1. Solve: $3+a / 3=6+2 / 3$
a. $11 / 3$
b. 11
c. $13 / 3$
d. 13
e. NOTA
2. If $\frac{5 x}{2 y}=12$, find the value of $\frac{5 x-6 y}{2 y}$
a. 3
b. 6
c. 9
d. 12
e. NOTA
3. The solution set of $|-3 x+ 1|>5$ is
a. $x<2$
b. $x<-4 / 3$
c. $x<-2$ or $x>4 / 3$
d. $x<-4 / 3$ or $x>2$
e. NOTA
4. Find the remainder when $x^2-2 x-5$ is divided by $x-2$.
a. $-5$
b. $-3$
c. 3
d. 29
e. NOTA
5. Find the midpoint of $\overline{A B}$, where $A(-1,3)$ and $B(4,-2)$ are the endpoints.
a. $(3 / 2,1 / 2)$
b. $(5 / 2,-5 / 2)$
c. $(-5 / 2,5 / 2)$
d. $(2,-1)$
e. NOTA
6. Solve for ${x}: 6 {x}^2+3 {x}-3=0$
a. $\{-1 / 2,1\}$
b. $\{-1,1 / 2\}$
c. $\{1 / 2,1\}$
d. $\{-1 / 2,-1\}$
e. NOTA
7. If $g(x)=3 x^2+1$ and $p(x)=2 x-3, g[p(x)]$ is
a. $4\left(12 x^2-9 x+7\right)$
b. $6\left(2 x^2-6 x+5\right)$
c. $6 x^2-1$
d. $2\left(3 x^2-2\right)$
e. NOTA
8. Find the value of $|5-12 i|$ where $i=\sqrt{-1}$
a. $\sqrt{119}$
b. $-\sqrt{119}$
c. 13
d. $-13$
e. NOTA
9. Solve: $3 x^2+x-2 \geq 0$
a. $x \geq 2 / 3$ and $x \leq-1$
b. $x \geq 2 / 3$ or $x \leq-1$
c. $x \leq-2 / 3$ and $x \geq 1$
d. $x \leq-2 / 3$ or $x \geq 1$
e. NOTA
10. Solve for $x$ and $y$ for $3 i y=-2 x+4+6 i$, where $i=\sqrt{-1}$
a. $(4,2)$
b. $(2,-2)$
c. $(2,2)$
d. $(2,6)$
e. NOTA
11. Solve for ${x}:(3 / 4)^{{x}^2+1}=(16 / 9)^{{x}}$
a. 1
b. $-1$
c. 2
d. $-2$
e. NOTA
12. For what values of ${k}$ will $2 {x}^2-{3 x + k}=0$ have two distinct real roots?
a. ${k}<9 / 8$
b. ${k}>9 / 8$
c. ${k}<-9 / 8$
d. $k>-9 / 8$
e. NOTA
13. Find the domain for $f(x)=\sqrt{\frac{2}{\left(-x^2+7 x-12\right)}}$
a. $3>x>-4$
b. $-3>x>-4$
c. $3<x<4$
d. $-3<x<-4$ e. NOTA
14. Find $\left[\begin{array}{ll}2 & 5 \\ 3 & 8\end{array}\right]^{-1}$
a. $\left[\begin{array}{ll}2 & 5 \\ 3 & 8\end{array}\right]$
b. $\left[\begin{array}{cc}-2 & -5 \\ -3 & -8\end{array}\right]$
c. $\left[\begin{array}{rr}2 & -5 \\ -3 & 8\end{array}\right]$
d. $\left[\begin{array}{rr}8 & -5 \\ -3 & 2\end{array}\right]$
e. NOTA
15. If ${f}({x})=3^x {x}$, , then ${f}^{-1}(x)=$
a. $3^x+8$
b. $3^x-8$
c. $\log _3(x-8)$
d. $\log _3(x+8)$
e. NOTA
16. Change $2435_6$ to base 8 .
a. $4657_8$
b. $1027_8$
c. $1117_8$
d. $1127_8$
e. NOTA
17. Find $8^{\sqrt{3}}+\sqrt{5} \cdot 16^{\sqrt{12}+\sqrt{20}}$
a. $211 \sqrt{3}+11 \sqrt{5}$
b. $2^{24 \sqrt{3}}+24 \sqrt{5}$
c. $2^{11 \sqrt{3}+11 \sqrt{5}}$
d. $128^{60}$
e. NOTA
18. Given $f(x)=\log _5 x$, then $f(5 x)-f(x / 5)=$
a. 0
b. 1
c. 2
d. 5
e. NOTA
19. $3 x+2 y-\quad z=4$ $2 x+5 y-2 z=5 \quad 6 x+6 y+6 z=?$ $4 {x}+2 {y}+12 {z}=27$
a. 18
b. 24
c. 30
d. 36
e. NOTA
20. Find the values of ${k}$ if one root is twice the other in ${x}^2 \cdot {kx}+18=0$
a. 3
b. 6
c. 9
d. 12
e. NOTA
21. A tank can be filled in nine hours by one pipe, in 12 hours by a second pipe, and can be drained when full by a third pipe, in 15 hours. How long would it take to fill the tank if it is empty, and if all pipes are in operation?
a. $719 / 23 \mathrm{hrs}$
b. $10.5 \mathrm{hrs}$
c. $1239 / 47 \mathrm{hrs}$
d. Tank never fills
e. NOTA
22. A theater has seats for 500 people. It is filled to capacity for each show and tickets cost $\$ 3.00$ per show. She estimates that for each $\$ .20$ increase in price, 25 fewer people will attend. What ticket price will maximize her income?
a. $\$ 3.20$
b. $\$ 3.50$
c. $\$ 3.70$
d. $\$ 3.75$
e. NOTA
23. Solve for $x:\left(4 \log _k x\right)\left(\log _4 k\right)=12$
a. 3
b. 4
c. 16
d. 64
e. NOTA
24. Characteristic of $\log _3 5000$ ?
a. 6
b. 7
c. 8
d. 9
e. NOTA
25. Find the equation of the parabola with its vertex at $(3,5)$ and its focus at $(3,2)$.
a. $(y-5)^2=-8(x-3)$
b. $(y-5)^2=8(x-3)$
c. $(x-3)^2=-12(y-5)$
d. $(x-3)^2=12(y-5)$
e. NOTA
26. Solve for $p: p r r=\frac{1}{q}$
a. $q r /(r-q)$
b. $(r-q) / q r$
c. ${qr}$
d. $q r /(q-r)$
e. NOTA
27. $\sqrt[6]{16}+\sqrt[6]{4}$
a. $\sqrt[6]{2}$
b. $\sqrt[6]{4}$
c. $6 \sqrt{8}$
d. $2\left({ }^6 \sqrt{2}\right)$
e. NOTA
28. How many fourths is $262 / 3 \%$ ?
a. $1 / 4$
b. $3 / 4$
c. $4 / 15$
d. $16 / 15$
e. NOTA
29. Simplify: $\frac{6}{4+\sqrt{2}}$
a. $\frac{12-6 \sqrt{2}}{7}$
b. $\frac{4-\sqrt{2}}{2}$
c. $\frac{4-\sqrt{2}}{3}$
d. $\frac{12-3 \sqrt{2}}{7}$
e. NOTA
30. If $f(x)=x^4+2 x^3-x^2+c x+k$, find $c$ such that $f(1)=0$ and $f(-1)=0$
a. $-2$
b. 0
c. 1
d. 2
e. NOTA