ALGEBRA 2B
2nd SEMESTER
FINAL EXAM REVIEW
The final will cover chapters 5-9. It will consist of two parts:
Part 1: Graphing. No calculator or note-card allowed. This portion of the test will consist of about 8-10 graphs
with basic transformations (vertical shifts, horizontal shifts, reflections, and stretches.) These graphs will cover
lines, absolute value, quadratic(parabola), square root, circles, ellipses and hyperbolas.
Part 2: Multiple Choice.
This portion will include about 40-50 multiple-choice questions. A graphing calculator will be necessary for some
of the questions. You will be allowed to use a note-card.
THE NOTE CARD

must be 3.5”  5” in size. (The small index cards)

must be handwritten.

may include any formulas, equations, or rules.

will be collected at the end of the exam.

can be written on both sides
CHAPTER 5: POLYNOMIALS
1. Simplify 6 y 2  3 y 3  2 y  4  3 y   y 2 
a. 18 y 3  5 y 2  24 y  9
b. 15 y 3  24 y 2  6 y  9
c. 15 y 3  18 y 2  9 y
d. 15 y 3  30 y 2  9 y
2. Simplify  5b  2   2b2  5b  4 
a. 10b3  29b 2  30b  8
c. 10b3  21b 2  10b  8
b. 10b3  21b 2  10b  8
d. 10b3  29b 2  30b  8
3. Given f  x   2 x 2  3x  7 . Evaluate f  2  .
a. f  2   15
4. Divide using long division.
4
x2
10
c. 3 x 2  x  3 
x2
a. 3 x 2  x  7 
b. f  2   5
 3x
3
d. f  2   7
c. f  2   7
 5 x 2  5 x  14    x  2 
b. 3 x 2  x  7
d. 3 x 2  x  7 
4
x2
5. For the polynomial function, use synthetic division or substitution to determine whether x=5 is a zero of the function.
f  x   3x 4  4 x3  73x 2  134 x  120
6. Use substitution or synthetic division to determine if x  5 is a factor of
3x4  16 x3  15x2  88x  60 .
Classify the polynomial by degree and number of terms, and then describe the end behavior.
f  x   3x 4  4 x3
7. f  x   4 x3  6 x 2  2 x  1
8.
9. Graph the function. Use your calculator to find the coordinates of the local maxima or minima. Round your answers
to the nearest tenth. Then, find the zeros of the function. . P  x   2 x5  4 x4  3x2  8x  3
Local Maxima: ______________________________
Local Minima: ______________________________
Zeros: ______________________________________
10. Find the real zeros of the function. Round to the nearest tenth, if necessary.
11. You are designing a rectangular wooden box with width 4 inches
greater than its height and length 3 times its height. The box has wood that
is 1 inch thick on each of the four sides and on the top and bottom.
Write a polynomial function, in standard form, for the volume of the inside
of the box.
f  x   x 4  x3  16 x 2  10 x  60
CHAPTER7: RADICALS AND INVERSES

12. Simplify x3 y
2

2
x
8
y4  4 .
1
1
x8
a.
13. Simplify
1

5 3

a.
16a 5b 7
32a 7 b3
x
y2
c.
d.
y
x2

5 1 .
a. 5  2 5
14. Simplify
1
xy
b.
b. 8  4 5
c. 2  4 5
d. 8  15  5
.
b 2
a
b.
b 2
2a
c.
b2 2
2a
d.
b2 2
2a 2
15. Solve for x. (2 x  3)3/2  8
a. x  6
16. Solve for x.
7
2
b. x  6
c. x 
b. x  22
c. x  22
d. x  9
5  2x  5  2
a. x  2
d. x  3
Simplify each radical expression:
7. 5(1000)4/3
20.
3
6a 3b 4  3 18a 5b8
18. 3 8  2 50  45
21.
18 x 3 y 6
2 xy
19.
9 x2 y 4  2 x6 y 2
22.
3
2 7
Simplify each expression.
23. x 2 / 3  x1/ 2
24.
x2 / 3
x1/ 2
25.
26. Determine whether the relation below is a function. State the domain and range.
16,18 , 11,1812,1212,16
27. If f ( x)  1  x 2 and g ( x)  1  x then find the product f g.
28. If f ( x)  4  x 2 and g ( x)  2  x then find the difference f  g .
29. For the pair of functions, f ( x)  6  2 x, g ( x)  x 2  2 ,
find f ( g ( x)) and g ( f ( x))
x 
2 / 3 1/ 2
__________________
_________________
________________
f(g(x)= ________________
g(f(x)=________________
30. Find the inverse of the function. f ( x) 
x2
.
7
________________
CHAP 8: RATIONAL FUNCTIONS
31. At what x value does the hole of y 
a) x=1
x2  6 x  8
occur?
x2  2x  8
b) x=-2
c) x=-3
32. Find the equation of the horizontal asymptote of y 
a) y=0
2 x2  2 x  3
.
3x 2  6 x
c) y 
b) y=2
33. Find the equation of the vertical asymptote(s) of y 
a) x=-4
2x  8
.
x 1
b) x=1
34. Find the domain of the function y 
d) x=4
2
3
d) no horizontal asymptote
c) x=2
d) no vertical asymptote
5
x  3x
2
a) All real numbers except x=0
c) All real numbers except x=0 and x=3
b) All real numbers except x=-5
d) x >-3
35. Which equation might have a graph shown at the right?
a) y 
3
x2
b) y 
3
x2
c) y 
x
x2
d) y 
x
x2
x 2  16
x 2  x  12
x 2  16
b) 2
x  x  12
36. Simplify the following expression:
a)
4
x 3
x2  2 x x2  5x  6
x2  9
x2
x3
b)
( x  3)( x  3)2
c)
x4
x3
d)
x4
x3
c)
10 x  6
9
d)
4
3
37. Simplify the following expression:
a)
( x  2)2
x( x  3)
38. Solve the equation
a) x 
5
2
3
1

. Check your solution(s).
x 1 x  2
7
b) x 
2
c) x 
7
4
d) no solution
Given the function identify the vertical asymptotes, horizontal asymptotes, and any holes in the graph. Then,
sketch a graph of the function.
39.
f ( x) 
2 x 2  18
3x 2  6 x  9
40.
f ( x) 
4x  5
8x  4
Holes ______________
Holes _________________
Vert. Asymp. ________
Vert. Asymp. ___________
Horiz. Asymp: _______
Horiz. Asymp: __________
Simplify each rational expression.
41.
x 2  10 x  25
24 x
x5
8x
42.
3 x  3 2 x  1

x 2  16 x 2  16
43.
x
3

x 3 x 4
Solve each rational equation. Check your solution(s).
44.
x4
5

x 1 x 1
45.
2x  4 x  2
3x


x
x2 x2
46. The cost of fueling your car for one year can be calculated using the equation
(Miles Driven)(Price per gallon)
FuelCost per Year=
Fuel Effiency Rate
Last year, you drove 12,500 miles, paid$2.15 per gallon of gasoline, and spent a total of $1225.50 on
gasoline. What is the fuel efficiency rate of your car?
47.
You are organizing your high school’s sports banquet. The banquet hall rental is $360. In addition, the
meal will cost $10 per plate. Let x represent the number of people who attend.
a) Write an equation that represents the total cost, C.
b) Write an equation that represents the average cost, A, per person.
c) How many people will need to attend the banquet in order for the average price to be $12 per person?
CHAPTER 6: EXPONENTS AND LOGARITHMS
48. Write x y  w in logarithmic form.
a. log y w  x
b. log x w  y
c. log y x  w
d. log w x  y
49. Write log 2 32  5 in exponential form.
a. 32
1
2
5
b. 52  32
c. 32
1
2
5
d. 25  32
50. Solve for x. log3  x  2   3
a. x  27
b. x  29
c. x  2
d. x  25
Solve the equation for x.
51.
1
 log 27 x
3


52. log 8 x 2  2 x  log 8 8
53. ln  5x  3  4
54. A new motorcycle costs $23,000. The value of the motorcycle decreases by 8% each
year. What is the value of the motorcycle after 7 years?
55. If you invest $2500 into an account that was compounded quarterly at a rate of 4.2%. How
much money do have after 15 years?
56. If you invested $1000 into an account that was compounded continuously at a rate of 6.3% how long would it take to
double your money?
57. Researchers have found that after 25 years of age, the average size of the pupil in a person’s eye decreases.
The relationship between pupil diameter d (in millimeters) and age a (in years) can be modeled by
d = -2.1158 ln a + 13.669. What is the average diameter of a pupil for a person 25 years old? 40 years old?
CHAP 9 – CONIC SECTIONS
58. Write the equation of a parabola whose vertex is at (6,2) and whose focus is at (4,2).
a) y  2 
1
( x  6) 2
8
b) x  6 
1
( y  2) 2
8
c) y  2 
1
( x  6) 2
2
d) y  2 
1
( x  6) 2
8
59. Write the equation of the circle graphed to the right.
a) ( x  1)2  ( y  2)2  4
b) ( x  1)2  ( y  2)2  2
c) ( x  1)2  ( y  2)2  4
d) ( x  1)2  ( y  2)2  2
60. Write the equation of the ellipse graphed to the right.
x2 y 2

1
9
1
x2 y 2
c)

1
9 1
a)
x2 y 2

1
1
9
x2 y 2
d)

1
3 1
b)
y2 x2
61. Find the coordinates of the foci of the hyperbola with equation
 1
16 9
a) (5,0) and (-5,0)
b) (0,5) and (0,-5)
c) ( 7, 0) and (  7, 0)
62. Find the equation of a circle that has a diameter with endpoints at (-1,6) and (-5,10)
d) (0, 7) and (0,  7 )
63. Write the equation x 2  y 2  8x  4 y  20  25 in standard form. Graph the result.
Find the coordinates of the foci.
64. Write the equation 9 x 2  36 y 2  324  0 in standard form. Graph the result.
Find the coordinates of the foci.
65. Write the equation x 2  6 x  y  4  0 in standard form. Graph the result.
Find the coordinates of the focus.
66. The cross section of a parabolic reflector is 14 meters across and the focus of the reflector is located 5 meters above
the vertex. Write an equation for the cross section of this reflector with its vertex at (0,0).
67. A furniture store advertises free delivery up to a 50 mi. radius from its store. If a customer lives 28 mi. east and 41
mi. north of the store, does the customer qualify for free delivery?
68. A rug in the shape of an ellipse has a length of 10 feet and a width of 6 feet. Write an equation for the perimeter of
the rug. Assume the major axis of the rug is horizontal.
Solve each system of non-linear equations.
 x 2  y 2  16
x  y  4
69. 
70.
 x 2  y 2  144
 2
2
 x  4 y  64
Algebra 2B
GRAPHING – NO CALCALATOR
+/-
y 
a function ( x - h)
VERTICAL LINE
x = b (b is constant)
ex: x = –5
y =3
QUADRATIC (parabola)
or
k
ABSOLUTE VALUE
ex: y = x
ex: y  x
y  a ( x  h)  k
3
2
ex:
yx
y  a xh k
SQUARE ROOT
y  a( x  h)  k
2
k
LINEAR (general)
y = mx + b
CUBIC
y  a ( x  h)  k
ex: y  x

h
a
HORIZONTAL LINE
y = b (b is a constant)
ex:
Name ____________________________________
ex: y 
3
x
CONICS:
SIDE PARABOLA
x  h  a( y  k ) 2
ex: x  y
2
CIRCLE
( x  h)2  ( y  k )2  r 2
ex:
x2  y 2  9
ELLIPSE
( x  h) 2 ( y  k ) 2

1
a2
b2
x2 y 2
ex:

1
16 4
HYPERBOLA
( x  h) 2 ( y  k ) 2

1
a2
b2
ex:
x2 y 2

1
16 4
TRY THESE!
1)
y
2
x4
3
5) y  x  3
3
8)
( y  2) 2 ( x  1) 2

1
4
1
2) y  3 x  2  4
3) y  2( x  3)  1
6) y 
7)
x 2 3
9)
4) x  2  ( y  5)
2
( x  2) 2 ( y  1) 2

1
4
1
( x  2) 2 ( y  1) 2

1
4
1
11)
2
x=0
10) ( x  2)  ( y  1)  9
2
2