// Numbas version: exam_results_page_options {"name": "Mystery derivatives", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": ["geogebra"], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "

Given a set of curves on axes, generated from a function and its first two derivatives, identify which curve corresponds to which derivative.

"}, "statement": "\n

The following graph (which may take a little while to load) shows three curves: a solid line, a dashed line and a dotted line. These curves represent a function and its derivatives; if we call the function \$f\$, then one curve represents \$f\$ and the other two curves represent \$f'\$ and \$f''\$.

\n

{geogebra_applet('BsRYG6PV',defs)}

", "functions": {}, "ungrouped_variables": ["defs"], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"defs": {"templateType": "anything", "name": "defs", "group": "Ungrouped variables", "description": "", "definition": "[\n ['b',b],\n ['c',c],\n ['d',d],\n ['e',g],\n ['f',f],\n ['cols','{'+linesText+'}'],\n ['sel',selector]\n]"}, "g": {"templateType": "anything", "name": "g", "group": "Function definition", "description": "", "definition": "random(2..3)"}, "linesText": {"templateType": "anything", "name": "linesText", "group": "Answer definition", "description": "", "definition": "join(lines,',')"}, "markMatrix": {"templateType": "anything", "name": "markMatrix", "group": "Answer definition", "description": "", "definition": "matrix(map(map(if(lines[a]=b,2,-1),a,0..2),b,[0,1,3]))"}, "c": {"templateType": "anything", "name": "c", "group": "Function definition", "description": "", "definition": "random(-10..10 except 0)/10"}, "f": {"templateType": "anything", "name": "f", "group": "Function definition", "description": "", "definition": "random(0,1)"}, "selector": {"templateType": "anything", "name": "selector", "group": "Function definition", "description": "", "definition": "random(0,1)"}, "b": {"templateType": "anything", "name": "b", "group": "Function definition", "description": "", "definition": "random(-10..10)/10"}, "d": {"templateType": "anything", "name": "d", "group": "Function definition", "description": "", "definition": "random(3..5)"}, "lines": {"templateType": "anything", "name": "lines", "group": "Answer definition", "description": "", "definition": "shuffle([0,1,3])"}}, "preamble": {"js": "", "css": ""}, "tags": [], "variable_groups": [{"name": "Function definition", "variables": ["b", "c", "d", "g", "f", "selector"]}, {"name": "Answer definition", "variables": ["lines", "linesText", "markMatrix"]}], "type": "question", "advice": "

Here are some questions to consider for this problem.

\n
\n
• What happens to even functions when you differentiate them? What about odd functions?
• \n
• Can you identify any maxima and minima and line them up with zeroes in other functions?
• \n
", "name": "Mystery derivatives", "parts": [{"choices": ["

Solid line

", "

Dashed line

", "

Dotted line

"], "layout": {"type": "all", "expression": ""}, "showFeedbackIcon": true, "matrix": "markMatrix", "showCorrectAnswer": true, "marks": 0, "displayType": "radiogroup", "warningType": "none", "prompt": "

For each curve, select the corresponding derivative. You will score \$2\$ points for each curve correctly identified, and \$-1\$ point for each curve incorrectly identified.