// Numbas version: finer_feedback_settings
{"name": "Bending moments", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Bending moments", "tags": [], "metadata": {"description": "<p>&nbsp;Question asks student to find zeros of a quadratic equation. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>We require \\(M=0\\), hence we need to solve the equation \\[\\simplify{{a}x^2+{b}x-{c}}=0\\]</p>\n<p>Using the quadratic formula we have \\begin{align} x&amp;=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}\\\\&amp;=\\frac{-\\var{b}\\pm\\sqrt{\\simplify[!collectNumbers]{{b}^2-4*{a}*{-c}}}}{\\var{2*a}}\\\\&amp;=\\frac{-\\var{b}+\\sqrt{\\simplify{{b}^2-4*{a}*{-c}}}}{\\var{2*a}}\\text{ or }\\frac{-\\var{b}-\\sqrt{\\simplify{{b}^2-4*{a}*{-c}}}}{\\var{2*a}}\\\\&amp;=\\var{ans}\\text{ or }\\var{ans2}\\end{align}</p>\n<p>Since we are told that \\(x\\ge 0\\) we can ignore the negative answer and conclude that the bending moment will be \\(0\\) at a distance approximately \\(\\var{precround({ans},2)}\\) m from the end of the beam.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(0.5..1.9 #0.1 except 1)", "description": "<p>Coefficient of x^2 in equation</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2.1..5.9 #0.1except [3.0,4.0,5.0])", "description": "<p>Ciefficient of x in equation</p>", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1.1..4.9 #0.1 except [2,3,4])", "description": "<p>constant term in equation</p>", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "(-b+sqrt(b^2+4*a*c))/(2*a)", "description": "<p>positive root of quadratic</p>", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "(-b-sqrt(b^2+4*a*c))/(2*a)", "description": "<p>negative root of quadratic</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "ans", "ans2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The bending moment, \\(M\\), of a beam&nbsp; is given by \\[\\simplify{M={a}x^2+{b}x-{c}}\\quad x\\ge 0\\]where \\(x\\) is the distance in metres along the beam.</p>\n<p>Find the value of \\(x\\) for which \\(M\\) is \\(0\\). Write your final answer in the box below and show full working on your handwritten notes.</p>\n<p>\\(x=\\)[[0]]m (round answer to 2 decimal places)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans}", "maxValue": "{ans}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Hanh Vo", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/12984/"}], "resources": []}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Hanh Vo", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/12984/"}]}