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Exam Review Chapters 7-13 Q1. Expand: 4 (2 - 3y) A1. 16 – 96y + 216y2 - 216y3 + 81y4 Q2. ix x) Find the coefficient 6 10 of a in (5 – 3a) . A2. 95,681,250 Q3. th 8 Find the term in the expansion 15 of (2x – 3) . A3. 8 -3,602,776,320x Q4. State the Law of Sines. A4. sinα = sinβ = sin γ a b c Q5. State the Law of Cosines. A5. a² = b² + c² - 2bccosα Q6. State the Pythagorean Identity. A6. cos²θ + sin²θ = 1 Q7. A vector is a quantity with ? and ?. A7. magnitude and direction Q8. A vector with a magnitude of one is called a ?. A8. unit vector Q9. A vector whose initial point is at the origin is called a ?. A9. position vector Q10. If v = ai + bj, then a and b are called the ?. A10. components Q11. The set of all points equidistant from a point and a line is called a(n) ?. A11. parabola Q12. The set of all points such that the sum of the distances from two fixed points is a constant is called a(n) ?. A12. ellipse Q13. The set of all points such that the difference of the distances from two fixed points is a constant is called a(n) ?. A13. hyperbola Q14. The line associated with a parabola is called the ?. A14. directrix Q15. The two fixed points of an ellipse or hyperbola are called ?. A15. foci Q16. Which conic has transverse and conjugate axes? A16. hyperbola Q17. What equation will help you find the foci for a hyperbola? A17. b² = c² - a² Q18. Identify the conic: 7 y 8 x 24 xy 2 2 4 5 x 2 5 y 15 0 A18. hyperbola Q19. A rectangular array of numbers is called a(n) ? A19. matrix Q20. A triangular display of binomial coefficients is called ? A20. Pascal’s Triangle Q21. What are the dimensions of the following matrix? 3 1 0 A21. 3x1 Q22. Write I3. A22. 1 0 0 0 1 0 0 0 1 Q23. A sequence is a function whose ? is the set of positive integers. A23. domain Q24. A sequence whose difference between successive terms is a constant is ?. A24. arithmetic Q25. A sequence whose ratio between successive terms is a constant is ?. A25. geometric Q26. Evaluate: 11 9 A26. 55 Q27. A vector with a magnitude of zero is called a ?. A27. zero vector Q28. Evaluate: a.) p(0) b.) lim p(s) x→0 A28. a.) 0 b.) DNE Q29. Evaluate: a.) G(2) b.) lim G(x) x→2 A29. a.) 3 b.) 1 Q30. Name another polar coordinate for (-2, -π/3) A30. (-2, 5π/3) (2, 2π/3) (2, -4π/3) Q31. Convert to polar coordinates: (-4, 0) A31. (4, π) (4, 180˚) Q32. Convert to rectangular coordinates: (-2, 5π/6) A32. (√3, -1) Q33. Write the rectangular form of the equation: r = 4sinθ A33. x² + (y-2)² = 4 Q34. How many petals does r = 3cos5θ? A34. 5 Q35. In which quadrant does -1 – 5i fall? A35. III quadrant Q36. Identify the graph: r = 4 – 5cosθ A36. limaçon with inner loop Q37. In which quadrant does the point with polar coordinates of (-3,2π/3) fall? A38. IV quadrant Q39. Simplify: 2 cos 62˚ + 2 sin 62˚ A39. 1 Q40. What is the length of the hypotenuse in the right triangle below? 43˚ 7 A40. 10.26 Q41. Find a: 14 38˚ 8 a A41. no such triangle Q42. If v · w = 0, then the two vectors v and w are ?. A42. orthogonal Q43. If v x u = 2i + j – 3k, then u x v = A43. -2i – j + 3k Q44. The following is the standard equation for which conic? ( y 2) ( x 1) 1 4 7 2 2 A44. hyperbola Q45. Solve: 6x – 4y = 20 4x + y = 6 A45. (2, -2) Q46. Solve: x² – y = 4 2x + y = -1 A46. (-3, 5) (1, -3) Q47. Solve: x+y+z=3 x-z=1 y – z = -4 A47. (3, -2, 2) Q48. Solve: x – √5y = 2.7 3.4x + 2y = 6.1 A48. (1.983, -.321) Q49. Evaluate: 1 0 5 7 2 1 4 3 2 0 3 4 2 4 2 3 A49. 0 Q50. Evaluate: 6 k k 8 11 A50. -2.56 Q51. Evaluate: x 1 lim x 1 x 1 4 A51. 4 Q52. Evaluate: lim 3 x 6 1/3 x 7 A52. 3