// Numbas version: exam_results_page_options
{"name": "Surds: multiplication", "extensions": [], "custom_part_types": [], "resources": [["question-resources/sqrt_Irff7Ni.png", "/srv/numbas/media/question-resources/sqrt_Irff7Ni.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["listsquares", "listprimes", "listsquare", "square1", "square2", "listprime", "arg2", "prime1", "prime2", "extra", "ansmult", "ansarg"], "name": "Surds: multiplication", "tags": ["irrationals", "surds"], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "2", "prompt": "<p>Simplify the surd product $\\var{square1[0]}\\sqrt{\\var{prime1}}\\times\\var{extra}\\sqrt{\\var{arg2}}$, entering your numbers in the gaps provided.</p>\n<p></p>\n<table cellpadding=\"0\" style=\"text-align: right;\">\n<tbody>\n<tr>\n<td>[[0]]</td>\n<td style=\"background-image: url('resources/question-resources/sqrt_Irff7Ni.png'); background-repeat: no-repeat;\">&nbsp; &nbsp;$\\,\\,\\,\\,$[[1]]</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "ansmult", "minValue": "ansmult", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "ansarg", "minValue": "ansarg", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\var{square1[0]}\\sqrt{\\var{prime1}}\\times\\var{extra}\\sqrt{\\var{arg2}}$ we could multiply the integer parts together and the surd parts together and then simplify, that is:</p>\n<table>\n<tbody>\n<tr>\n<td>$\\var{square1[0]}\\sqrt{\\var{prime1}}\\times\\var{extra}\\sqrt{\\var{arg2}}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{square1[0]}\\times\\var{extra}\\times\\sqrt{\\var{prime1}\\times\\var{arg2}}$</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{square1[0]*extra}\\times\\sqrt{\\var{prime1*arg2}}$</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{square1[0]*extra}\\times\\sqrt{\\var{square2[1]}\\times\\var{prime1*prime2}}$</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{square1[0]*extra}\\times\\sqrt{\\var{square2[1]}}\\times\\sqrt{\\var{prime1*prime2}}$</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{square1[0]*extra}\\times\\var{square2[0]}\\times\\sqrt{\\var{prime1*prime2}}$</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{ansmult}\\sqrt{\\var{ansarg}}$</td>\n</tr>\n</tbody>\n</table>\n<p>Or we could simplify the surds first, then multiply the integer parts and surd parts, and then simplify (if necessary) at the end, that is:</p>\n<table>\n<tbody>\n<tr>\n<td>$\\var{square1[0]}\\sqrt{\\var{prime1}}\\times\\var{extra}\\sqrt{\\var{arg2}}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{square1[0]}\\times\\sqrt{\\var{prime1}}\\times\\var{extra}\\times\\sqrt{\\var{square2[1]}\\times\\var{prime2}}$</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{square1[0]}\\times\\sqrt{\\var{prime1}}\\times\\var{extra}\\times\\sqrt{\\var{square2[1]}}\\times\\sqrt{\\var{prime2}}$</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{square1[0]}\\times\\sqrt{\\var{prime1}}\\times\\var{extra}\\times\\var{square2[0]}\\times\\sqrt{\\var{prime2}}$</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{square1[0]}\\times\\var{extra}\\times\\var{square2[0]}\\times\\sqrt{\\var{prime1}\\times\\var{prime2}}$</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td>$\\var{ansmult}\\sqrt{\\var{ansarg}}$</td>\n</tr>\n</tbody>\n</table>\n<p>The second approach is recommended since it keeps the numbers under the square root as small as possible, but it is important to realise both approaches are valid.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"extra": {"definition": "random(listprimes)", "templateType": "anything", "group": "Ungrouped variables", "name": "extra", "description": ""}, "ansmult": {"definition": "extra*square1[0]*square2[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ansmult", "description": ""}, "arg2": {"definition": "square2[1]*prime2", "templateType": "anything", "group": "Ungrouped variables", "name": "arg2", "description": ""}, "listsquare": {"definition": "shuffle(listsquares)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "listsquare", "description": ""}, "listprimes": {"definition": "[2,3,5,7,11,13,17]", "templateType": "anything", "group": "Ungrouped variables", "name": "listprimes", "description": ""}, "listprime": {"definition": "shuffle(listprimes)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "listprime", "description": ""}, "ansarg": {"definition": "prime1*prime2", "templateType": "anything", "group": "Ungrouped variables", "name": "ansarg", "description": ""}, "prime1": {"definition": "listprime[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "prime1", "description": ""}, "square1": {"definition": "listsquare[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "square1", "description": ""}, "square2": {"definition": "listsquare[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "square2", "description": ""}, "prime2": {"definition": "listprime[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "prime2", "description": ""}, "listsquares": {"definition": "map([n,n^2],n,2..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "listsquares", "description": ""}}, "metadata": {"notes": "<p>using background image in table to get a good looking square root symbol</p>\n<p></p>\n<p></p>\n<table cellpadding=\"0\" style=\"text-align: right;\">\n<tbody>\n<tr>\n<td>[[0]]</td>\n<td style=\"background-image: url('resources/question-resources/sqrt_Irff7Ni.png'); background-repeat: no-repeat;\">&nbsp; &nbsp;$\\,\\,\\,\\,$[[1]]</td>\n</tr>\n</tbody>\n</table>", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}