// Numbas version: finer_feedback_settings {"name": "Numerical Skills Indices 2 - Formative assessment", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "f1", "f2", "f3", "f4", "t1", "t2"], "name": "Numerical Skills Indices 2 - Formative assessment", "tags": [], "advice": "
Recall the laws of indices to help solve the problems:
\n$x^a \\times x^b = x^{a+b}$
\n$x^a \\div x^b = x^{a-b}$
\n$x^{-a} = \\frac{1}{x^a}$
\n$(x^a)^b = x^{ab}$
\n$(\\frac{x}{y})^a = \\frac{x^a}{y^a}$
\n$x^\\frac{a}{b} = \\sqrt[b]{x^a}$
\n$x^0 = 1$
", "rulesets": {}, "parts": [{"prompt": "$\\var{c}^{\\simplify{-1/{b}}}$
", "allowFractions": true, "variableReplacements": [], "maxValue": "1/2", "minValue": "1/2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "$\\var{d}^{\\simplify{-1/{a}}}$
", "allowFractions": true, "variableReplacements": [], "maxValue": "1/3", "minValue": "1/3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "$\\var{h}^{\\simplify{-{f}/{g}}}$
", "allowFractions": true, "variableReplacements": [], "maxValue": "3^-{f}", "minValue": "3^-{f}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "$\\var{l}^{\\simplify{-{k}/{j}}}$
", "allowFractions": true, "variableReplacements": [], "maxValue": "2^-k", "minValue": "2^-k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "$\\var{f3}^{\\simplify{-{f1}/{f2}}}$
", "allowFractions": true, "variableReplacements": [], "maxValue": "5^-f1", "minValue": "5^-f1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "$(3/11)^{-2}$
", "allowFractions": true, "variableReplacements": [], "maxValue": "121/9", "minValue": "121/9", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "$(1/\\var{f4})^{\\simplify{-{f2}/{f1}}}$
", "allowFractions": true, "variableReplacements": [], "maxValue": "5^{f2}", "minValue": "5^{f2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "$(\\var{t1}/\\var{t2})^{\\simplify{{f1}/{f2}}}$
", "allowFractions": true, "variableReplacements": [], "maxValue": "(2/3)^{f1}", "minValue": "(2/3)^{f1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "gcd({k},{j})=1"}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "f1": {"definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "c": {"definition": "2^b", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "f4": {"definition": "5^f1", "templateType": "anything", "group": "Ungrouped variables", "name": "f4", "description": ""}, "d": {"definition": "3^a", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(2..4 except f)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "3^g", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(2..4 except j)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "t2": {"definition": "3^f2", "templateType": "anything", "group": "Ungrouped variables", "name": "t2", "description": ""}, "l": {"definition": "2^j", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "f2": {"definition": "random(2..3 except f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "t1": {"definition": "2^f2", "templateType": "anything", "group": "Ungrouped variables", "name": "t1", "description": ""}, "f3": {"definition": "5^f2", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}}, "metadata": {"notes": "", "description": "Simplifying indices
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}]}], "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}