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Mathematics Section A covers sequences and equations, including quadratic and cubic factorisation, geometric series, line equations and distance, and proving constraints such as absence of real roots. Logic Section B includes exponential bounce-height threshold reasoning and grid-division/search problems requiring highest/lowest totals and identical-area partition counts, with work shown and calculators prohibited.",{"@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/westminster-international-university-in-tashkent-scholarship-test-june-2015/143984/",{"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/westminster-international-university-in-tashkent-scholarship-test-june-2015/143984.png","ImageObject",300,407,{"name":92,"@type":93},"Quinn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How long is the scholarship test and what is the candidate allowed to bring?","Question",{"text":113,"@type":114},"The test allows two hours. Candidates may bring pens, pencils, erasers, rulers, and protractors; correction fluid and calculators are not allowed.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is required for scoring in the Mathematics questions?",{"text":118,"@type":114},"All working must be presented on the same page as the question. Answers without evidence of calculations will not score marks.",{"name":120,"@type":111,"acceptedAnswer":121},"What Logic task is Question 6 asking about the bouncing ball?",{"text":122,"@type":114},"Question 6 asks for the number of bounces before the ball reaches a height that is less than 25% of the original, given each bounce height is 75% of the previous height.","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},143984,1787697829,{"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":41},962075114765,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","S21  \nScholarship Test  \nWestminster International University in Tashkent  \nJune 2015  \ni. Time allowed: Two(2) hours  \nii. There are five(5) Maths questions and five(5) Logic questions.  \nAnswer all questions.  \niii. It is advised that you work quickly and that you leave behind questions that are taking you too long to answer.  \niv. You should only bring in: pens, pencils, erasers, rulers, protractors.  \nCorrection fluid is NOT allowed.  \nv. No calculators are allowed.  \nvi. All your working must be presented on the same page as the question. Answers with no evidence of calculations will not score any marks.  \nvii. Write your answers in the spaces below the questions.  \nviii. Nothing should be removed from the exam room.  \nCandidate Number: Candidate signature:  \nSection A-Mathematics  \nQuestion 1  \nA farmer has a pay scheme to keep fruit pickers working throughout the 30 day season.  \nHe pays $a for the first day, $(a+d) for the second day, $(a+2d) for the third day, and so on.  \nA picker who works for all 30 days will earn $40.75 on the final day.  \n(a) Write an equation in a and d using this information (2 marks)  \n(b) A worker who works for all 30 days will earn a total of $1005.  \nShow that 15(a + 40 .75) = 1005 (2 marks)  \n(c) Hence find the value of a and d (2 marks) Write your answer using money notation  \na =   d =    \nTotal 6 marks  \nQuestion 2  \nA sequence is given by:  \nx 1 = 1  \nxn+1 = xn (p + xn)  \nwhere p is a constant (p≠0) .  \n(a) Work out x2 in terms of p and use this to show that x3 = 1 + 3p + 2p2  \n(2 marks)  \nGiven that x3 = 1,  \n(a) Find the value of p (2 marks)  \n(b) Write down the value of x2008 (2 mark) Give reasons foryour answer  \nTotal 6 marks  \nQuestion 3  \n(a) Factorise completely  \np(x) = x3 – 13x – 12 (2 marks)  \n(b) f(x) = (x + 1)(x2-4x +5)  \nFind the remainder when f(x) is divided by (x-2)  \nExpress f(x) in the form x3 + mx + nx + 5, stating the value of each of the integers m and n (2 marks)  \n(c) Show that the equation x2-4x +5 = 0 has no real roots (2 marks)  \nTotal 6 marks  \nQuestion 4  \nThe first three terms of a geometric series are 4p,(3p+15) and (5p+20) respectively, where p is a positive constant.  \n(a) Show that 11p2-10p-225 = 0 (2 marks)  \n(b) Use your answer from (a) to show that p = 5 (1 mark)  \n(c) Find the common ratio of this series (1 mark)  \n(d) Find the sum of the first ten terms of the series, leave your answer in the form S10 = ab (2 marks)  \nTotal 6 marks  \nQuestion 5  \n(a) Find an equation of the line joining A(7, 4) and B(2, 0), giving your answer in the form ax + by + c = 0 , where a , b , and c are integers. (2 marks)  \n(b) Find the length of AB , leaving your answer in surd form. (1 mark)  \n(a) The point C has coordinates (2, t), where t > 0, and AC = AB.  \nFind the value of t. (3 marks)  \nTotal 6 marks  \nSection B-Logic  \nQuestion 6  \nA ball is dropped and bounces up to a height that is 75% of the height from which it was dropped.  \nIt then bounces again to a height that is 75% of the previous height and so on.  \nHow many bounces does it make before it bounces up to less than 25% of the original height from which it was dropped?  \nExplain your answer.  \nAnswer    \nTotal 6 marks  \nQuestion 7  \nUsing diagonal joins and five numbers from the grid below find the following:  \n1. The Highest total  \n2. The Lowest total  \nThe arrows show diagonal joins and you can start from any square You must show the numbers you have used to find the totals  \n\n| 8 | | 15\u003Cbr>| 6 | 9 |\n| --- | --- | --- | --- | --- |\n| 14 | | | 18\u003Cbr>| 20 |\n| 18 |  | \u003Cbr>17 | \u003Cbr>2 | 5 |\n| 3 |  | 15 | 19 | 6 |\n\n1. The Highest total …………………….  \n2. The Lowest total    \nTotal 6 marks  \nQuestion 8  \nDivide the 4x4 grid below so that it has two identical areas and identical shape.  \nFind the greatest number of ways of dividing the grid into two identical parts by drawing along the lines of the grid.  \nShow the different divisions below  \n\n|  |  |  |  |\n| --- | --- | --- | --- |\n|  |  |  |  |\n|  |  |  |  |\n|  ","cbCaipsKhju7dOGB","https://ap.wps.com/l/cbCaipsKhju7dOGB","pdf",566221,12,"English","# Section A - Mathematics\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5\n# Section B - Logic\n## Question 6\n## Question 7\n## Question 8","[{\"question\":\"How long is the scholarship test and what is the candidate allowed to bring?\",\"answer\":\"The test allows two hours. Candidates may bring pens, pencils, erasers, rulers, and protractors; correction fluid and calculators are not allowed.\"},{\"question\":\"What is required for scoring in the Mathematics questions?\",\"answer\":\"All working must be presented on the same page as the question. Answers without evidence of calculations will not score marks.\"},{\"question\":\"What Logic task is Question 6 asking about the bouncing ball?\",\"answer\":\"Question 6 asks for the number of bounces before the ball reaches a height that is less than 25% of the original, given each bounce height is 75% of the previous height.\"}]","Westminster International University in Tashkent - Scholarship Test - June 2015 | PDF"]