Exam 1: Fundamentals

Express the statement as a formula and use the information to find the constant of proportionality: $Z$ is jointly proportional to $a$ , $b$ , and $c$ and inversely proportional to $d$ . If $c$ and $d$ have the same value, and if $a$ and $b$ are both $6$ , then $Z = 360$ .

Use a graphing calculator or computer to determine which of the viewing rectangles produces the most appropriate graph of the equation $y = 5 x ^ { 5 } - 4 x ^ { 4 }$ .

Use a Factoring Formula to factor the expression. $125 s ^ { 3 } - 216 t ^ { 3 }$

Find the sum, difference, or product. $2 ( 2 - 5 t ) - t ^ { 2 } ( t - 1 ) + \left( t ^ { 4 } - 1 \right)$

The gravitational force $F$ between two objects is inversely proportional to the square of the distance between the objects. If the force $F$ is $1.62 \times 10 ^ { - 6 }$ N when the two objects are $25$ cm apart, what is the gravitational force when the objects are $35$ cm apart?

Use properties of real numbers to write $12 ( z / 4 )$ without parentheses.

Simplify the expression. $\frac { x ^ { 2 } - x - 6 } { x ^ { 2 } + 2 x } \cdot \frac { x ^ { 2 } + x } { x ^ { 2 } - 2 x - 3 }$

Simplify the expression $\frac { y ^ { 2 } - 25 } { 2 y ^ { 2 } - 4 y - 30 }$

Multiply the algebraic expressions using a Special Product Formula and simplify. $( \sqrt { y } + \sqrt { 5 } ) ( \sqrt { y } - \sqrt { 5 } )$

Simplify the expression. $\frac { 1 } { a } - \frac { 2 } { a ^ { 2 } b } + \frac { 1 } { b ^ { 2 } }$

Write the following statement in terms of inequalities. $x$ is negative.

Determine whether the given values of the variables are solutions of the equation. $2 - [ 2 + ( 2 - x ) ] = x - ( x + 1 )$ (a) $x = 1$ (b) $x = 1000$

State whether the inequality is true or false. $\frac { 22 } { 7 } > \pi$

Solve the equation by completing the square. $x ^ { 2 } + 4 x - \frac { 9 } { 4 } = 0$

Solve the absolute value inequality. Express the answer using interval notation. $| 8 x + 7 | > 14$

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 4 ] { x ^ { 4 } y ^ { 4 } }$

Determine whether the given values of the variables are solutions of the equation. $( x - 3 ) + ( 2 - 3 x ) = 4 ( x - 2 ) + 1$ (a) $x = 0$ (b) $x = 1$

Find all real solutions of the equation. $| x - 1 | = - 1$

The difference of the squares of two consecutive integers is $1307$ . Find the integers.

Determine whether the given values of the variables are solutions of the equation. $\left( x - \frac { 1 } { 2 } \right) + ( 2 x - 1 ) = 2 \left( x - \frac { 1 } { 2 } \right) - ( 1 - x ) + \frac { 1 } { 2 }$ (a) $x = \frac { 3 } { 2 }$ (b) $x = \frac { 1 } { 2 }$