Uncertainty Quick Reference | Flowxiom<\/title>\n<meta name=\"description\" content=\"Uncertainty Quick Reference \u2014 Edexcel A-level Physics WPH. \">\n<link rel=\"canonical\" href=\"https:\/\/flowxiom.com\/edexcel-physics-uncertainty-quick-reference\/\">\n<script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@type\": \"FAQPage\",\n \"mainEntity\": [\n {\n \"@type\": \"Question\",\n \"name\": \"Q1. \\\\(m = 50.0 \\\\pm 0.1\\\\text{ g}\\\\), \\\\(V = 20.0 \\\\pm 0.5\\\\text{ cm}^3\\\\). Find the percentage uncertainty in density \\\\(\\\\rho = m\/V\\\\).\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(\\\\%U_m = 0.1\/50.0 \\\\times 100\\\\% = 0.2\\\\%\\\\) \\n \\\\(\\\\%U_V = 0.5\/20.0 \\\\times 100\\\\% = 2.5\\\\%\\\\) \\n \\\\(\\\\%U_\\\\rho = 0.2\\\\% + 2.5\\\\% = \\\\mathbf{2.7\\\\%}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q2. Formula \\\\(\\\\rho = m\/d^3\\\\), \\\\(\\\\%U_m = 2\\\\%\\\\), \\\\(\\\\%U_d = 1\\\\%\\\\). Find \\\\(\\\\%U_\\\\rho\\\\).\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(\\\\%U_{d^3} = 3 \\\\times 1\\\\% = 3\\\\%\\\\) \\n \\\\(\\\\%U_\\\\rho = 2\\\\% + 3\\\\% = \\\\mathbf{5\\\\%}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q3. 20 oscillations timed as \\\\(t = 30.0 \\\\pm 0.2\\\\text{ s}\\\\). Find the absolute uncertainty in the period \\\\(T\\\\).\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(T = 30.0\/20 = 1.50\\\\text{ s}\\\\) \\n \\\\(\\\\Delta T = 0.2\/20 = \\\\mathbf{0.01\\\\text{ s}}\\\\) \\n Write as: \\\\(T = 1.50 \\\\pm 0.01\\\\text{ s}\\\\)\"\n }\n }\n ]\n}\n<\/script>\n\n<script>\nMathJax = {\n tex: { inlineMath: [['\\\\(','\\\\)']], displayMath: [['\\\\[','\\\\]']] },\n svg: { fontCache: 'global' }\n};\n<\/script>\n<script async src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-svg.js\"><\/script>\n\n<style>\n:root{--accent:#2563eb;--warn-bg:#fef9c3;--warn-border:#ca8a04;--formula-bg:#eff6ff;--formula-border:#2563eb;}\nbody{font-family:system-ui,sans-serif;max-width:860px;margin:0 auto;padding:1.5rem;line-height:1.7;color:#1e293b;}\nh1{font-size:2rem;border-bottom:3px solid var(--accent);padding-bottom:.4rem;}\nh2{font-size:1.4rem;color:var(--accent);margin-top:2rem;}\nh3{font-size:1.1rem;margin-top:1.4rem;}\ntable{border-collapse:collapse;width:100%;margin:1rem 0;}\nth,td{border:1px solid #cbd5e1;padding:.5rem .75rem;text-align:left;}\nth{background:#e2e8f0;}\npre,code{background:#f1f5f9;border-radius:4px;}\npre{padding:1rem;overflow-x:auto;}\ncode{padding:.1rem .3rem;font-size:.9em;}\n.seo-warning-box{background:var(--warn-bg);border-left:4px solid var(--warn-border);padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\n.seo-note-box{background:#f0fdf4;border-left:4px solid #16a34a;padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\nsection.formula-card{background:var(--formula-bg);border:1px solid var(--formula-border);border-radius:8px;padding:1rem 1.25rem;margin:1.5rem 0;}\ndetails{border:1px solid #e2e8f0;border-radius:6px;padding:.5rem 1rem;margin:.75rem 0;}\nsummary{cursor:pointer;font-weight:600;}\n.answer-block{margin-top:.5rem;padding-top:.5rem;border-top:1px solid #e2e8f0;overflow-x:auto;}\n.answer-block p{margin:.25rem 0;}\n.numbered-step{padding-left:1.5rem;position:relative;}\nhr{border:none;border-top:1px solid #e2e8f0;margin:2rem 0;}\n.toc{background:#f8fafc;border:1px solid #e2e8f0;border-radius:8px;padding:1rem 1.5rem;margin-bottom:2rem;}\n.toc h2{margin-top:0;font-size:1.1rem;}\n.toc ul{margin:0;padding-left:1.2rem;}\n.toc a{color:var(--accent);text-decoration:none;}\n.site-footer{margin-top:3rem;padding-top:1rem;border-top:2px solid var(--accent);font-size:.9rem;color:#64748b;}\n<\/style>\n<\/head>\n<body>\n<nav class=\"toc\"><h2>Contents<\/h2><ul>\n <li><a href=\"#key-concepts\">Key Concepts<\/a><\/li>\n <li><a href=\"#estimating-uncertainty\">Estimating Uncertainty<\/a><\/li>\n <li><a href=\"#propagation-rules\">Propagation Rules<\/a><\/li>\n <li><a href=\"#summary-table\">Summary Table<\/a><\/li>\n <li><a href=\"#answer-format\">Answer Format<\/a><\/li>\n <li><a href=\"#graph-uncertainties-wph13-wph16\">Graph Uncertainties (WPH13 & WPH16)<\/a><\/li>\n <li><a href=\"#judging-experimental-success\">Judging Experimental Success<\/a><\/li>\n <li><a href=\"#practice-questions\">Practice Questions<\/a><\/li>\n<\/ul><\/nav>\n<h1>Uncertainty Quick Reference<\/h1>\n<p><strong>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<\/strong><\/p>\n<p><em>Not everything. Just what’s on the paper. High-frequency topics only \u2014 covering ~80% of exam marks.<\/em><\/p>\n<p>Every paper \u2014 pure format marks \u2014 memorise and collect them.<\/p>\n<hr>\n<h2 id=\"key-concepts\">Key Concepts<\/h2>\n<table>\n<thead><tr><th>Term<\/th><th>Meaning<\/th><\/tr><\/thead>\n<tr><td><strong>Random error<\/strong><\/td><td>Scatter randomly above\/below the true value \u2192 reduced by averaging repeated measurements<\/td><\/tr>\n<tr><td><strong>Systematic error<\/strong><\/td><td>Always offset in the same direction \u2192 cannot be reduced by repetition; must change the instrument or experimental design<\/td><\/tr>\n<tr><td><strong>Accuracy<\/strong><\/td><td>How close a measurement is to the true value \u2014 affected by systematic error<\/td><\/tr>\n<tr><td><strong>Precision<\/strong><\/td><td>How close repeated measurements are to each other \u2014 affected by random error<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\">\n<p>\u26a0\ufe0f Most common mistake: claiming that repetition reduces systematic error \u2014 it does <strong>NOT<\/strong>.<\/p>\n<\/div>\n<hr>\n<h2 id=\"estimating-uncertainty\">Estimating Uncertainty<\/h2>\n<table>\n<thead><tr><th>Situation<\/th><th>Method<\/th><\/tr><\/thead>\n<tr><td>Single reading<\/td><td>\\(\\Delta x = \\pm\\) half the smallest scale division (or one full division \u2014 follow question context)<\/td><\/tr>\n<tr><td>Repeated readings<\/td><td>\\(\\Delta x = \\dfrac{x_{max} – x_{min}}{2}\\)<\/td><\/tr>\n<\/table>\n\n<hr>\n<h2 id=\"propagation-rules\">Propagation Rules<\/h2>\n<h3 id=\"addition-subtraction-add-absolute-uncertainties\">Addition \/ Subtraction \u2192 Add absolute uncertainties<\/h3>\n<p>\\[y = a + b \\quad \\text{or} \\quad y = a – b\\]<\/p>\n<p>\\[\\Delta y = \\Delta a + \\Delta b\\]<\/p>\n<div class=\"seo-warning-box\">\n<p>\u26a0\ufe0f When <strong>subtracting<\/strong> quantities, you still <strong>ADD<\/strong> their uncertainties.<\/p>\n<p>Example: temperature difference \\(\\Delta\\theta = \\theta_2 – \\theta_1\\), uncertainty \\(= \\Delta\\theta_1 + \\Delta\\theta_2\\)<\/p>\n<\/div>\n<hr>\n<h3 id=\"multiplication-division-add-percentage-uncertainties\">Multiplication \/ Division \u2192 Add percentage uncertainties<\/h3>\n<p>\\[y = ab \\quad \\text{or} \\quad y = \\frac{a}{b}\\]<\/p>\n<p>\\[\\%U_y = \\%U_a + \\%U_b \\quad \\text{where} \\quad \\%U_a = \\frac{\\Delta a}{a} \\times 100\\%\\]<\/p>\n<hr>\n<h3 id=\"powers-multiply-percentage-uncertainty-by-the-index\">Powers \u2192 Multiply percentage uncertainty by the index<\/h3>\n<p>\\[y = a^n\\]<\/p>\n<p>\\[\\%U_y = n \\times \\%U_a\\]<\/p>\n<div class=\"seo-note-box\">\n<p>Example: volume \\(V = \\frac{4}{3}\\pi r^3\\) \u2014 if \\(r\\) has 2% uncertainty, then \\(V\\) has \\(3 \\times 2\\% = 6\\%\\) uncertainty.<\/p>\n<\/div>\n<hr>\n<h3 id=\"constants-carry-no-uncertainty\">Constants carry no uncertainty<\/h3>\n<p>Known constants such as \\(\\pi\\) and \\(g\\) contribute zero uncertainty.<\/p>\n<hr>\n<h2 id=\"summary-table\">Summary Table<\/h2>\n<table>\n<thead><tr><th>Operation<\/th><th>Which type<\/th><th>Rule<\/th><\/tr><\/thead>\n<tr><td>Add \/ Subtract<\/td><td><strong>Absolute<\/strong><\/td><td>Add directly<\/td><\/tr>\n<tr><td>Multiply \/ Divide<\/td><td><strong>Percentage<\/strong><\/td><td>Add directly<\/td><\/tr>\n<tr><td>Power \\(a^n\\)<\/td><td><strong>Percentage<\/strong><\/td><td>Multiply by index \\(n\\)<\/td><\/tr>\n<tr><td>Mean<\/td><td><strong>Absolute<\/strong><\/td><td>Range \u00f7 2<\/td><\/tr>\n<\/table>\n\n<hr>\n<h2 id=\"answer-format\">Answer Format<\/h2>\n<p><strong>Correct format:<\/strong><\/p>\n<p>\\[L = 1.50 \\pm 0.02 \\text{ m}\\]<\/p>\n<p><strong>Common errors:<\/strong><\/p>\n<ul>\n<li>\u274c \\(L = 1.5 \\pm 0.02\\) m \u2014 decimal places of value and uncertainty don’t match<\/li>\n<li>\u274c \\(L = 1.50 \\pm 0.023\\) m \u2014 uncertainty given to too many significant figures<\/li>\n<li>\u274c \\(L = 1.504 \\pm 0.02\\) m \u2014 result is more precise than the uncertainty<\/li>\n<\/ul>\n<p><strong>Rules:<\/strong><\/p>\n<p class=\"numbered-step\">Uncertainty: <strong>1 significant figure<\/strong> (occasionally 2)<\/p>\n<p class=\"numbered-step\">Decimal places of result must <strong>match<\/strong> those of the uncertainty<\/p>\n<hr>\n<h2 id=\"graph-uncertainties-wph13-wph16\">Graph Uncertainties (WPH13 & WPH16)<\/h2>\n<p><strong>Error bars:<\/strong> Plot error bars on the graph to show the uncertainty range for each data point.<\/p>\n<p><strong>Max-min gradient method:<\/strong><\/p>\n<p class=\"numbered-step\">Draw all error bars<\/p>\n<p class=\"numbered-step\">Draw the <strong>steepest<\/strong> possible line through all error bars \u2192 maximum gradient \\(k_{max}\\)<\/p>\n<p class=\"numbered-step\">Draw the <strong>shallowest<\/strong> possible line \u2192 minimum gradient \\(k_{min}\\)<\/p>\n<p class=\"numbered-step\">Uncertainty in gradient: \\(\\Delta k = \\dfrac{k_{max} – k_{min}}{2}\\)<\/p>\n<hr>\n<h2 id=\"judging-experimental-success\">Judging Experimental Success<\/h2>\n<p>\\[|\\text{experimental value} – \\text{theoretical value}| < \\text{total uncertainty}\\]<\/p>\n<p>If the condition is satisfied, write:<\/p>\n<p><em>“The result is consistent with the theoretical value within experimental uncertainty.”<\/em><\/p>\n<hr>\n<h2 id=\"practice-questions\">Practice Questions<\/h2>\n<p><strong>Q1.<\/strong> \\(m = 50.0 \\pm 0.1\\text{ g}\\), \\(V = 20.0 \\pm 0.5\\text{ cm}^3\\). Find the percentage uncertainty in density \\(\\rho = m\/V\\).<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(\\%U_m = 0.1\/50.0 \\times 100\\% = 0.2\\%\\)<\/p>\n<p>\\(\\%U_V = 0.5\/20.0 \\times 100\\% = 2.5\\%\\)<\/p>\n<p>\\(\\%U_\\rho = 0.2\\% + 2.5\\% = \\mathbf{2.7\\%}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q2.<\/strong> Formula \\(\\rho = m\/d^3\\), \\(\\%U_m = 2\\%\\), \\(\\%U_d = 1\\%\\). Find \\(\\%U_\\rho\\).<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(\\%U_{d^3} = 3 \\times 1\\% = 3\\%\\)<\/p>\n<p>\\(\\%U_\\rho = 2\\% + 3\\% = \\mathbf{5\\%}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q3.<\/strong> 20 oscillations timed as \\(t = 30.0 \\pm 0.2\\text{ s}\\). Find the absolute uncertainty in the period \\(T\\).<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(T = 30.0\/20 = 1.50\\text{ s}\\)<\/p>\n<p>\\(\\Delta T = 0.2\/20 = \\mathbf{0.01\\text{ s}}\\)<\/p>\n<p>Write as: \\(T = 1.50 \\pm 0.01\\text{ s}\\)<\/p><\/div><\/details>\n<hr>\n<p><em>Want more? Visit <a href=\"https:\/\/flowxiom.com\">flowxiom.com<\/a><\/em><\/p>\n<footer class=\"site-footer\">\n <p>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<br>\n High-frequency topics only, covering ~80% of exam marks.<\/p>\n<\/footer>\n<\/body>\n<\/html>\n\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Master 80% of uncertainty exam marks with Flowxiom\u2019s “Uncertainty Quick Reference” for Edexcel A-level Physics. This guide simplifies complex propagation rules, error analysis, and graph uncertainties into easy-to-memorize formats. Perfect for quick revision and ensuring perfect format marks on your physics papers!<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-28","post","type-post","status-publish","format-standard","hentry","category-exam-sprint-pack-physics-exam-sprint-pack"],"_links":{"self":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/28","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/comments?post=28"}],"version-history":[{"count":3,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/28\/revisions"}],"predecessor-version":[{"id":32,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/28\/revisions\/32"}],"wp:attachment":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/media?parent=28"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/categories?post=28"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/tags?post=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":28,"date":"2026-04-17T15:39:27","date_gmt":"2026-04-17T15:39:27","guid":{"rendered":"https:\/\/flowxiom.com\/?p=28"},"modified":"2026-04-17T16:06:18","modified_gmt":"2026-04-17T16:06:18","slug":"uncertainty-quick-reference","status":"publish","type":"post","link":"https:\/\/flowxiom.com\/index.php\/2026\/04\/17\/uncertainty-quick-reference\/","title":{"rendered":"Uncertainty Quick Reference"},"content":{"rendered":"\n\n\n\n\n\nUncertainty Quick Reference | Flowxiom<\/title>\n<meta name=\"description\" content=\"Uncertainty Quick Reference \u2014 Edexcel A-level Physics WPH. \">\n<link rel=\"canonical\" href=\"https:\/\/flowxiom.com\/edexcel-physics-uncertainty-quick-reference\/\">\n<script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@type\": \"FAQPage\",\n \"mainEntity\": [\n {\n \"@type\": \"Question\",\n \"name\": \"Q1. \\\\(m = 50.0 \\\\pm 0.1\\\\text{ g}\\\\), \\\\(V = 20.0 \\\\pm 0.5\\\\text{ cm}^3\\\\). Find the percentage uncertainty in density \\\\(\\\\rho = m\/V\\\\).\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(\\\\%U_m = 0.1\/50.0 \\\\times 100\\\\% = 0.2\\\\%\\\\) \\n \\\\(\\\\%U_V = 0.5\/20.0 \\\\times 100\\\\% = 2.5\\\\%\\\\) \\n \\\\(\\\\%U_\\\\rho = 0.2\\\\% + 2.5\\\\% = \\\\mathbf{2.7\\\\%}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q2. Formula \\\\(\\\\rho = m\/d^3\\\\), \\\\(\\\\%U_m = 2\\\\%\\\\), \\\\(\\\\%U_d = 1\\\\%\\\\). Find \\\\(\\\\%U_\\\\rho\\\\).\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(\\\\%U_{d^3} = 3 \\\\times 1\\\\% = 3\\\\%\\\\) \\n \\\\(\\\\%U_\\\\rho = 2\\\\% + 3\\\\% = \\\\mathbf{5\\\\%}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q3. 20 oscillations timed as \\\\(t = 30.0 \\\\pm 0.2\\\\text{ s}\\\\). Find the absolute uncertainty in the period \\\\(T\\\\).\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(T = 30.0\/20 = 1.50\\\\text{ s}\\\\) \\n \\\\(\\\\Delta T = 0.2\/20 = \\\\mathbf{0.01\\\\text{ s}}\\\\) \\n Write as: \\\\(T = 1.50 \\\\pm 0.01\\\\text{ s}\\\\)\"\n }\n }\n ]\n}\n<\/script>\n\n<script>\nMathJax = {\n tex: { inlineMath: [['\\\\(','\\\\)']], displayMath: [['\\\\[','\\\\]']] },\n svg: { fontCache: 'global' }\n};\n<\/script>\n<script async src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-svg.js\"><\/script>\n\n<style>\n:root{--accent:#2563eb;--warn-bg:#fef9c3;--warn-border:#ca8a04;--formula-bg:#eff6ff;--formula-border:#2563eb;}\nbody{font-family:system-ui,sans-serif;max-width:860px;margin:0 auto;padding:1.5rem;line-height:1.7;color:#1e293b;}\nh1{font-size:2rem;border-bottom:3px solid var(--accent);padding-bottom:.4rem;}\nh2{font-size:1.4rem;color:var(--accent);margin-top:2rem;}\nh3{font-size:1.1rem;margin-top:1.4rem;}\ntable{border-collapse:collapse;width:100%;margin:1rem 0;}\nth,td{border:1px solid #cbd5e1;padding:.5rem .75rem;text-align:left;}\nth{background:#e2e8f0;}\npre,code{background:#f1f5f9;border-radius:4px;}\npre{padding:1rem;overflow-x:auto;}\ncode{padding:.1rem .3rem;font-size:.9em;}\n.seo-warning-box{background:var(--warn-bg);border-left:4px solid var(--warn-border);padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\n.seo-note-box{background:#f0fdf4;border-left:4px solid #16a34a;padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\nsection.formula-card{background:var(--formula-bg);border:1px solid var(--formula-border);border-radius:8px;padding:1rem 1.25rem;margin:1.5rem 0;}\ndetails{border:1px solid #e2e8f0;border-radius:6px;padding:.5rem 1rem;margin:.75rem 0;}\nsummary{cursor:pointer;font-weight:600;}\n.answer-block{margin-top:.5rem;padding-top:.5rem;border-top:1px solid #e2e8f0;overflow-x:auto;}\n.answer-block p{margin:.25rem 0;}\n.numbered-step{padding-left:1.5rem;position:relative;}\nhr{border:none;border-top:1px solid #e2e8f0;margin:2rem 0;}\n.toc{background:#f8fafc;border:1px solid #e2e8f0;border-radius:8px;padding:1rem 1.5rem;margin-bottom:2rem;}\n.toc h2{margin-top:0;font-size:1.1rem;}\n.toc ul{margin:0;padding-left:1.2rem;}\n.toc a{color:var(--accent);text-decoration:none;}\n.site-footer{margin-top:3rem;padding-top:1rem;border-top:2px solid var(--accent);font-size:.9rem;color:#64748b;}\n<\/style>\n<\/head>\n<body>\n<nav class=\"toc\"><h2>Contents<\/h2><ul>\n <li><a href=\"#key-concepts\">Key Concepts<\/a><\/li>\n <li><a href=\"#estimating-uncertainty\">Estimating Uncertainty<\/a><\/li>\n <li><a href=\"#propagation-rules\">Propagation Rules<\/a><\/li>\n <li><a href=\"#summary-table\">Summary Table<\/a><\/li>\n <li><a href=\"#answer-format\">Answer Format<\/a><\/li>\n <li><a href=\"#graph-uncertainties-wph13-wph16\">Graph Uncertainties (WPH13 & WPH16)<\/a><\/li>\n <li><a href=\"#judging-experimental-success\">Judging Experimental Success<\/a><\/li>\n <li><a href=\"#practice-questions\">Practice Questions<\/a><\/li>\n<\/ul><\/nav>\n<h1>Uncertainty Quick Reference<\/h1>\n<p><strong>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<\/strong><\/p>\n<p><em>Not everything. Just what’s on the paper. High-frequency topics only \u2014 covering ~80% of exam marks.<\/em><\/p>\n<p>Every paper \u2014 pure format marks \u2014 memorise and collect them.<\/p>\n<hr>\n<h2 id=\"key-concepts\">Key Concepts<\/h2>\n<table>\n<thead><tr><th>Term<\/th><th>Meaning<\/th><\/tr><\/thead>\n<tr><td><strong>Random error<\/strong><\/td><td>Scatter randomly above\/below the true value \u2192 reduced by averaging repeated measurements<\/td><\/tr>\n<tr><td><strong>Systematic error<\/strong><\/td><td>Always offset in the same direction \u2192 cannot be reduced by repetition; must change the instrument or experimental design<\/td><\/tr>\n<tr><td><strong>Accuracy<\/strong><\/td><td>How close a measurement is to the true value \u2014 affected by systematic error<\/td><\/tr>\n<tr><td><strong>Precision<\/strong><\/td><td>How close repeated measurements are to each other \u2014 affected by random error<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\">\n<p>\u26a0\ufe0f Most common mistake: claiming that repetition reduces systematic error \u2014 it does <strong>NOT<\/strong>.<\/p>\n<\/div>\n<hr>\n<h2 id=\"estimating-uncertainty\">Estimating Uncertainty<\/h2>\n<table>\n<thead><tr><th>Situation<\/th><th>Method<\/th><\/tr><\/thead>\n<tr><td>Single reading<\/td><td>\\(\\Delta x = \\pm\\) half the smallest scale division (or one full division \u2014 follow question context)<\/td><\/tr>\n<tr><td>Repeated readings<\/td><td>\\(\\Delta x = \\dfrac{x_{max} – x_{min}}{2}\\)<\/td><\/tr>\n<\/table>\n\n<hr>\n<h2 id=\"propagation-rules\">Propagation Rules<\/h2>\n<h3 id=\"addition-subtraction-add-absolute-uncertainties\">Addition \/ Subtraction \u2192 Add absolute uncertainties<\/h3>\n<p>\\[y = a + b \\quad \\text{or} \\quad y = a – b\\]<\/p>\n<p>\\[\\Delta y = \\Delta a + \\Delta b\\]<\/p>\n<div class=\"seo-warning-box\">\n<p>\u26a0\ufe0f When <strong>subtracting<\/strong> quantities, you still <strong>ADD<\/strong> their uncertainties.<\/p>\n<p>Example: temperature difference \\(\\Delta\\theta = \\theta_2 – \\theta_1\\), uncertainty \\(= \\Delta\\theta_1 + \\Delta\\theta_2\\)<\/p>\n<\/div>\n<hr>\n<h3 id=\"multiplication-division-add-percentage-uncertainties\">Multiplication \/ Division \u2192 Add percentage uncertainties<\/h3>\n<p>\\[y = ab \\quad \\text{or} \\quad y = \\frac{a}{b}\\]<\/p>\n<p>\\[\\%U_y = \\%U_a + \\%U_b \\quad \\text{where} \\quad \\%U_a = \\frac{\\Delta a}{a} \\times 100\\%\\]<\/p>\n<hr>\n<h3 id=\"powers-multiply-percentage-uncertainty-by-the-index\">Powers \u2192 Multiply percentage uncertainty by the index<\/h3>\n<p>\\[y = a^n\\]<\/p>\n<p>\\[\\%U_y = n \\times \\%U_a\\]<\/p>\n<div class=\"seo-note-box\">\n<p>Example: volume \\(V = \\frac{4}{3}\\pi r^3\\) \u2014 if \\(r\\) has 2% uncertainty, then \\(V\\) has \\(3 \\times 2\\% = 6\\%\\) uncertainty.<\/p>\n<\/div>\n<hr>\n<h3 id=\"constants-carry-no-uncertainty\">Constants carry no uncertainty<\/h3>\n<p>Known constants such as \\(\\pi\\) and \\(g\\) contribute zero uncertainty.<\/p>\n<hr>\n<h2 id=\"summary-table\">Summary Table<\/h2>\n<table>\n<thead><tr><th>Operation<\/th><th>Which type<\/th><th>Rule<\/th><\/tr><\/thead>\n<tr><td>Add \/ Subtract<\/td><td><strong>Absolute<\/strong><\/td><td>Add directly<\/td><\/tr>\n<tr><td>Multiply \/ Divide<\/td><td><strong>Percentage<\/strong><\/td><td>Add directly<\/td><\/tr>\n<tr><td>Power \\(a^n\\)<\/td><td><strong>Percentage<\/strong><\/td><td>Multiply by index \\(n\\)<\/td><\/tr>\n<tr><td>Mean<\/td><td><strong>Absolute<\/strong><\/td><td>Range \u00f7 2<\/td><\/tr>\n<\/table>\n\n<hr>\n<h2 id=\"answer-format\">Answer Format<\/h2>\n<p><strong>Correct format:<\/strong><\/p>\n<p>\\[L = 1.50 \\pm 0.02 \\text{ m}\\]<\/p>\n<p><strong>Common errors:<\/strong><\/p>\n<ul>\n<li>\u274c \\(L = 1.5 \\pm 0.02\\) m \u2014 decimal places of value and uncertainty don’t match<\/li>\n<li>\u274c \\(L = 1.50 \\pm 0.023\\) m \u2014 uncertainty given to too many significant figures<\/li>\n<li>\u274c \\(L = 1.504 \\pm 0.02\\) m \u2014 result is more precise than the uncertainty<\/li>\n<\/ul>\n<p><strong>Rules:<\/strong><\/p>\n<p class=\"numbered-step\">Uncertainty: <strong>1 significant figure<\/strong> (occasionally 2)<\/p>\n<p class=\"numbered-step\">Decimal places of result must <strong>match<\/strong> those of the uncertainty<\/p>\n<hr>\n<h2 id=\"graph-uncertainties-wph13-wph16\">Graph Uncertainties (WPH13 & WPH16)<\/h2>\n<p><strong>Error bars:<\/strong> Plot error bars on the graph to show the uncertainty range for each data point.<\/p>\n<p><strong>Max-min gradient method:<\/strong><\/p>\n<p class=\"numbered-step\">Draw all error bars<\/p>\n<p class=\"numbered-step\">Draw the <strong>steepest<\/strong> possible line through all error bars \u2192 maximum gradient \\(k_{max}\\)<\/p>\n<p class=\"numbered-step\">Draw the <strong>shallowest<\/strong> possible line \u2192 minimum gradient \\(k_{min}\\)<\/p>\n<p class=\"numbered-step\">Uncertainty in gradient: \\(\\Delta k = \\dfrac{k_{max} – k_{min}}{2}\\)<\/p>\n<hr>\n<h2 id=\"judging-experimental-success\">Judging Experimental Success<\/h2>\n<p>\\[|\\text{experimental value} – \\text{theoretical value}| < \\text{total uncertainty}\\]<\/p>\n<p>If the condition is satisfied, write:<\/p>\n<p><em>“The result is consistent with the theoretical value within experimental uncertainty.”<\/em><\/p>\n<hr>\n<h2 id=\"practice-questions\">Practice Questions<\/h2>\n<p><strong>Q1.<\/strong> \\(m = 50.0 \\pm 0.1\\text{ g}\\), \\(V = 20.0 \\pm 0.5\\text{ cm}^3\\). Find the percentage uncertainty in density \\(\\rho = m\/V\\).<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(\\%U_m = 0.1\/50.0 \\times 100\\% = 0.2\\%\\)<\/p>\n<p>\\(\\%U_V = 0.5\/20.0 \\times 100\\% = 2.5\\%\\)<\/p>\n<p>\\(\\%U_\\rho = 0.2\\% + 2.5\\% = \\mathbf{2.7\\%}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q2.<\/strong> Formula \\(\\rho = m\/d^3\\), \\(\\%U_m = 2\\%\\), \\(\\%U_d = 1\\%\\). Find \\(\\%U_\\rho\\).<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(\\%U_{d^3} = 3 \\times 1\\% = 3\\%\\)<\/p>\n<p>\\(\\%U_\\rho = 2\\% + 3\\% = \\mathbf{5\\%}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q3.<\/strong> 20 oscillations timed as \\(t = 30.0 \\pm 0.2\\text{ s}\\). Find the absolute uncertainty in the period \\(T\\).<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(T = 30.0\/20 = 1.50\\text{ s}\\)<\/p>\n<p>\\(\\Delta T = 0.2\/20 = \\mathbf{0.01\\text{ s}}\\)<\/p>\n<p>Write as: \\(T = 1.50 \\pm 0.01\\text{ s}\\)<\/p><\/div><\/details>\n<hr>\n<p><em>Want more? Visit <a href=\"https:\/\/flowxiom.com\">flowxiom.com<\/a><\/em><\/p>\n<footer class=\"site-footer\">\n <p>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<br>\n High-frequency topics only, covering ~80% of exam marks.<\/p>\n<\/footer>\n<\/body>\n<\/html>\n\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Master 80% of uncertainty exam marks with Flowxiom\u2019s “Uncertainty Quick Reference” for Edexcel A-level Physics. This guide simplifies complex propagation rules, error analysis, and graph uncertainties into easy-to-memorize formats. Perfect for quick revision and ensuring perfect format marks on your physics papers!<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-28","post","type-post","status-publish","format-standard","hentry","category-exam-sprint-pack-physics-exam-sprint-pack"],"_links":{"self":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/28","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/comments?post=28"}],"version-history":[{"count":3,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/28\/revisions"}],"predecessor-version":[{"id":32,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/28\/revisions\/32"}],"wp:attachment":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/media?parent=28"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/categories?post=28"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/tags?post=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}