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1. Area of a rectangular garden ●○○○○ 10 ptsThe perimeter of a rectangular garden is 60 feet. If the length of the garden is twice the width, find the area of the garden, in square feet.
2. Piecewise function coefficients sum ●○○○○ 10 ptsLet $f(x) = \left\{ \begin{array}{cl} ax+3 & \text{ if }x>0, \\ ab & \text{ if }x=0, \\ bx+c & \text{ if }x<0. \end{array} \right.$ If $f(2)=5$, $f(0)=5$, and $f(-2)=-10$, and $a$, $b$, and $c$ are nonnegative integers, then find $a+b+c$.
3. Find x+y from a trigonometric system ●●○○○ 20 ptsGiven that $x+\sin y=2008$ and $x+2008 \cos y=2007$, where $0 \leq y \leq \frac{\pi}{2}$, find the value of $x+y$. Round to two decimal places.
4. Area of quadrilateral from circle and hyperbola ●●○○○ 20 ptsA convex quadrilateral is drawn in the coordinate plane such that each of its vertices $(x, y)$ satisfies the equations $x^{2}+y^{2}=73$ and $xy=24$. What is the area of this quadrilateral?
5. Self-inverse 2x2 matrices ●●○○○ 20 ptsThe matrix $\begin{pmatrix} a & 3 \\ -8 & d \end{pmatrix}$ is its own inverse, for some real numbers $a$ and $d$. Find the number of possible pairs $(a,d)$.
6. Quadratic equation in two variables ●●○○○ 20 ptsSolve the equation $x^{2}-2x+y^{2}-4y+5=0$ for real numbers $x$ and $y$. Find $x$ and $y$.
7. Scout troop after percentage growth ●●○○○ 20 ptsLast year, there were 30 more boys than girls in a scout troop. This year, the number of children in the troop increased by $10\%$, the number of boys increased by $5\%$, and the number of girls increased by $20\%$. How many children are in the troop this year?
8. Rational function with horizontal tangent ●●○○○ 20 ptsThe graph of $g(x) = \frac{ax+b}{(x-1)(x-4)}$ passes through the point $(2,-1)$ and has a horizontal tangent there. Find the values of $a$ and $b$.
9. Garden dimensions from perimeter and area ●●○○○ 20 ptsA rectangular garden has a perimeter of 68 ft and an area of 240 ft$^2$. Find its length and width. Give the width (the smaller value) first, then the length.
10. Third term of a power-plus-constant sequence ●●○○○ 20 ptsLet $\{a_n\}$ be the sequence given by $a_n = a^n + m$ for positive integers $n$, where $a < 0$ and $m$ are constants. Given $a_1 = 2$ and $a_2 = 4$, find $a_3$.

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