// Numbas version: finer_feedback_settings
{"name": "Lois's copy of Test1:  Combining algebraic fractions ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "nb", "a1", "p", "a2", "s1"], "name": "Lois's copy of Test1:  Combining algebraic fractions ", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "combining algebraic fractions", "common denominator"], "preamble": {"css": "", "js": ""}, "advice": "<p>A good choice for the denominator of the fraction we are looking for is &nbsp;$\\simplify{(x+{p})({a1}x+{b})({a2}x+{d})}$ since the denominators of both original fractions contain the factor $ \\simplify{(x+{p})}$.</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>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"], "std1": ["std", "collectNumbers"]}, "parts": [{"prompt": "<p>Write \\[\\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>Make sure that you simplify the numerator.</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Input as a single fraction and make sure that you simplify the numerator.</p>", "showStrings": false, "strings": [")-", ")+"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 1e-05, "vsetrange": [10, 11], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std1", "scripts": {}, "answer": "({a*a2 +  c*a1} * x + {a * d +  c * b})/ ((x+{p})({a1}*x + {b}) * ({a2}*x + {d}))", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p></p>\n<p>&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-9..9 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-9..9 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-9..9 except [0,round(b*a2/a1)])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "nb": {"definition": "if(c<0,'taking away','adding')", "templateType": "anything", "group": "Ungrouped variables", "name": "nb", "description": ""}, "a1": {"definition": "random(1..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "p": {"definition": "random(-9..9 except [round(b/a1),round(d/a2)])", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "a2": {"definition": "random(1..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "s1": {"definition": "if(c<0,-1,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}}, "metadata": {"notes": "<p><strong>5/08/2012:</strong></p>\n    <p>Added tags.</p>\n    <p>Added description.</p>\n    <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    <p><strong>12/08/2012:</strong></p>\n    <p>Back to one input of a fraction and trapped input in Forbidden Strings.</p>\n    <p>Used the except feature of ranges to get non-degenerate examples.</p>\n    <p>Checked calculation.OK.</p>\n    <p>Improved display in content areas.</p>\n    <p><strong>04/02/2013:</strong></p>\n    <p>Added statements about simplifying the numerator.</p>", "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>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}