Exam 1: Review of Basic Concepts

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 5,6,7,8,9,10,11,12,13,14,15 \} , \mathrm { M } = \{ 5,7,9,11 \} , \mathrm { N } = \{ 6,8,10,12,14 \} , \mathrm { Q } = \{ 5,7,9,11,13,15 \}$ , and $\mathrm { R } = \{ 5,6,7,8 \}$ . $\mathrm { N } ^ { \prime }$

Factor the polynomial by substitution. - $8 z ^ { 6 } + 6 z ^ { 3 } - 9$

Identify the set as finite or infinite. -{3, 5, 7, . . .}

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -The NSC Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss). Month Profit (Loss) in Dollars January -14,526 February 1874 March -8977 April -14,107 May 14,073 June 14,632 July -13,834 August -13,170 September -4860 October 6630 November -3338 December -974 The absolute value of the profit or loss was smallest in ? .

Perform the indicated operations. - $\frac { 3 } { 10 x } + \frac { 9 } { 14 x ^ { 2 } }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $8 + 0 = 8$

Evaluate the expression. - $216 ^ { 4 / 3 }$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { y ^ { 9 / 8 } } { y ^ { 5 / 8 } }$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| 5 - 10 | = | 5 | - | 10 |$

Find the sum or difference. - $( w - 4 ) ^ { 2 }$

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

Tell whether the statement is true or false. - $\{ 6,8,9,11 \} \cup \{ 0,10,8,13,6 \} = \{ 6,8 \}$

Evaluate the expression. -Let $x = 5 , y = - 1$ . Evaluate $\frac { | x + 2 | - | 2 y | } { | 3 y + 5 x | }$ .

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true. -

Factor the trinomial, if possible. - $\mathrm { u } ^ { 2 } - 2 \mathrm { uv } - 24 \mathrm { v } ^ { 2 }$

Find the sum or difference. - $\left( 2 x ^ { 2 } - 11 y \right) \left( - 4 x ^ { 2 } + 3 y + z \right)$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 2,3,4,5,6,7 \} , \mathrm { B } = \{ 4,6,8 \} , \mathrm { C } = \{ 2,3,5,7 \} , \mathrm { D } = \{ 2,7 \}$ , and $\mathrm { U } = \{ 2,3,4,5,6,7,8 \}$ . $\mathrm { C } \subset \mathrm { A }$

Factor by any method. - $10 a ^ { 3 } - 25 a ^ { 2 } b - 8 a b ^ { 2 } + 20 b ^ { 3 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 196 } + \sqrt { 49 }$

Use set notation, and list all the elements of the set. -The natural numbers between 3 and 5.