[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-436907-105":59,"doc-detail-436907-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","middle-grades-math-formulas-and-notations-reference-guide","Middle Grades Math Formulas and Notations - Reference Guide","","This document provides a comprehensive reference sheet for middle school mathematics, covering essential formulas, notations, and concepts. It details geometric formulas for circumference, area, and volume of various shapes such as circles, triangles, trapezoids, prisms, and spheres. Additionally, it includes algebraic expressions like the quadratic formula, distance and midpoint formulas, slope, and arithmetic or geometric series. Statistical measures such as mean absolute deviation, sample variance, and outlier detection are also provided, alongside set theory, permutations, and combinations, serving as an invaluable resource for students and educators in middle grades math curricula.",{"@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/middle-grades-math-formulas-and-notations-reference-guide/436907/",{"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/middle-grades-math-formulas-and-notations-reference-guide/436907.png","ImageObject",300,407,{"name":92,"@type":93},"Sarah ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-22","2026-09-29",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},"What is the formula for the volume of a sphere?","Question",{"text":112,"@type":113},"The volume of a sphere is calculated using the formula V = 4/3 πr³.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is the outlier in a data set defined?",{"text":117,"@type":113},"An outlier is defined as a value x where x \u003C Q1 - 1.5(IQR) or x > Q3 + 1.5(IQR).",{"name":119,"@type":110,"acceptedAnswer":120},"What is the quadratic formula used for solving equations?",{"text":121,"@type":113},"The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a, which is used to solve for the roots of a quadratic equation.","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},436907,1791131549,{"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":14,"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":24},962085320529,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","MIDDLE GRADES MATH FORMULAS AND NOTATIONS  \n\n| Formula | Description |\n| --- | --- |\n| C = πd = 2πr | Circumference of a circle |\n| A = πr2 | Area of a circle |\n| A = 12bh | Area of a triangle |\n| A = 􀂧􀂨􀂩 ~~ ~~b1~~ ~~+2~~ ~~b2~~ ~~􀂷􀂹􀂸 h | Area of a trapezoid |\n| A = Bh | Volume of a prism |\n| V = 1~~3~~ Bh | Volume of a right cone and a pyramid |\n| V = πr2h | Volume of a cylinder |\n| V = 4  3 3 πr | Volume of a sphere |\n| A = 4πr2 | Surface area of a sphere |\n| A = πrr2 + h 2 | Lateral surface area of a right circular cone |\n| (x-h)2 + (y-k)2 +(z-j)2 = r 2 | Equation of a sphere |\n| (x-h)2 + (y-k)2 = r 2 | Equation of a circle |\n| y = a(x-h)2+k | Equation of a parabola (vertex form) |\n| C=  x2 − x1 x\u003Cbr>1 | Percent change |\n| Sn = n2~~ ~~ [2a + (n – 1)d] = n 􀂧􀂩􀂨 a~~ ~~+2an~~ ~~􀂷􀂹􀂸 | Sum of an arithmetic series |\n| Sn = a(1 − rn )\u003Cbr>1 − r | Sum of a geometric series |\n| a2 + b2 = c 2 | Pythagorean formula |\n| d = (x2 − x1 )2 + (y2 − y1 )2 | Distance formula |\n\nFORMULAS AND NOTATIONS (continued)  \n\n| ∆y y2 − y1\u003Cbr>m =  = ~~ ~~\u003Cbr>∆x x2 − x1 |  | Slope formula |\n| --- | --- | --- |\n| 􀂧  x1 + x2 y1 + y2 􀂷􀂩􀂨 2 , 2 􀂹􀂸 |  | Midpoint formula |\n|  a  =  b  =  c \u003Cbr>sin A sin B sin C |  | Law of sines |\n| c2 = a2 + b2 – 2ab cos C |  | Law of cosines |\n| x \u003C Q1 − 1.5(IQR )\u003Cbr>x > Q3 + 1.5(IQR ) |  | Definition of an outlier |\n| ∑n xi − x~~ ~~  \u003Cbr>MAD = i =1 n |  | Mean absolute deviation (MAD) formula |\n| ∑n ( xi − x~~ ~~ )2\u003Cbr>2 i =1\u003Cbr>s =\u003Cbr>n − 1 |  | Sample variance |\n| s = rθ |  | Arc length |\n| x = | –b ± b2 – 4ac\u003Cbr>2a | Quadratic formula |\n| A' is the complement of set A |  | Set theory |\n| nPr = P(n,r) = ~~(~~n~~ ~~n–!r~~)~~! |  | Permutation |\n| nCr = C(n,r) = ~~ (~~n~~ ~~–nr!~~ )~~!r! |  | Combination |","cbCaibv6l0JKuS9X","https://ap.wps.com/l/cbCaibv6l0JKuS9X","pdf",196903,"English","# Geometric Formulas\n## Algebraic and Analytical Formulas\n## Trigonometric and Statistical Formulas\n## Discrete Math and Set Theory","[{\"question\":\"What is the formula for the volume of a sphere?\",\"answer\":\"The volume of a sphere is calculated using the formula V = 4/3 πr³.\"},{\"question\":\"How is the outlier in a data set defined?\",\"answer\":\"An outlier is defined as a value x where x \\u003c Q1 - 1.5(IQR) or x \\u003e Q3 + 1.5(IQR).\"},{\"question\":\"What is the quadratic formula used for solving equations?\",\"answer\":\"The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a, which is used to solve for the roots of a quadratic equation.\"}]","Middle Grades Math Formulas and Notations - Reference Guide | PDF",1790679406]