![](\"resources/question-resources/centroids_zSOgoBb.png\")
Homework set. Find centroids of shapes by dividing them into simple subshapes.
", "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": "Centroid of parts", "extensions": ["geogebra", "quantities", "sheets"], "custom_part_types": [{"source": {"pk": 242, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/242/edit"}, "name": "Spreadsheet", "short_name": "spreadsheet", "description": "An editable spreadsheet. Ranges of cells can be disabled, and you can specify ranges of cells to be marked. A cell is marked correct if its value is equal to the value in the expected answer spreadsheet.
", "help_url": "", "input_widget": "spread-sheet", "input_options": {"correctAnswer": "settings[\"correct_answer\"]", "hint": {"static": true, "value": ""}, "initial_sheet": {"static": false, "value": "disable_cells(settings[\"initial_sheet\"], settings[\"disable_ranges\"])"}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(sum(mark_ranges)=0,\n incorrect(),\n apply(mark_ranges)\n)\n\ninterpreted_answer:\nstudentAnswer\n\nrange_cells:\nmap(parse_range(ref),ref,values(settings[\"mark_ranges\"]))\n\ntotal_cells:\nlen(flatten(range_cells))\n\nrange_weights:\nswitch(\n settings[\"marking_method\"]=\"per_cell\",\n map(len(r)/total_cells, r, range_cells),\n // otherwise, mark per range\n repeat(1/len(range_cells), len(range_cells))\n)\n\nmark_ranges:\nmap(\n let(\n range_credit,\n sum(map(\n let(\n correctCellString, correctAnswer[c],\n correctCellNumber, parsenumber(correctCellString, notation_styles),\n studentCellString, studentAnswer[c],\n studentCellNumber, parsenumber(studentCellString, notation_styles),\n award(\n 1/len(cells), \n switch(\n correctCellString=\"\",\n isnan(studentCellNumber) or studentCellString=\"\",\n isnan(correctCellNumber),\n lower(correctCellString) = lower(studentCellString)\n ,\n abs(studentCellNumber - if(isnan(correctCellNumber),0,correctCellNumber)) <= settings[\"tolerance\"]\n )\n )\n ),\n c,\n cells\n )),\n message,\n switch(\n range_credit=0,\n if(len(cells)=1, \"This entry is incorrect.\", \"All entries in this range are incorrect.\"),\n range_credit=1,\n if(len(cells)=1, \"This entry is correct.\", \"All entries in this range are correct.\"),\n //otherwise\n \"Some entries in this range are correct.\"\n ),\n assert(len(cells)=0, add_credit(range_credit*w, \"{name}: \"+message)); \n range_credit\n ),\n [cells,w,name],\n zip(range_cells, range_weights, keys(settings[\"mark_ranges\"]))\n)\n\nnotation_styles:\n[\"plain\",\"si-en\"]\n\ncorrectAnswer:\nsettings[\"correct_answer\"]", "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": "if(sum(mark_ranges)=0,\n incorrect(),\n apply(mark_ranges)\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer"}, {"name": "range_cells", "description": "For each range to be marked, the addresses of the cells in that range.
", "definition": "map(parse_range(ref),ref,values(settings[\"mark_ranges\"]))"}, {"name": "total_cells", "description": "The total number of cells to be marked. Cells in overlapping ranges will be counted once for each range they're in.
", "definition": "len(flatten(range_cells))"}, {"name": "range_weights", "description": "The weight of each range, as a proportion of the available credit.
", "definition": "switch(\n settings[\"marking_method\"]=\"per_cell\",\n map(len(r)/total_cells, r, range_cells),\n // otherwise, mark per range\n repeat(1/len(range_cells), len(range_cells))\n)"}, {"name": "mark_ranges", "description": "Mark each of the ranges specified by the question author.
", "definition": "map(\n let(\n range_credit,\n sum(map(\n let(\n correctCellString, correctAnswer[c],\n correctCellNumber, parsenumber(correctCellString, notation_styles),\n studentCellString, studentAnswer[c],\n studentCellNumber, parsenumber(studentCellString, notation_styles),\n award(\n 1/len(cells), \n switch(\n correctCellString=\"\",\n isnan(studentCellNumber) or studentCellString=\"\",\n isnan(correctCellNumber),\n lower(correctCellString) = lower(studentCellString)\n ,\n abs(studentCellNumber - if(isnan(correctCellNumber),0,correctCellNumber)) <= settings[\"tolerance\"]\n )\n )\n ),\n c,\n cells\n )),\n message,\n switch(\n range_credit=0,\n if(len(cells)=1, \"This entry is incorrect.\", \"All entries in this range are incorrect.\"),\n range_credit=1,\n if(len(cells)=1, \"This entry is correct.\", \"All entries in this range are correct.\"),\n //otherwise\n \"Some entries in this range are correct.\"\n ),\n assert(len(cells)=0, add_credit(range_credit*w, \"{name}: \"+message)); \n range_credit\n ),\n [cells,w,name],\n zip(range_cells, range_weights, keys(settings[\"mark_ranges\"]))\n)"}, {"name": "notation_styles", "description": "Accepted number notation styles for a value in an individual cell.
", "definition": "[\"plain\",\"si-en\"]"}, {"name": "correctAnswer", "description": "", "definition": "settings[\"correct_answer\"]"}], "settings": [{"name": "initial_sheet", "label": "Initial sheet", "help_url": "", "hint": "Aspreadsheet object giving the initial state of the sheet that the student should fill in.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "correct_answer", "label": "Correct answer", "help_url": "", "hint": "A spreadsheet object representing a correct answer to the part.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "disable_ranges", "label": "Ranges to disable", "help_url": "", "hint": "A list of cell or range references, denoting the cells that should not be editable.", "input_type": "code", "default_value": "[]", "evaluate": true}, {"name": "mark_ranges", "label": "Ranges to mark", "help_url": "", "hint": "A dictionary of cell or range references, mapping names to ranges of cells, denoting the cells that should be compared for equality with the expected answer.", "input_type": "code", "default_value": "dict()", "evaluate": true}, {"name": "marking_method", "label": "Marking method", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "per_cell", "choices": [{"value": "per_cell", "label": "Each cell has the same weight"}, {"value": "per_range", "label": "Each range has the same weight"}]}, {"name": "tolerance", "label": "Allowed margin of error", "help_url": "", "hint": "", "input_type": "code", "default_value": "0", "evaluate": true}], "public_availability": "always", "published": true, "extensions": ["sheets"]}], "resources": ["question-resources/centroids.png", "question-resources/centroids_3A0rXlj.png", "question-resources/centroids_zSOgoBb.png"], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": [], "metadata": {"description": "Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "Fill the table with the coordinates of the centroids of the three shapes. Grid units are $[\\var{units}]$.
\n{applet}
\n{answer_table}
", "advice": "For a rectangle, the centroid is at the geometric center.
\nFor a right triangle, divide the base and height into thirds. The centroid is located at the intersection point nearest to the right angle.
\nFor a semicircle, the centroid is located on the axis of symmetry, a distance of $\\frac{4r}{3\\pi}$ from the straight edge.
\n\n
table filled with centroid coordinates
", "templateType": "anything", "can_override": false}, "dist": {"name": "dist", "group": "Ungrouped variables", "definition": "//(V) -> [siground(qty(V[0], units),3),siground(qty(V[1], units),3)]\n(V) -> [siground(V[0],3),siground(V[1],3)]", "description": "input vector, output rounded vector of quantities
", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "inputs", "definition": "[['R_1',R1],['R_2',R2],['T_1',T1],['T_2',T2],['C_1',C1],['C_2',C2]]", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "inputs", "definition": "geogebra_applet('xjjm7qqr',params)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "(R1-R2)[0] >= 2 and (R1-R2)[1] >= 2 and \n(T1-T2)[0] >= 2 and (T1-T2)[1] >= 2 and \nC1<>C2 and abs(C1-C2) > 2\n\n", "maxRuns": "200"}, "ungrouped_variables": ["units", "RC", "TC", "CC", "debug", "centroid_table", "answer_table", "dist"], "variable_groups": [{"name": "inputs", "variables": ["R1", "R2", "T1", "T2", "C1", "C2", "params", "applet"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "spreadsheet", "useCustomName": false, "customName": "", "marks": "30", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Don't include units in table values.
", "settings": {"initial_sheet": "centroid_table", "correct_answer": "answer_table", "disable_ranges": "[\"A1:C1\", \"A1:A4\"]", "mark_ranges": "[\"Rectangle\": \"B2:C2\", \"Triangle\": \"B3:C3\", \"Circle\": \"B4:C4\"]", "marking_method": "per_cell", "tolerance": "0.1"}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Centroid of a composite area: shape with hole", "extensions": ["geogebra", "quantities", "sheets"], "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.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,An editable spreadsheet. Ranges of cells can be disabled, and you can specify ranges of cells to be marked. A cell is marked correct if its value is equal to the value in the expected answer spreadsheet.
", "help_url": "", "input_widget": "spread-sheet", "input_options": {"correctAnswer": "settings[\"correct_answer\"]", "hint": {"static": true, "value": ""}, "initial_sheet": {"static": false, "value": "disable_cells(settings[\"initial_sheet\"], settings[\"disable_ranges\"])"}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(sum(mark_ranges)=0,\n incorrect(),\n apply(mark_ranges)\n)\n\ninterpreted_answer:\nstudentAnswer\n\nrange_cells:\nmap(parse_range(ref),ref,values(settings[\"mark_ranges\"]))\n\ntotal_cells:\nlen(flatten(range_cells))\n\nrange_weights:\nswitch(\n settings[\"marking_method\"]=\"per_cell\",\n map(len(r)/total_cells, r, range_cells),\n // otherwise, mark per range\n repeat(1/len(range_cells), len(range_cells))\n)\n\nmark_ranges:\nmap(\n let(\n range_credit,\n sum(map(\n let(\n correctCellString, correctAnswer[c],\n correctCellNumber, parsenumber(correctCellString, notation_styles),\n studentCellString, studentAnswer[c],\n studentCellNumber, parsenumber(studentCellString, notation_styles),\n award(\n 1/len(cells), \n switch(\n correctCellString=\"\",\n isnan(studentCellNumber) or studentCellString=\"\",\n isnan(correctCellNumber),\n lower(correctCellString) = lower(studentCellString)\n ,\n abs(studentCellNumber - if(isnan(correctCellNumber),0,correctCellNumber)) <= settings[\"tolerance\"]\n )\n )\n ),\n c,\n cells\n )),\n message,\n switch(\n range_credit=0,\n if(len(cells)=1, \"This entry is incorrect.\", \"All entries in this range are incorrect.\"),\n range_credit=1,\n if(len(cells)=1, \"This entry is correct.\", \"All entries in this range are correct.\"),\n //otherwise\n \"Some entries in this range are correct.\"\n ),\n assert(len(cells)=0, add_credit(range_credit*w, \"{name}: \"+message)); \n range_credit\n ),\n [cells,w,name],\n zip(range_cells, range_weights, keys(settings[\"mark_ranges\"]))\n)\n\nnotation_styles:\n[\"plain\",\"si-en\"]\n\ncorrectAnswer:\nsettings[\"correct_answer\"]", "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": "if(sum(mark_ranges)=0,\n incorrect(),\n apply(mark_ranges)\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer"}, {"name": "range_cells", "description": "For each range to be marked, the addresses of the cells in that range.
", "definition": "map(parse_range(ref),ref,values(settings[\"mark_ranges\"]))"}, {"name": "total_cells", "description": "The total number of cells to be marked. Cells in overlapping ranges will be counted once for each range they're in.
", "definition": "len(flatten(range_cells))"}, {"name": "range_weights", "description": "The weight of each range, as a proportion of the available credit.
", "definition": "switch(\n settings[\"marking_method\"]=\"per_cell\",\n map(len(r)/total_cells, r, range_cells),\n // otherwise, mark per range\n repeat(1/len(range_cells), len(range_cells))\n)"}, {"name": "mark_ranges", "description": "Mark each of the ranges specified by the question author.
", "definition": "map(\n let(\n range_credit,\n sum(map(\n let(\n correctCellString, correctAnswer[c],\n correctCellNumber, parsenumber(correctCellString, notation_styles),\n studentCellString, studentAnswer[c],\n studentCellNumber, parsenumber(studentCellString, notation_styles),\n award(\n 1/len(cells), \n switch(\n correctCellString=\"\",\n isnan(studentCellNumber) or studentCellString=\"\",\n isnan(correctCellNumber),\n lower(correctCellString) = lower(studentCellString)\n ,\n abs(studentCellNumber - if(isnan(correctCellNumber),0,correctCellNumber)) <= settings[\"tolerance\"]\n )\n )\n ),\n c,\n cells\n )),\n message,\n switch(\n range_credit=0,\n if(len(cells)=1, \"This entry is incorrect.\", \"All entries in this range are incorrect.\"),\n range_credit=1,\n if(len(cells)=1, \"This entry is correct.\", \"All entries in this range are correct.\"),\n //otherwise\n \"Some entries in this range are correct.\"\n ),\n assert(len(cells)=0, add_credit(range_credit*w, \"{name}: \"+message)); \n range_credit\n ),\n [cells,w,name],\n zip(range_cells, range_weights, keys(settings[\"mark_ranges\"]))\n)"}, {"name": "notation_styles", "description": "Accepted number notation styles for a value in an individual cell.
", "definition": "[\"plain\",\"si-en\"]"}, {"name": "correctAnswer", "description": "", "definition": "settings[\"correct_answer\"]"}], "settings": [{"name": "initial_sheet", "label": "Initial sheet", "help_url": "", "hint": "Aspreadsheet object giving the initial state of the sheet that the student should fill in.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "correct_answer", "label": "Correct answer", "help_url": "", "hint": "A spreadsheet object representing a correct answer to the part.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "disable_ranges", "label": "Ranges to disable", "help_url": "", "hint": "A list of cell or range references, denoting the cells that should not be editable.", "input_type": "code", "default_value": "[]", "evaluate": true}, {"name": "mark_ranges", "label": "Ranges to mark", "help_url": "", "hint": "A dictionary of cell or range references, mapping names to ranges of cells, denoting the cells that should be compared for equality with the expected answer.", "input_type": "code", "default_value": "dict()", "evaluate": true}, {"name": "marking_method", "label": "Marking method", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "per_cell", "choices": [{"value": "per_cell", "label": "Each cell has the same weight"}, {"value": "per_range", "label": "Each range has the same weight"}]}, {"name": "tolerance", "label": "Allowed margin of error", "help_url": "", "hint": "", "input_type": "code", "default_value": "0", "evaluate": true}], "public_availability": "always", "published": true, "extensions": ["sheets"]}], "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": ["centroids", "composite area method", "mechanics", "Mechanics", "statics", "Statics"], "metadata": {"description": "Find the centroid of a shape made from a rectangle, triangle, and circle.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius]])}
\nComplete the table below and detemine the coordinates of the centroid of the composite shape shown.
\nConsider the shape to be made up of a {if (m=1,'large','')} rectangle {if (m=0, 'plus a triangle', 'with a triangle removed')} with a {if(random(true,false), radius + \" \" + units + \" radius\" , 2 * radius + \" \" + units + \" diameter\")} circular hole centered at ({(center+A)[0]}, {(center+A)[1]}).
\n{table_add_q}
", "advice": "{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius],['visibility',m]])}
\n1. Divide the shape into three subshapes as described in the problem statement.
\n2. Know how to set up a table to collect the information, since it will not normally be provided.
\n3. Determine and enter the area and centroidal coordinates for each subshape into the table
\n$\\qquad A_i, \\bar{x}_i,\\bar{y}_i$
\n4. Multiply area by the centroidal coordinates to get the moment of areas for the pieces.
\n$\\qquad (Q_x)_i = A_i\\bar{y}_i ,\\quad(Q_y)_i=A_i\\bar{x}_i$.
\n5. Sum columns 3, 6 and 7 to find the total area and moments of area: $ A, Q_x, Q_y$
\n6. Find answers with
\n$\\qquad \\bar{x} = \\dfrac{Q_y}{A} =\\dfrac{\\Sigma A_i \\bar{x}_i}{\\Sigma A_i} = \\dfrac{\\var{siground(Q_total[1],3)}}{\\var{siground(area_total,3)}} = \\var{siground(centroid[0],3)}\\, \\var{units}$
\n$\\qquad \\bar{y} = \\dfrac{Q_x}{A} = \\dfrac{\\Sigma A_i \\bar{y}_i}{\\Sigma A_i}= \\dfrac{\\var{siground(Q_total[0],3)}}{\\var{siground(area_total,3)}}= \\var{siground(centroid[1],3)}\\, \\var{units} $
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"ht": {"name": "ht", "group": "Input values", "definition": "random(3..9#3)", "description": "\"height\" of triangle
\nhorizontal for n = 4,5,6,10,11,12
\nvertical for n = 1,2,3,7,8,9
", "templateType": "anything", "can_override": false}, "C_rect": {"name": "C_rect", "group": "centroids", "definition": "[vector(b1/2,h1/2) + A,\n if(n in [1,2,3], vector(b1/2,(h1-ht)/2)+A,\n if(n in [4,5,6], vector((b1+ht)/2,h1/2)+A,\n if(n in [7,8,9], vector(b1/2,(h1+ht)/2)+A,\n vector((b1-ht)/2,h1/2)+A)))] ", "description": "", "templateType": "anything", "can_override": false}, "C_circ": {"name": "C_circ", "group": "centroids", "definition": "[center +A ,center +A]", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Input values", "definition": "random('in', 'cm', 'ft' )", "description": "Offset of bottom right corner from originl
", "templateType": "anything", "can_override": false}, "area_circ": {"name": "area_circ", "group": "Calculated areas", "definition": "[- pi * radius^2, - pi* radius^2]", "description": "", "templateType": "anything", "can_override": false}, "area_total": {"name": "area_total", "group": "Calculated areas", "definition": "area_rect[0]+area_tri[0]+area_circ[0]", "description": "", "templateType": "anything", "can_override": false}, "area_tri": {"name": "area_tri", "group": "Calculated areas", "definition": "[if(n in [1,2,3,7,8,9], b1*ht/2,h1*ht/2),\n-if(n in [1,2,3,7,8,9], b1*ht/2,h1*ht/2)]", "description": "", "templateType": "anything", "can_override": false}, "center": {"name": "center", "group": "Input values", "definition": "vector(b1/2,h1/2) + random(0..3) *\nvector(if(n<=3,[0,-1],\nif(n<=6,[1,0],\nif(n<=9,[0,1],\n[-1,0]))))\n\n\n\n\n", "description": "center of the circle measured from bottom left of the rectangle
", "templateType": "anything", "can_override": false}, "Q_circ": {"name": "Q_circ", "group": "moments of area", "definition": "area_circ[m] * vector(C_circ[m][1],C_circ[m][0])", "description": "", "templateType": "anything", "can_override": false}, "radius": {"name": "radius", "group": "Input values", "definition": "random(1..(min(h1-1,b1-1)/2)#0.5)", "description": "radius of the circle
", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Input values", "definition": "-vector(random([0,0],[b1,0],[b1,h1],[0,h1],[b1/2,h1/2],[0,h1/2],[center[0],center[1]]))", "description": "This offsets the shape to one of the corners of the rect, the center of the rect, or the center of the circle.
", "templateType": "anything", "can_override": false}, "h1": {"name": "h1", "group": "Input values", "definition": "random(4..12#2)", "description": "vertical height of rectangle
", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Input values", "definition": "random(4..12#2)", "description": "horizontal base of rectangle
", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Input values", "definition": "random(1 .. 12#1)", "description": "Selects the position of the triangle, index gives vertex location
\n| \n | 9 | \n8 | \n7 | \n\n |
| 10 | \n\n | \n | \n | 6 | \n
| 11 | \n\n | rectangle | \n\n | 5 | \n
| 12 | \n\n | \n | \n | 4 | \n
| \n | 1 | \n2 | \n3 | \n\n |
determines location of centroid of triangle based on location and method
returns array of centroid coordinates, first term for m=0
This is the method used to solve the problem:
\nm=0: small rectangle + triangle - circle
\nm=1: big rectangle - triangle - circle
\nwhen n is in [2,5,8,11], use method 0, becauses otherwise it would require 2 negative triangles.
", "templateType": "anything", "can_override": false}, "Q_rect": {"name": "Q_rect", "group": "moments of area", "definition": "area_rect[m] * vector(C_rect[m][1],C_rect[m][0])", "description": "[Q_x,Q_y]
", "templateType": "anything", "can_override": false}, "area_rect": {"name": "area_rect", "group": "Calculated areas", "definition": "[b1*h1,if(n in [1,2,3,7,8,9],b1*(h1+ht),h1*(b1+ht))]", "description": "", "templateType": "anything", "can_override": false}, "centroid": {"name": "centroid", "group": "moments of area", "definition": "vector(Q_total[1]/area_total,Q_total[0]/area_total)", "description": "", "templateType": "anything", "can_override": false}, "Q_tri": {"name": "Q_tri", "group": "moments of area", "definition": "area_tri[m] * vector(C_tri[m][1],C_tri[m][0])", "description": "", "templateType": "anything", "can_override": false}, "Q_total": {"name": "Q_total", "group": "moments of area", "definition": "Q_rect+Q_tri+Q_circ", "description": "", "templateType": "anything", "can_override": false}, "blank_table": {"name": "blank_table", "group": "Ungrouped variables", "definition": "spreadsheet_from_base64_file(safe(\"centroid_table.xlsx\"), 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"description": "", "templateType": "spreadsheet", "can_override": false}, "params": {"name": "params", "group": "Ungrouped variables", "definition": "[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius]]", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_applet('fcfsjuv9',params)", "description": "", "templateType": "anything", "can_override": false}, "table_add_centroids": {"name": "table_add_centroids", "group": "Ungrouped variables", "definition": "fill_range(table_add_areas, \"D2:E4\", map((x)->[siground(x[m][0],3),siground(x[m][1],3)], [C_rect,c_tri, c_circ]))", "description": "", "templateType": "anything", "can_override": false}, "table_add_areas": {"name": "table_add_areas", "group": "Ungrouped variables", "definition": "fill_range(blank_table,\"C2:C5\",map(v->siground(v[m],3), [area_rect,area_tri, area_circ])+ [precround(area_total,2)])\n", "description": "", "templateType": "anything", "can_override": false}, "table_add_q": {"name": "table_add_q", "group": "Ungrouped variables", "definition": "fill_range(table_add_centroids, \"F2:G5\", map((x)->[siground(x[1],3),siground(x[0],3)],[Q_rect,Q_tri,Q_circ])+ [list(precround(q_total,1))])", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "// tries to prevent the circle from extending beyond the perimiter.\n\nif (n<=3, center[1]-2*radius > -(h1+ht/2),\nif (n<=6, (center[0]+2*radius) < (b1+ht/2),\nif (n<=9, (center[1]+2*radius) < (h1+ht/2),\n (center[0]-2*radius) > -(b1-ht/2))))\n", "maxRuns": 100}, "ungrouped_variables": ["blank_table", "table_add_areas", "table_add_centroids", "table_add_q", "params", "applet", "debug"], "variable_groups": [{"name": "Input values", "variables": ["A", "b1", "h1", "ht", "center", "units", "radius", "n", "m"]}, {"name": "Calculated areas", "variables": ["area_rect", "area_tri", "area_circ", "area_total"]}, {"name": "centroids", "variables": ["C_rect", "C_circ", "C_tri"]}, {"name": "moments of area", "variables": ["Q_rect", "Q_tri", "Q_circ", "Q_total", "centroid"]}], "functions": {}, "preamble": {"js": "\n", "css": "table.centroid{margin-left:0;}\n\ntable.centroid td {\n width:6em; \n vertical-align:center; \n text-align:center;}\ntable.centroid *.underline {border-bottom: 2px solid black;}\n\n"}, "parts": [{"type": "spreadsheet", "useCustomName": true, "customName": "Centroid Table", "marks": "36", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"initial_sheet": "blank_table", "correct_answer": "table_add_q", "disable_ranges": "[\"A1:B5\", \"A1:G1\", \"D5:E5\"]", "mark_ranges": "[\"$A_i$\": \"C2:C4\", \"$\\\\bar{x}_i$\": \"D2:D4\", \"$\\\\bar{y}_i$\": \"E2:E4\",\"$A_i\\\\bar{x}_i$\": \"F2:F4\", \"$A_i\\\\bar{y}_i$\": \"G2:G4\", \"$A$\": \"C5\", \"$Q_y$\": \"F5\",\"$Q_x$\": \"G5\"]", "marking_method": "per_cell", "tolerance": "0.05"}}, {"type": "gapfill", "useCustomName": true, "customName": "Centroid", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\bar{x} =\\dfrac{Q_y}{A} = $ [[0]]
\n$\\bar{y} =\\dfrac{Q_x}{A} = $ [[1]]
A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,An editable spreadsheet. Ranges of cells can be disabled, and you can specify ranges of cells to be marked. A cell is marked correct if its value is equal to the value in the expected answer spreadsheet.
", "help_url": "", "input_widget": "spread-sheet", "input_options": {"correctAnswer": "settings[\"correct_answer\"]", "hint": {"static": true, "value": ""}, "initial_sheet": {"static": false, "value": "disable_cells(settings[\"initial_sheet\"], settings[\"disable_ranges\"])"}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(sum(mark_ranges)=0,\n incorrect(),\n apply(mark_ranges)\n)\n\ninterpreted_answer:\nstudentAnswer\n\nrange_cells:\nmap(parse_range(ref),ref,values(settings[\"mark_ranges\"]))\n\ntotal_cells:\nlen(flatten(range_cells))\n\nrange_weights:\nswitch(\n settings[\"marking_method\"]=\"per_cell\",\n map(len(r)/total_cells, r, range_cells),\n // otherwise, mark per range\n repeat(1/len(range_cells), len(range_cells))\n)\n\nmark_ranges:\nmap(\n let(\n range_credit,\n sum(map(\n let(\n correctCellString, correctAnswer[c],\n correctCellNumber, parsenumber(correctCellString, notation_styles),\n studentCellString, studentAnswer[c],\n studentCellNumber, parsenumber(studentCellString, notation_styles),\n award(\n 1/len(cells), \n switch(\n correctCellString=\"\",\n isnan(studentCellNumber) or studentCellString=\"\",\n isnan(correctCellNumber),\n lower(correctCellString) = lower(studentCellString)\n ,\n abs(studentCellNumber - if(isnan(correctCellNumber),0,correctCellNumber)) <= settings[\"tolerance\"]\n )\n )\n ),\n c,\n cells\n )),\n message,\n switch(\n range_credit=0,\n if(len(cells)=1, \"This entry is incorrect.\", \"All entries in this range are incorrect.\"),\n range_credit=1,\n if(len(cells)=1, \"This entry is correct.\", \"All entries in this range are correct.\"),\n //otherwise\n \"Some entries in this range are correct.\"\n ),\n assert(len(cells)=0, add_credit(range_credit*w, \"{name}: \"+message)); \n range_credit\n ),\n [cells,w,name],\n zip(range_cells, range_weights, keys(settings[\"mark_ranges\"]))\n)\n\nnotation_styles:\n[\"plain\",\"si-en\"]\n\ncorrectAnswer:\nsettings[\"correct_answer\"]", "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": "if(sum(mark_ranges)=0,\n incorrect(),\n apply(mark_ranges)\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer"}, {"name": "range_cells", "description": "For each range to be marked, the addresses of the cells in that range.
", "definition": "map(parse_range(ref),ref,values(settings[\"mark_ranges\"]))"}, {"name": "total_cells", "description": "The total number of cells to be marked. Cells in overlapping ranges will be counted once for each range they're in.
", "definition": "len(flatten(range_cells))"}, {"name": "range_weights", "description": "The weight of each range, as a proportion of the available credit.
", "definition": "switch(\n settings[\"marking_method\"]=\"per_cell\",\n map(len(r)/total_cells, r, range_cells),\n // otherwise, mark per range\n repeat(1/len(range_cells), len(range_cells))\n)"}, {"name": "mark_ranges", "description": "Mark each of the ranges specified by the question author.
", "definition": "map(\n let(\n range_credit,\n sum(map(\n let(\n correctCellString, correctAnswer[c],\n correctCellNumber, parsenumber(correctCellString, notation_styles),\n studentCellString, studentAnswer[c],\n studentCellNumber, parsenumber(studentCellString, notation_styles),\n award(\n 1/len(cells), \n switch(\n correctCellString=\"\",\n isnan(studentCellNumber) or studentCellString=\"\",\n isnan(correctCellNumber),\n lower(correctCellString) = lower(studentCellString)\n ,\n abs(studentCellNumber - if(isnan(correctCellNumber),0,correctCellNumber)) <= settings[\"tolerance\"]\n )\n )\n ),\n c,\n cells\n )),\n message,\n switch(\n range_credit=0,\n if(len(cells)=1, \"This entry is incorrect.\", \"All entries in this range are incorrect.\"),\n range_credit=1,\n if(len(cells)=1, \"This entry is correct.\", \"All entries in this range are correct.\"),\n //otherwise\n \"Some entries in this range are correct.\"\n ),\n assert(len(cells)=0, add_credit(range_credit*w, \"{name}: \"+message)); \n range_credit\n ),\n [cells,w,name],\n zip(range_cells, range_weights, keys(settings[\"mark_ranges\"]))\n)"}, {"name": "notation_styles", "description": "Accepted number notation styles for a value in an individual cell.
", "definition": "[\"plain\",\"si-en\"]"}, {"name": "correctAnswer", "description": "", "definition": "settings[\"correct_answer\"]"}], "settings": [{"name": "initial_sheet", "label": "Initial sheet", "help_url": "", "hint": "Aspreadsheet object giving the initial state of the sheet that the student should fill in.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "correct_answer", "label": "Correct answer", "help_url": "", "hint": "A spreadsheet object representing a correct answer to the part.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "disable_ranges", "label": "Ranges to disable", "help_url": "", "hint": "A list of cell or range references, denoting the cells that should not be editable.", "input_type": "code", "default_value": "[]", "evaluate": true}, {"name": "mark_ranges", "label": "Ranges to mark", "help_url": "", "hint": "A dictionary of cell or range references, mapping names to ranges of cells, denoting the cells that should be compared for equality with the expected answer.", "input_type": "code", "default_value": "dict()", "evaluate": true}, {"name": "marking_method", "label": "Marking method", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "per_cell", "choices": [{"value": "per_cell", "label": "Each cell has the same weight"}, {"value": "per_range", "label": "Each range has the same weight"}]}, {"name": "tolerance", "label": "Allowed margin of error", "help_url": "", "hint": "", "input_type": "code", "default_value": "0", "evaluate": true}], "public_availability": "always", "published": true, "extensions": ["sheets"]}], "resources": ["question-resources/centroid-t-r.ggb"], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["centroids", "first moment of area", "mechanics", "Mechanics", "statics", "Statics"], "metadata": {"description": "Find the centroid of a shape made up of a rectangle and two triangles.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "Determine the coordinates of the centroid of a polygon made up of a ({b0} $\\times$ {h0}) rectangle, {if(sign1='+', 'plus', 'minus')} a ({b1} $\\times$ {h1}) triangle, {if(sign2='+', 'plus', 'minus')} a ({b2} $\\times$ {h2}) triangle. Length units are [{units}].
\n{applet()}
\n{answer_sheet}
", "advice": "$\\qquad\\bar{x} = \\dfrac{Q_y}{A} = \\dfrac{\\Sigma A_i\\bar{x}_i}{\\Sigma A_i}= \\dfrac{\\var{siground(QT[0],4)}}{\\var{AT}} =\\var{display(xbar)}$
\n$\\qquad \\bar{y} = \\dfrac{Q_x}{A} = \\dfrac{\\Sigma A_i \\bar{y}_i}{\\Sigma A_i}= \\dfrac{\\var{siground(QT[1],4)}}{\\var{AT}} =\\var{display(ybar)}$
\n[ai xbari, ai ybari]
", "templateType": "anything", "can_override": false}, "Q1": {"name": "Q1", "group": "geometry", "definition": "a1 c1", "description": "", "templateType": "anything", "can_override": false}, "Q2": {"name": "Q2", "group": "geometry", "definition": "a2 c2", "description": "", "templateType": "anything", "can_override": false}, "QT": {"name": "QT", "group": "geometry", "definition": "Q0+Q1+Q2", "description": "", "templateType": "anything", "can_override": false}, "answer_sheet": {"name": "answer_sheet", "group": "Ungrouped variables", "definition": "fill_range(centroids_sheet,\"E2:F5\",map(v->[siground(v[0],4),siground(v[1],4)],[Q0,Q1,Q2,QT]))", "description": "", "templateType": "anything", "can_override": false}, "xbar2": {"name": "xbar2", "group": "Unnamed group", "definition": "Qt[0]/(At)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "B[1]<>A[1] and B[0]<>C[0]", "maxRuns": "100"}, "ungrouped_variables": ["A", "B", "C", "D", "units", "debug", "blank_sheet", "areas_sheet", "centroids_sheet", "answer_sheet"], "variable_groups": [{"name": "geometry", "variables": ["b0", "h0", "b2", "h1", "b1", "h2", "sign1", "sign2", "A0", "A1", "A2", "AT", "C0", "C2", "C1", "Q0", "Q1", "Q2", "QT"]}, {"name": "Unnamed group", "variables": ["xbar", "ybar", "xbar2"]}], "functions": {"Q": {"parameters": [["area", "?"], ["distance", "?"]], "type": "quantity", "language": "jme", "definition": "display(area*distance*qty(1,units)*qty(1,units)*qty(1,units))"}, "display": {"parameters": [["q", "quantity"]], "type": "quantity", "language": "jme", "definition": "string(siground(q,4))"}, "bar": {"parameters": [["coord", "number"]], "type": "quantity", "language": "jme", "definition": "display(quantity(coord,units))"}, "applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "\n// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n material_id: 'ftkm8mfx',\n //alternate method, load from file.\n //filename: \"resources/question-resources/centroid-t-r.ggb\",\n //width:400,\n //height:300\n // was geogebra_applet('ftkm8mfx',[['A',A],['B',B],['C',C]])\n}\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n var app = d.app;\n question.applet = d;\n \n \nfunction setGGBPoint(name) {\n // moves point in GGB to location of Numbas Vector Variable\n var pt = question.scope.evaluate(name).value\n app.setFixed(name,false,false);\n app.setCoords(name, pt[0], pt[1]);\n app.setFixed(name,true,true);\n }\n\n setGGBPoint(\"A\");\n setGGBPoint(\"B\");\n setGGBPoint(\"C\");\n setGGBPoint(\"D\");\n app.setVisible(\"Centroid\",false);\n \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n try{\n var app = question.applet.app;\n \n app.setVisible(\"Centroid\",true);\n \n }\n catch(err){} \n})\n\n\n\n", "css": "table.centroid{margin-left:0;}\n\ntable.centroid td {\n width:6em; \n vertical-align:center; \n text-align:center;}\ntable.centroid *.underline {border-bottom: 2px solid black;}\n\n"}, "parts": [{"type": "spreadsheet", "useCustomName": true, "customName": "Centroid Table", "marks": "36", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"initial_sheet": "blank_sheet", "correct_answer": "answer_sheet", "disable_ranges": "[\"A1:F1\", \"A1:A5\", \"C5:D5\"]", "mark_ranges": "[\"$A_i$\": \"B2:B4\", \"$\\\\bar{x}$\": \"C2:C4\", \"$\\\\bar{y}$\": \"D2:D4\", \"$A_i\\\\bar{x}_i$\": \"E2:E4\", \"$A_i\\\\bar{y}_i$\": \"F2:F4\",\"$A$\":\"B5\", \"$Q_y$\": \"E5\", \"$Q_x$\":\"F5\"]", "marking_method": "per_cell", "tolerance": "0.05"}}, {"type": "gapfill", "useCustomName": true, "customName": "Results", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\bar{x} =\\dfrac{Q_y}{A} = $ [[0]]
\n$\\bar{y} =\\dfrac{Q_x}{A} = $ [[1]]
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$\\bar{x}$", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "xbar", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$\\bar{y}$", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "ybar", "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": "", "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": true, "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", "sheets"], "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.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,An editable spreadsheet. Ranges of cells can be disabled, and you can specify ranges of cells to be marked. A cell is marked correct if its value is equal to the value in the expected answer spreadsheet.
", "help_url": "", "input_widget": "spread-sheet", "input_options": {"correctAnswer": "settings[\"correct_answer\"]", "hint": {"static": true, "value": ""}, "initial_sheet": {"static": false, "value": "disable_cells(settings[\"initial_sheet\"], settings[\"disable_ranges\"])"}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(sum(mark_ranges)=0,\n incorrect(),\n apply(mark_ranges)\n)\n\ninterpreted_answer:\nstudentAnswer\n\nrange_cells:\nmap(parse_range(ref),ref,values(settings[\"mark_ranges\"]))\n\ntotal_cells:\nlen(flatten(range_cells))\n\nrange_weights:\nswitch(\n settings[\"marking_method\"]=\"per_cell\",\n map(len(r)/total_cells, r, range_cells),\n // otherwise, mark per range\n repeat(1/len(range_cells), len(range_cells))\n)\n\nmark_ranges:\nmap(\n let(\n range_credit,\n sum(map(\n let(\n correctCellString, correctAnswer[c],\n correctCellNumber, parsenumber(correctCellString, notation_styles),\n studentCellString, studentAnswer[c],\n studentCellNumber, parsenumber(studentCellString, notation_styles),\n award(\n 1/len(cells), \n switch(\n correctCellString=\"\",\n isnan(studentCellNumber) or studentCellString=\"\",\n isnan(correctCellNumber),\n lower(correctCellString) = lower(studentCellString)\n ,\n abs(studentCellNumber - if(isnan(correctCellNumber),0,correctCellNumber)) <= settings[\"tolerance\"]\n )\n )\n ),\n c,\n cells\n )),\n message,\n switch(\n range_credit=0,\n if(len(cells)=1, \"This entry is incorrect.\", \"All entries in this range are incorrect.\"),\n range_credit=1,\n if(len(cells)=1, \"This entry is correct.\", \"All entries in this range are correct.\"),\n //otherwise\n \"Some entries in this range are correct.\"\n ),\n assert(len(cells)=0, add_credit(range_credit*w, \"{name}: \"+message)); \n range_credit\n ),\n [cells,w,name],\n zip(range_cells, range_weights, keys(settings[\"mark_ranges\"]))\n)\n\nnotation_styles:\n[\"plain\",\"si-en\"]\n\ncorrectAnswer:\nsettings[\"correct_answer\"]", "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": "if(sum(mark_ranges)=0,\n incorrect(),\n apply(mark_ranges)\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer"}, {"name": "range_cells", "description": "For each range to be marked, the addresses of the cells in that range.
", "definition": "map(parse_range(ref),ref,values(settings[\"mark_ranges\"]))"}, {"name": "total_cells", "description": "The total number of cells to be marked. Cells in overlapping ranges will be counted once for each range they're in.
", "definition": "len(flatten(range_cells))"}, {"name": "range_weights", "description": "The weight of each range, as a proportion of the available credit.
", "definition": "switch(\n settings[\"marking_method\"]=\"per_cell\",\n map(len(r)/total_cells, r, range_cells),\n // otherwise, mark per range\n repeat(1/len(range_cells), len(range_cells))\n)"}, {"name": "mark_ranges", "description": "Mark each of the ranges specified by the question author.
", "definition": "map(\n let(\n range_credit,\n sum(map(\n let(\n correctCellString, correctAnswer[c],\n correctCellNumber, parsenumber(correctCellString, notation_styles),\n studentCellString, studentAnswer[c],\n studentCellNumber, parsenumber(studentCellString, notation_styles),\n award(\n 1/len(cells), \n switch(\n correctCellString=\"\",\n isnan(studentCellNumber) or studentCellString=\"\",\n isnan(correctCellNumber),\n lower(correctCellString) = lower(studentCellString)\n ,\n abs(studentCellNumber - if(isnan(correctCellNumber),0,correctCellNumber)) <= settings[\"tolerance\"]\n )\n )\n ),\n c,\n cells\n )),\n message,\n switch(\n range_credit=0,\n if(len(cells)=1, \"This entry is incorrect.\", \"All entries in this range are incorrect.\"),\n range_credit=1,\n if(len(cells)=1, \"This entry is correct.\", \"All entries in this range are correct.\"),\n //otherwise\n \"Some entries in this range are correct.\"\n ),\n assert(len(cells)=0, add_credit(range_credit*w, \"{name}: \"+message)); \n range_credit\n ),\n [cells,w,name],\n zip(range_cells, range_weights, keys(settings[\"mark_ranges\"]))\n)"}, {"name": "notation_styles", "description": "Accepted number notation styles for a value in an individual cell.
", "definition": "[\"plain\",\"si-en\"]"}, {"name": "correctAnswer", "description": "", "definition": "settings[\"correct_answer\"]"}], "settings": [{"name": "initial_sheet", "label": "Initial sheet", "help_url": "", "hint": "Aspreadsheet object giving the initial state of the sheet that the student should fill in.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "correct_answer", "label": "Correct answer", "help_url": "", "hint": "A spreadsheet object representing a correct answer to the part.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "disable_ranges", "label": "Ranges to disable", "help_url": "", "hint": "A list of cell or range references, denoting the cells that should not be editable.", "input_type": "code", "default_value": "[]", "evaluate": true}, {"name": "mark_ranges", "label": "Ranges to mark", "help_url": "", "hint": "A dictionary of cell or range references, mapping names to ranges of cells, denoting the cells that should be compared for equality with the expected answer.", "input_type": "code", "default_value": "dict()", "evaluate": true}, {"name": "marking_method", "label": "Marking method", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "per_cell", "choices": [{"value": "per_cell", "label": "Each cell has the same weight"}, {"value": "per_range", "label": "Each range has the same weight"}]}, {"name": "tolerance", "label": "Allowed margin of error", "help_url": "", "hint": "", "input_type": "code", "default_value": "0", "evaluate": true}], "public_availability": "always", "published": true, "extensions": ["sheets"]}], "resources": [["question-resources/centroids.png", "/srv/numbas/media/question-resources/centroids.png"], ["question-resources/centroids_3A0rXlj.png", "/srv/numbas/media/question-resources/centroids_3A0rXlj.png"], ["question-resources/centroids_zSOgoBb.png", "/srv/numbas/media/question-resources/centroids_zSOgoBb.png"], ["question-resources/centroid-t-r.ggb", "/srv/numbas/media/question-resources/centroid-t-r.ggb"]]}