Algebra Basic Skills Test

You have 30 minutes. You may only use a pen/pencil, and the paper provided. There are ten problems, all of equal weight. You must score 80% or higher. There will be no partial credit, so check your work carefully.

1.

Solve for x:

$$\frac{10x+1}{2x+7} = y$$

2.

Solve for x and y:

$$\begin{array} {rcl} 5x + 2y & = & 16\ 2x - 3y & = & -5\end{array}$$

3.

Where does the line 5x + 2y = 0 intersect the ellipse x² + 4y² = 104?

4.

Solve for x: $${\frac{2x-1}{x+1} + \frac{4x-1}{x-1} = -2}$$.

5.

Solve for x: x⁴ + 9x² + 8 = 0.

6.

List all the possible rational roots of 8x⁹ + 8x² - 5.

7.

Find all the roots of x³ + 6x² - 13x + 6.

8.

Find the center and radius of the circle x² + 10x + y² - 24y = 0.

9.

Find the remainder:

$$\frac{x^4+3x^2 - 2x + 1}{x^2 + 7}$$

10.

If $h\neq 0$, write the following expression as the ratio of two polynomials in h:

$$\frac{\frac{1}{2+h}-\frac{1}{2}}{h}$$