Algebra II Honors – Final Exam Review Guide
Mr. ttino
Name: __________________________
These are additional review problems to prepare for your exam. You should also review previous assessments,
assignments, and class work problems/examples.
Simplify 1 - 14 completely. No Fractional or Negative Exponents.
25 x 6 y 8
1.
2. 6 x 40 x 6 y 5
3. 5 20  180  7 54
4. (6  3 )(7  3 )
5.
5 2
3
5
y
14.
4
5
x
Solve 15 - 19.
15.
2
8.
4
9. (6  2i )( 2  5i)
10.
6  5i
3  2i
11.
8ax 5 24ax 5

6by 6 12by
4
7
x

5
12.
5
4
x5
13.
18.
3
2
4

 2
x  6 6  x x  36
19.
3x
1
x


x  2x  8 2  x x  4
4
3
 32a 5b 6
3 y  1 3x  4

8 xy
x3 y 2
1
17. x 3  8 x 3  15  0
6. 32 5
7.
x4 5
16. 3 x 2  5 x  2  0 (by completing the square)
6 2
3
3
2
20. Write a quadratic equation that has the roots
2  4i .
21. Given vertex (3,1) , and points (5,1) and
(1,1) , write a quadratic equation in standard
form.
22. Graph y  x 2  8 x  14 , and name the vertex,
x-intercepts, and y-intercept.
23. Find the distance and midpoint between (4,4)
and (6,2) .
24. Find the midpoint between (3 2 ,4 5 ) and
(4 2 ,6 5 ) .
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25. Given f ( x)  2 x 2  8 x  5 , write it in
y  a( x  h) 2  k form, name the vertex, focus,
equation of the axis of symmetry, equation of
the directrix, length of the latus rectum, state
whether the parabola opens up or down, and
graph it.
1
( x  1) 2  2 , name the vertex,
2
focus, equation of the axis of symmetry,
equation of the directrix, length of the latus
rectum, state whether the parabola opens up or
down, and graph it.
26. Given y 
27. Given ( x  2) 2  ( y  1) 2  16 , identify the
conic section, center, length of the radius, and
graph it.
28. Given 9 x 2  4 y 2  36 , identify the conic
section, center, foci, lengths of the major and
minor axes, and graph.
( x  3) 2 ( y  1) 2

 1 , identify the
29. Given
16
9
conic section, vertices, foci, slopes of the
asymptotes, and graph.
35. Given the polynomial
f ( x)  x 3  x 2  16 x  16 , and one of its
factors ( x  4) , find the remaining factors.
36. Given the polynomial f ( x)  x 3  x 2  x  15 ,
and one of its zeros 1 2i , find the remaining
roots.
37. Determine the number of positive real, negative
and imaginary roots for
p( x)  3 x 4  6 x 3  5 x 2  6 x  5 .
38. Find all the roots of the function
f ( x)  6 x 3  11x 2  3x  2 .
39. State the equations of the vertical and
3x
horizontal asymptote(s) of y  2
.
x  13 x  42
40. Graph y 
2x  1
.
x2
30. Write the equation of the ellipse if the
endpoints of the major axis are ( 2,12) and
(2,4) , and the endpoints of the minor axis are
(4,4) and (0,4) .
31. Write the equation of the hyperbola if the
center is (1,3) , and the length of the
horizontal transverse axis is 8 units, and the
length of the conjugate axis is 6 units.
32. Find f (2) , given f ( x)  2 x 3  3x 2  2 .
33. Graph a quintic function that has 2 imaginary
roots, one double root and whose leading
coefficient is negative.
34. Use the remainder theorem to determine if
x  6 , is a root of f ( x)  3x 3  2 x 2  3 . If
not, what is the remainder when f (x) is
divided by x  6 .
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