Exam 1: Fundamentals

For the points $\left( - 1 , - \frac { 4 } { 3 } \right)$ and $\left( \frac { 5 } { 3 } , 2 \right)$ : (a) Plot the points on a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the line segment that joins them.

Solve the equation. $x ^ { 2 } - 12 x + 32 = 0$

Find the approximate solutions of the equation $x ^ { 2 } + x - 3.36 = 0$ by drawing a graph in the interval $[ - 3,2 ]$ .

Perform the indicated operations. $\frac { \frac { 1 } { 10 } } { \frac { 1 } { 3 } - \frac { 1 } { 5 } }$

Find the area of a triangle formed by the coordinate axes and the line $\frac { 1 } { 2 } x + 2 y - 5 = 0$ .

Factor the expression. $64 x ^ { 3 } - 1$

Perform the indicated operation. $\frac { 1 } { 6 } \div \frac { 2 } { 3 }$

Find the sum of five consecutive even integers, if $n$ is the first integer of the five.

Find the slope and $y$ - intercept of the line $2 y + 5 = 0$ and draw its graph.

Evaluate the expression. $| 2 - | - 3 | - 3 |$

A wire $45$ in long is cut into two pieces. One piece is bent into the shape of a circle and the other a square. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?

Rationalize the numerator of the expression. $\sqrt { x ^ { 2 } - 2 x + 1 } - \sqrt { x }$

Simplify the expression. $\frac { x ^ { 4 } } { x + 2 } \div \frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 8 }$

Solve the equation. $\frac { 3 } { 2 } \left( t - \frac { 2 } { 3 } \right) + 7 = \frac { t + 1 } { 3 } - 1$

The cost C of printing a magazine is jointly proportional to the number of

Evaluate each expression. (a) $\left( \frac { 7 } { 3 } \right) ^ { 0 } 2 ^ { - 1 }$ (b) $\frac { 3 ^ { - 3 } } { 4 ^ { 0 } }$ (c) $\left( \frac { 1 } { 5 } \right) ^ { - 2 }$

State the property of real numbers being used. $2 ( x + 5 y ) = 2 x + 10 y$

Perform the indicated operations and simplify. $\left( x ^ { 2 } - b ^ { 2 } y ^ { 2 } \right) \left( x ^ { 2 } - c x y + a y ^ { 2 } \right)$

Caitlin's science professor gives an A for an average of $85$ or better, and a B for an average of $75$ or better in her course. Caitlin has obtained scores of $84,71$ , and $77$ on her midterm examinations. If the final exam counts for as much as the three midterms together, what score must she get on her final exam to receive a B? To receive an A? (Assume that the maximum possible score on each test is $100$ .)

Simplify the compound fractional expression. $\frac { 2 + \frac { 1 } { x - 3 } } { 2 - \frac { 1 } { x - 3 } }$