[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207785-en":3,"doc-seo-207785-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207785,1374402968488,"Đào","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",4,"Exam","AQA GCSE Mathematics Higher Tier 2023 Formulae Sheet","This document is a formulae sheet for the AQA GCSE Mathematics Higher Tier exams in 2023. It provides essential mathematical formulas related to perimeter, area, and volume, including the area of a trapezium, volume of a prism, circumference and area of a circle. The sheet also includes the quadratic formula for solving equations of the form ax^2 + bx + c = 0, and formulas for Pythagoras' theorem and trigonometry in right-angled triangles, such as sin A = a/c, cos A = b/c, and tan A = a/b. Additionally, it presents the sine rule (a/sinA = b/sinB = c/sinC) and cosine rule (a^2 = b^2 + c^2 - 2bc cos A) for any triangle, along with the formula for the area of a triangle (1/2 ab sin C). The compound interest formula and probability formulas are also provided. The document is for examination use only in 2023 and is marked with reference WP/M/SB/2023/8300/H/E1.","A  \nGCSE  \nMATHEMATICS HIGHER TIER  \nFormulae Sheet  \n8300  \nInsert  \nFOR EXAMS IN 2023 ONLY  \n[Turn over]  \nPERIMETER, AREA AND VOLUME  \nWhere a and b are the lengths of the parallel sides and his their perpendicular separation:  \n1  \nArea of a trapezium = (a + b)h  \n2  \nVolume of a prism = area of cross section × length Where r is the radius and d is the diameter:  \nCircumference of a circle = 2π r = π d  \nArea of a circle = π r2  \nQUADRATIC FORMULA  \nThe solution of ax2 + bx + c = 0 where a ≠ 0  \n–b±b 2 – 4ac  \nx = ~~ ~~  \n2a  \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 c are the length of the sides and c is the hypotenuse:  \nsin A = a  \nc cosA = bc tan A = ab  \n[Turn over]  \nIn any triangle ABC where a, b and c are the length of the sides:  \na b c  \nsine rule:   =   =    \nsinA sinB sinC  \ncosine rule: a 2 = b 2 + c 2 – 2bc cos A  \n1  \nArea of triangle = ab sin C  \n2  \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 + 1~~ ~~r00~~ ~~􀂷􀂹􀂸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 and B)  \nP (A and B) = P (A given B)P(B)  \nBLANK PAGE  \nCopyright © 2023 AQA and its licensors. All rights reserved.  \nWP/M/SB/2023/8300/H/E1","cbCaibN0n8vkZuvN","https://ap.wps.com/l/cbCaibN0n8vkZuvN","pdf",258554,1,6,"English","en",105,"# 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 in right-angled triangles\n## Sine Rule\n## Cosine Rule\n## Area of triangle\n# Compound Interest\n# Probability","[{\"question\":\"What are the key formulas for perimeter, area, and volume provided in the sheet?\",\"answer\":\"The sheet includes the formulas for the area of a trapezium, volume of a prism, circumference and area of a circle, and Pythagoras' theorem for right-angled triangles.\"},{\"question\":\"Which trigonometric formulas are included for any triangle?\",\"answer\":\"For any triangle, the sheet provides the sine rule (a/sinA = b/sinB = c/sinC), the cosine rule (a^2 = b^2 + c^2 - 2bc cos A), and the formula for the area of a triangle (1/2 ab sin C).\"},{\"question\":\"What is the quadratic formula provided on the sheet?\",\"answer\":\"The quadratic formula for solving the equation ax^2 + bx + c = 0 (where a ≠ 0) is given as x = [-b ± sqrt(b^2 - 4ac)] / 2a.\"}]","AQA GCSE Mathematics Higher Tier 2023 Formulae Sheet | PDF",1788601136,15,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"aqa-gcse-mathematics-higher-tier-2023-formulae-sheet","",{"@graph":36,"@context":84},[37,53,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/aqa-gcse-mathematics-higher-tier-2023-formulae-sheet/207785/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What are the key formulas for perimeter, area, and volume provided in the sheet?","Question",{"text":74,"@type":75},"The sheet includes the formulas for the area of a trapezium, volume of a prism, circumference and area of a circle, and Pythagoras' theorem for right-angled triangles.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Which trigonometric formulas are included for any triangle?",{"text":79,"@type":75},"For any triangle, the sheet provides the sine rule (a/sinA = b/sinB = c/sinC), the cosine rule (a^2 = b^2 + c^2 - 2bc cos A), and the formula for the area of a triangle (1/2 ab sin C).",{"name":81,"@type":72,"acceptedAnswer":82},"What is the quadratic formula provided on the sheet?",{"text":83,"@type":75},"The quadratic formula for solving the equation ax^2 + bx + c = 0 (where a ≠ 0) is given as x = [-b ± sqrt(b^2 - 4ac)] / 2a.","https://schema.org",{"og:url":52,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,103,108,112,117,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":101,"slug":102},70,"exam",{"id":104,"doc_module":4,"doc_module_name":46,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},"Technology",50,"technology",{"id":113,"doc_module":4,"doc_module_name":46,"category_name":114,"show_sort_weight":115,"slug":116},7,"Healthcare",40,"healthcare",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":119,"show_sort_weight":120,"slug":121},8,"Research & Report",30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":104,"slug":137},19,"General","general"]