// Numbas version: exam_results_page_options
{"name": "1.2.1.3 Write values using index notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.2.1.3 Write values using index notation", "tags": [], "metadata": {"description": "<p>Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write each of the following using index notation.</p>\n<p>To enter $3\\times\\left(\\frac{2}{7}\\right)^4$, type <code>3*(2/7)^4</code>.</p>", "advice": "<p>(a) $\\var{Q3aExpansion}=\\var{expression(Q3aBase)}^\\var{Q3aIdx}$</p>\n<p>(b) $\\var{Q3dExpansion}=\\left(\\frac{\\var{Q3dBaseNum}}{\\var{Q3dBaseDen}}\\right)^{\\var{Q3dIdx}}$</p>\n<p>(c) $\\var{Q3bExpansion}=\\var{expression(Q3bBase1)}^\\var{Q3bIdx1}\\var{expression(Q3bBase2)}^\\var{Q3bIdx2}$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Q3aBase": {"name": "Q3aBase", "group": "q3a", "definition": "random(random(['a','b','c','d','f','g','h','k','m','n','p','q','r','s','t','u','v','w','x','y','z']),string(random(2..29)))", "description": "", "templateType": "anything", "can_override": false}, "Q3aIdx": {"name": "Q3aIdx", "group": "q3a", "definition": "random(2..8)", "description": "", "templateType": "anything", "can_override": false}, "q3aBlockBit": {"name": "q3aBlockBit", "group": "q3a", "definition": "latex(Q3aBase + ' ' + '\\\\\\times')", "description": "", "templateType": "anything", "can_override": false}, "q3aExpansion": {"name": "q3aExpansion", "group": "q3a", "definition": "latex(join(iterate(x,x,Q3aBlockBit,q3aIdx-2),\" \")+' '+Q3aBase)", "description": "", "templateType": "anything", "can_override": false}, "q3bAlphabet": {"name": "q3bAlphabet", "group": "q3b", "definition": "shuffle(['a','b','c','d','f','g','h','k','m','n','p','q','r','s','t','u','v','w','x','y','z'])", "description": "", "templateType": "anything", "can_override": false}, "q3bIdxDeal": {"name": "q3bIdxDeal", "group": "q3b", "definition": "shuffle(2..8)[0..2]", "description": "", "templateType": "anything", "can_override": false}, "q3bBase1": {"name": "q3bBase1", "group": "q3b", "definition": "q3bAlphabet[0]", "description": "", "templateType": "anything", "can_override": false}, "q3bBase2": {"name": "q3bBase2", "group": "q3b", "definition": "q3bAlphabet[1]", "description": "", "templateType": "anything", "can_override": false}, "q3bIdx1": {"name": "q3bIdx1", "group": "q3b", "definition": "Q3bIdxDeal[0]", "description": "", "templateType": "anything", "can_override": false}, "q3bIdx2": {"name": "q3bIdx2", "group": "q3b", "definition": "Q3bIdxDeal[1]", "description": "", "templateType": "anything", "can_override": false}, "q3bBlockBit1": {"name": "q3bBlockBit1", "group": "q3b", "definition": "latex(Q3bBase1 + ' '+ '\\\\\\times')", "description": "", "templateType": "anything", "can_override": false}, "q3bBlockBit2": {"name": "q3bBlockBit2", "group": "q3b", "definition": "latex(Q3bBase2 + ' ' + '\\\\\\times')", "description": "", "templateType": "anything", "can_override": false}, "q3bExpansion": {"name": "q3bExpansion", "group": "q3b", "definition": "latex(\nlatex(join(iterate(x,x,Q3bBlockBit1,q3bIdx1-2),\" \"))+\" \"+q3bbase1\n+ latex(\"\\\\times\") + \" \" +\nlatex(join(iterate(x,x,Q3bBlockBit2,q3bIdx2-2),\" \"))+\" \"+q3bbase2\n)", "description": "", "templateType": "anything", "can_override": false}, "q3dBaseNum": {"name": "q3dBaseNum", "group": "q3d", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "q3dBaseDen": {"name": "q3dBaseDen", "group": "q3d", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "q3dIdx": {"name": "q3dIdx", "group": "q3d", "definition": "random(2..7)", "description": "", "templateType": "anything", "can_override": false}, "q3dBlockBit": {"name": "q3dBlockBit", "group": "q3d", "definition": "latex('\\\\\\frac{'+Q3DBaseNum+'}{'+Q3dBaseDen + '} '+ '\\\\\\times')", "description": "", "templateType": "anything", "can_override": false}, "q3dExpansion": {"name": "q3dExpansion", "group": "q3d", "definition": "latex(join(iterate(x,x,Q3dBlockBit,q3dIdx-2),\" \")+' '+'\\\\\\frac{'+Q3DBaseNum+'}{'+Q3dBaseDen + '} ')", "description": "", "templateType": "anything", "can_override": false}, "q3bBase1e": {"name": "q3bBase1e", "group": "q3b", "definition": "expression(q3bBase1)", "description": "<p>For display</p>", "templateType": "anything", "can_override": false}, "q3bBase2e": {"name": "q3bBase2e", "group": "q3b", "definition": "expression(q3bBase2)", "description": "<p>For display</p>", "templateType": "anything", "can_override": false}, "q3aBasee": {"name": "q3aBasee", "group": "q3a", "definition": "expression(q3abase)", "description": "<p>for display in the advice.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "q3a", "variables": ["Q3aBase", "Q3aIdx", "q3aBlockBit", "q3aExpansion", "q3aBasee"]}, {"name": "q3b", "variables": ["q3bAlphabet", "q3bIdxDeal", "q3bBase1", "q3bBase2", "q3bIdx1", "q3bIdx2", "q3bBlockBit1", "q3bBlockBit2", "q3bExpansion", "q3bBase1e", "q3bBase2e"]}, {"name": "q3d", "variables": ["q3dBaseNum", "q3dBaseDen", "q3dIdx", "q3dBlockBit", "q3dExpansion"]}], "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) $\\var{Q3aExpansion}$ = [[0]]</p>\n<p>(b) $\\var{Q3dExpansion}$ = [[1]]</p>\n<p>(c) $\\var{Q3bExpansion} =$ [[2]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "a", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], 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