Review1Fall2010

Review1Fall2010 - MAC 1147 Review 1 Fall 2010 Exam 1 covers...

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MAC 1147 Review 1, Fall 2010 Exam 1 covers Lectures 1-9 1. Write without absolute value signs and simplify: (a) 2 x + j ± x 2 ± 1 j x + 1 (b) j ± ± 5 j ± j 3 ± ± j (c) 3 j 12 ± 4 r j + j r ± 1 j if r > 3 2. Let A = ± p 2 ; 0 3 ; 0 : 9 ; p ± 4 ; ±; 3 p ± 8 ; 0 0 ; 3 0 ; 15 5 ; 1 2 ; 16 1 = 4 ; 0 : 08 ² . List the elements that belong to each set: (a) Natural numbers (b) Integers (c) Rational numbers (d) Irrational numbers (e) Real numbers 3. Perform the indicated operations and simplify: (a) x + 1 x ± 1 ± ³ x + 1 x ± 1 ´ ± 1 (b) 1 x 3 + 4 x 2 + 4 x ± 1 x 3 + 2 x 2 4. Factor completely: (a) 4 x 2 ( x + 2) 3 ± 6 x 3 ( x + 2) 2 + 2 x 2 ( x + 2) 2 (b) 4 x 4 ± x 2 ± 16 x 3 + 4 x (c) x 4 ± x 2 ± 12 (d) 32 x 5 ± 4 x 2 (e) 2 x (4 ± 3 x ) 4 = 3 ± 4 x 2 (4 ± 3 x ) 1 = 3 5. Reduce the fraction to the lowest terms. State its domain: 12 y 2 ± 4 y ± 5 6 y 2 ± y ± 2 6. Perform the operations and simplify. (a) 4 x 2 ± 4 x 2 ± x + 1 ² x 4 + x x 2 + 2 x + 1 (b) 6 x 2 + 5 x ± 6 3 x 2 ± 2 x ³ 8 x 3 + 27 4 x 3 ± 6 x 2 + 9 x 7. Simplify each complex fraction. State the domain of fraction in (a) and (b). (a) 1 ± 4 x + 4 x 2 1 ± 5 x + 6 x 2 (b) 3 x ± 4 x + 1 1 ± 1 x (c) x 3 (1 ± x ) ± 1 = 2 + x (1 ± x ) 1 = 2 x 2 8. Simplify each expression. Write answer using only positive exponents.

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Review1Fall2010 - MAC 1147 Review 1 Fall 2010 Exam 1 covers...

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