1. SIMPLIFY: $(10 \div 1 / 2+3) 3 \div 1 / 3-12 \div 3 / 4$
a. $-1$
b. 7
c. 63
d. 191
e. NOTA
2. The following statement is an illustration of which property of the real numbers:
$
2[a+(3+a)]=2[a+(a+3)]
$
a. commutative for multiplication
b. distributive
c. associative for addition
d. reflexive property of equality
e. NOTA
3. Name the sum of the one digit divisors of 29376648.
a. 33
b. 32
c. 39
d. 40
e. NOTA
4. The ratio of boys to girls in a certain high school is six to five. How many are boys if the school population is 2200 students?
a. 1200
b. 1100
c. 1000
d. 1180
e. NOTA
5. If $a=\frac{b(x-c)}{2 d}$, solve for $x$.
a. $\frac{2 a d+b c}{b}$
b. $b c+2 a d$
c. $\frac{b c-a b}{2 d}$
d. $\frac{2 a d-b c}{b}$
e. NOTA
6. 16 is $.5 \%$ of what number?
a. 8
b. $3 2 0$
c. $8 0 0$
d. 3200 e. NOTA
7. Solve for $x$ : $|x-6|<2$
a. $x=8$ or $x=4$
b. $x<8$ or $x>4$
c. $4<x<8$
d. $-8<x<-4$
e. NOTA
8. SIMPLIFY: $(3 x-2)^2-(3 x+2)^2$
a. 8
b. 0
c. $-24 x+8$
d. $-24 x$
e. NOTA
9. If $3 a+2 b=5$
And $5 a+3 b=7$
Find the sum of $a+b$.
a. 2
b. 3
c. 4
d. 5
e. NOTA
10. Solve for $x . \quad\left(4^2\right)\left(2^{x+2}\right)=2^{10}$
a. $\{3\}$
b. $\{4\}$
c. $\{1 / 2\}$
d. $\{6\}$
e. NOTA
11. Name the slope of the line through the points $(-2,3)(4,-9)$
a. $-1 / 2$
b. $-2$
c. 1
d. $1 / 2$
e. NOTA
12. $|3 x-2|=8$ Name the sum of the solutions.
a. $10 / 3$
b. 2
c. 0
d. $4 / 3$
e. NOTA
13. If the GCF of 56 and 238 is 14 , what is the LCM?
a. 13328
b. 952
C. 784
d. 3332
e. NOTA
14. If $f(x)=3 x^3+2 x^2$, find $f(-4)$
a. $-112$
b. $-4$
c. 222
d. $-160$
e. NOTA
15. Name the distance between $(-2,4)$ and $(4,-4)$.
a. 2
b. 14
c. $3 \sqrt{10}$
d. 10
e. NOTA
16. If set $A$ has 16 elements And the intersection of $A$ and $B$ has 12 elements And the union of $A$ and $B$ has 22 elements, Then how many elements are there in set B?
a. 10
b. 14
c. 18
d. 20
e. NOTA
17. Write an equation (in the form $A x+B y+C=0$ where $A, B, C \in\mathbb{Z}$, $A>0$ ) for a line that is the perpendicular bisector of the line segments whose end points are $(3,-2)$ and $(-3,6)$. Name the sum of $A+B+C$.
a. 7
b. $-7$
c. 1
d. 6
e. NOTA
18. If $\sqrt{x}=1 / 3$ then find the value of $\frac{\frac{3}{x}}{\frac{x}{3}}$
a. 81
b. 1
c. $7 2 9$
d. 27
e. NOTA
19. How many milliliters of water must be added to $120 \mathrm{ml}$ of $621 / 2 \%$ solution to dilute it to a $371 / 2 \%$ acid solution?
a. 75
b. 45
C. 60
d. 80
e. NOTA
20. SIMPLIFY:
$
\frac{\frac{x}{x+3}+\frac{x}{x^2-9}}{\frac{1}{x-3}+1}
$
a. $\frac{x}{x+3}$
b. $\frac{1}{x-3}$
c. $\frac{x+3}{x-3}$
d. $\frac{x-3}{x+3}$
e. NOTA
21. Joe does $2 / 3$ of a job in 4 hours. Kara can do $3 / 4$ of what remains to be done in 1 hour. Gloria can do what then remains to be done in 20 mins. How long would it take to do the job if the three worked together?
a. $3 / 2$ hrs
b. $4$ hrs.
c. $25 / 12$ hrs.
d. $5 / 3$ hrs.
e. NOTA
22. Find the value of $k$ that will produce a zero remainder for the following division problem.
$
\left(2 x^3-10 x^2+k x+66\right) \div(x-3)
$
a. $-10$
b. $-22$
c. $-12$
d. $-70$
e. NOTA
23. If $4 x^3-36 x=0$, name the sum of the solutions.
a. $2 / 3$
b. 0
c. 6
d. 3
e. NOTA
24. Factor $20 x^2-9 x-18$ into the form $(A x+B)(C x+D)$ and then name the sum of $A+B+C+D$.
a. 18
b. 6
c. 12
d. 15
e. NOTA
25. SIMPLIFY: $\frac{x^2+5 x+6}{x^2+5 x+4} \cdot \frac{x+1}{x-1} \div \frac{x^2+x-6}{x^2+3 x-4}$
a. 1
b. $\frac{x+2}{x-2}$
c. $\frac{x-1}{x+2}$
d. $\frac{x+2}{x-1}$
e. NOTA
26. The sum of the squares of two negative odd integers is 74 . Name the larger of the two integers.
a. $-7$
b. 5
c. $-5$
d. 7
e. NOTA
27. Compute the sum of $3 \sqrt{8}+2 \sqrt{72}-5 \sqrt{18}$
a. $9 \sqrt{2}$
b. $2 \sqrt{2}$
c. $3 \sqrt{2}$
d. $15 \sqrt{2}$
e. NOTA
28. Rationalize the denominator and simplify: $\frac{3+\sqrt{3}}{3-\sqrt{3}}$
a. $-1$
b. $2+6 \sqrt{3}$
c. $2+\sqrt{3}$
d. $2-\sqrt{3}$
e. NOTA
29. Solve for $x$ : $2 x^2-14 x+11=0$
a. $\{-7+3 \sqrt{3},-7-3 \sqrt{3}\}$
b. $\{-7+\sqrt{71},-7-\sqrt{71}\}$
c. $\left\{\frac{7+3 \sqrt{3}}{2}, \frac{7-3 \sqrt{3}}{2}\right\}$
d. $\left\{\frac{7+\sqrt{71}}{2}, \frac{7-\sqrt{71}}{2}\right\}$
e. NOTA
30. If $(x+y)^2=60$
And $(x-y)^2=40$
Find the value of $x^2+x y+y^2$
a. $1 0 0$
b. 55
c. 50
d. 20
e. NOTA