Polar Coordinates (College Board AP® Calculus BC): Exam Questions

The area of the shaded region shown on the graph of the polar curve $r=3+6\sin \theta$ is

The area of the closed region bounded by the polar curve $r=\sqrt{2+\sin \theta }$ is

Which of the following represents the graph of the polar curve $r=3\csc \theta$?

Which of the following is equal to the area of the region inside the polar curve $r=3\sin \theta$ and outside the polar curve $r=\sin \theta$ for $0\le \theta \le \pi$?

The value of $\frac{dy}{d\theta }$ at $\theta =\frac{\pi }{4}$on the polar curve $r=4+3\cos \theta$ is

An expression for the slope of a spiral defined by the polar curve $r=\theta$, where $\theta >0$, in terms of $\theta$ is

The shaded area shown below, between the two polar curves $r=4+3\sin \theta$ and $r=3+\sin \theta$, has an area of

A particle moves along the polar curve $r=2+\cos \theta$ with position $\left(x\left(t\right),y\left(t\right)\right)$, measured in centimeters, where $t$ is time, measured in seconds. If the motion of the particle is such that the angle $\theta$ always increases at a constant rate of 3 radians per second, then the rate at which the distance $r$ decreases at the point where $\theta =\frac{\pi }{6}$ is

A particle moves along the polar curve $r=2+{\theta }^2$ with position $\left(x\left(t\right),y\left(t\right)\right)$ at time $t\ge 0$. If $\frac{dx}{dt}=20$ at the point when $\theta =\frac{5\pi }{8}$, then $\frac{d\theta }{dt}$ at this point is

For the circle defined by the polar equation $r=a$ where $a$ is a positive constant and $0\le \theta <2\pi$, an expression for $\frac{d^{2}y}{d{x}^2}$ in terms of $\theta$ is