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Hon Advanced Algebra
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Final Exam Review 2015
The final is NO NOTES. It has a calculator section and a non-calculator section. It
covers problems like the ones you see below, though part of the final is multiple choice. I will make a practice
final available to you next week.
Chapter 5 Logarithmic Functions & Expressions (calculator okay):
 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and
the base b is 2, 10, or e; evaluate the logarithm using technology.
 Understand the inverse relationship between exponents and logarithms and use this relationship to solve
problems involving logarithms and exponents.
1. Rewrite the equation in logarithm form and solve.
2. Rewrite the equation in exponential form and solve.
7  3x
log3 x  4
 x
9
3. Solve. log 3 81  log 3    1
4. Solve 532  12 1.24 
x
Chapter 8 Conic Sections (no calculator):
 Given an equation in any form, graph a parabola, circle or ellipse.
( x  1) 2 ( y  4) 2

1
4
9
5. Write the equation in standard form and make a
graph: x 2  y 2  4 x  6 y  4  0
6. Graph
7. Graph x  2( y  4)2  5
8. Write the equation in vertex form and graph
 x2  2 x  y  1  0
Still Chapter 8 Rational Functions & Expressions (no calculator):
 Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and
showing end behavior.


Understand that rational expressions form a system analogous to the rational numbers, closed under
addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract,
multiply, and divide rational expressions.
Solve rational equations.
9. Graph y 
3
 2 . Mark all asymptotes and
x 1
10. Graph y 
4 x  12
. Mark all asymptotes and
x  7 x  12
2
holes.
holes.
11. Identify the asymptotes and any hole(s). Write the
location of a hole as a coordinate pair.
12. Identify the asymptotes and any hole(s). Write the
location of a hole as a coordinate pair.
HA:________VA:_______ Hole(s):__________
HA:________ VA:________ Hole(s):_________
13. Simplify.
14. Simplify.
15. Simplify.
16. Simplify.
17. Solve.
18. Solve.
Chapter 10 Probability (calculator okay):

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their
probabilities, and use this characterization to determine if they are independent.
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the
conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same
as the probability of B.
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified.
Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in
terms of the model.
Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the
answer in terms of the model.
Use permutations and combinations to compute probabilities of compound events and solve problems.






19. Evaluate. Do not use a calculator for this problem.
a.
14
P0
b.
14
C0
c. 9 C3
d.
9
e.
P3
15!
10!  5!
20. A car dealer has 8 exterior colors, 12 interior colors, and 7 option packages for new cars. In how many different
ways can a person buying a new car from this dealer select an exterior color, an interior color, and an option
package?
21. Suppose you roll one 6 sided die and one 4-sided die, and you calculate the sum. What is the expected value of
the sum?
22. Suppose 85% of the people who have a certain disease test positive and 96% of the people who do not have the
disease test negative. If 20% of the population really has this disease, find the probability that a positive test result
is accurate.
23. If A and B are mutually exclusive events, and P  A  0.3 and P  B   0.2 , find the following:
a. P  A and B 
b. P  Ac 
c. P  A or B 
24. If A and B are independent events, and P  A  0.6 and P  B   0.5 , find the following:
a. P  A and B 
b. P  B | A
c. P  A or B 
25. A bag of M&Ms contains 10 brown, 5 green, and 7 blue. If a handful of 9 M&Ms is randomly selected, find the
probability that it is comprised of 3 brown, 5 blue and 1 green.
26. For medical purposes, the
O
A
B
AB
managers of a company decide to
Women
8
5
4
2
record the blood type of all
Men
12
6
2
1
employees. The results are shown
at the right.
Suppose that a single person is randomly selected from the people in this company.
a. Find the probability that the person has type O blood or type A blood.
b. Find the probability that the person is a woman or has type A blood.
c. Find the probability that the person is a man, given that the person has type A blood.
27. A survey of 75 adults in one town found that 35 of them watch the evening news on TV, 48 of them read the
newspaper, and 28 of them watch the news on TV and read the newspaper.
a. Create a Venn Diagram for this situation and answer the following questions about a randomly selected adult
from this survey.
b. Find the probability the adult watches neither the evening news nor reads the newspaper.
a. Find the probability the adult only reads the newspaper.
b. Find the probability the adult watches the evening news or reads the newspaper.
c. Find the probability the adult watches the evening news given that she already reads the newspaper.
d. Are reading the newspaper and watching TV news independent? Explain and prove with math.
Chapter 2, 11 Probability, Measurement & Data (calculator OK):
 Use the 68-95-99.7 rule for normal distributions to estimate probabilities.
 Draw accurate representations of data, including histograms, relative frequency histograms, and box and
whisker plots.
 Find and interpret measures of center (mean, median, and mode) and measures of spread (IQR, range, and
standard deviation.)
 Analyze survey/experimental design, including finding potential sources of bias.
28. The weights of a box of cereal are normally distributed with a mean of 12.2 ounces and a standard deviation of
0.3 ounces. Find the probability of each event:
a. A box weighs less than 12.2 ounces.
b. A box weighs more than 12.5 ounces.
c. A box weighs between 11.6 and 12.5 ounces.
d. A box weighs more than 12 ounces.
29. The data below are the test scores for two tests in 8th period math. (continued on next page)
(a) Find the 5 number summaries for each test.
(b) Draw comparative box-and-whisker plots using the same number line.
Test 1:
Test 2:
50, 58, 59, 60, 62, 65, 66, 68,
65, 67 73, 74, 75, 77, 78, 80,
70, 71, 75, 81, 84, 85, 88, 93
81, 83, 84, 85, 87, 88, 90, 92
(c)
(d)
(e)
(f)
(g)
Compare the range and the interquartile range for the two tests.
Write a sentence comparing the median and the mean values for the two tests.
On test 1 you scored a 71, what percent of the class did you score higher than?
On test 2 you scored a 74, what percent of the class did you score higher than?
Which test did you do better on compared to the rest of the class? Explain.
A recent Gallup poll asked "Do you consider pro wrestling to be a sport, or not?" Of the people asked, 81% said "No." Here is what
Gallup says about the accuracy of this poll: The results below are based on telephone interviews with a randomly selected national
sample of 1,028 adults, 18 years and older, conducted August 16-18, 1999. For results based on this sample, one can say with 95
percent confidence that the maximum error attributable to sampling and other random effects is plus or minus 3 percentage points.
In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the
findings of public opinion polls. The next six questions concern this situation. They’re multiple choice.
30. The population for this poll appears to be
(a) all adults, 18 years and older.
(c) the 1028 adults who were interviewed.
31. The sample for this poll is
(a) all adults, 18 years and older.
(c) the 1028 adults who were interviewed.
(b) 95% of adults, 18 years and older.
(d) 95% of the 1028 adults who were
interviewed.
(b) 95% of adults, 18 years and older.
(d) 95% of the 1028 adults who were
interviewed.
32. In Gallup's statement, "95% confidence" means
(a) We know that 95% of all adults would give the same answer that this poll found.
(b) If repeated many times, 95% of all the polls would find that 81% of the people interviewed think pro wrestling is not a sport.
(c) This poll is one of the 95% of all Gallup polls that give correct results.
(d) If repeated many times, we’re 95% sure that the results would be within plus or minus three percentage points of our statistic.
33. Which of these sources of possible errors in the poll result are covered by the margin of error of plus or minus three points?
(a) The poll left out people without telephones.
(b) Some people chosen for the sample refused to answer.
(c) Some people did not tell the truth because they were embarrassed to admit they like pro wrestling.
(d) None of these.
(e) (b) and (c) but not (a).
34. In all, 151 people in the sample of 1028 adults said they were fans of pro wrestling. Gallup asked these 151 people, "Who is
your favorite pro wrestler?" Twenty-four percent said Steve Austin was their favorite. Gallup gave a margin of error for this result.
This margin of error is
(a) plus or minus three percentage points, just as for the overall poll.
(b) less than plus or minus three points because the sample for this question is smaller.
(c) greater than plus or minus three points because the sample for this question is smaller.
(d) less than plus or minus three points because the population of wrestling fans is smaller than the population of all adults.
35. If the sample size drops from 1028 to 151, the margin of error for 95% confidence changes from:
(a) 8% to 3%.
(b) 3% to 8%.
(c) 3% to 2%.
(d) 3% to 5%.
(e) 12% to 32%
Section 10.7 Polynomial Functions (calculator OK):
 Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive
integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.
 Be able to recognize and apply formulas to binomial probability events
36. Expand.  2a  3
5
37. Find the indicated term of the binomial expansion.
a. The 1st term of  2a  3
b. The 6th term of  2a  3
8
8
38. The probability that a Drake student gets an ice-cream cone from The Scoop any given day is 80%. If each
day is independent of the next, find the probability that a Drake student will get an ice-cream cone at Scoop on at
least 3 of the next four days.
Chapter 9 Sequences and Series (calculator okay):
 Identify a sequence as Arithmetic or Geometric.
 Find a given term in an Arithmetic or Geometric Sequence.
 Find a partial or infinite Geometric Sum.
 Find an Arithmetic Sum.
12
20
39. Evaluate.
 (100n  25)
40. Evaluate.
 3(4)
n 1
n 1
n 1

41. Find the sum of the first 20 multiples of 8.
42. Evaluate.
 7(-0.6)
k-1
if the sum exists
k 1
43. Find the sum if it exists.
44. Find the sum if it exists.
45. Find the sum if it exists.
46. Find the sum if it exists.
3  8.5 14 19.5  ... 102
160  40 10  2.5  .....
47. A grocery store display has 2 can on the top row, 4
cans on the 2nd row, and 6 cans on the third row, and so
on. How many cans are needed to make 25 rows?
120  60  30  ...  .9375
2  4  8 16  ........