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The test requires detailed working on the same page; no books, notes, calculators, or other assisting materials are allowed.",{"@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/2018-westminster-lyceum-math-exam-sample-entrance-test-mathematics-test-m1/142987/",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/2018-westminster-lyceum-math-exam-sample-entrance-test-mathematics-test-m1/142987.png","ImageObject",300,407,{"name":42,"@type":43},"Logic","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-20","2026-08-25",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",16,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What rules apply for answering the entrance test questions?","Question",{"text":63,"@type":64},"All questions require detailed answers with full working shown on the same page as the question. Draft-page or separate-sheet answers will not receive marks, and no books, notes, calculators, or other assisting materials are allowed.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are the multiple-choice answers presented in the test?",{"text":68,"@type":64},"For each question, the correct option must be circled from the listed choices (a, b, c, d, e). Answers without detailed solutions are not marked.",{"name":70,"@type":61,"acceptedAnswer":71},"What topics are included across the nine mathematics questions?",{"text":72,"@type":64},"The test includes geometry (triangles and angles), algebra and functions (composition and quadratic constraints), polynomial division/remainders, non-linear radical equation solving, prime-factor reasoning, and area calculation from composite shapes with a shaded region.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},142987,1787692173,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":113},1099513958762,"https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253","ENTRANCE TEST  \nMATHEMATICS  \nTest M1  \nTime allowed: 1 hour 20 minutes  \nANSWER ALL QUESTIONS IN DETAIL, SHOWING ALL YOUR WORK ON THE SAME PAGE AS THE QUESTION. THE ANSWERS PROVIDED IN THE DRAFT PAGE OR IN SEPARATE SHEETS WILL NOT BE CONSIDERED.  \nNO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE ALLOWED.  \nKITOB, DAFTAR, KALKULYATOR YOKI BOSHQA YORDAMCHI MATERIALLARDAN FOYDALANISH TAQIQLANADI.ПОЛЬЗОВАНИЕ КНИГОЙ, ТЕТРАДЬЮ, КАЛЬКУЛЯТОРОМ ИЛИ ЛЮБЫМ ВСПОМОГАТЕЛЬНЫММАТЕРИАЛОМ ЗАПРЕЩАЕТСЯ .  \n\n| For Office Use Only |\n| --- |\n| The Script Secure Code* |\n|  |\n|  |\n| The Script Secure Code* |\n\n\n| Application number: |  |\n| --- | --- |\n|  |  |\n| Signature: |  |\n\nPLEASE DO NOT TURN OVER THIS PAGE UNTIL TOLD TO DO SO  \nQuestion 1.  \nIn triangle ABC, an altitude is drawn from vertex C to the line containing AB. The length of this altitude is h and h=AB. Which of the following is true?  \nI. ∆ABC could be a right triangle.  \nII. Angle C cannot be a right angle.  \nIII. Angle C could be less than 45° .  \nAnswer without the detailed solutions will not be marked. Provide the detailed solution below:  \nCircle the correct answer:  \na) none  \nb) I, only  \nc) I and II, only  \nd) I and III, only  \ne) I, II, and III  \nTotal for page 5 marks  \nQuestion 2.  \nIn one month, Alice-the-lawyer earns half of what her husband, Bill-the-artist, earns in a year (12 months) . Together, the happy couple earns 168,000 dollars per year. What is Alice’s monthly income in dollars?  \nAnswer without the detailed solutions will not be marked. Provide the detailed solution below:  \nCircle the correct answer:  \na) 12,000  \nb) 10,000  \nc) 8,000  \nd) 4,000  \ne) 2,000  \nTotal for page 5 marks  \nQuestion 3.  \nPoint A is on the parabola y = x2 and has coordinates (–a/2, b) . Point B is also on the parabola and has coordinates (a, 4) .  \nWhat is the length of line segment AB?  \nAnswer without the detailed solutions will not be marked. Provide the detailed solution  \nbelow:  \nCircle the correct answer:  \na) 3√2 b) 4√2 c) 2√3  \nd) ~~ ~~5√23   \ne) 3√3  \nTotal for page 5 marks  \nQuestion 4.  \nPositive integer a has two different prime factors p and q (p\u003Cq) such that a = pq. Positive integer b is greater than a and the quotient a2/b is an integer. How many possible values of b are there?  \nAnswer without the detailed solutions will not be marked. Provide the detailed solution below:  \nCircle the correct answer:  \na) 2  \nb) 3  \nc) 4  \nd) 5  \ne) more than 5  \nTotal for page 5 marks  \nQuestion 5.  \nIf n is an integer, what is the remainder when 3x(2n+ 3)– 4x(2n + 2) + 5x(2n+ 1)– 8 is divided by (x + 1)?  \nAnswer without the detailed solutions will not be marked. Provide the detailed solution below:  \nCircle the correct answer:  \na) –20  \nb) –10  \nc) –4  \nd) 0  \ne) The remainder cannot be determined.  \nTotal for page 5 marks  \nQuestion 6.  \nIf 􀝂(􀝔) = √2􀝔 + 3 and 􀝃 (􀝔) = 􀝔 2 , for what value(s) of x does f(g(x)) = g(f(x))?  \n(please approximate when needed)  \nAnswer without the detailed solutions will not be marked. Provide the detailed solution below:  \nCircle the correct answer:  \na) –0.55  \nb) 1.46  \nc) 5.45  \nd) –0.55 and 5.45  \ne) 1.46 and 6.46  \nTotal for page 5 marks  \nQuestion 7.  \nA large square contains three squares with areas of 16, two rectangles with areas of 16, and one square with an area of  \nWhat is the area of the shaded region?  \nAnswer without the detailed solutions will not be marked. Provide the detailed solution below:  \nCircle the correct answer:  \na) 42  \nb) 49  \nc) 56  \nd) 63  \ne) 64  \nTotal for page 5 marks  \nQuestion 8.  \nSolve the non-linear equation:  \n􀝔 2 + 3􀝔 − 18 + 4√􀝔 2 + 3􀝔 − 6 = 0  \nAnswer without the detailed solutions will not be marked. Provide the detailed solution below:  \nCircle the correct answer:  \na) x=-5 and x=2  \nb) x= -6 and x=0  \nc) x=5  \nd) x=2  \ne) x=-5  \nTotal for page 5 marks  \nQuestion 9.  \nIff(x) = ax2 + bx + c and f (1) = 3 and f (–1) = 3, what will a + c be equal to?  \nAnswer without the detailed solutions will n","cbCaivPWrCBMd3I9","https://ap.wps.com/l/cbCaivPWrCBMd3I9","pdf",308193,12,"English","# Question 1\n## Geometry and angles in triangle ABC\n# Question 2\n## Income and monthly/annual rates\n# Question 3\n## Distance between points on a parabola\n# Question 4\n## Prime factors and counting possible quotients\n# Question 5\n## Remainder of an expression divided by (x+1)\n# Question 6\n## Solving f(g(x)) = g(f(x))\n# Question 7\n## Area of a shaded region in composite figures\n# Question 8\n## Solving a non-linear radical equation\n# Question 9\n## Finding a+c from quadratic constraints","[{\"question\":\"What rules apply for answering the entrance test questions?\",\"answer\":\"All questions require detailed answers with full working shown on the same page as the question. Draft-page or separate-sheet answers will not receive marks, and no books, notes, calculators, or other assisting materials are allowed.\"},{\"question\":\"How are the multiple-choice answers presented in the test?\",\"answer\":\"For each question, the correct option must be circled from the listed choices (a, b, c, d, e). Answers without detailed solutions are not marked.\"},{\"question\":\"What topics are included across the nine mathematics questions?\",\"answer\":\"The test includes geometry (triangles and angles), algebra and functions (composition and quadratic constraints), polynomial division/remainders, non-linear radical equation solving, prime-factor reasoning, and area calculation from composite shapes with a shaded region.\"}]","2018 Westminster Lyceum - MATH-EXAM-SAMPLE - Entrance Test Mathematics (Test M1) | PDF"]