// Numbas version: exam_results_page_options
{"name": "Improving display of algebraic fractions.", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Improving display of algebraic fractions.", "statement": "<p>Use the product rule to differentiate the following.</p>", "rulesets": {}, "metadata": {"description": "<p>Questions of the form $f(x) = g(x)/h(x) $</p>\n<p>Optimised for display of quotients using \\displaystyle - see first part - otherwise difficult to read.</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"type": "jme", "showFeedbackIcon": true, "showpreview": true, "expectedvariablenames": [], "checkingaccuracy": "0.000001", "stepsPenalty": "1", "checkvariablenames": false, "answer": "(({p1}{a}x^({p1}-1)+{p2}{b}x^({p2}-1))({c}x+{d})^{n}-({a}x^{p1}+{b}x^{p2}){n}{c}({c}x+{d})^({n}-1))/({c}x+{d})^{2n}", "variableReplacementStrategy": "originalfirst", "steps": [{"type": "jme", "showFeedbackIcon": true, "showpreview": true, "checkingaccuracy": 0.001, "checkvariablenames": false, "answer": "{a}x^{p1}+{b}x^{p2}", "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showCorrectAnswer": true, "checkingtype": "absdiff", "marks": "0.5", "scripts": {}, "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "prompt": "<p>Choose u</p>"}, {"type": "jme", "showFeedbackIcon": true, "showpreview": true, "checkingaccuracy": 0.001, "checkvariablenames": false, "answer": "({c}x+{d})^{n}", "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showCorrectAnswer": true, "checkingtype": "absdiff", "marks": "0.5", "scripts": {}, "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "prompt": "<p>Choose v</p>"}, {"type": "jme", "showFeedbackIcon": true, "showpreview": true, "checkingaccuracy": 0.001, "checkvariablenames": false, "answer": "{p1}{a}x^({p1}-1)+{p2}{b}x^({p2}-1)", "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showCorrectAnswer": true, "checkingtype": "absdiff", "marks": "0.5", "scripts": {}, "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "prompt": "<p>Differentiate u to give u'</p>"}, {"type": "jme", "showFeedbackIcon": true, "showpreview": true, "checkingaccuracy": 0.001, "checkvariablenames": false, "answer": "{n}{c}({c}x+{d})^({n}-1)", "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showCorrectAnswer": true, "checkingtype": "absdiff", "marks": "0.5", "scripts": {}, "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "prompt": "<p>Differentiate v to give v'</p>"}, {"type": "jme", "showFeedbackIcon": false, "showpreview": true, "checkingaccuracy": 0.001, "checkvariablenames": false, "answer": "(({p1}{a}x^({p1}-1)+{p2}{b}x^({p2}-1))({c}x+{d})^{n}-({a}x^{p1}+{b}x^{p2}){n}{c}({c}x+{d})^({n}-1))/({c}x+{d})^{2n}", "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showCorrectAnswer": true, "checkingtype": "absdiff", "marks": "2", "scripts": {}, "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "prompt": "<p>Use the quotient rule $\\displaystyle (uv)' = \\frac{u'v -uv'}{v^2}$ to give answer</p>"}], "answersimplification": "all", "showCorrectAnswer": true, "checkingtype": "absdiff", "marks": "4", "scripts": {}, "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": ["0.5", "0.6"], "prompt": "<p>Using display improvement:</p>\n<p><code>$\\displaystyle y=\\frac{\\simplify{{a}x^{p1}+{b}x^{p2}}}{\\simplify{({c}x+{d})^{n}}}$ or</code></p>\n<p><code>\\[y=\\frac{\\simplify{{a}x^{p1}+{b}x^{p2}}}{\\simplify{({c}x+{d})^{n}}}\\]</code></p>\n<p>we get:</p>\n<p>$\\displaystyle y=\\frac{\\simplify{{a}x^{p1}+{b}x^{p2}}}{\\simplify{({c}x+{d})^{n}}}$&nbsp;</p>\n<p>\\[\\mbox{or &nbsp;} y=\\frac{\\simplify{{a}x^{p1}+{b}x^{p2}}}{\\simplify{({c}x+{d})^{n}}}\\]</p>\n<p>If no display improvement:</p>\n<p>$y=\\frac{\\simplify{{a}x^{p1}+{b}x^{p2}}}{\\simplify{({c}x+{d})^{n}}}$</p>"}], "tags": [], "variable_groups": [], "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["a", "b", "c", "d", "n", "p1", "p2"], "variables": {"p2": {"name": "p2", "templateType": "anything", "definition": "random(-5..5)", "group": "Ungrouped variables", "description": ""}, "d": {"name": "d", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}, "a": {"name": "a", "templateType": "anything", "definition": "random(-9..9 except 0)", "group": "Ungrouped variables", "description": ""}, "p1": {"name": "p1", "templateType": "anything", "definition": "random(-5..5)", "group": "Ungrouped variables", "description": ""}, "n": {"name": "n", "templateType": "anything", "definition": "random(1..9)", "group": "Ungrouped variables", "description": ""}, "b": {"name": "b", "templateType": "anything", "definition": "random(-9..9)", "group": "Ungrouped variables", "description": ""}, "c": {"name": "c", "templateType": "anything", "definition": "random(1..9)", "group": "Ungrouped variables", "description": ""}}, "advice": "<p>Use the quotient rule.</p>", "extensions": [], "type": "question", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}