Practice Test 11 - AP Calculus AB

20 questions. Answer them in any order, then submit to see your score and every explanation.

Velocity is positive and decreasing at $t=5$ ; which statement about acceleration at $t=5$ is correct?
For a curve $y=f(x)$ , what does $\displaystyle \lim_{h\to 0}\frac{f(2+h)-f(2)}{h}$ represent?
A function satisfies $\dfrac{dy}{dx}=\dfrac{y}{x}$ . What is the general solution for $x\ne 0$ ?
Let $J(t)= -t^6+16t^2-3t+4$ . What is $J'(t)$ ?
Which integral gives the volume when the region under $y=x^2$ from $x=0$ to $x=2$ is revolved about the $x$ -axis?
A circular bracelet's radius decreases at $0.05$ cm/s when $r=20$ cm; how fast is its area changing?
Let $u$ be continuous on $[a,b]$ . If $u$ has no critical points in $(a,b)$ , which statement must be true?
Let $Q(x)=\ln\!\left(1+\sin\!\left(x^2\right)\right)$ . What is $Q'(x)$ ?
Define $g(x)=\int_{0}^{x}\dfrac{1}{1+\cos t}\,dt$ where defined. What is $g'(x)$ ?
A function $g$ has $g'(-2)=0$ and $g''(-2)<0$ . What can be concluded about $x=-2$ ?
For $r(x)=\dfrac{4}{(x-3)^3}$ , which limit expression matches the behavior of $r(x)$ as $x\to3^-$ ?
For $y=x^3-x$ and $y=0$ on $[-1,1]$ , which setup gives the total area between the curves?
For $y=x^2-1$ and $y=0$ on $[-2,2]$ , which setup gives the total area between curves?
A ball's height is $h(t)=16t-4t^2$ for $0\le t\le 4$ . What is the average height on $[0,4]$ ?
Given $y^2\sin x + x\cos y=2$ , what is $\dfrac{dy}{dx}$ at a general point $(x,y)$ ?
A function $J$ is continuous on $[-5,-1]$ with $J(-5)=6$ and $J(-1)=2$ . Does the Mean Value Theorem guarantee a $c$ with $J'(c)=-1$ ?
During a test, $f(x)=\arccos(4x)$ gives an angle reading. What is $f'(x)$ ?
A bank account satisfies $\frac{dA}{dt}=rA$ with $r\neq 0$ . Which is the general solution?
Which definite integral matches $\sum_{m=1}^{20} \cos\!\left(\pi+\frac{m\pi}{10}\right)\left(\frac{\pi}{10}\right)$ ?
If $x^2+\cos y=xy$ , what is $\dfrac{dy}{dx}$ in terms of $x$ and $y$ ?

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