// Numbas version: exam_results_page_options {"name": "Factorisation: finding factors", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["prime", "primepower", "p2pp", "xpower", "ypower", "xconstant", "xconstantpower", "failconstant", "failsafepower", "failsafepowerm1", "failsafepowerp1", "xcpowerm1", "xcpowerp1", "choices", "marks"], "name": "Factorisation: finding factors", "tags": ["algebra", "common factors", "factorisation", "Factorisation", "factorising", "factors", "Factors"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"maxAnswers": 0, "displayColumns": 0, "prompt": "

Which of the following are factors of $\\simplify{{prime^primepower}x^{xpower}y^{ypower}(x+{xconstant})^{xconstantpower} (z+{failconstant})^{failsafepower}}$?

", "matrix": "marks", "minAnswers": 0, "variableReplacements": [], "choices": "choices", "variableReplacementStrategy": "originalfirst", "displayType": "checkbox", "maxMarks": 0, "scripts": {}, "warningType": "none", "marks": 0, "showCorrectAnswer": true, "type": "m_n_2", "shuffleChoices": true, "minMarks": 0}, {"distractors": ["", "", ""], "prompt": "

Suppose that $\\var{factor1}${factor2} is a factor of an expression. What can be said of $-\\var{factor1}${factor2}?

", "matrix": ["1", 0, 0], "shuffleChoices": false, "variableReplacements": [], "choices": ["

It is also a factor.

", "

It is not necessarily a factor.

", "

It is definitely not a factor.

"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "marks": 0, "scripts": {}, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "", "variable_groups": [{"variables": ["factor1", "factor2"], "name": "b"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"prime": {"definition": "random(2,3,5,7)", "templateType": "anything", "group": "Ungrouped variables", "name": "prime", "description": ""}, "factor1": {"definition": "random(2..144)", "templateType": "anything", "group": "b", "name": "factor1", "description": ""}, "factor2": {"definition": "random('\\$x\\$','\\$x^2\\$','\\$xy\\$','\\$x^2y\\$','\\$xy^2\\$','\\$x^2y^2\\$','\\$(x+1)\\$','\\$(y-1)^3\\$')", "templateType": "anything", "group": "b", "name": "factor2", "description": ""}, "failsafepowerp1": {"definition": "failsafepower+1", "templateType": "anything", "group": "Ungrouped variables", "name": "failsafepowerp1", "description": ""}, "xconstantpower": {"definition": "random(0..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "xconstantpower", "description": ""}, "primepower": {"definition": "random(1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "primepower", "description": ""}, "xcpowerp1": {"definition": "xconstantpower+1", "templateType": "anything", "group": "Ungrouped variables", "name": "xcpowerp1", "description": ""}, "choices": {"definition": "['\\$1\\$','\\$\\\\var{prime}\\$','\\$\\\\var{prime^2}\\$','\\$\\\\simplify{{p2pp}x^{xpower}y^{ypower}(x+{xconstant})^{xconstantpower}(z+{failconstant})^{failsafepower}} \\$']+if(xpower<2 and ypower<2 and xconstantpower<2,['\\$(z+'+failconstant+')^'+failsafepowerm1+'\\$','\\$(z+'+failconstant+')^'+failsafepowerp1+'\\$'],if(xconstantpower>1,['\\$\\\\simplify{(x+{xconstant})^{xcpowerm1}}\\$','\\$(x+'+xconstant+')^'+xcpowerp1+'\\$'],['\\$(x+'+xconstant+')^'+xcpowerp1+'\\$'])+if(xpower>=1 and ypower>=1 and (xpower>2 or ypower>2),['\\$xy\\$','\\$x^2y^2\\$','\\$x^2y\\$'],['\\$x\\$','\\$y\\$'])+if(primepower>=1 and xconstantpower>=1, ['\\$\\\\simplify{{prime} (x+{xconstant})^{xconstantpower}}\\$'],[]))", "templateType": "anything", "group": "Ungrouped variables", "name": "choices", "description": "

$\\simplify{{prime^primepower}x^{xpower}y^{ypower}(x+{xconstant})^{xconstantpower} (z+{failconstant})^{failsafepower}}$

"}, "ypower": {"definition": "random(0..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ypower", "description": ""}, "failsafepowerm1": {"definition": "failsafepower-1", "templateType": "anything", "group": "Ungrouped variables", "name": "failsafepowerm1", "description": ""}, "xcpowerm1": {"definition": "xconstantpower-1", "templateType": "anything", "group": "Ungrouped variables", "name": "xcpowerm1", "description": ""}, "p2pp": {"definition": "prime^primepower", "templateType": "anything", "group": "Ungrouped variables", "name": "p2pp", "description": ""}, "marks": {"definition": "[1,if(primepower>=1,1,0),if(primepower>=2,1,0),1]+if(xpower<2 and ypower<2 and xconstantpower<2,[1,0],if(xconstantpower>1,[1,0],[0])+if(xpower>=1 and ypower>=1 and (xpower>2 or ypower>2),[1,if(xpower>=2 and ypower>=2,1,0),if(xpower>=2,1,0)],[if(xpower>=1,1,0),if(ypower>=1,1,0)])+if(primepower>=1 and xconstantpower>=1, [1],[]))", "templateType": "anything", "group": "Ungrouped variables", "name": "marks", "description": ""}, "xconstant": {"definition": "random(1..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "xconstant", "description": ""}, "failsafepower": {"definition": "if(xpower<2 and ypower<2 and xconstantpower<2,3,0 )", "templateType": "anything", "group": "Ungrouped variables", "name": "failsafepower", "description": ""}, "failconstant": {"definition": "random(1..12 except xconstant)", "templateType": "anything", "group": "Ungrouped variables", "name": "failconstant", "description": ""}, "xpower": {"definition": "random(0..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "xpower", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "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/"}]}