Practice Test 9 - 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 diffusion model uses $\int \frac{1}{x^2+10x+29}\,dx$. Which is an antiderivative?
2. Let $y$ be defined by $e^{y}+xy=4$. Which differentiation procedure is needed to find $\dfrac{dy}{dx}$?
3. Let $s$ be continuous on $[4,8]$ with $s(4)=11$ and $s(8)=15$. What must occur?
4. An antiderivative of $u(x)$ is $U(x)=\cos x-2x$. Compute $\int_{\pi/2}^{\pi} u(x)\,dx$.​
5. Let $A(t)$ be the area of a growing stain. Which quantity is the instantaneous rate of area change at $t=5$?​​
6. The relation $x\sqrt{y}+y\sqrt{x}=10$ defines $y$ implicitly. What is $\dfrac{dy}{dx}$ at a general point $(x,y)$?
7. Let $m(x)=\sqrt{\sec(2x)}$. What is $m'(x)$?
8. A function is $j(x)=\ln\!\left(\dfrac{1}{x^2+2}\right)$. What is $j'(x)$?
9. The number of books checked out is $B(t)$ after $t$ hours. Interpret $B'(2)=35$.
10. For $f(x)=\begin{cases}x+2,&x<0\\2,&x=0\\2-x,&x>0\end{cases}$, does $f'(0)$ exist, and why?
11. For $D(t)= -5t^4+0t^3+8t^2-7$, what is $D'(t)$?
12. Let $s(x)=x^3-2$ and $s(2)=6$. Find $(s^{-1})'(6)$.
13. Let $f$ be continuous on $[-1,1]$ with $f(-1)=2$ and $f(1)=2$; which statement must be true?
14. If $A(5)=0$ and $A'(5)=2$, use local linearity at $5$ to approximate $A(5.4)$.
15. A model for distance is $d(t)=2t^8-3t^2+5t^4$. What is $d'(t)$?
16. Region bounded by $y=\sqrt{4-x^2}$ and $y=0$ for $-2\le x\le2$ is revolved about $y=-3$. Which setup is correct?
17. A continuous function $H$ satisfies $H(-2)=\!-7$ and $H(0)=\!-1$. Which is guaranteed?
18. A function is $S(x)=\sqrt{\dfrac{x^2+1}{x^2-1}}$. Which differentiation rules are required to find $S'(x)$?
19. For $x^2+xy=\ln y$, what is $\dfrac{dy}{dx}$ at a general point $(x,y)$?
20. A continuous function $h$ on $[1,8]$ has critical points $x=3,7$. If $h(1)=6,h(3)=2,h(7)=4,h(8)=1$, where is the absolute minimum?

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