[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-315982-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-315982-en":130},{"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","methods-formula-sheet-part-3-and-4","Methods Formula Sheet - Part 3 and 4","","This document provides a comprehensive reference sheet for Mathematical Methods, specifically tailored for Exam 2 preparation. It summarizes essential formulas across three core mathematical domains: Mensuration, Calculus, and Probability. The Mensuration section covers geometric volume and area calculations for shapes like pyramids, cylinders, spheres, and triangles. The Calculus section details derivatives and integration rules, including product, quotient, and chain rules. The Probability section outlines fundamental statistical concepts, probability distributions for discrete and continuous variables, and methods for calculating sample proportions and confidence intervals. Designed as a quick-reference guide, it serves as a critical study aid for students aiming to review key mathematical principles and application methods efficiently for examinations.",{"@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/methods-formula-sheet-part-3-and-4/315982/",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/methods-formula-sheet-part-3-and-4/315982.png","ImageObject",300,407,{"name":42,"@type":43},"Oliver","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-09-20",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",10,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What specific geometric formulas are included for volume and area?","Question",{"text":63,"@type":64},"The sheet provides formulas for the area of a trapezium and triangle, as well as the volume of a pyramid, cylinder, and sphere.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which calculus rules are highlighted for derivatives?",{"text":68,"@type":64},"It lists fundamental derivative formulas for power, exponential, logarithmic, and trigonometric functions, along with the product, quotient, and chain rules.",{"name":70,"@type":61,"acceptedAnswer":71},"How does the document define statistical variance for a probability distribution?",{"text":72,"@type":64},"Variance is defined as the expected value of the squared deviation from the mean, represented as var(X) = σ² = E((X– μ)²) = E(X²)– μ², with specific summations or integrals for discrete and continuous distributions.","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},315982,1790024787,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,126],{"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":55,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":55,"slug":125},"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":96,"preview_page_count":4},8796095461610,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","MATHMETH EXAM 2  \nMathematical Methods formulas  \nMensuration  \n\n| area of a trapezium | 12 ( a + b ) h | volume of a pyramid | 13Ah |\n| --- | --- | --- | --- |\n| curved surface area of a cylinder | 2π rh | volume of a sphere | 4  3 π r\u003Cbr>3 |\n| volume of a cylinder | π r2h | area of a triangle | 12 bc sin ( A ) |\n| volume of a cone | 1 2\u003Cbr>3 π r h |  |  |\n\nCalculus  \n\n| ddx ( xn) = nxn −1 |  | ∫xn dx = n~~ ~~~~ ~~1 xn + 1 + c, n ≠ −1 |  |\n| --- | --- | --- | --- |\n| ddx ((ax + b)n) = an ( ax + b)n−1 |  | ∫ (ax + b)n dx = a(n1+1) (ax + b)n + 1 + c, n ≠ −1 |  |\n| ddx ( eax ) = aeax |  | ∫eax dx = 1a eax + c |  |\n| ddx (loge (x)) = 1x |  | ∫ ~~ ~~1x dx = loge (x) + c, x > 0 |  |\n| ddx (sin(ax) ) = a cos (ax) |  | ∫ sin(ax)dx =− ~~ ~~1a cos (ax) + c |  |\n| ddx ( cos(ax) )= − a sin(ax) |  | ∫ cos(ax)dx = 1a sin (ax) + c |  |\n| ddx ( tan(ax) )= ~~ ~~cosa2(ax) = a sec2 (ax) |  |  |  |\n| product rule | ddx ( uv ) = u ~~ ~~dvdx + v ~~ ~~ddux | quotient rule | du dvddx~~ ~~􀀟􀀞~~􀀝 ~~uv~~ ~~ 􀀜􀀛􀀚 = v~~  ~~dx~~ ~~−v2u~~  ~~dx |\n| chain rule | dy dy du\u003Cbr>~~ ~~ = ~~ ~~\u003Cbr>dx du dx |  |  |\n\n3 MATHMETH EXAM  \nProbability  \n\n| Pr(A) = 1 – Pr(A′) |  | Pr(A ∪ B) = Pr(A) + Pr(B)– Pr(A ∩ B) |  |\n| --- | --- | --- | --- |\n| Pr(A|B) = PrP(~~ ~~Ar~~(~~∩B) |  |  |  |\n| mean | µ = E(X) | variance | var(X) = σ 2 = E((X– µ)2) = E(X2)– µ2 |\n\n\n| Probability distribution |  | Mean | Variance |\n| --- | --- | --- | --- |\n| discrete | Pr(X = x) = p(x) | µ = ∑ xp(x) | σ 2 = ∑ (x – µ)2 p(x) |\n| continuous | Pr(a \u003C X \u003C b) = ∫ab f (x)dx | µ = ∫ x f (x)dx | σ 2 = ∫ (x − µ )2 f (x)dx |\n\nSample proportions  \n\n| ̂ XP = ~~  ~~n |  |  | mean | E() = p |\n| --- | --- | --- | --- | --- |\n| standard\u003Cbr>deviation | sd () = | | approximate\u003Cbr>confidence interval | 􀂨􀂧􀂩 − z ~~ ~~(~~ ~~1~~ ~~) ,  + z ~~ ~~(~~ ~~1~~ ~~) 􀂷􀂹􀂸 |\n\nEND OF FORMULA SHEET","cbCaimNBJXAXCJyh","https://ap.wps.com/l/cbCaimNBJXAXCJyh","pdf",298639,"English","# Mensuration\n## Geometry Formulas\n# Calculus\n## Differentiation and Integration\n## Rule Applications\n# Probability\n## Basic Probability\n## Distribution Statistics\n## Sample Proportions","[{\"question\":\"What specific geometric formulas are included for volume and area?\",\"answer\":\"The sheet provides formulas for the area of a trapezium and triangle, as well as the volume of a pyramid, cylinder, and sphere.\"},{\"question\":\"Which calculus rules are highlighted for derivatives?\",\"answer\":\"It lists fundamental derivative formulas for power, exponential, logarithmic, and trigonometric functions, along with the product, quotient, and chain rules.\"},{\"question\":\"How does the document define statistical variance for a probability distribution?\",\"answer\":\"Variance is defined as the expected value of the squared deviation from the mean, represented as var(X) = σ² = E((X– μ)²) = E(X²)– μ², with specific summations or integrals for discrete and continuous distributions.\"}]","Methods Formula Sheet - Part 3 and 4 | PDF",1789908744]