// Numbas version: exam_results_page_options
{"name": "Jinhua's copy of Solving equations with indices 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "b1", "c1", "d1", "a2", "b2", "c2", "d2", "a3", "b3", "c3", "d3", "e3", "a4", "b4", "c4", "d4", "e4", "a5", "b5", "c5", "d5", "e5", "f5"], "name": "Jinhua's copy of Solving equations with indices 3", "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>$x^\\simplify[all,fractionnumbers]{{b1}/{c1}} = \\var{d1}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{a1}^{c1}", "minValue": "{a1}^{c1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$x^{\\simplify[all,fractionnumbers]{{b2}/{{c2}}}} = \\var{d2}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{a2}^{c2}", "minValue": "{a2}^{c2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$x^{\\simplify[all,fractionnumbers]{-{b3}/{c3}}} = \\var{d3}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{a3}^{e3}", "minValue": "{a3}^{e3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$x^{\\simplify[all,fractionnumbers]{{e4}}}= \\var{d4}x^\\frac{1}{2}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{a4}^{-c4}", "minValue": "{a4}^{-c4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{e5}x^{\\simplify[all,fractionnumbers]{{b5}/{c5}}} - \\var{f5} = 0$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{a5}^{c5}", "minValue": "{a5}^{c5}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>Solve each of the following equations for x</p>\n<p>Express answers either as a positive integer or as a fraction&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"f5": {"definition": "e5*d5", "templateType": "anything", "group": "Ungrouped variables", "name": "f5", "description": ""}, "b4": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b5": {"definition": "random(3,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b5", "description": ""}, "b1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "d4": {"definition": "a4^b4", "templateType": "anything", "group": "Ungrouped variables", "name": "d4", "description": ""}, "d5": {"definition": "a5^b5", "templateType": "anything", "group": "Ungrouped variables", "name": "d5", "description": ""}, "d2": {"definition": "a2^b2", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d3": {"definition": "a3^b3", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "d1": {"definition": "a1^b1", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "e5": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "e5", "description": ""}, "c5": {"definition": "random(2..5 except 4 except a5 except b5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c5", "description": ""}, "a1": {"definition": "random(2..5 except 4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "random(2..5 except 4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2..5 except 4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(2..5 except 4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a4": {"definition": "random(2..5 except 4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "c3": {"definition": "random(2..5 except 4 except a3 except b3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "e4": {"definition": "-(b4/c4 )+ (1/2)", "templateType": "anything", "group": "Ungrouped variables", "name": "e4", "description": ""}, "c1": {"definition": "random(2..5 except 4 except a1 except b1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "e3": {"definition": "-c3", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "c4": {"definition": "random(2..5 except 4 except 3 except a4 except b4)", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "c2": {"definition": "random(2..5 except 4 except a2 except b2)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}}, "metadata": {"description": "<p>Sometimes randomisation creates error with variable: c4</p>", "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/"}]}