// Numbas version: exam_results_page_options
{"name": "How to enter functions - Getting Started", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "d", "description": ""}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(3..9)", "name": "b", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "a", "description": ""}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "c", "description": ""}}, "ungrouped_variables": ["a", "c", "b", "d"], "name": "How to enter functions - Getting Started", "functions": {}, "parts": [{"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "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>", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"answer": "sin(cos({a}x)+{b})", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": true, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": ["x"], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}, {"answer": "cos(sin({b}x)+{a})", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "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>", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"answer": "abs((x + {c}) / (x + {d}))", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}, {"answer": "ln(abs((x + {a}) / (x + {d})))", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "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>", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"answer": "{a} * t ^ { -b} * e ^ (( -{c}) * t) * sin({b} * t) + (t + {d} * t ^ 3) * e ^ ({c} * t)", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}, {"answer": "arctan(({c} * y ^ 2 + {d}) / ((y + {a}) * (y + {b})))", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p><strong>FUNCTIONS</strong></p>\n<ol>\n<li>The Numbas system recognises 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>$\\arcsin(x)$, $\\arccos(x)$ and $\\arctan(x)$ are all recognized as the standard inverse trig functions, and you input them as they are written.</li>\n</ol>\n<p>Here are some examples for you to try:</p>\n<p>(If you want help, press <em>Reveal Answers</em>&nbsp;to see correct inputs in the <em>Advice</em> section.)</p>", "tags": ["arctan", "brackets", "checked2015", "functions", "input", "introduction", "Numbas", "numbas", "standard functions"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Dealing with functions in Numbas.</p>"}, "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>", "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/"}]}]}], "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/"}]}