Practice Test 12 - AP Calculus AB

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

A cyclist's power output is $p(t)$ watts at time $t$ seconds. What does $\int_{0}^{120} p(t)\,dt$ represent?
For $U(x)=\begin{cases}x^2+2,&x\ne-3\\11,&x=-3\end{cases}$ , is $U$ continuous at $x=-3$ , and why?
If $w(x)=\cot(\pi x)$ , what is $w'(x)$ ?
A differentiable function $L(x)$ gives light intensity. Which expression represents the slope of $L$ at $x=1$ ?
A differentiable $f$ has $f'(1)=0$ and $f''(1)>0$ ; classify the point $x=1$ .
A tank's salt amount $S$ satisfies $\frac{dS}{dt}=0.03S$ . If $S(0)=50$ , which is $S(t)$ ?
If $f''(x)=3-x$ for all $x$ , where is $f$ concave up and where is it concave down?
If $f''(x)<0$ for $x<0$ and $f''(x)>0$ for $0<x<8$ , where is $f$ concave up?
A continuous function $g$ on $[-4,2]$ has $g(-4)=0$ and $g(2)=5$ ; which statement must be true?
Given $f''(x)>0$ for $x<1$ and $f''(x)<0$ for $x>1$ , where is $f$ concave up and concave down?
For $h(x)=\begin{cases}x+2,&x<1\\x^2,&x\ge 1\end{cases}$ , what type of discontinuity does $h$ have at $x=1$ ?
For $\gamma(x)=\begin{cases}x^2+1,&x\ne-2\\0,&x=-2\end{cases}$ , what type of discontinuity is at $x=-2$ ?
If $t$ is differentiable and one-to-one with $t(1)=2$ and $t'(1)=-6$ , what is $(t^{-1})'(2)$ ?
A particle's velocity is modeled by $v(t)=\sec(3t)$ . What is $v'(t)$ ?
A function satisfies $\dfrac{dy}{dx}=-4xy$ . What is the general solution for $y(x)$ ?
The velocity of a runner is $v(t)=15t^2+6t-1$ . Which is an antiderivative of $v(t)$ ?
The temperature of a cooling drink is $T(t)$ degrees Celsius after $t$ minutes. Interpret $T'(5)$ .
A particle has $v(2)<0$ and $a(2)>0$ ; which statement about direction at $t=2$ is correct?
A continuous function $g$ on $[0,6]$ has critical points $x=1,5$ . If $g(0)=3,g(1)=4,g(5)=2,g(6)=5$ , where is the absolute maximum?
If an antiderivative of $g$ is $G(x)=\sin x + x^2$ , find $\int_{0}^{\pi} g(x)\,dx$ .

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