// Numbas version: exam_results_page_options
{"name": "Perform arithmetic in Z_n", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"a5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5..9)", "description": "", "name": "a5"}, "ans2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a2*b2", "description": "", "name": "ans2"}, "ans3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a3*(b3+g3)", "description": "", "name": "ans3"}, "b4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(6..9)", "description": "", "name": "b4"}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "name": "b1"}, "b2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "b2"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "name": "a1"}, "g5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5..9)", "description": "", "name": "g5"}, "h5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5..9)", "description": "", "name": "h5"}, "ans4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a4*b4", "description": "", "name": "ans4"}, "g3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..6)", "description": "", "name": "g3"}, "b5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5..9)", "description": "", "name": "b5"}, "s5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "mod(a5+b5,9)", "description": "", "name": "s5"}, "a3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..6)", "description": "", "name": "a3"}, "ans1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a1+b1", "description": "", "name": "ans1"}, "a4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(6..9)", "description": "", "name": "a4"}, "b3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..6)", "description": "", "name": "b3"}, "ans5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(a5+b5)*(g5+h5)", "description": "", "name": "ans5"}, "a2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "a2"}, "t5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "mod(g5+h5,9)", "description": "", "name": "t5"}}, "ungrouped_variables": ["a1", "g5", "ans3", "g3", "ans1", "ans2", "t5", "ans4", "ans5", "s5", "h5", "b4", "b5", "a3", "a2", "a5", "b1", "b2", "b3", "a4"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Perform arithmetic in Z_n", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans1,2)}", "minValue": "{mod(ans1,2)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans1,9)}", "minValue": "{mod(ans1,9)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans1,10)}", "minValue": "{mod(ans1,10)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans2,2)}", "minValue": "{mod(ans2,2)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans2,9)}", "minValue": "{mod(ans2,9)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans2,10)}", "minValue": "{mod(ans2,10)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans3,2)}", "minValue": "{mod(ans3,2)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans3,9)}", "minValue": "{mod(ans3,9)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans3,10)}", "minValue": "{mod(ans3,10)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans4,2)}", "minValue": "{mod(ans4,2)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans4,9)}", "minValue": "{mod(ans4,9)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans4,10)}", "minValue": "{mod(ans4,10)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans5,2)}", "minValue": "{mod(ans5,2)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans5,9)}", "minValue": "{mod(ans5,9)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{mod(ans5,10)}", "minValue": "{mod(ans5,10)}", "correctAnswerFraction": false, "marks": 0.2, "showPrecisionHint": false}], "type": "gapfill", "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  ", "showCorrectAnswer": true, "marks": 0}], "statement": "", "tags": ["checked2015", "MAS3214", "Modular arithmetic", "modular arithmetic"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>16/08/2012:</strong></p>\n                <p><strong><br /></strong>Added tags.</p>\n                <p>Added description. &nbsp; &nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Calculations in $\\mathbb{Z_n}$ for three values of $n$. &nbsp; &nbsp;&nbsp;</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "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>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}