![](\"resources/question-resources/2_gears.gif\")
$\\var{a}+\\var{b}x=y$
\n$x=$[[0]]
\n$\\frac{1}{\\var{c}x}-\\var{d}=y$
\n$x=$[[0]]
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\n$x=$[[0]]
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Constant term in part b.
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", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "Positive coefficient of x^3
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\n(enter only the numerator of your answer, do not enter the denominator $\\frac{...}{(\\simplify{x+{f}})}$ )
", "answer": "{{d}-{c}*{f}+{b}*{f}^2-{a}*{f}^3}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "Find the remainder when $p(x) = \\simplify{x^3+{coef_x2}x^2+{coef_x}x+{const}}$ is divided by $\\simplify{x^2+{coef2_x}x+{const2}}$.
\n(enter only the numerator of your answer, do not enter the denominator $\\frac{...}{(\\simplify{x^2+{coef2_x}x+{const2}}}$ )
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\n", "advice": "", "rulesets": {}, "variables": {"T1": {"name": "T1", "group": "Ungrouped variables", "definition": "random(500 .. 1500#100)", "description": "", "templateType": "randrange"}, "T2": {"name": "T2", "group": "Ungrouped variables", "definition": "precround(T1*e^(u*(2*pi/3)),2)", "description": "", "templateType": "anything"}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "random(0.2 .. 0.5#0.1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["T1", "u", "T2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "$T_2=$[[0]] N
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(give your answers to 2 d.p.)
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When $P_{out}=\\var{P1out}$ W, and $P_{in}=\\var{P1in}$ W
\nThen $G=$[[0]] dB
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\nThen $G=$[[0]] dB
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The smaller gear has a circumference of: $C_1=$[[0]] cm
\n\nHence, the larger gear will rotate through an arc length of $L=$[[1]] cm
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\n\nThe period $T=$[[1]] ms
\n\nThe frequency $f=$[[2]] Hz
\n\nThe phase angle (in degrees) $\\phi=$[[3]] $^\\circ$
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\n\nAt $t=\\frac{1}{60}$ s, the current $i=$[[1]] mA
\n\nAt $t=\\frac{1}{30}$ s, the current $i=$[[2]] mA
\n\nAt $t=\\frac{1}{15}$ s, the current $i=$[[3]] mA
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{Current}", "maxValue": "{Current}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{Current}", "maxValue": "{Current}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{Current}", "maxValue": "{Current}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{Current}", "maxValue": "{Current}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "What do you notice about your results? Write a (short) sentence to describe your results.
", "answer": "same|equal|identical|{Current}|equivalent", "displayAnswer": "There are all the same.", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "How do you explain this?
", "answer": "sinehas period of $2\\pi$|sine repeats|sine oscilates|sine is periodic|sine is repeated|sine is repeating|sine is cyclic|", "displayAnswer": "sine is periodic", "matchMode": "regex"}], "type": "question"}, {"name": "08 - Trigonometry (Cosine Rule) v3", "extensions": [], "custom_part_types": [], "resources": [["question-resources/triangle1_pvA8r4l.png", "/srv/numbas/media/question-resources/triangle1_pvA8r4l.png"], ["question-resources/triangle1_9NJA1zm.png", "/srv/numbas/media/question-resources/triangle1_9NJA1zm.png"], ["question-resources/triangle3.svg", "/srv/numbas/media/question-resources/triangle3.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "![](\"resources/question-resources/triangle3.svg\")
(Give your answer to 3 s.f.)
\n\n", "advice": "", "rulesets": {}, "variables": {"AC": {"name": "AC", "group": "Ungrouped variables", "definition": "random(285 .. 299#1)", "description": "", "templateType": "randrange"}, "BC": {"name": "BC", "group": "Ungrouped variables", "definition": "random(400 .. 410#1)", "description": "", "templateType": "randrange"}, "Crad": {"name": "Crad", "group": "Ungrouped variables", "definition": "radians(Cdeg)", "description": "", "templateType": "anything"}, "AB": {"name": "AB", "group": "Ungrouped variables", "definition": "siground(sqrt((AC^2)+(BC^2)-(2*AC*BC*cos(Crad))), 3)", "description": "", "templateType": "anything"}, "Cdeg": {"name": "Cdeg", "group": "Ungrouped variables", "definition": "random(60 .. 85#1)", "description": "", "templateType": "randrange"}, "raw": {"name": "raw", "group": "Ungrouped variables", "definition": "precround(({BC}^2)+({AC}^2)-2*{BC}*{AC}*cos(Crad), 2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["AC", "BC", "Crad", "Cdeg", "AB", "raw"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "The distance $AB=$[[0]] m
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{AB}", "maxValue": "{AB}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "type": "question"}, {"name": "09 - Argand Diagrams", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Matthew Mears", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1688/"}], "tags": [], "metadata": {"description": "Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "\nPlot the following complex numbers on the Argand diagram below.
\n$A=\\var{a1}\\var{a2}i$ $B = \\var{b1}+\\var{b2}i$ $C =\\var{c1}\\var{c2}i$
\n$D=\\var{d1}+\\var{d2}i$ $E=\\var{e1}+\\var{e2}i$ $F=\\var{f1}+\\var{f2}i$
\n\n{dragpoints()}
", "advice": "", "rulesets": {}, "variables": {"f1": {"name": "f1", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything"}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything"}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything"}, "e2": {"name": "e2", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything"}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything"}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything"}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "2", "description": "", "templateType": "anything"}, "f2": {"name": "f2", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}, "e1": {"name": "e1", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}, "e3": {"name": "e3", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y", "a1", "a2", "b1", "b2", "c1", "c2", "d1", "d2", "e1", "e2", "e3", "f1", "f2"], "variable_groups": [], "functions": {"correctPoints": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[-11,11,11,-11],grid: true});\nvar board = div.board;\nquestion.board = board;\n\nvar a1 = Numbas.jme.unwrapValue(scope.variables.a1);\nvar a2 = Numbas.jme.unwrapValue(scope.variables.a2);\nvar b1 = Numbas.jme.unwrapValue(scope.variables.b1);\nvar b2 = Numbas.jme.unwrapValue(scope.variables.b2);\nvar c1 = Numbas.jme.unwrapValue(scope.variables.c1);\nvar c2 = Numbas.jme.unwrapValue(scope.variables.c2);\nvar d1 = Numbas.jme.unwrapValue(scope.variables.d1);\nvar d2 = Numbas.jme.unwrapValue(scope.variables.d2);\nvar e1 = Numbas.jme.unwrapValue(scope.variables.e1);\nvar e2 = Numbas.jme.unwrapValue(scope.variables.e2);\nvar f1 = Numbas.jme.unwrapValue(scope.variables.f1);\nvar f2 = Numbas.jme.unwrapValue(scope.variables.f2);\n\n\nvar a = board.create('point',[a1,a2],{name: 'A', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar b = board.create('point',[b1,b2],{name: 'B', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar c = board.create('point',[c1,c2],{name: 'C', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar d = board.create('point',[d1,d2],{name: 'D', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar e = board.create('point',[e1,e2],{name: 'E', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar f = board.create('point',[f1,f2],{name: 'F', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\n\n/*\nquestion.signals.on('HTMLAttached',function(e) {\n ko.computed(function(){ \n var x = parseFloat(question.parts[0].gaps[0].display.studentAnswer());\n var y = parseFloat(question.parts[0].gaps[1].display.studentAnswer());\n if(!(isNaN(x) || isNaN(y)) && board.mode!=board.BOARD_MODE_DRAG) {\n a.moveTo([x,y],100);\n }\n });\n});\n*/\n\nreturn div;"}, "dragpoints": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[-11,11,11,-11],grid: true, fillColor: 'white'});\nvar board = div.board;\nquestion.board = board;\n\n//var x = Numbas.jme.unwrapValue(scope.variables.x);\n//var y = Numbas.jme.unwrapValue(scope.variables.y);\n\nvar a = board.create('point',[10,10],{name: 'A', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar b = board.create('point',[10,9],{name: 'B', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: true});\nvar c = board.create('point',[10,8],{name: 'C', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: true});\nvar d = board.create('point',[10,7],{name: 'D', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: true});\nvar e = board.create('point',[10,6],{name: 'E', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: true});\nvar f = board.create('point',[10,5],{name: 'F', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: true});\n\nquestion.points = {\n a:a,b:b,c:c,d:d,e:e,f:f\n}\n\na.on('drag',function(){\n Numbas.exam.currentQuestion.parts[0].gaps[0].display.studentAnswer(a.X());\n Numbas.exam.currentQuestion.parts[0].gaps[1].display.studentAnswer(a.Y());\n});\nb.on('drag',function(){\n Numbas.exam.currentQuestion.parts[1].gaps[0].display.studentAnswer(b.X());\n Numbas.exam.currentQuestion.parts[1].gaps[1].display.studentAnswer(b.Y());\n});\nc.on('drag',function(){\n Numbas.exam.currentQuestion.parts[2].gaps[0].display.studentAnswer(c.X());\n Numbas.exam.currentQuestion.parts[2].gaps[1].display.studentAnswer(c.Y());\n});\nd.on('drag',function(){\n Numbas.exam.currentQuestion.parts[3].gaps[0].display.studentAnswer(d.X());\n Numbas.exam.currentQuestion.parts[3].gaps[1].display.studentAnswer(d.Y());\n});\ne.on('drag',function(){\n Numbas.exam.currentQuestion.parts[4].gaps[0].display.studentAnswer(e.X());\n Numbas.exam.currentQuestion.parts[4].gaps[1].display.studentAnswer(e.Y());\n});\nf.on('drag',function(){\n Numbas.exam.currentQuestion.parts[5].gaps[0].display.studentAnswer(f.X());\n Numbas.exam.currentQuestion.parts[5].gaps[1].display.studentAnswer(f.Y());\n});\n\n/*\nquestion.signals.on('HTMLAttached',function(e) {\n ko.computed(function(){ \n var x = parseFloat(question.parts[0].gaps[0].display.studentAnswer());\n var y = parseFloat(question.parts[0].gaps[1].display.studentAnswer());\n if(!(isNaN(x) || isNaN(y)) && board.mode!=board.BOARD_MODE_DRAG) {\n a.moveTo([x,y],100);\n }\n });\n});\n*/\n\nreturn div;\n\n"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.a.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "$A=\\var{a1}\\var{a2}i$.
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{a1}", "maxValue": "{a1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{a2}", "maxValue": "{a2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.b.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "$B = \\var{b1}+\\var{b2}i$.
\n\n$C =\\var{c1}\\var{c2}i$.
\n", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{c1}", "maxValue": "{c1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{c2}", "maxValue": "{c2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.d.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "$D=\\var{d1}+\\var{d2}i$.
\n\n$E=\\var{e1}+\\var{e2}i$.
\n$F=\\var{f1}+\\var{f2}i$.
\n\n![](\"resources/question-resources/4_Forces.png\")
The figure above shows coplanar forces $F_1, F_2,F_3$ and $F_4$ acting at a common point.
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\n\\[F=F_1+F_2+F_3+F_4\\]
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\n(Give your answers to 2 d.p.)
\n\n$F_1=$[[0]] N $\\angle$ [[1]] $^{\\circ}$ is equivalent to $F_1=$[[8]]$+j$[[9]]
\n$F_2=$[[2]] N $\\angle$ [[3]] $^{\\circ}$ is equivalent to $F_2=$[[10]]$+j$[[11]]
\n$F_3=$[[4]] N $\\angle$ [[5]] $^{\\circ}$ is equivalent to $F_3=$[[12]]$+j$[[13]]
\n$F_4=$[[6]] N $\\angle$ [[7]] $^{\\circ}$ is equivalent to $F_4=$[[14]]$+j$[[15]]
\n\n\nUsing this information, the resultant force $F$ can be written in rectangular form:
\n$F=$[[16]]$+j$[[17]]
\n\nThis can then be expressed, in polar form as:
\n$F=$[[18]]N $\\angle$[[19]]$^{\\circ}$
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"unitTests": [], "minValue": "{F_y}", "maxValue": "{F_y}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{magF}", "maxValue": "{magF}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{argF}", "maxValue": "{argF}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, 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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "\n\n
\n ", "advice": "", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "variables": {"a1": {"name": "a1", "group": "Ungrouped variables", "definition": " 1", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,round(b*a2/a1)])", "description": "", "templateType": "anything"}, "d_": {"name": "d_", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,round(b*a2/a1)])", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything"}, "a2_": {"name": "a2_", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything"}, "s1_": {"name": "s1_", "group": "Ungrouped variables", "definition": "if(c_<0,-1,1)", "description": "", "templateType": "anything"}, "nb_": {"name": "nb_", "group": "Ungrouped variables", "definition": "if(c_<0,'taking away','adding')", "description": "", "templateType": "anything"}, "c_": {"name": "c_", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "templateType": "anything"}, "b_": {"name": "b_", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "if(c<0,-1,1)", "description": "", "templateType": "anything"}, "a1_": {"name": "a1_", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything"}, "nb": {"name": "nb", "group": "Ungrouped variables", "definition": "if(c<0,'taking away','adding')", "description": "", "templateType": "anything"}, "a_": {"name": "a_", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d", "nb", "a1", "a2", "s1", "a_", "c_", "b_", "d_", "nb_", "a1_", "a2_", "s1_"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "
Split \\[\\simplify{({a*a2 + c*a1} * x + {a * d + c * b})/ (({a1}*x + {b}) * ({a2}*x + {d}))}\\] into partial fractions.
\nInput the partial fractions here: [[0]].
\n\n
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Input as the sum of partial fractions.
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\nInput the partial fractions here: [[0]].
\n\n
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Input as the sum of partial fractions.
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\nWhen calculating the argument pay particular attention to the quadrant in which the complex number lies.
\nInput all answers to 3 decimal places.
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\nInput both answers to 3 decimal places.
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\nInput both answers to 3 decimal places.
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\nInput both answers to 3 decimal places.
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\nInput both answers to 3 decimal places.
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\n![](\"resources/question-resources/Tunnel.png\")
The diameter of the tunnel $BZ=$[[0]] m
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\nThe impedance $Z$ of the circuit is $Z=\\var{R2}+j\\var{I2}$ $\\Omega$
\n\nDetermine the current $I$ where:
\n\\[I=\\frac{V}{Z}\\]
\n(Give your answers to 3 d.p.)
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