// Numbas version: exam_results_page_options {"name": "Clare's copy of Input 5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "

ALGEBRAIC FRACTIONS

This question concerns ratios of algebraic expressions.

By this we mean expressions of the form $\\displaystyle \\frac{p(x)}{q(x)}$ where $p(x)$ and $q(x)$ are algebraic expressions.

If you want to input such an expression into the system you HAVE TO BE CAREFUL AND USE BRACKETS or mistakes will occur.

Once again, the preview answer box displaying your input in mathematical notation beside the input boxes in parts a, b and c is very useful as it shows what the system thinks you have entered.

", "name": "Clare's copy of Input 5", "ungrouped_variables": ["c", "a", "d", "b"], "preamble": {"js": "", "css": ""}, "extensions": [], "variables": {"c": {"description": "", "name": "c", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)"}, "d": {"description": "", "name": "d", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9 except [round(b*c/a),c])"}, "b": {"description": "", "name": "b", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(3..15#2)"}, "a": {"description": "", "name": "a", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..16#2)"}}, "variable_groups": [], "metadata": {"description": "

Instructions on inputting ratios of algebraic expressions.

", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["all", "!collectNumbers"]}, "parts": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "

Suppose we wanted to input the expression $\\displaystyle \\frac{\\var{a}+\\var{b}x}{\\var{c}+\\var{d}y}$ into the system.

Which of the following input expressions are incorrect?

[[0]]

Choose the incorrect input(s).

After you have clicked Submit part, click on Show Feedback and you will be given more detail on your choices.

({a}+{b}x)/({c}+{d}y)

", "

{a}+{b}x/({c}+{d}y)

", "

{a}+{b}x/{c}+{d}y

", "

({a}+{b}x)/{c}+{d}y

"], "distractors": ["({a}+{b}x)/({c}+{d}y)
This is the correct input, so your choice is wrong!", "{a}+{b}x/({c}+{d}y)
Good choice: the system thinks this is $\\simplify[std]{ {a}+{b}x/({c}+{d}y)}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$.", "{a}+{b}x/{c}+{d}y
Good choice: the system thinks this is $\\simplify[std]{ {a}+{b}x/{c}+{d}y}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$.", "({a}+{b}x)/{c}+{d}y
Good choice: the system thinks this is $\\simplify[std]{ ({a}+{b}x)/{c}+{d}y}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$."], "displayType": "checkbox", "minAnswers": 0, "minMarks": 0, "showCellAnswerState": true, "useCustomName": false, "variableReplacements": [], "customMarkingAlgorithm": "", "displayColumns": 1, "marks": 0, "maxMarks": 0, "unitTests": [], "showCorrectAnswer": true, "shuffleChoices": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "matrix": ["0", "1", "1", "1"], "extendBaseMarkingAlgorithm": true, "maxAnswers": 0, "customName": "", "warningType": "none"}], "sortAnswers": false, "marks": 0}, {"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "

Input the expression $\\displaystyle \\frac{\\var{b}+\\var{a}y}{\\var{d}+\\var{c}z}$. [[0]]

", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "variableReplacements": [], "customMarkingAlgorithm": "", "gaps": [{"type": "jme", "checkingAccuracy": 0.001, "showFeedbackIcon": true, "checkingType": "absdiff", "failureRate": 1, "unitTests": [], "scripts": {}, "checkVariableNames": false, "variableReplacements": [], "customMarkingAlgorithm": "", "marks": "1", "showCorrectAnswer": true, "answerSimplification": "std", "valuegenerators": [{"name": "y", "value": ""}, {"name": "z", "value": ""}], "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "answer": "({b}+{a}y)/({d}+{c}z)", "extendBaseMarkingAlgorithm": true, "customName": "", "useCustomName": false, "vsetRange": [0, 1], "showPreview": true}], "sortAnswers": false, "marks": 0}, {"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "

Input the expression $\\displaystyle \\frac {\\var{d} z + \\var{b}} {(x + \\var{a}) (y + \\var{c})}$. [[0]]

", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "variableReplacements": [], "customMarkingAlgorithm": "", "gaps": [{"type": "jme", "checkingAccuracy": 0.001, "showFeedbackIcon": true, "checkingType": "absdiff", "failureRate": 1, "unitTests": [], "scripts": {}, "checkVariableNames": false, "variableReplacements": [], "customMarkingAlgorithm": "", "marks": "1.5", "showCorrectAnswer": true, "answerSimplification": "std", "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}, {"name": "z", "value": ""}], "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "answer": "({d} * z + {b}) / ((x + {a}) * (y + {c}))", "extendBaseMarkingAlgorithm": true, "customName": "", "useCustomName": false, "vsetRange": [0, 1], "showPreview": true}], "sortAnswers": false, "marks": 0}, {"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "

Input the expression $\\displaystyle \\simplify[std]{({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 * b}) * (y -{3* d}))}$. [[0]]

", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "variableReplacements": [], "customMarkingAlgorithm": "", "gaps": [{"type": "jme", "checkingAccuracy": 0.0001, "showFeedbackIcon": true, "checkingType": "absdiff", "failureRate": 1, "unitTests": [], "scripts": {}, "checkVariableNames": false, "variableReplacements": [], "customMarkingAlgorithm": "", "marks": "2.5", "showCorrectAnswer": true, "answerSimplification": "std", "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "answer": "({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 b}) * (y -{3* d}))", "extendBaseMarkingAlgorithm": true, "customName": "", "useCustomName": false, "vsetRange": [0, 1], "showPreview": true}], "sortAnswers": false, "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "functions": {}, "advice": "

a)

The correct input is ({a}+{b}x)/({c}+{d}y) - the rest are incorrect and you should have chosen those.

b)

A correct input is ({b} + {a}y) / ({c} + {d}z). Also correct is ({a}y+{b}) / ({c} + {d}z) etc.

c)

A correct input is ({d}z + {b}) / ((x + {a})*(y + {c})).

Note the denominator (the bottom of the ratio) has to have two brackets, i.e. ((x + {a})*(y + {c})) as otherwise the expression ({d}z + {b}) / (x + {a})*(y + {c}) is seen by the system as $\\displaystyle \\left(\\simplify[std]{({d} * z + {b}) / (x + {a})}\\right) (y + \\var{c})$

d)

A correct input is ({a} -({b}x + {c})*e ^ ( -{2}x)) / ((x + {2*b})*(y -{3*d})).

\n ", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}]}