// Numbas version: exam_results_page_options
{"name": "Combining algebraic fractions 3.0", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"s1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(c<0,-1,1)", "name": "s1", "description": ""}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,round(b2*a2/c)])", "name": "d", "description": ""}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..9 except a)", "name": "c", "description": ""}, "nb": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(c<0,'taking away','adding')", "name": "nb", "description": ""}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "name": "b1", "description": ""}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0", "name": "a", "description": ""}, "b2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..5 except  0)", "name": "b2", "description": ""}, "a2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "1", "name": "a2", "description": ""}}, "ungrouped_variables": ["a", "c", "d", "s1", "a2", "b1", "b2", "nb"], "name": "Combining algebraic fractions 3.0", "functions": {}, "parts": [{"customName": "", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "steps": [{"prompt": "<p>Note that:<br/>\\[\\simplify[std]{a + &nbsp;(c / d) = (a*d + c) / d}\\]</p>", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "useCustomName": false, "customName": "", "unitTests": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 0}], "useCustomName": false, "prompt": "\n        <p>Express \\[\\simplify[std]{{a}x+{b1} } +\\simplify[std]{ ({c}x+{b2}) / ({a2}x + {d})}\\] as a single fraction.</p>\n      <p>Input the fraction here: [[0]].</p>\n      <p>Click on Show steps to get more information. You will lose one mark if you do so.</p>\n      <p>&nbsp;</p>\n        ", "stepsPenalty": 1, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "gaps": [{"answer": "( {c+b1*a2} * x + {b1 * d +  b2 })/ ( ({a2}*x + {d}))", "scripts": {}, "answerSimplification": "std", "useCustomName": false, "checkingType": "absdiff", "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [10, 11], "showFeedbackIcon": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "checkingAccuracy": 1e-05, "variableReplacements": [], "failureRate": 1, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "checkVariableNames": false, "unitTests": [], "mustmatchpattern": {"message": "Enter your answer as a single fraction.", "pattern": "?/(`!$n)", "partialCredit": 0, "nameToCompare": ""}, "vsetRangePoints": 5, "showPreview": true, "marks": 2}], "type": "gapfill", "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "sortAnswers": false}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Express the following as a single fraction.</p>", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "checked2015", "combining algebraic fractions"], "rulesets": {"std": ["all", "fractionNumbers", "!noLeadingMinus", "!collectNumbers"]}, "preamble": {"css": "", "js": ""}, "type": "question", "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Express $\\displaystyle b+ &nbsp;\\frac{dx+p}{x + q}$&nbsp;as an algebraic single fraction.&nbsp;</p>"}, "advice": "<p>The formula for adding these expressions is:</p>\n    <p>\\[\\simplify[std]{a + (c / d) = (ad +&nbsp;c) / d}\\]</p>\n    <p>and for this exercise we have $\\simplify{a={b1}}$, $\\simplify{c={c}x+{b2}}$, $\\simplify{d={a2}x+{d}}$.</p>\n    <p>Hence we have:<br/>\\[\\begin{eqnarray*} \\simplify[std]{{b1} } +\\simplify[std]{ ({c}x+{b2}) / ({a2}x + {d})}&nbsp;&nbsp;&amp;=&amp; \\simplify{(({b1}) * ({a2}*x + {d}) + ({c}x+{b2}) ) / ( ({a2}*x + {d}))}\\\\ &amp;=&amp;\\simplify[std]{ (({b1*a2}x+{b1*d})+{c}x+{b2}) / ( ({a2}*x + {d}))}\\\\&amp;=&amp;\\simplify[std]{ ( {b1*a2+ c }x+{b1*d+b2}) / (({a2}*x + {d}))}\\end{eqnarray*}\\]</p>", "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/"}]}