// Numbas version: exam_results_page_options
{"name": "Difference tables", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "extensions": [], "ungrouped_variables": ["x0", "stp", "x1", "x2", "x3", "x4", "x5", "x6", "x7", "a", "b", "c", "d", "y0", "y1", "y2", "y3", "y4", "y5", "y6", "y7", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d20", "d21", "d22", "d23", "d24", "d25", "d30", "d31", "d32"], "tags": [], "advice": "<p>The difference table should take the form:</p>\n<p style=\"padding-left: 60px;\">\\(\\begin{matrix} {x}&amp;{f(x)}&amp;\\delta_1&amp;\\delta_2&amp;\\delta_3 \\\\ \\var{x0}&amp;\\var{y0}&amp;\\var{d10}&amp;\\var{d20}&amp;\\var{d30}\\\\\\var{x1}&amp;\\var{y1}&amp;\\var{d11}&amp;\\var{d21}&amp;\\var{d31}\\\\\\var{x2}&amp;\\var{y2}&amp;\\var{d12}&amp;\\var{d22}&amp;\\var{d32}\\\\\\var{x3}&amp;\\var{y3}&amp;\\var{d13}&amp;\\var{d23}&amp;\\var{d32}\\\\\\var{x4}&amp;\\var{y4}&amp;\\var{d14}&amp;\\var{d24}&amp;\\var{d32}\\\\\\var{x5}&amp;\\var{y5}&amp;\\var{d15}&amp;\\var{d25}\\\\\\var{x6}&amp;\\var{y6}&amp;\\var{d16}\\\\\\var{x7}&amp;\\var{y7}\\\\\\end{matrix}\\)</p>\n<p>All the 3rd differences equal the constant \\(\\var{d32}\\)</p>\n<p>The coefficient of \\(x^3\\) is given by the formula: &nbsp; \\(a=\\frac{constant}{3!*(step-size)^3}\\)</p>\n<p style=\"padding-left: 30px;\">\\(a=\\frac{\\var{d32}}{3!*(\\var{stp})^3}=\\var{a}\\)</p>", "rulesets": {}, "functions": {}, "variables": {"d14": {"description": "", "name": "d14", "group": "Ungrouped variables", "definition": "y5-y4", "templateType": "anything"}, "y4": {"description": "", "name": "y4", "group": "Ungrouped variables", "definition": "a*x4^3+b*x4^2+c*x4+d", "templateType": "anything"}, "a": {"description": "", "name": "a", "group": "Ungrouped variables", "definition": "random(2..7#1)", "templateType": "randrange"}, "d25": {"description": "", "name": "d25", "group": "Ungrouped variables", "definition": "d16-d15", "templateType": "anything"}, "d13": {"description": "", "name": "d13", "group": "Ungrouped variables", "definition": "y4-y3", "templateType": "anything"}, "stp": {"description": "", "name": "stp", "group": "Ungrouped variables", "definition": "random(0.1..1#0.1)", "templateType": "randrange"}, "x7": {"description": "", "name": "x7", "group": "Ungrouped variables", "definition": "x6+stp", "templateType": "anything"}, "d24": {"description": "", "name": "d24", "group": "Ungrouped variables", "definition": "d15-d14", "templateType": "anything"}, "d32": {"description": "", "name": "d32", "group": "Ungrouped variables", "definition": "d23-d22", "templateType": "anything"}, "x6": {"description": "", "name": "x6", "group": "Ungrouped variables", "definition": "x5+stp", "templateType": "anything"}, "d": {"description": "", "name": "d", "group": "Ungrouped variables", "definition": "random(6..24#1)", "templateType": "randrange"}, "y0": {"description": "", "name": "y0", "group": "Ungrouped variables", "definition": "a*x0^3+b*x0^2+c*x0+d", "templateType": "anything"}, "d30": {"description": "", "name": "d30", "group": "Ungrouped variables", "definition": "d21-d20", "templateType": "anything"}, "y2": {"description": "", "name": "y2", "group": "Ungrouped variables", "definition": "a*x2^3+b*x2^2+c*x2+d", "templateType": "anything"}, "d12": {"description": "", "name": "d12", "group": "Ungrouped variables", "definition": "y3-y2", "templateType": "anything"}, "d10": {"description": "", "name": "d10", "group": "Ungrouped variables", "definition": "y1-y0", "templateType": "anything"}, "y7": {"description": "", "name": "y7", "group": "Ungrouped variables", "definition": "a*x7^3+b*x7^2+c*x7+d", "templateType": "anything"}, "y1": {"description": "", "name": "y1", "group": "Ungrouped variables", "definition": "a*x1^3+b*x1^2+c*x1+d", "templateType": "anything"}, "y6": {"description": "", "name": "y6", "group": "Ungrouped variables", "definition": "a*x6^3+b*x6^2+c*x6+d", "templateType": "anything"}, "y3": {"description": "", "name": "y3", "group": "Ungrouped variables", "definition": "a*x3^3+b*x3^2+c*x3+d", "templateType": "anything"}, "d21": {"description": "", "name": "d21", "group": "Ungrouped variables", "definition": "d12-d11", "templateType": "anything"}, "d23": {"description": "", "name": "d23", "group": "Ungrouped variables", "definition": "d14-d13", "templateType": "anything"}, "x2": {"description": "", "name": "x2", "group": "Ungrouped variables", "definition": "x1+stp", "templateType": "anything"}, "d11": {"description": "", "name": "d11", "group": "Ungrouped variables", "definition": "y2-y1\n", "templateType": "anything"}, "d15": {"description": "", "name": "d15", "group": "Ungrouped variables", "definition": "y6-y5", "templateType": "anything"}, "b": {"description": "", "name": "b", "group": "Ungrouped variables", "definition": "random(-12..10#1)", "templateType": "randrange"}, "y5": {"description": "", "name": "y5", "group": "Ungrouped variables", "definition": "a*x5^3+b*x5^2+c*x5+d", "templateType": "anything"}, "x1": {"description": "", "name": "x1", "group": "Ungrouped variables", "definition": "x0+stp", "templateType": "anything"}, "x0": {"description": "", "name": "x0", "group": "Ungrouped variables", "definition": "random(0..5#1)", "templateType": "randrange"}, "x5": {"description": "", "name": "x5", "group": "Ungrouped variables", "definition": "x4+stp", "templateType": "anything"}, "d22": {"description": "", "name": "d22", "group": "Ungrouped variables", "definition": "d13-d12", "templateType": "anything"}, "d16": {"description": "", "name": "d16", "group": "Ungrouped variables", "definition": "y7-y6", "templateType": "anything"}, "x3": {"description": "", "name": "x3", "group": "Ungrouped variables", "definition": "x2+stp", "templateType": "anything"}, "c": {"description": "", "name": "c", "group": "Ungrouped variables", "definition": "random(0..15#1)", "templateType": "randrange"}, "d31": {"description": "", "name": "d31", "group": "Ungrouped variables", "definition": "d22-d21", "templateType": "anything"}, "d20": {"description": "", "name": "d20", "group": "Ungrouped variables", "definition": "d11-d10", "templateType": "anything"}, "x4": {"description": "", "name": "x4", "group": "Ungrouped variables", "definition": "x3+stp", "templateType": "anything"}}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>The following set of data was generated by a polynomial.</p>\n<p style=\"padding-left: 90px;\">\\(\\begin{matrix} {x}&amp;{f(x)} \\\\ \\var{x0}&amp;\\var{y0}\\\\\\var{x1}&amp;\\var{y1}\\\\\\var{x2}&amp;\\var{y2}\\\\\\var{x3}&amp;\\var{y3}\\\\\\var{x4}&amp;\\var{y4}\\\\\\var{x5}&amp;\\var{y5}\\\\\\var{x6}&amp;\\var{y6}\\\\\\var{x7}&amp;\\var{y7}\\\\\\end{matrix}\\)</p>\n<p style=\"padding-left: 30px;\"></p>", "name": "Difference tables", "metadata": {"description": "<p>Find the leading coefficient of a degree 3 polynomial using a difference table.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "parts": [{"type": "gapfill", "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": [], "prompt": "<p>Use a difference table to show it was generated by a degree 3 polynomial and hence calculate the leading coefficient, \\(a\\).</p>\n<p>\\(a=\\) [[0]]</p>", "gaps": [{"minValue": "{a}", "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": "2", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "maxValue": "{a}", "mustBeReduced": false}]}], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}