// Numbas version: exam_results_page_options
{"feedback": {"intro": "", "showtotalmark": true, "feedbackmessages": [], "showactualmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0}, "duration": 0, "timing": {"timeout": {"message": "", "action": "none"}, "timedwarning": {"message": "", "action": "none"}, "allowPause": true}, "navigation": {"onleave": {"message": "", "action": "none"}, "preventleave": true, "showresultspage": "oncompletion", "showfrontpage": true, "browse": true, "reverse": true, "allowregen": true}, "showQuestionGroupNames": false, "percentPass": 0, "metadata": {"licence": "None specified", "description": ""}, "name": "Custom Feedback in Numbas Demo May 2019", "showstudentname": true, "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Group", "questions": [{"name": "TP1", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_K0BP3FV.png", "/srv/numbas/media/question-resources/image_K0BP3FV.png"], ["question-resources/image_jS71fGY.png", "/srv/numbas/media/question-resources/image_jS71fGY.png"], ["question-resources/image_8rDGI2c.png", "/srv/numbas/media/question-resources/image_8rDGI2c.png"], ["question-resources/image_AgeDfYh.png", "/srv/numbas/media/question-resources/image_AgeDfYh.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}], "parts": [{"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>$3x+A=5+A$ [[0]]</p>", "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCellAnswerState": true, "type": "1_n_2", "scripts": {}, "customMarkingAlgorithm": "", "maxMarks": 0, "displayType": "radiogroup", "matrix": ["1", 0], "showCorrectAnswer": true, "showFeedbackIcon": true, "distractors": ["Well done. The statement is true, as we are adding the same thing to both sides. Increasing the left hand side and the right hand side by the same amount means that the sides are still equal.", "Your answer is incorrect. The statement is true, as we are adding the same thing to both sides. Increasing the left hand side and the right hand side by the same amount means that the sides are still equal."], "displayColumns": 0, "unitTests": [], "minMarks": 0, "marks": 0, "extendBaseMarkingAlgorithm": true, "choices": ["True", "False"], "shuffleChoices": false}], "unitTests": [], "variableReplacements": [], "marks": 0, "extendBaseMarkingAlgorithm": true}, {"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>$9x^2=25$ [[0]]</p>", "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCellAnswerState": true, "type": "1_n_2", "scripts": {}, "customMarkingAlgorithm": "", "maxMarks": 0, "displayType": "radiogroup", "matrix": ["1", 0], "showCorrectAnswer": true, "showFeedbackIcon": true, "distractors": ["Correct - the statement is true. Both sides were squared - i.e. the same thing was done to both sides. Multiplying both sides by the same thing means both sides are still equal. Since $3x=5$, multiplying by $3x$ is the same as multiplying by $5$ (i.e. multiplying the left hand side by $3x$ and the right hand side by $5$ is doing the same thing to both sides.)", "Incorrect - the statement is true. Both sides were squared - i.e. the same thing was done to both sides. Multiplying both sides by the same thing means both sides are still equal. Since $3x=5$, multiplying by $3x$ is the same as multiplying by $5$ (i.e. multiplying the left hand side by $3x$ and the right hand side by $5$ is doing the same thing to both sides.)"], "displayColumns": 0, "unitTests": [], "minMarks": 0, "marks": 0, "extendBaseMarkingAlgorithm": true, "choices": ["True", "False"], "shuffleChoices": false}], "unitTests": [], "variableReplacements": [], "marks": 0, "extendBaseMarkingAlgorithm": true}, {"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>$x=5-3$ [[0]]</p>", "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCellAnswerState": true, "type": "1_n_2", "scripts": {}, "customMarkingAlgorithm": "", "maxMarks": 0, "displayType": "radiogroup", "matrix": [0, "1"], "showCorrectAnswer": true, "showFeedbackIcon": true, "distractors": ["Incorrect - the statement is false. To get $x$ on its own on the left hand side, we need to divide by $3$. To keep both sides equal, we must do the same to the right hand side. If we subtract $3$ instead, we have done something different to each side, so the sides are no longer equal.", "Correct - the statement is false. To get $x$ on its own on the left hand side, we need to divide by $3$. To keep both sides equal, we must do the same to the right hand side. If we subtract $3$ instead, we have done something different to each side, so the sides are no longer equal."], "displayColumns": 0, "unitTests": [], "minMarks": 0, "marks": 0, "extendBaseMarkingAlgorithm": true, "choices": ["True", "False"], "shuffleChoices": false}], "unitTests": [], "variableReplacements": [], "marks": 0, "extendBaseMarkingAlgorithm": true}, {"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>$x=\\frac{5}{-3}$ [[0]]</p>", "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCellAnswerState": true, "type": "1_n_2", "scripts": {}, "customMarkingAlgorithm": "", "maxMarks": 0, "displayType": "radiogroup", "matrix": [0, "1"], "showCorrectAnswer": true, "showFeedbackIcon": true, "distractors": ["Incorrect - the statement is false. To get $x$ on its own on the left hand side, we need to divide by $3$. To keep both sides equal, we must do the same to the right hand side. If we divide the right hand side by $-3$  instead, we have divided the left by $3$ but the right by $-3$ i.e. we have done something different to each side, so they are no longer equal.", "Correct - the statement is false. To get $x$ on its own on the left hand side, we need to divide by $3$. To keep both sides equal, we must do the same to the right hand side. If we divide the right hand side by $-3$  instead, we have divided the left by $3$ but the right by $-3$ i.e. we have done something different to each side, so they are no longer equal."], "displayColumns": 0, "unitTests": [], "minMarks": 0, "marks": 0, "extendBaseMarkingAlgorithm": true, "choices": ["True", "False"], "shuffleChoices": false}], "unitTests": [], "variableReplacements": [], "marks": 0, "extendBaseMarkingAlgorithm": true}], "variable_groups": [], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>If $3x=5$,&nbsp;decide whether each&nbsp;of the following statements&nbsp;is true or false.</p>", "preamble": {"css": "", "js": ""}, "ungrouped_variables": [], "advice": "", "functions": {}, "variables": {}, "metadata": {"description": "", "licence": "None specified"}, "tags": [], "type": "question"}, {"name": "TP4 - new", "extensions": [], "custom_part_types": [{"source": {"pk": 2, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/2/edit"}, "name": "List of numbers", "short_name": "list-of-numbers", "description": "<p>The answer is a comma-separated list of numbers.</p>\n<p>The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.</p>\n<p>You can optionally treat the answer as a set, so the number of occurrences doesn't matter, only whether each number is included or not.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "join(\n  if(settings[\"correctAnswerFractions\"],\n    map(let([a,b],rational_approximation(x), string(a/b)),x,settings[\"correctAnswer\"])\n  ,\n    settings[\"correctAnswer\"]\n  ),\n  settings[\"separator\"] + \" \"\n)", "hint": {"static": false, "value": "if(settings[\"show_input_hint\"],\n  \"Enter a list of numbers separated by <code>{settings['separator']}</code>.\",\n  \"\"\n)"}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "bits:\nlet(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)\n\nexpected_numbers:\nlet(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)\n\nvalid_numbers:\nif(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )\n\nis_sorted:\nassert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )\n\nincluded:\nmap(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )\n\nall_included:\nall(included)\n\nno_extras:\nif(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )\n\ninterpreted_answer:\nif(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)\n\nmark:\nif(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)\n\nnotationStyles:\n[\"en\"]\n\nisSet:\nsettings[\"isSet\"]\n\nextra_numbers:\nfilter(not (x in expected_numbers),x,interpreted_answer)", "marking_notes": [{"name": "bits", "description": "<p>The separate items in the student's answer</p>", "definition": "let(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)"}, {"name": "expected_numbers", "description": "", "definition": "let(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)"}, {"name": "valid_numbers", "description": "<p>Is every number in the student's list valid?</p>", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )"}, {"name": "is_sorted", "description": "<p>Are the student's answers in ascending order?</p>", "definition": "assert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )"}, {"name": "included", "description": "<p>Is each number in the expected answer present in the student's list the correct number of times?</p>", "definition": "map(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )"}, {"name": "all_included", "description": "<p>Has every number been included the right number of times?</p>", "definition": "all(included)"}, {"name": "no_extras", "description": "<p>True if the student's list doesn't contain any numbers that aren't in the expected answer.</p>", "definition": "if(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "if(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)"}, {"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=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)"}, {"name": "notationStyles", "description": "", "definition": "[\"en\"]"}, {"name": "isSet", "description": "<p>Should the answer be considered as a set, so the number of times an element occurs doesn't matter?</p>", "definition": "settings[\"isSet\"]"}, {"name": "extra_numbers", "description": "<p>Numbers included in the student's answer that are not in the expected list.</p>", "definition": "filter(not (x in expected_numbers),x,interpreted_answer)"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The list of numbers that the student should enter. The order does not matter.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "allowFractions", "label": "Allow the student to enter fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "correctAnswerFractions", "label": "Display the correct answers as fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "isSet", "label": "Is the answer a set?", "help_url": "", "hint": "If ticked, the number of times an element occurs doesn't matter, only whether it's included at all.", "input_type": "checkbox", "default_value": false}, {"name": "show_input_hint", "label": "Show the input hint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": true}, {"name": "separator", "label": "Separator", "help_url": "", "hint": "The substring that should separate items in the student's list", "input_type": "string", "default_value": ",", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}], "parts": [{"extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "gaps": [{"showFeedbackIcon": true, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "type": "list-of-numbers", "customMarkingAlgorithm": "bits:\nfilter(x<>\"\",x,split(studentAnswer,\",\"))\n\nexpected_numbers:\nsettings[\"correctAnswer\"]\n\nvalid_numbers:\nif(all(map(not isnan(parsenumber(x,\"en\")),x,bits)),\n    true,\n    let(wrong,filter(isnan(parsenumber(x,\"en\")),x,bits)[0],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )\n\nis_sorted:\nassert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )\n\nincluded:\nmap(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\"Your answer does not contain \"+x+\" enough times.\");false\n          ,\n            incorrect(\"Your answer contains \"+x+\" too many times.\");false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )\n\nall_included:\nall(included)\n\nno_extras:\nif(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(filter(not (x in expected_numbers),x,interpreted_answer)[0]+\" is not in the list.\");\n    false\n  )\n\ninterpreted_answer:\nmap(parsenumber(x,\"en\"),x,bits)\n\nmark:\nif(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)", "variableReplacementStrategy": "originalfirst", "scripts": {"mark": {"order": "instead", "script": "var answer=this.studentAnswer;\n// mark the answer\nif(answer==[-4,4]) {\n  this.setCredit(1,'Correct. Well done!');\n} else if(answer==[4,-4]) {\n  this.setCredit(1,'Correct. Well done!');\n} else if(answer==4) {\n  this.setCredit(0.5,'Some good work here, but not quite there yet. Did you remember to take the positive and negative square root?');\n} else if(answer==-4){\n  this.setCredit(0.5, 'Some good work here, but not quite there yet. Did you remember to take the positive and negative square root?');\n} else{\n  this.setCredit(0,'Not correct. Click on \"Reveal answers\" below for advice on how to solve this quesion.');\n}\n\n// you must set this.answered to say if the student gave a valid answer\nthis.answered = answer!==undefined;"}}, "marks": "4", "unitTests": [], "variableReplacements": [], "settings": {"correctAnswer": "[-4,4]"}}], "marks": 0, "variableReplacements": [], "prompt": "<p>$x= $ [[0]]</p>\n<p></p>", "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "showCorrectAnswer": true, "sortAnswers": false, "unitTests": []}], "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"licence": "None specified", "description": ""}, "ungrouped_variables": [], "advice": "<p>A similar example would be to solve&nbsp;$\\sqrt{x^2+36}=10$ for $x$.</p>\n<p>We wish to solve for $x$, so we must get $x$ on its own. At the moment, the only $x$ in the equation is under the square root. Because there is something else (in this case a 36) being added to the $x^2$ under the square root, the $x^2$ and the&nbsp;36 are trapped together until the square root is gone.</p>\n<p>How can we get rid of a square root? Ans: Apply the inverse function of the square root (i.e. do the opposite of taking&nbsp;the square root) which is to square.</p>\n<p>Remember, if we wish to keep the equation balanced i.e. keep both sides equal, we must always do the same thing to both sides. So, if we square the left hand side in order to get rid of the square root, we must also square the right hand side:</p>\n<p>\\[ \\begin{align*} \\left( \\sqrt{x^2 + 36} \\right)^{\\color{red}{2}} &amp; = 10^{\\color{red}{2}}\\\\ \\Rightarrow \\&nbsp; x^2 +&nbsp;36 &amp; = 100 \\end{align*}\\]</p>\n<p>Now that the square root is gone, the $x^2$ and the&nbsp;36 are no longer trapped together. If we wish to get $x^2$ on its own therefore, we can now get rid of the&nbsp;36 that is being added on the left hand side. How do we do this? Ans: Apply the inverse function of adding (i.e. do the opposite to adding) which is subtracting. So we subtract 36. As before, if we wish to keep the equation balanced i.e. keep both sides equal, we must do the same to both sides. So, if we subtract&nbsp;36 from the left hand side, we must also subtract&nbsp;36 from&nbsp;the right hand side:</p>\n<p>\\[ \\begin{align*} x^2 +&nbsp;36 \\color{red}{- 36} &amp; = 100 \\color{red}{- 36}\\\\ \\Rightarrow \\ x^2 &amp; =&nbsp;64 &nbsp;\\end{align*} \\]</p>\n<p>Finally, we wish to find $x$ rather than $x^2$, so we apply the inverse function of squaring (i.e. do the opposite of squaring). The inverse of squaring is to take the square root. Again, in order to keep both sides equal, we must also take the square root of the right hand side:</p>\n<p>\\[ \\begin{align*} \\color{red}{\\sqrt{\\color{black}{x^2}}} &amp; = \\color{red}{\\sqrt{\\color{black}{64}}}\\\\ x &amp; = \\color{red}{\\pm}&nbsp;8 &nbsp;\\end{align*}.\\]</p>\n<p>Note: When taking the square root (or fourth root or sixth root or any even root) we must always remember to include the negative solutions e.g. $8^2=64$ but so also is $(-8)^2$. If we only include the positive square root of 8, we are missing out on the solution of -8.</p>\n<p>Use this advice to try the question again by clicking on \"Try another question like this one\".</p>", "variable_groups": [], "preamble": {"js": "", "css": ""}, "variables": {}, "tags": [], "rulesets": {}, "statement": "<p>Given the equation $\\sqrt{x^2+9}=5$, solve for $x$.</p>", "functions": {}, "type": "question"}, {"name": "CA2 (2018/19) Partial Fractions 4 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}], "metadata": {"licence": "None specified", "description": ""}, "rulesets": {}, "statement": "<p>Find the following integral:</p>", "functions": {}, "parts": [{"adaptiveMarkingPenalty": 0, "unitTests": [], "variableReplacementStrategy": "originalfirst", "checkingAccuracy": 0.001, "marks": "4", "customMarkingAlgorithm": "malrules:\n  [\n    [\"{2a}*ln(abs(x-1))-{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))\", \"Almost there! Did you forget to include the integration constant?\"],  \n    [\"{2a}*ln(x-1)-{a}*ln(x+2)+{5a}*ln(x-3)+C\", \"Don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)-{a}*ln(x+2)+{5a}*ln(x-3)\", \"Don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}/(x-1)-{a}/(x+2)+{5a}/(x-3)+C\",\"You have the correct values for $A$, $B$ and $C$ but haven't actually integrated.\"],\n    [\"{2a}/(x-1)-{a}/(x+2)+{5a}/(x-3)\",\"You have the correct values for $A$, $B$ and $C$ but haven't actually integrated.\"],\n    [\"{2a}*ln(abs(x-1))+{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))+{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))+{a}*ln(abs(x+2))-{5a}*ln(abs(x-3))+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))+{a}*ln(abs(x+2))-{5a}*ln(abs(x-3))\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{-2a}*ln(abs(x-1))+{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{-2a}*ln(abs(x-1))+{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{-2a}*ln(abs(x-1))-{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{-2a}*ln(abs(x-1))-{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{-2a}*ln(abs(x-1))+{a}*ln(abs(x+2))-{5a}*ln(abs(x-3))+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{-2a}*ln(abs(x-1))+{a}*ln(abs(x+2))-{5a}*ln(abs(x-3))\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))-{a}*ln(abs(x+2))-{5a}*ln(abs(x-3))+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))-{a}*ln(abs(x+2))-{5a}*ln(abs(x-3))\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{-2a}*ln(abs(x-1))-{a}*ln(abs(x+2))-{5a}*ln(abs(x-3))+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{-2a}*ln(abs(x-1))-{a}*ln(abs(x+2))-{5a}*ln(abs(x-3))\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(x-1)+{a}*ln(x+2)+{5a}*ln(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)+{a}*ln(x+2)+{5a}*ln(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)+{a}*ln(x+2)-{5a}*ln(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)+{a}*ln(x+2)-{5a}*ln(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{-2a}*ln(x-1)+{a}*ln(x+2)+{5a}*ln(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{-2a}*ln(x-1)+{a}*ln(x+2)+{5a}*ln(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{-2a}*ln(x-1)-{a}*ln(x+2)+{5a}*ln(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{-2a}*ln(x-1)-{a}*ln(x+2)+{5a}*ln(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{-2a}*ln(x-1)+{a}*ln(x+2)-{5a}*ln(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{-2a}*ln(x-1)+{a}*ln(x+2)-{5a}*ln(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)-{a}*ln(x+2)-{5a}*ln(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)-{a}*ln(x+2)-{5a}*ln(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{-2a}*ln(x-1)-{a}*ln(x+2)-{5a}*ln(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{-2a}*ln(x-1)-{a}*ln(x+2)-{5a}*ln(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}/(x-1)+{a}/(x+2)+{5a}/(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}/(x-1)+{a}/(x+2)+{5a}/(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}/(x-1)+{a}/(x+2)-{5a}/(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}/(x-1)+{a}/(x+2)-{5a}/(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-{2a}/(x-1)+{a}/(x+2)+{5a}/(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-{2a}/(x-1)+{a}/(x+2)+{5a}/(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-{2a}/(x-1)-{a}/(x+2)+{5a}/(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-{2a}/(x-1)-{a}/(x+2)+{5a}/(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-{2a}/(x-1)+{a}/(x+2)-{5a}/(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-{2a}/(x-1)+{a}/(x+2)-{5a}/(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}/(x-1)-{a}/(x+2)-{5a}/(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}/(x-1)-{a}/(x+2)-{5a}/(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-{2a}/(x-1)-{a}/(x+2)-{5a}/(x-3)+C\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-{2a}/(x-1)-{a}/(x+2)-{5a}/(x-3)\", \"Double check your calculations for $A$, $B$ and $C$. In particular, if $dA=e$, then $A=\\\\frac{e}{d}$, not $\\\\frac{e}{-d}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"ln(abs(x-1))-2ln(abs(x+2))+3ln(abs(x-3))+C\",\"Be careful when finding the values of $A$, $B$ and $C$. When subbing in the value of $x$ that eliminates the $B$ and $C$ terms, check that you correctly rearranged to find $A$. Similarly, for $B$ and $C$.\"],\n    [\"ln(abs(x-1))-2ln(abs(x+2))+3ln(abs(x-3))\",\"Be careful when finding the values of $A$, $B$ and $C$. When subbing in the value of $x$ that eliminates the $B$ and $C$ terms, check that you correctly rearranged to find $A$. Similarly, for $B$ and $C$.\"],\n    [\"ln(x-1)-2ln(x+2)+3ln(x-3)+C\",\"Be careful when finding the values of $A$, $B$ and $C$. When subbing in the value of $x$ that eliminates the $B$ and $C$ terms, check that you correctly rearranged to find $A$. Similarly, for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"ln(x-1)-2ln(x+2)+3ln(x-3)\",\"Be careful when finding the values of $A$, $B$ and $C$. When subbing in the value of $x$ that eliminates the $B$ and $C$ terms, check that you correctly rearranged to find $A$. Similarly, for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"1/(x-1)-2/(x+2)+3/(x-3)+C\",\"Be careful when finding the values of $A$, $B$ and $C$. When subbing in the value of $x$ that eliminates the $B$ and $C$ terms, check that you correctly rearranged to find $A$. Similarly, for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"1/(x-1)-2/(x+2)+3/(x-3)\",\"Be careful when finding the values of $A$, $B$ and $C$. When subbing in the value of $x$ that eliminates the $B$ and $C$ terms, check that you correctly rearranged to find $A$. Similarly, for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"1/{2a}*ln(abs(x-1))-1/{a}*ln(abs(x+2))+1/{5a}*ln(abs(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"1/{2a}*ln(abs(x-1))-1/{a}*ln(abs(x+2))+1/{5a}*ln(abs(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))-1/{a}*ln(abs(x+2))+1/{5a}*ln(abs(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))-1/{a}*ln(abs(x+2))+1/{5a}*ln(abs(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"1/{2a}*ln(abs(x-1))-{a}*ln(abs(x+2))+1/{5a}*ln(abs(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"1/{2a}*ln(abs(x-1))-{a}*ln(abs(x+2))+1/{5a}*ln(abs(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"1/{2a}*ln(abs(x-1))-1/{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"1/{2a}*ln(abs(x-1))-1/{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"1/{2a}*ln(abs(x-1))-{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"1/{2a}*ln(abs(x-1))-{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))-1/{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))-1/{a}*ln(abs(x+2))+{5a}*ln(abs(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))-{a}*ln(abs(x+2))+1/{5a}*ln(abs(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"{2a}*ln(abs(x-1))-{a}*ln(abs(x+2))+1/{5a}*ln(abs(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$.\"],\n    [\"1/{2a}*ln(x-1)-1/{a}*ln(x+2)+1/{5a}*ln(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"1/{2a}*ln(x-1)-1/{a}*ln(x+2)+1/{5a}*ln(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)-1/{a}*ln(x+2)+1/{5a}*ln(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)-1/{a}*ln(x+2)+1/{5a}*ln(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"1/{2a}*ln(x-1)-{a}*ln(x+2)+1/{5a}*ln(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"1/{2a}*ln(x-1)-{a}*ln(x+2)+1/{5a}*ln(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"1/{2a}*ln(x-1)-1/{a}*ln(x+2)+{5a}*ln(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"1/{2a}*ln(x-1)-1/{a}*ln(x+2)+{5a}*ln(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"1/{2a}*ln(x-1)-{a}*ln(x+2)+{5a}*ln(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"1/{2a}*ln(x-1)-{a}*ln(x+2)+{5a}*ln(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)-1/{a}*ln(x+2)+{5a}*ln(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)-1/{a}*ln(x+2)+{5a}*ln(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)-{a}*ln(x+2)+1/{5a}*ln(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"{2a}*ln(x-1)-{a}*ln(x+2)+1/{5a}*ln(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"1/({2a}*(x-1))-1/({a}*(x+2))+1/({5a}*(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"1/({2a}*(x-1))-1/({a}*(x+2))+1/({5a}*(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}/(x-1)-1/({a}*(x+2))+1/({5a}*(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}/(x-1)-1/({a}*(x+2))+1/({5a}*(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"1/({2a}*(x-1))-{a}/(x+2)+1/({5a}*(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"1/({2a}*(x-1))-{a}/(x+2)+1/({5a}*(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"1/({2a}*(x-1))-1/({a}*(x+2))+{5a}*(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"1/({2a}*(x-1))-1/({a}*(x+2))+{5a}*(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"1/({2a}*(x-1))-{a}*(x+2)+{5a}*(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"1/({2a}*(x-1))-{a}*(x+2)+{5a}*(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}*(x-1)-1/({a}*(x+2))+{5a}*(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}*(x-1)-1/({a}*(x+2))+{5a}*(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}*(x-1)-{a}*ln(x+2)+1/({5a}*(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"{2a}*(x-1)-{a}*ln(x+2)+1/({5a}*(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-6*ln(abs(x-1))+15ln(abs(x+2))+10*ln(abs(x-3))+C\",\"Double check your calculations for finding $A$, $B$ and $C$. When subbing in the value of $x$ that eliminates the $B$ and $C$ terms, check that you correctly rearranged to find $A$. Similarly for $B$ and $C$.\"],\n    [\"-6*ln(abs(x-1))+15ln(abs(x+2))+10*ln(abs(x-3))\",\"Double check your calculations for finding $A$, $B$ and $C$. When subbing in the value of $x$ that eliminates the $B$ and $C$ terms, check that you correctly rearranged to find $A$. Similarly for $B$ and $C$.\"],\n    [\"-6*ln(x-1)+15ln(x+2)+10*ln(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"-6*ln(x-1)+15ln(x+2)+10*ln(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to include the absolute value signs i.e. $\\\\ln \\\\left| x-1 \\\\right|$ etc. Enter $\\\\left|{x+a}\\\\right|$ by typing abs($x+a$).\"],\n    [\"-6/(x-1)+15/(x+2)+10/(x-3)+C\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"],\n    [\"-6/(x-1)+15/(x+2)+10/(x-3)\",\"Double check your calculations for finding $A$, $B$ and $C$. For example, if $mA=p$ then $A=\\\\frac{p}{m}$ not $\\\\frac{m}{p}$. Similarly for $B$ and $C$. Also, don't forget to integrate once you fill in for $A$, $B$ and $C$!\"]\n    ]\n\n\nparsed_malrules: \n    map(\n        [\"expr\":parse(x[0]),\"feedback\":x[1]],\n        x,\n        malrules\n    )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n    map(\n        len(filter(not x ,x,map(\n            try(\n                resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n                message,\n                false\n            ),\n            vars,\n            vset\n        )))<settings[\"failureRate\"],\n        malrule,\n        parsed_malrules\n    )\n\nmatched_malrules:\n  filter(x[0],x,zip(agree_malrules,parsed_malrules))\n  \nmalrule_feedback:\n    assert(numericallyCorrect,\n        assert(len(matched_malrules)=0,\n            set_credit(0,matched_malrules[0][1][\"feedback\"])\n        )\n    )\n\nmark:\n    apply(studentExpr);\n    apply(unexpectedVariables);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty)", "checkingType": "absdiff", "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\int \\frac{\\simplify{6{a}x^2+7{a}x-25{a}}}{(x-1)(x+2)(x-3)} \\ dx$</p>", "showFeedbackIcon": true, "checkVariableNames": false, "failureRate": 1, "answer": "2{a}*ln(abs(x-1))-{a}*ln(abs(x+2))+5{a}*ln(abs(x-3))+C", "type": "jme", "useCustomName": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}], "showPreview": true, "customName": "", "vsetRangePoints": 5, "showCorrectAnswer": true}], "variables": {"a": {"group": "Ungrouped variables", "name": "a", "templateType": "anything", "description": "", "definition": "random(1..3)"}}, "preamble": {"js": "", "css": ""}, "tags": [], "variable_groups": [], "advice": "", "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"]}, {"name": "Substitution v2 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}], "functions": {}, "parts": [{"showCorrectAnswer": true, "unitTests": [], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "showFeedbackIcon": true, "prompt": "<p>$\\int x \\left( \\var{b} + x^2 \\right)^{\\var{c}} \\ dx$</p>\n<p>[[0]]</p>", "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "gaps": [{"showCorrectAnswer": true, "unitTests": [], "vsetRange": [0, 1], "type": "jme", "scripts": {}, "showFeedbackIcon": true, "valuegenerators": [{"value": "", "name": "c"}, {"value": "", "name": "x"}], "customName": "", "adaptiveMarkingPenalty": 0, "showPreview": true, "variableReplacements": [], "marks": "2", "checkingType": "absdiff", "useCustomName": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"u^({c+1})/({2*(c+1)})+C\", \"Don't forget to sub back in for $u$. Your answer must be in terms of $x$ (the original variable in the question).\"],\n    [\"u^({c+1})/({2*(c+1)})\", \"Don't forget to sub back in for $u$. Your answer must be in terms of $x$ (the original variable in the question).\"],\n    [\"1/2*({b}+x^2)^({c+1})/({c+1})\", \"Almost there! Did you forget to include the integration constant?\"],\n    [\"({b}+x^2)^({c+1})/({c+1})+C\", \"You're on the right track. Double check the relationship between $du$ and $dx$.\"],\n    [\"({b}+x^2)^({c+1})/({c+1})\", \"You're on the right track. Double check the relationship between $du$ and $dx$.\"],\n    [\"u^({c+1})/(({c+1}))+C\", \"You're on the right track. Double check the relationship between $du$ and $dx$. Also, don't forget to give your answer in terms of the original variable in the question i.e. in terms of $x$.\"],\n    [\"u^({c+1})/(({c+1}))\", \"You're on the right track. Double check the relationship between $du$ and $dx$. Also, don't forget to give your answer in terms of the original variable in the question i.e. in terms of $x$.\"],\n    [\"1/2*u^{c}+C\",\"You haven't actually integrated anything. You simply subbed in for $\\\\var{b}+x^2$. Also, once you have integrated, make sure you sub back in for $u$ - you must give your answer in terms of the original variable in the question i.e. in terms of $x$.\"],\n    [\"1/2*u^{c}\",\"You haven't actually integrated anything. You simply subbed in for $\\\\var{b}+x^2$. Also, once you have integrated, make sure you sub back in for $u$ - you must give your answer in terms of the original variable in the question i.e. in terms of $x$.\"],\n    [\"1/2*({b}+x^2)^{c}+C\",\"You haven't actually integrated anything. You simply subbed in for $\\\\var{b}+x^2$ and then subbed back again without actually integrating.\"],\n    [\"1/2*({b}+x^2)^{c}\",\"You haven't actually integrated anything. You simply subbed in for $\\\\var{b}+x^2$ and then subbed back again without actually integrating.\"],\n    [\"({b}+x^2)/({2*(c+1)})\", \"Look carefully at how you subbed back in for $u$ in the end. Did you do this correctly? Did you remember to include the power on the bracket?\"],\n    [\"({b}+x^2)/({2*(c+1)})+C\", \"Look carefully at how you subbed back in for $u$ in the end. Did you do this correctly? Did you remember to include the power on the bracket?\"],\n    [\"2*u^({c+1})/({c+1})+C\", \"Double check the relationship between $du$ and $dx$. Also, don't forget to sub back in for $u$. Your answer must be in terms of $x$ (the original variable in the question).\"],\n    [\"2*u^({c+1})/({c+1})\", \"Double check the relationship between $du$ and $dx$. Also, don't forget to sub back in for $u$. Your answer must be in terms of $x$ (the original variable in the question).\"],\n    [\"2*({b}+x^2)^({c+1})/({c+1})+C\", \"Double check the relationship between $du$ and $dx$.\"],\n    [\"2*({b}+x^2)^({c+1})/({c+1})\", \"Double check the relationship between $du$ and $dx$.\"]\n    ]\n\n\nparsed_malrules: \n    map(\n        [\"expr\":parse(x[0]),\"feedback\":x[1]],\n        x,\n        malrules\n    )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n    map(\n        len(filter(not x ,x,map(\n            try(\n                resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n                message,\n                false\n            ),\n            vars,\n            vset\n        )))<settings[\"failureRate\"],\n        malrule,\n        parsed_malrules\n    )\n\nmatched_malrules:\n  filter(x[0],x,zip(agree_malrules,parsed_malrules))\n  \nmalrule_feedback:\n    assert(numericallyCorrect,\n        assert(len(matched_malrules)=0,\n            set_credit(0,matched_malrules[0][1][\"feedback\"])\n        )\n    )\n\nmark:\n    apply(studentExpr);\n    apply(unexpectedVariables);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty)", "answer": "({b}+x^2)^({c}+1)/({2*(c+1)})+C", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false}]}], "ungrouped_variables": ["a", "b", "c"], "advice": "", "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Find&nbsp;the following indefinite integral using the letter $C$ for the constant of integration.</p>", "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>Integration by substitution with feedback for some common errors.</p>"}, "preamble": {"js": "", "css": ""}, "variables": {"b": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(1..15)", "name": "b"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(2..20)", "name": "a"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(2..20)", "name": "c"}}, "tags": [], "variable_groups": []}]}], "type": "exam", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}], "extensions": [], "custom_part_types": [{"source": {"pk": 2, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/2/edit"}, "name": "List of numbers", "short_name": "list-of-numbers", "description": "<p>The answer is a comma-separated list of numbers.</p>\n<p>The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.</p>\n<p>You can optionally treat the answer as a set, so the number of occurrences doesn't matter, only whether each number is included or not.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "join(\n  if(settings[\"correctAnswerFractions\"],\n    map(let([a,b],rational_approximation(x), string(a/b)),x,settings[\"correctAnswer\"])\n  ,\n    settings[\"correctAnswer\"]\n  ),\n  settings[\"separator\"] + \" \"\n)", "hint": {"static": false, "value": "if(settings[\"show_input_hint\"],\n  \"Enter a list of numbers separated by <code>{settings['separator']}</code>.\",\n  \"\"\n)"}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "bits:\nlet(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)\n\nexpected_numbers:\nlet(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)\n\nvalid_numbers:\nif(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )\n\nis_sorted:\nassert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )\n\nincluded:\nmap(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )\n\nall_included:\nall(included)\n\nno_extras:\nif(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )\n\ninterpreted_answer:\nif(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)\n\nmark:\nif(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)\n\nnotationStyles:\n[\"en\"]\n\nisSet:\nsettings[\"isSet\"]\n\nextra_numbers:\nfilter(not (x in expected_numbers),x,interpreted_answer)", "marking_notes": [{"name": "bits", "description": "<p>The separate items in the student's answer</p>", "definition": "let(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)"}, {"name": "expected_numbers", "description": "", "definition": "let(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)"}, {"name": "valid_numbers", "description": "<p>Is every number in the student's list valid?</p>", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )"}, {"name": "is_sorted", "description": "<p>Are the student's answers in ascending order?</p>", "definition": "assert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )"}, {"name": "included", "description": "<p>Is each number in the expected answer present in the student's list the correct number of times?</p>", "definition": "map(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )"}, {"name": "all_included", "description": "<p>Has every number been included the right number of times?</p>", "definition": "all(included)"}, {"name": "no_extras", "description": "<p>True if the student's list doesn't contain any numbers that aren't in the expected answer.</p>", "definition": "if(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "if(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)"}, {"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=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)"}, {"name": "notationStyles", "description": "", "definition": "[\"en\"]"}, {"name": "isSet", "description": "<p>Should the answer be considered as a set, so the number of times an element occurs doesn't matter?</p>", "definition": "settings[\"isSet\"]"}, {"name": "extra_numbers", "description": "<p>Numbers included in the student's answer that are not in the expected list.</p>", "definition": "filter(not (x in expected_numbers),x,interpreted_answer)"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The list of numbers that the student should enter. The order does not matter.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "allowFractions", "label": "Allow the student to enter fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "correctAnswerFractions", "label": "Display the correct answers as fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "isSet", "label": "Is the answer a set?", "help_url": "", "hint": "If ticked, the number of times an element occurs doesn't matter, only whether it's included at all.", "input_type": "checkbox", "default_value": false}, {"name": "show_input_hint", "label": "Show the input hint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": true}, {"name": "separator", "label": "Separator", "help_url": "", "hint": "The substring that should separate items in the student's list", "input_type": "string", "default_value": ",", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [["question-resources/image_K0BP3FV.png", "/srv/numbas/media/question-resources/image_K0BP3FV.png"], ["question-resources/image_jS71fGY.png", "/srv/numbas/media/question-resources/image_jS71fGY.png"], ["question-resources/image_8rDGI2c.png", "/srv/numbas/media/question-resources/image_8rDGI2c.png"], ["question-resources/image_AgeDfYh.png", "/srv/numbas/media/question-resources/image_AgeDfYh.png"]]}