Practice Test 2 - AP Calculus AB

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

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1. A measured angle satisfies $h(x)=\arccos(x^2)$. What is $h'(x)$?
2. A curve has slope $y'(x)=25x^4$. Which is an antiderivative of $y'(x)$?
3. A reservoir has water depth $h(t)$; the outflow rate is proportional to $\sqrt{h(t)}$. Which differential equation models $h$ decreasing?
4. A profit function is $P(x)=x^9-3x^4+2x^2$. What is $P'(x)$?
5. Which definite integral matches $\sum_{i=1}^{n}\left(\frac{4i}{n}\right)^3\frac{4}{n}$?
6. For $t(x)=\dfrac{2}{1-x}$, which limit expression represents the behavior of $t(x)$ as $x\to1^-$?
7. A function $b$ is continuous on $[3,11]$ with $b(3)=20$ and $b(11)=4$. Does the Mean Value Theorem guarantee a $c$ with $b'(c)=-2$?
8. The height of a ball is $h(t)$. Which represents the ball's instantaneous vertical velocity at $t=1$?
9. What is the correct washer-method integral for the volume when the region between $y=x+2$ and $y=x^2+1$ on $[0,1]$ is revolved about the x-axis?
10. A tank's net flow rate is $r(t)=6-2t$ gal/min for $0\le t\le 4$. Net change in volume?
11. For $h(x)=\ln\left(\dfrac{(x^2+1)^5}{\sqrt{3x-2}}\right)$, which rules should be used to find $h'(x)$?​
12. If $R(x)=\int_{1}^{x}\frac{e^{t}}{t}\,dt$ for $x>0$, what is $R'(x)$?
13. Let $P(x) = ax^3 + bx^2 + cx + d$ where $a$, $b$, $c$, and $d$ are constants. If $\frac{d}{dx}[P(x) + Q(x)] = 6x^2 - 4x + 7$ and $Q'(x) = 2x^2 + x - 3$, what is $P'(x)$?
14. A position function has velocity $v(t)=2-t$ for $0\le t\le 4$. What is the net displacement?
15. Find $\lim\limits_{h\to 0}\dfrac{(5+h)^2-25}{h}$, representing a difference quotient at $x=5$.
16. Let $g(x)=-5x^3+4x^6-9x$. What is $g'(x)$?
17. Let f and g be functions such that $\lim_{x \to 2} g(x) = 3$. If f is continuous at $x=3$ and $f(3) = 5$, what is $\lim_{x \to 2} f(g(x))$?
18. A formula uses $f(x)=\arctan(\tfrac{3}{2}x)$. What is $f'(x)$?
19. Find the washer-method integral when the region between $x=\tfrac{2}{y}+5$ and $x=\tfrac{y}{2}+2$ on $[1,2]$ is revolved about the y-axis.
20. Let $t(x)=\begin{cases}\frac{\sin x}{x},&x\ne0\\1,&x=0\end{cases}$. What type of discontinuity occurs at $x=0$?

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