距ECnATHOcaerecneryomen caie hitp/yceum wiut uzlyceumndexphpleadmisionlenryrequiemenig  \nQuestion 3  \nTriangle ABC has vertices A(1,3)B(3,7)and C(-1,9).(a)Find the gradient of AB  \n(1 mark)  \n(3 marks)  \n(b)Show that angle ABC is a right angle.  \nYou MUST state how you know it is a right angle  \nCo6cTBeHHOCT Me沃AyHapo4HOro BecTMMHCTepCKoroyHMBepCATeTa B TauKeHTe  \n..  \n(c)Find the coordinates of the mid-point of AC  \n(1 mark)  \n(Total for page 5 marks)  \nAng nonb3OBaHMR B HeKOMMepyecKMX uengx  \n3w ereaveHaoHue drpu Mox0 BEcATHOokavar2ocneayouen cunmce.htp/yceum wut uzlyceumindexphplenladmistonlentryrequirements  \nQuestion 4  \n()woat outhevalueo 5o +18  \n(2 marks)  \n三  \n(b)Express the following in the form,m+n7 where,mand n are integers(3 marks)2√7-12√7+5  \nCo6cTBeHHOCTb MeAyHapo4HOro BecTMMHCTepCKoro yHMBepcMTeTaB TauKeHTe  \n(Total for page 5 marks)  \nAng nonb30BaHMR B HeKOMMepyecKMX uengX  \nQuestion 5On the grid below  \na)draw the line of the equation x²+y²=17  \nQuestion 6  \nb)draw the line of the equation y=x+3  \ndropped.A ball is dropped and bounces up to a heightthatis 75%of the height from which it was  \n(You must remember to put a scale on each axis)  \n8富ia2  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\nIt then bounces again to a height that is 75%of the previous height and so on.original height from which it was dropped?How many bounces does it make before it bounces up to less than 25%of the  \nclub  \n…6…c3 aow udneioneef0156HO01b Mekrwe  \nternuZ  \nFind the points of intersection  \nme/ma  \nPoints of intersection","cbCaisiPvxhBb0FT","https://ap.wps.com/l/cbCaisiPvxhBb0FT","pdf",983376,"English","# Question 1\n## Infinite geometric series and arithmetic difference\n# Question 2\n## Polynomial factorization\n# Question 3\n## Coordinate geometry: gradient, right angle, midpoint\n# Question 4\n## Simplification and expressing surds\n# Question 5\n## Drawing curves/lines on a grid\n# Question 6\n## Ball bounce height and intersection points\n# Question 7\n## Cuboid dimensions from surface area and ratios\n# Question 8\n## Paint mixing to recover target ratio","[{\"question\":\"How do you show the common ratio of the infinite geometric series in Question 1?\",\"answer\":\"Use the infinite geometric series sum relation with the given first term and sum to infinity, then solve for r.\"},{\"question\":\"What does Question 2 require for the polynomial p(x)=x³-13x-12?\",\"answer\":\"It asks to express p(x) as the product of three linear factors.\"},{\"question\":\"How is a right angle determined in Question 3 for angle ABC?\",\"answer\":\"Compute the gradients of AB and BC and use that a right angle corresponds to perpendicular lines (product of gradients equals -1), then state the reasoning explicitly.\"},{\"question\":\"What is the key idea for Question 8 about mixing Sea Green and Azure Blue paints?\",\"answer\":\"Convert each paint color into its yellow/blue ratio composition, combine them, then determine the extra yellow needed so the final mixture matches the Sea Green ratio again.\"}]","Lyceum of Westminster International University in Tashkent - Mathematic5 - Test B1 - Entrance Test - Question Set | PDF"]