Practice Test 2 - AP Calculus BC

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

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1. A cooling object satisfies $\frac{dT}{dt}=-\frac{1}{10}(T-20)$ with $T(0)=80$. Find $T(t)$.
2. A series for oscillations is $\sum_{n=1}^{\infty}(-1)^n\frac{1}{n^2+n}$. Does it converge?
3. A series for alternating work is $\sum_{n=1}^{\infty}(-1)^n\frac{\arctan(n)}{n}$. Does it converge?
4. A particle's velocity is $v(t)=6t^2-4t+9$ meters per second; which function is an antiderivative of $v(t)$?
5. For a revenue adjustment, compute $\lim_{x\to 0}\frac{(1+x)^2-1}{x}$ using expansion and cancellation.
6. A signal filter accumulates noise $\sum_{n=1}^{\infty} \frac{1}{n^p}$; for which $p$ is the accumulated noise finite?
7. Let $R$ be bounded by $y=x^2$ and $y=4$ for $0\le x\le2$. Revolve $R$ about $y=5$. Which setup gives the volume?
8. A cylindrical tank has volume $V=\pi r^2h$ with fixed radius $r=5$; which setup relates $\dfrac{dV}{dt}$ and $\dfrac{dh}{dt}$?
9. Consider $\sum_{n=1}^{\infty} \frac{2n}{n^2+1}$. What does the nth-term test imply?
10. A particle's velocity is $v(t)=\sqrt{t}$ for $0\le t\le4$ and $s(0)=-2$; what is $s(4)$?
11. For $q(x)=\frac{|x|}{x}$ when $x\ne 0$ and $q(0)=0$, what type of discontinuity occurs at $x=0$?​
12. An antiderivative of $w$ is $W(x)=x\ln x-x$. Determine $\int_{1}^{4} w(x)\,dx$.
13. Let $G(x)=\int_{3}^{x}\frac{1}{1+t^2}\,dt$. Which is true about $G$ for all real $x$?
14. Let $f$ be a function such that $f''(x)$ exists for all $x$. The expression $\lim_{h \to 0} \frac{f'(x+h) - f'(x)}{h}$ is equivalent to which of the following?
15. At $x=\tfrac{3}{2}$, $J'(\tfrac{3}{2})=0$ and $J''(\tfrac{3}{2})=-10$; classify the critical point.
16. Using $P_3(x)=1+\frac{x}{2}-\frac{x^2}{8}+\frac{x^3}{16}$ for $\sqrt{1+x}$ about $0$, and $|f^{(4)}(x)|\le 5$ on $[0,0.6]$, what maximum error at $x=0.6$?
17. A website gains users at rate $G(t)$ users/day; what does $\int_{10}^{20} G(t)\,dt$ represent?
18. A function $t$ has $t'(x)<0$ on $( -2,0)$ and $t'(x)>0$ on $(0,4)$; where is a local minimum?
19. Consider $sum_{n=1}^{infty}frac{n^2+5}{n^4-1}$ from a computation routine. Which comparison justifies convergence?
20. For $\sum_{n=1}^{\infty} \frac{n!}{(n+1)!}$, what does the nth-term test conclude?

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