// Numbas version: finer_feedback_settings
{"name": "03. Vector Addition Trig Methods", "metadata": {"description": "<p>Homwork Set. &nbsp;Covers graphical, and trigonometric&nbsp;methods of vector addition.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Vector Addition: 2 forces, no diagram", "extensions": ["quantities"], "custom_part_types": [{"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": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "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": "switch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "evaluate": true}, {"name": "right", "label": "Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"name": "close", "label": " Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"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": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(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\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "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": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "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"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["Mechanics", "mechanics", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"description": "<p>Sum three force vectors&nbsp;based on a written description of the situation.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>&nbsp;Given two forces acting at point $P$:</p>\n<ul>\n<li>Force $\\textbf{A}$&nbsp;has a magnitude of {qty(A,unit)} and acts {theta}&deg; CCW from the {dirA[0]}.&nbsp;</li>\n<li>Force $\\textbf{B}$ has a magnitude of {qty(B,unit)} and acts along a ray from point $P$ with a slope of $\\left(\\frac{\\var{rise}}{\\var{run}}\\right)$.&nbsp;</li>\n</ul>", "advice": "<ol>\n<li>Draw a neat, scaled diagram of the vector addition. &nbsp;</li>\n<li>Use geometry to find one angle in the triangle.</li>\n<li>Use law of cosines or law of sines to find the magnitude of $\\mathbf{R}$ and the angle it makes with the $x$ axis.</li>\n</ol>\n<!--div style=\"padding-left: 100px;\">\n<p><strong>Given</strong></p>\n<p style=\"padding-left: 30px;\">$\\mathbf{A}$ = {A} {unit} &nbsp;at {alpha}&deg; &nbsp;</p>\n<p style=\"padding-left: 30px;\">$\\mathbf{B}$ = {B}&nbsp;{unit} at {precround(beta,2)}&deg;</p>\n<p style=\"padding-left: 30px;\">$\\mathbf{C}$ = {C}&nbsp;{unit} at {gamma}&deg;</p>\n<p><strong>Find Scalar Components</strong></p>\n<table style=\"padding-left: 30px' width: 352.328125px; float: left;\" border=\"1px solid black\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"height: 17px; text-align: center; padding-left: 30px; width: 35px;\"></td>\n<td style=\"height: 17px; text-align: center; width: 123px;\">$F_x$</td>\n<td style=\"height: 17px; text-align: center; width: 147.328125px;\">$F_y$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; text-align: right; width: 35px;\">$\\mathbf{A}$</td>\n<td style=\"height: 18px; text-align: center; width: 123px;\">{precround(Ax,2)}&nbsp;{unit}&nbsp;</td>\n<td style=\"height: 18px; text-align: center; width: 147.328125px;\">{precround(Ay,2)} {unit}</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"height: 17px; text-align: right; width: 35px;\">$\\mathbf{B}$</td>\n<td style=\"height: 17px; text-align: center; width: 123px;\">{precround(Bx,2)} {unit}</td>\n<td style=\"height: 17px; text-align: center; width: 147.328125px;\">{precround(By,2)} {unit}</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"height: 17px; text-align: right; width: 35px;\">$\\mathbf{C}$</td>\n<td style=\"height: 17px; text-align: center; width: 123px;\">{precround(Cx,2)} {unit}<span class=\"Apple-tab-span\"> </span></td>\n<td style=\"height: 17px; text-align: center; width: 147.328125px;\">{precround(Cy,2)} {unit}</td>\n</tr>\n</tbody>\n</table>\n<p style=\"clear: both;\"><strong>Find rectangular components of the Resultant</strong></p>\n<p style=\"padding-left: 30px;\">$R_x = A_x + B_x +C_x = \\var{precround(Rx,2)}$&nbsp;{unit}</p>\n<p style=\"padding-left: 30px;\">$R_y = A_y + B_y +C_y = \\var{precround(Ry,2)}$&nbsp;{unit}</p>\n<p><strong>Find the Magnitude of the Resultant</strong></p>\n<p style=\"padding-left: 30px;\">$R = &nbsp;\\sqrt{{R_x}^2 + {R_y}^2} = \\var{precround(R,2)}$ &nbsp;{unit}</p>\n<p><strong>Find the Direction of the Resultant</strong></p>\n<p style=\"padding-left: 30px;\">The angle in a right triangle with sides of length $R_x$ and $R_y$ is</p>\n<p style=\"padding-left: 30px;\">$\\alpha = \\arctan{\\left|\\dfrac{R_y}{R_x}\\right|} = \\var{siground(degrees(arctan(abs(Ry/Rx))),4)}$&deg;</p>\n<p style=\"padding-left: 30px;\">Since $R_x = \\var{siground(qty(Rx,unit),3)}$ and $R_y = \\var{siground(qty(Ry,unit),3)}$ force $\\textbf{R}$ points {if(Rx &gt; 0, \"right\", \"left\")} and {if(Ry &gt; 0, \"up\", \"down\")}, therefore the angle between $\\textbf{R}$ and the positive $x$ axis is:</p>\n<p style=\"padding-left: 30px;\">$\\theta = &nbsp;\\var{(if(Rx&gt;0,if(Ry &gt; 0, \"$\\\\alpha$\",\"$-\\\\alpha$\"),if(Ry &gt; 0, \"$180&deg;-\\\\alpha$\", \"$-180&deg; + \\\\alpha$\")))} &nbsp;&nbsp; = \\var{siground(theta_r,4)} $&deg;</p>\n</div -->", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "random(10..60#5)\n\n", "description": "<p>Magnitude of force A</p>\n<p></p>", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "random(30..80#10)", "description": "", "templateType": "anything", "can_override": false}, "unit": {"name": "unit", "group": "Ungrouped variables", "definition": "random(['N','lb'])", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "random(10..60#5)", "description": "", "templateType": "anything", "can_override": false}, "dirC": {"name": "dirC", "group": "Ungrouped variables", "definition": "random(['left',180],['right',0],['up',90],['down',270])", "description": "<p>Description and angle for direction of B</p>", "templateType": "anything", "can_override": false}, "rise": {"name": "rise", "group": "Ungrouped variables", "definition": "random([-1,-3,-4,1,3,4])", "description": "", "templateType": "anything", "can_override": false}, "run": {"name": "run", "group": "Ungrouped variables", "definition": "random([-1,-3,-4,1,3,4])", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "random([30,60])", "description": "", "templateType": "anything", "can_override": false}, "dirA": {"name": "dirA", "group": "Ungrouped variables", "definition": "random([\n    [\"positive $x$ axis\",0+theta],\n     [\"positive $y$ axis\",90+theta],\n     [\"negative $x$ axis\",180+theta],\n     [\"negative $y$ axis\",270+theta]])\n    \n    \n    ", "description": "<p>Description and angle for direction of&nbsp;A</p>", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "dirA[1]", "description": "", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "Ungrouped variables", "definition": "degrees(atan2(rise,run))", "description": "", "templateType": "anything", "can_override": false}, "gamma": {"name": "gamma", "group": "Ungrouped variables", "definition": "dirC[1]", "description": "", "templateType": "anything", "can_override": false}, "ax": {"name": "ax", "group": "answers", "definition": "A cos(radians(alpha))", "description": "", "templateType": "anything", "can_override": false}, "bx": {"name": "bx", "group": "answers", "definition": "B cos(radians(beta))", "description": "", "templateType": "anything", "can_override": false}, "ay": {"name": "ay", "group": "answers", "definition": "A sin(radians(alpha))", "description": "", "templateType": "anything", "can_override": false}, "by": {"name": "by", "group": "answers", "definition": "B sin(radians(beta))", "description": "", "templateType": "anything", "can_override": false}, "rx": {"name": "rx", "group": "answers", "definition": "ax+bx", "description": "", "templateType": "anything", "can_override": false}, "ry": {"name": "ry", "group": "answers", "definition": "ay+by", "description": "", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "answers", "definition": "sqrt(rx^2+ry^2)", "description": "", "templateType": "anything", "can_override": false}, "theta_R": {"name": "theta_R", "group": "answers", "definition": "degrees(atan2(ry,rx))", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(rise) <> abs(run) and\nRx <>0 and\nRy <>0", "maxRuns": 100}, "ungrouped_variables": ["A", "B", "unit", "C", "rise", "run", "theta", "dirA", "dirC", "alpha", "beta", "gamma", "debug"], "variable_groups": [{"name": "answers", "variables": ["ax", "bx", "ay", "by", "rx", "ry", "R", "theta_R"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Find Vector Sum", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "alwaysreplace", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the magnitude of the resultant $\\textbf{R} = \\mathbf{A} + \\mathbf{B}$ and the angle the resultant makes with the positive $x$-axis.</p>\n<ul>\n<li>$R=$ [[0]] &nbsp;&nbsp;</li>\n<li>$\\theta =$ [[1]]&nbsp;&nbsp;$(-180&deg; \\le \\theta \\le 180&deg;)$</li>\n</ul>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$R$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(R,unit)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "angle-quantity-from-reference", "useCustomName": true, "customName": "$\\theta$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correct_quantity": "precround(qty(theta_r,'deg'),2)", "right": "0.1", "restrict_angle": false, "C1": "75", "close": "0.5", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Parallelogram Rule: Pull Stake", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"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": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "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": "switch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "evaluate": true}, {"name": "right", "label": "Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"name": "close", "label": " Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"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": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(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\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "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": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "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"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": ["question-resources/triangle_j1bJHMI.svg"], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["Mechanics", "mechanics", "parallelogram rule", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"description": "<p>Use the parallelogram rule to solve a force triangle.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Two forces are used to pull a stake from the ground as shown. &nbsp;</p>\n<p>{geogebra_applet('keqyzya4',[theta: theta + \"&deg;\", textA: '\"' + A + \"\\\\text\\{ \" + units + '\\}\"',textB: '\"' + B + \"\\\\text\\{ \" + units + '\\}\"'])}</p>\n<p>Use the parallelogram rule and trigonometry to find the angle $\\alpha$ which makes the resultant of the two forces vertical, and the corresponding magnitude of the resultant.</p>", "advice": "<p>1. Draw a triangle or parallellogram representing the situation, and let</p>\n<p style=\"padding-left: 40px;\">$ A = \\var{qty(A,units)}$, &nbsp;$ B = \\var{qty(B,units)}$ and $\\theta =\\var{theta}&deg;$.</p>\n<p style=\"padding-left: 40px;\"><img src=\"resources/question-resources/triangle_j1bJHMI.svg\"/></p>\n<p style=\"padding-left: 40px;\">(diagram not to scale)</p>\n<p>2. Use Law of Sines to find angle $\\alpha$.</p>\n<p style=\"padding-left: 40px;\">$\\dfrac{B}{\\sin \\alpha} = \\dfrac{A}{\\sin\\theta}$</p>\n<p style=\"padding-left: 40px;\">$\\dfrac{\\var{B}}{\\sin \\alpha} = \\dfrac{\\var{A}}{\\sin (\\var{theta}&deg;)}$</p>\n<p style=\"padding-left: 40px;\">$\\alpha = \\var{precround(alpha,1)}&deg;$</p>\n<p>3. Find remaining angle in triangle</p>\n<p style=\"padding-left: 40px;\">$\\phi = 180&deg; - \\alpha - \\beta = \\var{precround(phi,1)}&nbsp;&deg;$</p>\n<p>4. Use Law of Cosines to find $R$.</p>\n<p style=\"padding-left: 40px;\">$R^2 =A^2 + B^2 - 2 A B \\cos \\phi$</p>\n<p style=\"padding-left: 40px;\">$R^2 = \\var{A}^2 + \\var{B}^2 - 2 A B \\cos \\var{precround(phi,1)}&deg;$</p>\n<p style=\"padding-left: 40px;\">$ R = \\var{precround(qty(R,units),2)}$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_applet('keqyzya4',[theta: theta + \"\u00b0\", \n    textA: '\"' + A + \"\\\\text\\{ \" + units + '\\}\"',\n    textB: '\"' + B + \"\\\\text\\{ \" + units + '\\}\"'])", "description": "<p>not used because this method doesn't resume correctly</p>", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "random(25..55) ", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "random(10..60#5)", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "random(10..60#5)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "\"lb\"", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Unnamed group", "definition": "degrees(arcsin(B/A sin(radians(theta))))", "description": "", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Unnamed group", "definition": "A cos(radians(alpha)) + B cos(radians(theta))", "description": "", "templateType": "anything", "can_override": false}, "phi": {"name": "phi", "group": "Unnamed group", "definition": "180-alpha-theta", "description": "", "templateType": "anything", "can_override": false}, "R'": {"name": "R'", "group": "Unnamed group", "definition": "sqrt(A^2 + B^2 - 2 A B cos(radians(phi)))", "description": "<p>Check using law of cosines</p>", "templateType": "anything", "can_override": false}, "check": {"name": "check", "group": "Unnamed group", "definition": "R=R'", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "A<>B and\nB/A sin(radians(theta)) < 1", "maxRuns": 100}, "ungrouped_variables": ["applet", "theta", "A", "B", "units"], "variable_groups": [{"name": "Unnamed group", "variables": ["alpha", "R", "phi", "R'", "check"]}], "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": "<p>$\\alpha = $ [[0]]&nbsp; &nbsp;</p>\n<p>$R = $ [[1]]</p>", "gaps": [{"type": "angle-quantity-from-reference", "useCustomName": true, "customName": "$\\alpha$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correct_quantity": "precround(qty(alpha,'deg'),2)", "right": "0.2", "restrict_angle": true, "C1": "75", "close": "1.0", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "R", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(R,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vector addition: parallelogram rule", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "<p>Adjusts all angles to 0 &lt; $\\theta$ &lt; 360.</p>\n<p>Accepts '&deg;' and 'deg' as units.</p>\n<p>Penalizes if not close enough or no units.</p>\n<p>90&deg; = -270&deg; = 450&deg;</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['expected_answer']) ", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "original_student_scalar:\nmatchnumber(studentAnswer,['plain','en'])[1]\n\nstudent_scalar:\nmod(original_student_scalar,360)\n\n\nstudent_unit:\nstudentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]\n\ninterpreted_unit:\nif(trim(student_unit)='\u00b0','deg',student_unit)\n\ninterpreted_answer:\nqty(mod(student_scalar,360),'deg')\n\nclose:\nwithintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))\n\ncorrect_scalar:\nmod(scalar(settings['expected_answer']),360)\n\nright:\nwithintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))\n\ngood_unit:\nsame(qty(1,interpreted_unit),qty(1,'deg'))\n\nmark:\nassert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))", "marking_notes": [{"name": "original_student_scalar", "description": "<p>Retuns the scalar part of students answer (which is a quantity) as a number.</p>", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "<p>Normalize angle with mod 360</p>", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "<p>matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"</p>", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "<p>Allows student to use degree symbol or 'deg' for units.</p>", "definition": "if(trim(student_unit)='\u00b0','deg',student_unit)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(mod(student_scalar,360),'deg')"}, {"name": "close", "description": "", "definition": "withintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))"}, {"name": "correct_scalar", "description": "<p>Normalize expected_answer with mod 360</p>", "definition": "mod(scalar(settings['expected_answer']),360)"}, {"name": "right", "description": "", "definition": "withintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))"}, {"name": "good_unit", "description": "", "definition": "same(qty(1,interpreted_unit),qty(1,'deg'))"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "assert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))"}], "settings": [{"name": "expected_answer", "label": "Expected Answer", "help_url": "", "hint": "Expected angle as a quantity.", "input_type": "code", "default_value": "qty(30,'deg')", "evaluate": true}, {"name": "unit_penalty", "label": "Unit penalty", "help_url": "", "hint": "Penalty for not including degree sign or 'deg'.", "input_type": "percent", "default_value": "20"}, {"name": "close_penalty", "label": "Close Penalty", "help_url": "", "hint": "Penalty for close answer.", "input_type": "percent", "default_value": "20"}, {"name": "close_tol", "label": "Close", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked close. &nbsp;&nbsp;", "input_type": "code", "default_value": "0.5", "evaluate": false}, {"name": "right_tol", "label": "Right ", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked correct. &nbsp;", "input_type": "code", "default_value": "0.1", "evaluate": false}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"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": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(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\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "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": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "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"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["mechanics, statics, parallelogram rule, vector addition"], "metadata": {"description": "<p>Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet('udgn8s84',['A_x':&nbsp;Ax&nbsp;,&nbsp;'A_y':&nbsp;Ay,&nbsp;'&theta;_B':&nbsp;dirB + '&deg;' ])}</p>\n<p>Forces $\\mathbf{A}$ and $\\mathbf{B}$ point in the directions shown and have magnitudes $A &nbsp;= \\var{qty(2 FB, units)}$ and $B = \\var{qty(FB,units)}$.</p>\n<p><strong>Graphical Solution:</strong> Using a ruler and protractor, carefully draw a neat, labeled, accurately scaled parallelogram representing the vector addition $\\mathbf{R} = \\mathbf{A}+\\mathbf{B}$. Based on your scaled diagram, estimate the magnitude of resultant and its direction from positive $x$-axis.</p>\n<p><strong>Exact Solution:</strong> Let the three angles inside the triangle be called $\\theta_A$, $\\theta_B$, and $\\theta_R$, where the subscripts are the names of the sides opposite, and then use trigonometry to find the angles and the magnitude of the resultant exactly.</p>", "advice": "<p>Procedure:</p>\n<ol>\n<li>Draw a neat diagram and label the unknown side and angles.</li>\n<li>Determine the angle opposite the&nbsp;unknown force $\\textbf{R}$.</li>\n<li>Use law of cosines&nbsp;to determine the magnitude $|\\textbf{R}|$</li>\n<li>Use either the law of sines or cosines to determine the other two angles.</li>\n<li>Use the angles you have found to determine the direction of force&nbsp;$\\textbf{R}$ from the <em>x</em>-axis.</li>\n</ol>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"thetaR": {"name": "thetaR", "group": "Ungrouped variables", "definition": "loc(R,A,B)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Results", "definition": "2 FB vector(cos(radians(dirA)),sin(radians(dirA)))", "description": "<p>Force A</p>", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Results", "definition": "A + B", "description": "", "templateType": "anything", "can_override": false}, "thetaA": {"name": "thetaA", "group": "Ungrouped variables", "definition": "loc(A,B,R)", "description": "", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Inputs", "definition": "random(5..100#5)", "description": "<p>Magnitude of force B, &nbsp;Magnitude of A is twice this value.</p>", "templateType": "anything", "can_override": false}, "Ay": {"name": "Ay", "group": "Inputs", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "thetaB": {"name": "thetaB", "group": "Ungrouped variables", "definition": "loc(B,A,R)", "description": "", "templateType": "anything", "can_override": false}, "dirA": {"name": "dirA", "group": "Inputs", "definition": "degrees(atan2(Ay,Ax))", "description": "<p>Direction of force A, based on Ax and Ay.</p>", "templateType": "anything", "can_override": false}, "Ax": {"name": "Ax", "group": "Inputs", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random(['lb','N','kN'])", "description": "", "templateType": "anything", "can_override": false}, "dirB": {"name": "dirB", "group": "Inputs", "definition": "(random(0..360#15 except 0..360#45))", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Results", "definition": "FB vector(cos(radians(dirB)),sin(radians(dirB)))\n", "description": "<p style=\"padding-left: 30px;\">Force B</p>", "templateType": "anything", "can_override": false}, "dirR": {"name": "dirR", "group": "Results", "definition": "degrees(atan2(R[1],r[0]))", "description": "", "templateType": "anything", "can_override": false}, "ang": {"name": "ang", "group": "Ungrouped variables", "definition": "(a)-> precround(qty(a, \"deg\"),1)", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "true", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(dirA- dirB) > 25 and abs(dirA-dirB) < 160 ", "maxRuns": "200"}, "ungrouped_variables": ["thetaA", "thetaB", "thetaR", "ang", "debug"], "variable_groups": [{"name": "Inputs", "variables": ["FB", "dirB", "Ax", "Ay", "dirA", "units"]}, {"name": "Results", "variables": ["A", "B", "R", "dirR"]}], "functions": {"direction": {"parameters": [["v", "vector"]], "type": "number", "language": "javascript", "definition": "return Math.atan2(v[1],v[0])\n"}, "loc": {"parameters": [["A", "vector"], ["B", "vector"], ["C", "vector"]], "type": "number", "language": "jme", "definition": "degrees(arccos((abs(A)^2-abs(B)^2-abs(C)^2)/(-2 * abs(B) * abs(C))))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Graphical Solution", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "\n    ", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<ol></ol>\n<p>$|\\mathbf{R}|$ &nbsp;= [[1]]</p>\n<p>$\\theta_x$ = [[0]]</p>", "gaps": [{"type": "angle", "useCustomName": true, "customName": "$\\theta_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "ang(dirR)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$R$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "precround(qty(abs(R),units),0)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Trigonometric (Exact) Solution", "marks": 0, "scripts": {"mark": {"script": "//numbasGGBApplet0.setVisible('show',true);\n//numbasGGBApplet0.setValue('show',true);", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\theta_A =$&nbsp;[[0]]&nbsp;</p>\n<p>$\\theta_B = $[[1]]</p>\n<p>$\\theta_R =$ [[2]]&nbsp;</p>\n<p>$|\\mathbf{R}| =$ [[3]]&nbsp;</p>\n<p></p>", "gaps": [{"type": "angle", "useCustomName": true, "customName": "$\\theta_A$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "ang(thetaA)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "angle", "useCustomName": true, "customName": "$\\theta_B$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "ang(thetaB)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "angle", "useCustomName": true, "customName": "$\\theta_R$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "ang(thetaR)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$|R|$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(R),units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "typeendtoleave": false, "startpassword": "", "autoSubmit": true, "allowAttemptDownload": false, "downloadEncryptionKey": "kp77", "showresultspage": "oncompletion"}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"enterreviewmodeimmediately": true, "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showpartfeedbackmessageswhen": "always", "showexpectedanswerswhen": "inreview", "showadvicewhen": "inreview", "allowrevealanswer": true, "intro": "", "end_message": "", "results_options": {"printquestions": false, "printadvice": true}, "feedbackmessages": [], "reviewshowexpectedanswer": true, "showanswerstate": true, "reviewshowfeedback": true, "showactualmark": true, "showtotalmark": true, "reviewshowscore": true, "reviewshowadvice": true}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "extensions": ["geogebra", "quantities"], "custom_part_types": [{"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": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "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": "switch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "evaluate": true}, {"name": "right", "label": "Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"name": "close", "label": " Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "<p>Adjusts all angles to 0 &lt; $\\theta$ &lt; 360.</p>\n<p>Accepts '&deg;' and 'deg' as units.</p>\n<p>Penalizes if not close enough or no units.</p>\n<p>90&deg; = -270&deg; = 450&deg;</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['expected_answer']) ", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "original_student_scalar:\nmatchnumber(studentAnswer,['plain','en'])[1]\n\nstudent_scalar:\nmod(original_student_scalar,360)\n\n\nstudent_unit:\nstudentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]\n\ninterpreted_unit:\nif(trim(student_unit)='\u00b0','deg',student_unit)\n\ninterpreted_answer:\nqty(mod(student_scalar,360),'deg')\n\nclose:\nwithintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))\n\ncorrect_scalar:\nmod(scalar(settings['expected_answer']),360)\n\nright:\nwithintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))\n\ngood_unit:\nsame(qty(1,interpreted_unit),qty(1,'deg'))\n\nmark:\nassert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))", "marking_notes": [{"name": "original_student_scalar", "description": "<p>Retuns the scalar part of students answer (which is a quantity) as a number.</p>", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "<p>Normalize angle with mod 360</p>", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "<p>matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"</p>", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "<p>Allows student to use degree symbol or 'deg' for units.</p>", "definition": "if(trim(student_unit)='\u00b0','deg',student_unit)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(mod(student_scalar,360),'deg')"}, {"name": "close", "description": "", "definition": "withintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))"}, {"name": "correct_scalar", "description": "<p>Normalize expected_answer with mod 360</p>", "definition": "mod(scalar(settings['expected_answer']),360)"}, {"name": "right", "description": "", "definition": "withintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))"}, {"name": "good_unit", "description": "", "definition": "same(qty(1,interpreted_unit),qty(1,'deg'))"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "assert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))"}], "settings": [{"name": "expected_answer", "label": "Expected Answer", "help_url": "", "hint": "Expected angle as a quantity.", "input_type": "code", "default_value": "qty(30,'deg')", "evaluate": true}, {"name": "unit_penalty", "label": "Unit penalty", "help_url": "", "hint": "Penalty for not including degree sign or 'deg'.", "input_type": "percent", "default_value": "20"}, {"name": "close_penalty", "label": "Close Penalty", "help_url": "", "hint": "Penalty for close answer.", "input_type": "percent", "default_value": "20"}, {"name": "close_tol", "label": "Close", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked close. &nbsp;&nbsp;", "input_type": "code", "default_value": "0.5", "evaluate": false}, {"name": "right_tol", "label": "Right ", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked correct. &nbsp;", "input_type": "code", "default_value": "0.1", "evaluate": false}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"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": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(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\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "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": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "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"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/triangle_j1bJHMI.svg", "/srv/numbas/media/question-resources/triangle_j1bJHMI.svg"]]}