Ratios of Algebraic Expressions.
\nBy this we mean expressions of the form $\\displaystyle \\frac{p(x)}{q(x)}$ where $p(x)$ and $q(x)$ are algebraic expressions.
\nIf you want to input such an expression into the system you HAVE TO BE CAREFUL AND USE BRACKETS otherwise mistakes will occur.
\nOnce again, the box displaying your input in mathematical notation beside the input boxes in parts 2, 3 and 4 is very useful as it shows what the system thinks you have entered.
\nFor complicated expressions this is essential as you can check you have written what you really meant.
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\nSuppose we wanted to input the expression $\\displaystyle \\frac{\\var{a}+\\var{b}x}{\\var{c}+\\var{d}y}$ into the system.
\nWhich of the following input expressions are incorrect?
\n[[0]]
\nChoose the incorrect input(s): (You lose 3 marks if you choose the wrong one!)
\nIf you click on Submit part, then on Show feedback, you will be given more detail on your choices.
\nYou can click on Reveal at the top of the window to see solutions, but it's best to work these through yourself. Remember you can always redo the question by clicking on Try another question like this one at the bottom.
", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "distractors": ["This is the correct input, so your choice is wrong!", "Good choice as the system thinks this is $\\simplify[std]{ {a}+{b}x/({c}+{d}y)}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$", "Good choice as the system thinks this is $\\simplify[std]{ {a}+{b}x/{c}+{d}y}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$", "Good choice as the system thinks this is $\\simplify[std]{ ({a}+{b}x)/{c}+{d}y}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$"], "maxAnswers": 0, "displayColumns": 1, "matrix": [-3, 1, 1, 1], "type": "m_n_2", "useCustomName": false, "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}, "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
Input the expression $\\displaystyle \\frac{\\var{b}+\\var{a}y}{\\var{d}+\\var{c}z}$ here: [[0]]
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", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "answerSimplification": "std", "checkingType": "absdiff", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "x"}, {"value": "", "name": "y"}, {"value": "", "name": "z"}], "variableReplacements": [], "scripts": {}, "checkVariableNames": false, "failureRate": 1, "marks": 1, "unitTests": [], "customName": "", "answer": "({d} * z + {b}) / ((x + {a}) * (y + {c}))", "showCorrectAnswer": true, "vsetRangePoints": 5, "checkingAccuracy": 0.001, "extendBaseMarkingAlgorithm": true, "showPreview": true}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "customName": "", "prompt": "Input the expression $\\displaystyle \\simplify[std]{({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 * b}) * (y -{3* d}))}$ here: [[0]]
", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "answerSimplification": "std", "checkingType": "absdiff", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "x"}, {"value": "", "name": "y"}], "variableReplacements": [], "scripts": {}, "checkVariableNames": false, "failureRate": 1, "marks": 1, "unitTests": [], "customName": "", "answer": "({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 b}) * (y -{3* d}))", "showCorrectAnswer": true, "vsetRangePoints": 5, "checkingAccuracy": 0.0001, "extendBaseMarkingAlgorithm": true, "showPreview": true}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}}], "advice": "a) The correct input is ({a}+{b}x)/({c}+{d}y) - the rest are incorrect and you should have ticked 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}))