Times up
"}, "timedwarning": {"action": "warn", "message": "5 minutes remaining
"}}, "metadata": {"description": "", "licence": "None specified"}, "question_groups": [{"pickingStrategy": "all-ordered", "name": "Group", "pickQuestions": 1, "questions": [{"name": "Vectors: adding, multiply by scalar, magnitude", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "h"], "tags": ["rebel", "Rebel", "REBEL", "rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "The vector $\\mathbf{x}+\\mathbf{y}$ is [[0]]$\\mathbf{i}+$[[1]]$\\mathbf{j}+$[[2]]$\\mathbf{k}$.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{a}+{d}", "minValue": "{a}+{d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b}+{f}", "minValue": "{b}+{f}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{c}+{g}", "minValue": "{c}+{g}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 2, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "The vector {h}$\\mathbf{x}$ is [[0]]$\\mathbf{i}+$[[1]]$\\mathbf{j}+$[[2]]$\\mathbf{k}$.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{h}*{a}", "minValue": "{h}*{a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 2, "type": "numberentry", "showPrecisionHint": false}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{h}*{b}", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{h}*{c}", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "precisionType": "dp", "prompt": "Find $|\\mathbf{x}|$, the magnitude of $\\mathbf{x}$ to the nearest whole number.
", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "sqrt{a^2+b^2+c^2}", "strictPrecision": true, "minValue": "sqrt{a^2+b^2+c^2}", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "If $\\mathbf{x}=x_1\\mathbf{i}+x_2\\mathbf{j}+x_3\\mathbf{k}$, then $|x|=\\sqrt{x_1^2+x_2^2+x_3^2}$.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 8, "type": "numberentry", "showPrecisionHint": false}], "statement": "Let $\\mathbf{x}=${a}$\\mathbf{i}+${b}$\\mathbf{j}+${c}$\\mathbf{k}$ and $\\mathbf{y}=${d}$\\mathbf{i}+${f}$\\mathbf{j}+${g}$\\mathbf{k}$
\n", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}}, "metadata": {"description": "Magnitude of a vector, adding vectors, multiply by a scalar.
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "resultant displacement", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}], "tags": ["rebel", "REBEL", "Rebel", "rebelmaths", "resultant displacement"], "metadata": {"description": "resultant displacement
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(10..90)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(10..90)", "description": "", "templateType": "anything", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "random('John', 'Michael', 'Keane', 'Peter')", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "name1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "{name1} travels {a} km east and then {b} km south. Determine how far {name1} is from his starting point and give his bearings with respect to the eastward direction.
\nDistance [[0]] km (to the nearest km)
\nAngle: East [[1]] $^\\circ$ South (to the nearest degree)
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 10, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sqrt(a^2+b^2)", "maxValue": "sqrt(a^2+b^2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 10, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "arctan(b/a)/pi*180", "maxValue": "arctan(b/a)/pi*180", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "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}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "3d - angle between two vectors", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "s4", "inner", "theta"], "tags": ["dot product", "dot product of two vectors", "inner product", "Rebel", "REBEL", "rebel", "rebelmaths", "scalar product", "three dimensional vectors", "vectors"], "advice": "(a)
\n\\[ \\begin{eqnarray*} \\boldsymbol{a\\cdot b}&=& (\\var{a}, \\var{b},\\var{c}) \\cdot (\\var{d}, \\var{f},\\var{g})\\\\ &=&({\\var{a}\\times\\var{d})+(\\var{b}\\times\\var{f})+(\\var{c}\\times\\var{g})}\\\\ &=& \\var{inner} \\end{eqnarray*} \\]
\n(b)
\n\\[\\theta=\\cos^{-1}\\left(\\frac{\\var{inner}}{\\sqrt{(\\var{a})^2+(\\var{b})^2+(\\var{c})^2}\\sqrt{(\\var{d})^2+(\\var{f})^2+(\\var{g})^2}}\\right)\\]
\n\\[\\theta=\\var{theta}\\]
\nThen round to the nearest degree.
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", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "a*d+b*f+c*g", "minValue": "a*d+b*f+c*g", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 10, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "For $\\mathbf{a}=a_1\\mathbf{i}+a_2\\mathbf{j}+a_3\\mathbf{k}$ and $\\mathbf{b}=b_1\\mathbf{i}+b_2\\mathbf{j}+b_3\\mathbf{k}$,
\nthe scalar or dot product of $\\mathbf{a}$ and $\\mathbf{b}$ is given by
\n\\[\\mathbf{a} \\cdot \\mathbf{b}= a_1b_1+a_2b_2+a_3b_3\\]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "precisionType": "dp", "prompt": "Find the angle between $\\mathbf{a}$ and $\\mathbf{b}$ to the nearest degree.
", "marks": 10, "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": 0, "maxValue": "arccos((a*d+b*f+c*g)/(sqrt(a^2+b^2+c^2)*sqrt(d^2+f^2+g^2)))/pi*180", "minValue": "arccos((a*d+b*f+c*g)/(sqrt(a^2+b^2+c^2)*sqrt(d^2+f^2+g^2)))/pi*180", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "steps": [{"prompt": "$\\mathbf{a}\\cdot \\mathbf{b}=|\\mathbf{a}||\\mathbf{b}|\\cos\\theta$, where $\\theta$ is the angle between the vector $\\mathbf{a}$ and $\\mathbf{b}$.
\nRearrange to get $\\cos \\theta =\\frac{\\mathbf{a}\\cdot \\mathbf{b}}{|\\mathbf{a}||\\mathbf{b}|}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "precisionPartialCredit": 0, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}], "statement": "Given the vectors:
\\[\\boldsymbol{a}=\\simplify[std]{{a}v:i+{b}v:j+{c}v:k},\\;\\;\\;\\boldsymbol{b}=\\simplify[std]{{d}v:i+{f}v:j+{g}v:k}\\]
answer the following question:
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\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Work done by a force", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["p2", "f1", "f2", "f3", "p3", "p1", "q3", "q1", "q2"], "tags": ["rebel", "Rebel", "REBEL", "rebelmaths", "Vector", "vector", "work"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "Find the work done by a force $\\mathbf{F}=$ {f1}$\\mathbf{i}+$ {f2}$\\mathbf{j}+${f3}$\\mathbf{k}$ in moving an object from the point P({p1},{p2},{p3}) to the point Q({q1},{q2},{q3}).
\n[[0]] Joules
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "First find the displacement vector $\\simplify{vec:d}$= $\\simplify{vec:PQ}$.
\nNote
\n$\\simplify{vec:d =vec:PQ =vec:Q-vec:P}$.
\nWork done$=$ $\\simplify{vec:F}$ $\\cdot$ $\\simplify{vec:d}$ (Scalar Product)
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "f1*(q1-p1)+f2*(q2-p2)+f3*(q3-p3)", "minValue": "f1*(q1-p1)+f2*(q2-p2)+f3*(q3-p3)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 20, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"p2": {"definition": "random(-9..2 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "p2", "description": ""}, "f1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "f3": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "q2": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "q2", "description": ""}, "p3": {"definition": "random(-9..2 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "p3", "description": ""}, "q3": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "q3", "description": ""}, "q1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "q1", "description": ""}, "p1": {"definition": "random(-9..2 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}}, "metadata": {"description": "rebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Cross product 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "s5", "s4", "inner"], "tags": ["3 dimensional vector", "cross product", "Rebel", "REBEL", "rebel", "rebelmaths", "three dimensional vectors", "Vector", "vector", "vector product", "vectors"], "advice": "\\[ \\begin{eqnarray*} \\boldsymbol{a\\times b}&=& \\begin{vmatrix} \\boldsymbol{i} & \\boldsymbol{j} &\\boldsymbol{k}\\\\ \\var{a} & \\var{b} & \\var{g}\\\\ \\var{c} & \\var{d} & \\var{f} \\end{vmatrix}\\\\ \\\\ &=&\\simplify[]{({b}*{f}-{g}*{d})v:i + ({g}*{c} - {a}*{f})v:j+({a}*{d}-{b}*{c})v:k}\\\\ \\\\ &=&\\simplify[std]{{b*f-g*d}v:i+{g*c-a*f}v:j+{a*d-b*c}v:k} \\end{eqnarray*} \\]
", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "Find $\\boldsymbol{a\\times b} =\\;\\;$ [[0]]$\\boldsymbol{i}$+[[1]]$\\boldsymbol{j}$+[[2]]$\\boldsymbol{k}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{b*f-g*d}", "minValue": "{b*f-g*d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 6, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{g*c-a*f}", "minValue": "{g*c-a*f}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 6, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a*d-b*c}", "minValue": "{a*d-b*c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 6, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Given the vectors:
\\[\\boldsymbol{a}=\\simplify[std]{{a}v:i+{b}v:j+{g}v:k},\\;\\;\\;\\boldsymbol{b}=\\simplify[std]{{c}v:i+{d}v:j+{f}v:k}\\]
answer the following question:
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\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "percentPass": "80", "type": "exam", "contributors": [{"name": "Aoife O'Brien", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1693/"}], "extensions": [], "custom_part_types": [], "resources": []}