// Numbas version: finer_feedback_settings
{"name": "Expression simplification practice", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Expression simplification practice", "tags": [], "metadata": {"description": "<p>You can enter an expression and rearrange it in the following steps. Numbas checks that each arrangement is equivalent to the original expression.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Practice simplifying expressions. You can use the sample expressions given here (changes each time you reload the question), or you can enter your own expression and simplify it. Variable names need to be a single letter (e.g. 's', not 'sec')</p>\n<p>Enter your working one line at a time and you'll be told whether it is still equal to the original expression.</p>\n<p>$\\displaystyle{\\var{expr}}$&nbsp; (copy and paste this: <code>{code}</code> )</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"expr": {"name": "expr", "group": "Ungrouped variables", "definition": "simplify(expressions[idx][\"expr\"],\"basic\")", "description": "", "templateType": "anything", "can_override": false}, "code": {"name": "code", "group": "Ungrouped variables", "definition": "expressions[idx][\"code\"]", "description": "", "templateType": "anything", "can_override": false}, "letters": {"name": "letters", "group": "Ungrouped variables", "definition": "shuffle([\"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}, "letter0": {"name": "letter0", "group": "Ungrouped variables", "definition": "letters[0]", "description": "", "templateType": "anything", "can_override": false}, "expressions": {"name": "expressions", "group": "Ungrouped variables", "definition": "[[\"expr\": simplify(expression(vars[0]*vars[1]+letter0+\"^2+\"+vars[1]+letter0),\"all\"), \n    \"code\": string(simplify(expression(vars[0]*vars[1]+letter0+\"^2+\"+vars[1]+letter0),\"all\"))\n  ],\n [\"expr\": simplify(expression(\"(\"+vars[0]+\"*\"+letter0+\"+\"+vars[1]+\")*(\"+letter0+\"+\"+vars[2]+\")\"),[\"expandBrackets\",\"all\"]),\n    \"code\": string(simplify(expression(\"(\"+vars[0]+\"*\"+letter0+\"+\"+vars[1]+\")*(\"+letter0+\"+\"+vars[2]+\")\"),[\"expandBrackets\",\"all\"]))\n  ],\n [\"expr\": expression(\"ln(abs(\"+vars[0]+\"))+ln(abs(\"+vars[1]+\"))+ln(abs(\"+vars[2]+\")^\"+vars[3]+\")-\"+vars[4]+\"ln(abs(\"+vars[5]+\"))\" ),\n    \"code\":string(simplify(expression(\"ln(abs(\"+vars[0]+\"))+ln(abs(\"+vars[1]+\"))+ln(abs(\"+vars[2]+\")^\"+vars[3]+\")-\"+vars[4]+\"ln(abs(\"+vars[5]+\"))\" ),\"basic\"))\n  ],\n [\"expr\": expression(\"((\"+vars[0]+\"*\"+letter0+\"+\"+vars[0]*vars[1]+\")/(\" + vars[2]*vars[4] + \"))*1*((\" + vars[2]+\"*\"+letter0+\"+\"+vars[2]*vars[3]  + \")/(\"+ letter0 +\"+\"+ vars[1] +\"))\"  ),\n    \"code\":string(simplify(expression(\"((\"+vars[0]+\"*\"+letter0+\"+\"+vars[0]*vars[1]+\")/(\" + vars[2]*vars[4] + \"))*1*((\" + vars[2]+\"*\"+letter0+\"+\"+vars[2]*vars[3]  + \")/(\"+ letter0 +\"+\"+ vars[1] +\"))\"  ),\"basic\"))\n    ],\n [\"expr\": expression(\"((\"  + vars[2]+\"*\"+letter0+\"+\"+vars[2]*vars[3]  + \")/(\"+ letter0 +\"+\"+ vars[1]+ \"))/((\"+ vars[2]*vars[4]+\")/(\"  +vars[0]+\"*\"+letter0+\"+\"+vars[0]*vars[1]+\"))\"  ),\n    \"code\":string(simplify(expression(\"((\"  + vars[2]+\"*\"+letter0+\"+\"+vars[2]*vars[3]  + \")/(\"+ letter0 +\"+\"+ vars[1]+ \"))/((\"+ vars[2]*vars[4]+\")/(\"  +vars[0]+\"*\"+letter0+\"+\"+vars[0]*vars[1]+\"))\"  ),\"basic\"))\n    ],\n]", "description": "<p>expression(\"ln(abs(\"=vars[0]+\"))+ln(abs(\"+vars[1]+\"))+ln(abs(\"+vars[2]+\")^\"+vars[3]+\")-\"+vars[4]+\"ln(abs(\"+vars[5]+\"))\" )</p>", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "Ungrouped variables", "definition": "random(0..length(expressions)-1)", "description": "<p>0: ax^2+bx</p>\n<p>1: ax^2 + bx + c (a quadratic with integer roots)</p>\n<p>2: add and subtract logs</p>\n<p>3: multiplication of algebraic fractions</p>\n<p>4: division of algebraic fractions</p>", "templateType": "anything", "can_override": false}, "vars": {"name": "vars", "group": "Ungrouped variables", "definition": "shuffle(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "Ungrouped variables", "definition": "expression(\"(\"+vars[0]*vars[1]+\"*\"+letter0+\"+\"+vars[0]*vars[1]*vars[2]+\")/(\" + vars[3]*vars[5] + \")*(\" + vars[3]*vars[4]+\"*\"+letter0+\"+\"+vars[3]*vars[4]*vars[5]  + \")/(\"+ letter0 + vars[0] +\")\"  )", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["expr", "code", "letters", "letter0", "expressions", "idx", "vars", "test"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": true, "customName": "original expression", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter the expression given above, or enter your own expression here</p>", "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 4", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 5", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 6", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 7", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 8", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 9", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "step 10", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "expr", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "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/"}], "resources": []}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}