// Numbas version: finer_feedback_settings
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"a3", "a2", "a5", "b1", "b2", "b3", "a4"], "tags": ["checked2015", "MAS3214", "Modular arithmetic", "modular arithmetic"], "advice": "<p>In the the last part, working out $(\\var{a5}+\\var{b5})\\times (\\var{g5}+\\var{h5}) \\bmod{X}$, it is sometimes easier to work out $(\\var{a5}+\\var{b5}) \\bmod{X}$ and $(\\var{g5}+\\var{h5}) \\bmod{X}$ separately, giving two numbers in the range $[0 \\dots X-1]$, and then to multiply them together.</p>\n<p>For example, working $\\bmod{9}$ we have:</p>\n<p>\\begin{align}<br/>\\var{a5}+\\var{b5}&amp;\\equiv \\var{mod(a5+b5,9)} \\bmod{9}, \\\\<br/> \\var{g5}+\\var{h5}&amp;\\equiv \\var{mod(g5+h5,9)} \\bmod{9}. \\\\ \\\\ <br/>(\\var{a5}+\\var{b5})\\times (\\var{g5}+\\var{h5}) &amp;\\equiv \\var{s5} \\times \\var{t5} \\bmod{9} \\\\ <br/>&amp;\\equiv \\var{mod(ans5,9)} \\bmod{9}<br/>\\end{align}</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "\n  \n  \n  <p>Perform the following calculations in $\\mathbb{Z}_{2},\\;\\;\\mathbb{Z}_{9},\\;\\;\\mathbb{Z}_{10}$.</p>\n  \n  \n  \n  <table border=\"1\">\n  \n  <tr>\n  \n  <th></th>\n  \n  <th>$\\mathbb{Z}_{2}$</th>\n  \n  <th>$\\mathbb{Z}_{9}$</th>\n  \n  <th>$\\mathbb{Z}_{10}$</th>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$\\var{a1}+\\var{b1}$</td>\n  \n  <td>[[0]]</td>\n  \n  <td>[[1]]</td>\n  \n  <td>[[2]]</td>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$\\var{a2}\\times\\var{b2}$</td>\n  \n  <td>[[3]]</td>\n  \n  <td>[[4]]</td>\n  \n  <td>[[5]]</td>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$\\var{a3}\\times(\\var{b3}+\\var{g3})$</td>\n  \n  <td>[[6]]</td>\n  \n  <td>[[7]]</td>\n  \n  <td>[[8]]</td>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$\\var{a4}\\times\\var{b4}$</td>\n  \n  <td>[[9]]</td>\n  \n  <td>[[10]]</td>\n  \n  <td>[[11]]</td>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$(\\var{a5}+\\var{b5})\\times (\\var{g5}+\\var{h5})$</td>\n  \n  <td>[[12]]</td>\n  \n  <td>[[13]]</td>\n  \n  <td>[[14]]</td>\n  \n  </tr>\n  \n  </table>\n  \n  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"group": "Ungrouped variables", "name": "h5", "description": ""}, "b4": {"definition": "random(6..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b5": {"definition": "random(5..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b5", "description": ""}, "a3": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(5..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "b1": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "a4": {"definition": "random(6..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}}, "metadata": {"notes": "<p><strong>16/08/2012:</strong></p>\n                <p><strong><br /></strong>Added tags.</p>\n                <p>Added description. &nbsp; &nbsp;</p>", "description": "<p>Calculations in $\\mathbb{Z_n}$ for three values of $n$. &nbsp; &nbsp;&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Factorise four numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian 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"extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "checkingAccuracy": 0.001, "showPreview": true, "variableReplacements": [], "marks": "0.25"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "sortAnswers": false}, {"customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "useCustomName": false, "prompt": "<p>$\\var{numbers[2]} =$ [[0]]</p>", "unitTests": [], "showFeedbackIcon": true, "scripts": {}, "gaps": [{"answer": "{numbers[2]}", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "checkingType": "absdiff", "vsetRangePoints": 5, "failureRate": 1, "customName": "", "checkVariableNames": false, "unitTests": [], "valuegenerators": [], "vsetRange": [0, 1], "showFeedbackIcon": true, "scripts": {"constructor": {"script": "question.createFactorisePart(this);", "order": "after"}, "mark": {"script": "question.markFactorisePart(this);", "order": "instead"}}, "extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "checkingAccuracy": 0.001, "showPreview": true, "variableReplacements": [], "marks": "0.25"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "sortAnswers": false}, {"customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "useCustomName": false, "prompt": "<p>$\\var{numbers[3]} =$ [[0]]</p>", "unitTests": [], "showFeedbackIcon": true, "scripts": {}, "gaps": [{"answer": "{numbers[3]}", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "checkingType": "absdiff", "vsetRangePoints": 5, "failureRate": 1, "customName": "", "checkVariableNames": false, "unitTests": [], "valuegenerators": [], "vsetRange": [0, 1], "showFeedbackIcon": true, "scripts": {"constructor": {"script": "question.createFactorisePart(this);", "order": "after"}, "mark": {"script": "question.markFactorisePart(this);", "order": "instead"}}, "extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "checkingAccuracy": 0.001, "showPreview": true, "variableReplacements": [], "marks": "0.25"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "sortAnswers": false}], "variables": {"numbers": {"group": "Ungrouped variables", "templateType": "anything", "definition": "shuffle(list(1900..2015))[0..4]", "description": "", "name": "numbers"}}, "ungrouped_variables": ["numbers"], "functions": {"list": {"type": "number", "language": "javascript", "definition": "return r.slice(3);", "parameters": [["r", "range"]]}}, "variable_groups": [], "preamble": {"css": "", "js": "question.createFactorisePart = function(p) {\n  var n = 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factorisation.</p>"}, "advice": ""}, {"name": "Factorise numbers into products of prime powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [], "variables": {"e2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "if(e1>1,0,2)", "description": "", "name": "e2"}, "lgp": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[59,61,67,73,79]", "description": "", "name": "lgp"}, "e1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2,3)", "description": "", "name": "e1"}, "p1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(sgp)", "description": "", "name": "p1"}, "e3": {"group": "Ungrouped variables", "templateType": "anything", "definition": "1", "description": "", "name": "e3"}, "p3": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(mgp)", "description": "", "name": "p3"}, "e5": {"group": "Ungrouped variables", "templateType": "anything", "definition": "1", "description": "", "name": "e5"}, "p5": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(lgp)", "description": "", "name": "p5"}, "sgp": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[2,2,2,3,3,3,5,5,5,7,7,7,11,11,13]", "description": "", "name": "sgp"}, "p2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(sgp)", "description": "", "name": "p2"}, "mgp": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[17,19,23,29,31,37,41,43,47]", "description": "", "name": "mgp"}, "ntbf": {"group": "Ungrouped variables", "templateType": "anything", "definition": "p1^e1 * p2^e2 * p3^e3 * p5^e5", "description": "", "name": "ntbf"}}, "ungrouped_variables": ["p2", "p3", "p1", "p5", "sgp", "ntbf", "mgp", "e5", "lgp", "e1", "e3", "e2"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "showQuestionGroupNames": false, "functions": {}, "parts": [{"scripts": {}, "gaps": [{"answer": "{p1^e1*p2^e2*p3^e3*p5^e5}", "musthave": {"message": "<p>Split into factors, each factor a power of a prime number and include the multiplication sign <code>*</code> between the factors</p>", "showStrings": false, "partialCredit": 0, "strings": ["*", "^"]}, "vsetrange": [0, 1], "scripts": {"constructor": {"script": "question.createFactorisePart(this);", "order": "after"}, "mark": {"script": "question.markFactorisePart(this);", "order": "instead"}}, "answersimplification": "unitPower,zeroPower,unitFactor", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, 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