1. If $f(x)=\frac{3 x}{x-2}, f^{-1}\left(\frac{1}{5}\right)=$ ? a) $\frac{-1}{7}$ b) $\frac{-2}{17}$ c) 1 d) $-3$ e) NOTA 2. A particle travels a circular path at $40 \mathrm{~cm} / \mathrm{min}$. If it traverses an arc of 15 degrees in 30 seconds, what is the radius of the circular path? a) $\frac{240}{\pi}$ b) $\frac{480}{\pi}$ c) $\frac{150}{\pi}$ d) $\frac{120}{\pi}$ e) NOTA 3. The graph of $y=-10 e^{-x}$ a) is in quadrants 1 and 2 only. b) is symmetric about the y-axis. c) increases for all $x$. d) passes through $(-10,0)$ e) is the image of $y=10 e^x$ in the $y$ axis. 4. What is the domain of $y=[\log (\cos x)]^2-[\log (\sin x)]^2$ ? a) $\left\{x \in R, x \neq n \pi, x \neq \frac{n k}{2}, n \in\right.$ Integers $\}$ b) $\left\{\pi n<x<\frac{\pi}{2}+\pi n, n \in\right.$ Integers $\}$ c) $\left\{0<x<\frac{\pi}{2}\right\}$ d) $\left\{2 \pi n<x<\frac{\pi}{2}+2 \pi n, n \in\right.$ Integers $\}$ e) NOTA 5. If the infinite geometric series $x^2-x^3+x^4-\ldots$ converges to $\frac{x}{5}$, what is $x$ ? a) $\frac{1}{20}$ b) $\frac{1}{4}$ $\begin{array}{ll}\text { c) } \frac{1}{12} & \text { d) } \frac{1}{6}\end{array}$ e) NOTA 6. Three letters are chosen at random without replacements from the word DRAWING. What is the probability of choosing at least one vowel? a) $\frac{5}{21}$ b) $\frac{2}{7}$ c) $\frac{4}{7}$ d) $\frac{5}{7}$ e) NOTA 7. If $\left(\begin{array}{l}8 \\ 2\end{array}\right)-\left(\begin{array}{l}8 \\ x\end{array}\right)=0$. Find $x, x+2$. a) 1 b) 4 c) 5 d) $\varnothing$ e) NOTA 8. If $\log _b 9=a, \log _b 81-\log _b 4=c$, and $9^x=4.5$, then $x^2=$ ? a) $\frac{c}{2 a}$ b) $\frac{4 c^2}{a^2}$ c) $\frac{c^2}{4 a^2}$ d) $2 c^2-4 a^2$ e) NOTA 9. Solve for all $x, x \in R: \frac{x}{|x-4|}<x+3$ a) $x>4$ or $-2<x<2$ b) $1-\sqrt{13}<x<1+\sqrt{13}$ c) $x>2+2 \sqrt{13}$ d) $-2 \sqrt{3}<x<2 \sqrt{3}$ or $x>1+\sqrt{13}$ e) NOTA 10. Find the period of the function $f(x)$ if $f(x)=\sin (2 \pi x)+\cos (3 \pi x)$. a) 1 b) 2 c) 6 d) $6 \pi$ e) NOTA 11. If $x$ varies as $y$ and $z^2$ and inversely as the square root of $w$, what is the effect on $y$ when $x$ is doubled, $z$ is halved, and $w$ is multiplied by 4 ? a) $y$ is divided by 2 b) $y$ is multiplied by 8 c) $y$ is multiplied by 16 d) $y$ is divided by 16 e) NOTA 12. A sphere with a radius of 7 is inscribed in a right circular cylinder. Find the exact volume of the cylinder. a) $\frac{343 \pi}{3}$ b) $343 \pi$ c) $686 \pi$ d) $1372 \pi$ e) NOTA 13. If $a * b=\frac{a^2+b^2}{2}$ and $a \# b=a^2-b^2$, list all values for which $a * b=a * b$. a) $a=\sqrt{3} b$ b) $a=3 b$ c) $a=\pm \sqrt{b}$ d) $a=\pm \sqrt{2 b}$ e) NOTA 14. The periods of time it takes two air-filter pumps to change 1 cubic meter of air in a storage vault differ by 1 minute. Together it takes the pumps 1 hour to change 27 cubic meters of air in the vault. How long does it take each of them to change 1 cubic meter? a) $\frac{5}{9} \min , \frac{14}{9} \min$ b) $3 \mathrm{~min}, 4 \mathrm{~min}$ c) $\frac{5}{27} \min , \frac{32}{27} \min$ d) $4 \mathrm{~min}, 5 \mathrm{~min}$ e) NOTA 15. As $\theta$ increases from $\frac{\pi}{4}$ to $\frac{5 \pi}{4}$ the value of $4 \cos \left(\frac{\theta}{2}\right)+2$ a) increases then decreases b) decreases then increases c) decreases throughout d) increases throughout e) NOTA 16. Find the resultant of two vectors of lengths 30 and 36 which form and angle of 60 degrees. a) $6 \sqrt{91}$ b) $18 \sqrt{17}$ c) $66 \sqrt{3}$ d) $56 \sqrt{37}$ e) NOTA 17. Find a valid conclusion based on all premises: $ \sim t,\quad \sim r \rightarrow j,\quad \sim(p \wedge \sim q),\quad \sim s \rightarrow k,\quad t \lor p,\quad (r \wedge s) \rightarrow \sim q \text {. } $ a) $k$ b) $j\lor k$ c) $\sim t \rightarrow j$ d) $\sim j \rightarrow \sim k$ e) NOTA 18. Suppose $c_1 x^3+c_2 x^2+c_3 x+c_4=(x-a)\left(b_1 x^2+b_2 x+b_3\right)+R$, where $R$ is the remainder. $b_2=$ ? a) $c_2+a_1$ b) $a_1+c_3$ c) $a c_1+a_2$ d) $a b_1+a c_2$ e) NOTA 19. Find the sum of all $x$ such that $1-\sin x=\cos x, 0 \leq x<2 \pi$. a) 0 b) $\pi$ c) $\frac{3 \pi}{2}$ d) $2 \pi$ e) NOTA 20. In parallelogram $OABC$, $M$ is the midpoint of side $\overline{{CB}} . \overline{{OM}}$ intersects $\overline{{AC}}$ at point ${x}$. What is the ratio of ${AX}$ to ${XC}$ ? a) $1: 2$ b) $2: 1$ c) $2: 3$ d) $2: 5$ e) NOTA 21. The Great Pyramid of Cheops in Egypt has a square base 230 meters on each side. The faces of the pyramid make an angle of $51^{\circ} 50^{\prime}$ with the horizontal. If $\sin 38^{\circ} 10^{\prime}=.618$ then what (to the nearest whole number) is the shortest distance you would have to climb up a face to reach the top? a) 146 b) 218 c) 186 d) 372 e) NOTA 22. If $f(x)=\sqrt[3]{x}-1$ then what is the range of $f(|x|)$ ? a) $y \geq-1$ b) $y \geq 0$ c) $y \geq 1$ d) Reals e) NOTA 23. In triangle $A B C, B C=18, m \angle A=120, m \angle B=45$. Find $A C$. a) $6 \sqrt{6}$ b) $6 \sqrt{2}$ c) $18 \sqrt{2}$ d) $36 \sqrt{6}$ e) NOTA