Practice Test 10 - 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 heat-transfer model leads to $\int \frac{3}{(x+1)(x+7)}\,dx$; find an antiderivative.
2. A quantity satisfies $\frac{dy}{dt}=\ln 2\, y$ with $y(0)=5$. Find $y(1)$.
3. Which slope field corresponds to $\dfrac{dy}{dx}=\sin x$ for a curve $y(x)$ modeling vertical displacement?
4. A bacteria culture satisfies $\frac{dN}{dt}=\frac{4}{t}N$. What is the general solution for $N(t)$?
5. Let $p(t)=(\tan t)(t^2-1)$. What is $p'(t)$?
6. For $f(x)=x^3-6x^2+9x$, on which interval(s) is $f$ increasing?
7. The region bounded by $x=4-y^2$ and the y-axis on $-2\le y\le 2$ is revolved about the y-axis; which integral gives volume?
8. A series is $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{1}{n(n+1)}$. Does it converge?
9. Which integral represents the volume: base bounded by $y=2x$ and $y=0$ for $0\le x\le 3$; cross sections ⟂ $x$-axis are equilateral triangles?
10. Using $P_3$ about $x=0$ to approximate $s(0.6)$, given $|s^{(4)}(x)|\le 2$ on $[0,0.6]$, what is the maximum error?
11. Looking at the graph of $z(x)$, there's a gap in the curve at $x = -3$. The left piece of the curve ends at $(-3, 5)$ with an open circle, and the right piece begins at $(-3, 5)$ with an open circle. What is $\lim_{x \to -3} z(x)$?
12. A function $g$ has $g'(-1)=0$ and $g''(-1)=7$; what is the classification of $x=-1$?
13. If $f'(x)=(x-2)(x+1)$ for all real $x$, on which interval(s) is $f$ increasing?
14. A bacteria culture satisfies $\frac{dP}{dt}=0.5P(1-P)$. Which expression gives the general solution for $P(t)$?
15. A population satisfies $\frac{dN}{dt}=kN$, $N(0)=3$, and $N(4)=3e^{2}$. Find $k$.
16. The area is modeled by $A(x)=\sin x\,(x^3-1)$. What is $A'(x)$?
17. For $p(x)=\frac{1}{x}$ on $[1,\infty)$, does $\int_{1}^{\infty} p(x)\,dx$ converge, and to what value?​
18. Let $p(x)=\dfrac{\ln x}{x}$. What is $p'(x)$?​
19. Let $r(x)=\dfrac{x^2+1}{x^2-9}$. Which statement correctly identifies all vertical asymptotes?
20. The cost function is $C(x)=12x^4-5x^3+2x+11$. What is $C'(x)$?

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