// Numbas version: finer_feedback_settings
{"name": "Solve equations which include a single even power (e.g. x^even=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 even power (e.g. x^even=blah)", "tags": [], "metadata": {"description": "<p>Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even).&nbsp;</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Please complete the following.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"cxcoeff": {"name": "cxcoeff", "group": "c", "definition": "if(cc-cb>0,random(2..12),random(-12..-2))", "description": "", "templateType": "anything", "can_override": false}, "intrhs": {"name": "intrhs", "group": "a", "definition": "intsoln^intpower\n", "description": "", "templateType": "anything", "can_override": false}, "bpower": {"name": "bpower", "group": "b", "definition": "powers[1]", "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}, "bc": {"name": "bc", "group": "b", "definition": "bsoln^bpower*bxcoeff+bb", "description": "", "templateType": "anything", "can_override": false}, "ddenom": {"name": "ddenom", "group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "can_override": false}, "powers": {"name": "powers", "group": "a", "definition": "shuffle([2,4,6,8])", "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)", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "c", "definition": "random(-100..100)", "description": "", "templateType": "anything", "can_override": false}, "brhs": {"name": "brhs", "group": "b", "definition": "(bc-bb)/bxcoeff", "description": "", "templateType": "anything", "can_override": false}, "cb": {"name": "cb", "group": "c", "definition": "random(-100..100 except [0,cc])", "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=2, random(2..12), intpower=4, random(2..5), intpower=6, random(2..3), 2)", "description": "", "templateType": "anything", "can_override": false}, "intpower": {"name": "intpower", "group": "a", "definition": "powers[0]", "description": "", "templateType": "anything", "can_override": false}, "bsoln": {"name": "bsoln", "group": "b", "definition": "switch(bpower=2, random(2..10), bpower=4, random(2..4), bpower=6, random(2..3), 2)", "description": "", "templateType": "anything", "can_override": false}, "cpower": {"name": "cpower", "group": "c", "definition": "powers[2]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["dc", "db", "ddenom"], "variable_groups": [{"name": "a", "variables": ["powers", "intpower", "intrhs", "intsoln"]}, {"name": "b", "variables": ["bpower", "bsoln", "bxcoeff", "bb", "bc", "brhs"]}, {"name": "c", "variables": ["cpower", "cc", "cb", "cxcoeff"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "marked_original_order (Mark the gaps in the original order, mainly to establish if every gap has a valid answer):\n    map(\n        mark_part(gap[\"path\"],studentAnswer),\n        [gap,studentAnswer],\n        zip(gaps,studentAnswer)\n    )\n\ninterpreted_answers (The interpreted answers for each gap, in the original order):\n    map(\n        res[\"values\"][\"interpreted_answer\"],\n        res,\n        marked_original_order\n    )\n\nanswers (The student's answers to each gap): interpreted_answers\n\ngap_feedback (Feedback on each of the gaps):\n    map(\n        try(\n            let(\n                answer, studentAnswer[answer_number],\n                result, submit_part(gaps[gap_number][\"path\"],answer),\n                gap, gaps[gap_number],\n                name, gap[\"name\"],\n                noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n                non_warning_feedback, filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]),\n                    assert(noFeedbackIcon,\n                        assert(name=\"\" or len(gaps)=1 or len(non_warning_feedback)=0,feedback(translate('part.gapfill.feedback header',[\"name\": name])))\n                    );\n                    concat_feedback(non_warning_feedback, if(marks>0,result[\"marks\"]/marks,1/len(gaps)), noFeedbackIcon);\n                    result\n            ),\n            err,\n            fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n        ),\n        [gap_number, answer_number],\n        zip(gap_adaptive_order, gap_adaptive_order)\n    )\n\nall_valid (Are the answers to all of the gaps valid?):\n  all(map(res[\"valid\"], res, marked_original_order))\n\ncheck_answers:\n if(\n   answers[1]=answers[0],\n   sub_credit(1/2, \"Numbers cannot be the same. \"),\n   feedback(\"\")\n )\n\nmark:\n  assert(all_valid or not settings[\"sortAnswers\"], fail(translate(\"question.can not submit\")));\n  apply(answers);\n  apply(check_answers);\n  apply(gap_feedback)\n\ninterpreted_answer:\n  answers\n\npre_submit:\n    map(\n        let(\n            answer, studentAnswer[answer_number],\n            result, submit_part(gaps[gap_number][\"path\"],answer),\n            check_pre_submit(gaps[gap_number][\"path\"], answer, exec_path)\n        ),\n        [gap_number,answer_number],\n        zip(gap_order,answer_order)\n    )", "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]], or&nbsp;[[1]].</p>", "stepsPenalty": "2", "steps": [{"type": "information", "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><strong>Note:</strong> Suppose you wanted to solve $x^2=4$, that is, you wanted the number that squares to give four. The number $2$ comes to mind, however, $-2$ is also a solution since $(-2)^2=(-2)\\times(-2)=4$. &nbsp;Recall the product of two negatives is a positive, so the product of any even number of negative numbers is positive. This means when we find a positive solution to an equation like $x^4=10\\,000$ there will also be a negative solution, in particular, the solution to $x^4=10\\,000$ would be $x=\\pm\\sqrt[4]{10\\,000}=\\pm10$.</p>\n<p></p>\n<p>a) Since the power in $x^\\var{intpower}=\\var{intrhs}$ is even we will take the plus or minus $\\var{intpower}$<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 to get two solutions.</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;\">$\\pm\\sqrt[\\var{intpower}]{\\var{intrhs}}$</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;\">$\\pm\\var{intsoln}$</td>\n</tr>\n</tbody>\n</table>\n<p>That is, $x$ equals $-\\var{intsoln}$ or $\\var{intsoln}$.</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, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "{intsoln}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "answer": "{-intsoln}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"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, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "{-intsoln}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "answer": "{intsoln}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": true}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "marked_original_order (Mark the gaps in the original order, mainly to establish if every gap has a valid answer):\n    map(\n        mark_part(gap[\"path\"],studentAnswer),\n        [gap,studentAnswer],\n        zip(gaps,studentAnswer)\n    )\n\ninterpreted_answers (The interpreted answers for each gap, in the original order):\n    map(\n        res[\"values\"][\"interpreted_answer\"],\n        res,\n        marked_original_order\n    )\n\nanswers (The student's answers to each gap): interpreted_answers\n\ngap_feedback (Feedback on each of the gaps):\n    map(\n        try(\n            let(\n                answer, studentAnswer[answer_number],\n                result, submit_part(gaps[gap_number][\"path\"],answer),\n                gap, gaps[gap_number],\n                name, gap[\"name\"],\n                noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n                non_warning_feedback, filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]),\n                    assert(noFeedbackIcon,\n                        assert(name=\"\" or len(gaps)=1 or len(non_warning_feedback)=0,feedback(translate('part.gapfill.feedback header',[\"name\": name])))\n                    );\n                    concat_feedback(non_warning_feedback, if(marks>0,result[\"marks\"]/marks,1/len(gaps)), noFeedbackIcon);\n                    result\n            ),\n            err,\n            fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n        ),\n        [gap_number, answer_number],\n        zip(gap_adaptive_order, gap_adaptive_order)\n    )\n\nall_valid (Are the answers to all of the gaps valid?):\n  all(map(res[\"valid\"], res, marked_original_order))\n\ncheck_answers:\n if(\n   answers[1]=answers[0],\n   sub_credit(1/2, \"Numbers cannot be the same. \"),\n   feedback(\"\")\n )\n\nmark:\n  assert(all_valid or not settings[\"sortAnswers\"], fail(translate(\"question.can not submit\")));\n  apply(answers);\n  apply(check_answers);\n  apply(gap_feedback)\n\ninterpreted_answer:\n  answers\n\npre_submit:\n    map(\n        let(\n            answer, studentAnswer[answer_number],\n            result, submit_part(gaps[gap_number][\"path\"],answer),\n            check_pre_submit(gaps[gap_number][\"path\"], answer, exec_path)\n        ),\n        [gap_number,answer_number],\n        zip(gap_order,answer_order)\n    )", "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]], or&nbsp;[[1]].</p>", "stepsPenalty": "2", "steps": [{"type": "information", "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></p>\n<p>Given $\\simplify{{bxcoeff}y^{bpower}+{bb}}=\\var{bc}$, we can rearrange the equation to get $y^\\var{bpower}$ by itself and then we can take the plus or minus $\\var{bpower}$<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 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;\">$\\pm\\sqrt[\\var{bpower}]{\\var{brhs}}$</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;\">$\\pm\\var{bsoln}$</td>\n</tr>\n</tbody>\n</table>\n<p>That is, $y$ equals $-\\var{bsoln}$, or $\\var{bsoln}$.</p>\n<p></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, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "{bsoln}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "answer": "{-bsoln}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"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, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "{-bsoln}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "answer": "{bsoln}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": true}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "marked_original_order (Mark the gaps in the original order, mainly to establish if every gap has a valid answer):\n    map(\n        mark_part(gap[\"path\"],studentAnswer),\n        [gap,studentAnswer],\n        zip(gaps,studentAnswer)\n    )\n\ninterpreted_answers (The interpreted answers for each gap, in the original order):\n    map(\n        res[\"values\"][\"interpreted_answer\"],\n        res,\n        marked_original_order\n    )\n\nanswers (The student's answers to each gap): interpreted_answers\n\ngap_feedback (Feedback on each of the gaps):\n    map(\n        try(\n            let(\n                answer, studentAnswer[answer_number],\n                result, submit_part(gaps[gap_number][\"path\"],answer),\n                gap, gaps[gap_number],\n                name, gap[\"name\"],\n                noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n                non_warning_feedback, filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]),\n                    assert(noFeedbackIcon,\n                        assert(name=\"\" or len(gaps)=1 or len(non_warning_feedback)=0,feedback(translate('part.gapfill.feedback header',[\"name\": name])))\n                    );\n                    concat_feedback(non_warning_feedback, if(marks>0,result[\"marks\"]/marks,1/len(gaps)), noFeedbackIcon);\n                    result\n            ),\n            err,\n            fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n        ),\n        [gap_number, answer_number],\n        zip(gap_adaptive_order, gap_adaptive_order)\n    )\n\nall_valid (Are the answers to all of the gaps valid?):\n  all(map(res[\"valid\"], res, marked_original_order))\n\ncheck_answers:\n if(\n   answers[1]=answers[0],\n   sub_credit(1/2, \"Numbers cannot be the same. \"),\n   feedback(\"\")\n )\n\nmark:\n  assert(all_valid or not settings[\"sortAnswers\"], fail(translate(\"question.can not submit\")));\n  apply(answers);\n  apply(check_answers);\n  apply(gap_feedback)\n\ninterpreted_answer:\n  answers\n\npre_submit:\n    map(\n        let(\n            answer, studentAnswer[answer_number],\n            result, submit_part(gaps[gap_number][\"path\"],answer),\n            check_pre_submit(gaps[gap_number][\"path\"], answer, exec_path)\n        ),\n        [gap_number,answer_number],\n        zip(gap_order,answer_order)\n    )", "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></p>\n<p>If &nbsp;$\\simplify{{cxcoeff}z^{cpower}+{cb}}=\\var{cc}$, then $z=$ [[0]], or&nbsp;[[1]].</p>", "stepsPenalty": "2", "steps": [{"type": "information", "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>Given $\\simplify{{cxcoeff}z^{cpower}+{cb}}=\\var{cc}$, we can rearrange the equation to get $z^\\var{cpower}$ by itself and then we can take the plus or minus $\\var{cpower}$<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 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;\">\n<div data-jme-visible=\"gcd(cc-cb,cxcoeff)&lt;&gt;1\">$z^\\var{cpower}$</div>\n</td>\n<td>\n<div data-jme-visible=\"gcd(cc-cb,cxcoeff)&lt;&gt;1\">$=$</div>\n</td>\n<td style=\"text-align: left;\">\n<div data-jme-visible=\"gcd(cc-cb,cxcoeff)&lt;&gt;1\">$\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}}$</div>\n</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;\">$\\pm\\sqrt[\\var{cpower}]{\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}}}$</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;\">$\\pm\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}^{1/{cpower}}}$</td>\n</tr>\n</tbody>\n</table>\n<p>That is, $z$ equals $-\\sqrt[\\var{cpower}]{\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}}}$, or&nbsp;$\\sqrt[\\var{cpower}]{\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}}}$.</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, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "({(cc-cb)/cxcoeff})^(1/{cpower})", "answerSimplification": "fractionNumbers", "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": []}], "answer": "-({(cc-cb)/cxcoeff})^(1/{cpower})", "answerSimplification": "fractionNumbers", "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": []}, {"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, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "-({(cc-cb)/cxcoeff})^(1/{cpower})", "answerSimplification": "fractionNumbers", "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": []}], "answer": "({(cc-cb)/cxcoeff})^(1/{cpower})", "answerSimplification": "fractionNumbers", "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": true}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "marked_original_order (Mark the gaps in the original order, mainly to establish if every gap has a valid answer):\n    map(\n        mark_part(gap[\"path\"],studentAnswer),\n        [gap,studentAnswer],\n        zip(gaps,studentAnswer)\n    )\n\ninterpreted_answers (The interpreted answers for each gap, in the original order):\n    map(\n        res[\"values\"][\"interpreted_answer\"],\n        res,\n        marked_original_order\n    )\n\nanswers (The student's answers to each gap): interpreted_answers\n\ngap_feedback (Feedback on each of the gaps):\n    map(\n        try(\n            let(\n                answer, studentAnswer[answer_number],\n                result, submit_part(gaps[gap_number][\"path\"],answer),\n                gap, gaps[gap_number],\n                name, gap[\"name\"],\n                noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n                non_warning_feedback, filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]),\n                    assert(noFeedbackIcon,\n                        assert(name=\"\" or len(gaps)=1 or len(non_warning_feedback)=0,feedback(translate('part.gapfill.feedback header',[\"name\": name])))\n                    );\n                    concat_feedback(non_warning_feedback, if(marks>0,result[\"marks\"]/marks,1/len(gaps)), noFeedbackIcon);\n                    result\n            ),\n            err,\n            fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n        ),\n        [gap_number, answer_number],\n        zip(gap_adaptive_order, gap_adaptive_order)\n    )\n\nall_valid (Are the answers to all of the gaps valid?):\n  all(map(res[\"valid\"], res, marked_original_order))\n\ncheck_answers:\n if(\n   answers[1]=answers[0],\n   sub_credit(1/2, \"Numbers cannot be the same. \"),\n   feedback(\"\")\n )\n\nmark:\n  assert(all_valid or not settings[\"sortAnswers\"], fail(translate(\"question.can not submit\")));\n  apply(answers);\n  apply(check_answers);\n  apply(gap_feedback)\n\ninterpreted_answer:\n  answers\n\npre_submit:\n    map(\n        let(\n            answer, studentAnswer[answer_number],\n            result, submit_part(gaps[gap_number][\"path\"],answer),\n            check_pre_submit(gaps[gap_number][\"path\"], answer, exec_path)\n        ),\n        [gap_number,answer_number],\n        zip(gap_order,answer_order)\n    )", "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]], or&nbsp;[[1]].</p>", "stepsPenalty": "2", "steps": [{"type": "information", "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>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 plus or minus $\\var{bpower}$<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, 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;\">$\\pm\\sqrt[\\var{bpower}]{\\var{dc*ddenom}}$</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;\">$\\pm\\sqrt[\\var{bpower}]{\\var{dc*ddenom}}$</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;\">$\\pm\\simplify{root({dc*ddenom},{bpower})-{db}}$</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;\">$\\pm\\simplify{{dc*ddenom}^(1/{bpower})-{db}}$</td>\n</tr>\n</tbody>\n</table>\n<p>That is, $z$ equals $-\\simplify{root({dc*ddenom},{bpower})-{db}}$, or $\\simplify{root({dc*ddenom},{bpower})-{db}}$.</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, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "({dc*ddenom})^(1/{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": []}], "answer": "-({dc*ddenom})^(1/{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": []}, {"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, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "-({dc*ddenom})^(1/{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": []}], "answer": "({dc*ddenom})^(1/{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": true}], "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/"}]}