s":1},{"id":"c6895fdb-13a9-4bb7-b441-777b3cd8f6b3","cardType":"basic","front":"What is the derivative of a constant (e.g., 11)?","back":"Zero","points":1},{"id":"8f30fc7d-d0bd-454e-95b8-05292ff9d476","cardType":"basic","front":"What is the derivative of a linear term such as $7x$?","back":"$$7$","points":1},{"id":"6e8e98bc-efa5-47a7-9f3d-7bf258476bbd","cardType":"cloze","front":"To differentiate a term like $\\frac{1}{x}$, first rewrite it as $\\text{[...]}$.","back":"To differentiate a term like $\\frac{1}{x}$, first rewrite it as $\\boxed{x^{-1}}$.","points":null},{"id":"157a65a4-feb9-41c4-aff2-f7e5367cf41c","cardType":"basic","front":"Differentiate the term $x^{-1}$.","back":"$$-x^{-2}$ (or $-\\frac{1}{x^2}$)","points":1},{"id":"7dff4cce-505b-4fad-a7d5-46cdfcd750dd","cardType":"basic","front":"What is the required condition for a stationary point?","back":"$$\\frac{dy}{dx} = 0$","points":1},{"id":"7d009d91-d75e-41c0-b283-6ed401bd8f74","cardType":"basic","front":"Describe the tangent at a stationary point.","back":"It is horizontal (gradient is zero).","points":1},{"id":"e2eee804-c4ba-41bd-873e-2b19d5965053","cardType":"basic","front":"How do you find the $y$-coordinate of a stationary point once you have the $x$-coordinate?","back":"Substitute the $x$-value into the original equation for $y$.","points":2},{"id":"f7510955-47a4-472e-a4b7-90ef2d231b01","cardType":"basic","front":"What inequality is used to find where a curve has a negative gradient?","back":"$$\\frac{dy}{dx} < 0$","points":1},{"id":"f79104be-c813-4880-afa2-725fed2bcc94","cardType":"basic","front":"Why are strict inequalities used when finding a range for negative gradients?","back":"At the endpoints, the gradient is zero, not negative.","points":2},{"id":"29bb2aae-4236-4f40-8eb2-a0599a9e4e6d","cardType":"basic","front":"If $\\frac{dy}{dx}$ is an upward-opening quadratic, where is the gradient negative?","back":"Between the two roots.","points":2},{"id":"248a0f99-eadc-4b89-9a1c-b066b53e590d","cardType":"basic","front":"In particle motion, how is velocity ($v$) calculated from displacement ($s$)?","back":"$$v = \\frac{ds}{dt}$","points":1},{"id":"d998709f-b285-48be-ac33-3fce68b790a6","cardType":"basic","front":"In particle motion, how is acceleration ($a$) calculated from velocity ($v$)?","back":"$$a = \\frac{dv}{dt}$","points":1},{"id":"bcd94474-d853-40a1-94d8-3207d354df7a","cardType":"basic","front":"What is the physical condition for a particle to be instantaneously at rest?","back":"Velocity is zero ($v=0$).","points":1},{"id":"deb88988-2f73-4e9b-99d1-a02a7657dd78","cardType":"basic","front":"How do you find acceleration from a displacement equation?","back":"Differentiate twice with respect to $t$.","points":2},{"id":"aa8ec16b-e187-4519-a3ae-3667ecb12a1f","cardType":"cloze","front":"A [ ] is a straight line that touches a curve at one point and has the same direction as the curve at that point.","back":"A tangent is a straight line that touches a curve at one point and has the same direction as the curve at that point.","points":null},{"id":"442083ea-6d10-40b0-b870-35fbc674aac7","cardType":"cloze","front":"A tangent is a straight line that touches a curve at one point and has the same [ ] as the curve at that point.","back":"A tangent is a straight line that touches a curve at one point and has the same direction as the curve at that point.","points":null},{"id":"f82d708e-6c59-4299-8997-69f082c01466","cardType":"cloze","front":"A negative power like $x^{-2}$ means the term belongs in the

Differentiation Flashcards

Differentiation Flashcards

Differentiation Flashcards

Differentiation Flashcards