// Numbas version: exam_results_page_options
{"name": "Numbas Input: 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"], "name": "Numbas Input: Algebraic Fractions", "tags": ["algebraic input", "brackets", "input", "introduction", "mathematical expressions", "Numbas", "numbas", "Ratios", "ratios"], "preamble": {"css": "", "js": ""}, "advice": "<h4 class=\"partheader\">a)</h4>\n  <p>The correct input is <code>({a}+{b}x)/({c}+{d}y)</code> - the rest are incorrect and you should have chosen those.</p>\n  <h4 class=\"partheader\">b)</h4>\n  <p>A correct input is <code>({b} + {a}y) / ({c} + {d}z)</code>. Also correct is <code>({a}y+{b}) / ({c} + {d}z)</code> etc.</p>\n  <h4 class=\"partheader\">c)</h4>\n  <p>A correct input is <code>({d}z + {b}) / ((x + {a})*(y + {c}))</code>.</p>\n  <p>Note the denominator (the bottom of the ratio) has to have two brackets, i.e. <code>((x + {a})*(y + {c}))</code> as otherwise the expression <code>({d}z + {b}) / (x + {a})*(y + {c})</code> is seen by the system as $\\displaystyle \\left(\\simplify[std]{({d} * z + {b}) / (x + {a})}\\right) (y + \\var{c})$</p>\n  <h4 class=\"partheader\">d)</h4>\n  <p>A correct input is <code>({a} -({b}x + {c})*e ^ ( -{2}x)) / ((x + {2*b})*(y -{3*d}))</code>.</p>\n  ", "rulesets": {"std": ["all", "!collectNumbers"]}, "parts": [{"prompt": "<p>Suppose you want to input the expression $\\displaystyle \\frac{\\var{a}+\\var{b}x}{\\var{c}+\\var{d}y}$.</p>\n<p>Choose which of the following inputs are <em><strong>incorrect</strong></em>?</p>\n<p></p>\n<p>[[0]]</p>\n<p>After you have clicked <em>Submit part</em>, click on <em>Show Feedback</em>&nbsp;and you will be given more detail on your choices.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"maxAnswers": 0, "displayColumns": 1, "matrix": ["-1", 1, 1, 1], "shuffleChoices": true, "variableReplacements": [], "minAnswers": 0, "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "distractors": ["<code>({a}+{b}x)/({c}+{d}y)</code><br/> This is the correct input, so your choice is wrong!", "<code>{a}+{b}x/({c}+{d}y)</code><br/> Good choice: the system thinks this is $\\simplify[std]{ {a}+{b}x/({c}+{d}y)}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$.", "<code>{a}+{b}x/{c}+{d}y</code><br/> Good choice: the system thinks this is $\\simplify[std]{ {a}+{b}x/{c}+{d}y}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$.", "<code>({a}+{b}x)/{c}+{d}y</code><br/> Good choice: the system thinks this is $\\simplify[std]{ ({a}+{b}x)/{c}+{d}y}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$."], "showCorrectAnswer": true, "scripts": {}, "warningType": "none", "marks": 0, "choices": ["<p><code>({a}+{b}x)/({c}+{d}y)</code></p>", "<p><code>{a}+{b}x/({c}+{d}y)</code></p>", "<p><code>{a}+{b}x/{c}+{d}y</code></p>", "<p><code>({a}+{b}x)/{c}+{d}y</code></p>"], "type": "m_n_2", "displayType": "checkbox", "minMarks": 0}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Input the expression $\\displaystyle \\frac{\\var{b}+\\var{a}y}{\\var{d}+\\var{c}z}$. [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({b}+{a}y)/({d}+{c}z)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Input the expression $\\displaystyle \\frac {\\var{d} z + \\var{b}} {(x + \\var{a}) (y + \\var{c})}$. [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({d} * z + {b}) / ((x + {a}) * (y + {c}))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>As a final challenge, input the expression $\\displaystyle \\simplify[std]{({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 * b}) * (y -{3* d}))}$. [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.0001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2  b}) * (y -{3* d}))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>This question shows you how to input algebraic fractions.</p>\n<p>You need to be careful to use brackets to show what goes into the numerator (top) and what into the denominator (bottom) of the fraction.</p>\n<p>Remember that you will see what the system thinks you have entered.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..16#2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(3..15#2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..9 except [round(b*c/a),c])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "<p>Instructions on inputting ratios of algebraic expressions. Could link to calculator input.</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/"}]}