// Numbas version: finer_feedback_settings {"name": "Exam 2 Math6005 2023", "metadata": {"description": "", "licence": "None specified"}, "duration": 2700, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Numbas questions", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Solving systems: multiple choice (CA 2023)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

In each part, select the correct answer.

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "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": "

If the augmented matrix of the system $A\\bar{x} = \\bar{b}$ has a row of the form $\\begin{bmatrix} 0 & 0 & 0 & \\ldots & 0 & 9\\end{bmatrix}$, then the system $A\\bar{x} = \\bar{b}$ has:

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["no solution.", "infinitely many solutions", "a unique solution", "no solution or infinitely many solutions – cannot be determined without more work"], "matrix": ["0.5", "0", "0", 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "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": "

If $\\det(A) = 0$, then the system $A\\bar{x}=\\bar{b}$ has:

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["no solution.", "infinitely many solutions", "a unique solution", "no solution or infinitely many solutions – cannot be determined without more work"], "matrix": ["0", "0", "0", "0.5"], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "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": "

If the augmented matrix of the system $A\\bar{x} = \\bar{b}$ has a row of the form $\\begin{bmatrix} 0 & 0 & 0 & \\ldots & 0 & 0\\end{bmatrix}$, then the system $A\\bar{x} = \\bar{b}$ has:

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["no solution.", "infinitely many solutions", "a unique solution", "no solution or infinitely many solutions – cannot be determined without more work"], "matrix": ["0", "0.5", "0", "0"], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "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": "

Which of these calculations could be used to solve for $y$ in the system:

\\[4x-6y=4\\]\\[x+5y=14\\]

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$y =\\frac{
\\begin{vmatrix}
4 & 1 \\\\
-6 & 5
\\end{vmatrix}
}{26}$

", "$y=\\frac{
\\begin{vmatrix}
4 & 4 \\\\
1 & 14
\\end{vmatrix}
}{26}$", "$y=\\frac{
\\begin{vmatrix}
4 & -6 \\\\
14 & 5
\\end{vmatrix}
}{26}$", "$y=\\frac{
\\begin{vmatrix}
4 & 4 \\\\
-6 & 14
\\end{vmatrix}
}{26}$"], "matrix": ["0", "0.5", "0", "0"], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "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": "

Which of the following equations describes the solution of a system of equation in form of $AX = B$?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$A^{-1}AX = A^{-1}B$", "$B^{-1}AX = A^{-1}B$", "$A^{-1}AX = BA^{-1}$", "$AXA^{-1} = A^{-1}BA$"], "matrix": ["0.5", "0", "0", "0"], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "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": "

Consider the following augmented matrix \\[\\begin{bmatrix} 1 & 3 & 3 & | & 5 \\\\ 0 & -6 & -7 & | & -14 \\\\ 0 & 0 & 0 & | & b+8\\end{bmatrix}\\] \u200bFor which value of b is the system consistent?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$-2$", "It is consistent for all values of $b$", "-8", "8"], "matrix": ["0", "0", "0.5", "0"], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Marie's copy of 2x2 Cramer's Rule Question", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Use Cramer's rule to solve for $x$ and $y$ in the following system of equations:

\\[ \\begin{eqnarray*} \\simplify[!noLeadingMinus,unitFactor]{{a}x + {b}y} &=& \\var{m}\\\\ \\simplify[!noLeadingMinus,unitFactor]{{c}x + {d}y} &=& \\var{n} \\end{eqnarray*} \\]

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-4..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..8)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-3..10 except 0 except a)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-1..5 except 0 except -b)", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "random(-15..15)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-3..20)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "a*x+b*y", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "c*x+d*y", "description": "", "templateType": "anything", "can_override": false}, "DetA": {"name": "DetA", "group": "Ungrouped variables", "definition": "{a*d}-{b*c}", "description": "", "templateType": "anything", "can_override": false}, "DetAx": {"name": "DetAx", "group": "Ungrouped variables", "definition": "{m*d}-{b*n}", "description": "", "templateType": "anything", "can_override": false}, "DetAy": {"name": "DetAy", "group": "Ungrouped variables", "definition": "{a*n}-{m*c}", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "a*d-b*c>0 or a*d-b*c<0", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "x", "y", "m", "n", "DetA", "DetAx", "DetAy"], "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": "

First find the determinants of the matrices $A$, $A_x$ and $A_y$:

$\\det A = $ [[0]]

$\\det A_x = $ [[1]]

$\\det A_y = $ [[2]]

Then solve for $x$ and $y$:

$x= $ [[0]]

$y= $ [[1]]

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "DetA", "part": "p0g0", "must_go_first": false}, {"variable": "DetAx", "part": "p0g1", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{DetAx}/{DetA}", "maxValue": "{DetAx}/{DetA}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "DetA", "part": "p0g0", "must_go_first": false}, {"variable": "DetAy", "part": "p0g2", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{DetAy}/{DetA}", "maxValue": "{DetAy}/{DetA}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Marie's copy of Vector algebra", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "tags": [], "metadata": {"description": "

Vector addition, subtraction, scalar multiplication, magnitude, unit vectors

", "licence": "None specified"}, "statement": "

Consider the vectors $\\mathbf{u}=(\\var{u1}, \\var{u2}, \\var{u3}, \\var{u4}, \\var{u5})$ and $\\mathbf{v}=(\\var{v1}, \\var{v2}, \\var{v3}, \\var{v4}, \\var{v5})$. Calculate each of the following:

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..8)", "description": "", "templateType": "anything", "can_override": false}, "w1": {"name": "w1", "group": "Ungrouped variables", "definition": "vector(1+{a}*5, 3+{a}*2, -1+{a}*(-1), 10+{a}*4, 0+{a}*6)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..5 except[0,1])", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(4..9)", "description": "", "templateType": "anything", "can_override": false}, "v1": {"name": "v1", "group": "Ungrouped variables", "definition": "random(-4..4)", "description": "", "templateType": "anything", "can_override": false}, "v2": {"name": "v2", "group": "Ungrouped variables", "definition": "random(-4..4)", "description": "", "templateType": "anything", "can_override": false}, "v3": {"name": "v3", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "v4": {"name": "v4", "group": "Ungrouped variables", "definition": "random(-4..4)", "description": "", "templateType": "anything", "can_override": false}, "v5": {"name": "v5", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "u1": {"name": "u1", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "u2": {"name": "u2", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "u3": {"name": "u3", "group": "Ungrouped variables", "definition": "random(-4..4 except[0,1])", "description": "", "templateType": "anything", "can_override": false}, "u4": {"name": "u4", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "u5": {"name": "u5", "group": "Ungrouped variables", "definition": "random(-4..4)", "description": "", "templateType": "anything", "can_override": false}, "Mag": {"name": "Mag", "group": "Ungrouped variables", "definition": "{u1}^2 + {u2}^2+ {u3}^2 + {u4}^2 + {u5}^2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "v1", "v2", "v3", "v4", "v5", "w1", "u1", "u2", "u3", "u4", "u5", "Mag"], "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": "

$\\mathbf{u} + \\var{a} \\mathbf{v} = \\big($ [[0]], [[1]], [[2]], [[3]], [[4]] $\\big)$

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{u1}+{a}*{v1}", "maxValue": "{u1}+{a}*{v1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{u2}+{a}*{v2}", "maxValue": "{u2}+{a}*{v2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{u3}+{a}*{v3}", "maxValue": "{u3}+{a}*{v3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{u4}+{a}*{v4}", "maxValue": "{u4}+{a}*{v4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{u5}+{a}*{v5}", "maxValue": "{u5}+{a}*{v5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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": "

$\\var{b} \\mathbf{u} - \\var{c} \\mathbf{v} = \\big($ [[0]], [[1]], [[2]] ,[[3]],[[4]] $\\big)$

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{u1}*{b}-{c}*{v1}", "maxValue": "{b}*{u1}-{c}*{v1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b}*{u2}-{c}*{v2}", "maxValue": "{b}*{u2}-{c}*{v2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b}*{u3}-{c}*{v3}", "maxValue": "{b}*{u3}-{c}*{v3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b}*{u4}-{c}*{v4}", "maxValue": "{b}*{u4}-{c}*{v4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b}*{u5}-{c}*{v5}", "maxValue": "{b}*{u5}-{c}*{v5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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": "

the unit vector $\\mathbf{\\widehat{u}}$ in the same direction of the vector $\\mathbf{u}$.

Write your answers as fractions, using sqrt($x$) to write the square root of $x$ e.g. to write $\\sqrt{22}$, type sqrt(22).

$\\mathbf{\\widehat{u}} = \\big($ [[0]], [[1]], [[2]], [[3]], [[4]] $\\big)$

", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{u1}/sqrt({Mag})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{u2}/sqrt({Mag})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{u3}/sqrt({Mag})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{u4}/sqrt({Mag})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{u5}/sqrt({Mag})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "Written question", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "Written question CA2 2023 - unique solution", "extensions": [], "custom_part_types": [{"source": {"pk": 189, "author": {"name": "Chris Graham", "pk": 369}, "edit_page": "/part_type/189/edit"}, "name": "Submit an answer on paper", "short_name": "submit-an-answer-on-paper", "description": "

Submit an answer on paper (in an invigilated exam)

", "help_url": "", "input_widget": "checkboxes", "input_options": {"correctAnswer": "[True]", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["I have completed this question in my answer book"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nset_credit(0,'This will be marked later.')\n\ninterpreted_answer:\nstudentAnswer", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "set_credit(0,'This will be marked later.')"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer"}], "settings": [{"name": "message", "label": "message", "help_url": "", "hint": "", "input_type": "html", "default_value": "

A message

", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

For the following question, write your solution in the answer booklet provided and hand this to your lecturer at the end of the exam.

", "advice": "

\$ \\text{Augmented matrix:} \\begin{bmatrix} \\var{a11}&\\var{a12}&\\var{a13}&\\var{b11}\\\\ \\simplify{{m1}{a11}}\u200b & \\simplify{{a22}+{m1}{a12}}& \\simplify{{a23}+{m1}{a13}}&\\simplify{{b21}+ {m1}{b11}}\\\\ \\simplify{{m2}{a11}}&\\simplify{{m3}+{m2}{a12}}& \\simplify{{a33} + {m2}{a13} + {m3}{a23}} & \\simplify{{b31}+{m3}{b21} + {m2}{b11}}\\end{bmatrix}\$

\$R2 := R2 - \\var{m1}R1 \\qquad \\begin{bmatrix} \\var{a11}&\\var{a12}&\\var{a13}&\\var{b11}\\\\ 0\u200b&\\simplify{{a22}}&\\simplify{{a23}} &\\simplify{{b21}}\\\\ \\simplify{{m2}{a11}}&\\simplify{{m3}+{m2}{a12}}& \\simplify{{a33} + {m2}{a13} + {m3}{a23}} & \\simplify{{b31}+{m3}{b21} + {m2}{b11}} \\end{bmatrix} \\qquad\\color{red}{\\text{[1]}}\$

\$R3 := R3 - \\var{m2}R1 \\qquad \\begin{bmatrix} \\var{a11}&\\var{a12}&\\var{a13}&\\var{b11}\\\\ 0\u200b&\\var{a22}&\\var{a23}&\\var{b21}\\\\0&\\simplify{{m3}}&\\simplify{{a33}+{m3}{a23}}&\\simplify{{b31}+{m3}{b21}} \\end{bmatrix} \\qquad\\color{red}{\\text{[1]}}\$

\$R3 := R3 - \\var{m3}R2 \\qquad \\begin{bmatrix} \\var{a11}&\\var{a12}&\\var{a13}&\\var{b11}\\\\ 0&\\var{a22}&\\var{a23}&\\var{b21}\\\\0&0&\\var{a33} & \\var{b31} \\end{bmatrix} \\qquad \\color{red}{\\text{[1]}}\$

Solution $z= \\frac{\\var{b31}}{\\var{a33}} = \\var{z}$, $y=\\simplify{{b21}/{a22}} - \\simplify{{a23}/{a22}*({b31}/{a33})} = \\var{y}$, $x = \\var{b11}-(\\simplify{{a13}*({b31}/{a33})})-(\\simplify{{a12}{b21}/{a22}}) + \\simplify{{a12}{a23}/{a22} *({b31}/{a33})} = \\var{x} \\qquad \\color{red}{\\text{[3]}}$

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a11": {"name": "a11", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "a12": {"name": "a12", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "a13": {"name": "a13", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "a21": {"name": "a21", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "a22": {"name": "a22", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "a23": {"name": "a23", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "a31": {"name": "a31", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "a32": {"name": "a32", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "b11": {"name": "b11", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b21": {"name": "b21", "group": "Ungrouped variables", "definition": "random(1..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "m1": {"name": "m1", "group": "Ungrouped variables", "definition": "random(2..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "m2": {"name": "m2", "group": "Ungrouped variables", "definition": "random(2..6 except 0 except m1)", "description": "", "templateType": "anything", "can_override": false}, "m3": {"name": "m3", "group": "Ungrouped variables", "definition": "random(1..5 except v)", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "-m2*(a12)", "description": "", "templateType": "anything", "can_override": false}, "a33": {"name": "a33", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b31": {"name": "b31", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "z": {"name": "z", "group": "Ungrouped variables", "definition": "b31/a33", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "{b21}/{a22} - {a23}/{a22}*({b31}/{a33})", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "{b11}-{a13}*({b31}/{a33})-{a12}{b21}/{a22} + {a12}{a23}/{a22} *({b31}/{a33})", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a11", "a12", "a13", "a21", "a22", "a23", "a31", "a32", "a33", "b11", "b21", "b31", "m1", "m2", "m3", "v", "z", "y", "x"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "submit-an-answer-on-paper", "useCustomName": false, "customName": "", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Use Gaussian elimination to solve the following system of equations

\\[\\begin{eqnarray*} \\simplify{{a11}x+{a12}y+{a13}z} &=& \\var{b11} \\\\ \\simplify{{m1}{a11}x+({a22}+{m1}{a12})y+({a23}+{m1}{a13})z} &=& \\simplify{{b21}+ {m1}{b11}} \\\\ \\simplify{{m2}{a11}x+({m3}+{m2}{a12})y+ ({a33} + {m2}{a13} + {m3}{a23}) z} &=& \\simplify{{b31}+{m3}{b21} + {m2}{b11}} \\end{eqnarray*}\\]

Clearly show all workings and indicate what row operation you are performing at each step.

[6 marks]

", "settings": {"message": "

A message

"}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Written question CA2 2023 - infinitely many solutions", "extensions": [], "custom_part_types": [{"source": {"pk": 189, "author": {"name": "Chris Graham", "pk": 369}, "edit_page": "/part_type/189/edit"}, "name": "Submit an answer on paper", "short_name": "submit-an-answer-on-paper", "description": "

Submit an answer on paper (in an invigilated exam)

A message

For the following question, write your solution in the answer booklet provided and hand this to your lecturer at the end of the exam.

", "advice": "

\$ \\text{Augmented matrix:} \\begin{bmatrix} \\var{a11}&\\var{a12}&\\var{a13}& \\vdots & \\var{b11}\\\\ \\simplify{{m1}{a11}}\u200b&\\simplify{{a22}+{m1}{a12}}&\\simplify{{a23}+{m1}{a13}}&\\vdots&\\simplify{{b21}+ {m1}{b11}}\\\\ \\simplify{{m2}{a11}}&\\simplify{{m3}+{m2}{a12}}&\\var{a}&\\vdots&\\var{b} \\end{bmatrix} \\qquad\$

\$R_2 \\longrightarrow R_2 - \\var{m1}R_1 \\qquad \\begin{bmatrix} \\var{a11}&\\var{a12}&\\var{a13}&\\vdots&\\var{b11}\\\\ 0\u200b&\\simplify{{a22}}&\\simplify{{a23}} &\\vdots&\\simplify{{b21}}\\\\ \\simplify{{m2}{a11}}&\\simplify{{m3}+{m2}{a12}}& \\var{a} &\\vdots & \\var{b} \\end{bmatrix} \\qquad\\color{red}{\\text{[1]}}\$

\$R_3 \\longrightarrow R_3 - \\var{m2}R_1 \\qquad \\begin{bmatrix} \\var{a11}&\\var{a12}&\\var{a13}&\\vdots&\\var{b11}\\\\ 0\u200b&\\var{a22}&\\var{a23}&\\vdots&\\var{b21}\\\\0&\\simplify{{m3}}&\\simplify{{a}-{m2}{a13}}&\\vdots&\\simplify{{b}-{m2}{b11}} \\end{bmatrix} \\qquad\\color{red}{\\text{[1]}}\$

\$R_3 \\longrightarrow R_3 - \\var{m3}R_2 \\qquad \\begin{bmatrix} \\var{a11}&\\var{a12}&\\var{a13}&\\vdots&\\var{b11}\\\\ 0&\\var{a22}&\\var{a23}&\\vdots&\\var{b21}\\\\0&0&\\simplify{{a}-{m2}{a13}-{m3}/{a22}{{a23}}}&\\vdots&\\simplify{{b}-{m2}{b11}-{m3}/{a22}{b21}} \\end{bmatrix} \\qquad \\color{red}{\\text{[1]}}\$

Discarding the zero row, gives \\begin{bmatrix} \\var{a11}&\\var{a12}&\\var{a13}&\\vdots&\\var{b11}\\\\ 0&\\var{a22}&\\var{a23}&\\vdots&\\var{b21} \\end{bmatrix}

Let $z=t, t \\in \\bf{R}$. $\\qquad \\color{red}{\\text{[1]}}$

Then from $R_2$, $\\ \\ \\simplify{{a22}y + {a23}z} = \\var{b21} \\ \\ \\ \\Rightarrow \\simplify{{a22}y + {a23}t} = \\var{b21} \\ \\ \\ \\Rightarrow \\ y=\\simplify{{b21}/{a22} - {a23}/{a22}t} \\qquad \\color{red}{\\text{[1]}}$

From $R_1$, $\\ \\ \\simplify{{a11}x + {a12}y + {a13}z} = \\var{b11} \\ \\ \\ \\Rightarrow \\simplify{{a11}x} + \\simplify{{a12}({b21}/{a22} - {a23}/{a22}t)} + \\simplify{{a13}t} = \\var{b11} \\ \\ \\ \\Rightarrow x = \\simplify{ {b11}-{a13}t-{a12}{b21}/{a22} + {a12}{a23}/{a22} t} \\qquad \\color{red}{\\text{[1]}}$

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a11": {"name": "a11", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "a12": {"name": "a12", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "a13": {"name": "a13", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "a21": {"name": "a21", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "a22": {"name": "a22", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "a23": {"name": "a23", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "a31": {"name": "a31", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "a32": {"name": "a32", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "b11": {"name": "b11", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b21": {"name": "b21", "group": "Ungrouped variables", "definition": "random(1..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "m1": {"name": "m1", "group": "Ungrouped variables", "definition": "random(2..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "m2": {"name": "m2", "group": "Ungrouped variables", "definition": "random(2..6 except 0 except m1)", "description": "", "templateType": "anything", "can_override": false}, "m3": {"name": "m3", "group": "Ungrouped variables", "definition": "random(1..5 except v)", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "-m2*(a12)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "m2*a13+(m3/a22)*a23", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "m2*b11+(m3/a22)*b21", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a11", "a12", "a13", "a21", "a22", "a23", "a31", "a32", "b11", "b21", "m1", "m2", "m3", "v", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "submit-an-answer-on-paper", "useCustomName": false, "customName": "", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Use Gaussian elimination to solve the following system of equations

Clearly show all workings and indicate what row operation you are performing at each step.

[6 marks]

", "settings": {"message": "

A message

"}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}], "allowPrinting": false, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": false, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "typeendtoleave": false, "startpassword": "", "allowAttemptDownload": false, "downloadEncryptionKey": ""}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "warn", "message": "

There are 5 minutes remaining. Please ensure you submit answeers to all questions before the time is up.

"}}, "feedback": {"showactualmark": false, "showtotalmark": true, "showanswerstate": false, "allowrevealanswer": false, "advicethreshold": 0, "intro": "", "end_message": "", "reviewshowscore": false, "reviewshowfeedback": false, "reviewshowexpectedanswer": false, "reviewshowadvice": false, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "never", "showactualmarkwhen": "never", "showtotalmarkwhen": "always", "showanswerstatewhen": "never", "showadvicewhen": "never"}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "type": "exam", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "extensions": [], "custom_part_types": [{"source": {"pk": 189, "author": {"name": "Chris Graham", "pk": 369}, "edit_page": "/part_type/189/edit"}, "name": "Submit an answer on paper", "short_name": "submit-an-answer-on-paper", "description": "

Submit an answer on paper (in an invigilated exam)

A message

", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": []}