[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-144074-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-144074-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","westminstermath-4-june-answers","WestminsterMath 4 June Answers","","Answer solutions for a WestminsterMath worksheet dated 4 June. The set includes word problems and algebra tasks on percentage and remainder relationships, solving linear equations, forming equations of straight lines and curves from given coordinate points, simplifying expressions, working with right-triangle and Pythagorean relationships, applying volume change to find radius, calculating lengths in a bent geometry diagram, determining map scale, interpreting fish-consumption percentages, finding patterned tile area via simultaneous equations, and solving quadratic equations and nth-term expressions. It also includes vector component writing and a unit-conversion speed-record comparison with full working.",{"@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/westminstermath-4-june-answers/144074/",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/westminstermath-4-june-answers/144074.png","ImageObject",300,407,{"name":42,"@type":43},"Evangeline","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/vnd.openxmlformats-officedocument.wordprocessingml.document","2026-10-31","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},"How is the original birthday money found from the 40% spending and remainder steps?","Question",{"text":63,"@type":64},"Let the total birthday money be x. After spending 40%, the remainder is 60%, and half of that (30%) goes to perfume. Since 70% is spent in total, 30% equals the given £16.50, giving x = £55.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you form equations of straight lines from two coordinate points?",{"text":68,"@type":64},"Use y = aX + b. Compute a from the slope between the two points, then substitute one point to solve for b, yielding the required line equation (e.g., y = X + 3, y = -X + 2, y = -X - 4).",{"name":70,"@type":61,"acceptedAnswer":71},"How do you decide whether Ana breaks the land speed record using unit conversions?",{"text":72,"@type":64},"Convert Ana’s speed to miles per hour using the given timing and the provided mile-to-kilometre conversion. The results are 600 km/h and equivalently 375 miles/h, which matches the comparison to the record, so the answer is YES.","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},144074,1787698179,{"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":96,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":144},13056703019662,"https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188","1) Nina spends 40% of her birthday money on a bracelet and of the remainder on perfume.\nShe has $16.50 left. How much birthday money did she have in the first place?\nAnswer  Birthday money = x                            1)   40% spent on breakfast, 60% is left\n½ of 60% =30% spent on perfume\n40% + 30%= 70% is spent in total\n30% is left\n2) 30%-> $16,50\n100%-> x                    x=16,50x100=55$\n30                   3 marks\n2) The sum of 2 numbers is 64. One number is 7 times as big as the other.\nWhat is the bigger number? (You MUST show working\nAnswer \u001a\u001a𝑋+𝑦=64\u001b𝑋=7𝑦\u001b\u001b                               7y+y=64  8y=64  y=8\nX=7y=7x8=56                                                                   2 marks\n3) Give the equation of each straight line or curve\nTake 2 points from each straight line\nY=aX+b  (-2;1)  (1;4) \u001a\u001a1=𝑎\u001a−2\u001b+𝑏\u001b4=𝑎𝑥1+𝑏\u001b\u001b         -3=-3a\na=1 b=3      -> y=1xX+3\ny=aX+b  (1;1) (1;4) \u001a\u001a1=𝑎𝑥1+𝑏\u001b−2=𝑎𝑥4+𝑏\u001b\u001b              3=-3a\na=-1 b=2     -> y=-X+2\nY=aX+b  (0;-4)  (2;-6) \u001a\u001a−4=𝑎𝑥0+𝑏\u001b4=𝑎𝑥2+𝑏\u001b\u001b         2=-2a\na=-1 b=-4      -> y=-X-4\nY=a\u001a𝑥\u001b2\u001b +c           (0;0) (1;1) (2;4)\u000b\u001a\u001a0=𝑎𝑥\u001a0\u001b2\u001b+𝑏𝑥0+𝑐\u001b1=𝑎𝑥\u001a1\u001b2\u001b+𝑏𝑥1+𝑐\u001b4=𝑎𝑥\u001a2\u001b2\u001b+𝑏𝑥2+𝑐\u001b\u001b   ( \u001a\u001a1=𝑎+𝑏\u001b4=4𝑎+2𝑏\u001b\u001b( \u001a\u001a2=2𝑎+2𝑏\u001b4=4𝑎+2𝑏\u001b\u001b ( -2=-2a a=1   1=a+b 1=1+b b=0\nY=1x\u001a𝑋\u001b2\u001b+0X+0\nY=\u001a𝑋\u001b2\u001b\u000b                                                                                                                                8 marks\n4)   z=kx                         a) z=kx                 b)z=kx                                  c)z=kx\n4=kx1                        z=4x3                z=4X                                    z=4X\nk=4                          z=12                16=4xX                               z=4x5,5\nX=4                                    z=22\n5) When 3 litres of oil is removed from an upright cylindrical can, the level falls by 10 cm. Find the radius of the can\nV cylinder= π\u001a𝑅\u001b2\u001bh              3litres=3000\u001a𝑐𝑚\u001b2\u001b\n3000\u001a𝑐𝑚\u001b2\u001b=3x\u001a𝑅\u001b2\u001b10cm\n100\u001a𝑐𝑚\u001b2\u001b=\u001a𝑅\u001b2\u001b    R=10cm                                                                                5 marks\n6) A thin wire of length 18cm is bent in the shape shown\n3+3+a=18\na=12\nCalculate the length from A to B to 1 decimal place\n\u001a3\u001b2\u001b+\u001a9\u001b2\u001b=\u001a𝑋\u001b2\u001b\n90=\u001a𝑋\u001b2\u001b\nX=√90  =9.5                                                                                   4 marks\n7) The most well-known right angled triangle is the 3,4,5 triangle (32 + 42 = 52)\n\u001a5\u001b2\u001b+12=\u001a𝑋\u001b2\u001b\n\u001a𝑋\u001b2\u001b=169\nX=12                                                                        \u001a7\u001b2\u001b+\u001a24\u001b2\u001b=\u001a𝑌\u001b2\u001b\n\u001a𝑌\u001b2\u001b=625  y=25\n\u001a𝑍\u001b2\u001b+\u001a40\u001b2\u001b=\u001a41\u001b2\u001b\n\u001a𝑍\u001b2\u001b=81→𝑍=9            Total mark for page 10 marks\n8) Simplify as far as possible\nAnswers only 1) a/5b\n2) 1\n3) 6                                                     Total mark for page 6 marks\n9) On a map two points are 1.5 cm apart. In real life the points are 60 km apart. What is the scale of the map?\n60km=60 000km= 6 000 000cm\nScale map:real\n1.5cm:6 000 000cm\n3: 12 000 000\n1: 4 000 000                    answer 1: 4 000 000                       3 marks\n10) .A crocodile has been eating fish from a lake. It has eaten 70% of the fish. There are 600 fish left. How many fish were originally in the lake?\n30%-> 600\n100%->x                  30X=60 000   X=2000                   answer 2000           2 marks\n11) A pattern is made using identical rectangular tiles. Find the total area of the pattern The diagram is not drawn to scal\n-\u001a\u001a2𝑋+𝑌=11\u001b𝑋+𝑌=7\u001b\u001b         X=4   Y=3                area= 3cmx4cm=12\u001a𝑐𝑚\u001b2\u001b\nTotal area= 4x12\u001a𝑐𝑚\u001b2\u001b=48\u001a𝑐𝑚\u001b2\u001b                4 marks\n12) Solve  3\u001a𝑥\u001b2\u001b+6x-\u001a𝑐𝑥\u001b2\u001b+6=0                                X1= -4-2/2=-3\n2\u001a𝑥\u001b2\u001b+8𝑥+6=0                                   X2=-4+2/2=-1\n\u001a𝑥\u001b2\u001b+4𝑥+3=0\nD=16-4x3=4                                              -3and-1                1 marks\n(\u001a\u001a𝑎\u001b2+5−6\u001b)\u001b3\u001b=\u001a𝑎\u001b3\u001b                               2 marks\n13) Find an expression for the nth term of the sequence\n1/3  2/3  3/3  4/3…….n/3                                     3 marks\n14) A cake weighing 550g has three ingredients: flour, sugar and butter. There is twice as much f","cbCaivALTF1nNT6R","https://ap.wps.com/l/cbCaivALTF1nNT6R","docx",18379,"English","# Answers\n## Algebra and Equations\n## Geometry, Measurement and Applications\n## Sequences, Vectors and Conversions","[{\"question\":\"How is the original birthday money found from the 40% spending and remainder steps?\",\"answer\":\"Let the total birthday money be x. After spending 40%, the remainder is 60%, and half of that (30%) goes to perfume. Since 70% is spent in total, 30% equals the given £16.50, giving x = £55.\"},{\"question\":\"How do you form equations of straight lines from two coordinate points?\",\"answer\":\"Use y = aX + b. Compute a from the slope between the two points, then substitute one point to solve for b, yielding the required line equation (e.g., y = X + 3, y = -X + 2, y = -X - 4).\"},{\"question\":\"How do you decide whether Ana breaks the land speed record using unit conversions?\",\"answer\":\"Convert Ana’s speed to miles per hour using the given timing and the provided mile-to-kilometre conversion. The results are 600 km/h and equivalently 375 miles/h, which matches the comparison to the record, so the answer is YES.\"}]","WestminsterMath 4 June Answers | DOCX",13]