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Part of HELM Book 2.2.2.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Explain what is meant by the term 'parameter'.</p>", "advice": "<p>If $x=\\sqrt(t)$ then $x^2=t=y$.</p>\n<p>When $t=0, x=0$</p>\n<p>When $t=10, x=\\sqrt{10}$</p>\n<p>Hence $y=x^2,\\quad 0\\leq x\\leq \\sqrt{10}$</p>\n<p style=\"text-align: center;\">{diagram}</p>", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"diagram": {"name": "diagram", "group": "Ungrouped variables", "definition": "jsxgraph(\n  300,300,\n  [graphxmin, graphymax, graphxmax,graphymin],\n  [\n    \"f\":['functiongraph',[function]]\n  ]\n)  ", "description": "", "templateType": "anything", "can_override": false}, "function": {"name": "function", "group": "Ungrouped variables", "definition": "expression(\"x^2\")", "description": "", "templateType": "anything", "can_override": false}, "graphxmax": {"name": "graphxmax", "group": "Ungrouped variables", "definition": "4", "description": "", "templateType": "anything", "can_override": false}, "graphxmin": {"name": "graphxmin", "group": "Ungrouped variables", "definition": "-1", "description": "", "templateType": "anything", "can_override": false}, "graphymax": {"name": "graphymax", "group": "Ungrouped variables", "definition": "11", "description": "", "templateType": "anything", "can_override": false}, "graphymin": {"name": "graphymin", "group": "Ungrouped variables", "definition": "-1", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["diagram", "function", "graphxmax", "graphxmin", "graphymax", "graphymin"], "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>Consider the parametric equations $x =\\sqrt{t}$, $y=t$, for $t\\geq 0$.<br/><br/>(a) Draw up a table of values of $t$, $x$ and $y$ for values of $t$ between $0$ and $10$.<br/>(b) Plot a graph of this function.<br/>(c) Obtain an explicit equation for y in terms of x.</p>\n<p>$y=$ [[0]].</p>\n<p>Domain:&nbsp; [[1]] $\\leq x \\leq$ [[2]]&nbsp;</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "y", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "x^2", "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": "x", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "domain min", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": true, "customName": "domain max", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "sqrt(10)", "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": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}