Name:
Algebra 2
Final Exam Review
Topics on Exam:
1. Ch. 5 Polynomial Functions: #1 – 10
a. Synthetic Division
b. Finding zeroes
c. Factoring
2. Ch. 6 Radicals and Functions: #27 – 32
a. Simplifying radicals – factor tree
b. Inverse functions: f-1 (x)
c. Composite functions: f og(x)
d. Parent functions and transformations; h and k
i. Iphone family functions
e. Solving radical equations
 Solving Rational Equations: #17 – 23
3. Ch. 8 Simplifying and
a. Variations – inverse, direct, and joint
b. Graphing rational equations – “boomerangs” and finding asymptotes
c. Multiplying and dividing – keep change flip; factor each part and cancel
d. Adding and subtracting – LCD
e. Solving – find LCD first, then cross out the denominator to solve
4. Sequences and Series: #24 – 26
a. Rule versus sum formulas
b. Arithmetic (linear) versus geometric (infinite)
5. Statistics: #11 – 15
a. Standard deviation and z-score
b. Normal distribution curve and the percentages
c. Permutation and Combination
d. Regression – line or curve of best fit
6. Exponential and Logarithmic Functions: #33 – 40
a. Graphing; asymptotes
b. Domain and range
c. Solving exponential equations
d. Solving logarithmic equations
e. Expanding and condensing logs
Practice Questions:
Please solve the following problems. Show your work to receive credit. CIRCLE your answer.
1. Given roots of 3, 0, and
–2, write a polynomial
function.
2. Divide using synthetic
2a 4  5a 3  8a  3
division
.
a 3
3. Find P(2) using synthetic
division when
P(x) = 3x3 – 2x2 – x + 4.
4. Solve 4x2 –13x = 12
5. Solve (y – 8)2 + 7 = 61.
6. Find the roots of
n2 – 8n + 14 = 0
7. Find all of the zeros of
g(x) = x3 – 6x2 + 10x – 8
given that 4 is a zero.
8. Find all of the zeros of
g(x) = x3 + 4x2 – 11x – 30 .
9. Is x + 1 a factor of
x5 + x4 + x3 + x2 + x + 1?
(Hint: use synthetic division;
what should the remainder
equal?)
10. Factor 8x3 – 125.
11. At one college, SAT scores for
incoming students are normally
distributed with a mean of 1200 and
a standard deviation of 85. Kyle
scored a 1290 on his SATs. At that
same college, ACT scores are
normally distributed with a mean of
26 and a standard deviation of 2.5.
Janet scored a 28 on her ACTs.
Who has the better chance of
getting into the school?
13. Using the same problem
from #12, what is the
percentage of human
pregnancies that last more
than 280 days?
12. The length of human
pregnancies varies according
to a normal distribution with a
mean of 266 and a standard
deviation of 16 days. Draw
and label all the percentages
and each standard deviation
line of the normal curve.
15. Decide if the situation is a
permutation or combination,
then solve accordingly.
16. Decide if the situation is a
permutation or combination,
then solve accordingly.
A school newspaper has an editorin-chief and an assistant. The staff
of the newspaper has 12 students.
In how many ways can students be
chosen for these two positions?
A school newspaper committee has
12 students. The sponsor needs to
choose 2 students to go to a
workshop. In how many ways can
two students be chosen?
14. Using the same problem
from #12, if the survey asked
900 people, how many
pregnancies lasted between
250 and 266 days?
16. If y varies directly with x
and y = 16 when x = 20,
a) find k
b) find y when x = 15.
3x  2 1
3x
18. If w is inversely

proportional to the square of t, 19. Simplify x 2  4 9 x 2  7 x .
and w = 1 when t = 6, find w
when t = 2.
20. Simplify
23. Solve
x2  y2 y5
.

yx
y8
5
2m
19

 .
6 2m  3 6
21. Simplify
y
8

.
2 y  16 y  8
24. Evaluate, no calculator.
22. Simplify
3a  2
4

.
a  b 2 a  2b
25. Sequence: 5, 15, 45…
6
Use the formula!
 (3n  6) .
n 1
a) Write a rule for the
sequence.
b) Find the 6th term.
c) Find the sum of the first 7
terms (no calculator, use
the formula).
d) Explain why there is no
sum if this is infinite.
26. Write a rule and then find
the 20th term of the sequence
3, 10, 17, …
27. Simplify 64

5
6
28. Simplify
4
48x 5 y 8 z 3
3
2
y  5  23 y .
31. Find the inverse f -1(x)
when f(x) = -7x + 4.
29. Solve ( x  6)  8 .
30. Solve
32. f(x) = x – 7 and
g(x) = 3x2 + 1
33. Solve e5x+2 = ex.
34. Solve 2 x  3 
36. Evaluate ln 3.12 to the
nearest thousandth.
37. Evaluate log5 123 to the
nearest thousandth.
39. Condense
log2 5 + 8log2 a - 3log2 b.
40. Solve
log8 x + log8 (x + 2) = log8 3
3
1
.
16
a) Find g(f(x)).
b) Find f(g(x)).
35. Solve 3x – 5 = 7. (Keep
exact answer.)
38. Expand log3
7x
.
y5
Graph and label the following. Think about h and k when necessary. Highlight asymptotes first.
41. y  x  2  3
Domain:
Range:



44. y  2 x 1
Domain:
Range:
Asymptote:
2
1
x 4
Domain:
Range:
H.A.:
V.A.

47. y 

4 x 1
2x  6
Domain:
Range:
H.A.:
V.A.
42. y 
.
45. y  log( x  3)  2
Domain:
Range:
Asymptote:
48. y  3x 1  2
Domain:
Range:
Asymptote:
1
3
x 2
Domain:
Range:
H.A.:
V.A.
43. y 
.

46. y   x 1  4
Domain:
Range:


49. y  log( x  4)
Domain:
Range:
Asymptote:
.