// Numbas version: exam_results_page_options
{"name": "Q7 (simultaneous equations to solve forces in a system, and 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": ["a", "b", "c", "a1", "b1", "c1", "ans1", "ans2", "num1", "num2", "num3", "ans"], "name": "Q7 (simultaneous equations to solve forces in a system, and solve for x)", "tags": ["rebelmaths", "simultaneous equations", "Simultaneous equations", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Have a look at this youtube video to understand simultaneous equations better:&nbsp;<a href=\"https://www.youtube.com/watch?v=Lwto-lQzmec\">Simultaneous Equations</a></p>\n<p>Part 1:</p>\n<p>To find $F_1$:</p>\n<p>$\\frac{((\\var{b} \\times \\var{c1}) - (\\var{b1} \\times \\var{c}))}{((\\var{a1} \\times \\var{b}) - (\\var{a} \\times \\var{b1}))} = \\var{ans1}$</p>\n<p>To find&nbsp;$F_2$:</p>\n<p>$\\frac{(\\var{c1} - (\\var{a1} \\times \\var{ans1}))}{\\var{b1}} = \\var{ans2}$</p>\n<p>Part 2:</p>\n<p>$\\frac{(-\\var{num3} - (\\var{num1}*\\var{num3}))}{((\\var{num1}*\\var{num2})-\\var{num2})} = \\var{ans}$</p>\n<p></p>", "rulesets": {"std": ["all"]}, "parts": [{"prompt": "<p>$\\simplify{{a}F_1 + {b}F_2 = {c}}$</p>\n<p>$\\simplify{{a1}F_1 + {b1}F_2 = {c1}}$</p>\n<p>$F_1$: &nbsp;[[0]]</p>\n<p>$F_2$: &nbsp;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}+0.5", "strictPrecision": false, "minValue": "{ans1}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2} +0.5", "strictPrecision": false, "minValue": "{ans2} -0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Solve for $x$, correct to 2 decimal places:</p>\n<p>$\\frac{\\var{num1}(\\var{num2}x + \\var{num3})}{\\var{num2}x - \\var{num3}} = 1$</p>\n<p>$x=$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans}+0.5", "strictPrecision": false, "minValue": "{ans}-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>The forces $F_1$ and $F_2$ in a system are described by the simultaneous equations given below.</p>\n<p>Solve for&nbsp;$F_1$ and $F_2$:</p>\n<p><em>Correct to one decimal place!!</em></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(6..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "(ans1*a)+(ans2*b)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(5..9 except [a])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "num1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "random(2..9 except num1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "random(2..9 except [num1,num2])", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "ans1": {"definition": "random(1.1..2.5#0.1 except 2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "random(2.6..3.9#0.1 except 3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "a1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "b1": {"definition": "random(-8..9 except[a1,0])", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "ans": {"definition": "(-num3 - (num1*num3))/((num1*num2)-num2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}, "c1": {"definition": "(ans1*a1)+(ans2*b1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}}, "metadata": {"description": "<p>Simultaneous Equations</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/"}]}