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{"name": "AB9 HCF of Algebraic Terms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "AB9 HCF of Algebraic Terms", "tags": [], "metadata": {"description": "<p>Fiind the Highest Common Factor of two algebraic expressions involving a coefficient and powers of $x$ and $y$.</p>\n<p></p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>What is the highest common factor of $\\var{c[0]}x^\\var{xp[0]}y^\\var{yp[0]}$ and $\\var{c[1]}x^\\var{xp[1]}y^\\var{yp[1]}$?</p>", "advice": "<p>In order to find the highest common factor of two single term algebraic expressions you can first find the highest common factor of the coefficients.</p>\n<p></p>\n<p>In this case the Highest common factor of $\\var{c[0]}$ and $\\var{c[1]}$ is $\\var{cans}$.</p>\n<p>Then work through each of the variables (letters) in turn and see what powers of each appear. In the first expression there is $x^\\var{xp[0]}$ and the second expression there is $x^\\var{xp[1]}$. So they both have <strong>at least</strong> $x^\\var{xpans}$ in them. Similarly, the first expression there is $y^\\var{yp[0]}$ and the second expression there is $y^\\var{yp[1]}$. So they both have <strong>at least</strong> $y^\\var{ypans}$ in them.</p>\n<p>Hence, the Highest Common Factor (HCF) of the two expressions is:</p>\n<p>\\[\\var{cans}x^\\var{xpans}y^\\var{ypans}.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Collect\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "repeat(2*random(6..25),2)", "description": "", "templateType": "anything", "can_override": false}, "xp": {"name": "xp", "group": "Ungrouped variables", "definition": "repeat(random(1..8),2)", "description": "", "templateType": "anything", "can_override": false}, "yp": {"name": "yp", "group": "Ungrouped variables", "definition": "repeat(random(1..8 except [xp[0],xp[1]]),2)", "description": "", "templateType": "anything", "can_override": false}, "cans": {"name": "cans", "group": "Ungrouped variables", "definition": "GCD(c[0],c[1])", "description": "", "templateType": "anything", "can_override": false}, "xpans": {"name": "xpans", "group": "Ungrouped variables", "definition": "min(xp[0],xp[1])", "description": "", "templateType": "anything", "can_override": false}, "ypans": {"name": "ypans", "group": "Ungrouped variables", "definition": "min(yp[0],yp[1])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "xp[0]<>xp[1] AND c[0]<>c[1]", "maxRuns": 100}, "ungrouped_variables": ["c", "xp", "yp", "cans", "xpans", "ypans"], "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, "answer": "{cans}*x^{xpans}*y^{ypans}", "answerSimplification": "basic", "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": [{"name": "x", "value": ""}, {"name": "y", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}]}]}], "contributors": [{"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}]}