// Numbas version: exam_results_page_options {"name": "Magnitude and direction of three vectors ", "extensions": ["geogebra", "quantities", "weh"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "

A value with units marked right if within an adjustable % error of the correct value.  Marked close if within a wider margin of error.

Does clumsy substitution to

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1. replace '-' with ' '

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2. replace '°' with ' deg'

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to allow answers like 10 ft-lb and 30°

", "name": "student_units"}, {"definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n", "description": "", "name": "good_units"}, {"definition": "switch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n", "description": "

This fixes the student answer for two common errors.

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If student_units are wrong  - replace with correct units

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If student_scalar has the wrong sign - replace with right sign

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If student makes both errors, only one gets fixed.

", "name": "student_quantity"}, {"definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n ", "description": "", "name": "percent_error"}, {"definition": "percent_error <= settings['right']\n", "description": "", "name": "right"}, {"definition": "right_sign and percent_error <= settings['close']", "description": "

Only marked close if the student actually has the right sign.

", "name": "close"}, {"definition": "sign(student_scalar) = sign(correct_quantity) ", "description": "", "name": "right_sign"}], "settings": [{"input_type": "code", "evaluate": true, "hint": "The correct answer given as a JME quantity.", "default_value": "", "label": "Correct Quantity.", "help_url": "", "name": "correctAnswer"}, {"input_type": "code", "evaluate": true, "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "default_value": "0.2", "label": "% Accuracy for right.", "help_url": "", "name": "right"}, {"input_type": "code", "evaluate": true, "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "default_value": "1.0", "label": "% Accuracy for close.", "help_url": "", "name": "close"}, {"input_type": "percent", "hint": "Partial Credit for close value with appropriate units.  if correct answer is 100 N and close is ±1%,
99  N is accepted.", "default_value": "75", "label": "Close with units.", "help_url": "", "name": "C1"}, {"input_type": "percent", "hint": "Partial credit for forgetting units or using wrong sign.
If the correct answer is 100 N, both 100 and -100 N are accepted.", "default_value": "50", "label": "No units or wrong sign", "help_url": "", "name": "C2"}, {"input_type": "percent", "hint": "Partial Credit for close value but forgotten units.
This value would be close if the expected units were provided.  If the correct answer is 100 N, and close is ±1%,
99 is accepted.", "default_value": "25", "label": "Close, no units.", "help_url": "", "name": "C3"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 23, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/23/edit"}, "name": "Drop-down axis reference", "short_name": "drop-down-axis-reference", "description": "

Choose a reference axis. Returns an integer index between 0 and 3.  0 =+x axis 1 = +y axis 2 = -x axis 3 = -y axis

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To work with angle quantity part type, include a list variable angle_from_ref, and use the axis choice as index. Replace theta with name of angle.

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let(ang,theta,
[if(ang>180,ang-360,ang),
if(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),
if(ang>0,ang-180,ang+180),
if(ang>90,ang-270,90+ang)])

\n

\n

and this (modified as necessary) in the mark student answer (after) script:

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angles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('angle_from_ref'));
ans = Qty(angles[index]+' deg');
this.parentPart.gaps[1].settings.correct_quantity.value=ans;
this.markingComment(\"For your axis, the direction is \" + ans.toString() +'.');

\n

", "help_url": "", "input_widget": "dropdown", "input_options": {"correctAnswer": "0", "hint": {"value": "", "static": true}, "choices": {"value": ["Positive x-axis", "Positive y-axis", "Negative x-axis", "Negative y-axis"], "static": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\ncorrect('You chose the ' \n+ ['positive x',\n 'positive y',\n 'negative x',\n 'negative y'][interpreted_answer] +'-axis.')\n \n \n \n\ninterpreted_answer:\nstudentAnswer", "marking_notes": [{"definition": "correct('You chose the ' \n+ ['positive x',\n 'positive y',\n 'negative x',\n 'negative y'][interpreted_answer] +'-axis.')\n \n \n ", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "name": "mark"}, {"definition": "studentAnswer", "description": "A value representing the student's answer to this part.", "name": "interpreted_answer"}], "settings": [{"label": "dummy", "input_type": "string", "name": "dummy", "hint": "", "subvars": false, "help_url": "", "default_value": "'ignore'"}], "public_availability": "restricted", "published": false, "extensions": []}, {"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "

Angle as a quantity in degrees.

For force $\\textbf{A}$

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$A = \\sqrt{{A_x}^2 + {A_y}^2} = \\sqrt{\\var{FA[0]}^2 +\\var{FA[1]}^2}$ = {siground(mag_A,4)}

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$\\theta_A = \\tan^{-1}\\left(\\left|\\dfrac{A_y}{A_x}\\right|\\right) = \\tan^{-1}\\left(\\left|\\dfrac{\\var{FA[1]}}{\\var{FA[0]}}\\right|\\right) =\\var{siground(degrees(arctan(abs(FA[1]/FA[0]))),4)}°$

\n

and similarly for $\\textbf{B}$ and $\\textbf{C}$.

", "extensions": ["geogebra", "quantities", "weh"], "parts": [{"variableReplacementStrategy": "originalfirst", "customName": "", "useCustomName": false, "showFeedbackIcon": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "settings": {"C3": "25", "close": "1.0", "correctAnswer": "mag_A", "C1": "75", "right": "0.2", "C2": "50"}, "customName": "", "useCustomName": false, "showFeedbackIcon": true, "marks": "4", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "engineering-answer", "scripts": {}, "customMarkingAlgorithm": ""}, {"variableReplacementStrategy": "originalfirst", "settings": {"dummy": "'ignore'"}, "customName": "", "useCustomName": false, "showFeedbackIcon": true, "marks": "0", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "drop-down-axis-reference", "scripts": {"mark": {"order": "after", "script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('a_from_ref'));\nans = Qty(angles[index]+' deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value=ans;\nthis.markingComment(\"For your axis, the direction is \" + ans.toPrec('0.1 deg').toString() +'.');"}}, "customMarkingAlgorithm": ""}, {"variableReplacementStrategy": "originalfirst", "settings": {"C3": "25", "correct_quantity": "qty(a_from_ref[ref],'deg')", "restrict_angle": true, "C2": "50", "C1": "75", "right": "0.2", "close": "1.0"}, "customName": "", "useCustomName": false, "showFeedbackIcon": true, "marks": "4", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "angle-quantity-from-reference", "scripts": {}, "customMarkingAlgorithm": ""}], "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "prompt": "

Find the magnitude and direction of A.

\n

$A$ = [[0]]

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$\\theta_A$ = [[2]] measured from the  [[1]]

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magnitude = {siground(mag_A,4)}

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direction={theta_A}  {a_from_ref}

", "showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": ""}, {"variableReplacementStrategy": "originalfirst", "customName": "", "useCustomName": false, "showFeedbackIcon": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "settings": {"C3": "25", "close": "1.0", "correctAnswer": "mag_B", "C1": "75", "right": "0.2", "C2": "50"}, "customName": "", "useCustomName": false, "showFeedbackIcon": true, "marks": "4", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "engineering-answer", "scripts": {}, "customMarkingAlgorithm": ""}, {"variableReplacementStrategy": "originalfirst", "settings": {"dummy": "'ignore'"}, "customName": "", "useCustomName": false, "showFeedbackIcon": true, "marks": "0", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "drop-down-axis-reference", "scripts": {"mark": {"order": "after", "script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('b_from_ref'));\nans = Qty(angles[index]+' deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value=ans;\nthis.markingComment(\"For your axis, the direction is \" + ans.toPrec('0.1 deg').toString() +'.');"}}, "customMarkingAlgorithm": ""}, {"variableReplacementStrategy": "originalfirst", "settings": {"C3": "25", "correct_quantity": "qty(b_from_ref[ref],'deg')", "restrict_angle": true, "C2": "50", "C1": "75", "right": "0.2", "close": "1.0"}, "customName": "", "useCustomName": false, "showFeedbackIcon": true, "marks": "4", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "angle-quantity-from-reference", "scripts": {}, "customMarkingAlgorithm": ""}], "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "prompt": "

Find the magnitude and direction of B.

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$B$ = [[0]]

\n

$\\theta_B$ = [[2]] measured from the  [[1]]

\n

magnitude = {siground(mag_B,4)}

\n

direction={theta_B} {b_from_ref}

", "showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": ""}, {"variableReplacementStrategy": "originalfirst", "customName": "", "useCustomName": false, "showFeedbackIcon": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "settings": {"C3": "25", "close": "1.0", "correctAnswer": "mag_B", "C1": "75", "right": "0.2", "C2": "50"}, "customName": "", "useCustomName": false, "showFeedbackIcon": true, "marks": "4", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "engineering-answer", "scripts": {}, "customMarkingAlgorithm": ""}, {"variableReplacementStrategy": "originalfirst", "settings": {"dummy": "'ignore'"}, "customName": "", "useCustomName": false, "showFeedbackIcon": true, "marks": "0", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "drop-down-axis-reference", "scripts": {"mark": {"order": "after", "script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('c_from_ref'));\nans = Qty(angles[index]+' deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value=ans;\nthis.markingComment(\"For your axis, the direction is \" + ans.toPrec('0.1 deg').toString() +'.');"}}, "customMarkingAlgorithm": ""}, {"variableReplacementStrategy": "originalfirst", "settings": {"C3": "25", "correct_quantity": "qty(b_from_ref[ref],'deg')", "restrict_angle": true, "C2": "50", "C1": "75", "right": "0.2", "close": "1.0"}, "customName": "", "useCustomName": false, "showFeedbackIcon": true, "marks": "4", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "type": "angle-quantity-from-reference", "scripts": {}, "customMarkingAlgorithm": ""}], "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "prompt": "

Find the magnitude and direction of C.

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$C$ = [[0]]

\n

$\\theta_C$ = [[2]] measured from the  [[1]]

\n

magnitude = {siground(mag_C,4)}

\n

direction={theta_C} {C_from_ref}

", "showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": ""}], "name": "Magnitude and direction of three vectors ", "rulesets": {}, "functions": {}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "

Given three vectors with integer components, find the corresponding magnitude and direction.

"}, "statement": "

Three forces, A, B, and C are drawn to scale of 1 square = {scale} units.  Find the magnitude and direction of each.

\n

{geogebra_applet('qdbwtfa9', [['fa',FA],['fb',FB],['fc',FC]])}

\n

", "variablesTest": {"condition": "abs(FA)>=3 and abs(FB)>=3 and abs(FC)>=3", "maxRuns": "100"}, "variable_groups": [{"name": "Inputs", "variables": ["A1", "FA", "B1", "FB", "C1", "FC", "units", "debug", "scale"]}, {"name": "Outputs", "variables": ["mag_a", "theta_a", "mag_b", "theta_b", "mag_c", "theta_c"]}], "variables": {"units": {"templateType": "anything", "definition": "random(['cm','N'])", "group": "Inputs", "name": "units", "description": ""}, "FB": {"templateType": "anything", "definition": "vector(random(-5..5),random(-5..5 except 0))", "group": "Inputs", "name": "FB", "description": ""}, "FC": {"templateType": "anything", "definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "group": "Inputs", "name": "FC", "description": ""}, "FA": {"templateType": "anything", "definition": "vector(random(-5..5 except 0),random(-5..5))", "group": "Inputs", "name": "FA", "description": ""}, "debug": {"templateType": "anything", "definition": "false", "group": "Inputs", "name": "debug", "description": ""}, "C1": {"templateType": "anything", "definition": "vector(5,0)\n", "group": "Inputs", "name": "C1", "description": "

Position of point C

"}, "a_from_ref": {"templateType": "anything", "definition": "let(ang,theta_a,\n[if(ang>180,ang-360,ang),\nif(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),\nif(ang>0,ang-180,ang+180),\nif(ang>90,ang-270,90+ang)])", "group": "Ungrouped variables", "name": "a_from_ref", "description": ""}, "mag_c": {"templateType": "anything", "definition": "qty(abs(FC),units[1]) scale", "group": "Outputs", "name": "mag_c", "description": ""}, "mag_b": {"templateType": "anything", "definition": "qty(abs(FB),units[1]) scale", "group": "Outputs", "name": "mag_b", "description": ""}, "theta_c": {"templateType": "anything", "definition": "degrees(atan2(FC[1],FC[0]))", "group": "Outputs", "name": "theta_c", "description": ""}, "ref": {"templateType": "anything", "definition": "0", "group": "Ungrouped variables", "name": "ref", "description": "

placeholder for reference axis

"}, "A1": {"templateType": "anything", "definition": "vector(-5,0)", "group": "Inputs", "name": "A1", "description": "

Position of point A  (start point for force A)  fixed in this problem

"}, "c_from_ref": {"templateType": "anything", "definition": "let(ang,theta_c,\n[if(ang>180,ang-360,ang),\nif(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),\nif(ang>0,ang-180,ang+180),\nif(ang>90,ang-270,90+ang)])\n", "group": "Ungrouped variables", "name": "c_from_ref", "description": ""}, "B1": {"templateType": "anything", "definition": "vector(0,0)\n", "group": "Inputs", "name": "B1", "description": "

Position of point B

"}, "scale": {"templateType": "anything", "definition": "random(0.1,0.25,0.5,2,4,5,10,20)", "group": "Inputs", "name": "scale", "description": ""}, "theta_b": {"templateType": "anything", "definition": "degrees(atan2(FB[1],FB[0]))", "group": "Outputs", "name": "theta_b", "description": ""}, "b_from_ref": {"templateType": "anything", "definition": "let(ang,theta_b,\n[if(ang>180,ang-360,ang),\nif(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),\nif(ang>0,ang-180,ang+180),\nif(ang>90,ang-270,90+ang)])\n", "group": "Ungrouped variables", "name": "b_from_ref", "description": ""}, "theta_a": {"templateType": "anything", "definition": "degrees(atan2(FA[1],FA[0]))", "group": "Outputs", "name": "theta_a", "description": ""}, "mag_a": {"templateType": "anything", "definition": "qty(abs(FA),) scale", "group": "Outputs", "name": "mag_a", "description": ""}}, "type": "question", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}