// Numbas version: exam_results_page_options
{"name": "Solving equations with indices 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "a2", "b2", "a3", "b3", "a4", "b4", "a5", "b5", "c5", "d5", "e5", "f5"], "name": "Solving equations with indices 2", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>The idea here is to get all powers of x on one side of the equation, and all numbers on the other. Then, raise each side of the equation to an appropriate power, so that the value of x becomes clear.</p>\n<p>It may be useful to refamiliarise yourself with the laws of indices:</p>\n<p>$x^a \\times x^b = x^{a+b}$</p>\n<p>$x^a \\div x^b = x^{a-b}$</p>\n<p>$x^{-a} = \\frac{1}{x^a}$</p>\n<p>$(x^a)^b = x^{ab}$</p>\n<p>$(\\frac{x}{y})^a = \\frac{x^a}{y^a}$</p>\n<p>$x^\\frac{a}{b} = \\sqrt[b]{x^a}$</p>\n<p>$x^0 = 1$</p>", "rulesets": {}, "parts": [{"prompt": "<p>$x^{\\frac{1}{2}} = \\var{a1}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "{a1}^2", "minValue": "{a1}^2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$x^{\\frac{1}{\\var{a2}}} = \\var{b2}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "{b2}^{a2}", "minValue": "{b2}^{a2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{a3}x^\\frac{1}{2} + \\var{b3} = 0$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "({b3}/{a3})^2", "minValue": "({b3}/{a3})^2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$x^\\frac{-1}{\\var{a4}}&nbsp;= \\var{b4}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{b4}^-{a4}", "minValue": "{b4}^-{a4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{e5}x^\\frac{1}{\\var{a5}} = x^{\\simplify[all,fractionnumbers]{{f5}}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "1/{d5}", "minValue": "1/{d5}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Solve each of the following equations for x</p>\n<p>Express answers either as an integer or as a fraction&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"b4": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "f5": {"definition": "c5-b5", "templateType": "anything", "group": "Ungrouped variables", "name": "f5", "description": ""}, "a1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "b5": {"definition": "random(2..5 except 3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b5", "description": ""}, "a3": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(2..5 except 3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a4": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "b2": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(2..9 except a3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "e5": {"definition": "d5^(b5)", "templateType": "anything", "group": "Ungrouped variables", "name": "e5", "description": ""}, "d5": {"definition": "random(2..5 except 3)", "templateType": "anything", "group": "Ungrouped variables", "name": "d5", "description": ""}, "c5": {"definition": "1/a5", "templateType": "anything", "group": "Ungrouped variables", "name": "c5", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}