// Numbas version: finer_feedback_settings {"name": "Quiz 1 - computing terms", "metadata": {"description": "Recurrence relations quiz", "licence": "None specified"}, "duration": 900, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Quiz - Computing terms Q1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "metadata": {"licence": "None specified", "description": ""}, "variables": {"c": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(80..100)", "name": "c"}, "d": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "c-1", "name": "d"}, "b": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..5)", "name": "b"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..9)", "name": "a"}, "f": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "c-2", "name": "f"}}, "parts": [{"showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "prompt": "
Compute the first four terms of this recurrence relation.
\nC(1) = [[0]]
\nC(2) = [[1]]
\nC(3) = [[2]]
\nC(4) = [[3]]
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\n$C(\\var{c}) = C(\\var{d}) + $[[0]]
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\n$C(\\var{c}) = C(\\var{f}) + $[[0]]
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\n\\[C(n)=\\begin{cases}\\var{b} & if & n=1\\\\ C(n-1) + \\var{a} & if & n\\geq2 \\end{cases}\\]
\n", "type": "question"}, {"name": "Quiz - Computing terms Q2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "ungrouped_variables": ["a", "b", "c"], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "Consider the following recurrence relation:
\n\\[P(n)=\\begin{cases}\\var{a} & if & n=1\\\\ P(n-1) + n & if & n \\geq 2\\\\ \\end{cases}\\]
\n", "metadata": {"description": "", "licence": "None specified"}, "rulesets": {}, "functions": {}, "advice": "", "variables": {"b": {"description": "", "group": "Ungrouped variables", "name": "b", "templateType": "anything", "definition": "random(1..4 except a)"}, "a": {"description": "", "group": "Ungrouped variables", "name": "a", "templateType": "anything", "definition": "random(0..5)"}, "c": {"description": "", "group": "Ungrouped variables", "name": "c", "templateType": "anything", "definition": "random(1..5)"}}, "parts": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "Compute the first four terms of this recurrence relation.
\nP(1) = [[0]]
\nP(2) = [[1]]
\nP(3) = [[2]]
\nP(4) = [[3]]
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\n\\[F(n)=\\begin{cases}\\var{a} & if & n=1\\\\ \\var{b} & if & n=2\\\\ F(n-1) + F(n-2) & if & n\\geq3 \\end{cases}\\]
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\nF(1) = [[0]]
\nF(2) = [[1]]
\nF(3) = [[2]]
\nF(4) = [[3]]
\nF(5) = [[4]]
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