[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-619527-105":59,"doc-detail-619527-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","formulae-and-identities-gcsea-level-essential-math-summary-physics-and-calculus-included","Formulae and identities GCSE/A-level - Essential math summary - Physics and calculus included","","A compact revision sheet of essential GCSE and A-level mathematics formulae and identities, organized by major topics. It covers coordinate geometry and straight-line equations, arithmetic and geometric sequences, logarithm and index laws, kinematics with variable acceleration, vector magnitude, and core trigonometric identities. It also includes statistics (mean and standard normal), mensuration for circle sector arc length and area, and calculus with differentiation and integration rules, plus forces and equilibrium using weight, friction, and Newton’s second law.",{"@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/formulae-and-identities-gcsea-level-essential-math-summary-physics-and-calculus-included/619527/",{"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/formulae-and-identities-gcsea-level-essential-math-summary-physics-and-calculus-included/619527.png","ImageObject",300,407,{"name":92,"@type":93},"Noah","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-20",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Which topics of GCSE/A-level maths are summarized in this document?","Question",{"text":112,"@type":113},"It covers coordinate geometry, sequences, logarithm and index laws, kinematics, vectors, trigonometry, statistics, mensuration, calculus (differentiation and integration), and forces/equilibrium.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is the perpendicular condition for two straight lines stated?",{"text":117,"@type":113},"Two straight lines with gradients m1 and m2 are perpendicular when m1·m2 = -1.",{"name":119,"@type":110,"acceptedAnswer":120},"What differentiation and integration rules are included?",{"text":121,"@type":113},"The sheet lists derivative rules for powers, trig functions, exponential and logarithmic forms, and sum/difference/product/chain rules, plus corresponding basic integration results and the area-under-a-curve expression.","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},619527,1792860334,{"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":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":81,"preview_page_count":4},8796095462418,"https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780","Formulae and identities you’ll need to know  \nRemember:  \nyou'll still need your GCSE formulaeat A-level  \nCoordinate geometry  \nA straight line graph, gradient m passing through (x1, y1 ) has equation  \ny-y1 = m (x-x1 )  \nStraight lines with gradients m1 and m2 are perpendicular when  \nm1 m 2 = -1  \nSequences  \nGeneral term of an arithmetic progression:  \nun = a + ( n-1)d  \nGeneral term of a geometric progression:  \nu = arn-1  \nn  \nLaws of Logarithms  \nx = an ‹=› n = log ax for a> 0 and x> 0  \nlog ax + logay---loga (xy)  \nlog ax-logay---loga ~~(~~yx~~) ~~klogax---loga (xk)  \nKinematics  \nFor motion in a straight line with variable acceleration:  \nv = rtr = ∫vdt  \na =  = dd v = ∫ad t  \nVectors  \n|xi+yj+zk|=√ (x2 +y2 +z2 )  \nTrigonometry  \ncos 2A + sin 2A---1 sec 2A---1 + tan 2Acosec 2A---1 + cot 2Asin2A---2sinAcosA cos2A---cos 2A-sin2Atan2A---~~1 2~~-t~~ ~~atnaAn~~2~~A  \nLaws of Indices  \nax ay---ax+y  \nax ÷ ay---ax-y  \n( ax ) y---axy  \nStatistics  \nThe mean of a set of data:  \nx = Σnx = Σ~~ƒ~~xΣƒ  \nThe standard Normal variable:  \nZ = X- µσ  \nwhere X ~ N (µ,σ2 )  \nMensuration  \nFor a circle of radius r, where an angle at the centre of Θ radians subtendsan arc of length s and encloses an associated sector of area A:  \ns = rΘ A = ½ r2 Θ  \nCalculus and  \nDifferential Equations  \nDifferentiation  \n\n| Function | Derivative |\n| --- | --- |\n| xn | nx n-1 |\n| sinkx | k coskx |\n| coskx | -ksinkx |\n| ekx | kekx |\n| Inx | 1 x |\n| f(x ) + g (x ) | f'(x ) + g'(x ) |\n| f(x ) g (x ) | f'(x ) g (x ) + f(x ) g'(x ) |\n| f( g (x )) | f'( g (x )) g'(x ) |\n\nIntegration  \n\n| Function | Integral |\n| --- | --- |\n| xn | n~~ ~~~~1~~xn+1 + c, n≠ -1 |\n| coskx | ~~1k~~sinkx + c |\n| sinkx | -~~1k~~ coskx + c |\n| ekx | 1 kx ke + c |\n| 1 x | In|x | + c, x ≠0 |\n| f'(x ) + g'(x ) | f(x ) + g (x ) + c |\n| f'( g (x )) g'(x ) | f( g (x )) + c |\n\nArea under a curve:  \n=  y dx (y ≥ 0)  \na  \nForces and Equilibrium  \nWeight = mass x g  \nFriction:  \nF ≤ µR  \nNewton's second law in the form:  \nF = ma","cbCaiqwTH4XMJglA","https://ap.wps.com/l/cbCaiqwTH4XMJglA","pdf",450989,"English","# Coordinate geometry\n# Sequences\n# Laws of logarithms\n# Kinematics\n# Vectors\n# Trigonometry\n# Laws of indices\n# Statistics\n# Mensuration\n# Calculus and differential equations\n## Differentiation\n## Integration\n# Forces and equilibrium","[{\"question\":\"Which topics of GCSE/A-level maths are summarized in this document?\",\"answer\":\"It covers coordinate geometry, sequences, logarithm and index laws, kinematics, vectors, trigonometry, statistics, mensuration, calculus (differentiation and integration), and forces/equilibrium.\"},{\"question\":\"How is the perpendicular condition for two straight lines stated?\",\"answer\":\"Two straight lines with gradients m1 and m2 are perpendicular when m1·m2 = -1.\"},{\"question\":\"What differentiation and integration rules are included?\",\"answer\":\"The sheet lists derivative rules for powers, trig functions, exponential and logarithmic forms, and sum/difference/product/chain rules, plus corresponding basic integration results and the area-under-a-curve expression.\"}]","Formulae and identities GCSE/A-level - Essential math summary - Physics and calculus included | PDF",1792463033]