Math 0320 Final Exam Review

Transcription

1 Math 0320 Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Factor out the GCF using the Distributive Property. 1) 6x 3 + 9x 1) Objective: (6.1) Factor Out GCF 2) 3x 2 y x 2 y 5 2) Objective: (6.1) Factor Out GCF Factor by grouping. 3) 40r ry - 8xr - 5xy 3) Objective: (6.1) Factor by Grouping 4) x 2 + 5x + xy + 5y 4) Objective: (6.1) Factor by Grouping Factor, if possible, using the difference or sum of squares. If a polynomial is not factorable, write "prime." 5) y 2 5) Objective: (6.2) Factor Sum or Difference of Squares 6) 49x ) Objective: (6.2) Factor Sum or Difference of Squares Factor the trinomial completely using the general factoring strategy. If a trinomial is not factorable, write "prime." 7) 8x x 2 + 9x 7) Objective: (6.3) Factor Using General Strategy 8) 24x 3-104x 2-80x 8) Objective: (6.3) Factor Using General Strategy Determine if the trinomial is a perfect square trinomial. If it is, factor it. If it is not, write "prime." 9) z 2-2z + 1 9) Objective: (6.4) Factor Perfect Square Trinomial 10) 25x x ) Objective: (6.4) Factor Perfect Square Trinomial Factor the polynomial completely using the general factoring strategy. If the polynomial is not factorable, write "prime." 11) y y y 11) Objective: (6.5) Factor Out Common Factor 12) 3(x - 2) - a(x - 2) 12) Objective: (6.5) Factor Out Common Factor 1

2 Simplify the rational expression. 3x ) x 2-25 Math 0320 Final Exam Review 13) Objective: (7.1) Simplify Rational Expression 14) 5x x 2 + 4x ) Objective: (7.1) Simplify Rational Expression Multiply the rational expressions and write the answer in lowest terms. 15) 21m5 p 2 m + p m - p 3m 8 p 15) Objective: (7.2) Multiply Rational Expressions 16) d d - 7 d 2-7d d 2-5d ) Objective: (7.2) Multiply Rational Expressions Divide the rational expressions and write the answer in lowest terms. 17) 2k2 + 17k k 2-24k k2 + 17k k ) Objective: (7.2) Divide Rational Expressions 18) x 2 + 7x + 10 x x x - x2 2x ) Objective: (7.2) Divide Rational Expressions Simplify using the product rule for radicals. 19) ) Objective: (8.1) Simplify Using Product Rule 20) ) Objective: (8.1) Simplify Using Product Rule Simplify. Assume that all variables represent real numbers. 49m 21) - 2 n 2 21) Objective: (8.1) Simplify Square Root 22) (x - 1) 2 22) Objective: (8.1) Simplify Square Root 2

3 Math 0320 Final Exam Review Multiply. Write the answer in simplified radical form. Assume that all variables represent positive real numbers. 23) 5y 35y 23) Objective: (8.2) Multiply Square Roots 24) 3x 3 6x 2 24) Objective: (8.2) Multiply Square Roots Divide. Write the answer in simplified radical form. Assume that all variables represent positive real numbers. 25) ) Objective: (8.2) Divide Square Roots 26) ) Objective: (8.2) Divide Square Roots Solve and write the solution using set notation. 27) -7x - 10 = x ) Objective: (8.3) Solve Equation Containing Square Root (Square Binomial) 28) x + 1 = x ) Objective: (8.3) Solve Equation Containing Square Root (Square Binomial) Simplify using the product rule or quotient rule for radicals. Write the answer in simplified radical form. Assume that all variables represent positive real numbers. 29) ) Objective: (8.5) Simplify Radical Using Product Rule or Quotient Rule 30) 5 32 x 4 y 28 30) Objective: (8.5) Simplify Radical Using Product Rule or Quotient Rule Evaluate. 31) 27 2/3 31) Objective: (8.5) Evaluate with Rational Exponents 32) /2 32) Objective: (8.5) Evaluate with Rational Exponents Find the functional value and write the answer as an ordered pair. 33) h(x) = 3x 2-7x - 4, h(-5) 33) Objective: (9.1) Find Functional Value (Number) 3

4 Math 0320 Final Exam Review 34) f(t) = -3t 3 + 6t 2 - t - 41, f(-2) 34) Objective: (9.1) Find Functional Value (Number) Find the functional value. 35) g(x) = 2x 2-5x - 3, g(x - 1) 35) Objective: (9.1) Find Functional Value (Variable Expression) 36) f(x) = 8x + 8, f(a + h) - f(a) h 36) Objective: (9.1) Find Functional Value (Variable Expression) Find the following function and its domain. 37) Let f(x) = 4 3x and g(x) = x - 2 x 2. Find (f + g)(x). 37) - 4 Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions 38) Let f(x) = 2x 2-3 and g(x) = 7x - 4. Find (f - g)(x). 38) Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions 39) Let f(x) = 5x 2-2 and g(x) = 4x + 1. Find (f g)(x). 39) Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions 40) Let f(x) = 5x + 1 and g(x) = 2x - 5. Find f (x). 40) g Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions Perform the indicated operations and write the answer in the standard form a + bi. 41) ( i) - (5-2i) 41) Objective: (10.1) Add or Subtract Complex Numbers 42) (-6-7i) + (12 + 4i) 42) Objective: (10.1) Add or Subtract Complex Numbers 43) (7-4i)(7 + 4i) 43) Objective: (10.1) Multiply or Divide Complex Numbers 44) 1-2i 7 + i 44) Objective: (10.1) Multiply or Divide Complex Numbers Solve using the Zero Factor Property. 45) x(6x - 1) = 0 45) Objective: (10.2) Solve Using Zero Factor Property 4

5 Math 0320 Final Exam Review 46) 7x x - 6 = 0 46) Objective: (10.2) Solve Using Zero Factor Property Solve using the Square Root Property. 47) x 2 = ) Objective: (10.2) Solve Using Square Root Property 48) (3s + 9) 2 = 64 48) Objective: (10.2) Solve Using Square Root Property Solve by completing the square. 49) 3x x = ) Objective: (10.2) Solve by Completing the Square 50) x 2 + 6x = 31 50) Objective: (10.2) Solve by Completing the Square Solve using the Quadratic Formula. 51) 5x 2 + 8x = 4 51) Objective: (10.3) Solve Using Quadratic Formula 52) 17x 2-2x = 0 52) Objective: (10.3) Solve Using Quadratic Formula 5

6 Answer Key Testname: MATH_0320_FINAL_SPRING_2014_II_REVIEW 1) 3x(2x 2 + 3) 2) 3x 2 y 5 (y + 5) 3) (8r + 5y)(5r - x) 4) (x + 5)(x + y) 5) (10 + y)(10 - y) 6) Prime 7) x(2x + 3)(4x + 3) 8) 8x(3x + 2)(x - 5) 9) (z - 1) 2 10) (5x + 3) 2 11) y(y y + 50) 12) (3 - a)(x - 2) 3 13) x ) 1 3x + 2 7pm - 7p2 15) m 3 (m + p) 16) d 2 + 5d k ) 3k ) -2 19) ) ) -7 m n 22) x ) 5y 7 24) 3x 2 2x 25) 4 26) 30 27) {-2} 28) {4} 29) ) 2y 5 5 x 4 y 3 31) 9 32) ) (-5, 106) 34) (-2, 9) 35) 2x 2-9x ) 8 7x ), D = {x x -2 and x 2} (x - 2)(x + 2) 6

7 Answer Key Testname: MATH_0320_FINAL_SPRING_2014_II_REVIEW 38) 2x 2-7x + 1, D = (, ) 39) 20x 3 + 5x 2-8x - 2, D = (, ) 40) 5x + 1 2x - 5, D = x x ) i 42) 6-3i 43) i 1 44) i 45) 0, ) -3, ) - 9 7, ) , ) {-3, -2} 50) { , } 51) -2, ) 0,

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27