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{"name": "MATH1023 Week 2 vocabulary", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "MATH1023 Week 2 vocabulary", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Complete the passage with the words and phrases from the following list:</p>\n<table style=\"width: 692px;\" height=\"56\">\n<tbody>\n<tr>\n<td style=\"width: 108.531px;\">explicit</td>\n<td style=\"width: 126.609px;\">medium</td>\n<td style=\"width: 129.625px;\">reciprocal</td>\n<td style=\"width: 137.656px;\">separable</td>\n<td style=\"width: 108.578px;\">terminal</td>\n</tr>\n<tr>\n<td style=\"width: 108.531px;\">implicit</td>\n<td style=\"width: 126.609px;\">proportionality</td>\n<td style=\"width: 129.625px;\">satisfies</td>\n<td style=\"width: 137.656px;\">standard</td>\n<td style=\"width: 108.578px;\">tractable</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "advice": "", "rulesets": {}, "extensions": [], "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": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A first order differential equation is in [[0]]<b> </b>form if it is written as $\\frac{dy}{dx} = f(x,y)$.</p>\n<p>A solution to a differential equation is a function that [[1]]<b> </b>the equation. In other words, when the solution is substituted into the equation, the equation is true.</p>\n<p>There are many different types of differential equations, and there are many different methods for solving them. Some differential equations are [[2]], meaning that they can be solved using relatively simple methods. Others are intractable, meaning that there is no known method for solving them exactly.</p>\n<p>A differential equation is [[3]] if it can be written in the form $f(y) dy = g(x) dx$ where $f$ and $g$ are any functions.</p>\n<p>We can solve the separable differential equation $\\frac{dy}{dx} = 3y^2$ by taking the [[4]]<b> </b>of both sides to get $\\frac{dx}{dy} = \\frac{1}{3y^2}$ and integrating both sides with respect to $y$.</p>\n<p>One way to classify equations is by whether they are explicit or implicit. An [[5]]<b> </b>equation for $y$ is one where $y$ is isolated on one side of the equation. Otherwise the equation is [[6]].</p>\n<p>The [[7]]<b> </b>velocity of an object is the constant velocity that it reaches when it is falling through a [[8]], such as air or water. A simple model for this situation could be $\\frac{dv}{dt} = g - kv$, where $v$ is the velocity of the object, $g$ is the acceleration due to gravity, and $k$ is a constant of [[9]] that depends on the medium.</p>", "gaps": [{"type": "patternmatch", "useCustomName": true, "customName": "gap1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "standard", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "gap2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": 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