// Numbas version: exam_results_page_options
{"name": "Input 5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Input 5", "tags": ["Numbas", "algebraic input", "brackets", "input", "introduction", "mathematical expressions", "numbas", "ratios"], "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 we wanted to input the expression $\\displaystyle \\frac{\\var{a}+\\var{b}x}{\\var{c}+\\var{d}y}$ into the system.</p>\n      <p>Which of the following input expressions are <em><strong>incorrect</strong></em>?</p>\n      <p>[[0]]</p>\n      <p>Choose the incorrect input(s). (You lose 3 marks if you choose the wrong one!)</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>\n      <p>You can click on <em>Reveal answers</em> at the bottom of the screen to see solutions, but it's best to work through&nbsp;these questions yourself. Remember you can always redo the question by clicking on the&nbsp;<em>Try another question like this one</em>&nbsp;button at the bottom of the screen.</p>", "gaps": [{"maxanswers": 0.0, "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 $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$."], "matrix": [-3.0, 1.0, 1.0, 1.0], "minanswers": 0.0, "shufflechoices": true, "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>"], "displaytype": "checkbox", "maxmarks": 0.0, "marks": 0.0, "displaycolumns": 1.0, "type": "m_n_2", "minmarks": 0.0}], "type": "gapfill", "marks": 0.0}, {"prompt": "<p>Input the expression $\\displaystyle \\frac{\\var{b}+\\var{a}y}{\\var{d}+\\var{c}z}$. [[0]]</p>", "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 1.0, "answer": "({b}+{a}y)/({d}+{c}z)", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}, {"prompt": "<p>Input the expression $\\displaystyle \\frac {\\var{d} z + \\var{b}} {(x + \\var{a}) (y + \\var{c})}$. [[0]]</p>", "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 1.0, "answer": "({d} * z + {b}) / ((x + {a}) * (y + {c}))", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}, {"prompt": "<p>Input the expression $\\displaystyle \\simplify[std]{({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 * b}) * (y -{3* d}))}$. [[0]]</p>", "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 0.0001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 1.0, "answer": "({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2  b}) * (y -{3* d}))", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "<p>This question concerns ratios of algebraic expressions.</p>\n  <p>By this we mean expressions of the form $\\displaystyle \\frac{p(x)}{q(x)}$ where $p(x)$ and $q(x)$ are algebraic expressions.</p>\n  <p>If you want to input such an expression into the system you <strong>HAVE TO BE CAREFUL AND USE BRACKETS</strong> or mistakes will occur.</p>\n  <p>Once again, the box displaying your input in mathematical notation beside the input boxes in parts <em>a</em>, <em>b</em> and <em>c</em> is very useful as it shows what the system thinks you have entered.</p>", "variable_groups": [], "progress": "in-progress", "type": "question", "variables": {"a": {"definition": "random(2..16#2)", "name": "a"}, "c": {"definition": "random(2..9)", "name": "c"}, "b": {"definition": "random(3..15#2)", "name": "b"}, "d": {"definition": "random(2..9 except [round(b*c/a),c])", "name": "d"}}, "metadata": {"notes": "", "description": "<p>Instructions on inputting ratios of algebraic expressions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}