Rates of Change (Leaving Cert Mathematics): Quizzes

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Rates of Change
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What does dydx=2\frac{dy}{dx} = 2 mean?

yy increases 2 units per 1 unit xx rises

How does the rate of change differ between linear and curved functions?

Linear: constant; Curved: varies

What formula gives the average rate of change between points P(x1,y1)(x_1, y_1) and Q(x2,y2)(x_2, y_2)?

y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}

What line type represents instantaneous rate of change at a point?

Tangent line

What formula represents velocity in terms of displacement ss?

dsdt\frac{ds}{dt}

What does positive velocity indicate about a particle's motion?

Moving away from a fixed point

What is the formula for acceleration in terms of displacement ss?

d2sdt2\frac{d^2s}{dt^2}

What are the units of acceleration?

m/s²

What does negative acceleration indicate?

Speed is decreasing

When is a moving body at rest?

When velocity equals zero

If V=3t2+4t+2V = 3t^2 + 4t + 2, what is dVdt\frac{dV}{dt} when t=2t = 2?

16

For s=3t3−4t+6s = 3t^3 - 4t + 6, when is the body at rest?

t=23t = \frac{2}{3}

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