// Numbas version: exam_results_page_options
{"name": "Solve equations which include a single odd power (e.g. x^odd=blah)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variable_groups": [{"variables": ["intpower", "intrhs", "intsoln"], "name": "a"}, {"variables": ["bpower", "bsoln", "bxcoeff", "bb", "bc", "brhs"], "name": "b"}, {"variables": ["cpower", "cxcoeff", "cc", "cb", "csolnapprox"], "name": "c"}], "tags": [], "parts": [{"variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "customName": "", "failureRate": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "vsetRangePoints": 5, "checkingType": "absdiff", "variableReplacements": [], "valuegenerators": [], "scripts": {}, "marks": 1, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "vsetRange": [0, 1], "useCustomName": false, "answer": "{intsoln}", "unitTests": [], "type": "jme", "showPreview": true, "checkVariableNames": false}], "unitTests": [], "type": "gapfill", "prompt": "<p>If &nbsp;$x^\\var{intpower}=\\var{intrhs}$, then $x=$ [[0]].</p>"}, {"variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "customName": "", "failureRate": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "vsetRangePoints": 5, "checkingType": "absdiff", "variableReplacements": [], "valuegenerators": [], "scripts": {}, "marks": 1, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "vsetRange": [0, 1], "useCustomName": false, "answer": "{bsoln}", "unitTests": [], "type": "jme", "showPreview": true, "checkVariableNames": false}], "unitTests": [], "type": "gapfill", "prompt": "<p>If &nbsp;$\\simplify{{bxcoeff}y^{bpower}+{bb}}=\\var{bc}$, then $y=$ [[0]].</p>"}, {"variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "useCustomName": false, "marks": 1, "extendBaseMarkingAlgorithm": true, "checkingType": "absdiff", "vsetRange": [0, 1], "showCorrectAnswer": true, "type": "jme", "showPreview": true, "valuegenerators": [], "checkVariableNames": false, "failureRate": 1, "answerSimplification": "fractionNumbers", "customName": "", "scripts": {}, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "answer": "({(cc-cb)/cxcoeff})^(1/{cpower})"}], "unitTests": [], "type": "gapfill", "prompt": "<p>For this question input the&nbsp;<em>exact</em> value by using a <em>fractional power</em> to indicate a root. For example, if the answer was $\\sqrt[3]{\\frac{35}{11}}$, then enter &nbsp;(35/11)^(1/3).</p>\n<p>If &nbsp;$\\simplify{{cxcoeff}z^{cpower}+{cb}}=\\var{cc}$, then $z=$ [[0]].</p>"}, {"variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "useCustomName": false, "marks": 1, "extendBaseMarkingAlgorithm": true, "checkingType": "absdiff", "vsetRange": [0, 1], "showCorrectAnswer": true, "type": "jme", "showPreview": true, "valuegenerators": [], "checkVariableNames": false, "failureRate": 1, "answerSimplification": "basic", "customName": "", "scripts": {}, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "answer": "({dc*ddenom})^(1/{bpower})-{db}"}], "unitTests": [], "type": "gapfill", "prompt": "<p>For this question input the&nbsp;<em>exact</em> value by using a <em>fractional power</em> to indicate a root. For example, if the answer was $\\sqrt[3]{\\frac{35}{11}}$, then enter &nbsp;(35/11)^(1/3).</p>\n<p>If &nbsp;$\\displaystyle{\\simplify{((z+{db})^{bpower})/({ddenom})}}=\\var{dc}$, then $z=$ [[0]].</p>"}], "functions": {}, "name": "Solve equations which include a single odd power (e.g. x^odd=blah)", "ungrouped_variables": ["dc", "db", "ddenom"], "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd).&nbsp;</p>"}, "extensions": [], "statement": "<p>Please complete the following.</p>", "advice": "<p>a)&nbsp;Given $x^\\var{intpower}=\\var{intrhs}$, we can take the $\\var{intpower}$<span data-jme-visible=\"intpower=2\">nd</span> <span data-jme-visible=\"intpower=3\">rd</span> <span data-jme-visible=\"intpower&gt;3\">th</span> &nbsp;root of both sides.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$x^\\var{intpower}$</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;\">$\\sqrt[\\var{intpower}]{x^\\var{intpower}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\sqrt[\\var{intpower}]{\\var{intrhs}}$</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&nbsp;$\\simplify{{bxcoeff}y^{bpower}+{bb}}=\\var{bc}$, we can rearrange the equation&nbsp;to get $y^\\var{bpower}$ by itself and then we can take the $\\var{bpower}$<span data-jme-visible=\"bpower=2\">nd</span> <span data-jme-visible=\"bpower=3\">rd</span> <span data-jme-visible=\"bpower&gt;3\">th</span> &nbsp;root of both sides to get $y$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\simplify{{bxcoeff}y^{bpower}+{bb}}$</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;\">$\\simplify{{bxcoeff}y^{bpower}}$</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;\">$\\simplify{{bxcoeff}y^{bpower}}$</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;\">$y^\\var{bpower}$</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;\">$y^\\var{bpower}$</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;\">$\\sqrt[\\var{bpower}]{y^\\var{bpower}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\sqrt[\\var{bpower}]{\\var{brhs}}$</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&nbsp;$\\simplify{{cxcoeff}z^{cpower}+{cb}}=\\var{cc}$, we can rearrange the equation&nbsp;to get $z^\\var{cpower}$ by itself and then we can take the $\\var{cpower}$<span data-jme-visible=\"cpower=2\">nd</span> <span data-jme-visible=\"cpower=3\">rd</span> <span data-jme-visible=\"cpower&gt;3\">th</span> &nbsp;root of both sides to get $z$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\simplify{{cxcoeff}z^{cpower}+{cb}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{cc}$&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;\">$\\simplify{{cxcoeff}z^{cpower}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[basic]{{cc}-{cb}}$</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;\">$\\simplify{{cxcoeff}z^{cpower}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify{{cc-cb}}$</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;\">$z^\\var{cpower}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[!basic]{{cc-cb}/{cxcoeff}}$</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;\">$z^\\var{cpower}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}}$</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;\">$\\sqrt[\\var{cpower}]{z^\\var{cpower}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\sqrt[\\var{cpower}]{\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}}}$</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;\">$\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}^{1/{cpower}}}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p>d) Given $\\displaystyle{\\simplify{((z+{db})^{bpower})/({ddenom})}}=\\var{dc}$, we can rearrange the equation&nbsp;to get $\\simplify{(z+{db})^{bpower}}$ by itself, then we can take the $\\var{bpower}$<span data-jme-visible=\"cpower=2\">nd</span> <span data-jme-visible=\"bpower=3\">rd</span> <span data-jme-visible=\"bpower&gt;3\">th</span> &nbsp;root of both sides to get $\\simplify{z+{db}}$ by itself, and then rearrange to get $z$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{((z+{db})^{bpower})/({ddenom})}}$</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;\">$\\simplify{(z+{db})^{bpower}}$</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;\">$\\simplify{(z+{db})^{bpower}}$</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;\">$\\sqrt[\\var{bpower}]{\\simplify{(z+{db})^{bpower}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\sqrt[\\var{bpower}]{\\var{dc*ddenom}}$</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;\">$\\simplify{z+{db}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\sqrt[\\var{bpower}]{\\var{dc*ddenom}}$</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;\">$z$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify{root({dc*ddenom},{bpower})-{db}}$</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;\">$\\simplify{{dc*ddenom}^(1/{bpower})-{db}}$</td>\n</tr>\n</tbody>\n</table>", "variables": {"cb": {"description": "", "definition": "random(-100..100 except [0,cc])", "group": "c", "name": "cb", "templateType": "anything"}, "intpower": {"description": "", "definition": "random(3..9#2)", "group": "a", "name": "intpower", "templateType": "anything"}, "cc": {"description": "", "definition": "random(-100..100)", "group": "c", "name": "cc", "templateType": "anything"}, "brhs": {"description": "", "definition": "(bc-bb)/bxcoeff", "group": "b", "name": "brhs", "templateType": "anything"}, "cpower": {"description": "", "definition": "random(3..9#2)", "group": "c", "name": "cpower", "templateType": "anything"}, "csolnapprox": {"description": "", "definition": "root(((cc-cb)/cxcoeff),(1/cpower))", "group": "c", "name": "csolnapprox", "templateType": "anything"}, "db": {"description": "", "definition": "random(-100..100 except -1..1)", "group": "Ungrouped variables", "name": "db", "templateType": "anything"}, "ddenom": {"description": "", "definition": "random(2..15)", "group": "Ungrouped variables", "name": "ddenom", "templateType": "anything"}, "bsoln": {"description": "", "definition": "switch(bpower=3, random(-10..10 except -1..1), bpower=5, random(-4..4 except -1..1), bpower=7, random(-3..3 except -1..1), 2)", "group": "b", "name": "bsoln", "templateType": "anything"}, "bc": {"description": "", "definition": "bsoln^bpower*bxcoeff+bb", "group": "b", "name": "bc", "templateType": "anything"}, "bxcoeff": {"description": "", "definition": "random(-3..3 except 0..1)", "group": "b", "name": "bxcoeff", "templateType": "anything"}, "bb": {"description": "", "definition": "random(1..100)", "group": "b", "name": "bb", "templateType": "anything"}, "cxcoeff": {"description": "", "definition": "random(-12..12 except -1..1)", "group": "c", "name": "cxcoeff", "templateType": "anything"}, "intrhs": {"description": "", "definition": "intsoln^intpower\n", "group": "a", "name": "intrhs", "templateType": "anything"}, "bpower": {"description": "", "definition": "random(3..9#2)", "group": "b", "name": "bpower", "templateType": "anything"}, "intsoln": {"description": "", "definition": "switch(intpower=3, random(2..12), intpower=5, random(2..5), intpower=7, random(2..3), 2)", "group": "a", "name": "intsoln", "templateType": "anything"}, "dc": {"description": "", "definition": "random(-100..100 except -1..1)", "group": "Ungrouped variables", "name": "dc", "templateType": "anything"}}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}