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AATH Long Term Assignment Semester I Review – Multiple Choice Multiple Choice – circle your answers. 1. What is h(x + 1) if h(x) = x2 +3x? A) x2 + 5x + 4 B) x2 + 3x + 1 Name __________________ D) x2 + 4x + 1 C) x + 1 x 2 3x 10 3x 15 2 2 x 25 x 6x 8 x4 3 3 A) B) C) 3 4 x4 2. Simplify: x3 3x 2 x 2 7 x 12 x 3 x( x 3) x A) B) 3( x 4) 3( x 4) D) 1 x4 3. Simplify: 2x 6 8 2 x 7 x 12 3 x 13 x 4 3x 1 2(3 x 1) A) B) 4 8 4. Simplify: 5. Simplify: A) B) 4 2 x 3 x 1 B) 7. Simplify: 6x 3 x 9 x3 A) 3 x3 C) x 4 C) 45 y 28 x 21xy D) 3 x4 D) 16 (3 x 1)( x 4) 2 15 4 7x 3y 6 2x 2 A) 3x 5 ( x 4)( x 3) 2 2 19 21xy 6. Simplify: C) 19 7x 3y D) 73 yx 21xy 6x 2 ( x 3)( x 1) C) 3 x 1 6x 3 x x 12 C) 3 x D) 3x 9 x2 9 6 x 15 3( x y ) D) 7 x y D) 2 B) 2 2x 3 6 x y 3x 3 y 2x 9 2x 5 A) B) 4( x y ) x y 8. Simplify: C) 3 x 9. 4 8 9 5 A. 44.4 B. 8.9 2 C. 80 10. Find 3b + 4d if b = 4 and d = -3 A. 12 B. -12 C. 24 11. Simplify: 6(2a + 3b) + 5(3a - 4b) A. 27a – b B. 27a – 2b D. 67.2 E. 34 D. -24 E. 0 C. 27a + 38b E. 16a – 2b D. 16a - b 1 3 (7p + 3q) + (6p - 4q) 2 4 3 3 A. 8 p q B. p q C. p q 2 2 12. Simplify: 13. Solve: 2 y 4 6 8 A. 3, - 3 B. 3, -11 D. 8 p 3 q 2 E. 8 p D. –3, -5 C. 3, -5 3 q 2 E. –3, -11 14. Solve: 3x 7 4 2 A. –3, 5 3 15. Solve: 5 A. y -13 B. 3, y3 2 5 3 C. –3, B. y -13 13 3 D. 3, C. y < -13 16. Solve: 3m – 2 < 7 or 2m + 1 > 13 A. 3 < m < 6 B. 3 m 6 D. m 3 or m 6 E. no solution C. d -1 or d -3 18. Solve: 2 y 5 3 A. 1 < y < 4 B. 1 y 4 C. y < 1 or y > 4 A. 5 C. -1 20. Write the equation in standard form: y = A. 2x – 3y –24 = 0 E. no solution C. m < 3 or m>6 B. 1 < d <3 3x 4 , find g(2) x B. -5 E. no solution D. y > -13 17. Solve: 3d 6 3 A. d > -1 or d < -3 19. If g(x) = 13 3 D. 1 D. –3 < d < -1 D. y -4 or y -1 E. no solution E. no solution E. 0 2 x+8 3 B. 2x – 3y + 24 = 0 C. 3x – 2y = -24 D. 2 x – y = -8 3 E. y = 2 x+8 3 21. Write an equation in slope-intercept form that passes through (1,1) & is parallel to the line 2x + 3y = -5. A. y 2 5 x 3 3 B. y 3 1 x 2 2 2 5 C. y x 3 3 D. y 3 x2 2 3 E. y x 1 2 22. Write an equation in slope-intercept form that passes through (6, -2) and is perpendicular to the line –x + 8y = 5. 1 11 1 23 A. y 8 x 46 B. y 8 x 46 C. y 8 x 50 D. y x E. y x 8 4 8 4 23. Solve by substitution: 2 x 3 y 10 x 6 32 A. (-14, 26) C. (26, -14) E. (-38, 22) 24. Solve by elimination: 3x 2 y 20 2 x 3 y 9 B. (-26, 14) D. (38, -22) A. (6.5, -4) C. (6, 1) E. (-4, 2) B. (1, 6) D. (5, 13) 2 x y z 7 25. Solve the system of equations: 3 x y 2 z 15 x 4 y z 2 A. (1, 2, 3) B. (1, 2, 4) C. (2, 3, 4) D. (4, 2, 1) E. (4, 1, 2) 2 - 1 3 26. State the dimensions of the following matrix: 0 6 5 A. 3 X 3 B. 2 X 2 C. 2 X 3 D. 3 X 2 E. 6 X 2 2x 27. Solve: - y 3z 16 18 21 A. (8, -18, -7) B. (-7, -18, 8) C. (4, -9, -3.5) D. (0, 2, 6) E. no solution 3 5 2 6 28. Solve: - 7 2 8 - 1 5 1 A. 15 3 1 11 B. 1 1 34 13 C. 30 44 1 1 D. E. no solution 1 1 5 29. Solve: 0 - 1 3 2 3 5 A. 1 6 0 C. 2 6 B. 5 3 0 D. 4 E. no solution 6 - 2 7 - 1 30. Solve: 5 2 5 4 4 3 44 12 A. 33 26 13 3 B. 9 7 3 2 1 31. Solve: - 2 - 1 0 3 4 A. 11 2 16 8 C. 17 14 48 24 D. 51 42 E. no solution 2 11 D. 4 3 E. no solution 1 10 D. 1 6 E. no solution D. 1 0 5 E. no solution - 4 5 2 1 B. 2 4 3 2 32. Solve: 8 15 5 2 24 30 A. B. 6 10 40 30 1 - 6 2 33. Solve: 0 5 1 2 - 3 14 4 A. 10 B. 5 8 7 2 19 C. 4 9 6 C. 10 C. 4 5 7 34. Simplify: (5x2)-3 A. 5x-1 B. 125x-1 8 x 2 y 4 32 x 3 y 7 A. 4x5y3 B. –4x-6y11 1 C. .25x-1y-3 D. 4 x5 y 3 35. Simplify: E. 4 x y3 5 C. 1 125 x 6 D. 125x-6 E. 5x-6 36. Simplify: (3.1 X 105)(2 X 104) A. 6.2 X 101 C. 1.55 X 1020 E. 1 1.55 X 10 20 B. 6.2 X 109 1 D. 6.2 X 109 7.6 10 4 37. Simplify: 4 108 A. 1.9 X 104 B. 1.9 X10-4 C. 30.4 X1012 D. 3.04 X 1011 E. no solution 38. Simplify: (4x3 - 7x2 + 5x + 4) + (3x3 + 4x2 - 7x + 1) A. 7x3 – 3x2 – 2x + 5 D. 7x3 – 3x4 – 2x2 +5 B. 7x3 + 11x2 – 2x + 5 E. 12x9 – 28x4 – 35x + 4 C. 12x3 – 28x2 – 35x +4 39. Simplify: (2x2 - 3x +11) – (7x2 +2x - 8) A. –14x2 – 6x - 88 D. 9x2 + 5x + 19 B. 5x2 – x + 3 E. –5x4 – 5x2 + 19 C. –5x2 – 5x + 19 41. Simplify: (4x-3)2 A. 16x2 – 9 B. 16x2 –24x + 9 C. 16x2 + 9 D. 16x2 –12x + 9 E. 16x – 9 40. Simplify: (3x - 5)(2x - 1) A. –5x – 5 B. 6x2 + 13x – 5 C. 6x2 + 5 D. 5x + 5 E. 6x2 – 13x + 5 42. Use long division to find the quotient: (a4-5a3-13a2+1) (a+1) A. a3 – 6a2 – 7a + 7 - 6 a 1 D. a4 – 6a3 – 7a2 + 7a + 3 B. a3 – 6a2 – 7a + 7 C. a2 + 6a - 7 E. no solution 43. Use long division to find the quotient: (x3+3x2+3x+2) (x2+x+1) A. x2 + 2x B. x2 - 2x + 0 C. x – 2 D. x+ 2 E. no solution 44. Use synthetic division to find the quotient: (m3+3m2-7m-21) (m+3). A. m3 - 7 B. m3 – 7m2 C. m2 - 7 45. Use synthetic division to find the quotient: 56 x3 5 4 3 2 D. x – 3x + 2x – 6x + 19x - 56 A. x4 – 3x3 + 2x2 – 6x + 19 - D. 7m + 21 E. no solution x5 7 x3 x 1 x3 B. x4 – 3x3 + 2x2 – 6x + 19 C. x3 + 3x2 – 2x - 37 E. no solution 46. Factor: x2 - 9 A. ( x 3) 2 B. ( x 3)( x 3) C. ( x 3) 2 D. x( x 9) E. x( x 3)( x 3) 47. Factor: x2 + 8x +15 A. ( x 7)( x 8) B. x( x 8) 15 C. ( x 5)( x 3) D. ( x 5)( x 3) E. no solution B. (2 x 5)( x 1) C. 2( x 7) 5 D. 2( x 7 x) 5 E. no solution B. ( x 5)(3x 3) C. (3x 3)( x 5) D. (3x 5)( x 3) E. no solution 48. Factor: 2x2 - 7x + 5 A. (2 x 5)( x 1) 49. Factor: 3x2 - 4x - 15 A. ( x 5)(3x 3) 50. Factor: n3 + 125 A. (n 5)(n 2 5n 25) D. (n 5)(n 2 5n 25) B. (n 5)(n 2 5n 25) E. no solution C. (n 5)(n 2 5n 25) 51. Factor: 3x2 + 6xy - 4x - 8y A. ( x 2 y )(3x 4) D. 3x( x 2 y) 4( x y) B. x(3x 6 y ) 4( x y ) E. no solution C. ( x 2 y )(3x 4) 52. Solve the following equation by factoring: x2 +12x = 45 A. 15, -3 B. –15, 3 C. 12, -45 D. 0, 0 E. no solution 53. Solve the following equation by factoring: 2x2 +5x = -3 A. 3 ,1 2 B. 2 , -1 3 C. 2 ,1 3 D. 3 , -1 2 E. no solution 54. Solve the following equation by factoring: 5x2 = 20x A. 0, -4 B. 0, 4 C. 5, 4 D. 5, -4 E. no solution Free Response. 1. Use synthetic division to determine if (x - 4) is a factor of 2x3 + x2 – 41x + 20. 2. State whether the relation is a function. If so, state the domain and range. {(1, 2), (2, 3), (-5, 7), (3, 3)} 3. Graph the function: g(x) = 2 x 2 4. Graph the inequality: y > x - 2 5. Graph the inequality: 3x - 2y 4 x y 2 6. Solve by graphing: y x 4 7. Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. 4 x 5 y 10 y 6 2 x y 2 AATH 46. B 47. D 48. A 49. D 50. B 51. C 52. B 53. D 54. B Multiple Choice – KEY 1. A 2. C 3. B 4. A 5. C 6. B 7. A 8. B 9. C 10. E 11. B 12. D 13. B 14. E 15. D 16. C 17. C 18. A 19. D 20. B 21. C 22. A 23. C 24. C 25. E 26. C 27. A 28. B 29. E 30. C 31. D 32. E 33. B 34. C 35. D 36. B 37. B 38. A 39. C 40. E 41. B 42. A 43. D 44. C 45. A 7. (0, 2), (-2, 6), (5,6) Free Response 1. yes, it is a factor 2. Yes, Domain {1, 2, -5, 3} 3. 4. 5. 6.