Math Analysis
Review Packet Problems
Name: ____________________________
Date: ______________
All work is to be done in the space provided. Be neat. Illegible work will not be accepted.
SOLVING EQUATIONS AND INEQUALITIES
__________ 1.
1
2
14
( x  6)   x 
3
5
15
2x 
__________ 2.
4
6

3
7
x  14  2 3 x
__________ 3.
3
__________ 4.
2
2
10

 2
t  3 t  2 t  5t  6
__________ 5. Solve:
4x3 + 8x = 12x2
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__________ 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
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__________ 9. Solve by matrices
4x + 5y = -7
1
y=3–
x
3
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 -
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3 3
x – 7x2 + 9x + 6
2
Page 3
__________ 15. Write the function given the zeros:
-1, 2, 3 + i, 3 – i
RATIONAL EXPRESSIONS
__________ 16. Simplify:
2x  1
5

2
x 2
x 4
__________ 17. Simplify:
x 3  3x 2
5x 3

2x
x 2  5x  6
__________ 18. Simplify:
3x 3  6x 2
x3 8
 2
x 2
x  8x  20
SIMPLIFYING COMPLEX FRACTIONS
4
4
__________ 19. Simplify: x
1
2
x
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x2
2
__________ 20. Simplify: x  1
3x
x 1
EXPONENTS AND RADICALS
Simplify # 21-28.
 x 3 y 2 

__________ 21. 
 z 
 3x 2 y 3 

__________ 22. 
2 
 xw 
4
3

3 x 2 2 x  5 x 1
__________ 23.
3

__________ 24. 3x 2 y 3 z

 xy 
2
4
__________ 25. x2  x3  x4
3

__________26. A2  


2
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__________ 27. Evaluate without a calculator
1
27
1
3
3
 1 2
__________ 28. Evaluate without a calculator  
 64 
LOGS
__________________ 29. Expand
log
__________________ 30. Expand
log
__________________ 31. Condense
4
3
5x 3
12y 2
7x 5
2
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
natural logs for each.
CHANGE OF BASE FORMULA.
Use both common and
__________ 33. log 4 81
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__________ 34. log2 19
GRAPHING
Some parts may not have an answer. In that case, write the symbol for the empty set,
y
.
35. y = x2 + 3x – 4
vertex _________
x
Axis of symmetry: _________
zeros: _________
domain: _________
range: _________
y
36. y = x + 2 – 3
vertex _________
x
domain: _________
range: _________
y
2x  1;
37. y = 

 x  4  2;
x  0 

x  0 
x
domain: _________
range: _________
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y
38. y = ln (x + 2)
x – intercept: _________
y – intercept: _________
x
vertical asymptote: _________
domain: _________
range: _________
39. y = 4  1 
2
x 4
3
y
x – intercept: _________
y – intercept: _________
x
horizontal asymptote: _________
domain: _________
range: _________
40. y =
2x  4
x 1
y
vertical asymptote: _________
horizontal asymptote: _________
slant asymptote: _________
x
x – intercept: _________
y – intercept: _________
domain: _________
range: _________
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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
3
lie in?
4
__________ 43. What quadrant does the angle -320 lie in?
__________ 44. Sketch the angle
5
in standard position below.
3
__________ 45. Give two coterminal angles (one pos, one neg) for -150.
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__________ 46. Change 144 to radians (no calculator!)
__________ 47. Change
13
to degrees (no calculator!)
6
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_____
t
 6 11 
  , 
 13 13 
49. Evaluate (if possible) the 6 trig functions that correspond to t =
sin t _____
csc t_____
cos t_____
sec t_____
tan t_____
cot t_____
__________ 50. If cos t =
Math Analysis; updated 06/20/09
5
.
4
4
, then find cos ( t +  )
5
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__________ 51. Evaluate the trig function sin
13
using the period as an aid.
6
__________ 52. Simplify using the trig identities:
cos x tan x
__________ 53. Simplify using the trig identities:
cot x
csc x
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:
(y + 1)2 (x  2)2

 1
4
16
y
center: _________
a-value: _________
b-value: _________
x
domain: _________
range: _________
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56. Identify and graph the following conic:
( x  4) 2 ( y  2) 2

1
25
9
y
x
__________ 57. Classify the given conic and graph the equation.
-9x2 + 16y2 + 54x + 64y - 161=0
y
x
__________ 58. Graph the hyperbola with foci (-5, 0) and (5, 0) and vertices (2, 0)
y
and (-2, 0).
x
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