// Numbas version: exam_results_page_options
{"name": "Combining algebraic fractions", "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)", "description": "", "name": "s1"}, "a2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..8)", "description": "", "name": "a2"}, "p": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except [round(b/a1),round(d/a2)])", "description": "", "name": "p"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "name": "b"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "name": "c"}, "nb": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(c<0,'taking away','adding')", "description": "", "name": "nb"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,round(b*a2/a1)])", "description": "", "name": "d"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..8)", "description": "", "name": "a1"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "name": "a"}}, "ungrouped_variables": ["a", "c", "b", "d", "nb", "a1", "p", "a2", "s1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Combining algebraic fractions", "functions": {}, "showQuestionGroupNames": false, "parts": [{"stepsPenalty": 1, "scripts": {}, "gaps": [{"answer": "({a*a2 +  c*a1} * x + {a * d +  c * b})/ ((x+{p})({a1}*x + {b}) * ({a2}*x + {d}))", "vsetrange": [10, 11], "checkingaccuracy": 1e-05, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input as a single fraction.</p>\n            <p>Also make sure that the numerator of your answer is input in the $(ax+b)$ with no brackets other than the ones shown.</p>", "showStrings": false, "partialCredit": 0, "strings": [")-", ")+"]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "std1", "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "\n        <p>Express \\[\\simplify{{a} /((x+{p}) ({a1}x + {b})) + ({c} /( (x+{p})({a2}x + {d})))}\\] as a single fraction.</p>\n        <p>Input the fraction here: [[0]].</p>\n        <p>&nbsp;Click on Show steps if you need help. You will lose one mark of you do so.</p>\n        ", "steps": [{"type": "information", "prompt": "\n            <p>Note that the denominators both have the factor $\\simplify{x+{p}}$ hence we see that a common denominator is $\\simplify{(x+{p})({a1}x+{b})({a2}x+{d})}$ as both denominators, $\\simplify{(x+{p})({a1}x+{b})}$ and&nbsp;&nbsp;$\\simplify{(x+{p})({a2}x+{d})}$,&nbsp;divide into it.</p>\n            <p>Note that in your answer you do not need to expand the denominator.</p>\n            ", "showCorrectAnswer": true, "scripts": {}, "marks": 0}], "showCorrectAnswer": true, "marks": 0}], "statement": "<p>Add the following two fractions together and express as a single fraction over a common denominator.</p>\n    <p>&nbsp;Make sure that your answer has a numerator which you input in form $(ax+b)$ with no brackets other than the ones shown.</p>", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "checked2015", "combining algebraic fractions", "common denominator", "MAS1601", "mas1601"], "rulesets": {"std1": ["std", "collectNumbers"], "std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n                        \t\t                        \t\t<p><strong>5/08/2012:</strong></p>\n                        \t\t                        \t\t                        <p>Added tags.</p>\n                        \t\t                        \t\t                        <p>Added description.</p>\n                        \t\t                        \t\t                        <p>Changed to two questions, for the numerator and denomimator, rather than one as difficult to trap student input for this example. Still some ambiguity however.</p>\n                        \t\t                        \t\t                        <p><strong>12/08/2012:</strong></p>\n                        \t\t                        \t\t                        <p>Back to one input of a fraction and trapped input in Forbidden Strings.</p>\n                        \t\t                        \t\t                        <p>Used the except feature of ranges to get non-degenerate examples.</p>\n                        \t\t                        \t\t                        <p>Checked calculation.OK.</p>\n                        \t\t                        \t\t                        <p>Improved display in content areas.</p>\n                        \t\t                        \n                        \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Express $\\displaystyle \\frac{a}{(x+r)(px + b)} + \\frac{c}{(x+r)(qx + d)}$&nbsp;as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "\n    <p>Show steps tells us that a good choice for the denominator of the algebraic fraction we are looking for is &nbsp;$\\simplify{(x+{p})({a1}x+{b})({a2}x+{d})}$.</p>\n    <p>Hence we have:<br/>\\[\\begin{eqnarray*} \\simplify{{a} /((x+{p}) ({a1}x + {b})) + ({c} /( (x+{p})({a2}x + {d})))}&nbsp;&nbsp;&amp;=&amp; \\simplify[std]{({a} * ({a2}*x + {d}) + {c} * ({a1}*x + {b})) / ((x+{p})({a1}*x + {b}) * ({a2}*x + {d})) }\\\\&amp;=&amp; \\simplify{({a*a2 + c*a1} * x + {a * d + c * b}) / ((x+{p})({a1}*x + {b}) * ({a2}*x + {d}))}\\end{eqnarray*}\\]</p>\n    ", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}