Solving Equations and Inequalities



Math Analysis Name: ____________________________

Review Packet Problems Date: ______________

All work is to be done in the space provided. Be neat. Illegible work will not be accepted.

SOLVING EQUATIONS and INEQUALITIES

__________ 1. [pic]

__________ 2. [pic]

__________ 3. [pic]

__________ 4. [pic]

__________ 5. Solve: 4x3 + 8x = 12x2

__________ 6. Find all zeros, real and imaginary. f(x) = x3 – 2x2 + 4x – 8

SOLVING SYSTEMS

Solve each of the following systems of equations. Write your final answer as a coordinate point.

__________ 7. Solve by substitution 3x + y = 1

-2x + y = -5

__________ 8. Solve by elimination 5x + y = 5

9x – 4y = -20

__________ 9. Solve by matrices 4x + 5y = -7

y = 3 – [pic] x

Solving Quadratic Equations

__________ 10. Solve by factoring. f(x) = x2 – x – 6

__________ 11. Solve by quadratic formula. f(x) = 2x2 + 3x – 1

__________ 12. Solve by completing the square. x2 + 6x = 5

POLYNOMIAL FUNCTIONS

__________ 13. Find the rational zeros: f(x) = x3 + 3x2 – 5x – 15

__________ 14. Find the rational zeros: f(x) =x4 - [pic]x3 – 7x2 + 9x + 6

__________ 15. Write the function given the zeros: -1, 2, 3 + i, 3 – i

RATIONAL EXPRESSIONS

__________ 16. Simplify: [pic]

__________ 17. Simplify: [pic]

__________ 18. Simplify: [pic]

SIMPLIFYING COMPLEX FRACTIONS

__________ 19. Simplify: [pic]

__________ 20. Simplify: [pic]

EXPONENTS AND RADICALS

Simplify # 21-28.

__________ 21. [pic]

__________ 22. [pic]

__________ 23. [pic]

__________ 24. [pic]

__________ 25. x2 ( x3 ( x4

__________26. [pic]

__________ 27. Evaluate without a calculator [pic]

__________ 28. Evaluate without a calculator [pic]

LOGS

__________________ 29. Expand log 4 [pic]

__________________ 30. Expand log 3 [pic]

__________________ 31. Condense 7 log 4 y + 3 log 4 2 – 2 log 4 x

__________________ 32. Condense:

log 7 5 + log 7 9 + 6 log 7 x + 3 log 7 y – (3 log 7 2 + 2 log 7 x)

For #33 and #34, evaluate using the change of base formula. Use both common and natural logs for each.

__________ 33. log 4 81

__________ 34. log2 19

GRAPHING

Some parts may not have an answer. In that case, write the symbol for the empty set, (.

35. y = x2 + 3x – 4

vertex _________

Axis of symmetry: _________

zeros: _________

domain: _________

range: _________

36. y = (x + 2( – 3

vertex _________

domain: _________

range: _________

37. y = [pic]

domain: _________

range: _________

38. y = ln (x + 2)

x – intercept: _________

y – intercept: _________

vertical asymptote: _________

domain: _________

range: _________

39. y = [pic]

x – intercept: _________

y – intercept: _________

horizontal asymptote: _________

domain: _________

range: _________

40. y = [pic]

vertical asymptote: _________

horizontal asymptote: _________

slant asymptote: _________

x – intercept: _________

y – intercept: _________

domain: _________

range: _________

41. f(x) = -x4 – 2x3 + 3x2 + 3x + 4

(just give a rough sketch of this graph)

rel max: _____________________

rel min: _____________________

abs max: _____________________

abs min: _____________________

zeros: _____________________

describe the end behavior:

give the intervals where f(x) is increasing and decreasing:

TRIGONOMETRY

__________ 42. What quadrant does the angle [pic] lie in?

__________ 43. What quadrant does the angle -320( lie in?

__________ 44. Sketch the angle [pic] in standard position below.

__________ 45. Give two coterminal angles (one pos, one neg) for -150(.

__________ 46. Change 144( to radians (no calculator!)

__________ 47. Change [pic] to degrees (no calculator!)

48. Find the 6 trig functions (if possible) that correspond to the graph below.

sin t _____ csc t_____

cos t_____ sec t_____

tan t_____ cot t_____

49. Evaluate (if possible) the 6 trig functions that correspond to t = [pic].

sin t _____ csc t_____

cos t_____ sec t_____

tan t_____ cot t_____

__________ 50. If cos t = [pic], then find cos ( t + ( )

__________ 51. Evaluate the trig function sin [pic] using the period as an aid.

__________ 52. Simplify using the trig identities: cos x tan x

__________ 53. Simplify using the trig identities: [pic]

CONICS

__________ 54. Write an equation of the parabola whose vertex is at (-4, -1) and

whose focus is at (-4,2).

55. Identify and graph the following conic: [pic]

center: _________

a-value: _________

b-value: _________

domain: _________

range: _________

56. Identify and graph the following conic: [pic]

__________ 57. Classify the given conic and graph the equation.

-9x2 + 16y2 + 54x + 64y - 161=0

__________ 58. Graph the hyperbola with foci (-5, 0) and (5, 0) and vertices (2, 0)

and (-2, 0).

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