// Numbas version: exam_results_page_options
{"name": "Combining algebraic fractions 0", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Combining algebraic fractions 0", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "checked2015", "combining algebraic fractions", "common denominator"], "metadata": {"description": "<p>Express $\\displaystyle a \\pm&nbsp; \\frac{c}{x + d}$&nbsp;as an algebraic single fraction.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Add the following &nbsp;together and express as a single algebraic fraction.</p>\n  <p>&nbsp;</p>", "advice": "<p>We have:</p>\n  <p>\\[\\simplify[std]{{a} + ({c} / ({a2}*x + {d})) = ({a} * ({a2}*x + {d}) + {c}) &nbsp;/ (({a2}*x + {d})) = ({a*a2} * x + {a * d + c}) / ( ({a2}*x + {d}))}\\]</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "variables": {"s1": {"name": "s1", "group": "Ungrouped variables", "definition": "if(c<0,-1,1)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9..9 except a2)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,a,-a])", "description": "", "templateType": "anything"}, "nb": {"name": "nb", "group": "Ungrouped variables", "definition": "if(c<0,'taking away','adding')", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "d", "nb", "a2", "s1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Express \\[\\simplify[std]{{a} &nbsp;+ ({c} / ({a2}x + {d}))}\\] as a single algebraic fraction.</p>\n      <p>Input the fraction here: [[0]].</p>\n      <p>You can click on Show steps for help. You will lose 1 mark if you do so.</p>\n      <p>&nbsp;</p>", "stepsPenalty": 1, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The formula for adding these expressions is :<br/>\\[\\simplify[std]{a + {s1} * (c / d) = (ad + {s1} * bc) / d}\\]</p>\n          <p>and for this exercise we have &nbsp;$\\simplify{d={a2}x+{d}}$.</p>\n          <p>&nbsp;</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 2, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "({a*a2}x+{a*d+c})/({a2}x+{d})", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 1e-05, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [10, 11], "checkVariableNames": false, "minlength": {"length": 12, "partialCredit": 0, "message": "<p>Input as a single fraction.</p>"}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}