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{"name": "Math 3 REVIEW for TEST Logarithms and Exponentials", "showQuestionGroupNames": false, "question_groups": [{"name": "Group", "pickQuestions": 1, "pickingStrategy": "all-ordered", "questions": [{"name": "Math 3 Change of Base Formula", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["base", "value", "answer"], "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"prompt": "<p>$ \\log_{ \\var{base} }( \\var{value} )&nbsp; = $[[0]]</p>", "customName": "", "useCustomName": false, "unitTests": [], "variableReplacements": [], "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "variableReplacementStrategy": "originalfirst", 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"correctAnswerStyle": "plain", "variableReplacements": [], "unitTests": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "marks": 1, "maxValue": "answer", "adaptiveMarkingPenalty": 0, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "precision": "4", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"]}], "variables": {"base": {"name": "base", "definition": "random(2..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "value": {"name": "value", "definition": "random(2..100)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "definition": "log(value)/log(base)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "metadata": {"description": "", "licence": "All rights reserved"}, "variable_groups": [], "rulesets": {}, "advice": "", "functions": {}, "statement": "<p>Use the change of base formula.&nbsp; Then 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"useCustomName": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "marks": 1, "type": "numberentry", "precisionPartialCredit": "75", "notationStyles": ["plain", "en", "si-en"], "minValue": "answer", "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "unitTests": []}], "ungrouped_variables": ["b", "value", "answer"], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "All rights reserved"}, "functions": {}, "rulesets": {}, "variable_groups": [], "statement": "<p>Evaluate.&nbsp; Round your answer to 4 decimal places.</p>\n<p>$ log_{ \\var{b} } \\var{value} $</p>", "variables": {"answer": {"definition": "precround(log(value)/log(b),4)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "answer"}, "b": {"definition": "random(2..11)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b"}, "value": {"definition": 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"plain", "unitTests": [], "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "maxValue": "answer", "adaptiveMarkingPenalty": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "precision": "4", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"]}], "variables": {"value": {"name": "value", "definition": "random(0.1..100#0.125)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "answer": {"name": "answer", "definition": "precround(log(value),4)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "metadata": {"description": "", "licence": "All rights reserved"}, "rulesets": {}, "functions": {}, "variable_groups": [], "statement": "<p>Evaluate.&nbsp; Round your answer to 4 decimal places.</p>\n<p>Given:&nbsp; $\\log \\var{value}$</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}}, {"name": "Math 3 Evaluate logarithms with log base 10 fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "preamble": {"js": "", "css": ""}, "tags": [], "advice": "", "parts": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "useCustomName": false, "adaptiveMarkingPenalty": 0, "customName": "", "strictPrecision": false, "showCorrectAnswer": true, "minValue": "answer", "allowFractions": false, "variableReplacements": [], "customMarkingAlgorithm": "", "precisionType": "dp", "precision": "4", "mustBeReduced": false, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "correctAnswerFraction": false, "marks": 1, "type": "numberentry", "precisionPartialCredit": "75", "notationStyles": ["plain", "en", "si-en"], "maxValue": "answer", "showPrecisionHint": false, "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "unitTests": []}], "ungrouped_variables": ["value", "answer"], "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "rulesets": {}, "variable_groups": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Evaluate.&nbsp; Round your answer to 4 decimal places.</p>\n<p>Given:&nbsp; $\\log \\frac{\\var{value[0]}}{\\var{value[1]}}$</p>", "variables": {"answer": {"definition": "precround(log(value[0]/value[1]),4)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "answer"}, "value": {"definition": "rational_approximation(random(0.1..100#0.125))", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "value"}}}, {"name": "Math 3 Evaluate natural logarithms with decimals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": 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"75", "mustBeReduced": false, "showPrecisionHint": false, "adaptiveMarkingPenalty": 0, "customName": "", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "scripts": {}, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "type": "numberentry", "maxValue": "answer", "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "answer", "correctAnswerFraction": false, "precision": "4"}], "preamble": {"js": "", "css": ""}, "statement": "<p>Evaluate.&nbsp; Round your answer to 4 decimal places.</p>\n<p>Given:&nbsp; $\\ln \\var{value}$</p>", "tags": []}, {"name": "Math 3 Evaluate natural logarithms with fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": 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"extendBaseMarkingAlgorithm": true, "unitTests": []}], "rulesets": {}, "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Evaluate.&nbsp; Round your answer to 4 decimal places.</p>\n<p>Given:&nbsp; $\\ln \\frac{\\var{value[0]}}{\\var{value[1]}}$</p>", "variables": {"answer": {"definition": "precround(ln(value[0]/value[1]),4)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "answer"}, "value": {"definition": "rational_approximation(random(0.1..100#0.125))", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "value"}}}, {"name": "Math 3 Evaluate natural logarithms with fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "preamble": {"js": "", "css": ""}, "tags": [], "advice": "", "functions": {}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["value", "answer"], "parts": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the correct precision.", "customName": "", "strictPrecision": false, "showCorrectAnswer": true, "minValue": "answer", "customMarkingAlgorithm": "", "allowFractions": false, "variableReplacements": [], "showPrecisionHint": false, "precisionType": "dp", "precision": "4", "mustBeReduced": false, "useCustomName": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "marks": 1, "type": "numberentry", "precisionPartialCredit": "75", "notationStyles": ["plain", "en", "si-en"], "maxValue": "answer", "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "unitTests": []}], "rulesets": {}, "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Evaluate.&nbsp; Round your answer to 4 decimal places.</p>\n<p>Given:&nbsp; $\\ln \\frac{\\var{value[0]}}{\\var{value[1]}}$</p>", "variables": {"answer": {"definition": "precround(ln(value[0]/value[1]),4)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "answer"}, "value": {"definition": "rational_approximation(random(0.1..100#0.125))", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "value"}}}, {"name": "Math 3 Evaluate natural logarithms with fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["value", "answer"], "advice": "", "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"licence": "All rights reserved", "description": ""}, "parts": [{"showCorrectAnswer": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "useCustomName": false, "unitTests": [], "marks": 1, "adaptiveMarkingPenalty": 0, "minValue": "answer", "precisionType": "dp", "customName": "", "mustBeReduced": false, "precision": "4", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "maxValue": "answer", "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": false, "precisionPartialCredit": "75", "type": "numberentry", "scripts": {}}], "preamble": {"js": "", "css": ""}, "statement": "<p>Evaluate.&nbsp; Round your answer to 4 decimal places.</p>\n<p>Given:&nbsp; $\\ln \\frac{\\var{value[0]}}{\\var{value[1]}}$</p>", "variables": {"value": {"templateType": "anything", "definition": "rational_approximation(random(0.1..100#0.125))", "group": "Ungrouped variables", "description": "", "name": "value"}, "answer": {"templateType": "anything", "definition": "precround(ln(value[0]/value[1]),4)", "group": "Ungrouped variables", "description": "", "name": "answer"}}, "tags": [], "variable_groups": []}, {"name": "Math 3 Expand each logarithm Numerical", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["val1", "val2", "base"], "parts": [{"customMarkingAlgorithm": "", "displayAnswer": "log_{base}({val1})+log_{base}({val2})", "scripts": {}, "unitTests": [], "showFeedbackIcon": true, "answer": "log_{base}({val1})+log_{base}({val2})", "showCorrectAnswer": true, "type": "patternmatch", "customName": "", "marks": 1, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "matchMode": "exact", "adaptiveMarkingPenalty": 0, "variableReplacements": []}], "functions": {}, "advice": "", "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"base": {"group": "Ungrouped variables", "definition": "random(2..9)", "name": "base", "description": "", "templateType": "anything"}, "val1": {"group": "Ungrouped variables", "definition": "random(2,3,5,7,11)", "name": "val1", "description": "", "templateType": "anything"}, "val2": {"group": "Ungrouped variables", "definition": "random([2,3,5,7,11] except val1)", "name": "val2", "description": "", "templateType": "anything"}}, "tags": [], "statement": "<p>Expand the logarithm.&nbsp;&nbsp;<em><strong>NOTE:&nbsp; Enter&nbsp; $ log_4(3)$ as log_4(3)</strong></em></p>\n<p>Given:&nbsp; $ \\log_{ \\var{base} }(\\var{val1} \\cdot \\var{val2}) $</p>", "rulesets": {}, "variable_groups": [], "metadata": {"licence": "All rights reserved", "description": ""}}, {"name": "Math 3 Expand each logarithm Product", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["variables", "var1", "var2", "base", "exp1", "exp2"], "parts": [{"customMarkingAlgorithm": "", "displayAnswer": "{exp1}log_{base}({var1})+{exp2}log_{base}({var2})", "scripts": {}, "unitTests": [], "showFeedbackIcon": true, "answer": "{exp1}log_{base}({var1})+{exp2}log_{base}({var2})", "showCorrectAnswer": true, "type": "patternmatch", "customName": "", "marks": 1, "extendBaseMarkingAlgorithm": true, 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"description": "", "templateType": "anything"}, "exp1": {"group": "Ungrouped variables", "definition": "random(2..9)", "name": "exp1", "description": "", "templateType": "anything"}}, "tags": [], "statement": "<p>Expand the logarithm.</p>\n<p>Given:&nbsp; $&nbsp; \\log_{\\var{base}}(&nbsp; \\var{var1}^{\\var{exp1}}&nbsp; \\var{var2}^{\\var{exp2} }&nbsp; )&nbsp; $</p>", "rulesets": {}, "variable_groups": [], "metadata": {"licence": "All rights reserved", "description": ""}}, {"name": "Math 3 Expand each logarithm Product by 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["variables", "var1", "var2", "base", "exp1", "exp2", "var3", "exp3"], "variablesTest": {"condition": "", "maxRuns": 100}, "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"var1": {"templateType": "anything", "name": "var1", "description": "", "definition": "random(variables)", "group": "Ungrouped variables"}, "base": {"templateType": "anything", "name": "base", "description": "", "definition": "random(2..9)", "group": "Ungrouped variables"}, "var2": {"templateType": "anything", "name": "var2", "description": "", "definition": "random(variables except var1)", "group": "Ungrouped variables"}, "exp2": {"templateType": "anything", "name": "exp2", "description": "", "definition": "random(2..9)", "group": "Ungrouped variables"}, "exp3": {"templateType": "anything", "name": "exp3", "description": "", "definition": "random(2..9)", "group": "Ungrouped variables"}, "exp1": {"templateType": "anything", "name": "exp1", "description": "", "definition": "random(1..9)", "group": "Ungrouped variables"}, "var3": {"templateType": "anything", "name": "var3", "description": "", "definition": "random(variables except [var1,var2])", "group": 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"variableReplacements": []}], "functions": {}, "advice": "", "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"exp3": {"group": "Ungrouped variables", "definition": "random(2..9)", "name": "exp3", "description": "", "templateType": "anything"}, "base": {"group": "Ungrouped variables", "definition": "random(2..9)", "name": "base", "description": "", "templateType": "anything"}, "var3": {"group": "Ungrouped variables", "definition": "random(variables except [var1,var2])", "name": "var3", "description": "", "templateType": "anything"}, "var2": {"group": "Ungrouped variables", "definition": "random(variables except var1)", "name": "var2", "description": "", "templateType": "anything"}, "exp2": {"group": "Ungrouped variables", "definition": "random(2..9)", "name": "exp2", "description": "", "templateType": "anything"}, "variables": {"group": "Ungrouped variables", "definition": "[\"x\",\"y\",\"z\",\"a\",\"b\",\"c\",\"k\",\"m\",\"n\",\"p\",\"q\"]", "name": "variables", "description": "", "templateType": "anything"}, "var1": {"group": "Ungrouped variables", "definition": "random(variables)", "name": "var1", "description": "", "templateType": "anything"}, "exp1": {"group": "Ungrouped variables", "definition": "random(2..9)", "name": "exp1", "description": "", "templateType": "anything"}}, "tags": [], "statement": "<p>Expand the logarithm.</p>\n<p>Given:&nbsp; $&nbsp; \\log_{\\var{base}} \\left( \\frac{ \\var{var1}^{\\var{exp1}}}{ \\var{var2}^{\\var{exp2} }&nbsp; } \\right)&nbsp; $</p>", "rulesets": {}, "variable_groups": [], "metadata": {"licence": "All rights reserved", "description": ""}}, {"name": "Math 3 Expand each logarithm Quotient with numerical", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["variables", "var1", "var2", "base", "exp1", "exp2", "var3", "exp3", "c1", "c2", "c"], "tags": [], "advice": "", "parts": [{"matchMode": "exact", "answer": "log_{base}({c[0]})+{exp1}log_{base}({var1})-log_{base}({c[1]})-{exp2}log_{base}({var2})", "customName": "", "displayAnswer": "log_{base}({c[0]})+{exp1}log_{base}({var1})-log_{base}({c[1]})-{exp2}log_{base}({var2})", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "variableReplacements": [], "type": "patternmatch", "scripts": {}}], "variables": {"c2": {"name": "c2", "definition": "random(2..25 except c1)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "base": {"name": "base", "definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "exp3": {"name": "exp3", "definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "exp2": {"name": "exp2", "definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "c": {"name": "c", "definition": "rational_approximation(c1/c2)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "exp1": {"name": "exp1", "definition": "random(1..9)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "var2": {"name": "var2", "definition": "random(variables except var1)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "var1": {"name": "var1", "definition": "random(variables)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "c1": {"name": "c1", "definition": "random(2..25)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "variables": {"name": "variables", "definition": "[\"x\",\"y\",\"z\",\"a\",\"b\",\"c\",\"k\",\"m\",\"n\",\"p\",\"q\"]", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "var3": {"name": "var3", "definition": "random(variables except [var1,var2])", "group": "Ungrouped variables", "templateType": "anything", "description": ""}}, "metadata": {"description": "", "licence": "All rights reserved"}, "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "variable_groups": [], "statement": "<p>Expand the logarithm.</p>\n<p>Given:&nbsp; $&nbsp; \\log_{\\var{base}} \\left( \\frac{ \\var{c1}\\var{var1}^{\\var{exp1}}}{\\var{c2} \\var{var2}^{\\var{exp2} }&nbsp; } \\right)&nbsp; $</p>"}, {"name": "Math 3 Inverse Exponential Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "choice": {"definition": "(signb+1)/2", "group": "Ungrouped variables", "templateType": "anything", "name": "choice", "description": ""}, "operator": {"definition": "[\"+\",\"-\"]", "group": "Ungrouped variables", "templateType": "anything", "name": "operator", "description": ""}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "signb": {"definition": "sign(b)", "group": "Ungrouped variables", "templateType": "anything", "name": "signb", "description": ""}, "b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "signb", "choice", "operator"], "statement": "<p>Find the inverse of the given function:</p>\n<p>$y = \\simplify{ {base}^(x/{a}) +{b}} &nbsp;$&nbsp;</p>", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log((x-{b})^{a},{base})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "<p>The inverse function is:&nbsp;<em><strong>*** enter $\\log_{3}(x-5)$ as --&gt; log(x-5,3) ***</strong></em></p>\n<p>$f^{-1}(x) = $[[0]]</p>", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse Log Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "advice": "", "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "c"], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "variables": {"b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b"}, "a": {"definition": "random(-10..10 except 0)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a"}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "base"}, "c": {"definition": "random(-25..25)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "c"}}, "statement": "<p>Find the inverse of the given function:</p>\n<p>$y =&nbsp; \\log_{\\var{base}} (\\simplify{ {a}x+{b}}) + \\var{c} $</p>", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"prompt": "<p>The inverse function is:&nbsp; $f^{-1}(x)= $ [[0]]</p>", "marks": 0, "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "type": "gapfill", "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"customName": "", "unitTests": [], "checkingAccuracy": 0.001, "variableReplacements": [], "showPreview": true, "scripts": {}, "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "marks": 1, "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "answer": "({base}^(x-{c})-{b})/{a}", "failureRate": "2", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}]}]}], "variable_groups": []}, {"name": "Math 3 Inverse of Exponential Function with Rational Exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"base": {"definition": "rational_approximation(random(0.05..9#0.01))", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "a": {"definition": "random(-25..25 except 0)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "b": {"definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b"], "statement": "<p>Find the inverse of the given function:</p>\n<p>$ f(x) = \\simplify{ ( ({base[0]}/{base[1]})^x + {a}&nbsp; )^(1/{b})&nbsp; &nbsp; &nbsp;} $</p>", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log(x^{b}-{a},{base[0]}/{base[1]})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "<p>The inverse function is:&nbsp;&nbsp;<strong>***&nbsp;enter your answer as log(expression,base) *</strong></p>\n<p>$f^{-1}(x) = $[[0]]</p>", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse of Log function with rational exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "tags": [], "ungrouped_variables": ["base", "a", "b", "c"], "rulesets": {}, "functions": {}, "parts": [{"customName": "", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "useCustomName": false, "showFeedbackIcon": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "gapfill", "scripts": {}, "gaps": [{"showPreview": true, "adaptiveMarkingPenalty": 0, "useCustomName": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "marks": 1, "failureRate": 1, "variableReplacementStrategy": "originalfirst", "answer": "(({base}^x-{c})/{a})^(1/{b})", "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "checkingAccuracy": 0.001, "type": "jme", "valuegenerators": [{"value": "", "name": "x"}], "scripts": {}, "vsetRange": [0, 1], "checkingType": "absdiff"}], "variableReplacements": [], "prompt": "<p>The inverse of the function is:</p>\n<p>$f^{-1}(x) = $[[0]]</p>"}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "variables": {"c": {"group": "Ungrouped variables", "definition": "random(-15..15 except 0)", "description": "", "templateType": "anything", "name": "c"}, "base": {"group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "name": "base"}, "a": {"group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "name": "a"}, "b": {"group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "name": "b"}}, "statement": "<p>Find the inverse of the given function:</p>\n<p>$f(x) = \\log_\\var{base}(\\simplify{ {a}x^{b}+{c} })&nbsp; $</p>", "advice": ""}, {"name": "Math 3 Rewrite in exponential form log base fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "All rights reserved"}, "ungrouped_variables": ["b", "exponent", "value"], "advice": "", "rulesets": {}, "variables": {"b": {"name": "b", "group": "Ungrouped variables", "templateType": "anything", "definition": "[random(1,2,3),random(5,7,11,13)]", "description": ""}, "exponent": {"name": "exponent", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-4..4 except [-1,0,1])", "description": ""}, "value": {"name": "value", "group": "Ungrouped variables", "templateType": "anything", "definition": "precround((b[0]/b[1])^exponent,4)", "description": ""}}, "parts": [{"useCustomName": false, "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "answer": "({b[0]}/{b[1]})^{exponent}={value}", "marks": 1, "adaptiveMarkingPenalty": 0, "customName": "", "matchMode": "exact", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "variableReplacements": [], "displayAnswer": "({b[0]}/{b[1]})^{exponent}={value}", "type": "patternmatch"}], "preamble": {"js": "", "css": ""}, "statement": "<p>Rewrite in exponential form:</p>\n<p>Given:&nbsp; $\\log_{\\frac{ \\var{b[0]} }{ \\var{b[1]} }}{\\var{value}}=\\var{exponent}&nbsp; &nbsp;$</p>", "tags": []}, {"name": "Math 3 Rewrite in exponential form log base whole number", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["b", "exponent", "value"], "variablesTest": {"condition": "", "maxRuns": 100}, "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"value": {"templateType": "anything", "name": "value", "description": "", "definition": "precround(b^exponent,4)", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "name": "b", "description": "", "definition": "random(2..5)", "group": "Ungrouped variables"}, "exponent": {"templateType": "anything", "name": "exponent", "description": "", "definition": "random(-4..4 except [-1,0,1])", "group": "Ungrouped variables"}}, "parts": [{"marks": 1, "showCorrectAnswer": true, "answer": "{b}^{exponent}={value}", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "showFeedbackIcon": true, "unitTests": [], "displayAnswer": "{b}^{exponent}={value}", "customName": "", "scripts": {}, "adaptiveMarkingPenalty": 0, "matchMode": "exact", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "patternmatch", "customMarkingAlgorithm": ""}], "rulesets": {}, "tags": [], "variable_groups": [], "advice": "", "metadata": {"licence": "All rights reserved", "description": ""}, "statement": "<p>Rewrite in exponential form:</p>\n<p>Given:&nbsp; $\\log_{\\var{b}}{\\var{value}}=\\var{exponent}&nbsp; &nbsp;$</p>"}, {"name": "Math 3 Rewrite in exponential form log with decimals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "preamble": {"js": "", "css": ""}, "tags": [], "advice": "", "functions": {}, "ungrouped_variables": ["b", "exponent", "value"], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"scripts": {}, "answer": "{b}^{exponent}={value}", "type": "patternmatch", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "useCustomName": false, "marks": 1, "customName": "", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "matchMode": "exact", "displayAnswer": "{b}^{exponent}={value}", "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": ""}], "rulesets": {}, "variables": {"exponent": {"definition": "random(-5..5 except[-1,0,1])", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "exponent"}, "b": {"definition": "random(0.1..5#0.1)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b"}, "value": {"definition": "precround(b^exponent,4)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "value"}}, "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Rewrite in exponential form:</p>\n<p>Given:&nbsp; $\\log_{\\var{b}}{\\var{value}}=\\var{exponent}&nbsp; &nbsp;$</p>", "variable_groups": []}, {"name": "Math 3 Rewrite in exponential form with natural log", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "All rights reserved"}, "ungrouped_variables": ["exponent", "value"], "advice": "", "rulesets": {}, "variables": {"exponent": {"description": "", "name": "exponent", "definition": "random(-5..5 except[-1,0,1])", "group": "Ungrouped variables", "templateType": "anything"}, "value": {"description": "", "name": "value", "definition": "precround(e^exponent,4)", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"useCustomName": false, "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "answer": "e^{exponent}={value}", "marks": 1, "adaptiveMarkingPenalty": 0, "customName": "", "matchMode": "exact", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "displayAnswer": "e^{exponent}={value}", "type": "patternmatch"}], "preamble": {"js": "", "css": ""}, "statement": "<p>Rewrite in exponential form:</p>\n<p>Given:&nbsp; $\\ln{\\var{value}}=\\var{exponent}&nbsp; &nbsp;$</p>", "tags": []}, {"name": "Math 3 Rewrite in log form 0<b<1 fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["b", "exponent", "value"], "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"value": {"templateType": "anything", "name": "value", "definition": "rational_approximation((b[0]/b[1])^exponent)", "description": "<p>x</p>", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "name": "b", "definition": "rational_approximation(random(0..1#0.2 except[0,1]))", "description": "", "group": "Ungrouped variables"}, "exponent": {"templateType": "anything", "name": "exponent", "definition": "random(-3..3 except [-1,0,1])", "description": "", "group": "Ungrouped variables"}}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "tags": [], "parts": [{"scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "type": "patternmatch", "answer": "log_{b[0]/b[1]}({value[0]}/{value[1]})={exponent}", "displayAnswer": "log_{b[0]/b[1]}({value[0]}/{value[1]})={exponent}", "customName": "", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0, "matchMode": "exact", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "customMarkingAlgorithm": ""}], "advice": "", "metadata": {"licence": "All rights reserved", "description": ""}, "statement": "<p>Re-write in log form.</p>\n<p>Given:&nbsp; $\\left( \\frac{\\var{b[0]}}{ \\var{b[1]}} \\right)^{\\var{exponent}} = \\simplify{ {value[0]}/{value[1]} }$</p>\n<p><em><strong>CAUTION:&nbsp; Be sure your value in the log is written as a fraction, i.e. 5 = 5/1.&nbsp; Also, if needed, express your base as a decimal in your answer.</strong></em></p>\n<p><em><strong>EXAMPLE ANSWER:&nbsp; log_4(64/1)=3</strong></em></p>"}, {"name": "Math 3 Rewrite in log form b is decimal", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["b", "exponent", "value"], "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"matchMode": "exact", "answer": "log_{b}({value})={exponent}", "customName": "", "displayAnswer": "log_{b}({value})={exponent}", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "type": "patternmatch", "scripts": {}}], "variables": {"value": {"name": "value", "definition": "precround((b)^exponent,4)", "group": "Ungrouped variables", "description": "<p>x</p>", "templateType": "anything"}, "b": {"name": "b", "definition": "random(0..5#0.01 except[0,1])", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "exponent": {"name": "exponent", "definition": "random(-3..3 except [-1,0,1])", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "metadata": {"description": "", "licence": "All rights reserved"}, "rulesets": {}, "advice": "", "functions": {}, "variable_groups": [], "statement": "<p>Re-write in log form.</p>\n<p>Given:&nbsp; $\\left( \\var{b}&nbsp;\\right)^{\\var{exponent}} =&nbsp;\\var{value}$</p>\n<p><em><strong>CAUTION:&nbsp; Be sure your value in the log is written as a fraction, i.e. 5 = 5/1.&nbsp; Also, if needed, express your base as a decimal in your answer.</strong></em></p>\n<p><em><strong>EXAMPLE ANSWER:&nbsp; log_4(64/1)=3</strong></em></p>", "preamble": {"css": "", "js": ""}}, {"name": "Math 3 Rewrite in log form b is value \"e\" exponent is decimal", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["exponent", "value"], "advice": "", "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Re-write in log form.</p>\n<p>Given:&nbsp; $e^{\\var{exponent}} =&nbsp;\\var{value}$</p>\n<p><em><strong>CAUTION:&nbsp; Be sure your value in the log is written as a fraction, i.e. 5 = 5/1.&nbsp; Also, if needed, express your base as a decimal in your answer.</strong></em></p>\n<p><em><strong>EXAMPLE ANSWER:&nbsp; log_4(64/1)=3</strong></em></p>", "parts": [{"marks": 1, "showCorrectAnswer": true, "displayAnswer": "ln({value})={exponent}", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "answer": "ln({value})={exponent}", "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "type": "patternmatch", "customName": "", "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "matchMode": "exact"}], "preamble": {"js": "", "css": ""}, "variables": {"value": {"group": "Ungrouped variables", "templateType": "anything", "definition": "precround(e^exponent,4)", "description": "", "name": "value"}, "exponent": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-3..3#0.1 except [-1,0,1])", "description": "", "name": "exponent"}}, "tags": [], "variable_groups": [], "metadata": {"licence": "All rights reserved", "description": ""}}, {"name": "Math 3 Rewrite in log form b is value \"e\" exponent is fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "All rights reserved"}, "ungrouped_variables": ["exponent", "value"], "advice": "", "rulesets": {}, "variables": {"exponent": {"description": "", "name": "exponent", "definition": "[random(-3..3 except 0),random(5,7,11)]", "group": "Ungrouped variables", "templateType": "anything"}, "value": {"description": "", "name": "value", "definition": "precround(e^(exponent[0]/exponent[1]),4)", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"useCustomName": false, "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "answer": "ln({value})={exponent[0]}/{exponent[1]}", "marks": 1, "adaptiveMarkingPenalty": 0, "customName": "", "matchMode": "exact", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "displayAnswer": "ln({value})={exponent[0]}/{exponent[1]}", "type": "patternmatch"}], "preamble": {"js": "", "css": ""}, "statement": "<p>Re-write in log form.</p>\n<p>Given:&nbsp; $e^{\\frac{\\var{exponent[0]}}{\\var{exponent[1]} }} =&nbsp;\\var{value}$</p>\n<p></p>", "tags": []}, {"name": "Math 3 Rewrite in log form b>1 whole number", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "preamble": {"css": "", "js": ""}, "variables": {"b": {"templateType": "anything", "name": "b", "group": "Ungrouped variables", "definition": "random(2..10)", "description": ""}, "exponent": {"templateType": "anything", "name": "exponent", "group": "Ungrouped variables", "definition": "random(-5..5 except [-1,0,1])", "description": ""}, "value": {"templateType": "anything", "name": "value", "group": "Ungrouped variables", "definition": "rational_approximation(b^exponent)", "description": "<p>x</p>"}}, "ungrouped_variables": ["b", "exponent", "value"], "advice": "", "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"licence": "All rights reserved", "description": ""}, "statement": "<p>Re-write in log form.</p>\n<p>Given:&nbsp; $\\var{b}^{\\var{exponent}} = \\simplify{ {value[0]}/{value[1]} }$</p>\n<p><em><strong>CAUTION:&nbsp; Be sure your value in the log is written as a fraction, i.e. 5 = 5/1.&nbsp;&nbsp;&nbsp;Also, if needed, express your base as a decimal in your answer.</strong></em></p>\n<p><em><strong>EXAMPLE ANSWER:&nbsp; log_4(64/1)=3</strong></em></p>", "parts": [{"marks": 1, "scripts": {}, "customName": "", "answer": "log_{b}({value[0]}/{value[1]})={exponent}", "showFeedbackIcon": true, "useCustomName": false, "displayAnswer": "log_{b}({value[0]}/{value[1]})={exponent}", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "adaptiveMarkingPenalty": 0, "extendBaseMarkingAlgorithm": true, "type": "patternmatch", "matchMode": "exact", "showCorrectAnswer": true, "variableReplacements": [], "unitTests": []}], "rulesets": {}, "tags": [], "functions": {}, "variable_groups": []}, {"name": "Math 3 Write expansion as a single logarithm Variable Combo", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "All rights reserved"}, "ungrouped_variables": ["base", "variables", "var1", "var2", "exp1", "exp2", "var3", "exp3"], "advice": "", "rulesets": {}, "variables": {"var2": {"templateType": "anything", "name": "var2", "definition": "random(variables except var1)", "group": "Ungrouped variables", "description": ""}, "exp3": {"templateType": "anything", "name": "exp3", "definition": "random(2..20)", "group": "Ungrouped variables", "description": ""}, "variables": {"templateType": "anything", "name": "variables", "definition": "[\"x\",\"y\",\"z\",\"a\",\"b\",\"c\",\"k\",\"m\",\"n\",\"p\",\"q\"]", "group": "Ungrouped variables", "description": ""}, "var3": {"templateType": "anything", "name": "var3", "definition": "random(variables except [var1,var2])", "group": "Ungrouped variables", "description": ""}, "exp1": {"templateType": "anything", "name": "exp1", "definition": "random(2..20)", "group": "Ungrouped variables", "description": ""}, "base": {"templateType": "anything", "name": "base", "definition": "random(2..9)", "group": "Ungrouped variables", "description": ""}, "exp2": {"templateType": "anything", "name": "exp2", "definition": "random(2..20)", "group": "Ungrouped variables", "description": ""}, "var1": {"templateType": "anything", "name": "var1", "definition": "random(variables)", "group": "Ungrouped variables", "description": ""}}, "parts": [{"customName": "", "useCustomName": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "caseSensitive": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "answer": "log_{base}({var1}^{exp1}{var2}^{exp2}/{var3}^{exp3})", "type": "patternmatch", "adaptiveMarkingPenalty": 0, "matchMode": "exact", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "displayAnswer": "log_{base}({var1}^{exp1}{var2}^{exp2}/{var3}^{exp3})", "marks": 1, "partialCredit": "75"}], "preamble": {"js": "", "css": ""}, "statement": "<p>Write the logarithm as a single logarithm.</p>\n<p>Given:&nbsp; $ \\var{exp1}\\log_\\var{base}(&nbsp;\\var{var1} ) + \\var{exp2}\\log_\\var{base}( \\var{var2} ) - \\var{exp3}\\log_\\var{base}( \\var{var3} ) $</p>", "tags": []}, {"name": "Math 3 Write expansion as a single logarithm Variable Difference", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "All rights reserved"}, "ungrouped_variables": ["base", "variables", "var1", "var2", "exp1", "exp2"], "advice": "", "rulesets": {}, "variables": {"var2": {"name": "var2", "definition": "random(variables except var1)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "variables": {"name": "variables", "definition": "[\"x\",\"y\",\"z\",\"a\",\"b\",\"c\",\"k\",\"m\",\"n\",\"p\",\"q\"]", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "exp1": {"name": "exp1", "definition": "random(2..20)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "base": {"name": "base", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "exp2": {"name": "exp2", "definition": "random(2..20)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "var1": {"name": "var1", "definition": "random(variables)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"useCustomName": false, "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "caseSensitive": true, "extendBaseMarkingAlgorithm": true, "answer": "log_{base}({var1}^{exp1}/{var2}^{exp2})", "marks": 1, "adaptiveMarkingPenalty": 0, "customName": "", "matchMode": "exact", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "displayAnswer": "log_{base}({var1}^{exp1}/{var2}^{exp2})", "type": "patternmatch", "partialCredit": "75"}], "preamble": {"js": "", "css": ""}, "statement": "<p>Write the logarithm as a single logarithm.</p>\n<p>Given:&nbsp; $ \\var{exp1}\\log_\\var{base}(&nbsp;\\var{var1} )&nbsp;-\\var{exp2}\\log_\\var{base}( \\var{var2} )&nbsp; $</p>", "tags": []}, {"name": "Math 3 Write expansion as a single logarithm Variable Sum", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["base", "variables", "var1", "var2", "exp1", "exp2"], "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"var1": {"group": "Ungrouped variables", "name": "var1", "description": "", "definition": "random(variables)", "templateType": "anything"}, "base": {"group": "Ungrouped variables", "name": "base", "description": "", "definition": "random(2..9)", "templateType": "anything"}, "var2": {"group": "Ungrouped variables", "name": "var2", "description": "", "definition": "random(variables except var1)", "templateType": "anything"}, "exp2": {"group": "Ungrouped variables", "name": "exp2", "description": "", "definition": "random(2..20)", "templateType": "anything"}, "exp1": {"group": "Ungrouped variables", "name": "exp1", "description": "", "definition": "random(2..20)", "templateType": "anything"}, "variables": {"group": "Ungrouped variables", "name": "variables", "description": "", "definition": "[\"x\",\"y\",\"z\",\"a\",\"b\",\"c\",\"k\",\"m\",\"n\",\"p\",\"q\"]", "templateType": "anything"}}, "parts": [{"scripts": {}, "displayAnswer": "log_{base}({var1}^{exp1}{var2}^{exp2})", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "answer": "log_{base}({var1}^{exp1}{var2}^{exp2})", "type": "patternmatch", "partialCredit": "75", "showCorrectAnswer": true, "customName": "", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0, "matchMode": "exact", "variableReplacements": [], "useCustomName": false, "unitTests": [], "marks": 1, "extendBaseMarkingAlgorithm": true, "caseSensitive": true}], "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "tags": [], "variable_groups": [], "advice": "", "metadata": {"licence": "All rights reserved", "description": ""}, "statement": "<p>Write the logarithm as a single logarithm.</p>\n<p>Given:&nbsp; $ \\var{exp1}\\log_\\var{base}(&nbsp;\\var{var1} ) + \\var{exp2}\\log_\\var{base}( \\var{var2} )&nbsp; $</p>"}, {"name": "Math 3 Write expansion as a single logarithm Variable Sum v2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "All rights reserved"}, "ungrouped_variables": ["base", "variables", "var1", "var2", "exp1", "exp2"], "advice": "", "rulesets": {}, "parts": [{"useCustomName": false, "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "caseSensitive": true, "extendBaseMarkingAlgorithm": true, "answer": "log_{base}({var1}{var2}^{exp2})", "type": "patternmatch", "adaptiveMarkingPenalty": 0, "customName": "", "matchMode": "exact", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "displayAnswer": "log_{base}({var1}{var2}^{exp2})", "marks": 1, "partialCredit": "75"}], "preamble": {"js": "", "css": ""}, "tags": [], "statement": "<p>Write the logarithm as a single logarithm.</p>\n<p>Given:&nbsp; $ \\log_\\var{base}(&nbsp;\\var{var1} ) + \\var{exp2}\\log_\\var{base}( \\var{var2} )&nbsp; $</p>", "variables": {"var2": {"name": "var2", "definition": "random(variables except var1)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "variables": {"name": "variables", "definition": "[\"x\",\"y\",\"z\",\"a\",\"b\",\"c\",\"k\",\"m\",\"n\",\"p\",\"q\"]", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "exp1": {"name": "exp1", "definition": "1", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "base": {"name": "base", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "exp2": {"name": "exp2", "definition": "random(2..20)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "var1": {"name": "var1", "definition": "random(variables)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}}, {"name": "Math 3 Write expansion as single logarithm Numerical Difference", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "All rights reserved"}, "ungrouped_variables": ["base", "val1", "val2", "quotient"], "advice": "", "rulesets": {}, "variables": {"val1": {"description": "", "name": "val1", "definition": "random(2..50)", "group": "Ungrouped variables", "templateType": "anything"}, "val2": {"description": "", "name": "val2", "definition": "random(2..50 except val1)", "group": "Ungrouped variables", "templateType": "anything"}, "base": {"description": "", "name": "base", "definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything"}, "quotient": {"description": "", "name": "quotient", "definition": "rational_approximation(val1/val2)", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"customName": "", "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "answer": "log_{base}({quotient[0]}/{quotient[1]})", "marks": 1, "adaptiveMarkingPenalty": 0, "matchMode": "exact", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "displayAnswer": "log_{base}({quotient[0]}/{quotient[1]})", "type": "patternmatch"}], "preamble": {"js": "", "css": ""}, "tags": [], "statement": "<p>Write as a single logarithm.</p>\n<p>Given:&nbsp; $ \\log_{\\var{base}}(\\var{val1}) -&nbsp; \\log_{\\var{base}}(\\var{val2})&nbsp;$</p>"}, {"name": "Math 3 Write expansion as single logarithm Numerical Sum", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["base", "val1", "val2", "product"], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variables": {"product": {"group": "Ungrouped variables", "name": "product", "description": "", "definition": "val1*val2", "templateType": "anything"}, "val2": {"group": "Ungrouped variables", "name": "val2", "description": "", "definition": "random(2..50 except val1)", "templateType": "anything"}, "val1": {"group": "Ungrouped variables", "name": "val1", "description": "", "definition": "random(2..50)", "templateType": "anything"}, "base": {"group": "Ungrouped variables", "name": "base", "description": "", "definition": "random(2..9)", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"scripts": {}, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "answer": "log_{base}({product})", "showFeedbackIcon": true, "unitTests": [], "showCorrectAnswer": true, "customName": "", "marks": 1, "displayAnswer": "log_{base}({product})", "adaptiveMarkingPenalty": 0, "matchMode": "exact", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "patternmatch"}], "tags": [], "variable_groups": [], "advice": "", "metadata": {"licence": "All rights reserved", "description": ""}, "statement": "<p>Write as a single logarithm.</p>\n<p>Given:&nbsp; $ \\log_{\\var{base}}(\\var{val1}) +&nbsp; \\log_{\\var{base}}(\\var{val2})&nbsp;$</p>"}, {"name": "NC Math 3 Evaluate an Exponential Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "parts": [{"precisionType": "dp", "showCorrectAnswer": true, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "marks": 1, "minValue": "fx1", "showFeedbackIcon": true, "customName": "", "mustBeReducedPC": 0, "adaptiveMarkingPenalty": 0, "precision": "2", "variableReplacements": [], "useCustomName": false, "strictPrecision": false, "customMarkingAlgorithm": "", "mustBeReduced": false, "correctAnswerFraction": false, "allowFractions": false, "prompt": "<p>$x = \\var{x1}$</p>", "correctAnswerStyle": "plain", "maxValue": "fx1", "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true, "scripts": {}, "precisionPartialCredit": "75", "extendBaseMarkingAlgorithm": true}, {"precisionType": "dp", "showCorrectAnswer": true, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "marks": 1, "minValue": "fx2", "showFeedbackIcon": true, "customName": "", "mustBeReducedPC": 0, "adaptiveMarkingPenalty": 0, "precision": "2", "variableReplacements": [], "useCustomName": false, "strictPrecision": false, "customMarkingAlgorithm": "", "mustBeReduced": false, "correctAnswerFraction": false, "allowFractions": false, "prompt": "<p>$x=\\var{x2}$</p>", "correctAnswerStyle": "plain", "maxValue": "fx2", "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true, "scripts": {}, "precisionPartialCredit": "75", "extendBaseMarkingAlgorithm": true}], "ungrouped_variables": ["A", "b", "h", "k", "x1", "x2", "fx1", "fx2", "operator", "kSign", "kabs"], "advice": "", "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Evaluate the following function at the indicated values.</p>\n<p>$f(x) = \\var{A} ( \\var{b} )^{&nbsp; \\simplify{x + {h}} }&nbsp; \\var{ operator[ {kSign} ] }&nbsp;\\var{kabs} $</p>", "metadata": {"licence": "All rights reserved", "description": ""}, "preamble": {"js": "", "css": ""}, "variables": {"kSign": {"templateType": "anything", "group": "Ungrouped variables", "definition": "award(1,k<0)", "description": "", "name": "kSign"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "b"}, "fx1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(A*b^(x1+h)+k,2)", "description": "", "name": "fx1"}, "A": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "name": "A"}, "h": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-2..2)", "description": "", "name": "h"}, "kabs": {"templateType": "anything", "group": "Ungrouped variables", "definition": "abs(k)", "description": "", "name": "kabs"}, "k": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "name": "k"}, "fx2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(A*b^(x2+h)+k,2)", "description": "", "name": "fx2"}, "x2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "name": "x2"}, "operator": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[\"$+$\",\"$-$\"]", "description": "", "name": "operator"}, "x1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..-1)", "description": "", "name": "x1"}}, "tags": [], "variable_groups": []}, {"name": "NC Math 3 Exponential Growth or Decay given fractional base", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "preamble": {"js": "", "css": ""}, "tags": [], "advice": "", "parts": [{"scripts": {}, "customName": "", "showFeedbackIcon": true, "minMarks": 0, "useCustomName": false, "choices": ["$\\var{choices[{check}]}$", "$\\var{choices[{notChoice}]}$"], "showCorrectAnswer": true, "distractors": ["", ""], "maxMarks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "showCellAnswerState": true, "adaptiveMarkingPenalty": 0, "shuffleChoices": true, "matrix": ["1", "0"], "unitTests": []}], "ungrouped_variables": ["A", "bnum", "bden", "bValue", "check", "choices", "notChoice"], "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "rulesets": {}, "variable_groups": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>State whether the function shows exponential Growth or Decay.</p>\n<p>$f(x) = \\var{A}(\\frac{\\var{bnum}}{\\var{bden}})^x$</p>", "variables": {"bValue": {"definition": "bnum/bden", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "bValue"}, "bnum": {"definition": 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"showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["A1", "bd", "bg", "A2"], "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"bg": {"templateType": "anything", "name": "bg", "description": "", "definition": "random(1.1..9#0.1)", "group": "Ungrouped variables"}, "A2": {"templateType": "anything", "name": "A2", "description": "", "definition": "random(2..9)", "group": "Ungrouped variables"}, "A1": {"templateType": "anything", "name": "A1", "description": "", "definition": "random(2..15)", "group": "Ungrouped variables"}, "bd": {"templateType": "anything", "name": "bd", "description": "", "definition": "random(0.1..0.99#0.1)", "group": "Ungrouped variables"}}, "parts": [{"displayType": "radiogroup", "shuffleChoices": false, "showCorrectAnswer": true, "maxMarks": 0, "type": "1_n_2", "customName": "", "marks": 0, "adaptiveMarkingPenalty": 0, "useCustomName": false, "variableReplacements": [], "unitTests": [], "choices": ["GROWTH", "DECAY"], "showFeedbackIcon": true, "showCellAnswerState": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "minMarks": 0, "matrix": ["1", 0], "distractors": ["", ""], "displayColumns": 0, "extendBaseMarkingAlgorithm": true, "scripts": {}}], "rulesets": {}, "tags": [], "variable_groups": [], "advice": "", "metadata": {"licence": "All rights reserved", "description": ""}, "statement": "<p>State whether the function shows exponential Growth or Decay.</p>\n<p>$f(x) = \\var{A1}(\\var{bg})^x$</p>"}, {"name": "NC Math 3 Exponential Growth or Decay given function 0<b<1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": 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"GorD", "gdChoice", "rPercent", "gdFactor"], "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"gdChoice": {"group": "Ungrouped variables", "name": "gdChoice", "description": "", "definition": "award(1,r<0)", "templateType": "anything"}, "sign": {"group": "Ungrouped variables", "name": "sign", "description": "", "definition": "award(1,r>0)", "templateType": "anything"}, "A": {"group": "Ungrouped variables", "name": "A", "description": "", "definition": "random(1..25#0.1)", "templateType": "anything"}, "rPercent": {"group": "Ungrouped variables", "name": "rPercent", "description": "", "definition": "abs(r)*100", "templateType": "anything"}, "one": {"group": "Ungrouped variables", "name": "one", "description": "", "definition": "1", "templateType": "anything"}, "rabs": {"group": "Ungrouped variables", "name": "rabs", "description": "", "definition": "abs(r)", "templateType": "anything"}, "operator": {"group": "Ungrouped variables", "name": "operator", "description": "", "definition": "[\"$-$\",\"$+$\"]", "templateType": "anything"}, "GorD": {"group": "Ungrouped variables", "name": "GorD", "description": "", "definition": "[\"Growth\",\"Decay\"]", "templateType": "anything"}, "r": {"group": "Ungrouped variables", "name": "r", "description": "", "definition": "random(-0.9..0.9#0.015 except 0)", "templateType": "anything"}, "gdFactor": {"group": "Ungrouped variables", "name": "gdFactor", "description": "", "definition": "1+r", "templateType": "anything"}}, "parts": [{"marks": 0, "showCorrectAnswer": true, "prompt": "<p>Growth or Decay? 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"description": "", "group": "Ungrouped variables"}, "rPercent": {"templateType": "anything", "name": "rPercent", "definition": "abs(r)*100", "description": "", "group": "Ungrouped variables"}, "operator": {"templateType": "anything", "name": "operator", "definition": "[\"$-$\",\"$+$\"]", "description": "", "group": "Ungrouped variables"}, "gdChoice": {"templateType": "anything", "name": "gdChoice", "definition": "award(1,r<0)", "description": "", "group": "Ungrouped variables"}, "one": {"templateType": "anything", "name": "one", "definition": "1", "description": "", "group": "Ungrouped variables"}, "gdFactor": {"templateType": "anything", "name": "gdFactor", "definition": "1+r", "description": "", "group": "Ungrouped variables"}, "rabs": {"templateType": "anything", "name": "rabs", "definition": "abs(r)", "description": "", "group": "Ungrouped variables"}, "A": {"templateType": "anything", "name": "A", "definition": "random(1..25#0.1)", "description": "", "group": "Ungrouped variables"}}, "parts": [{"scripts": {}, "useCustomName": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "sortAnswers": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>Growth or Decay? 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["plain", "en", "si-en"], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "marks": 1, "maxValue": "{A}", "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "{A}", "correctAnswerFraction": false}, {"scripts": {}, "useCustomName": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "answer": "{rPercent}%", "prompt": "<p>Rate of Growth or Decay as a percent?</p>", "marks": 1, "adaptiveMarkingPenalty": 0, "customName": "", "matchMode": "exact", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "variableReplacements": [], "displayAnswer": "{rPercent}%", "type": "patternmatch"}, {"useCustomName": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReduced": false, "showFractionHint": true, "prompt": "<p>Growth or Decay factor?</p>", "adaptiveMarkingPenalty": 0, "customName": "", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "scripts": {}, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "marks": 1, "maxValue": "gdFactor", "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "gdFactor", "correctAnswerFraction": false}], "preamble": {"js": "", "css": ""}, "statement": "<p>Determine if each exponential function is growth/decay, state initial amount, growth or decay rate as a&nbsp;<em><strong>percent (%)</strong></em>, and the growth or decay factor.</p>\n<p>$f(t) = \\var{A}( \\simplify{1 + {r}} )^t$</p>", "tags": []}, {"name": "NC Math 3 Solve an exponential decay problem -- Depreciation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "ungrouped_variables": ["A", "r", "rPercent", "dFactor", "tDepreciate", "valueNow"], "parts": [{"customMarkingAlgorithm": "", "displayAnswer": "Decay", "scripts": {}, "unitTests": [], "showFeedbackIcon": true, "prompt": "<p>Is the value of the truck exponential growth or decay?</p>", "answer": "decay", "showCorrectAnswer": true, "type": "patternmatch", "customName": "", "marks": 1, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "matchMode": "exact", "adaptiveMarkingPenalty": 0, "variableReplacements": []}, {"customMarkingAlgorithm": "", "scripts": {}, "unitTests": [], "gaps": [{"correctAnswerFraction": false, "showFractionHint": true, "type": "numberentry", "maxValue": "A", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "useCustomName": false, "mustBeReduced": false, "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "minValue": "A", "scripts": {}, "mustBeReducedPC": 0, "customName": "", "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false}], "showFeedbackIcon": true, "prompt": "<p>What is the original value of the truck?</p>\n<p>$\\$$[[0]]</p>", "showCorrectAnswer": true, "type": "gapfill", "customName": "", "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "sortAnswers": false, "adaptiveMarkingPenalty": 0, "variableReplacements": []}, {"customMarkingAlgorithm": "", "displayAnswer": "{rPercent}%", "scripts": {}, "unitTests": [], "showFeedbackIcon": true, "prompt": "<p>What is the growth or decay rate as a percent?</p>", "answer": "{rPercent}%", "showCorrectAnswer": true, "type": "patternmatch", "customName": "", "marks": 1, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "matchMode": "exact", "adaptiveMarkingPenalty": 0, "variableReplacements": []}, {"customMarkingAlgorithm": "", "scripts": {}, "unitTests": [], "gaps": [{"correctAnswerFraction": false, "precisionPartialCredit": "50", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "type": "numberentry", "maxValue": "valueNow", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "useCustomName": false, "precision": "2", "adaptiveMarkingPenalty": 0, "showPrecisionHint": false, "customMarkingAlgorithm": "", "minValue": "valueNow", "scripts": {}, "mustBeReducedPC": 0, "precisionMessage": "Money always is expressed with two decimal places.", "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "strictPrecision": true, "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "customName": "", "allowFractions": false}], "showFeedbackIcon": true, "prompt": "<p>What is the value of the truck $\\var{tDepreciate}$ years after it was built?</p>\n<p>$\\$$[[0]]</p>", "showCorrectAnswer": true, "type": "gapfill", "customName": "", "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "sortAnswers": false, "adaptiveMarkingPenalty": 0, "variableReplacements": []}], "functions": {}, "advice": "", "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"tDepreciate": {"group": "Ungrouped variables", "definition": "random(2..6)", "name": "tDepreciate", "description": "", "templateType": "anything"}, "dFactor": {"group": "Ungrouped variables", "definition": "1-r", "name": "dFactor", "description": "", "templateType": "anything"}, "r": {"group": "Ungrouped variables", "definition": "random(0.1..0.25#0.01)", "name": "r", "description": "", "templateType": "anything"}, "rPercent": {"group": "Ungrouped variables", "definition": "100*r", "name": "rPercent", "description": "", "templateType": "anything"}, "valueNow": {"group": "Ungrouped variables", "definition": "precround(A*(dFactor)^tDepreciate,2)", "name": "valueNow", "description": "", "templateType": "anything"}, "A": {"group": "Ungrouped variables", "definition": "random(40000..80000)", "name": "A", "description": "", "templateType": "anything"}}, "tags": [], "statement": "<p>The value, $y$, of a truck can be modeled by $ y = \\var{A}(\\var{dFactor})^t $, where $t$ is the number of years since the truck was built.</p>", "rulesets": {}, "variable_groups": [], "metadata": {"licence": "All rights reserved", "description": ""}}, {"name": "NC Math 3 Write and solve an exponential growth equation -- Bacteria", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": 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false, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "allowFractions": false, "prompt": "<p>If a person went back to that dish at $\\var{tEnd}$ P.M. on the same day, how many bacteria would be in the dish?</p>", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "scripts": {}, "showFractionHint": true, "extendBaseMarkingAlgorithm": true, "maxValue": "totalBacteria"}], "ungrouped_variables": ["A", "tStart", "tEnd", "rPercent", "r", "gFactor", "totalBacteria"], "advice": "", "rulesets": {}, "variables": {"totalBacteria": {"templateType": "anything", "group": "Ungrouped variables", "definition": "trunc(A*(gFactor)^((12-tStart)+tEnd))", "description": "", "name": "totalBacteria"}, "tStart": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..11)", "description": "<p>Time in the A.M.</p>", "name": "tStart"}, "gFactor": {"templateType": "anything", "group": "Ungrouped variables", "definition": "1+r", "description": "", "name": "gFactor"}, "A": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(50..200)", "description": "", "name": "A"}, "rPercent": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..25)", "description": "", "name": "rPercent"}, "r": {"templateType": "anything", "group": "Ungrouped variables", "definition": "rPercent/100", "description": "", "name": "r"}, "tEnd": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..11)", "description": "<p>time in the P.M.</p>", "name": "tEnd"}}, "statement": "<p>In a petri dish, there were $\\var{A}$ bacteria at $\\var{tStart}$ A.M. on Monday.&nbsp; It has been estimated the bacteria in that dish grow at a rate of $\\var{rPercent}$% each hour.</p>", "metadata": {"licence": "All rights reserved", "description": ""}, "preamble": {"js": "", "css": ""}, "tags": [], "variable_groups": []}]}], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": "Students will review and practice problems involving logs and exponentials."}, "feedback": {"showtotalmark": true, "intro": "", "feedbackmessages": [], "allowrevealanswer": true, "showanswerstate": true, "showactualmark": true, "advicethreshold": 0}, "timing": {"timeout": {"action": "none", "message": ""}, "allowPause": true, "timedwarning": {"action": "none", "message": ""}}, "showstudentname": true, "navigation": {"startpassword": "", "onleave": {"action": "none", "message": ""}, "reverse": true, "allowsteps": true, "preventleave": true, "browse": true, "showfrontpage": true, "showresultspage": "oncompletion", "allowregen": true}, "percentPass": 0, "duration": 0, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "extensions": [], "custom_part_types": [], "resources": []}