A demo of the main new features in Numbas v5: explore mode, alternative answers and \"Choose from a menu\" question navigation.
", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "percentPass": "0", "showQuestionGroupNames": true, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Explore mode", "pickingStrategy": "all-ordered", "pickQuestions": "1", "questionNames": ["", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], []], "questions": [{"name": "Decide if a coin is biased", "extensions": ["stats"], "custom_part_types": [{"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.
", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n correct(),\n incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "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(studentanswer=correct_answer,\n correct(),\n incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates totrue or false.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "An interactive experiment about probability: the student must first 'design' the experiment by deciding how many times they're going to flip a coin, and define what number of heads would make them believe the coin is biased. They must then enter the results of their coin flips, calculate the percentage of heads, and finally decide if the coin is biased, using the condition they specified in the design stage. There are optional hints at each stage.In this exercise you will decide if a coin is biased by flipping it repeatedly and deciding if it lands heads more often than you'd expect.
"}, {"type": "numberentry", "useCustomName": true, "customName": "Decide number of flips", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Define 'biased'", "rawLabel": "", "otherPart": 2, "variableReplacements": [{"variable": "num_flips", "definition": "interpreted_answer"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Design the experiment", "prompt": "How many times will you flip your coin?
", "minValue": "1", "maxValue": "infinity", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Define 'biased'", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Enter data", "rawLabel": "", "otherPart": 4, "variableReplacements": [{"variable": "raw_critical_number", "definition": "interpreted_answer"}], "availabilityCondition": "answered and credit=1", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}, {"label": "What do you expect an unbiased coin do?", "rawLabel": "", "otherPart": 3, "variableReplacements": [], "availabilityCondition": "not (answered or credit=1)", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Design the experiment", "prompt": "How many heads would make you think the coin is biased?
", "minValue": "0", "maxValue": "100", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "What do you expect an unbiased coin do?", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "With an unbiased coin, how many flips would you expect to land heads up?
", "minValue": "num_flips/2-0.5", "maxValue": "num_flips/2+0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "patternmatch", "useCustomName": true, "customName": "Enter data", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "right_length:\n if(len(parse_flips(studentAnswer))=num_flips,\n correct(\"You have entered your data correctly.\"),\n incorrect(\"You have not entered the right number of flips.\")\n )\n\nmark:\n apply(right_length)\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Calculate proportion of heads", "rawLabel": "", "otherPart": 5, "variableReplacements": [{"variable": "flips_string", "definition": "interpreted_answer"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Enter data", "prompt": "Flip the coin {num_flips} times. Each time it lands heads, write an H in the box below. Each time it lands tails, write a T.
", "answer": "[, hHtT]*", "displayAnswer": "", "matchMode": "regex"}, {"type": "numberentry", "useCustomName": true, "customName": "Calculate proportion of heads", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Show frequencies of heads and tails", "rawLabel": "", "otherPart": 6, "variableReplacements": [], "availabilityCondition": "not (answered and credit=1)", "penalty": "Showed frequencies of heads and tails", "penaltyAmount": "1", "lockAfterLeaving": false}, {"label": "Is the coin biased?", "rawLabel": "", "otherPart": 7, "variableReplacements": [], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Calculate proportion of heads", "prompt": "Your flips were:
\n{cleaned_flips_string}
\nWhat percentage of the flips landed heads?
", "minValue": "percent_heads", "maxValue": "percent_heads", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": true, "customName": "Show frequencies of heads and tails", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "| Result | \nHeads | \nTails | \n
| Frequency | \n{num_heads} | \n{num_tails} | \n
Do you think your coin is biased?
", "settings": {"correct_answer_expr": "is_biased"}}, {"type": "numberentry", "useCustomName": true, "customName": "Calculate the critical likelihood", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": "Decide if the coin is biased", "prompt": "You said that a coin is biased if it comes up heads at least {critical_number} times out of {num_flips}. What's that as a percentage?
", "minValue": "100*critical_likelihood", "maxValue": "100*critical_likelihood", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": "100", "precisionMessage": "", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "explore", "maxMarks": 0, "objectives": [{"name": "Calculate proportion of heads", "limit": "2", "mode": "sum"}, {"name": "Decide if the coin is biased", "limit": "5", "mode": "sum"}, {"name": "Design the experiment", "limit": "2", "mode": "sum"}, {"name": "Enter data", "limit": "1", "mode": "sum"}], "penalties": [{"name": "Showed frequencies of heads and tails", "limit": "1", "mode": "sum"}, {"name": "Hint about critical likelihood", "limit": "1", "mode": "sum"}], "objectiveVisibility": "always", "penaltyVisibility": "when-active"}, {"name": "Factorise a number", "extensions": ["stats"], "custom_part_types": [{"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.
", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n correct(),\n incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "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(studentanswer=correct_answer,\n correct(),\n incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates totrue or false.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "An example of an iterative procedure: the student must factorise a given number. At each step, they're asked if the number is factorised. If not, they must give a prime factor. If it is fully factorised, they can then work out the number of factors of the number.This is advice.
", "rulesets": {}, "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "prod(actual_factors)", "description": "The number to factorise.
", "templateType": "anything"}, "factors": {"name": "factors", "group": "Ungrouped variables", "definition": "[]", "description": "The prime factors entered by the student.
", "templateType": "anything"}, "fully_factorised": {"name": "fully_factorised", "group": "Ungrouped variables", "definition": "all(map(mod(current_n,k)<>0,k,2..floor(sqrt(current_n))))", "description": "Is the number fully factorised? True if no integer between 2 and $\\sqrt{\\texttt{current_n}}$ divides current_n, so it's prime.
The part of $n$ still left to factorise.
", "templateType": "anything"}, "weighted_primes": {"name": "weighted_primes", "group": "Ungrouped variables", "definition": "[2,2,2,2,3,3,3,5,5,7,11]", "description": "A list of prime numbers, weighted so smaller primes are picked more often
", "templateType": "anything"}, "num_factors": {"name": "num_factors", "group": "Ungrouped variables", "definition": "prod(map(len(filter(x=k,x,actual_factors))+1,k,set(actual_factors)))", "description": "The number of factors of $n$.
", "templateType": "anything"}, "actual_factors": {"name": "actual_factors", "group": "Ungrouped variables", "definition": "repeat(random(weighted_primes),3)", "description": "Pick three (not necessarily unique) prime factors for $n$.
", "templateType": "anything"}, "factorisation_latex": {"name": "factorisation_latex", "group": "Ungrouped variables", "definition": "latex(current_n+if(len(factors),' \\\\times '+join(factors,' \\\\times '),''))", "description": "LaTeX expression showing the current statre of the factorisation.
", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["weighted_primes", "actual_factors", "n", "factors", "fully_factorised", "current_n", "num_factors", "factorisation_latex"], "variable_groups": [], "functions": {"isprime": {"parameters": [["n", "number"]], "type": "boolean", "language": "jme", "definition": "n>=2 and isint(n) and all(map(mod(n,k)>0,k,2..floor(sqrt(n))))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "yes-no", "useCustomName": true, "customName": "Is it factorised?", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Write a factor", "rawLabel": "", "otherPart": 1, "variableReplacements": [], "availabilityCondition": "not interpreted_answer", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}, {"label": "How many factors?", "rawLabel": "", "otherPart": 2, "variableReplacements": [], "availabilityCondition": "interpreted_answer", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Is $\\var{n} = \\var{factorisation_latex}$ fully factorised?
", "settings": {"correct_answer_expr": "fully_factorised"}}, {"type": "numberentry", "useCustomName": true, "customName": "Write a factor", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "is_factor:\n if(mod(current_n,studentNumber)=0,\n if(isprime(studentNumber),\n correct()\n ,\n set_credit(0.5,\"Your answer is a factor of {current_n} but is not prime.\")\n )\n ,\n incorrect(\"Your answer is not a factor of {current_n}\")\n )\n \n\nmark (Mark the student's answer):\n apply(validNumber);\n apply(is_factor)", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Is it factorised?", "rawLabel": "", "otherPart": 0, "variableReplacements": [{"variable": "factors", "definition": "factors+[interpreted_answer]"}], "availabilityCondition": "answered and credit=1", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Identify the factors of $\\var{n}$", "prompt": "Write a prime factor of $\\var{current_n}$.
", "minValue": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "How many factors?", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Calculate how many factors", "prompt": "How many factors does $\\var{n} = \\var{factorisation_latex}$ have?
", "minValue": "num_factors", "maxValue": "num_factors", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "explore", "maxMarks": "4", "objectives": [{"name": "Identify the factors of $\\var{n}$", "limit": "3", "mode": "sum"}, {"name": "Calculate how many factors", "limit": "2", "mode": "sum"}], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Find Dracula", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question demonstrates how to use explore mode to simulate a game, where each choice made by the student changes the state of the game.You're trying to find Dracula. You've reached the grand gallery of Castle Dracula, and you know that the Count is hiding in one of the rooms. But which?
\nAll the rooms are on one side of the gallery. They each have internal doors between them, that only Dracula can use. Each time you look in a room that Dracula isn't in, he moves from the room he's in to an adjacent one.
\nCan you find Dracula?
", "advice": "", "rulesets": {}, "variables": {"cells": {"name": "cells", "group": "Ungrouped variables", "definition": "repeat(true,n)", "description": "For each room, whether Dracula can be in that room.
", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "4", "description": "The number of rooms
", "templateType": "anything"}, "cells_after_pick": {"name": "cells_after_pick", "group": "Ungrouped variables", "definition": "map(\n let(ncells,map(if(k=j,false,cells[k]),k,0..n-1),\n map(if(k>0,ncells[k-1],false) or if(kcells after looking in that room.", "templateType": "anything"}, "room_names": {"name": "room_names", "group": "Ungrouped variables", "definition": "map(\"Room \"+j,j,1..n)", "description": "The names of the rooms, for display.
", "templateType": "anything"}, "dracula": {"name": "dracula", "group": "Ungrouped variables", "definition": "random(0..n-1)", "description": "The room Dracula is in.
", "templateType": "anything"}, "dracula_choices": {"name": "dracula_choices", "group": "Ungrouped variables", "definition": "switch(\n dracula=0,[1],\n dracula=n-1,[n-2],\n [dracula-1,dracula+1]\n)", "description": "The rooms Dracula can move to.
", "templateType": "anything"}, "chosen_room": {"name": "chosen_room", "group": "Ungrouped variables", "definition": "0", "description": "The last room that was looked in.
", "templateType": "anything"}, "look_marking": {"name": "look_marking", "group": "Ungrouped variables", "definition": "map(award(1,j=dracula),j,0..n-1)", "description": "Award 1 mark for looking in the room containing Dracula.
", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "dracula", "cells", "cells_after_pick", "room_names", "dracula_choices", "chosen_room", "look_marking"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "How many rooms does Castle Dracula have?", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Look in a room", "rawLabel": "", "otherPart": 1, "variableReplacements": [{"variable": "n", "definition": "interpreted_answer"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "How many rooms does Castle Dracula have?
\n(You can pick - a smaller number is easier, while a larger number will mean it takes longer to find Dracula)
", "minValue": "1", "maxValue": "100", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "Look in a room", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_choice: indices(interpreted_answer,[true])[0]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Open the door", "rawLabel": "Open the door", "otherPart": 2, "variableReplacements": [{"variable": "chosen_room", "definition": "student_choice"}, {"variable": "cells", "definition": "cells_after_pick[student_choice]"}, {"variable": "dracula", "definition": "random(dracula_choices)"}], "availabilityCondition": "answered and student_choice<>dracula", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}, {"label": "Open the door", "rawLabel": "Open the door", "otherPart": 4, "variableReplacements": [], "availabilityCondition": "answered and student_choice=dracula", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Find Dracula", "prompt": "Which room would you like to look in now?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": "map(\"Room \"+j,j,1..n)", "matrix": "repeat(0,n)"}, {"type": "information", "useCustomName": true, "customName": "Dracula wasn't in the room", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Where could Dracula be?", "rawLabel": "", "otherPart": 3, "variableReplacements": [], "availabilityCondition": "", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}, {"label": "Look in another room", "rawLabel": "Look in another room", "otherPart": 1, "variableReplacements": [], "availabilityCondition": "", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Dracula wasn't in room {chosen_room+1}. Drat!
\nYou go back to the hall, and close the door. Dracula leaves the room he is in and moves to an adjacent room.
"}, {"type": "m_n_2", "useCustomName": true, "customName": "Where could Dracula be?", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Which rooms could Dracula be in right now?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": "room_names", "matrix": "map(if(cells[k],1,-1),k,0..n-1)"}, {"type": "1_n_2", "useCustomName": true, "customName": "Confront Dracula!", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Find Dracula", "prompt": "You open the door and find the dread Count himself!
\nWhat do you do?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["A quick stake to the heart and the job's done. Bish bash bosh!", "Let him go."], "matrix": ["1", 0], "distractors": ["", ""]}], "partsMode": "explore", "maxMarks": 0, "objectives": [{"name": "Find Dracula", "limit": "1", "mode": "sum"}], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Show an optional hint when the student makes a particular error", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question shows how to reveal a part if the student enters an incorrect answer that you're expecting - in this case, by not following the order of operations.What is $\\simplify[]{ {a} + {b}*{c} + {d} }$?
", "minValue": "a+b*c+d", "maxValue": "a+b*c+d", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": true, "customName": "Order of operations hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Did you evaluate the expression from left to right, without accounting for the order of operations?
\nPerform multiplication first: $\\simplify[]{ {a} + {b}*{c} + {d} } = \\simplify[]{ {a} + {b*c} + {d} }$
"}], "partsMode": "explore", "maxMarks": 0, "objectives": [{"name": "Evaluate an expression", "limit": 1, "mode": "sum"}], "penalties": [{"name": "Hint", "limit": "0.5", "mode": "sum"}], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Lock a part after leaving it", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question demonstrates how to lock a part in explore mode after moving to the next part, to prevent the student changing their answer and invalidating the rest of the question.Write a number.
", "minValue": "-infinity", "maxValue": "infinity", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Double the number", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Double the number", "prompt": "$x = \\var{x}$.
\nWhat is $2x$?
", "minValue": "2x", "maxValue": "2x", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": true, "customName": "Get some inspiration", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Maybe you'd like to write the number {random(100..200)}?
"}], "partsMode": "explore", "maxMarks": 0, "objectives": [{"name": "Double the number", "limit": 1, "mode": "sum"}], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Posting a parcel", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "An interactive activity: the student enters the dimensions of a parcel, then has to calculate its volume, and classify its size by comparing against a table of maximum dimensions.You would like to post a parcel. The cost of postage depends on the size of your parcel.
"}, {"type": "gapfill", "useCustomName": true, "customName": "Enter the parcel's measurements", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Calculate volume", "rawLabel": "", "otherPart": 2, "variableReplacements": [{"variable": "width", "definition": "interpreted_answer[0]"}, {"variable": "height", "definition": "interpreted_answer[1]"}, {"variable": "length", "definition": "interpreted_answer[2]"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Enter the dimensions of your parcel, in centimetres.
\nWidth: [[0]]
\nLength: [[1]]
\nHeight: [[2]]
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Width", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "infinity", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Length", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "infinity", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Height", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "infinity", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "numberentry", "useCustomName": true, "customName": "Calculate volume", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Pick the appropriate size", "rawLabel": "", "otherPart": 3, "variableReplacements": [], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Calculate the parcel's volume", "prompt": "Your parcel measures $\\var{width} \\times \\var{length} \\times \\var{height}$cm.
\nWhat is the volume of your parcel, in cubic centimetres?
", "minValue": "volume", "maxValue": "volume", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "Pick the appropriate size", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Pick the size of the parcel", "prompt": "The post company categorises parcels according to the following table:
\n{size_table}
\nWhat size is your parcel?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": "map(size[\"name\"],size,sizes)", "matrix": "map(award(1,x=best_size), x, 0..len(sizes)-1)"}], "partsMode": "explore", "maxMarks": 0, "objectives": [{"name": "Calculate the parcel's volume", "limit": "1", "mode": "sum"}, {"name": "Pick the size of the parcel", "limit": "1", "mode": "sum"}], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Offer hints at different levels of detail", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question demonstrates how you can offer a selection of hints, with each giving a different level of detail and applying a different penalty.In this question, you need to write the number 3435.
\nIf you need help, ask for a hint.
", "minValue": "3435", "maxValue": "3435", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": true, "customName": "Vague hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "The thing you need to write is an integer.
"}, {"type": "information", "useCustomName": true, "customName": "More specific hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Use the digit keys on your keyboard to write the number.
"}, {"type": "gapfill", "useCustomName": true, "customName": "Guided steps", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Try writing the digits one at a time.
\nWrite 3: [[0]]
\nWrite 4: [[1]]
\nWrite 3 again: [[2]]
\nWrite 5: [[3]]
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Write 3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Write the number 3435", "minValue": "3", "maxValue": "3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Write 4", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Write the number 3435", "minValue": "4", "maxValue": "4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Write 3 again", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Write the number 3435", "minValue": "3", "maxValue": "3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Write 5", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Write the number 3435", "minValue": "5", "maxValue": "5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "explore", "maxMarks": 0, "objectives": [{"name": "Write the number 3435", "limit": "10", "mode": "sum"}], "penalties": [{"name": "Hints revealed", "limit": "3", "mode": "sum"}], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Find the root(s) of a quadratic equation.", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "The student is asked to identify the number of roots of a quadratic equation, and then to give the root or roots. There is a hint to calculate the discriminant, and then further hints with the formula for the discriminant and the decision to make based on its value.$f(x) = \\simplify{{c1}x^2 + {c2}x + {c3}}$
", "advice": "", "rulesets": {}, "variables": {"root1": {"name": "root1", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "root2": {"name": "root2", "group": "Ungrouped variables", "definition": "random(root1,random(-5..5 except root1))", "description": "50% chance of being the same as root1
", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random([1,1,1]+list(2..7))", "description": "", "templateType": "anything"}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "a", "description": "", "templateType": "anything"}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "a*(-root2 -root1)", "description": "", "templateType": "anything"}, "c3": {"name": "c3", "group": "Ungrouped variables", "definition": "a*root1*root2", "description": "", "templateType": "anything"}, "num_roots": {"name": "num_roots", "group": "Ungrouped variables", "definition": "if(root1=root2,1,2)", "description": "", "templateType": "anything"}, "discriminant": {"name": "discriminant", "group": "Ungrouped variables", "definition": "c2^2-4*c1*c3", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["root1", "root2", "a", "c1", "c2", "c3", "num_roots", "discriminant"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "How many roots?", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Enter the root", "rawLabel": "", "otherPart": 1, "variableReplacements": [], "availabilityCondition": "interpreted_answer=1", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}, {"label": "Enter the roots", "rawLabel": "", "otherPart": 2, "variableReplacements": [], "availabilityCondition": "interpreted_answer=2", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}, {"label": "Calculate the discriminant", "rawLabel": "", "otherPart": 3, "variableReplacements": [], "availabilityCondition": "credit<1", "penalty": "Discriminant hint", "penaltyAmount": "0.5", "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Write the number of roots", "prompt": "How many distinct solutions does $f(x)=0$ have?
", "minValue": "num_roots", "maxValue": "num_roots", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Enter the root", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "mark (Mark the student's answer):\n apply(validNumber);\n if(studentNumber in [root1,root2],\n correct(),\n incorrect(\"Your answer is not a root of the equation\")\n )", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Identify the root(s)", "minValue": "root1", "maxValue": "root1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": true, "customName": "Enter the roots", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "distinct_roots: \n set(answers)\n\ncorrect_roots:\n filter(x in [root1,root2],x,distinct_roots)\n\nincorrect_roots:\n filter(not (x in [root1,root2]),x,distinct_roots)\n\nq1: len(correct_roots)=len(set([root1,root2]))\n\nq:\n switch(\n len(correct_roots)=len(set([root1,root2])),\n correct();\n if(len(incorrect_roots)>0,\n sub_credit(0.5,\"One of your answers is not a solution of the equation $f(x) = 0$.\")\n ),\n len(correct_roots)>0,\n if(len(incorrect_roots)>0,\n set_credit(0.5,\"One of your answers is not a solution of the equation $f(x) = 0$.\"),\n set_credit(0.5,\"You have written the same solution twice.\")\n ),\n //otherwise\n incorrect(\"Neither of your answers is a solution of the equation $f(x) = 0$.\")\n )\n\nmark:\n assert(all_valid or not settings[\"sortAnswers\"], fail(translate(\"question.can not submit\")));\n apply(q)", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Identify the root(s)", "prompt": "Write the two roots, $x_1$ and $x_2$, of the equation $f(x)=0$, such that $x_1 \\lt x_2$:
\n$x_1 = $ [[0]]
\n$x_2 = $ [[1]]
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "$x_1$", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Identify the root(s)", "minValue": "min(root1,root2)", "maxValue": "min(root1,root2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "$x_2$", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Identify the root(s)", "minValue": "max(root1,root2)", "maxValue": "max(root1,root2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": true}, {"type": "numberentry", "useCustomName": true, "customName": "Calculate the discriminant", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "See how to calculate the discriminant", "rawLabel": "See how to calculate the discriminant", "otherPart": 4, "variableReplacements": [], "availabilityCondition": "", "penalty": "Formula for the discriminant", "penaltyAmount": "0.25", "lockAfterLeaving": false}, {"label": "What to do with the discriminant", "rawLabel": "", "otherPart": 5, "variableReplacements": [], "availabilityCondition": "answered and credit=1", "penalty": "What to do with the discriminant", "penaltyAmount": "0.25", "lockAfterLeaving": false}], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": "Calculate the discriminant", "prompt": "What is the discriminant of $f(x)$?
", "minValue": "discriminant", "maxValue": "discriminant", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": true, "customName": "Discriminant formula", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "For a quadratic equation in the form $ax^2 + bx + c$, the discriminant $D$ is
\n\\[ D = b^2-4ac \\]
"}, {"type": "information", "useCustomName": true, "customName": "What to do with the discriminant", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "The number of distinct roots of the equation depends on the value of the discriminant:
\nThe student must calculate the number of digits a given decimal number would have when written in a different base. Alternative answers catch some common mal-rules and give appropriate feedback.
Based on table 2 from \"diagnosing student errors in e-assessment questions\" by Philip Walker, D. Rhys Gwynllyw and Karen L. Henderson.
How many digits does $\\var{n}_{10}$ have in base $\\var{b}$?
", "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "Converted to base b", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "You converted $\\var{n}$ to base $b$. You were asked to give the number of digits in this representation.
", "useAlternativeFeedback": false, "minValue": "converted", "maxValue": "converted", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Multiplied n by b", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "You have multiplied $\\var{n}$ and $\\var{b}$ together. You were asked to calculate how many digits the base-$\\var{b}$ representation of $\\var{n}$ has.
", "useAlternativeFeedback": false, "minValue": "n*b", "maxValue": "n*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "floor(log(n,b))", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "Did you calculate $\\simplify{floor(log({n},{b}))}$?
\nConsider the following example:
\n$\\simplify{floor(log(13,10))} = 1$, but $13$ has two digits.
", "useAlternativeFeedback": false, "minValue": "floor(log(n,b))", "maxValue": "floor(log(n,b))", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "floor(log(n,b))-1", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "Did you calculate $\\simplify{floor(log({n},{b}))}-1$?
\nConsider the following example:
\n$\\simplify{floor(log(13,10))}-1 = 0$, but $13$ has two digits.
", "useAlternativeFeedback": false, "minValue": "floor(log(n,b))", "maxValue": "floor(log(n,b))", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "ceil(log(n,b))+1", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "Did you calculate $\\simplify{ceil(log({n},{b}))}+1$? You might have made an off-by-one error.
\nConsider the following example:
\n$\\simplify{ceil(log(13,10))}+1 = 3$, but $13$ has two digits.
", "useAlternativeFeedback": false, "minValue": "ceil(log(n,b))+1", "maxValue": "ceil(log(n,b))+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "num_digits", "maxValue": "num_digits", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [{"name": "Number of digits", "limit": 1, "mode": "sum"}], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Write a number whose square is the given number", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "A demonstration of the use of alternative answers to accept more than one correct answer. The student must write a number whose square is $n^2$. Both $n$ and $-n$ are accepted.Write a number whose square is $\\var{n^2}$.
", "alternatives": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": true, "minValue": "-n", "maxValue": "-n", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "n", "maxValue": "n", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Reveal a hint based on the alternative answer used", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "The student must write a number to 2 decimal places. The number has a trailing zero, and an alternative answer is used to detect when the student omits it. If the student omits the trailing zero, they're offered an optional hint.Write $\\frac{3}{5}$ to two decimal places.
", "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "No trailing zero", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "You've written the right number, but you haven't included a trailing zero.
", "useAlternativeFeedback": false, "minValue": "3/5", "maxValue": "3/5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "3/5", "maxValue": "3/5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": true, "customName": "Hint about trailing zeros", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "While $0.6$ and represent the same number as $0.60$, they do not convey the same amount of precision. You must include zeros at the end of the number to make up the required number of decimal places.
"}], "partsMode": "explore", "maxMarks": 0, "objectives": [{"name": "Write to 2 decimal places", "limit": "1", "mode": "sum"}], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Alternative answers: expanding range of accepted answers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "The student is asked to add two four-digit numbers. Alternative answers are set up with progressively expanding ranges of accepted values, so the student gets more marks for getting closer to the true answer.Calculate $\\var{a} + \\var{b}$.
\n(Try getting the answer slightly wrong: you're awarded more marks the closer you get to the correct answer.)
", "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "Within 10", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "You're within 10 of the correct answer.
", "useAlternativeFeedback": false, "minValue": "total-10", "maxValue": "total+10", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Within 100", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "You're within 100 of the correct answer.
", "useAlternativeFeedback": false, "minValue": "total-100", "maxValue": "total+100", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Within 1000", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "You're within 1000 of the correct answer.
", "useAlternativeFeedback": false, "minValue": "total-1000", "maxValue": "total+1000", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "total", "maxValue": "total", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "menu", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "Numbas v5 introduces the \"explore mode\" for questions, alternative answers for individual parts, and the \"Choose from a menu\" navigation mode for exams.
\nThe questions below demonstrate the new features in v5. Try them out!
", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}], "extensions": ["stats"], "custom_part_types": [{"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.
", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n correct(),\n incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "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(studentanswer=correct_answer,\n correct(),\n incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates totrue or false.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": []}