// Numbas version: exam_results_page_options
{"name": "Francis 's copy of Indices: fractional powers (algebraic)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["root1", "root2", "power2", "root3", "power3"], "name": "Francis 's copy of Indices: fractional powers (algebraic)", "tags": ["exponent", "exponents", "fractional", "index", "index laws", "indices", "power", "powers", "rational", "roots"], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>By using the definition of the square root you should see that $(\\sqrt{q})^2=q$.</p>\n<p>By using index laws you should see that $(q^{1/2})^2=q$.</p>\n<p>The above equations imply that $\\sqrt{q}$ can also be written as &nbsp;[[0]].</p>\n<p></p>\n<p>Note: If you want to use a fraction as a power you should use brackets to surround your power, for example, type 12^(2/3) for $12^\\frac{2}{3}$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["sqrt", "root"], "partialCredit": 0}, "variableReplacements": [], "expectedvariablenames": [], "checkingaccuracy": "0.00001", "type": "jme", "showpreview": false, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "basic", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "maxlength": {"length": "11", "message": "<p>Your answer is&nbsp;longer than necessary.</p>", "partialCredit": 0}, "answer": "q^(1/2)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["^"], "partialCredit": 0}}], "steps": [{"prompt": "<p>Given \\[(\\sqrt{q})^2=q=(q^{1/2})^2\\]</p>\n<p>we can say \\[\\sqrt{q}=q^{1/2}\\]</p>\n<p>Which we would type in as $q\\wedge(1/2)$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>By using the definition of the cube root you should see that $(\\sqrt[3]{p})^3=p$.</p>\n<p>By using index laws you should see that $(p^{1/3})^3=p$.</p>\n<p>The above equations imply that $\\sqrt[3]{p}$ can also be written as &nbsp;[[0]].</p>\n<p></p>\n<p>Note: If you want to use a fraction as a power you should use brackets to surround your power, for example, type 12^(2/3) for $12^\\frac{2}{3}$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["^0", "sqrt", "root"], "partialCredit": 0}, "variableReplacements": [], "expectedvariablenames": [], "checkingaccuracy": "0.00001", "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "basic", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "maxlength": {"length": "11", "message": "<p>Your answer is&nbsp;longer than necessary.</p>", "partialCredit": 0}, "answer": "p^(1/3)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["^"], "partialCredit": 0}}], "steps": [{"prompt": "<p>Given \\[(\\sqrt[3]{p})^3=p=(p^{1/3})^3\\]</p>\n<p>we can say \\[\\sqrt[3]{p}=p^{1/3}\\]</p>\n<p>Which we would type in as $p\\wedge(1/3)$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Use the same approach you used in the above questions to simplify the following in index form.</p>\n<p><br/>$\\sqrt[\\var{root1}]{g}$ =&nbsp;[[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["^0", "sqrt", "root"], "partialCredit": 0}, "variableReplacements": [], "expectedvariablenames": [], "checkingaccuracy": "0.00001", "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "basic", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "maxlength": {"length": "11", "message": "<p>Your answer is&nbsp;longer than necessary.</p>", "partialCredit": 0}, "answer": "g^(1/{root1})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["^"], "partialCredit": 0}}], "steps": [{"prompt": "<p>By the same reasoning as used in the above questions we have $\\sqrt[n]{a}=a^{\\frac{1}{n}}$.&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>$\\displaystyle\\left(\\sqrt[\\var{root2}]{e}\\right)^\\var{power2}$ =&nbsp;[[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["^0", "sqrt", "root"], "partialCredit": 0}, "variableReplacements": [], "expectedvariablenames": [], "checkingaccuracy": "0.00001", "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "basic", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "maxlength": {"length": "11", "message": "<p>Your answer is&nbsp;longer than necessary.</p>", "partialCredit": 0}, "answer": "e^({power2}/{root2})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["^"], "partialCredit": 0}}], "steps": [{"prompt": "<p><em>Convert the root to a fractional power and then use the index laws to deal with the two different powers.</em></p>\n<hr/>\n<p>For example, \\[\\sqrt[3]{2}^5=(2^{\\frac{1}{3}})^5=2^{\\frac{5}{3}}\\]&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>$\\sqrt[\\var{root3}]{r^\\var{power3}}$ =&nbsp;[[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["^0", "sqrt", "root"], "partialCredit": 0}, "variableReplacements": [], "expectedvariablenames": [], "checkingaccuracy": "0.00001", "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "basic", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "maxlength": {"length": "11", "message": "<p>Your answer is&nbsp;longer than necessary.</p>", "partialCredit": 0}, "answer": "r^({power3}/{root3})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "showStrings": false, "strings": ["^"], "partialCredit": 0}}], "steps": [{"prompt": "<p><em>Convert the root to a fractional power and then use the index laws to deal with the two different powers.</em></p>\n<hr/>\n<p>For example, \\[\\sqrt[3]{2^5}=(2^5)^{\\frac{1}{3}}=2^{\\frac{5}{3}}\\]&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "<p>Simplify the following without the use of a calculator. Write your answer in index form using ^ to signify powers.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"root1": {"definition": "random(4..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "root1", "description": ""}, "power3": {"definition": "random(2..12 except [root2,root3])", "templateType": "anything", "group": "Ungrouped variables", "name": "power3", "description": ""}, "power2": {"definition": "random(2..12 except root2)", "templateType": "anything", "group": "Ungrouped variables", "name": "power2", "description": ""}, "root3": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "root3", "description": ""}, "root2": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "root2", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Francis Duah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/339/"}]}]}], "contributors": [{"name": "Francis Duah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/339/"}]}