// Numbas version: finer_feedback_settings
{"name": "Input 6", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Input 6", "tags": ["Numbas", "arctan", "brackets", "functions", "input", "introduction", "numbas", "standard functions"], "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Input:</p>\n      <ul>\n      <li>$\\sin(\\cos(\\var{a}x)+\\var{b})$: [[0]]</li>\n      <li>$\\cos(\\sin(\\var{b}x)+\\var{a})$: [[1]]</li>\n      </ul>", "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "sin(cos({a}x)+{b})", "checkvariablenames": false, "type": "jme"}, {"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "cos(sin({b}x)+{a})", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}, {"prompt": "<p>Input:</p>\n      <ul>\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      </ul>", "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "abs((x + {c}) / (x + {d}))", "checkvariablenames": false, "type": "jme"}, {"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "ln(abs((x + {a}) / (x + {d})))", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}, {"prompt": "<p>Input:</p>\n      <ul>\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      </ul>", "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "{a} * t ^ { -b} * e ^ (( -{c}) * t) * sin({b} * t) + (t + {d} * t ^ 3) * e ^ ({c} * t)", "checkvariablenames": false, "type": "jme"}, {"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "arctan(({c} * y ^ 2 + {d}) / ((y + {a}) * (y + {b})))", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "<h3>Functions</h3>\n  <p>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>sin x</code>, <code>ln(a)</code> not <code>ln a</code>.</p>\n  <p>The absolute value function is input as <code>abs(a)</code>.</p>\n  <p>The inverse trigonometric functions <code>arcsin(x)</code>, <code>arccos(x)</code> and <code>arctan(x)</code> are all recognized, and you input them as they are written.</p>\n  <p>Here are some examples for you to try.</p>\n  <p>If you want help, press <em>Reveal answers</em> at the bottom of the screen to see correct inputs.</p>", "variable_groups": [], "progress": "in-progress", "type": "question", "variables": {"a": {"definition": "random(2..9)", "name": "a"}, "c": {"definition": "random(2..9)", "name": "c"}, "b": {"definition": "random(3..9)", "name": "b"}, "d": {"definition": "random(2..9)", "name": "d"}}, "metadata": {"notes": "", "description": "<p>Instructions on dealing with functions in Numbas.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}