// Numbas version: exam_results_page_options
{"name": "1.2.2.1 Write expressions with a single index", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.2.2.1 Write expressions with a single index", "tags": [], "metadata": {"description": "<p>Use the index laws to simplify 3 simple expressions;</p>\n<p>n^a*n^b,&nbsp;n^a/n^b,&nbsp;(n^a)^b, where n is a randomised variable or number, and a and b are randomised nonzero integers.</p>\n<p>Part of HELM Book 1.2</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Rewrite each of the following expressions with a single index. In each case, write the value of the index in the box.</p>", "advice": "<p>(a)</p>\n<p>\\[\\var{abase}^\\var{ex1_idx[0]}\\var{abase}^\\var{ex1_idx[1]}=\\var{abase}^{(\\var{ex1_idx[0]})+(\\var{ex1_idx[1]})}=\\var{abase}^{\\var{ex1_idx[0]+ex1_idx[1]}}\\]</p>\n<p>(b)</p>\n<p>\\[\\frac{\\var{bbase}^\\var{ex1_idx[2]}}{\\var{bbase}^\\var{ex1_idx[3]}}=\\var{bbase}^{(\\var{ex1_idx[2]})-(\\var{ex1_idx[3]})}= \\var{bbase}^{\\var{ex1_idx[2]-ex1_idx[3]} } \\]</p>\n<p>(c)</p>\n<p>\\[\\left(\\var{cbase}^\\var{ex1_idx[4]}\\right)^\\var{ex1_idx[5]}=\\var{cbase}^{(\\var{ex1_idx[4]})\\times (\\var{ex1_idx[5]}) }=\\var{cbase}^{\\var{ex1_idx[4]*ex1_idx[5]} } \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"alphabet": {"name": "alphabet", "group": "Ungrouped variables", "definition": "['a','b','k','m','n','w','x','y','z']", "description": "", "templateType": "anything", "can_override": false}, "ex1_base": {"name": "ex1_base", "group": "Ungrouped variables", "definition": "[random(string(random(2..29)),random(alphabet)),\n  random(string(random(2..29)),random(alphabet)),\n  random(string(random(2..29)),random(alphabet))]", "description": "", "templateType": "anything", "can_override": false}, "ex1_idx": {"name": "ex1_idx", "group": "Ungrouped variables", "definition": "[random(random(-10..-2),random(2..10)),\n  random(random(-10..-2),random(2..10)),\n  random(random(-10..-2),random(2..10)),\n  random(random(-10..-2),random(2..10)),\n  random(random(-10..-2),random(2..10)),\n  random(random(-10..-2),random(2..10))\n]", "description": "", "templateType": "anything", "can_override": false}, "ex1_base_expr": {"name": "ex1_base_expr", "group": "Ungrouped variables", "definition": "[expression(ex1_base[0]),expression(ex1_base[1]),expression(ex1_base[2])]", "description": "", "templateType": "anything", "can_override": false}, "cbase": {"name": "cbase", "group": "Ungrouped variables", "definition": "expression(ex1_base[2])", "description": "<p>(m^7)^-5 is not accepting 1/m^35 as an answer, but it does accept m^-35</p>", "templateType": "anything", "can_override": false}, "ans1b": {"name": "ans1b", "group": "Ungrouped variables", "definition": "expression(ex1_base[1] + \"^\" + string(ex1_idx[2]-ex1_idx[3]))", "description": "", "templateType": "anything", "can_override": false}, "ans1a": {"name": "ans1a", "group": "Ungrouped variables", "definition": "expression(ex1_base[0] + \"^\" + string(ex1_idx[0]+ex1_idx[1]))", "description": "", "templateType": "anything", "can_override": false}, "abase": {"name": "abase", "group": "Ungrouped variables", "definition": "expression(ex1_base[0])", "description": "", "templateType": "anything", "can_override": false}, "bbase": {"name": "bbase", "group": "Ungrouped variables", "definition": "expression(ex1_base[1])", "description": "", "templateType": "anything", "can_override": false}, "ans1c": {"name": "ans1c", "group": "Ungrouped variables", "definition": "expression(ex1_base[0] + \"^\" + string(ex1_idx[4]*ex1_idx[5]))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alphabet", "ex1_base", "ex1_idx", "ex1_base_expr", "ans1a", "ans1b", "ans1c", "abase", "bbase", "cbase"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>(a) $\\var{abase}^\\var{ex1_idx[0]}$ $\\var{abase}^\\var{ex1_idx[1]} =&nbsp; \\var{abase}^u$, where $u=$[[0]]</p>\n<p>(b) $\\frac{\\var{bbase}^\\var{ex1_idx[2]}}{\\var{bbase}^\\var{ex1_idx[3]}} = \\var{bbase}^u$, where $u=$[[1]]</p>\n<p>(c) $\\left(\\var{cbase}^\\var{ex1_idx[4]}\\right)^\\var{ex1_idx[5]} = \\var{cbase}^u$, where $u=$[[2]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "a index", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ex1_idx[0]+ex1_idx[1]", "maxValue": "ex1_idx[0]+ex1_idx[1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "b index", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ex1_idx[2]-ex1_idx[3]", "maxValue": "ex1_idx[2]-ex1_idx[3]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "c index", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ex1_idx[4]*ex1_idx[5]", "maxValue": "ex1_idx[4]*ex1_idx[5]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}