[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-207140-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-207140-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","gcse-mathematics-higher-tier-formulae-sheet","GCSE Mathematics Higher Tier Formulae Sheet","","This document is the GCSE Mathematics Higher Tier Formulae Sheet for 2022. It provides essential formulas for calculations in geometry, algebra, and probability. Key areas covered include perimeter, area, and volume formulas for various shapes such as trapeziums, prisms, and circles, alongside the quadratic formula for solving equations. It also details Pythagoras' Theorem and trigonometric ratios (sine, cosine, tangent) for right-angled triangles, as well as the sine and cosine rules, and the formula for the area of a triangle using sine. Compound interest calculations are explained with the relevant formula, and probability formulas for the union and intersection of events are included. The sheet is designed to serve as a reference for students during their GCSE Mathematics Higher Tier examinations, ensuring they have access to the necessary mathematical tools for problem-solving.",{"@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/gcse-mathematics-higher-tier-formulae-sheet/207140/",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/gcse-mathematics-higher-tier-formulae-sheet/207140.png","ImageObject",300,407,{"name":42,"@type":43},"Aditya","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-09-05",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 are the formulas for basic geometric shapes?","Question",{"text":63,"@type":64},"The sheet includes formulas for the area of a trapezium (1/2 (a+b)h), volume of a prism (area of cross section × length), circumference of a circle (2πr or πd), and area of a circle (πr²).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How is the quadratic formula presented?",{"text":68,"@type":64},"The quadratic formula is given as x = -b ± √(b² - 4ac) / 2a, for solving equations of the form ax² + bx + c = 0 where a ≠ 0.",{"name":70,"@type":61,"acceptedAnswer":71},"What trigonometric formulas are provided for right-angled triangles?",{"text":72,"@type":64},"For any right-angled triangle with sides a, b, and hypotenuse c, the sheet provides sin A = a/c, cos A = b/c, and tan A = a/b.","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},207140,1788598522,{"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":26,"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":96},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","GCSE  \nMATHEMATICS HIGHER TIER  \nFormulae Sheet  \nInsert  \nPerimeter, area and volume  \nWhere a and b are the lengths of the parallel sides and h is their perpendicular separation:  \nArea of a trapezium = 12 (a + b) h  \nVolume of a prism = area of cross section × length Where r is the radius and d is the diameter:  \nCircumference of a circle = 2πr = πd Area of a circle = πr2  \nQuadratic formula  \nThe solution of ax2 + bx + c = 0 where a ≠ 0  \nx = –~~ ~~b~~ ~~±~~ ~~b22a~~ ~~–~~ ~~4ac  \nPythagoras’ Theorem and Trigonometry  \nIn any right-angled triangle where a, b and c are the length of the sides and c is the hypotenuse:  \na 2 + b2 = c 2  \nIn any right-angled triangle ABC where a, b and care the length of the sides and c is the hypotenuse:  \nsinA = ac~~ ~~ cos A = bc~~ ~~ tan A = ab  \nIn any triangle ABC where a, b and c are the length of the sides:  \nsine rule: sianA = sibnB = sicnC  \ncosine rule: a 2 = b 2 + c 2 – 2bc cos A Area of triangle = 12 ab sin C  \nCompound Interest  \nWhere P is the principal amount, r is the interest rate over a given period and n is number of times that the interest is compounded:  \nTotal accrued = P 􀂧􀂨􀂩 1 + 1r00~~ ~~ 􀂷􀂹􀂸 n  \nProbability  \nWhere P (A) is the probability of outcome A and P (B) is the probability of outcome B:  \nP (A or B) = P(A) + P(B)– P(A andB) P (A andB) = P (A given B) P(B)","cbCaivyMhuByXyLS","https://ap.wps.com/l/cbCaivyMhuByXyLS","pdf",245129,"English","# Perimeter, area and volume\n## Area of a trapezium\n## Volume of a prism\n## Circumference of a circle\n## Area of a circle\n# Quadratic formula\n# Pythagoras’ Theorem and Trigonometry\n## Pythagoras’ Theorem\n## Trigonometry (Right-angled triangle)\n## Sine rule\n## Cosine rule\n## Area of triangle\n# Compound Interest\n# Probability","[{\"question\":\"What are the formulas for basic geometric shapes?\",\"answer\":\"The sheet includes formulas for the area of a trapezium (1/2 (a+b)h), volume of a prism (area of cross section × length), circumference of a circle (2πr or πd), and area of a circle (πr²).\"},{\"question\":\"How is the quadratic formula presented?\",\"answer\":\"The quadratic formula is given as x = -b ± √(b² - 4ac) / 2a, for solving equations of the form ax² + bx + c = 0 where a ≠ 0.\"},{\"question\":\"What trigonometric formulas are provided for right-angled triangles?\",\"answer\":\"For any right-angled triangle with sides a, b, and hypotenuse c, the sheet provides sin A = a/c, cos A = b/c, and tan A = a/b.\"}]","GCSE Mathematics Higher Tier Formulae Sheet | PDF"]