Name: ate: 1. What are the factors of z + z 2 + 25z + 25? 5. Factor completely: (7x + 2) 2 6 (z + 1)(z + 5)(z 5) (z 1)(z + 5i) 2 (49x + 1)(x 8) (7x 4)(7x + 8) (7x + 4)(7x 8) (7x + 4)(x 9) (z 1)(z + 5i)(z 5i) (z + 1)(z + 5i)(z 5i) 2. Expand and simplify: (7x + 2i )(7x 2i ) 49x 2 12x + 6 49x 2 12 49x 2 + 12 14x 2 + 4 6. Find x 2 + 6x 4 if x = 2a 2 b. 4(a 4 b 6 + a 2 b 1) 4(a 4 b 5 + a 2 b 1) 2(a 4 b 9 + 6a 2 b 2) 2(a 4 b 6 + 6a 2 b 2). ccording to the Fundamental Theorem of lgebra, how many roots does the following equation have? x + 4 = 5x 2 7x 2 4 6 7. Factor: x 4 1 (x + 1)(x 1)(x 2 + 1) (x 2 + 1) 2 (x 2 1) 2 4. What is the greatest monomial factor in 0h 7 k 6 18h 5 k 6 + 0h 4 k 4? (2x 2 + 1)(2x 2 1) 6h 5 k 4 6h 4 k 4 6h 4 k 2 6h k page 1
8. Simplify: (x, y 0) 4x 2 y(6x 5xy) + x 4 (4y 8xy) 4x y 2, 11. Simplify: (x 2 8)(x 7x 2 2) x 5 15x 7 + 54x 2 + 16 xy 5 x 5y 5 xy 5x y x 5 7x 4 8x + 54x 2 + 16 x 6 15x 7 8x + 54x 2 + 16 x 5 7x 4 8x + 56x 2 2x + 16 9. Factor: x 6 8 (x 2 2) (x 2 2)(x 2 + 2x + 4) (x 2 2)(x 4 + 2x + 4) (x 2 2)(x 4 + 2x 2 + 4) 12. Write the division statement for 2x 5x 2 10x 6. x + 4 (x + 4)(2x 2 1x + 42) 174 (x 4)(2x 2 + x + 2) 2 (x + 4)(2x 2 + x + 2) + 2 (x + 4)(2x 2 + 1x 42) + 174 10. Find the area of the shaded region in terms of x. 1. What are the zeros of the function f (x) = x + 4x 2 + x 6? x 2 + x + 2 4x 2 x + x 2 + x + 6 x 2 + 9x 2, 2, and 1 2, 1, and 1, 2, and 1, 2, and page 2
14. etermine the solution set of the equation x(x 2 + 1)(x 2 4) = 0. { 2, 2} { 2, 1, 1, 2} { 2, 0, 2} {0, 1, 1} 18. Which of the following graphs best illustrates the graph of y = a(x b)(x c)(x d)(x e)(x f )(x g) where a < 0 and b c d e f g? 15. How many terms are in the expansion of (x + 2y) 8? 8 9 16 5 16. What is the sum of the coefficients of the expansion of (x + y) 7? 49 128 64 98 19. Which of the following is the graph of y = a(x + 1)(x 2)(x 2), where a > 0? 17. Solve the following system for x and y. y = x 2 + 12x + 14 y x = 4 ( 9, 9), (12, 6) (9, 1), (2, 6) ( 1, 9), (2, 4) ( 9, 1), ( 2, 6) page
20. Simplify: (x 2 49)(x 2 81) x 2 + 15x + 56 (x 7)(x 2 81) x + 8 (x 9)(x 2 81) x + 8 (x + 8)(x 2 81) x + 7 (x + 9)(x 2 81) x + 24. Simplify: 7xy + 2xy 6 6 7xy + 2x ( 7x 2 ) y 21x 2 6x ( ) 14x 49x 2 4 7xy + 2xy 6y 7xy + 2y 6 21. Simplify: x + 2 x x 2 x 4 x 2 x 2 5x + 6 x + 2 x does not simplify 25. Simplify: 5x x 1 2x x 2 x 2 8x (x 1)(x 2) x 2 + 8x (x 1)(x 2) 7x 2 + 12x (x 1)(x 2) x 2 + 12x (x 1)(x 2) 22. Simplify: (x 5) 2(x + 5) (x 5) (x + 5) x 15 4 x2 25 2x 10 x 5 4 (x 5) 2(x + 5) 26. Simplify: x x 2 + 5 x + 2 x 2 + 4x 16 x 2 4 5x 15 x 2 4 x 15 2x x + 2 x 2 4 2. Multiply: x 2 + 6x + 5 x 2 + 2x 8 x 2 5x + 6 x 2 + 2x 15 27. Solve: 6x + 1 = 5 x + 1 x + 4 x 1 x + 4 x + 1 x 4 x 1 x 4 4 6 18 25 page 4
28. Solve: 7x + = 2x 1. How many solutions are shown by the graph of the quadratic function? 4 4 4 Ø 29. Solve for x: 2 x 2 + 5 x 2 4x + 4 = { 11, 1 } { 4, 1 } { 11, 1 } { 8, 1 } zero one two three 0. Use the graph below to find the point of intersection for the functions. q(x) = 4x r(x) = x + 7 y 2. What are the roots of the function whose graph is shown? x { 1, } {1, 4} {} { 1} ( 4, ) ( 1, 1) ( 2, 5) (1, 7) page 5
. What are the solutions to the quadratic function in the graph? 6. When x is a real number, which of the following is the graph of y = x + 2? no real roots 2 and 1 0 and 5 2 4. State the range of the function. 4 y 4 2 y 2 y 4 { 2, 1, 0, 1, 2} 5. Given the graph, describe the domain. x 1 y 2 y 2 x 1 page 6
7. Which of the following represents the graph of 1 y = x 2 9? 8. Which of the following could be the graph of a rational function that is not a polynomial function? page 7
9. Which one of the following sketches is a reasonable graph of y = 2 x +? 41. If 2 x 1 = ( 1 8 )2, then what is the value of x? 7 5 7 no solution 42. If 9 x = 27 x+9, then what is the value of x? 2 2 9 4. Solve: 8(8) x = 2 2 2 2 4 40. Which one of the following sketches is a reasonable graph of y = 2 x? 44. If y = 10 x, then: y = log x 10 y = log 10 x x = log 10 y x = log y 10 45. Solve for x: log 5 x = 5 125 81 15 page 8
46. Solve for x: log 625 = 4 log x ±5 25 155 5 51. Given log x = log a 1 2 log b + 4 log c, determine an expression for x. a b 2 4 c a 4 c b 2 a c 4 b ac 4 b 47. Solve: log 2 (x ) + log 2 (x + 1) = 5 7, 5 7, 5 5, 7 7 52. Write log w + log v log z as the logarithm of a single quantity. 48. Simplify: log 1 9 27 log wv z log w v z log wv z log w + v z 49. Evaluate log 6 12 to 2 decimal places. 0.7 1.78 2.12 2.7 5. The expression log M2 2N is equal to: log M 2 log 2N 50. If z = x, then log z is equal to: y2 2 log M log 2 + log N 2 log M log 2 log N log x 2 log y 2 log x y 2 log M log 2 + log N (log x log y) log x 2 log y 2 page 9
54. Use the properties of logarithms to expand the expression log x 2y. log x log 2y log x log 2 + log y log + log x log 2 + log y log + log x log 2 log y page 10
Problem-ttic format version 4.4.220 c 2011 2014 Educide Software Licensed for use by fchannor@atlanta.k12.ga.us Terms of Use at www.problem-attic.com 05/19/2015 1. N.N.8 15. PR.5 2. N.N.8 16. PR.5. N.N.9 17. REI.7 4. SSE.1 18. F.IF.7 5. SSE.1 19. F.IF.7 6. SSE.1 20. PR.6 7. SSE.2 21. PR.6 8. 9. 10. 11. 12. 1. 14. SSE.2 SSE.2 PR.1 PR.1 PR.2 PR. PR. 22. 2. 24. 25. 26. 27. PR.7 PR.7 PR.7 PR.7 PR.7 REI.2
Teacher s Key Page 2 28. REI.2 29. REI.2 0. REI.11 1. F.IF.4 2. F.IF.4. F.IF.4 4. F.IF.5 5. F.IF.5 6. F.IF.7 7. F.IF.7 8. F.IF.7 9. F.IF.7E 40. F.IF.7E 41. F.IF.8 42. F.IF.8 4. F.F.5 44. F.F.5 45. F.F.5 46. F.F.5 47. F.F.5 48. F.F.5 49. F.F.5 50. F.F.5 51. F.F.5 52. F.F.5 5. F.F.5 54. F.F.5