// Numbas version: exam_results_page_options
{"name": "Surds: Simplifying Expressions 3b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Surds: Simplifying Expressions 3b", "tags": [], "metadata": {"description": "<p>Simplifying expressions of the form $(a_1+b_1 \\sqrt{c}) - (a_2 + b_2 \\sqrt{c})$.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify the following expression:</p>\n<p>\\[ (\\simplify[!collectNumbers,unitFactor]{{a1}+{sgn1*b1}sqrt({c})})-(\\simplify[!expandBrackets,unitFactor]{{a2}+{sgn2*b2}sqrt({c})})\\]</p>", "advice": "<p>To simplify the expression we want to expand the brackets and collect like-terms:</p>\n<p>\\[ \\begin{split}(\\simplify[!collectNumbers,unitFactor]{{a1}+{sgn1*b1}sqrt({c})})-(\\simplify[!expandBrackets,unitFactor]{{a2}+{sgn2*b2}sqrt({c})}) &amp;\\,= \\simplify[!collectNumbers,unitFactor]{{a1}-{a2}+{sgn1*b1}sqrt({c})-{sgn2*b2}sqrt({c})} \\\\ &amp;\\,=\\simplify[!noLeadingMinus,zeroTerm,unitFactor]{{a1-a2}+{sgn1*b1-sgn2*b2}sqrt({c})}\\end{split} \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(1..6 except b1)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2,3,5,6,7)", "description": "", "templateType": "anything", "can_override": false}, "sgn1": {"name": "sgn1", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything", "can_override": false}, "sgn2": {"name": "sgn2", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a1", "a2", "b1", "b2", "c", "sgn1", "sgn2"], "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, "prompt": "<p><em>You can type sqrt(x) to get $\\sqrt{x}$.</em></p>", "answer": "{a1-a2}+{sgn1*b1-sgn2*b2}sqrt({c})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "{a1-a2}+{sgn1*b1-sgn2*b2}sqrt({c})", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}