// Numbas version: exam_results_page_options
{"name": "Solve equations which include a single root  (e.g. \\sqrt{x}=blah)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "preamble": {"css": "", "js": ""}, "variables": {"db": {"description": "", "name": "db", "definition": "random(-100..100 except -1..1)", "templateType": "anything", "group": "Ungrouped variables"}, "bb": {"description": "", "name": "bb", "definition": "random(1..100)", "templateType": "anything", "group": "b"}, "dc": {"description": "", "name": "dc", "definition": "random(-100..100 except -1..1)", "templateType": "anything", "group": "Ungrouped variables"}, "bxcoeff": {"description": "", "name": "bxcoeff", "definition": "random(-3..3 except 0..1)", "templateType": "anything", "group": "b"}, "intpower": {"description": "", "name": "intpower", "definition": "random(2..9)", "templateType": "anything", "group": "a"}, "intsoln": {"description": "", "name": "intsoln", "definition": "intrhs^intpower", "templateType": "anything", "group": "a"}, "bsoln": {"description": "", "name": "bsoln", "definition": "bnice^bpower", "templateType": "anything", "group": "b"}, "bnice": {"description": "<p>((bc-bb)/bxcoeff)^(1/bpower)</p>", "name": "bnice", "definition": "switch(bpower=3 or bpower=2, random(-10..10 except -1..1), bpower=5 or bpower =4, random(-4..4 except -1..1), bpower=7 or bpower=6, random(-3..3 except -1..1), 2)", "templateType": "anything", "group": "b"}, "bc": {"description": "", "name": "bc", "definition": "bnice*bxcoeff+bb", "templateType": "anything", "group": "b"}, "bpower": {"description": "", "name": "bpower", "definition": "random(2..9)", "templateType": "anything", "group": "b"}, "ddenom": {"description": "", "name": "ddenom", "definition": "random(2..15)", "templateType": "anything", "group": "Ungrouped variables"}, "dpower": {"description": "", "name": "dpower", "definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables"}, "intrhs": {"description": "<p>intsoln^intpower</p>", "name": "intrhs", "definition": "switch(intpower=3 or intpower=4, random(2..12), intpower=5 or intpower=6, random(2..5), intpower=7 or intpower=8, random(2..3), 2)\n", "templateType": "anything", "group": "a"}}, "statement": "<p>Please complete the following.</p>", "tags": [], "parts": [{"sortAnswers": false, "customName": "", "type": "gapfill", "gaps": [{"vsetRangePoints": 5, "vsetRange": [0, 1], "failureRate": 1, "customName": "", "type": "jme", "checkVariableNames": false, "showPreview": true, "variableReplacements": [], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "valuegenerators": [], "customMarkingAlgorithm": "", "checkingAccuracy": 0.001, "showFeedbackIcon": true, "marks": 1, "extendBaseMarkingAlgorithm": true, "unitTests": [], "checkingType": "absdiff", "showCorrectAnswer": true, "answer": "{intsoln}", "scripts": {}}], "variableReplacements": [], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "prompt": "<p>If &nbsp;$\\sqrt[\\var{intpower}]{x}=\\var{intrhs}$, then $x=$ [[0]].</p>", "scripts": {}}, {"sortAnswers": false, "customName": "", "type": "gapfill", "gaps": [{"vsetRangePoints": 5, "vsetRange": [0, 1], "failureRate": 1, "customName": "", "type": "jme", "checkVariableNames": false, "showPreview": true, "variableReplacements": [], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "valuegenerators": [], "customMarkingAlgorithm": "", "checkingAccuracy": 0.001, "showFeedbackIcon": true, "marks": 1, "extendBaseMarkingAlgorithm": true, "unitTests": [], "checkingType": "absdiff", "showCorrectAnswer": true, "answer": "{bsoln}", "scripts": {}}], "variableReplacements": [], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "prompt": "<p>If &nbsp;$\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}=\\var{bc}$, then $y=$ [[0]].</p>", "scripts": {}}, {"sortAnswers": false, "customName": "", "type": "gapfill", "gaps": [{"useCustomName": false, "checkVariableNames": false, "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "answerSimplification": "basic", "extendBaseMarkingAlgorithm": true, "failureRate": 1, "showPreview": true, "checkingType": "absdiff", "vsetRangePoints": 5, "valuegenerators": [], "unitTests": [], "variableReplacements": [], "customName": "", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "marks": 1, "type": "jme", "showCorrectAnswer": true, "answer": "({dc*ddenom})^({dpower})-{db}"}], "variableReplacements": [], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "prompt": "<p>For this question, if the answer was $\\left(\\frac{35}{11}\\right)^{11}-24$, then you could&nbsp;enter &nbsp;(35/11)^(11)-24.</p>\n<p>If &nbsp;$\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}=\\var{dc}$, then $z=$ [[0]].</p>", "scripts": {}}], "functions": {}, "extensions": [], "advice": "<p>a)&nbsp;Given $\\sqrt[\\var{intpower}]{x}=\\var{intrhs}$, we raise both sides to the power of $\\var{intpower}$ to get $x$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\sqrt[\\var{intpower}]{x}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{intrhs}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\left(\\sqrt[\\var{intpower}]{x}\\right)^{\\var{intpower}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[basic]{({intrhs})^{intpower}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{intsoln}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>b) Given $\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}=\\var{bc}$, we can rearrange the equation&nbsp;to get $y^\\frac{1}{\\var{bpower}}$ by itself and then we can raise both sides to the power of $\\var{bpower}$&nbsp;to get $y$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{bc}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\simplify{{bxcoeff}y^(1/{bpower})}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[basic]{{bc}-{bb}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\simplify{{bxcoeff}y^(1/{bpower})}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify{{bc-bb}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$y^\\frac{1}{\\var{bpower}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[!basic]{{bc-bb}/{bxcoeff}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$y^\\frac{1}{\\var{bpower}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify{{bc-bb}/{bxcoeff}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\left(y^\\frac{1}{\\var{bpower}}\\right)^{\\var{bpower}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[basic]{({(bc-bb)/bxcoeff})^{bpower}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{bsoln}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>c) Given $\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}=\\var{dc}$, we can rearrange the equation&nbsp;to get $\\simplify{(root(z+{db},{dpower}))}$ by itself, then we can raise both sides to the power of $\\var{dpower}$, and finally&nbsp;rearrange to get $z$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{dc}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{(root(z+{db},{dpower}))}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[basic]{{dc}*{ddenom}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{(root(z+{db},{dpower}))}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{dc*ddenom}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\left(\\sqrt[\\var{dpower}]{\\simplify{z+{db}}}\\right)^\\var{dpower}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[basic]{({dc*ddenom})^{dpower}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\simplify{z+{db}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"dc*ddenom&lt;0 and mod(dpower,2)=1\">$\\simplify[basic]{-{abs(dc*ddenom)}^{dpower}}$</span> &nbsp;<span data-jme-visible=\"dc*ddenom&lt;0 and mod(dpower,2)=0\">$\\simplify[basic]{({abs(dc*ddenom)})^{dpower}}$</span> &nbsp;<span data-jme-visible=\"dc*ddenom&gt;=0\">$\\simplify[basic]{({(dc*ddenom)})^{dpower}}$</span>&nbsp;&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$z$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"dc*ddenom&lt;0 and mod(dpower,2)=1\">$\\simplify[basic]{-{abs(dc*ddenom)}^{dpower}-{db}}$</span> &nbsp;<span data-jme-visible=\"dc*ddenom&lt;0 and mod(dpower,2)=0\">$\\simplify[basic]{({abs(dc*ddenom)})^{dpower}-{db}}$</span> &nbsp;<span data-jme-visible=\"dc*ddenom&gt;=0\">$\\simplify[basic]{({(dc*ddenom)})^{dpower}-{db}}$</span>&nbsp;&nbsp;</td>\n</tr>\n</tbody>\n</table>", "variable_groups": [{"name": "a", "variables": ["intpower", "intrhs", "intsoln"]}, {"name": "b", "variables": ["bpower", "bnice", "bsoln", "bxcoeff", "bb", "bc"]}], "name": "Solve equations which include a single root  (e.g. \\sqrt{x}=blah)", "metadata": {"description": "<p>Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them).&nbsp;</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "ungrouped_variables": ["dpower", "dc", "db", "ddenom"], "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}