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Includes quadratic solving, logarithm rules, complex number representations, differentiation and integration tables, product/quotient/chain rules, Trapezium and Simpson’s numerical integration rules, and common trigonometric identities and measurement formulas. Designed to support answering questions in the corresponding question and answer booklets during the examination.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":46,"@type":70,"position":76},"https://docshare.wps.com/template/paper-templates/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/level-3-calculus-2024-formulae-and-tables-booklet/573141/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/level-3-calculus-2024-formulae-and-tables-booklet/573141.png","ImageObject",442,249,{"name":88,"@type":89},"dhado","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":9},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What topics and formula sets are included in this booklet?","Question",{"text":108,"@type":109},"It covers algebra (quadratics, logarithms, complex numbers), straight line coordinate geometry, calculus differentiation and integration rules, numerical methods (Trapezium and Simpson’s rules), trigonometry (identities and solutions), and measurement formulas for common shapes.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How should the booklet be used during the exam?",{"text":113,"@type":109},"Use it to answer questions in the corresponding question and answer booklets, and verify that pages 2–4 are in the correct order and not blank.",{"name":115,"@type":106,"acceptedAnswer":116},"What calculus rules are provided for differentiation?",{"text":117,"@type":109},"It includes differentiation tables plus the Product Rule, Quotient Rule, and Composite Function/Chain Rule with corresponding derivative expressions.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},573141,1792052166,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":45,"category_name":46,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":9,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":79,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":73},5909893218464,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","L3–CAL CF   \n993203  \n3  \nLevel 3 Calculus 2024  \n\n| \u003Cbr>| |\n| --- | --- |\n\nFORMULAE AND TABLES BOOKLET  \nfor 91577, 91578, and 91579  \nRefer to this booklet to answer the questions in your Question and Answer Booklets.  \nCheck that this booklet has pages 2–4 in the correct order and that none of these pages is blank.  \nYOU MAY KEEP THIS BOOKLET AT THE END OF THE EXAMINATION.  \n© New Zealand Qualifications Authority, 2024. All rights reserved.  \nNo part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority.  \n2  \nMATHEMATICS – USEFUL FORMULAE  \nALGEBRA Quadratics  \nIf ax2 + bx + c = 0  \nthen x = −b ± b2 − 4ac  \n2a  \nLogarithms  \ny = logb x ⇔ x = by logb (xy) = logb x + logb y logb ⎜ ~~ ~~xy~~ ~~ ⎟ = logb x − logb y logb (xn ) = nlogb x logb x = log~~l~~ogaa~~ ~~xb  \nComplex numbers  \nz = x + iy  \n= r cisθ  \n= r(cosθ + isinθ )  \nz~~ ~~ = x − iy  \n= r cis (−θ )  \n= r(cosθ − isinθ )  \nr =  z = zz~~ ~~ = (x2 + y2 )  \nθ = arg z where cosθ = xrand sinθ = yr  \nDe Moivre’s Theorem  \nIf n is any integer, then (r cis θ )n = rn cis (nθ )  \nCOORDINATE GEOMETRY Straight Line  \nEquation y − y1 = m(x − x1 )  \nCALCULUS Differentiation  \n\n| y = f (x) | dydx = f ʹ(x) |\n| --- | --- |\n| ln x |  1\u003Cbr>x |\n| eax | ax ae |\n| sin x | cos x |\n| cos x | − sin x |\n| tan x | 2 sec x |\n| sec x | sec x tan x |\n| cosec x | −cosec x cotx |\n| cotx | 2 −cosec x |\n\nIntegration  \n\n| f (x) | ∫ f (x) dx |  |\n| --- | --- | --- |\n| xn\u003Cbr> 1\u003Cbr>x\u003Cbr>f ʹ(x)\u003Cbr>f (x) | n+1 x\u003Cbr>n + 1 | + c |\n|  | ( n ≠ −1) ln x  + c\u003Cbr>ln f (x) + c |  |\n\nParametric Function  \ndy  dy dt  \n= .  \ndx dt dx  \nd 2y d  ⎛ dy  ⎞ dtdx2 = dt ⎜⎝ dx ⎠⎟ . dx  \n3  \nProduct Rule  \n( f . g) = g.f  + f . g or if y = uv then dy~~d~~x = v ~~ ~~du~~d~~x + u ~~ ~~d~~d~~vx  \nQuotient Rule  \nfg~~ ~~  = g.f~~ ~~g~~ ~~2f~~ ~~.g or if y = uv then dy~~d~~x = v ~~ ~~du~~d~~xv~~ ~~2 u ~~ ~~d~~d~~vx  \nComposite Function or Chain Rule  \n( f ( g )) = f  ( g ) .g   \nor if y = f (u) and u = g (x) then dy~~d~~x = dy~~d~~u . ~~ ~~d~~d~~ux  \nNUMERICAL METHODS  \nTrapezium Rule  \nb 1  \nf (x) dx  ~~ ~~ h y0 + yn + 2(y1 + y2 + ... + yn 1 )  \na 2  \nwhere h = b~~  ~~n~~ ~~a andyr = f (xr )  \nSimpson’s Rule  \nb 1  \nf (x) dx  ~~ ~~ h y0 + yn + 4(y1 + y3 + ... + yn 1 ) + 2(y2 + y4 + ... + yn 2 )  \na 3  \nwhere h = b~~  ~~n~~ ~~a , yr = f (xr ) and n is even.  \n4  \nL 3–CAL CF  \nTRIGONOMETRY  \ncosec! = s~~i~~1n~~! ~~sec! = co1s~~! ~~cot! = ta1n~~!~~​  \ncot! = coss~~i~~n~~!~~​!  \nSine Rule  \na b c  \n~~ ~~ = ~~ ~~ = ~~  ~~sin A sinB sin C  \nCosine Rule  \nc2 = a2 + b2 ! 2ab cos C  \nIdentities  \ncos2 ! + sin2 ! = 1 tan2 ! + 1 = sec2 !  \ncot2 ! + 1 = cosec2 !  \nGeneral Solutions  \nIf sin ! = sin \" then ! = n! + (\"1)n \"If cos ! = cos \" then ! = 2n! ± \"If tan ! = tan \" then ! = n! + \"where n is any integer  \nCompound Angles  \nsin(A ± B) = sin AcosB ± cosAsin Bcos(A ± B) = cosAcos B! sin AsinB tan(A ± B) =  tan A ± tan B   \n1 ! tan AtanB  \nDouble Angles  \nsin 2 A = 2sin AcosA  \n2 tan Atan 2 A = ~~ ~~  \n1 ! tan2 Acos 2 A = cos2 A ! sin2 A  \n= 2cos2 A ! 1  \n= 1! 2sin2 A  \nProducts  \n2 sin AcosB = sin( A+ B) + sin (A − B)  \n2cosAsin B = sin( A+ B) − sin (A − B)  \n2cosAcos B = cos( A+ B) + cos( A − B)  \n2 sin Asin B = cos ( A − B) − cos( A+ B)  \nSums  \nsinC + sinD = 2sin ~~ ~~C~~ ~~+2~~ ~~D cos ~~ ~~C~~ ~~−2~~ ~~DsinC − sinD = 2cos ~~ ~~C~~ ~~+2~~ ~~D sinC~~ ~~−2~~ ~~DcosC + cosD = 2cos ~~ ~~C~~ ~~+2~~ ~~D cos ~~ ~~C~~ ~~−2~~ ~~DcosC − cosD = −2sin ~~ ~~C~~ ~~+2~~ ~~D sin ~~ ~~C~~ ~~−2~~ ~~D  \nMEASUREMENT  \nTriangle  \nArea = 12 absin C  \nTrapezium  \nArea = 12 (a + b)h  \nSector  \nArea = 12 r 2θ Arc length = rθ  \nCylinder  \nVolume = ! r 2 h  \nCurved surface area = 2! rh  \nCone  \nVolume = 13! r2 h  \nCurved surface area = ! rl where l = slant height  \nSphere  \nVolume = 43 ! r 3  \nSurface area = 4! r 2","cbCaiqKYIgEbVnPx","https://ap.wps.com/l/cbCaiqKYIgEbVnPx","pdf",848097,"English","# Mathematics – Useful Formulæ\n## Algebra\n## Coordinate Geometry - Straight Line\n## Calculus - Differentiation\n## Calculus - Integration\n## Product Rule, Quotient Rule, Chain Rule\n## Numerical Methods\n## Trigonometry\n## Measurement","[{\"question\":\"What topics and formula sets are included in this booklet?\",\"answer\":\"It covers algebra (quadratics, logarithms, complex numbers), straight line coordinate geometry, calculus differentiation and integration rules, numerical methods (Trapezium and Simpson’s rules), trigonometry (identities and solutions), and measurement formulas for common shapes.\"},{\"question\":\"How should the booklet be used during the exam?\",\"answer\":\"Use it to answer questions in the corresponding question and answer booklets, and verify that pages 2–4 are in the correct order and not blank.\"},{\"question\":\"What calculus rules are provided for differentiation?\",\"answer\":\"It includes differentiation tables plus the Product Rule, Quotient Rule, and Composite Function/Chain Rule with corresponding derivative expressions.\"}]","Level 3 Calculus 2024 - FORMULAE AND TABLES BOOKLET | PDF",1791933172]