[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-143292-105":59,"doc-detail-143292-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","lyceum-exam-maths-2015-question-practice","Lyceum Exam Maths 2015 - Question Practice","","Mathematics exam practice covering a range of question types. Includes evaluating and simplifying expressions, finding equations of lines through given points and calculating distances in surd form, solving geometry-related coordinate conditions to determine parameters. Further tasks cover sequences and surds, polynomial remainder and factor proofs using divisors, solving f(x)=0, constructing graphs on a grid with specified equations, finding intersections, using arithmetic sequences in word problems, calculating sums over a time period, and applying algebra to areas of squares.",{"@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-exam-maths-2015-question-practice/143292/",{"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-question-practice/143292.png","ImageObject",300,407,{"name":92,"@type":93},"Aurora","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find the equation of the line joining A(7,4) and B(2,0)?","Question",{"text":113,"@type":114},"Determine the line through the two points, then express it in the form ax+by+c=0 with integers a, b, and c.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What does it mean to find the remainder when f(x) is divided by (x-3)?",{"text":118,"@type":114},"Evaluate f(3) using the factor theorem idea, since the remainder is the value that satisfies the division by (x-3).",{"name":120,"@type":111,"acceptedAnswer":121},"How can you draw and use the graph to find points of intersection for the given equations?",{"text":122,"@type":114},"Plot each curve on the provided grid with an appropriate scale, then identify the shared coordinate(s) where the two graphs cross.","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},143292,1787694250,{"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":19,"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":52},4810365810221,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","(a)Work out the value of 8  \n(b)Simplify fully  \n(2 marks)  \n(3 marks)  \nQuestion 2  \n(a)Find an equation of the line joining A(7,4)and B(2,0),giving your answer inthe 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.Find the value of t.(2 marks)  \nQuestion 3  \nA sequence of positive numbers is defined by  \n,n≥1  \nGiven that a₁=2  \n(2 marks)  \n(a)Find a2 and a3,leaving your answer in surd form.  \na2………   …………   …  \na₃……………………………  \n(2 marks)  \n(b)Show that a₅=4  \n(c)Write√(75)-√(27)in the form k√x,where k and x are integers.(2 marks)  \nQuestion 4  \n(a)Find the remainder when f(x)is divided by(x-3)  \n(1 mark)  \n(b)Show that(x-5)is a factor of f(x)  \nHence or otherwise,find all the solutions of f(x)=0(4 marks)  \nQuestion 5On the grid below  \na)draw the line of the equation x²+y²=20  \nb)draw the line of the equation y=X-6  \n(You must remember to put a scale on each axis)  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\nt.me/mathclub  \nFind the points of intersection  \nPoints of intersection…………………….  \n-    -        -  \nQuestion 6  \nA 40 year building programme for new houses began in London in the year 1961(year 1)andfinished in 2000(Year 40).  \nThe number of houses built each year form an arithmetic sequence with the first tem a andcommon difference d.  \nGiven that 2400 new houses were built in 1970 and 600 new houses were built in 2000,find  \na)the value of d  \nb)the value of a  \nc)the total number of houses built in London over the 40 year period  \nne/westernU  \nAnswer a)……………………  \nAnswer b)…  ……………………  \nAnswer c)……………………………  \nThe rectangle has sides of length mand n.Find the area of the square in terms of m and n.  \nmelwP  \nAnswer…………………  \nTotal for page 5 marks  \n# Question 8\n\nP and Q are two whole numbers.P is greater than 10 and less than 20Qis greater than 100 and less than 200  \na)What is the largest value that (P+Q)could have  \nb)What is the smallest difference there could be between Pand Q?  \nm  \nernu  \nAnswer a)…………………………………  \nAnswer b)……………………………  \nTotal for page 5 marks  \nEND OF TEST  \nTOTAL FOR TEST 40 MARKS","cbCailFsNLOTnklx","https://ap.wps.com/l/cbCailFsNLOTnklx","pdf",128598,"English","# Question 2\n## Line equation and distance\n## Coordinate condition for t\n# Question 3\n## Sequence terms in surd form\n## Show a5 value\n## Simplify surd expression\n# Question 4\n## Remainder and factor\n## Solve f(x)=0\n# Question 5\n## Draw x^2+y^2=20\n## Draw y=x-6 and find intersections\n# Question 6\n## Arithmetic sequence for houses in London\n## Find d, a, and total\n# Area and algebra\n## Square area in terms of m and n\n# Question 8\n## Bounds for P and Q\n## Largest P+Q and smallest difference","[{\"question\":\"How do you find the equation of the line joining A(7,4) and B(2,0)?\",\"answer\":\"Determine the line through the two points, then express it in the form ax+by+c=0 with integers a, b, and c.\"},{\"question\":\"What does it mean to find the remainder when f(x) is divided by (x-3)?\",\"answer\":\"Evaluate f(3) using the factor theorem idea, since the remainder is the value that satisfies the division by (x-3).\"},{\"question\":\"How can you draw and use the graph to find points of intersection for the given equations?\",\"answer\":\"Plot each curve on the provided grid with an appropriate scale, then identify the shared coordinate(s) where the two graphs cross.\"}]","Lyceum Exam Maths 2015 - Question Practice | PDF"]