// Numbas version: exam_results_page_options
{"name": "Jinhua's copy of Solving equations with indices 1", "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", "a1", "b1", "c1", "d1", "a2", "b2", "a3", "b3", "a4", "b4", "c4", "a5", "b5", "c5", "d5", "e5", "a6", "b6", "c6", "d6", "e6", "f6", "g6", "h6"], "name": "Jinhua's copy of Solving equations with indices 1", "tags": [], "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>$\\var{a}x^{\\var{c}} = \\var{d}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "{b}", "minValue": "{b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{d1}x^{\\var{c1}} = \\var{a1}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "1/{b1}", "minValue": "1/{b1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$x^3 + \\var{b2} = 0$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "-{a2}", "minValue": "-{a2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{a3}x^{-1}=\\var{b3}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{a3}/{b3}", "minValue": "{a3}/{b3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$x^{\\var{a4}}= \\var{c4}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "1/{b4}", "minValue": "1/{b4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{d5}x^{-\\var{a5}} = \\frac{1}{\\var{e5}} x^{\\var{b5}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{c5}", "minValue": "{c5}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\frac{\\var{e6}}{\\var{f6}}x^\\var{d6} = \\frac{\\var{h6}}{\\var{g6}}x^{-\\var{c6}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{b6}/{a6}", "minValue": "{b6}/{a6}", "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, and put the answer in the box.&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"f6": {"definition": "b6^c6", "templateType": "anything", "group": "Ungrouped variables", "name": "f6", "description": ""}, "h6": {"definition": "b6^d6", "templateType": "anything", "group": "Ungrouped variables", "name": "h6", "description": ""}, "b4": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b5": {"definition": "random(2..4 except a5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b5", "description": ""}, "b6": {"definition": "random(2..5 except 4 except a6)", "templateType": "anything", "group": "Ungrouped variables", "name": "b6", "description": ""}, "b1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "a2^3", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(2..9 except a3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "d6": {"definition": "random(1..3 except c6)", "templateType": "anything", "group": "Ungrouped variables", "name": "d6", "description": ""}, "d5": {"definition": "c5^a5", "templateType": "anything", "group": "Ungrouped variables", "name": "d5", "description": ""}, "d1": {"definition": "a1*b1^c1", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "g6": {"definition": "a6^d6", "templateType": "anything", "group": "Ungrouped variables", "name": "g6", "description": ""}, "a1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a4": {"definition": "random(-5..-2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "a6": {"definition": "random(2..5 except 4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a6", "description": ""}, "e5": {"definition": "c5^b5", "templateType": "anything", "group": "Ungrouped variables", "name": "e5", "description": ""}, "c1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "e6": {"definition": "a6^c6", "templateType": "anything", "group": "Ungrouped variables", "name": "e6", "description": ""}, "c6": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c6", "description": ""}, "c5": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "c5", "description": ""}, "c4": {"definition": "b4^-a4", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "a": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "a*b^c", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "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": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}