// Numbas version: finer_feedback_settings {"percentPass": 0, "timing": {"allowPause": true, "timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}}, "question_groups": [{"pickingStrategy": "all-ordered", "pickQuestions": 1, "name": "Group", "questions": [{"name": "PreCal Write the equation of an ellipse from its graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"templateType": "anything", "name": "a", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables"}, "a2": {"templateType": "anything", "name": "a2", "definition": "a*a", "description": "", "group": "Ungrouped variables"}, "choicek": {"templateType": "anything", "name": "choicek", "definition": "(1+signk)/2", "description": "", "group": "Ungrouped variables"}, "C": {"templateType": "anything", "name": "C", "definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "description": "", "group": "Ungrouped variables"}, "hVal": {"templateType": "anything", "name": "hVal", "definition": "abs(C[0])", "description": "", "group": "Ungrouped variables"}, "b2": {"templateType": "anything", "name": "b2", "definition": "b*b", "description": "", "group": "Ungrouped variables"}, "signk": {"templateType": "anything", "name": "signk", "definition": "sign(C[1])", "description": "", "group": "Ungrouped variables"}, "operator": {"templateType": "anything", "name": "operator", "definition": "[\"+\",\"-\"]", "description": "", "group": "Ungrouped variables"}, "kVal": {"templateType": "anything", "name": "kVal", "definition": "abs(C[1])", "description": "", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "name": "b", "definition": "random(2..9 except a)", "description": "", "group": "Ungrouped variables"}, "signh": {"templateType": "anything", "name": "signh", "definition": "sign(C[0])", "description": "", "group": "Ungrouped variables"}, "choiceh": {"templateType": "anything", "name": "choiceh", "definition": "(1+signh)/2", "description": "", "group": "Ungrouped variables"}}, "tags": [], "statement": "

GIVEN:  The ellipse shown below.

\n

{geogebra_applet('https://www.geogebra.org/m/watryunh',[ ['a',a], ['b',b], ['C',C] ])}

", "functions": {}, "ungrouped_variables": ["C", "a", "b", "a2", "b2", "signh", "signk", "hVal", "kVal", "operator", "choiceh", "choicek"], "variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "patternmatch", "answer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "customName": "", "adaptiveMarkingPenalty": 0, "extendBaseMarkingAlgorithm": true, "matchMode": "exact", "displayAnswer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "prompt": "

Write the standard form equation of this ellipse.

", "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "advice": "", "type": "question"}, {"name": "PreCal Write the equation of an ellipse from its graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"templateType": "anything", "name": "a", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables"}, "a2": {"templateType": "anything", "name": "a2", "definition": "a*a", "description": "", "group": "Ungrouped variables"}, "choicek": {"templateType": "anything", "name": "choicek", "definition": "(1+signk)/2", "description": "", "group": "Ungrouped variables"}, "C": {"templateType": "anything", "name": "C", "definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "description": "", "group": "Ungrouped variables"}, "hVal": {"templateType": "anything", "name": "hVal", "definition": "abs(C[0])", "description": "", "group": "Ungrouped variables"}, "b2": {"templateType": "anything", "name": "b2", "definition": "b*b", "description": "", "group": "Ungrouped variables"}, "signk": {"templateType": "anything", "name": "signk", "definition": "sign(C[1])", "description": "", "group": "Ungrouped variables"}, "operator": {"templateType": "anything", "name": "operator", "definition": "[\"+\",\"-\"]", "description": "", "group": "Ungrouped variables"}, "kVal": {"templateType": "anything", "name": "kVal", "definition": "abs(C[1])", "description": "", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "name": "b", "definition": "random(2..9 except a)", "description": "", "group": "Ungrouped variables"}, "signh": {"templateType": "anything", "name": "signh", "definition": "sign(C[0])", "description": "", "group": "Ungrouped variables"}, "choiceh": {"templateType": "anything", "name": "choiceh", "definition": "(1+signh)/2", "description": "", "group": "Ungrouped variables"}}, "tags": [], "statement": "

GIVEN:  The ellipse shown below.

\n

{geogebra_applet('https://www.geogebra.org/m/watryunh',[ ['a',a], ['b',b], ['C',C] ])}

", "functions": {}, "ungrouped_variables": ["C", "a", "b", "a2", "b2", "signh", "signk", "hVal", "kVal", "operator", "choiceh", "choicek"], "variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "patternmatch", "answer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "customName": "", "adaptiveMarkingPenalty": 0, "extendBaseMarkingAlgorithm": true, "matchMode": "exact", "displayAnswer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "prompt": "

Write the standard form equation of this ellipse.

", "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "advice": "", "type": "question"}, {"name": "PreCal Write the equation of an ellipse from its graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"templateType": "anything", "name": "a", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables"}, "a2": {"templateType": "anything", "name": "a2", "definition": "a*a", "description": "", "group": "Ungrouped variables"}, "choicek": {"templateType": "anything", "name": "choicek", "definition": "(1+signk)/2", "description": "", "group": "Ungrouped variables"}, "C": {"templateType": "anything", "name": "C", "definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "description": "", "group": "Ungrouped variables"}, "hVal": {"templateType": "anything", "name": "hVal", "definition": "abs(C[0])", "description": "", "group": "Ungrouped variables"}, "b2": {"templateType": "anything", "name": "b2", "definition": "b*b", "description": "", "group": "Ungrouped variables"}, "signk": {"templateType": "anything", "name": "signk", "definition": "sign(C[1])", "description": "", "group": "Ungrouped variables"}, "operator": {"templateType": "anything", "name": "operator", "definition": "[\"+\",\"-\"]", "description": "", "group": "Ungrouped variables"}, "kVal": {"templateType": "anything", "name": "kVal", "definition": "abs(C[1])", "description": "", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "name": "b", "definition": "random(2..9 except a)", "description": "", "group": "Ungrouped variables"}, "signh": {"templateType": "anything", "name": "signh", "definition": "sign(C[0])", "description": "", "group": "Ungrouped variables"}, "choiceh": {"templateType": "anything", "name": "choiceh", "definition": "(1+signh)/2", "description": "", "group": "Ungrouped variables"}}, "tags": [], "statement": "

GIVEN:  The ellipse shown below.

\n

{geogebra_applet('https://www.geogebra.org/m/watryunh',[ ['a',a], ['b',b], ['C',C] ])}

", "functions": {}, "ungrouped_variables": ["C", "a", "b", "a2", "b2", "signh", "signk", "hVal", "kVal", "operator", "choiceh", "choicek"], "variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "patternmatch", "answer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "customName": "", "adaptiveMarkingPenalty": 0, "extendBaseMarkingAlgorithm": true, "matchMode": "exact", "displayAnswer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "prompt": "

Write the standard form equation of this ellipse.

", "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "advice": "", "type": "question"}, {"name": "PreCal Write the equation of an ellipse from its graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"templateType": "anything", "name": "a", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables"}, "a2": {"templateType": "anything", "name": "a2", "definition": "a*a", "description": "", "group": "Ungrouped variables"}, "choicek": {"templateType": "anything", "name": "choicek", "definition": "(1+signk)/2", "description": "", "group": "Ungrouped variables"}, "C": {"templateType": "anything", "name": "C", "definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "description": "", "group": "Ungrouped variables"}, "hVal": {"templateType": "anything", "name": "hVal", "definition": "abs(C[0])", "description": "", "group": "Ungrouped variables"}, "b2": {"templateType": "anything", "name": "b2", "definition": "b*b", "description": "", "group": "Ungrouped variables"}, "signk": {"templateType": "anything", "name": "signk", "definition": "sign(C[1])", "description": "", "group": "Ungrouped variables"}, "operator": {"templateType": "anything", "name": "operator", "definition": "[\"+\",\"-\"]", "description": "", "group": "Ungrouped variables"}, "kVal": {"templateType": "anything", "name": "kVal", "definition": "abs(C[1])", "description": "", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "name": "b", "definition": "random(2..9 except a)", "description": "", "group": "Ungrouped variables"}, "signh": {"templateType": "anything", "name": "signh", "definition": "sign(C[0])", "description": "", "group": "Ungrouped variables"}, "choiceh": {"templateType": "anything", "name": "choiceh", "definition": "(1+signh)/2", "description": "", "group": "Ungrouped variables"}}, "tags": [], "statement": "

GIVEN:  The ellipse shown below.

\n

{geogebra_applet('https://www.geogebra.org/m/watryunh',[ ['a',a], ['b',b], ['C',C] ])}

", "functions": {}, "ungrouped_variables": ["C", "a", "b", "a2", "b2", "signh", "signk", "hVal", "kVal", "operator", "choiceh", "choicek"], "variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "patternmatch", "answer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "customName": "", "adaptiveMarkingPenalty": 0, "extendBaseMarkingAlgorithm": true, "matchMode": "exact", "displayAnswer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "prompt": "

Write the standard form equation of this ellipse.

", "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "advice": "", "type": "question"}, {"name": "PreCal Write the equation of an ellipse from its graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"templateType": "anything", "name": "a", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables"}, "a2": {"templateType": "anything", "name": "a2", "definition": "a*a", "description": "", "group": "Ungrouped variables"}, "choicek": {"templateType": "anything", "name": "choicek", "definition": "(1+signk)/2", "description": "", "group": "Ungrouped variables"}, "C": {"templateType": "anything", "name": "C", "definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "description": "", "group": "Ungrouped variables"}, "hVal": {"templateType": "anything", "name": "hVal", "definition": "abs(C[0])", "description": "", "group": "Ungrouped variables"}, "b2": {"templateType": "anything", "name": "b2", "definition": "b*b", "description": "", "group": "Ungrouped variables"}, "signk": {"templateType": "anything", "name": "signk", "definition": "sign(C[1])", "description": "", "group": "Ungrouped variables"}, "operator": {"templateType": "anything", "name": "operator", "definition": "[\"+\",\"-\"]", "description": "", "group": "Ungrouped variables"}, "kVal": {"templateType": "anything", "name": "kVal", "definition": "abs(C[1])", "description": "", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "name": "b", "definition": "random(2..9 except a)", "description": "", "group": "Ungrouped variables"}, "signh": {"templateType": "anything", "name": "signh", "definition": "sign(C[0])", "description": "", "group": "Ungrouped variables"}, "choiceh": {"templateType": "anything", "name": "choiceh", "definition": "(1+signh)/2", "description": "", "group": "Ungrouped variables"}}, "tags": [], "statement": "

GIVEN:  The ellipse shown below.

\n

{geogebra_applet('https://www.geogebra.org/m/watryunh',[ ['a',a], ['b',b], ['C',C] ])}

", "functions": {}, "ungrouped_variables": ["C", "a", "b", "a2", "b2", "signh", "signk", "hVal", "kVal", "operator", "choiceh", "choicek"], "variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "patternmatch", "answer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "customName": "", "adaptiveMarkingPenalty": 0, "extendBaseMarkingAlgorithm": true, "matchMode": "exact", "displayAnswer": "(x{operator[{choiceh}]}{hVal})^2/{a2}+(y{operator[{choicek}]}{kVal})^2/{b2}=1", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "prompt": "

Write the standard form equation of this ellipse.

", "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "advice": "", "type": "question"}, {"name": "PreCal Identify key characteristics of an ellipse from a graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"vertexRight": {"name": "vertexRight", "templateType": "anything", "definition": "vector(C[0]+a,C[1])", "description": "", "group": "Ungrouped variables"}, "vertexTop": {"name": "vertexTop", "templateType": "anything", "definition": "vector(C[0],C[1]+b)", "description": "", "group": "Ungrouped variables"}, "eccentricity": {"name": "eccentricity", "templateType": "anything", "definition": "[cFoci[orient]/b,cFoci[orient]/a]", "description": "", "group": "Ungrouped variables"}, "C": {"name": "C", "templateType": "anything", "definition": "vector(random(-5..5),random(-5..5))", "description": "", "group": "Ungrouped variables"}, "vertexLeft": {"name": "vertexLeft", "templateType": "anything", "definition": "vector(C[0]-a,C[1])", "description": "", "group": "Ungrouped variables"}, "foci2": {"name": "foci2", "templateType": "anything", "definition": "[vector(C[0],C[1]+cFoci[orient]),vector(C[0]+cFoci[orient],C[1])]", "description": "

fo

", "group": "Ungrouped variables"}, "a": {"name": "a", "templateType": "anything", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables"}, "signOrient": {"name": "signOrient", "templateType": "anything", "definition": "sign(a-b)", "description": "", "group": "Ungrouped variables"}, "foci1": {"name": "foci1", "templateType": "anything", "definition": "[vector(C[0],C[1]-cFoci[orient]),vector(C[0]-cFoci[orient],C[1])]", "description": "", "group": "Ungrouped variables"}, "vertexBottom": {"name": "vertexBottom", "templateType": "anything", "definition": "vector(C[0],C[1]-b)", "description": "", "group": "Ungrouped variables"}, "cFoci": {"name": "cFoci", "templateType": "anything", "definition": "[sqrt(b^2-a^2),sqrt(a^2-b^2)]", "description": "", "group": "Ungrouped variables"}, "b": {"name": "b", "templateType": "anything", "definition": "random(2..9 except a)", "description": "", "group": "Ungrouped variables"}, "orient": {"name": "orient", "templateType": "anything", "definition": "(1+signOrient)/2", "description": "", "group": "Ungrouped variables"}}, "tags": [], "advice": "", "functions": {}, "ungrouped_variables": ["C", "a", "b", "cFoci", "signOrient", "orient", "foci2", "foci1", "vertexTop", "vertexBottom", "vertexLeft", "vertexRight", "eccentricity"], "variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{C}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "prompt": "

Identify the center of the ellipse.  Enter your answer as: vector(x,y)

", "checkingType": "absdiff", "failureRate": 1}, {"type": "gapfill", "adaptiveMarkingPenalty": 0, "customName": "", "marks": 0, "sortAnswers": false, "useCustomName": false, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "prompt": "

Identify the vertices of the given ellipse:

\n

Left Vertex: [[0]]

\n

Right Vertex: [[1]]

\n

Bottom Vertex: [[2]]

\n

Top Vertex: [[3]]

", "variableReplacementStrategy": "originalfirst", "gaps": [{"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexLeft}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexRight}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexBottom}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexTop}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}, {"type": "gapfill", "adaptiveMarkingPenalty": 0, "customName": "", "marks": 0, "sortAnswers": false, "useCustomName": false, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "prompt": "

Identify the focii of the ellipse: Enter values to 3 decimal places

\n

Left/Bottom Foci: [[0]]

\n

Right/Top Foci:  [[1]]

", "variableReplacementStrategy": "originalfirst", "gaps": [{"customName": "", "marks": 1, "checkingAccuracy": 3, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{foci1[orient]}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "dp", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 3, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{foci2[orient]}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "dp", "failureRate": 1}], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}, {"type": "gapfill", "adaptiveMarkingPenalty": 0, "customName": "", "marks": 0, "sortAnswers": false, "useCustomName": false, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "prompt": "

What is the eccentricity of this ellipse? [[0]]

", "variableReplacementStrategy": "originalfirst", "gaps": [{"correctAnswerStyle": "plain", "customName": "", "showPrecisionHint": true, "marks": 1, "mustBeReduced": false, "precisionPartialCredit": "75", "allowFractions": false, "customMarkingAlgorithm": "", "scripts": {}, "useCustomName": false, "mustBeReducedPC": 0, "maxValue": "eccentricity[orient]", "strictPrecision": true, "minValue": "eccentricity[orient]", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "unitTests": [], "precision": "2", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"]}], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "statement": "

GIVEN:  The ellipse shown below.

\n

{geogebra_applet('https://www.geogebra.org/m/watryunh',[ ['a',a], ['b',b], ['C',C] ])}

", "type": "question"}, {"name": "PreCal Identify key characteristics of an ellipse from a graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"vertexRight": {"name": "vertexRight", "templateType": "anything", "definition": "vector(C[0]+a,C[1])", "description": "", "group": "Ungrouped variables"}, "vertexTop": {"name": "vertexTop", "templateType": "anything", "definition": "vector(C[0],C[1]+b)", "description": "", "group": "Ungrouped variables"}, "eccentricity": {"name": "eccentricity", "templateType": "anything", "definition": "[cFoci[orient]/b,cFoci[orient]/a]", "description": "", "group": "Ungrouped variables"}, "C": {"name": "C", "templateType": "anything", "definition": "vector(random(-5..5),random(-5..5))", "description": "", "group": "Ungrouped variables"}, "vertexLeft": {"name": "vertexLeft", "templateType": "anything", "definition": "vector(C[0]-a,C[1])", "description": "", "group": "Ungrouped variables"}, "foci2": {"name": "foci2", "templateType": "anything", "definition": "[vector(C[0],C[1]+cFoci[orient]),vector(C[0]+cFoci[orient],C[1])]", "description": "

fo

", "group": "Ungrouped variables"}, "a": {"name": "a", "templateType": "anything", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables"}, "signOrient": {"name": "signOrient", "templateType": "anything", "definition": "sign(a-b)", "description": "", "group": "Ungrouped variables"}, "foci1": {"name": "foci1", "templateType": "anything", "definition": "[vector(C[0],C[1]-cFoci[orient]),vector(C[0]-cFoci[orient],C[1])]", "description": "", "group": "Ungrouped variables"}, "vertexBottom": {"name": "vertexBottom", "templateType": "anything", "definition": "vector(C[0],C[1]-b)", "description": "", "group": "Ungrouped variables"}, "cFoci": {"name": "cFoci", "templateType": "anything", "definition": "[sqrt(b^2-a^2),sqrt(a^2-b^2)]", "description": "", "group": "Ungrouped variables"}, "b": {"name": "b", "templateType": "anything", "definition": "random(2..9 except a)", "description": "", "group": "Ungrouped variables"}, "orient": {"name": "orient", "templateType": "anything", "definition": "(1+signOrient)/2", "description": "", "group": "Ungrouped variables"}}, "tags": [], "advice": "", "functions": {}, "ungrouped_variables": ["C", "a", "b", "cFoci", "signOrient", "orient", "foci2", "foci1", "vertexTop", "vertexBottom", "vertexLeft", "vertexRight", "eccentricity"], "variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{C}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "prompt": "

Identify the center of the ellipse.  Enter your answer as: vector(x,y)

", "checkingType": "absdiff", "failureRate": 1}, {"type": "gapfill", "adaptiveMarkingPenalty": 0, "customName": "", "marks": 0, "sortAnswers": false, "useCustomName": false, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "prompt": "

Identify the vertices of the given ellipse:

\n

Left Vertex: [[0]]

\n

Right Vertex: [[1]]

\n

Bottom Vertex: [[2]]

\n

Top Vertex: [[3]]

", "variableReplacementStrategy": "originalfirst", "gaps": [{"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexLeft}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexRight}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexBottom}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexTop}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}, {"type": "gapfill", "adaptiveMarkingPenalty": 0, "customName": "", "marks": 0, "sortAnswers": false, "useCustomName": false, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "prompt": "

Identify the focii of the ellipse: Enter values to 3 decimal places

\n

Left/Bottom Foci: [[0]]

\n

Right/Top Foci:  [[1]]

", "variableReplacementStrategy": "originalfirst", "gaps": [{"customName": "", "marks": 1, "checkingAccuracy": 3, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{foci1[orient]}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "dp", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 3, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{foci2[orient]}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "dp", "failureRate": 1}], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}, {"type": "gapfill", "adaptiveMarkingPenalty": 0, "customName": "", "marks": 0, "sortAnswers": false, "useCustomName": false, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "prompt": "

What is the eccentricity of this ellipse? [[0]]

", "variableReplacementStrategy": "originalfirst", "gaps": [{"correctAnswerStyle": "plain", "customName": "", "showPrecisionHint": true, "marks": 1, "mustBeReduced": false, "precisionPartialCredit": "75", "allowFractions": false, "customMarkingAlgorithm": "", "scripts": {}, "useCustomName": false, "mustBeReducedPC": 0, "maxValue": "eccentricity[orient]", "strictPrecision": true, "minValue": "eccentricity[orient]", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "unitTests": [], "precision": "2", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"]}], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "statement": "

GIVEN:  The ellipse shown below.

\n

{geogebra_applet('https://www.geogebra.org/m/watryunh',[ ['a',a], ['b',b], ['C',C] ])}

", "type": "question"}, {"name": "PreCal Identify key characteristics of an ellipse from a graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"vertexRight": {"name": "vertexRight", "templateType": "anything", "definition": "vector(C[0]+a,C[1])", "description": "", "group": "Ungrouped variables"}, "vertexTop": {"name": "vertexTop", "templateType": "anything", "definition": "vector(C[0],C[1]+b)", "description": "", "group": "Ungrouped variables"}, "eccentricity": {"name": "eccentricity", "templateType": "anything", "definition": "[cFoci[orient]/b,cFoci[orient]/a]", "description": "", "group": "Ungrouped variables"}, "C": {"name": "C", "templateType": "anything", "definition": "vector(random(-5..5),random(-5..5))", "description": "", "group": "Ungrouped variables"}, "vertexLeft": {"name": "vertexLeft", "templateType": "anything", "definition": "vector(C[0]-a,C[1])", "description": "", "group": "Ungrouped variables"}, "foci2": {"name": "foci2", "templateType": "anything", "definition": "[vector(C[0],C[1]+cFoci[orient]),vector(C[0]+cFoci[orient],C[1])]", "description": "

fo

", "group": "Ungrouped variables"}, "a": {"name": "a", "templateType": "anything", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables"}, "signOrient": {"name": "signOrient", "templateType": "anything", "definition": "sign(a-b)", "description": "", "group": "Ungrouped variables"}, "foci1": {"name": "foci1", "templateType": "anything", "definition": "[vector(C[0],C[1]-cFoci[orient]),vector(C[0]-cFoci[orient],C[1])]", "description": "", "group": "Ungrouped variables"}, "vertexBottom": {"name": "vertexBottom", "templateType": "anything", "definition": "vector(C[0],C[1]-b)", "description": "", "group": "Ungrouped variables"}, "cFoci": {"name": "cFoci", "templateType": "anything", "definition": "[sqrt(b^2-a^2),sqrt(a^2-b^2)]", "description": "", "group": "Ungrouped variables"}, "b": {"name": "b", "templateType": "anything", "definition": "random(2..9 except a)", "description": "", "group": "Ungrouped variables"}, "orient": {"name": "orient", "templateType": "anything", "definition": "(1+signOrient)/2", "description": "", "group": "Ungrouped variables"}}, "tags": [], "advice": "", "functions": {}, "ungrouped_variables": ["C", "a", "b", "cFoci", "signOrient", "orient", "foci2", "foci1", "vertexTop", "vertexBottom", "vertexLeft", "vertexRight", "eccentricity"], "variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{C}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "prompt": "

Identify the center of the ellipse.  Enter your answer as: vector(x,y)

", "checkingType": "absdiff", "failureRate": 1}, {"type": "gapfill", "adaptiveMarkingPenalty": 0, "customName": "", "marks": 0, "sortAnswers": false, "useCustomName": false, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "prompt": "

Identify the vertices of the given ellipse:

\n

Left Vertex: [[0]]

\n

Right Vertex: [[1]]

\n

Bottom Vertex: [[2]]

\n

Top Vertex: [[3]]

", "variableReplacementStrategy": "originalfirst", "gaps": [{"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexLeft}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexRight}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexBottom}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{vertexTop}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "absdiff", "failureRate": 1}], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}, {"type": "gapfill", "adaptiveMarkingPenalty": 0, "customName": "", "marks": 0, "sortAnswers": false, "useCustomName": false, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "prompt": "

Identify the focii of the ellipse: Enter values to 3 decimal places

\n

Left/Bottom Foci: [[0]]

\n

Right/Top Foci:  [[1]]

", "variableReplacementStrategy": "originalfirst", "gaps": [{"customName": "", "marks": 1, "checkingAccuracy": 3, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{foci1[orient]}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "dp", "failureRate": 1}, {"customName": "", "marks": 1, "checkingAccuracy": 3, "customMarkingAlgorithm": "", "scripts": {}, "vsetRangePoints": 5, "useCustomName": false, "vsetRange": [0, 1], "valuegenerators": [], "checkVariableNames": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "jme", "answer": "{foci2[orient]}", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "showPreview": true, "checkingType": "dp", "failureRate": 1}], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}, {"type": "gapfill", "adaptiveMarkingPenalty": 0, "customName": "", "marks": 0, "sortAnswers": false, "useCustomName": false, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "prompt": "

What is the eccentricity of this ellipse? [[0]]

", "variableReplacementStrategy": "originalfirst", "gaps": [{"correctAnswerStyle": "plain", "customName": "", "showPrecisionHint": true, "marks": 1, "mustBeReduced": false, "precisionPartialCredit": "75", "allowFractions": false, "customMarkingAlgorithm": "", "scripts": {}, "useCustomName": false, "mustBeReducedPC": 0, "maxValue": "eccentricity[orient]", "strictPrecision": true, "minValue": "eccentricity[orient]", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "unitTests": [], "precision": "2", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"]}], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "statement": "

GIVEN:  The ellipse shown below.

\n

{geogebra_applet('https://www.geogebra.org/m/watryunh',[ ['a',a], ['b',b], ['C',C] ])}

", "type": "question"}, {"name": "PreCal Write equation of an ellipse via complete the square", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "advice": "", "functions": {}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["h", "k", "a", "b", "cx2", "cy2", "cx", "cy", "f", "signh", "signk", "operator", "oph", "opk", "hVal", "kVal", "a2", "b2"], "tags": [], "variables": {"cx": {"definition": "-2*b^2*h", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "cx"}, "operator": {"definition": "[\"+\",\"-\"]", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "operator"}, "h": {"definition": "random(-10..10)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "h"}, "a2": {"definition": "a^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a2"}, "cx2": {"definition": "b^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "cx2"}, "cy2": {"definition": "a^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "cy2"}, "kVal": {"definition": "abs(k)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "kVal"}, "a": {"definition": "random(2..10)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a"}, "cy": {"definition": "-2*a^2*k", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "cy"}, "k": {"definition": "random(-10..10)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "k"}, "opk": {"definition": "operator[(1+signk)/2]", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "opk"}, "hVal": {"definition": "abs(h)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "hVal"}, "b": {"definition": "random(2..10 except a)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b"}, "b2": {"definition": "b^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b2"}, "signh": {"definition": "sign(h)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "signh"}, "oph": {"definition": "operator[(1+signh)/2]", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "oph"}, "f": {"definition": "a^2*b^2-b^2*h^2-a^2*k^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "f"}, "signk": {"definition": "sign(k)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "signk"}}, "statement": "

Write the equation of the ellipse in standard from given the equation:

\n

$\\simplify{{cx2}x^2+{cy2}y^2+{cx}x+{cy}y-{f}=0}$

", "parts": [{"prompt": "

The standard form equation of the ellipse is: [[0]]

", "marks": 0, "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "type": "gapfill", "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"marks": 1, "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "answer": "(x{oph}{hVal})^2/{a2}+(y{opk}{kVal})^2/{b2}=1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "type": "patternmatch", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "displayAnswer": "(x{oph}{hVal})^2/{a2}+(y{opk}{kVal})^2/{b2}=1", "matchMode": "exact"}]}], "variable_groups": [], "type": "question"}, {"name": "PreCal Write equation of an ellipse via complete the square", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "advice": "", "functions": {}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["h", "k", "a", "b", "cx2", "cy2", "cx", "cy", "f", "signh", "signk", "operator", "oph", "opk", "hVal", "kVal", "a2", "b2"], "tags": [], "variables": {"cx": {"definition": "-2*b^2*h", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "cx"}, "operator": {"definition": "[\"+\",\"-\"]", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "operator"}, "h": {"definition": "random(-10..10)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "h"}, "a2": {"definition": "a^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a2"}, "cx2": {"definition": "b^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "cx2"}, "cy2": {"definition": "a^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "cy2"}, "kVal": {"definition": "abs(k)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "kVal"}, "a": {"definition": "random(2..10)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a"}, "cy": {"definition": "-2*a^2*k", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "cy"}, "k": {"definition": "random(-10..10)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "k"}, "opk": {"definition": "operator[(1+signk)/2]", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "opk"}, "hVal": {"definition": "abs(h)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "hVal"}, "b": {"definition": "random(2..10 except a)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b"}, "b2": {"definition": "b^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b2"}, "signh": {"definition": "sign(h)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "signh"}, "oph": {"definition": "operator[(1+signh)/2]", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "oph"}, "f": {"definition": "a^2*b^2-b^2*h^2-a^2*k^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "f"}, "signk": {"definition": "sign(k)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "signk"}}, "statement": "

Write the equation of the ellipse in standard from given the equation:

\n

$\\simplify{{cx2}x^2+{cy2}y^2+{cx}x+{cy}y-{f}=0}$

", "parts": [{"prompt": "

The standard form equation of the ellipse is: [[0]]

", "marks": 0, "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "type": "gapfill", "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"marks": 1, "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "answer": "(x{oph}{hVal})^2/{a2}+(y{opk}{kVal})^2/{b2}=1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "type": "patternmatch", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "displayAnswer": "(x{oph}{hVal})^2/{a2}+(y{opk}{kVal})^2/{b2}=1", "matchMode": "exact"}]}], "variable_groups": [], "type": "question"}]}], "showstudentname": true, "name": "PreCal CW Ellipse Equations and Characteristics", "duration": 0, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": "Practice identifying characteristics of an ellipse and writing their equation in standard form from an equation or graph."}, "navigation": {"allowsteps": true, "preventleave": true, "reverse": true, "onleave": {"action": "none", "message": ""}, "showfrontpage": true, "startpassword": "", "showresultspage": "oncompletion", "allowregen": true, "browse": true}, "feedback": {"advicethreshold": 0, "allowrevealanswer": true, "showanswerstate": true, "showactualmark": true, "showtotalmark": true, "intro": "", "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "showQuestionGroupNames": false, "type": "exam", "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": []}