[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207786-en":3,"doc-seo-207786-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},207786,24189269381491,"Bill Black","https://ap-avatar.wpscdn.com/avatar/160000cf11732dd8392?x-image-process=image/resize,m_fixed,w_180,h_180&k=1788146458752108895",4,"Exam","GCSE Mathematics Additional Support Materials (Foundation Tier)-Summer 2023","This document provides essential additional support materials for the GCSE Mathematics Foundation Tier exam in Summer 2023. It covers key formulas and concepts, including distance, average speed, perimeter, area, and volume calculations for shapes like rectangles and circles. The document also details how to calculate the gradient of a line, geometric principles related to angles in straight lines, triangles, and polygons, and introduces Pythagoras' Theorem for right-angled triangles. Furthermore, it explains the calculation of the mean for a set of data, including estimated mean for grouped frequency distributions, and outlines the principles of pie charts and probability, ensuring comprehensive coverage of the foundational mathematics required for the examination.","General Certificate of Secondary Education Summer 2023  \nGCSE Mathematics  \nFOUNDATION TIER  \nADDITIONAL SUPPORT MATERIALS  \n(For use in Summer 2023)  \nFOUNDATION TIER ADDITIONAL SUPPORT MATERIALS (Summer 2023)  \nDistance Average Speed = Time  \n14099 FOUNDATION 2  \nPerimeter, Area and Volume  \nThe perimeter of a polygon is the distance around the outside of the polygon.  \nL  \nThe area of a rectangle is found by multiplying the length of the rectangle by the breadth. A = L × B, where A is the area, L is length and B is breadth.  \nThe volume of a cuboid is found by multiplying the length by the breadth by the height of the cuboid. V = L × B × H where V is volume, L is length, B is breadth and H is height.  \nThe area of a circle is A = πr2 where r is the radius of the circle.  \nGradient of Line  \n increase in vertical distance   \nGradient of line =  \nincrease in horizontal distance  \nGeometry and Angles  \nThere are 180° on a straight line.  \nThere are 180° inside a triangle.  \nAn isosceles triangle is a triangle with 2 equal sides and 2 equal angles.  \nThe sum of all the angles inside a polygon is given by 180(n – 2) where n is the number of sides in the polygon.  \n14099 FOUNDATION 3  \nPythagoras’Theorem  \nIf a, b and c are the sides of a right angled triangle shown below, then  \na2 + b2 = c2  \nb  \nMean  \nThe mean of a set of data is the sum of all the data values divided by the number of data values.  \nEstimate for the mean of a grouped frequency distribution  \nEstimated mean = sum of (mid interval values multiplied by their frequency) divided by the sum of all the frequencies.  \nPie Chart  \nIn a pie chart, the total angle that corresponds to the entire data set is 360°  \nProbability  \nThe sum of the probabilities of all outcomes equals 1  \n14099 FOUNDATION 4","cbCaihjOzyLxE1IE","https://ap.wps.com/l/cbCaihjOzyLxE1IE","pdf",215266,1,"English","en",105,"# GCSE Mathematics\n## FOUNDATION TIER\n### Perimeter, Area and Volume\n### Gradient of Line\n### Geometry and Angles\n### Pythagoras’ Theorem\n### Mean\n### Pie Chart\n### Probability","[{\"question\":\"What is the formula for the area of a rectangle?\",\"answer\":\"The area of a rectangle is found by multiplying its length by its breadth, represented as A = L × B.\"},{\"question\":\"How is the volume of a cuboid calculated?\",\"answer\":\"The volume of a cuboid is calculated by multiplying its length, breadth, and height: V = L × B × H.\"},{\"question\":\"What is the Pythagorean theorem?\",\"answer\":\"For a right-angled triangle with sides a, b, and c (where c is the hypotenuse), the Pythagorean theorem states that a² + b² = c².\"}]","GCSE Mathematics Additional Support Materials (Foundation Tier)-Summer 2023 | PDF",1788601136,10,{"code":4,"msg":30,"data":31},"ok",{"site_id":23,"language":22,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"gcse-mathematics-additional-support-materials-foundation-tier-summer-2023","",{"@graph":35,"@context":84},[36,52,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/exam/",3,{"item":51,"name":13,"@type":42,"position":11},"https://docshare.wps.com/document/gcse-mathematics-additional-support-materials-foundation-tier-summer-2023/207786/",{"url":51,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-09-06","2026-09-05",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What is the formula for the area of a rectangle?","Question",{"text":74,"@type":75},"The area of a rectangle is found by multiplying its length by its breadth, represented as A = L × B.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How is the volume of a cuboid calculated?",{"text":79,"@type":75},"The volume of a cuboid is calculated by multiplying its length, breadth, and height: V = L × B × H.",{"name":81,"@type":72,"acceptedAnswer":82},"What is the Pythagorean theorem?",{"text":83,"@type":75},"For a right-angled triangle with sides a, b, and c (where c is the hypotenuse), the Pythagorean theorem states that a² + b² = c².","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":23},{"code":4,"msg":5,"data":91},[92,96,100,103,108,113,118,123,128,131,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":101,"slug":102},70,"exam",{"id":104,"doc_module":4,"doc_module_name":45,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":109,"doc_module":4,"doc_module_name":45,"category_name":110,"show_sort_weight":111,"slug":112},6,"Technology",50,"technology",{"id":114,"doc_module":4,"doc_module_name":45,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":119,"doc_module":4,"doc_module_name":45,"category_name":120,"show_sort_weight":121,"slug":122},8,"Research & Report",30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":28,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":28,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":104,"slug":137},19,"General","general"]