e":"1.6.4 Parametric equations in modelling (A-level only) Flashcards","topicId":"74df085b-a07b-40f5-a328-fe184794b4c7","topicSlug":"parametric-equations-in-modelling","cards":[{"id":"1a9e2a52-7fa5-41e0-b28f-a9c75afb84dd","cardType":"basic","front":"In a parametric model, what does the parameter often represent?","back":"A changing quantity such as time or angle.","points":1,"mcqOptions":null},{"id":"6b26c3aa-8608-452c-8ef9-185de76cf35a","cardType":"cloze","front":"Each permitted value of the parameter determines [ ].","back":"Each permitted value of the parameter determines a point on the curve.","points":null,"mcqOptions":null},{"id":"801e9f79-1368-407a-8135-a68d6f54a7fa","cardType":"basic","front":"For $x=3t-2$ and $y=5-t^2$, where is the particle at $t=2$?","back":"The particle is at $(4,1)$.","points":1,"mcqOptions":null},{"id":"28e1b541-ddb9-4f9d-8329-e420a7422bcb","cardType":"basic","front":"For $x=3t-2$ and $y=5-t^2$, how does the particle move from $t=0$ to $t=2$?","back":"It moves right and down.","points":2,"mcqOptions":null},{"id":"bea1bd90-ef3a-4c2f-9a23-252b03900a30","cardType":"cloze","front":"Only the curve section corresponding to the [ ] belongs to the model.","back":"Only the curve section corresponding to the permitted parameter range belongs to the model.","points":null,"mcqOptions":null},{"id":"ccac74bf-07dd-47e0-90e3-73bd4ed94e37","cardType":"basic","front":"Why might a projectile model exclude parameter values after it hits the ground?","back":"They may predict physically meaningless positions below ground.","points":2,"mcqOptions":null},{"id":"e28ecded-1cfc-4c9e-8826-bf66664ea549","cardType":"cloze","front":"For constant horizontal velocity $u$, the horizontal position is $\\text{[...]}$.","back":"For constant horizontal velocity $u$, the horizontal position is $\\boxed{x=x_0+ut}$.","points":null,"mcqOptions":null},{"id":"2444d9da-e3aa-4f62-beec-7e12cfdba066","cardType":"cloze","front":"For constant vertical velocity $v$, the vertical position is $\\text{[...]}$.","back":"For constant vertical velocity $v$, the vertical position is $\\boxed{y=y_0+vt}$.","points":null,"mcqOptions":null},{"id":"d888abf4-3120-4728-8b89-b2efd7a139af","cardType":"basic","front":"A boat starts at $(20,5)$ and moves east at $4$ m s$^{-1}$ and north at $3$ m s$^{-1}$. Where is it after 6 seconds?","back":"The boat is at $(44,23)$.","points":2,"mcqOptions":null},{"id":"f5e7ceda-ca1e-4b45-9b6c-a2adc10598ad","cardType":"basic","front":"What parametrisation models a circle of radius $r$ centred at $(a,b)$?","back":"$x=a+r\\cos\\theta,\\quad y=b+r\\sin\\theta$","points":2,"mcqOptions":null},{"id":"c22e6642-8e91-4c6a-8997-a97cd74b8cbd","cardType":"basic","front":"In the standard circle parametrisation, what motion occurs as $\\theta$ increases from $0$ to $2\\pi$?","back":"One complete anticlockwise revolution.","points":1,"mcqOptions":null},{"id":"200d962f-f216-4330-886f-f508e683909f","cardType":"basic","front":"Where does the standard circle parametrisation start when $\\theta=0$?","back":"At $(a+r,b)$.","points":1,"mcqOptions":null},{"id":"2d5a58f0-bf07-491a-abe9-6dd52657ae03","cardType":"cloze","front":"Swapping sine and cosine or inserting a minus sign can change a circular model's [ ].","back":"Swapping sine and cosine or inserting a minus sign can change a circular model's starting point and direction.","points":null,"mcqOptions":null},{"id":"ae4be621-45dd-4421-bb8b-59771828e314","cardType":"basic","front":"What parametric equations model a circle of radius 5 centred at $(2,-1)$?","back":"$x=2+5\\cos\\theta,\\quad y=-1+5\\sin\\theta$","points":2,