[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-144232-105":59,"doc-detail-144232-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","westminster-math-difficult-one-best-buys-conversion-graphs-lcmhcf-compound-interest-reverse-percentages","Westminster Math Difficult One - Best Buys - Conversion Graphs - LCM/HCF - Compound Interest - Reverse Percentages","","Set of challenging Westminster-style math questions covering multiple topics across algebra, number theory, and problem solving. Tasks include converting between currencies using conversion graphs, calculating LCM/HCF, modelling decay with compound interest percentages, reversing percentage loss to find an original amount, and counting problems using product rule constraints. The sheet also includes bracket expansion, factorising quadratics, sequence nth-term calculations, rearranging formulas, inequalities and regions, line geometry, iteration, tangent equation, curve area and graph sketching, and an algebraic proof task.",{"@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/westminster-math-difficult-one-best-buys-conversion-graphs-lcmhcf-compound-interest-reverse-percentages/144232/",{"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-math-difficult-one-best-buys-conversion-graphs-lcmhcf-compound-interest-reverse-percentages/144232.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":56},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What topics are included in this Westminster math worksheet?","Question",{"text":112,"@type":113},"It includes currency conversion, LCM/HCF, compound interest and reverse percentages, counting by product rule, algebraic expansion and factorising, sequence nth terms, inequalities, line equations, iteration, tangents, graphing, and algebraic proof.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do the compound interest and reverse percentages questions work?",{"text":117,"@type":113},"The compound interest question models percentage decay over years to reach a target mass. The reverse percentages question finds the original amount by using the given percentage loss and the current quantity.",{"name":119,"@type":110,"acceptedAnswer":120},"What kinds of graph and geometry tasks appear on the sheet?",{"text":121,"@type":113},"There are tasks such as drawing quadratic graphs for given x-values and finding the equation of a tangent line to a circle at a specified point, plus a question comparing race completion times using a graph.","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},144232,1787698811,{"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":56,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":129,"read_time":144},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068","1. BEST BUYS  \nTwo shops sell the same type of perfume.  \nA 100ml bottle of perfume normally costs £40.  \n3. CONVERSION GRAPHS  \n(a) Change £30 into Euros.  \n......................... Euros  \n(2)  \n(b) Change 200 Euros into Pounds (£)  \n+998944905775 @westminstermath  \n£.........................  \n(2)  \n4. LCM/HCF  \nFind the lowest common multiple (LCM) of 28 and 63.  \n+998944905775 @westminstermath  \n(2)  \n5. COMPOUND INTEREST  \nA radioactive substance decays over time.  \nEvery year its mass decreases by 14% .  \nHow many years will it take for 500kg of the substance to decay to a mass less than 200kg?  \n.........................years  \n(3)  \n6. REVERSE PERCENTAGES  \nA fish tank sprung a leak and loses 45% of its water.  \nThere is now 363 litres of water in the fish tank.  \nHow much water was in the fish tank before the leak?  \n.........................l  \n7. PRODUCT RULE FOR COUNTING  \nJim picks a five digit even number.  \nThe second digit is less than 5.  \nThe fourth digit is a cube number.  \nThe first digit is a prime number.  \nHow many different numbers could he pick?  \n+998944905775 @westminstermath  \n(3)  \n8. EXPANDING TWO/THREE BRACKETS  \n(a) Expand and simplify (x + 9)(x − 4)  \n(2)  \n(b) Expand and simplify (x + 1)(x + 2)(x − 3)  \n.............................  \n(2)  \n9. FACTORISING QUADRATICS  \n(a) Factorise x² − x − 30  \n(2)  \n(b) Factorise 3y² + 10y − 8  \n10. NTH TERM-LINEAR  \nThe first 5 terms in a number sequence are  \n2 2.5 3 3.5 4      \n(a) Work out the nth term of the sequence.  \n(2)  \n(b) Work out the 20th term of the sequence.  \n(2)  \n11. QUADRATIC NTH TERM  \nHere are the first 5 terms of a quadratic sequence  \n4 10 18 28 40  \nFind an expression, in terms of n, for the nth term of this quadratic sequence.  \n+998944905775 @westminstermath  \n12. CHANGING THE SUBJECT  \nRearrange y + 3 = x(y + 2) to make y the subject of the formula.  \ny = .........................  \n(4)  \n13. INEQUALITIES-REGIONS  \nThe region labelled R satisfies three inequalities.  \nState the three inequalities  \n14. QUADRATIC INEQUALITIES  \nSolve the inequality 2x² + 9x + 10 > 0  \n(4)  \n15. PARALLEL/PERPENDICULAR LINES  \nThe straight line K has equation y = 2x − 5  \nThe straight line J is perpendicular to line K and passes through the  \npoint (−4, 8) .  \nFind the equation of line J  \n(3)  \n16. ITERATION  \n(a) Show that the equation 3x − x³ = −11 can be rearranged to give  \n+998944905775 @westminstermath  \n+998944905775 @westminstermath  \n(3)  \n17. EQUATION OF A TANGENT  \nHere is a circle, centre O, and the tangent to the circle at the point (2, −4) .  \nFind the equation of the tangent at the point P.  \n18. AREA UNDER A CURVE  \nHarry and Jack ran a 300 metre race.  \nHere is a graph for the first 4 seconds of Harry’s race.  \nHarry completed the race at a constant speed of 6 m/s  \nJack completed the race in 51 seconds.  \nDid Harry finish before Jack? You must show your working.  \n……………………………………………………………………………………………  \n……………………………………………………………………………………………  \n(3)  \n+998944905775 @westminstermath  \n19. QUADRATIC GRAPHS  \nOn the grid, draw the graph of y = x² + x + 2 for the values of x from-3 to 3.  \n(2)  \n20. ALGEBRAIC PROOF  \nProve the sum of four consecutive odd numbers is always a multiple of 8  \n98944905775westminstermath (4)","cbCailUxGbJGKP2A","https://ap.wps.com/l/cbCailUxGbJGKP2A","pdf",2151030,21,"English","# Best Buys\n# Conversion Graphs\n# LCM/HCF\n# Compound Interest\n# Reverse Percentages\n# Product Rule for Counting\n# Expanding Two/Three Brackets\n# Factorising Quadratics\n# nth Term-Linear\n# Quadratic nth Term\n# Changing the Subject\n# Inequalities-Regions\n# Quadratic Inequalities\n# Parallel/Perpendicular Lines\n# Iteration\n# Equation of a Tangent\n# Area Under a Curve\n# Quadratic Graphs\n# Algebraic Proof","[{\"question\":\"What topics are included in this Westminster math worksheet?\",\"answer\":\"It includes currency conversion, LCM/HCF, compound interest and reverse percentages, counting by product rule, algebraic expansion and factorising, sequence nth terms, inequalities, line equations, iteration, tangents, graphing, and algebraic proof.\"},{\"question\":\"How do the compound interest and reverse percentages questions work?\",\"answer\":\"The compound interest question models percentage decay over years to reach a target mass. The reverse percentages question finds the original amount by using the given percentage loss and the current quantity.\"},{\"question\":\"What kinds of graph and geometry tasks appear on the sheet?\",\"answer\":\"There are tasks such as drawing quadratic graphs for given x-values and finding the equation of a tangent line to a circle at a specified point, plus a question comparing race completion times using a graph.\"}]","Westminster Math Difficult One - Best Buys - Conversion Graphs - LCM/HCF - Compound Interest - Reverse Percentages | PDF",53]