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It also provides standard algebra tools for quadratic equations and distance from a point to a plane. Calculus coverage includes derivative tables, derivative rules, chain/product/quotient-related properties, arc length for parametric curves, integration by parts, and volume of revolution using integral setups. Includes a South Australia reference.",{"@graph":14,"@context":72},[15,34,55],{"@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/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/paper-templates/","Paper 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integrals?",{"text":71,"@type":63},"It provides derivative formulae and derivative properties, arc length for parametric curves, integration by parts, and integral expressions for volumes of revolution about coordinate axes.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},572238,1792066568,{"code":4,"msg":81,"data":82},"success",[83,88,93,98,103,108,113,118,122],{"id":84,"doc_module":22,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},11,"Presentations",90,"presentations",{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},12,"Resumes",80,"resumes",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},14,"Invoices",70,"invoices",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},15,"Posters",60,"posters",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},16,"Social 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MATHEMATICS FORMULA SHEET  \nCircular functions  \nsin 2 A􀀌 cos2 A 􀀞 1 tan 2 A􀀌1 􀀞 sec2 A 1􀀌 cot2 A 􀀞 cosec 2 A  \nsin􀀉A B 􀀊 􀀞 sin AcosB cosAsin B  \ncos 􀀉 A B 􀀊 􀀞 tan 􀀉 A B 􀀊 􀀞  \ncosAcos B sin Asin B  tan A tanB   \n􀀎  \n1􀀌 tan AtanB  \nsin 2A 􀀞 2 sinAcosA cos2A 􀀞 cos2 A􀀎sin2 A  \n􀀞 2 cos2 A􀀎1  \n􀀞 1􀀎 2 sin 2 A  \n2 tan Atan 2A 􀀞 ~~ ~~  \n1􀀎 tan2 A  \n2 sin AcosB 􀀞 sin 􀀉A􀀌 B 􀀊 􀀌 sin 􀀉A􀀎 B 􀀊 2cosAcos B 􀀞 cos 􀀉 A 􀀌 B􀀊 􀀌 cos􀀉 A􀀎 B 􀀊 2 sin Asin B 􀀞 cos 􀀉 A􀀎 B 􀀊􀀎cos􀀉 A􀀌 B 􀀊 sinA  sin B 􀀞 2 sin ~~ ~~122 􀀉 A B 􀀊 cos ~~ ~~12 􀀉 A B 􀀊 cosA􀀌 cos B 􀀞 2cos ~~ ~~12 􀀉 A􀀌 B 􀀊 cos ~~ ~~12 􀀉 A􀀎 B 􀀊 cosA 􀀎 cos B 􀀞􀀎 2 sin ~~ ~~12 􀀉 A􀀌 B 􀀊sin ~~ ~~12 􀀉 A􀀎 B 􀀊  \nMatrices and determinants  \nIf A ¬«ª ac bd º¼» then det A A  ad 􀀐 bc and 1 1 ª d 􀀐bº  \nA 􀀐  A   ¬« 􀀐c a ¼» .  \nMeasurement  \n1 2  \nArea of sector, A 􀀞 2 r R , where R is in radians. Arc length, l 􀀞 rR , where R is in radians.  \nIn any triangle ABC􀀛  \nA  \nB a  \nC  \nArea of triangle ~~ ~~􀀔􀀕 abVLQC  \na b c  \nsin A 􀀞 sin B 􀀞 sin Ca2 􀀞 b2 􀀌 c2 􀀎 2bc cos A  \nQuadratic equations  \nIf ax2 􀀌 bx 􀀌 c 􀀞 0 then x 􀀞 􀀎b  b2 􀀎 4ac  .  \n2a  \nDistance from a point to a plane  \nThe distance from 􀀉x1 , y1 , z1 􀀊 to Ax 􀀌 By 􀀌 Cz 􀀌 D 􀀞 0 is given by  \nAx1 􀀌 By1 􀀌 Cz1 􀀌 D  \nA2 􀀌 B2 􀀌 C2  \n.  \nDerivatives  \n\n| f 􀀋 x 􀀌 y | f c 􀀋x 􀀌 ~~ ~~d~~d~~yx |\n| --- | --- |\n| DUFVLQ x | 1\u003Cbr>|\n| DUFFRV x | 􀀐1\u003Cbr>|\n| DUFWDQ x | 1\u003Cbr>1 􀀎 x2 |\n\nProperties of derivatives  \nddx 􀀋 f 􀀋 x 􀀌 g 􀀋 x 􀀌 􀀌 f c 􀀋 x 􀀌 g 􀀋 x 􀀌 􀀎 f  \n􀀋 x 􀀌 gc 􀀋 x 􀀌  \n d § f 􀀋 x 􀀌  · dx ©¨ g 􀀋 x 􀀌 ¹¸ ddx f 􀀋 g 􀀋 x 􀀌􀀌  \nf c 􀀋 x 􀀌 g 􀀋 x 􀀌􀀐 f 􀀋 x 􀀌 gc 􀀋 x 􀀌􀀋 g 􀀋 x 􀀌􀀌2  \nf c 􀀋 g 􀀋 x 􀀌􀀌 gc 􀀋 x 􀀌  \nArc length along a parametric curve  \nb  \nl ¶´ v \u003C v dt , where a d t d b. a  \nIntegration by parts  \n¶´ f c 􀀋x 􀀌 g 􀀋 x 􀀌dx f 􀀋 x 􀀌 g 􀀋 x 􀀌􀀐 ¶´ f 􀀋 x 􀀌 gc 􀀋x 􀀌dx  \nVolumes of revolution  \nAbout x axis, V  \nAbout y axis, V function of x.  \nb  \n¶´ Sy2dx , where y is a function of x. a  \nd  \n¶´ Sx2dy , where y is a one-to-one c  \n© SACE Board of South Australia","cbCaijV76QyQ76iX","https://ap.wps.com/l/cbCaijV76QyQ76iX","pdf",829666,"English","# Circular functions\n# Matrices and determinants\n# Measurement\n# Quadratic equations\n# Distance from a point to a plane\n# Derivatives\n## Properties of derivatives\n# Arc length along a parametric curve\n# Integration by parts\n# Volumes of revolution","[{\"question\":\"What circular function identities are included?\",\"answer\":\"The sheet lists relationships involving sin, cos, tan, sec, cot, and cosec, including angle-doubling style expressions and product-to-sum forms.\"},{\"question\":\"Which algebra and geometry formulas are provided?\",\"answer\":\"It includes the quadratic equation solution form, triangle area using sides and included angles, sector area and arc length in radians, and the distance from a point to a plane using a standard coordinate formula.\"},{\"question\":\"What calculus topics are covered for derivatives and integrals?\",\"answer\":\"It provides derivative formulae and derivative properties, arc length for parametric curves, integration by parts, and integral expressions for volumes of revolution about coordinate axes.\"}]","Specialist Mathematics Formula Sheet - Circular functions - Matrices, determinants - Measurement - Quadratic equations - Derivatives - Arc length and integration - Volumes of revolution | PDF",1791926316]