{"id":9670,"date":"2024-11-08T13:22:19","date_gmt":"2024-11-08T13:22:19","guid":{"rendered":"https:\/\/mathsweekengland.co.uk\/?p=9670"},"modified":"2024-11-08T13:29:35","modified_gmt":"2024-11-08T13:29:35","slug":"ks4-solutions","status":"publish","type":"post","link":"https:\/\/mathsweekengland.co.uk\/?p=9670","title":{"rendered":"KS4 Solutions"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"9670\" class=\"elementor elementor-9670\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-790c56ba e-flex e-con-boxed e-con e-parent\" data-id=\"790c56ba\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-62b11eaf e-con-full e-flex e-con e-child\" data-id=\"62b11eaf\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-52420061 elementor-widget elementor-widget-heading\" data-id=\"52420061\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">2024 Daily Puzzles - Key Stage 4 Solutions<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6330898 elementor-widget elementor-widget-image\" data-id=\"6330898\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"768\" height=\"768\" src=\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4-768x768.png\" class=\"attachment-medium_large size-medium_large wp-image-9671\" alt=\"Monday: 28%. The areas of the three circles in cm2 are 9\u03c0, 16\u03c0 and 25\u03c0. The shaded area is 16\u03c0 \u2013 9\u03c0 = 7\u03c0, which is 7 \u00f7 25 = 28% of the area of the large circle. Tuesday: 9 ops. Work backwards: want to aim for 50 times 2 = 100 in as few steps as possible. So second to last step must be 25 times 2 = 50. To get to 25, 0 + 1 = 1; 1 times 2 = 2; 2 + 1 = 3; 3 times 2 = 6; 6 x 2 = 12; 12 times 2 = 24; 24 + 1 = 25; 25 times 2 = 50; 50 times 2 = 100&quot; Wednesday: 11 points Thursday: 10 kg. Friday: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 The sums are giving square numbers. So sum of the first n numbers will be n squared. As n squared = 2 704, n = square root of 2 704 = 52\" srcset=\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4-768x768.png 768w, https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4-300x300.png 300w, https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4-1024x1024.png 1024w, https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4-150x150.png 150w, https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4.png 1080w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>KS4 Solutions<\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_cbd_carousel_blocks":"[]","footnotes":""},"categories":[50,67,73,63,38],"tags":[],"class_list":["post-9670","post","type-post","status-publish","format-standard","hentry","category-50","category-2024-daily-puzzles","category-ks4-2024-daily-puzzles","category-ks4","category-primary"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>KS4 Solutions - Maths Week England<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathsweekengland.co.uk\/?p=9670\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KS4 Solutions - Maths Week England\" \/>\n<meta property=\"og:description\" content=\"KS4 Solutions\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathsweekengland.co.uk\/?p=9670\" \/>\n<meta property=\"og:site_name\" content=\"Maths Week England\" \/>\n<meta property=\"article:published_time\" content=\"2024-11-08T13:22:19+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-11-08T13:29:35+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1080\" \/>\n\t<meta property=\"og:image:height\" content=\"1080\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Sam Hartburn\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Sam Hartburn\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670\"},\"author\":{\"name\":\"Sam Hartburn\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/550ba1223e711011fb8439ae5c6df22b\"},\"headline\":\"KS4 Solutions\",\"datePublished\":\"2024-11-08T13:22:19+00:00\",\"dateModified\":\"2024-11-08T13:29:35+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670\"},\"wordCount\":8,\"publisher\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/#organization\"},\"image\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670#primaryimage\"},\"thumbnailUrl\":\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4-768x768.png\",\"articleSection\":[\"2024\",\"2024 Daily Puzzles\",\"KS4\",\"KS4\",\"Primary\"],\"inLanguage\":\"en-GB\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670\",\"url\":\"https:\/\/mathsweekengland.co.uk\/?p=9670\",\"name\":\"KS4 Solutions - Maths Week England\",\"isPartOf\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670#primaryimage\"},\"image\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670#primaryimage\"},\"thumbnailUrl\":\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4-768x768.png\",\"datePublished\":\"2024-11-08T13:22:19+00:00\",\"dateModified\":\"2024-11-08T13:29:35+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670#breadcrumb\"},\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathsweekengland.co.uk\/?p=9670\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670#primaryimage\",\"url\":\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4.png\",\"contentUrl\":\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4.png\",\"width\":1080,\"height\":1080,\"caption\":\"Monday: 28%. The areas of the three circles in cm2 are 9\u03c0, 16\u03c0 and 25\u03c0. The shaded area is 16\u03c0 \u2013 9\u03c0 = 7\u03c0, which is 7 \u00f7 25 = 28% of the area of the large circle. Tuesday: 9 ops. Work backwards: want to aim for 50 times 2 = 100 in as few steps as possible. So second to last step must be 25 times 2 = 50. To get to 25, 0 + 1 = 1; 1 times 2 = 2; 2 + 1 = 3; 3 times 2 = 6; 6 x 2 = 12; 12 times 2 = 24; 24 + 1 = 25; 25 times 2 = 50; 50 times 2 = 100\\\" Wednesday: 11 points Thursday: 10 kg. Friday: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 The sums are giving square numbers. So sum of the first n numbers will be n squared. As n squared = 2 704, n = square root of 2 704 = 52\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9670#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathsweekengland.co.uk\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"KS4 Solutions\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#website\",\"url\":\"https:\/\/mathsweekengland.co.uk\/\",\"name\":\"Maths Week England\",\"description\":\"11th - 17th November 2024\",\"publisher\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathsweekengland.co.uk\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-GB\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#organization\",\"name\":\"Maths Week England\",\"url\":\"https:\/\/mathsweekengland.co.uk\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2023\/09\/MWElogo.png\",\"contentUrl\":\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2023\/09\/MWElogo.png\",\"width\":1602,\"height\":946,\"caption\":\"Maths Week England\"},\"image\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/550ba1223e711011fb8439ae5c6df22b\",\"name\":\"Sam Hartburn\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/3e5422498c5d12df034b3437aea5b9998e45961ff6bf2db93ba2bfb566798119?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/3e5422498c5d12df034b3437aea5b9998e45961ff6bf2db93ba2bfb566798119?s=96&d=mm&r=g\",\"caption\":\"Sam Hartburn\"},\"url\":\"https:\/\/mathsweekengland.co.uk\/?author=11\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"KS4 Solutions - Maths Week England","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathsweekengland.co.uk\/?p=9670","og_locale":"en_GB","og_type":"article","og_title":"KS4 Solutions - Maths Week England","og_description":"KS4 Solutions","og_url":"https:\/\/mathsweekengland.co.uk\/?p=9670","og_site_name":"Maths Week England","article_published_time":"2024-11-08T13:22:19+00:00","article_modified_time":"2024-11-08T13:29:35+00:00","og_image":[{"width":1080,"height":1080,"url":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4.png","type":"image\/png"}],"author":"Sam Hartburn","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Sam Hartburn","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathsweekengland.co.uk\/?p=9670#article","isPartOf":{"@id":"https:\/\/mathsweekengland.co.uk\/?p=9670"},"author":{"name":"Sam Hartburn","@id":"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/550ba1223e711011fb8439ae5c6df22b"},"headline":"KS4 Solutions","datePublished":"2024-11-08T13:22:19+00:00","dateModified":"2024-11-08T13:29:35+00:00","mainEntityOfPage":{"@id":"https:\/\/mathsweekengland.co.uk\/?p=9670"},"wordCount":8,"publisher":{"@id":"https:\/\/mathsweekengland.co.uk\/#organization"},"image":{"@id":"https:\/\/mathsweekengland.co.uk\/?p=9670#primaryimage"},"thumbnailUrl":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4-768x768.png","articleSection":["2024","2024 Daily Puzzles","KS4","KS4","Primary"],"inLanguage":"en-GB"},{"@type":"WebPage","@id":"https:\/\/mathsweekengland.co.uk\/?p=9670","url":"https:\/\/mathsweekengland.co.uk\/?p=9670","name":"KS4 Solutions - Maths Week England","isPartOf":{"@id":"https:\/\/mathsweekengland.co.uk\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mathsweekengland.co.uk\/?p=9670#primaryimage"},"image":{"@id":"https:\/\/mathsweekengland.co.uk\/?p=9670#primaryimage"},"thumbnailUrl":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4-768x768.png","datePublished":"2024-11-08T13:22:19+00:00","dateModified":"2024-11-08T13:29:35+00:00","breadcrumb":{"@id":"https:\/\/mathsweekengland.co.uk\/?p=9670#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathsweekengland.co.uk\/?p=9670"]}]},{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/mathsweekengland.co.uk\/?p=9670#primaryimage","url":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4.png","contentUrl":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS4.png","width":1080,"height":1080,"caption":"Monday: 28%. The areas of the three circles in cm2 are 9\u03c0, 16\u03c0 and 25\u03c0. The shaded area is 16\u03c0 \u2013 9\u03c0 = 7\u03c0, which is 7 \u00f7 25 = 28% of the area of the large circle. Tuesday: 9 ops. Work backwards: want to aim for 50 times 2 = 100 in as few steps as possible. So second to last step must be 25 times 2 = 50. To get to 25, 0 + 1 = 1; 1 times 2 = 2; 2 + 1 = 3; 3 times 2 = 6; 6 x 2 = 12; 12 times 2 = 24; 24 + 1 = 25; 25 times 2 = 50; 50 times 2 = 100\" Wednesday: 11 points Thursday: 10 kg. Friday: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 The sums are giving square numbers. So sum of the first n numbers will be n squared. As n squared = 2 704, n = square root of 2 704 = 52"},{"@type":"BreadcrumbList","@id":"https:\/\/mathsweekengland.co.uk\/?p=9670#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathsweekengland.co.uk\/"},{"@type":"ListItem","position":2,"name":"KS4 Solutions"}]},{"@type":"WebSite","@id":"https:\/\/mathsweekengland.co.uk\/#website","url":"https:\/\/mathsweekengland.co.uk\/","name":"Maths Week England","description":"11th - 17th November 2024","publisher":{"@id":"https:\/\/mathsweekengland.co.uk\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathsweekengland.co.uk\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-GB"},{"@type":"Organization","@id":"https:\/\/mathsweekengland.co.uk\/#organization","name":"Maths Week England","url":"https:\/\/mathsweekengland.co.uk\/","logo":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/mathsweekengland.co.uk\/#\/schema\/logo\/image\/","url":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2023\/09\/MWElogo.png","contentUrl":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2023\/09\/MWElogo.png","width":1602,"height":946,"caption":"Maths Week England"},"image":{"@id":"https:\/\/mathsweekengland.co.uk\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/550ba1223e711011fb8439ae5c6df22b","name":"Sam Hartburn","image":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/3e5422498c5d12df034b3437aea5b9998e45961ff6bf2db93ba2bfb566798119?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/3e5422498c5d12df034b3437aea5b9998e45961ff6bf2db93ba2bfb566798119?s=96&d=mm&r=g","caption":"Sam Hartburn"},"url":"https:\/\/mathsweekengland.co.uk\/?author=11"}]}},"_links":{"self":[{"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/posts\/9670","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9670"}],"version-history":[{"count":6,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/posts\/9670\/revisions"}],"predecessor-version":[{"id":9681,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/posts\/9670\/revisions\/9681"}],"wp:attachment":[{"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}