This is to help you and has no bearing on your grade.

1. Simplify $\large\frac{1}{x+1} - \frac{x+1}{x-1}$

   $\large -\frac{x}{2}$      $ -x^2-x-2$      $\large\frac{x}{x+1} $     $\large \frac{x^2+x+2}{1-x^2}$

2. If we know the temperature outside in degrees Celsius, then we can convert to degrees Fahrenheit by the following process:
   Multiply your known temperature by $9$, divide the result by $5$, then add $32$. Write a mathematical expression that states this.

   $\large\frac{9t+32}{5}$      $\large \frac{9}{5}\normalsize x + 32$      $(\large \frac95 \normalsize+ 32)x$      $32+\large\frac{9}{5t}$

3. Write $(-3.2 \times 10^8) + (9.35 \times 10^9)$ in scientific notation.

   $12.49 \times 10^9 $      $9.03 \times 10^9$      $6.15 \times 10^8$      $1.249 \times 10^8$

4. Using that there are $5280$ feet in a mile and $3.28$ feet per meter, convert $26,400$ meters per second into miles per minute.

   $\large \frac{26,400 \times 3.28}{5280}$ miles per minute      $\large \frac{5280 \times 3.28 \times 60}{26,400}$ miles per minute      $\large \frac{26,400 \times 3.28 \times 60}{5280}$ miles per minute      $\large \frac{5280 \times 3.28}{26,400}$ miles per minute     

5. Simplify into a single fraction, written in lowest terms: $\large\frac{3}{5-3}\cdot\Large\frac{\frac{1}{2} + \frac{2}{3}}{\frac{1}{4} + \frac{4}{5}}$

   $\large\frac{5}{2}$      $\large\frac{10}{3}$      $\large\frac{9}{15}$      $\large\frac34$

6. Simplify $\Large\frac{(4^3 \cdot 3^4)^5}{2^{50}}$ by writing this as $a^b$ for some numbers $a$ and $b$.

   $a=2$ and $b=40$      $a=\large\frac34$ and $b=25$      $a=\large\frac38$ and $b=15$      $a=\large\frac32$ and $b=20$

7. Last year you invested $\$1000$ by buying $10$ shares of Stock X at $\$50$ per share (for $\$500$ total) and $50$ shares of Stock Y at $\$10$ per share.
   This year you sold your $10$ shares of Stock X at $\$55$ per share and your $50$ shares of Stock Y at $\$15$ per share.
   Find the percentage increase of your original $\$1000$ investment.

   $20\%$      $25\%$      $30\%$      $40\%$

8. The volume that a gas occupies is its mass divided by its density. It is known that the density of air (at room temperature) is about
   $7.5 \times 10^{-2}$ pounds per cubic foot (i.e., $.075$ lbs/ft$^3$). How many cubic feet does 150 pounds of air occupy?

   $20$ cubic feet      $2,000$ cubic feet      $1.125$ cubic feet      $1,125$ cubic feet

9. Consider a right triangle with one angle measuring $\pi/3$ and the length of the side opposite this angle equal to $10$. Find the length of the hypotenuse.

   $\large\frac{10}{\sqrt{3}}$      $20$      $\large\frac{20\sqrt{3}}{3}$      $10\sqrt{3}$.

10. At what value of $x$ do these equations intersect:   $3x+4y=8$   and   $x-2y=1$.

    $2$      $1$      $\large\frac34$      $\large\frac12$

11. If $2\log (A) = \log(x^2) - \log(y) + \log(1)$ then $A=$?

    $\large\frac{x}{\sqrt{y}}$      $\large\frac{x^2+1}{y}$      $\large\frac{x+1}{\sqrt{y}}$      $\sqrt{x^2-y+1}$

    Use the following graph to answer the following two questions

        

12. Which function best matches the blue curve?

    $y= e^{-\large x}$      $y=\large \frac{1}{x}$      $y=x$      $y=x^2$

13. Which function best matches the green curve?

    $y= e^{-\large x}$      $y=\large \frac{1}{x}$      $y=x$      $y=x^2$

14. A solid rectangular block has a volume equal to $100$ cubic meters. If its length, width, and height are each doubled,
    what would its new volume be?

    $200$ cubic meters      $400$ cubic meters      $800$ cubic meters      $1600$ cubic meters

15. Evaluate $\sin^2(\pi/8) + \cos^2(\pi/8)+\large\frac{\cos(\pi/3)}{\sin(\pi/4)}$

    $2\sqrt{2}$      $\large\frac{\sqrt{3}}{2}$      $\large\frac{2+\sqrt{2}}{2}$      $1$

16. Which positive value of $p$ satisfies $p^2-4p-21=0$?

    $3$      $7$      $8$      $21$

17. What is the largest value of $x$ that satisfies $x^2-3x+\large\frac74\normalsize=0$?

    $\frac{5}{2}$      $\frac12(3+\sqrt{2})$      $\frac12(3+\sqrt{7})$      $\frac13(2+\sqrt{5})$

18. In a certain chemical reaction, nitrogen dioxide molecules (NO$_2$) are consumed at a constant rate of $2.0 \times 10^9$ molecules per second.
    If we start with $5.0 \times 10^{12}$ NO$_2$ molecules, write an equation for the number of molecules remaining after $t$ seconds (provided the
    chemical reaction has not stopped).

    $(2.0 \times 10^9)t$      $5.0 \times 10^{12} - (2.0 \times 10^9)t $      $5.0 \times 10^{12} +(2.0 \times 10^9)t $      $-(2.0 \times 10^9)t$

19. Write the equation for the line through the points $(3,1)$ and $(-1,7)$.

    $y = \frac{4}{3}x-3$      $y = -3x + 4$      $y = -7x$      $y=-\large\frac32\normalsize x +\large \frac{11}{2}$

20. Modern widescreen televisions have a $16:9$ aspect ratio. The standard method of reporting the size of a tv is by giving the length of the
    screen's diagonal. For a modern television with diagonal measure of $55$ inches, roughly how long (in inches) is the longest side?

    $40$ inches $44$ inches $48$ inches $52$ inches