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{"name": "W1c - How to enter expressions in online tests and Matlab", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "ungrouped_variables": ["a", "c", "b", "d"], "parts": [{"useCustomName": false, "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "type": "gapfill", "gaps": [{"vsetRangePoints": 5, "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "customName": "", "showFeedbackIcon": true, "answer": "sin(cos({a}x)+{b})", "answerSimplification": "all", "customMarkingAlgorithm": "", "unitTests": [], "showPreview": true, "useCustomName": false, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": true, "checkingType": "absdiff", "scripts": {}, "valuegenerators": [{"value": "", "name": "x"}], "variableReplacements": [], "failureRate": 1}, {"vsetRangePoints": 5, "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "customName": "", "showFeedbackIcon": true, "answer": "cos(sin({b}x)+{a})", "answerSimplification": "all", "customMarkingAlgorithm": "", "unitTests": [], "showPreview": true, "useCustomName": false, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "checkingType": "absdiff", "scripts": {}, "valuegenerators": [{"value": "", "name": "x"}], "variableReplacements": [], "failureRate": 1}], "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "unitTests": [], "customName": "", "prompt": "<p>Input:</p>\n<ol>\n<li>$\\sin(\\cos(\\var{a}x)+\\var{b})$: [[0]]</li>\n<li>$\\cos(\\sin(\\var{b}x)+\\var{a})$: [[1]]</li>\n</ol>", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}}, {"useCustomName": false, "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "type": "gapfill", "gaps": [{"vsetRangePoints": 5, "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "customName": "", "showFeedbackIcon": true, "answer": "abs((x + {c}) / (x + {d}))", "answerSimplification": "all", "customMarkingAlgorithm": "", "unitTests": [], "showPreview": true, "useCustomName": false, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "checkingType": "absdiff", "scripts": {}, "valuegenerators": [{"value": "", "name": "x"}], "variableReplacements": [], "failureRate": 1}, {"vsetRangePoints": 5, "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "customName": "", "showFeedbackIcon": true, "answer": "ln(abs((x + {a}) / (x + {d})))", "answerSimplification": "all", "customMarkingAlgorithm": "", "unitTests": [], "showPreview": true, "useCustomName": false, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "checkingType": "absdiff", "scripts": {}, "valuegenerators": [{"value": "", "name": "x"}], "variableReplacements": [], "failureRate": 1}], "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "unitTests": [], "customName": "", "prompt": "<p>Input:</p>\n<ol>\n<li>$\\displaystyle \\simplify[all]{Abs((x + {c}) / (x + {d}))}$: [[0]]</li>\n<li>$\\displaystyle \\simplify[all]{ln(Abs((x + {a}) / (x + {d})))}$: [[1]]</li>\n</ol>", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}}, {"useCustomName": false, "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "type": "gapfill", "gaps": [{"vsetRangePoints": 5, "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "customName": "", "showFeedbackIcon": true, "answer": "{a} * t ^ { -b} * e ^ (( -{c}) * t) * sin({b} * t) + (t + {d} * t ^ 3) * e ^ ({c} * t)", "answerSimplification": "all", "customMarkingAlgorithm": "", "unitTests": [], "showPreview": true, "useCustomName": false, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "checkingType": "absdiff", "scripts": {}, "valuegenerators": [{"value": "", "name": "t"}], "variableReplacements": [], "failureRate": 1}, {"vsetRangePoints": 5, "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "customName": "", "showFeedbackIcon": true, "answer": "arctan(({c} * y ^ 2 + {d}) / ((y + {a}) * (y + {b})))", "answerSimplification": "all", "customMarkingAlgorithm": "", "unitTests": [], "showPreview": true, "useCustomName": false, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "checkingType": "absdiff", "scripts": {}, "valuegenerators": [{"value": "", "name": "y"}], "variableReplacements": [], "failureRate": 1}], "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "unitTests": [], "customName": "", "prompt": "<p>Input:</p>\n<ol>\n<li>$\\simplify[all]{{a} * t ^ { -b} * e ^ (( -{c}) * t) * Sin({b} * t) + (t + {d} * t ^ 3) * e ^ ({c} * t)}$: [[0]]</li>\n<li>$\\displaystyle \\simplify[all]{arctan(({c} * y ^ 2 + {d}) / ((y + {a}) * (y + {b})))}$: [[1]]</li>\n</ol>", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}}], "functions": {}, "name": "W1c - How to enter expressions in online tests and Matlab", "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p><strong>FUNCTIONS</strong></p>\n<ol>\n<li>The online tests and Matlab recognise all standard functions but you must use brackets for the arguments of the functions, e.g. <code>sin(x)</code> not <code>sinx</code>, <code>ln(a)</code> not <code>lna</code>.</li>\n<li>The absolute value function is written <code>abs(a)</code>.</li>\n<li>When unsure, put brackets around everything.</li>\n</ol>\n<p>You can do this as many times as you need to feel comfortable with it. When stuck, press <em>Reveal Answers</em> and try again.</p>\n<p>Turn inputs into Matlab form:</p>", "preamble": {"css": "", "js": ""}, "rulesets": {}, "variable_groups": [], "advice": "<p>Correct inputs for these questions are as follows, although there may be other correct ways of inputting these: &nbsp;</p>\n<h4>a)</h4>\n<ol>\n  <li><code>sin(cos({a}x)+{b})</code></li>\n  <li><code>cos(sin({a}x + {b}))</code></li>\n</ol>\n<h4>b)</h4>\n<ol>\n  <li><code>abs((x + {c}) / (x + {d}))</code></li>\n  <li><code>ln(abs((x + {a}) / (x + {d})))</code></li>\n</ol>\n<h4>c)</h4>\n<ol>\n  <li><code>{a}t^({-b})*e^({-c}t)*sin({b}t) + (t + {d}t ^ 3)*e ^ ({c}t)</code></li>\n  <li><code>arctan(({c}y ^ 2 + {d}) / ((y + {a})*(y + {b})))</code></li>\n</ol>", "variables": {"d": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..9)", "name": "d"}, "b": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(3..9)", "name": "b"}, "c": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..9)", "name": "c"}, "a": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..9)", "name": "a"}}, "metadata": {"description": "<p>Dealing with expressions in online tests and in Matlab.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}]}], "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}