Exam Review Chapters 7-13

Q1. Expand: (2 - 3y) 4

A1. 16 – 96y + 216y y y 4

Q2. Find the coefficient of a 6 in (5 – 3a) 10. ix x)

A2. 95,681,250

Q3. Find the 8 th term in the expansion of (2x – 3) 15.

A3. -3,602,776,320x 8

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:

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?

A21. 3 x 1

Q22. Write I 3.

A22.

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:

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: cos 2 62˚ + sin 2 62˚

A39. 1

Q40. What is the length of the hypotenuse in the right triangle below? 43˚ 7

A

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?

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 = x + 2y = 6.1

A48. (1.983, -.321)

Q49. Evaluate:

A49. 0

Q50. Evaluate:

A

Q51. Evaluate:

A51. 4

Q52. Evaluate:

A52. 3