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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