// Numbas version: exam_results_page_options
{"name": "1.2.4 Task: Simplify an expression using only positive indices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.2.4 Task: Simplify an expression using only positive indices", "tags": [], "metadata": {"description": "<p>Write an expression (a^k1*a^k2)/a^k3 using a single positive index. Variable a is randomised and can be a number or a letter. k1,k2 and k3 are randomised positive numbers.</p>\n<p>Part of HELM Book 1.2</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify $\\displaystyle{\\var{q2_expr}}$. Do not use any negative indices in your answer.</p>", "advice": "<p>First simplify the numerator using the first law of indices.</p>\n<p>\\[\\var{q2_expr}=\\frac{\\var{v}^{(\\var{q2_idx1})+(\\var{q2_idx2})}}{\\var{v}^{(\\var{q2_idx3})}}=\\frac{\\var{v}^{(\\var{q2_idx1+q2_idx2})}}{\\var{v}^{(\\var{q2_idx3})}}\\]</p>\n<p>Then use the second law.</p>\n<p>\\[=\\var{v}^{(\\var{q2_idx1+q2_idx2})-(\\var{q2_idx3})}=\\var{v}^{\\var{q2_idx1+q2_idx2-q2_idx3}}\\]</p>\n<p><span data-jme-visible=\"(q2_idx1+q2_idx2-q2_idx3)=0\">\\[=1\\]</span></p>\n<p><span data-jme-visible=\"(q2_idx1+q2_idx2-q2_idx3)=1\">\\[=\\var{v}\\]</span></p>\n<p><span data-jme-visible=\"(q2_idx1+q2_idx2-q2_idx3)&lt;0\">Finally, convert to a positive index.</span></p>\n<p><span data-jme-visible=\"(q2_idx1+q2_idx2-q2_idx3)&lt;0\">\\[=\\frac{1}{\\var{v}^{\\var{-1*(q2_idx1+q2_idx2-q2_idx3)}}}\\]</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"q2_expr": {"name": "q2_expr", "group": "Ungrouped variables", "definition": "expression( \n  \"(\" + q2_letter + \"^\" + q2_idx1 + \"*\" + q2_letter + \"^\" + q2_idx2 + \")\" +\n  \"/\" + q2_letter + \"^\" + q2_idx3 )", "description": "", "templateType": "anything", "can_override": false}, "q2_ans": {"name": "q2_ans", "group": "Ungrouped variables", "definition": "simplify(if(q2_idx > 0,\n  expression(q2_letter+\"^\"+q2_idx),\n  expression(\"1/\"+q2_letter+\"^\"+q2_negidx)\n),[\"basic\",\"unitPower\",\"zeroPower\",\"simplifyFractions\"])", "description": "", "templateType": "anything", "can_override": false}, "alphabet": {"name": "alphabet", "group": "Ungrouped variables", "definition": "['a','b','c','d','f','g','h','k','m','n','p','q','r','s','t','v','w','x','y','z']", "description": "", "templateType": "anything", "can_override": false}, "q2_letter": {"name": "q2_letter", "group": "Ungrouped variables", "definition": "random(random(alphabet),random(2..20))", "description": "", "templateType": "anything", "can_override": false}, "q2_idx": {"name": "q2_idx", "group": "Ungrouped variables", "definition": "q2_idx1+q2_idx2-q2_idx3", "description": "", "templateType": "anything", "can_override": false}, "q2_negidx": {"name": "q2_negidx", "group": "Ungrouped variables", "definition": "-q2_idx", "description": "", "templateType": "anything", "can_override": false}, "q2_idx1": {"name": "q2_idx1", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "q2_idx2": {"name": "q2_idx2", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "q2_idx3": {"name": "q2_idx3", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "if(type(q2_letter)=\"string\",\n  expression(q2_letter),\n  expression(string(q2_letter))\n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alphabet", "q2_letter", "q2_expr", "q2_ans", "q2_idx", "q2_negidx", "q2_idx1", "q2_idx2", "q2_idx3", "v"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "stepsPenalty": 0, "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>First simplify the numerator using the first law of indices.</p>"}, {"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>Then use the second law.</p>"}, {"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>Finally, convert to a positive index, if needed.</p>"}], "answer": "{q2_ans}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": ["0.7", "0.8"], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": true, "caseSensitive": false, "notallowed": {"strings": ["-"], "showStrings": false, "partialCredit": 0, "message": ""}, "mustmatchpattern": {"pattern": "$v^$n`? `| 1/$v^$n`? `| $n^$n`? `| 1/$n^$n`? `| 1", "partialCredit": 0, "message": "You need to give the answer as a single variable to a positive power.", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}