// Numbas version: exam_results_page_options
{"name": "Find the curl of a vector field", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"p4": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(0..4)", "description": "", "name": "p4"}, "a1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)*sign(random(-1,1))", "description": "", "name": "a1"}, "p1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(0..4)", "description": "", "name": "p1"}, "p9": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(0..4)", "description": "", "name": "p9"}, "b1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)*sign(random(-1,1))", "description": "", 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"ungrouped_variables": ["p2", "p3", "p1", "p6", "p7", "p4", "p5", "p8", "p9", "a1", "b1", "c1"], "name": "Find the curl of a vector field", "functions": {}, "preamble": {"css": "", "js": ""}, "parts": [{"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\boldsymbol{\\nabla}\\times\\boldsymbol{u}=($[[0]]$,$[[1]]$,$[[2]]$)$.</p>", "unitTests": [], "showFeedbackIcon": true, "scripts": {}, "gaps": [{"answer": "{c1*p8}*x^{p7}*y^{p8-1}*z^{p9}-{b1*p6}*x^{p4}*y^{p5}*z^{p6-1}", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "answerSimplification": "all", "extendBaseMarkingAlgorithm": true, "showPreview": true, "checkVariableNames": true, "checkingType": "absdiff", "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "failureRate": 1, "scripts": {}, "vsetRangePoints": 5, "type": "jme", "unitTests": [], "checkingAccuracy": 0.001, "expectedVariableNames": ["x", "y", "z"], "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}, {"answer": "{a1*p3}*x^{p1}*y^{p2}*z^{p3-1}-{c1*p7}*x^{p7-1}*y^{p8}*z^{p9}", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "answerSimplification": "all", "extendBaseMarkingAlgorithm": true, "showPreview": true, "checkVariableNames": true, "checkingType": "absdiff", "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "failureRate": 1, "scripts": {}, "vsetRangePoints": 5, "type": "jme", "unitTests": [], "checkingAccuracy": 0.001, "expectedVariableNames": ["x", "y", "z"], "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}, {"answer": "{b1*p4}*x^{p4-1}*y^{p5}*z^{p6}-{a1*p2}*x^{p1}*y^{p2-1}*z^{p3}", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "answerSimplification": "all", "extendBaseMarkingAlgorithm": true, "showPreview": true, "checkVariableNames": true, "checkingType": "absdiff", "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "failureRate": 1, "scripts": {}, "vsetRangePoints": 5, "type": "jme", "unitTests": [], "checkingAccuracy": 0.001, "expectedVariableNames": ["x", "y", "z"], "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "sortAnswers": false}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Find the curl $\\boldsymbol{\\nabla}\\times\\boldsymbol{u}$ of the vector field $\\boldsymbol{u}=\\pmatrix{\\simplify{{a1}*x^{p1}*y^{p2}*z^{p3}},\\simplify{{b1}*x^{p4}*y^{p5}*z^{p6}},\\simplify{{c1}*x^{p7}*y^{p8}*z^{p9}}}$.</p>", "tags": ["checked2015"], "rulesets": {}, "extensions": [], "type": "question", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Curl of a vector field.</p>\n<p>Should warn that multiplied terms need * to denote multiplication.</p>"}, "advice": "<p>The curl of a vector field $\\boldsymbol{u}=\\pmatrix{u_x,u_y,u_z}$ is given by</p>\n  <p>\\[\\boldsymbol{\\nabla}\\times\\boldsymbol{u}=\\pmatrix{\\frac{\\partial u_z}{\\partial y}-\\frac{\\partial u_y}{\\partial z},\\frac{\\partial u_x}{\\partial z}-\\frac{\\partial u_z}{\\partial x},\\frac{\\partial u_y}{\\partial x}-\\frac{\\partial u_x}{\\partial y}}.\\]</p>\n  <p>Hence, in this example, after straight forward partial differentiation</p>\n  <p>\\[\\boldsymbol{\\nabla}\\times\\boldsymbol{u}=\\pmatrix{\\simplify{{c1*p8}*x^{p7}*y^{p8-1}*z^{p9}-{b1*p6}*x^{p4}*y^{p5}*z^{p6-1}},\\simplify{{a1*p3}*x^{p1}*y^{p2}*z^{p3-1}-{c1*p7}*x^{p7-1}*y^{p8}*z^{p9}},\\simplify{{b1*p4}*x^{p4-1}*y^{p5}*z^{p6}-{a1*p2}*x^{p1}*y^{p2-1}*z^{p3}}}.\\]</p>", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}