// 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": [{"name": "Solve equations which include a single odd power (e.g. x^odd=blah)", "tags": [], "metadata": {"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>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "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>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"bsoln": {"name": "bsoln", "group": "b", "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)", "description": "", "templateType": "anything", "can_override": false}, "intrhs": {"name": "intrhs", "group": "a", "definition": "intsoln^intpower\n", "description": "", "templateType": "anything", "can_override": false}, "powers": {"name": "powers", "group": "a", "definition": "shuffle([3,5,7,9])", "description": "", "templateType": "anything", "can_override": false}, "ddenom": {"name": "ddenom", "group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "can_override": false}, "cxcoeff": {"name": "cxcoeff", "group": "c", "definition": "random(-12..12 except -1..1)", "description": "", "templateType": "anything", "can_override": false}, "bc": {"name": "bc", "group": "b", "definition": "bsoln^bpower*bxcoeff+bb", "description": "", "templateType": "anything", "can_override": false}, "bpower": {"name": "bpower", "group": "b", "definition": "powers[1]", "description": "", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "b", "definition": "random(1..100)", "description": "", "templateType": "anything", "can_override": false}, "dc": {"name": "dc", "group": "Ungrouped variables", "definition": "random(2..100 except -1..1)", "description": "", "templateType": "anything", "can_override": false}, "intpower": {"name": "intpower", "group": "a", "definition": "powers[0]", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "c", "definition": "if(cxcoeff>0,cb+random(10..50),cb-random(10..50))", "description": "<p>This is to force the root to be taken of a positive power since the student input of negative ^ fraction leads to a complex number and I don't want the students to input using the root syntax</p>", "templateType": "anything", "can_override": false}, "brhs": {"name": "brhs", "group": "b", "definition": "(bc-bb)/bxcoeff", "description": "", "templateType": "anything", "can_override": false}, "bxcoeff": {"name": "bxcoeff", "group": "b", "definition": "random(-3..3 except 0..1)", "description": "", "templateType": "anything", "can_override": false}, "intsoln": {"name": "intsoln", "group": "a", "definition": "switch(intpower=3, random(2..12), intpower=5, random(2..5), intpower=7, random(2..3), 2)", "description": "", "templateType": "anything", "can_override": false}, "cpower": {"name": "cpower", "group": "c", "definition": "powers[2]", "description": "", "templateType": "anything", "can_override": false}, "db": {"name": "db", "group": "Ungrouped variables", "definition": "random(-100..100 except -1..1)", "description": "", "templateType": "anything", "can_override": false}, "cb": {"name": "cb", "group": "c", "definition": "random(-100..100)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["dc", "db", "ddenom"], "variable_groups": [{"name": "a", "variables": ["intpower", "intrhs", "intsoln", "powers"]}, {"name": "b", "variables": ["bpower", "bsoln", "bxcoeff", "bb", "bc", "brhs"]}, {"name": "c", "variables": ["cpower", "cxcoeff", "cb", "cc"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If &nbsp;$x^\\var{intpower}=\\var{intrhs}$, then $x=$ [[0]]. (This answer should be a whole number, use a calculator if necessary)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{intsoln}", "maxValue": "{intsoln}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If &nbsp;$\\simplify{{bxcoeff}y^{bpower}+{bb}}=\\var{bc}$, then $y=$ [[0]]. (This answer should be a whole number, use a calculator if necessary)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{bsoln}", "maxValue": "{bsoln}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "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>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "root({(cc-cb)/cxcoeff},{cpower})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "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>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "root({dc*ddenom},{bpower})-{db}", "answerSimplification": "basic", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}]}