Advanced Algebra with Trig
Study Guide.
FINAL EXAM
Name________________________
OUTLINE of TOPICS:
I. Polynomials
A. Evaluate given a value
B. Multiply binomials (foil)
C. Square a binomial
D. Factor by grouping
E. Factor trinomials
F. Descartes’ Rule of signs
G. The Rational zero theorem
H. List zeros with multiplicity
II. Solving Equations
A. Linear
B. Absolute Value
C. Quadratic by quadratic formula
D. Quadratic by Completing the Square
E. Exponential Equations
F. Logarithmic Equations
III. Logarithmic and Exponential Functions
A. Condense and Expand logarithmic expressions
B. Solve equations involving logarithmic and exponential functions
C. Solve problems involving compounded interest
D. Find pH
E. Find magnitude and/or Richter scale number for earthquakes
IV. Graphing
A. Discuss transformations
B. Sine and cosine functions
C. Determine which graphs are functions
V. Functions
A. Use of function notation: f(x)
B. Evaluate functions
C. Find domain algebraically
VI. Trigonometry
A. Angles and arcs: s   r ,180   , coterminal, complements, supplements, radian measure
o a o
B. Trigonometric Functions of Acute Angles: S C T
h h a
C. Trigonometric Functions of any angle: use of reference angle, a point on the terminal side
D. Trigonometric Functions of Real numbers: Unit Circle
E. Graphs of Sine and Cosine
You will be given this Formula Sheet to use on Exam Day
PLEASE- remember to bring: Your textbook to return, your calculator and a pencil.
ax 2  bx  c  0
x
b  b2  4ac
2a
a 2  b2  c2
c
a
b
Interest:
I  prt
A  P(1  r )t
r
A  P(1  ) nt
n
rt
A  Pe
 I 
M  log  
 I0 
Law of Sine’s
SinA SinB SinC


a
b
c
pH = - log [H+]
Advanced Alg Trig
Final Exam Practice 2014
Name______________________________
BE PREPARED! Bring your calculator, pencils, erasers. Don’t’ forget your textbook to hand in.
.Work out all the problems show all steps.
1. List the zeros of f(x) = x(x-3)3(x+5)2 , along with any multiplicities.
2. Use the Rational Zero Theorem to list all the possible rational zeros of the following.
P( x)  4 x3  2 x 2  7 x  12 . .
3. Use Descartes’ rule of signs to determine the number of possible positive and negative real zeros.
P( x)  4 x3  2 x 2  7 x  12
4. Find all the real zeros by factoring:
P( x)  3 x 3  4 x 2  4 x
5. Given f(x) = x + 5 and g(x) = x 2  25 , find each of the following
g ( x)
a. The domain of
b. f ( g ( x))
f ( x)
c. f g (2)
d. ( g  f )( x)
Solve for x.
6) 3 | 2 x  1| 18
7) log3  x   log3  x  6  3
8) Use the quadratic formula:
2 x2  5x  7  1
9) Complete the square:
2 x 2  6 x  20  0
14. Find the domain of each function:
a.
2x  6
b.
x
x5
c..
x5
x  x  12
2
FACTOR COMPLETELY.
15. 8 x 2  10 x  3
16. 9 x 2  30 xy  25 y 2
SIMPLIFY.
17.
3  2i  4  i 
18.
2  3i
4  2i
6
gx  = sin x 
4
19. How do you determine if a graph is a function?
Is this a graph of a function? Why or why not?
6
a.
b.
c.
4
2
2
-10
-10
-5
-5
5
5
10
-2
-2
-4
Write each of the following as a single log..
-4
20. log x3  log y  log w2  log 3 z
21. ln( x  3)  ln x5  ln x  1
22. Expand using the properties of logarithms.
a. log 3
x2 y
wz 3
b. log 5
y3 x
 wz 
2
Solve each equation.
24. ( 3) n 1  9n 1
23. 26 x  45 x 2
25. 493 p 1  7 p 5
Write each equation in logarithmic form.
26. 73  343
27. 52 
1
25
28. 5 x3  15
Write each equation in exponential form.
29. log 7 49  2
30. ln x  5.46
31. 40  1
Evaluate. If decimals occur, round to the nearest hundredth.
32. ln e 7
33. n log n 3
34. log(1, 000)
35. log n n 2.5
36. log b 1
37. log3 21
Solve each equation.
39. log 4 x 
38. logb 9  2
1
2
40. log7  x  4  2
41. log12  log(5 x  3)
43. log 4 (3x  2)  2
44. log 7 x  log 7 ( x  1)  log 7 12
45. 3x  2  52 x 5 (exact answer)
46. Find the pH of baking soda with H+ = 3.98 X 10-9 mole per liter.
47. Find the intensity of an earthquake that measures 6.7 on the Richter scale.
Find the balance of $4,500 invested in an account for 3 years, at an interest rate of 1.6%,
when:
a. interest is compounded monthly
b. interest is compounded continually
48. If $4,500 is invested in an account that has an annual interest rate of 6%, how long will it take to double
the amount in the account if the interest is compounded semiannually? Compounded continuosly?
49. Compare the intensities of the two earthquakes, earthquake of 1960 in Chile with a Richter scale
magnitude of 9.5, and the 2012 earthquake in the Philippines with a Richter scale magnitude of 5.2.
50. If a chemical has a pH of 7.2, find the number of hydrogen ions in moles per liter.
51. A tree casts a 23 meter shadow on the ground and the angle of elevation to the top
of the tree is 35 . Find the height of the tree.
T
R
E
E
35 
GROUND
52. Find the exact value, show all work. No Calculator!
 3 
 
 
sin   tan    cos  
 2 
4
3
53. Given the point (x, y) on the terminal side of an angle in standard position, find all six trigonometric ratios.
If radicals occur, leave answers in simplest radical form. NO Calculator!
a. (3, -4)
Sin θ
b. (-2, 0)
Csc θ
Cos θ
Sec θ
Tan θ
Cot θ
c. (0, 5)
Sin θ
Csc θ
Cos θ
Sec θ
Tan θ
Cot θ
d. (6, -3)
Sin θ
Csc θ
Sin θ
Csc θ
Cos θ
Sec θ
Cos θ
Sec θ
Tan θ
Cot θ
Tan θ
Cot θ
54. Find the exact of each.
a. sin 150˚
 3 
b. sec   
 4 
c. cot -225˚
 10
d. cos 
 3
 
 
 sin  tan  
6

3
55. Find the complement and supplement of each. Answer in radians if given radians and in degrees if given
degrees.
a.

6
b.
3
8
c. 25˚
d. 125
56. A central angle of 45˚ intercepts an arc. If the circle has a radius of 8 cm, what is the length of the arc?
57. Given sin β =
a. cos β
 2
and 270˚ < β <360˚; find each of the following.
2
b. csc β
c. tan β
Find the amplitude, period and state 5 critical points. Graph two periods of each. NO Graphing Calculator
58. y  2sin 3x
1
59. y  3cos x
2
60. Use Law of Sines to solve each of the oblique triangles, if there are two triangles solve for both. Your
calculator needs to be in degrees.
B = 32˚, c = 14, b = 9.0