Practice Test 9 - AP Calculus BC

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

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1. Which integral gives area between $x=7-y^2$ (right) and $x=1+ y$ (left) for $-1\le y\le 2$?
2. Let $S=\sum_{n=1}^{\infty}(-1)^{n-1}\frac{n}{n^2+4}$. What is the error bound for approximation by $S_{10}$?
3. The region under $y=\frac{1}{1-x}$ above the x-axis on $0\le x\le \frac{1}{2}$ is revolved about the x-axis; which setup is correct?
4. Which comparison test correctly determines whether $\sum_{n=1}^\infty \frac{\ln(n+1)}{n^2}$ converges?​
5. On $[-1,1]$, $f(x)=2-x^2$ and $g(x)=x$ with $f(x)\ge g(x)$; which integral gives the area between them?
6. A swimmer's position is $\mathbf{r}(t)=\langle \cos(3t),\ \sin(3t),\ t^2\rangle$; compute $\mathbf{r}'(t)$.
7. If $f(2)=5$, $\lim_{x\to2}f(x)=5$, and $f'(2)$ does not exist, which statement must be true?
8. The sum $\sum_{j=1}^{n} \left(\left(3+\frac{2j}{n}\right)^2\right)\frac{2}{n}$ is a Riemann sum. Which integral matches it?
9. For $\dfrac{dy}{dx}=y(1-y)$, is $y=\dfrac{1}{1+e^{-x}}$ a solution on all real $x$?
10. Based on the numerical evidence provided, what is the most probable value of $\lim_{t \to 1} h(t)$?
11. The doors open at $t=0$ and there are no people in the venue initially. Which of the following integrals represents the number of people in the venue at time $t=4$ hours?
12. If $x(t)=e^t$ and $y(t)=t e^t$, what is $\dfrac{d^2y}{dx^2}$ expressed in terms of $t$?
13. For $\dfrac{dy}{dx}=2y$, is the function $y=e^{2x}$ a solution on all real $x$?
14. Region bounded by $y=\ln x$, the $x$-axis, and $x=1$ to $x=e$ is revolved about the $x$-axis; choose the setup.
15. Using this data, what is the approximate rate of change of the amount of the drug in the bloodstream at $t=2.25$ hours, in mg per hour?
16. A temperature correction uses $p(x)=\frac{x}{1-x}$ for $|x|<1$; which power series equals $p(x)$?
17. Determine whether the series $\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n}$ converges absolutely, conditionally, or diverges.
18. A chemist models concentration by $C(t)=\frac{5t+1}{t^2-4}$. What is $\int \frac{5t+1}{t^2-4}\,dt$?
19. A sensor's cumulative drift is $\sum_{n=2}^{\infty}\frac{\ln n}{n^2}$. Use the integral test to determine convergence.
20. For $\sum_{k=1}^{\infty}(-1)^{k-1}\frac{6}{k(k+1)}$, what is the maximum error using $S_9$?

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