Exam 1: Review of Basic Concepts

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -If a rock falls from a height of 70 meters above the ground, the height $\mathrm { H }$ (in meters) after $x$ seconds can be approximated using the formula $\mathrm { H } = 70 - 4.9 \mathrm { x } ^ { 2 }$ . What is the height of the rock after 2 seconds?

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 2 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $11 c ^ { 5 } - 4 c ^ { 4 } - 6 c ^ { 3 }$

Find the domain of the expression. - $\frac { y } { y ^ { 2 } - 64 }$

Find the distance between two points given their coordinates. -Find the distance between points $P$ and $Q$ on a number line, with coordinates 5 and $- 12$ , respectively.

Find the product. Assume variables represent positive real numbers. - $y ^ { 3 / 13 } \left( y ^ { 5 / 13 } - 3 y ^ { 2 / 13 } \right)$

Factor by any method. - $15(m-6)^{2}-22(m-6)-5$

Simplify the expression. Assume all variables represent nonzero real numbers. - $( 8 x y ) ^ { 4 }$

Factor by any method. - $81 \mathrm { k } ^ { 3 } \mathrm {~m} - 192 \mathrm {~m} ^ { 4 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { 6 } { 7 } }$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -During a certain football game, a player gained 38 yards rushing and $- 54$ yards returning fumbles. Find his total yardage. Is this the same as the sum of the absolute values of the two categories? Why or why not?

Find the sum or difference. - $\left( 5 x ^ { 4 } - 9 x ^ { 2 } + x \right) - \left( 2 x ^ { 3 } + 8 x ^ { 2 } + 3 x \right) + \left( 4 x ^ { 2 } - x \right)$

Perform the indicated operations. - $\frac { 2 a b } { a ^ { 2 } - b ^ { 2 } } - \frac { b } { a - b } + \frac { 4 } { 2 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 5 } { x - h } + \frac { 5 } { x } } { 2 x - h }$

Factor by any method. - $15 z ^ { 6 } + 8 z ^ { 3 } - 16$

Find the sum or difference. - $( p + 3 q ) ( p - 3 q )$

Factor the trinomial, if possible. - $64 m ^ { 2 } - 160 m n + 100 n ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 27 }$

Simplify the expression. - $\sqrt { ( - 49 ) ^ { 2 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 14 } } { x ^ { - 2 } }$