// Numbas version: exam_results_page_options
{"name": "Q2 (Algebra equations solve for x)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["num1p", "num1n", "ans11", "ans21", "numh", "num3p", "num3n", "posa", "nega", "ans41", "ans31", "posb", "neg", "ans51"], "name": "Q2 (Algebra equations solve for x)", "tags": ["rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part 1:</p>\n<p>$x$:</p>\n<p>$\\frac{(\\var{numh[0]}-\\var{num1p[1]})}{(\\var{num1p[0]}-\\var{num1p[2]})} = \\var{ans11}$</p>\n<p>Part 2:</p>\n<p>$x$:</p>\n<p>$\\frac{((\\var{num1p[7]} \\times \\var{num1p[6]})-(\\var{num1p[4]} \\times \\var{num1n[2]})}{((\\var{num1p[1]} \\times \\var{num1p[5]})-(\\var{num1p[7]} \\times \\var{num1n[7]})} = \\var{ans21}$</p>\n<p>Part 3:</p>\n<p>$x$:</p>\n<p>$\\frac{((\\var{num3p[4]} \\times \\var{num3p[5]})+\\var{num3p[6]}+(\\var{num3n[4]} \\times \\var{num3n[5]})-\\var{num3p[0]}-(\\var{num3p[1]} \\times \\var{num3n[0]})-(\\var{num3n[1]} \\times \\var{num3n[2]}))} &nbsp;{((\\var{num3p[1]} \\times \\var{num3p[2]})+(\\var{num3n[1]} \\times \\var{num3p[3]})-(\\var{num3p[4]} \\times \\var{num3n[3]})-(\\var{num3n[4]} \\times \\var{num3p[7]}))} = \\var{ans31}$</p>\n<p>Part 4:</p>\n<p>$x$:</p>\n<p>$\\frac{(\\var{nega[3]}-\\frac{\\var{nega[1]}}{\\var{posa[1]}}+\\frac{\\var{posa[5]}}{\\var{posa[3]}}-\\frac{\\var{nega[2]}}{\\var{posa[6]}})} &nbsp;{(\\frac{\\var{posa[2]}}{\\var{posa[1]}}-\\frac{\\var{posa[4]}}{\\var{posa[3]}}+\\frac{\\var{posa[7]}}{\\var{posa[6]}})} = \\var{ans41}$</p>\n<p>Part 5:</p>\n<p>$x$:</p>\n<p>$\\frac{((\\var{posb[3]} \\times \\var{nega[4]}) - (\\var{posb[1]} \\times \\var{posb[5]}))}{((\\var{posb[1]} \\times \\var{posb[4]}) - (\\var{posb[3]} \\times \\var{posb[2]}))}&nbsp;= \\var{ans51}$</p>", "rulesets": {"std": ["all", "basic", "simplifyFractions"], "ruleset1": []}, "parts": [{"prompt": "<p>$\\var{num1p[0]}x + \\var{num1p[1]} =&nbsp;\\var{num1p[2]}x + \\var{numh[0]}$</p>\n<p>$x =$ &nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({ans11}+0.5)", "strictPrecision": false, "minValue": "({ans11}-0.5)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{num1p[4]}(\\var{num1p[5]} &nbsp;\\var{num1n[2]}x) = \\var{num1p[7]}(\\var{num1p[6]} &nbsp;\\var{num1n[7]}x)$</p>\n<p>$x =$ &nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({ans21}+0.5)", "strictPrecision": false, "minValue": "({ans21}-0.5)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": "0", "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{num3p[0]} + \\var{num3p[1]}(\\var{num3p[2]}x \\var{num3n[0]})\\var{num3n[1]}(\\var{num3p[3]}x \\var{num3n[2]}) = \\var{num3p[4]}(\\var{num3p[5]} &nbsp;\\var{num3n[3]}x) + \\var{num3p[6]} \\var{num3n[4]}(\\var{num3p[7]}x \\var{num3n[5]})$</p>\n<p>$x =$ &nbsp;[[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}+0.5", "strictPrecision": false, "minValue": "{ans31}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>$\\frac{1}{\\var{posa[1]}}(\\var{posa[2]}x \\var{nega[1]})-\\frac{1}{\\var{posa[3]}}(\\var{posa[4]}x +\\var{posa[5]})+\\frac{1}{\\var{posa[6]}}(\\var{posa[7]}x \\var{nega[2]}) = \\var{nega[3]}$</p>\n<p>$x =$ &nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Get a common denominator like in question 1. The multiply both sides of the equation by that common denominator to get rid of the fractions.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans41}+0.5", "strictPrecision": false, "minValue": "{ans41}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{posb[1]}}{\\var{posb[2]}x\\var{neg[4]}}= \\frac{\\var{posb[3]}}{\\var{posb[4]}x+\\var{posb[5]}}$</p>\n<p>$x =$ &nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans51}+0.5", "strictPrecision": false, "minValue": "{ans51}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Solve&nbsp;for $x$ in&nbsp;the following, to 2 decimal places:</p>\n<p>Watch the video below for help with the questions:</p>\n<p><a href=\"https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-solving-basic-equations/v/solving-equations-1\">Solving Equations</a></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num3n": {"definition": "shuffle(-10..-2)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num3n", "description": ""}, "num1n": {"definition": "shuffle(-9..-2)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num1n", "description": ""}, "ans41": {"definition": "(nega[3]-(nega[1]/posa[1])+(posa[5]/posa[3])-(nega[2]/posa[6]))/((posa[2]/posa[1])-(posa[4]/posa[3])+(posa[7]/posa[6]))\n", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "posb": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "posb", "description": ""}, "posa": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "posa", "description": ""}, "ans11": {"definition": "(numh[0]-num1p[1])/(num1p[0]-num1p[2])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "num1p": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num1p", "description": ""}, "neg": {"definition": "shuffle(-9..-2)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "neg", "description": ""}, "ans31": {"definition": "((num3p[4] * num3p[5])+num3p[6]+(num3n[4] *num3n[5])-num3p[0]-(num3p[1] * num3n[0])-(num3n[1] * num3n[2])) / ((num3p[1] * num3p[2])+(num3n[1] * num3p[3])-(num3p[4] * num3n[3])-(num3n[4] * num3p[7])) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "nega": {"definition": "shuffle(-9..-2)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "nega", "description": ""}, "num3p": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num3p", "description": ""}, "numh": {"definition": "shuffle(20..40)[0..15]", "templateType": "anything", "group": "Ungrouped variables", "name": "numh", "description": ""}, "ans21": {"definition": "((num1p[7] * num1p[6])-(num1p[4] * num1p[5]))/((num1p[4] * num1n[2])-(num1p[7] * num1n[7])) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "ans51": {"definition": "((posb[3] * neg[4]) - (posb[1] * posb[5]))/((posb[1] * posb[4]) - (posb[3] * posb[2]))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans51", "description": ""}}, "metadata": {"description": "<p>Simple Linear Equations involving basic transposition</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}