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Quarter 4 Test Review: Sequences and Series, Statistics, Logarithms
Part 1: Sequences and Series
Mile 1
1. What type of graph does an arithmetic sequence represent? Give an example of an
equation or rule. Draw a picture.
2. What type of graph does a geometric sequence represent? Give an example of an
equation or rule. Draw a picture.
Write the rule for each sequence. Then find a8.
3. 162, -54, 18, -6, …
4.
-4, 3, 10, 17, 24, …
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Mile 2
For the problems below, determine if a sum exists (is there a formula that you could use to find
the sum?). Find the sum even if it exists.
1 k 1
 32 
k 1
7
5.
100
6.
3n  5
n 1


h 1
1 5 
 3 4 
h 1

7.

8.
2.5
k 1
k 1


Mile 3
Look at the questions below. State which FORMULA you would use. Determine if finite or
infinite (if necessary). Then answer the question asked.
Problem
9. Find the sum of the first
ten terms: 2, 5, 8, 11…
10. Find the sum of the first
ten terms: 2, 12, 72, 432…
11. A pendulum swings 32
inches on its first swing. Each
successive swing is 80% of
the previous swing. What is
the total distance traveled?
12. Given a3 = 21 and
d = -3, write a rule for the
arithmetic sequence.
Formula
Solution
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Part 2: Exponents and Logs
Mile 4
1. How are exponents and logs similar and different? (Think domain and range too)
2. How can you determine if a function is exponential growth or decay? Give an example
of each.
3. What type of asymptote does an exponent graph have? A log graph? Draw pictures.
4. a) Rewrite in the other form: log2 32 = 5
b) Rewrite in the other form: 3x = 27
Mile 5
x3y6
5. a) Expand: log 2
5
b) Expand: log8 hk 3

6. a) Condense: 2 log 5 x  6 log 5 (x  4)  3log 5 y
7. Rewrite using the change of base formula: log1/2 57
b) Condense: 5ln y 2ln(x 7)
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Mile 6
Solve the following equations.
8. 23x5 16x1
9. log2 y  log2 ( y  4)  5
10. log5 (7 x  3)  2
11. 4ex  3  9
Mile 7
Graph the equations. State the domain, range, and any asymptotes.
7.
y  2(x 4)  3
8.
y  ln(x1)  2
Domain: _____________
Domain: ______________
Range: ______________
Range: _______________
Asymptote: __________
Asymptote: ____________
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Part 3: Statistics
Mile 8
1. How do you find mean, median, standard deviation, and range (explain) on a calculator?
2. What is z-score used for? What does it tell you about a piece of data?
3. Draw and label all the percentages of a normal curve. Label the mean and each standard
deviation.
The data set below gives the number of points per game made by the top 10 scorers in the NBA
during the 2009 – 2010 NBA regular season.
30, 26, 25, 24, 24, 27, 28, 24, 30, 23
4. Find (***Round all answers to the Hundredths Place***):
a) Mean
c) Mode
e) Standard deviation
b) Median
d) Range
e) Variance
Mile 9
5. In the 2005 – 2006 season, the highest number of points scored per game in the NBA was
35 by Kobe Bryant. Find the z-score for this player and explain what this means.
6. Using the mean and standard deviation above and assume a normal distribution.
a) What percentage of basketball players made more than 24 points? Draw a sketch
and shade.
b) How many points represent 68% of the data (from where to where)? 95% of the
data? 99.7% of the data?
c) If the mean and standard deviation above represent a normal distribution of 500
basketball players, how many players made fewer than 27 points?
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Mile 10
For #7 – 10, decide if it is a combination or permutation and solve accordingly.
Label n and r.
7. A certain road only uses odd numbers between 1 and 9 for their address signs. Each address
has four digits. How many possible address are there if none of the digits are repeated in any
address?
Permutation or Combination?
n=
r=
Answer to question:
8. Ms. Carew is picking 3 students to run an errand for her. If her class has 20 students, how
many possible groups of three are there?
Permutation or Combination?
n=
r=
Answer to question:
9. Students are being placed in teams for a tournament. How many different ways can 12
students be placed in teams of 4?
Permutation or Combination?
n=
r=
Answer to question:
10. In Virginia, there are 7 characters on a license plate. Each character can be a letter of the
alphabet or a digit (0 to 9). Characters cannot be repeated. How many possible license plates are
there?
Permutation or Combination?
n=
r=
Answer to question: