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"extendBaseMarkingAlgorithm": true, "scripts": {}, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "<p>$\\var{f1}^{0}=$[[0]]</p>", "scripts": {}, "customMarkingAlgorithm": ""}, {"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "sortAnswers": false, "customName": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 0, "gaps": [{"correctAnswerFraction": false, "showFeedbackIcon": true, "variableReplacements": [], "allowFractions": false, "maxValue": "{g1}^{g2}", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 1, "minValue": "{g1}^{g2}", "useCustomName": false, "mustBeReduced": false, "customName": "", "showFractionHint": true, "mustBeReducedPC": 0, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "scripts": {}, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "<p>$(\\var{g1})^{\\var{g2}}=$[[0]]</p>", "scripts": {}, "customMarkingAlgorithm": ""}], "advice": "<p>a)&nbsp; &nbsp;$\\var{abc1}^{\\var{P1}}=&nbsp;\\var{abc1} \\times\\var{abc1} \\times... (\\var{P1}&nbsp; \\text{ times}) = \\var{a}$</p>\n<p>b)&nbsp; &nbsp;$\\var{abc1}^{\\var{P2}}=&nbsp;&nbsp;\\var{abc1} \\times\\var{abc1} \\times... (\\var{P2}&nbsp; \\text{ times}) =\\var{b}$</p>\n<p>c)&nbsp; &nbsp;$\\var{abc1}^{\\var{P3}}&nbsp;= \\var{abc1} \\times\\var{abc1} \\times... (\\var{P3}&nbsp; \\text{ times}) =\\var{c}$</p>\n<p>d)&nbsp; &nbsp;$\\var{d1}^{\\var{d2}}&nbsp;= \\var{d1} \\times\\var{d1} \\times... (\\var{d2}&nbsp; \\text{ times}) =\\var{d}$</p>\n<p>e)&nbsp;&nbsp;$\\var{e1}^{2}=\\var{e1} \\times \\var{e1} =\\var{e2} $</p>\n<p>f)&nbsp; &nbsp;Any number to the power of&nbsp; $0$&nbsp; is equal to&nbsp; $1$,&nbsp; so&nbsp; $\\var{f1}^{0}=1$</p>\n<p>g)&nbsp; &nbsp;$(\\var{g1})^{\\var{g2}}=\\var{g}$</p>\n<p>&nbsp; &nbsp; &nbsp; Notice that an odd power of a negative number gives a negative answer.</p>", "statement": "<p>Evaluate the following:</p>", "preamble": {"css": "", "js": ""}, "rulesets": {}, "tags": [], "functions": {}, "metadata": {"description": "<p>Indices and Roots</p><p>Questions based on Exercise Intro(b) from the Textbook \"Engineering Maths through Applications\" by Kuldeep Singh.</p><p>Intended for use as Homework Exercises.Indices and Roots</p>", "licence": "Creative Commons Attribution 4.0 International"}}, {"name": "00b - Engineering Arithmetic: 002", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "functions": {}, "advice": "<p>a)&nbsp; &nbsp;Since&nbsp; $\\var{a1} \\times \\var{a1}=\\var{a2}$&nbsp; and also $(-\\var{a1}) \\times (-\\var{a1})=\\var{a2}$,&nbsp; so:</p>\n<p>\\[\\pm \\sqrt{\\var{a2}}=\\pm \\var{a1}\\]</p>\n<p>b)&nbsp; &nbsp;Using your calculator:</p>\n<p>\\[\\pm \\sqrt{\\var{b2}}=\\pm \\var{b1}\\]</p>\n<p>c)&nbsp; &nbsp;Similarly:</p>\n<p>\\[ \\sqrt{\\var{c2}}=\\var{c1}\\]</p>\n<p>d)&nbsp; &nbsp;Your calculator will have a&nbsp; $\\sqrt[3]{}$&nbsp; button. Use it to evaluate:</p>\n<p>\\[ \\sqrt[3]{\\var{d2}}=\\var{d1}\\]</p>\n<p>e)&nbsp; &nbsp;</p>\n<p>\\[ \\sqrt[3]{\\var{e2}}=\\var{e1}\\]</p>\n<p>f)&nbsp; &nbsp;Since we need the 4<sup>th</sup> root (even) of $\\var{f2}$, we will have two numbers. Using your calculator:</p>\n<p>\\[\\pm \\sqrt[4]{\\var{f2}}=\\pm \\var{f1}\\]</p>\n<p>g)&nbsp; &nbsp;</p>\n<p>\\[\\pm \\sqrt[4]{\\var{g2}}=\\pm \\var{g1}\\]</p>\n<p>h)&nbsp; &nbsp;Again, the calculator shows the 8<sup>th</sup> root (even) of $\\var{h2}$ as&nbsp; $\\var{h1}$. Are there any other roots? Yes,&nbsp;$-\\var{h1}$. Hence:</p>\n<p>\\[\\pm \\sqrt[8]{\\var{h2}}=\\pm \\var{h1}\\]</p>\n<p>i)&nbsp; &nbsp;Using the calculator gives&nbsp; &nbsp;$ \\sqrt[5]{\\var{i2}}=\\var{i1}$</p>\n<p>j)&nbsp; &nbsp;Since we are interested in the 5<sup>th</sup> root (odd), there can only be one answer:</p>\n<p>\\[ \\sqrt[5]{(\\var{j2})}=\\var{j1}\\]</p>", "statement": "<p>Using your calculator or otherwise, compute:</p>", "tags": [], "rulesets": {}, "ungrouped_variables": ["a1", "a2", "b1", "b2", "c1", "c2", "d1", "d2", "e1", "e2", "f1", "f2", "g1", "g2", "h1", "h2", "i1", "i2", "j1", "j2"], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Indices and Roots</p><p>Questions based on Exercise Intro(b) from the Textbook \"Engineering Maths through Applications\" by Kuldeep Singh.</p><p>Intended for use as Homework Exercises.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"customMarkingAlgorithm": "", "gaps": 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"group": "Ungrouped variables", "name": "b2", "description": ""}, "e2": {"definition": "{e1}^(3)", "templateType": "anything", "group": "Ungrouped variables", "name": "e2", "description": ""}, "f2": {"definition": "{f1}^(4)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "h1": {"definition": "random(2 .. 5#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "h1", "description": ""}, "c1": {"definition": "random(333 .. 555#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "c1", "description": ""}, "h2": {"definition": "{h1}^(8)", "templateType": "anything", "group": "Ungrouped variables", "name": "h2", "description": ""}, "d2": {"definition": "{d1}^(3)", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "e1": {"definition": "random(5 .. 15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "e1", "description": ""}, "f1": {"definition": "random(2 .. 9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "f1", "description": ""}}}, {"name": "00b - Engineering Arithmetic: 003", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "variable_groups": [], "parts": [{"scripts": {}, "marks": 0, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "marks": 1, "mustBeReduced": false, "customMarkingAlgorithm": "", "unitTests": [], "useCustomName": false, "allowFractions": false, "correctAnswerStyle": "plain", "minValue": "{a1}", "showFeedbackIcon": true, "type": "numberentry", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "maxValue": "{a1}", "notationStyles": ["plain", "en", "si-en"], "customName": "", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "showFractionHint": true, "showCorrectAnswer": true}], "sortAnswers": false, "unitTests": [], "useCustomName": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\sqrt{\\var{a4}-\\var{a3}}=$[[0]]</p>", "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true}, {"scripts": {}, "marks": 0, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "marks": 1, "mustBeReduced": false, "customMarkingAlgorithm": "", "unitTests": [], "useCustomName": false, "allowFractions": false, "correctAnswerStyle": "plain", "minValue": "{b1}", "showFeedbackIcon": true, "type": "numberentry", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "maxValue": "{b1}", "notationStyles": ["plain", "en", "si-en"], "customName": "", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "showFractionHint": true, "showCorrectAnswer": true}], "sortAnswers": false, "unitTests": [], "useCustomName": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\sqrt{\\var{b4}+\\var{b3}}=$[[0]]</p>", "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true}, {"scripts": {}, "marks": 0, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "marks": 1, "mustBeReduced": false, "customMarkingAlgorithm": "", "unitTests": [], "useCustomName": false, "allowFractions": false, "correctAnswerStyle": "plain", "minValue": "{c1}", "showFeedbackIcon": true, "type": "numberentry", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "maxValue": "{c1}", "notationStyles": ["plain", "en", "si-en"], "customName": "", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "showFractionHint": true, "showCorrectAnswer": true}], "sortAnswers": false, "unitTests": [], "useCustomName": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\sqrt{\\var{c4}-\\var{c3}}=$[[0]]</p>", "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true}, {"scripts": {}, "marks": 0, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "marks": 1, "mustBeReduced": false, "customMarkingAlgorithm": "", "unitTests": [], "useCustomName": false, "allowFractions": false, "correctAnswerStyle": "plain", "minValue": "{d1}", "showFeedbackIcon": true, "type": "numberentry", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "maxValue": "{d1}", "notationStyles": ["plain", "en", "si-en"], "customName": "", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "showFractionHint": true, "showCorrectAnswer": true}], "sortAnswers": false, "unitTests": [], "useCustomName": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\sqrt[4]{\\var{d4}-\\var{d3}}=$[[0]]</p>", "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true}, {"scripts": {}, "marks": 0, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "marks": 1, "mustBeReduced": false, "customMarkingAlgorithm": "", "unitTests": [], "useCustomName": false, "allowFractions": false, "correctAnswerStyle": "plain", "minValue": "{e1}", "showFeedbackIcon": true, "type": "numberentry", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "maxValue": "{e1}", "notationStyles": ["plain", "en", "si-en"], "customName": "", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "showFractionHint": true, "showCorrectAnswer": true}], "sortAnswers": false, "unitTests": [], "useCustomName": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\sqrt[3]{\\var{e3}+\\var{e3}}=$[[0]]</p>", "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true}, {"scripts": {}, "marks": 0, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "marks": 1, "mustBeReduced": false, "customMarkingAlgorithm": "", "unitTests": [], "useCustomName": false, "allowFractions": false, "correctAnswerStyle": "plain", "minValue": "-{e1}", "showFeedbackIcon": true, "type": "numberentry", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "maxValue": "-{e1}", "notationStyles": ["plain", "en", "si-en"], "customName": "", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "showFractionHint": true, "showCorrectAnswer": true}], "sortAnswers": false, "unitTests": [], "useCustomName": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\sqrt[3]{(-\\var{e3}-\\var{e3})}=$[[0]]</p>", "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Indices and Roots</p><p>Questions based on Exercise Intro(b) from the Textbook \"Engineering Maths through Applications\" by Kuldeep Singh.</p><p>Intended for use as Homework Exercises.</p>"}, "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "statement": "<p>Using your calculator or otherwise, calculate:</p>", "tags": [], "variables": {"c1": {"description": "", "definition": "random(31 .. 51#1)", "group": "Ungrouped variables", "templateType": "randrange", "name": "c1"}, "b4": {"description": "", "definition": "{b2}-{b3}", "group": "Ungrouped variables", "templateType": "anything", "name": "b4"}, "e2": {"description": "", "definition": "{e1}^(3)", "group": "Ungrouped variables", "templateType": "anything", "name": "e2"}, "c4": {"description": "", "definition": "{c2}+{c3}", "group": "Ungrouped variables", "templateType": "anything", "name": "c4"}, "e1": {"description": "", "definition": "random(6 .. 16#2)", "group": "Ungrouped variables", "templateType": "randrange", "name": "e1"}, "d4": {"description": "", "definition": "{d2}+{d3}", "group": "Ungrouped variables", "templateType": "anything", "name": "d4"}, "a3": {"description": "", "definition": "random(99 .. 199#1)", "group": "Ungrouped variables", "templateType": "randrange", "name": "a3"}, "b3": {"description": "", "definition": "random(3..({b1}-1))", "group": "Ungrouped variables", "templateType": "anything", "name": "b3"}, "d1": {"description": "", "definition": "random(3 .. 9#1)", "group": "Ungrouped variables", "templateType": "randrange", "name": "d1"}, "d2": {"description": "", "definition": "{d1}^(4)", "group": "Ungrouped variables", "templateType": "anything", "name": "d2"}, "e3": {"description": "", "definition": "{e2}*0.5", "group": "Ungrouped variables", "templateType": "anything", "name": "e3"}, "d3": {"description": "", "definition": "random(299 .. 499#1)", "group": "Ungrouped variables", "templateType": "randrange", "name": "d3"}, "a2": {"description": "", "definition": "{a1}^(2)", "group": "Ungrouped variables", "templateType": "anything", "name": "a2"}, "a4": {"description": "", "definition": "{a3}+{a2}", "group": "Ungrouped variables", "templateType": "anything", "name": "a4"}, "c3": {"description": "", "definition": "random(299 .. 499#1)", "group": "Ungrouped variables", "templateType": "randrange", "name": "c3"}, "b2": {"description": "", "definition": "{b1}^(2)", "group": "Ungrouped variables", "templateType": "anything", "name": "b2"}, "b1": {"description": "<p>b1</p>", "definition": "random(6..35 except a1)", "group": "Ungrouped variables", "templateType": "anything", "name": "b1"}, "c2": {"description": "", "definition": "{c1}^(2)", "group": "Ungrouped variables", "templateType": "anything", "name": "c2"}, "a1": {"description": "", "definition": "random(3 .. 9#1)", "group": "Ungrouped variables", "templateType": "randrange", "name": "a1"}}, "preamble": {"css": "", "js": ""}, "advice": "<p>For these questions, we first need to carry out the arithmetic then take the root of the result:</p>\n<p>a)&nbsp; &nbsp;$\\sqrt{\\var{a4}-\\var{a3}}=\\sqrt{\\var{a2}}=\\var{a1}$</p>\n<p>b)&nbsp; &nbsp;$\\sqrt{\\var{b4}+\\var{b3}}=\\sqrt{\\var{b2}}=\\var{b1}$</p>\n<p>c)&nbsp; &nbsp;$\\sqrt{\\var{c4}-\\var{c3}}=\\sqrt{\\var{c2}}=\\var{c1}$</p>\n<p>d)&nbsp; &nbsp;$\\sqrt[4]{\\var{d4}-\\var{d3}}=\\sqrt[4]{\\var{d2}}=\\var{d1}$</p>\n<p>e)&nbsp; &nbsp;$\\sqrt[3]{\\var{e3}+\\var{e3}}=\\sqrt[3]{\\var{e2}}=\\var{e1}$</p>\n<p>f)&nbsp; &nbsp;$\\sqrt[3]{(-\\var{e3}-\\var{e3})}=\\sqrt[3]{-\\var{e2}}=-\\var{e1}$</p>", "ungrouped_variables": ["a1", "a2", "a3", "a4", "b1", "b2", "b3", "b4", "c1", "c2", "c3", "c4", "d1", "d2", "d3", "d4", "e1", "e2", "e3"]}, {"name": "00b - Engineering Arithmetic: 004", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "metadata": {"description": "<p>Indices and Roots</p><p>Questions based on Exercise Intro(b) from the Textbook \"Engineering Maths through Applications\" by Kuldeep Singh.</p><p>Intended for use as Homework Exercises.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"js": "", "css": ""}, "functions": {}, "ungrouped_variables": ["Sq", "a1", "a1a", "a2", "a2a", "a3", "a4", "b1", "b1a", "b2", "b2a", "b3", "b4", "c1", "c1a", "c2", "c3", "c4", "c3a"], "tags": [], "statement": "<p>Evaluate:</p>", "advice": "<p>In these questions order does not matter. It is often easier to take roots inside and then do the multiplication or division</p>\n<p>a)&nbsp;&nbsp; $\\sqrt{\\var{a1} \\times \\var{a2}}=\\sqrt{\\var{a1}} \\times \\sqrt{\\var{a2}}=\\var{a1a} \\times \\var{a2a}=\\var{a3}$</p>\n<p>b)&nbsp;&nbsp; $\\sqrt{\\var{b1} \\times \\var{b2}}=\\sqrt{\\var{b1}} \\times \\sqrt{\\var{b2}}=\\var{b1a} \\times \\var{b2a}=\\var{b3}$</p>\n<p>The same applies to division:</p>\n<p>c)&nbsp;&nbsp; $\\sqrt{\\frac{144}{\\var{c3}}}=\\frac{\\sqrt{144}}{\\sqrt{\\var{c3}}}=\\frac{\\var{c1a}}{\\var{c3a}}=\\var{c4}$</p>\n<p>d)&nbsp;&nbsp; $\\sqrt{\\frac{225}{25}}=\\frac{\\sqrt{225}}{\\sqrt{25}}=\\frac{15}{5}=3$</p>\n<p>For e) and f) the numbers/roots given are not so easy to identify - after all, who memorises 5<sup>th</sup> roots? So better to use your calculator (with care). But the above method still works:</p>\n<p>e)&nbsp;&nbsp; $\\sqrt[5]{\\frac{7776}{243}}=\\frac{\\sqrt[5]{7776}}{\\sqrt[5]{243}}=\\frac{6}{3}=2$</p>\n<p>f)&nbsp;&nbsp; Remember to use brackets to get the correct answer from your calculator, $=-2$</p>", "parts": [{"variableReplacements": [], "sortAnswers": false, "prompt": "<p>$\\sqrt{\\var{a1} \\times \\var{a2}}=$[[0]]</p>", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "gaps": [{"mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "{a3}", "mustBeReducedPC": 0, "minValue": "{a3}", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 1, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "numberentry", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false}]}, {"variableReplacements": [], "sortAnswers": false, "prompt": "<p>$\\sqrt{\\var{b1} \\times \\var{b2}}=$[[0]]</p>", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "gaps": [{"mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "{b3}", "mustBeReducedPC": 0, "minValue": "{b3}", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 1, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "numberentry", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false}]}, {"variableReplacements": [], "sortAnswers": false, "prompt": "<p>$\\sqrt{\\frac{144}{\\var{c3}}}=$[[0]]</p>", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "gaps": [{"mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "{c4}", "mustBeReducedPC": 0, "minValue": "{c4}", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 1, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "numberentry", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false}]}, {"variableReplacements": [], "sortAnswers": false, "prompt": "<p>$\\sqrt{\\frac{225}{\\var{25}}}=$[[0]]</p>", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "gaps": [{"mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "3", "mustBeReducedPC": 0, "minValue": "3", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 1, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "numberentry", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false}]}, {"variableReplacements": [], "sortAnswers": false, "prompt": "<p>$\\sqrt[5]{\\frac{7776}{243}}=$[[0]]</p>", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "gaps": [{"mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "2", "mustBeReducedPC": 0, "minValue": "2", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 1, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "numberentry", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false}]}, {"variableReplacements": [], "sortAnswers": false, "prompt": "<p>$\\sqrt[5]{-(\\frac{7776}{243})}=$[[0]]</p>", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "gaps": [{"mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "-2", "mustBeReducedPC": 0, "minValue": "-2", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 1, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "numberentry", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false}]}], "variable_groups": [], "variables": {"a1": {"definition": "random(Sq)", "name": "a1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a2a": {"definition": "{a2}^(1/2)", "name": "a2a", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c3": {"definition": "random(c2)", "name": "c3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a4": {"definition": "({a1}*{a2})", "name": "a4", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "b3": {"definition": "({b1}*{b2})^(1/2)", "name": "b3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c3a": {"definition": "{c3}^(1/2)", "name": "c3a", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "Sq": {"definition": "[ 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400 ]", "name": "Sq", "description": "", "templateType": "list of numbers", "group": "Ungrouped variables"}, "a1a": {"definition": "{a1}^(1/2)", "name": "a1a", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a2": {"definition": "random(Sq except a1)", "name": "a2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c2": {"definition": "[ 4, 9, 16, 36 ]", "name": "c2", "description": "", "templateType": "list of numbers", "group": "Ungrouped variables"}, "b1a": {"definition": "{b1}^(1/2)", "name": "b1a", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "b2a": {"definition": "{b2}^(1/2)", "name": "b2a", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c1": {"definition": "144", "name": "c1", "description": "", "templateType": "number", "group": "Ungrouped variables"}, "b4": {"definition": "({b1}*{b2})", "name": "b4", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a3": {"definition": "({a1}*{a2})^(1/2)", "name": "a3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "b2": {"definition": "random(Sq except a1 except a2 except b1)", "name": "b2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c4": {"definition": "({c1}/{c3})^(1/2)", "name": "c4", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "b1": {"definition": "random(Sq except a1 except a2)", "name": "b1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c1a": {"definition": "{c1}^(1/2)", "name": "c1a", "description": "<p>c1a</p>", "templateType": "anything", "group": "Ungrouped variables"}}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}}]}], "feedback": {"advicethreshold": 0, "showanswerstate": true, "showtotalmark": true, "allowrevealanswer": true, "feedbackmessages": [], "intro": "", "showactualmark": true}, "showstudentname": true, "contributors": [{"name": "Michael Proudman", "profile_url": 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