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{"name": "Musa's copy of 3 Index laws", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Musa's copy of 3 Index laws", "tags": [], "metadata": {"description": "<p>Questions testing rather basic understanding of the index laws.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>(a) Add the powers: $\\var{m} + \\var{n}=\\var{m+n}$ (first index law).</p>\n<p>(b) Multiply the powers $\\var{m1} \\times \\var{n1}=\\var{m1*n1}$ (second index law).</p>\n<p>(c) Multiply $\\var{xx}$ and $\\var{y}$ to get $\\var{xx*y}$, with the power unchanged at $\\var{t}$. 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{"name": "m2", "group": "Ungrouped variables", "definition": "random(-15..15 except 0)", "description": "", "templateType": "anything"}, "m31": {"name": "m31", "group": "Ungrouped variables", "definition": "random(-5,-3,-1,1,3,5,7,9,11)", "description": "", "templateType": "anything"}, "m32": {"name": "m32", "group": "Ungrouped variables", "definition": "random(2,4,6,8,10,12,14,16)", "description": "", "templateType": "anything"}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "random(3..9)", "description": "", "templateType": "anything"}, "m41": {"name": "m41", "group": "Ungrouped variables", "definition": "random(6..15)", "description": "", "templateType": "anything"}, "m42": {"name": "m42", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "x5": {"name": "x5", "group": "Ungrouped variables", "definition": "random(3..15)", "description": "", "templateType": "anything"}, "m52": {"name": "m52", "group": 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"description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "m", "n", "m1", "t", "n1", "y", "xx", "x2", "y2", "x3", "y3", "m2", "m31", "m32", "x4", "m41", "m42", "x5", "m52", "m51", "kk1", "xx1", "d8", "n8", "n88", "k8", "m8", "m9", "n99", "k9", "n9", "a1", "t1", "d55", "c55", "b55", "a55", "t55", "n55", "f55", "m55"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Express the following as a single power of $\\var{a}$:</p>\n<p>\\[\\var{a}^{\\var{m}} \\times \\var{a}^{\\var{n}}\\]</p>\n<p>Enter the power [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{m+n}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.0001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": "<p>Input as a fraction or an integer, not as a decimal.</p>"}, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Express the following as a single power of $\\var{b}$:</p>\n      <p>\\[(\\var{b}^{\\var{m1}})^{\\var{n1}}\\]</p>\n      <p>Enter the power [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{m1*n1}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.0001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": "<p>Input as a fraction or an integer, not as a decimal.</p>"}, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Simplify as power of &nbsp; $\\var{x5}:$</p>\n<p></p>\n<p>${\\frac{1}{\\var{x5}^\\var{m52}}}$ &nbsp;&nbsp; = [[0]]<br/><br/></p>\n<p>&nbsp;</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{x5}^{-m52}", "answerSimplification": "fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Simplify as in the form&nbsp; $a \\sqrt{b}$ such that b is not a square number (use \"sqrt\" for square root):</p>\n<p></p>\n<p>$\\sqrt{\\simplify{({xx1}^2)*{kk1}}} $ &nbsp;&nbsp; = [[0]]</p>\n<p>&nbsp;</p>\n<p>&nbsp;</p>", "gaps": [{"type": "jme", 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University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}