// Numbas version: exam_results_page_options {"name": "BC Calculus Fall - Final Project", "metadata": {"description": "", "licence": "None specified"}, "duration": 240000, "percentPass": "50", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], [], [], [], [], [], [], []], "questions": [{"name": "Antiderivative of 1/(e^x + 1)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute: [Hint: let $u = e^x$.]

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$A_x \\bigg(\\displaystyle{\\frac{1}{e^x + 1}}\\bigg)$

", "answer": "x - ln(e^x + 1) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AA", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute:

$A_x \\sin \\sqrt{x}$

", "answer": "2sin(sqrt(x)) - 2sqrt(x) * cos(sqrt(x)) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AB", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute:

$A_x \\bigg( \\displaystyle{\\frac{x + 1}{x^3 - 1}}\\bigg)$

", "answer": "(2/3)ln(abs(x - 1)) - (1/3)ln(abs(x^2 + x + 1)) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AC", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute:

$A_x \\big( x \\sec^2 x \\big)$

", "answer": "x * tan(x) + ln(abs(cos(x))) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AD", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute:

$A_x \\big( x \\arcsin x \\big)$

", "answer": "(1/4)x * sqrt(1 - x^2) + (1/4)(2x^2 - 1) * arcsin(x) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AE", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute:

$A_x \\bigg(\\displaystyle{\\frac{e^{6x}}{e^{2x} + 1}}\\bigg)$

", "answer": "-(1/2)e^(2x) + (1/4)e^(4x) + (1/2)ln(e^(2x) + 1) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AF", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute:

$A_x \\bigg( \\displaystyle{\\frac{\\sqrt{4 + \\sqrt{x}}}{\\sqrt{x}}}\\bigg)$

", "answer": "(4/3)(4 + sqrt(x))^(3/2) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AG", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute: [Hint: Complete the square under the radical sign. Write the quadratic in the form $a^2 - (x + b)^2$.]

$A_x \\sqrt{21 - 4x - x^2}$

", "answer": "(1/2)(x + 2) * sqrt(21 - 4x - x^2) + (25/2) arcsin((x + 2)/5) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AH", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute: [Hint: Insert a harmless factor of $1 = x'$ inside the antiderivative sign. Use parts.]

$A_x \\,(\\ln x)^2$

", "answer": "x * (ln(x))^2 - 2x * ln(x) + 2x + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AI", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute: [Hint: Repeated antidifferentiation by parts, use tabular method covered in class on Monday.]

$A_x \\big\\{(2x^3 + 8x + 5)\\sin 2x \\big\\}$

", "answer": "-(1/2)(5 + 5x + 2x^3) * cos(2x) + (1/4)(5 + 6x^2) * sin(2x) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AJ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute: [Hint: Use the recursive formula for powers of sine.]

$A_x \\, \\sin^3 x$

", "answer": "-(2/3)cos(x) - (1/3)cos(x) * (sin(x))^2 + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AK", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute: [Hint: Use the inverse function rule. The inverse of the function shown is a polynomial.]

$A_x \\sqrt{4 + \\sqrt{x}}$

", "answer": "(4/15)(4 + sqrt(x))^(3/2) * (3sqrt(x) - 8) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AL", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute:

$A_x \\bigg(\\displaystyle{\\frac{x}{x^3 + 1}}\\bigg)$

", "answer": "(1/6)ln(abs(x^2 - x + 1)) - (1/3)ln(abs(x + 1)) + (sqrt(3)/3) arctan((2x - 1)/sqrt(3)) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AM", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute: [Hint: Separate off a factor of $\\sec x \\tan x$ to serve as a $du$ for the substitution $u = \\sec x$.]

$A_x \\big(\\tan^3 x \\sec^7 x \\big)$

", "answer": "(1/9)(sec(x))^9 - (1/7)(sec(x))^7 + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Antiderivative AN", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Compute: [Hint: $a \\sin x + b \\cos x = \\sqrt{a^2 + b^2}\\, \\sin\\big(x + \\arctan(b/a)\\big)$ when $a > 0$ and $b > 0$, using the sine of a sum formula and the identities $\\sin(\\arctan x) = x/\\sqrt{1 + x^2}$ and $\\cos(\\arctan x) = 1/\\sqrt{1 + x^2}$.]

$A_x \\bigg(\\displaystyle{\\frac{1}{3\\sin x + 4\\cos x}}\\bigg)$

", "answer": "(1/5)ln(abs(cosec(x + arctan(4/3)) - cot(x + arctan(4/3)))) + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": false, "showfrontpage": true, "showresultspage": "never", "navigatemode": "sequence", "onleave": {"action": "warnifunattempted", "message": "

You are about to leave the current question.

"}, "preventleave": true, "typeendtoleave": false, "startpassword": "u-sub", "allowAttemptDownload": true, "downloadEncryptionKey": "SU(2)symmetry"}, "timing": {"allowPause": true, "timeout": {"action": "warn", "message": "

Your time is up.

"}, "timedwarning": {"action": "warn", "message": "

You have 5 minutes left.

"}}, "feedback": {"showactualmark": false, "showtotalmark": false, "showanswerstate": false, "allowrevealanswer": false, "advicethreshold": 0, "intro": "

Time is essentially unlimited (3000 minutes). You may pause the assessment at any time. As you work on each problem, you must do a fully explained and detailed write-up of all the steps you took in your computations. Handwrite this on your own paper; you will be handing that in to me for verification purposes.

To submit an answer, type the formula (some expression in the variable 'x' and the arbitrary additive constant 'C') into the answer field shown using standard ASCII syntax. For instance, \"(1/2)ln(abs(x^2 + x + 1)) + C\" gives half the natural logarithm of the absolute value of a certain quadratic function, plus an arbitrary constant. Another example: \"x*sin(x) - cos(x)\" is x times the sine of x, minus the cosine of x. Another: \"arctan((x - sqrt(2))/5)\" is the arctangent of one fifth of x minus the square root of 2.

The password to start the assessment is \"u-sub\".

EXTREMELY IMPORTANT: At the end of the assessment, you MUST click on \"download your exam data\". An encrypted .txt file will be downloaded to your computer, containing a record of your answers and attempts. You will then upload this to a specially created assignment in Google Classroom. I can then collect the data and record the scores. Without doing this step, your work would have been in vain, as I will not have a score for you (!).

", "end_message": "

Thank you for submitting your final project!

", "reviewshowscore": true, "reviewshowfeedback": false, "reviewshowexpectedanswer": false, "reviewshowadvice": false, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Joseph Stern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21918/"}], "extensions": [], "custom_part_types": [], "resources": []}