Boston Public Schools
Assessment: Course 456 – End Module Chapter 11
2007-2008
Boston Public Schools
Course 456 - Advanced Algebra
End Module Mathematics Examination
Chapter 11 – Revised 1-08
This examination is based on the mathematics that you have done in your math class. Please do all
computation and scratch work on this examination. Choose the one best response for each question
and completely fill in the corresponding bubble on your answer sheet using a #2 pencil or softer. Be
sure to completely erase any stray marks. Read all of the answer choices before making your
selection. Diagrams on this test are not drawn to scale. Calculators are allowed on this exam.
Name: ______________________________School:_____________________________
1.
A restaurant is running a promotion where a diner gets to answer a trivia question to try to
win a jackpot. The jackpot starts at $500 for the first night and increases $75 each night that there is
no winner. You are going to the restaurant on the 8th night of the promotion. How much will the
jackpot be for that night if no one wins by then?
A. $1,100
B. $1,025
C. $600
D. $525
1,B,12.P.2,Algebra,Arithmetic Sequences,Solve with arithmetic sequences in app.,Glencoe Algebra
2,11.1,12
Student:
A-Set up an incorrect formula for the arithmetic sequence as 500  75n .
B-Correct Answer
C-Determined by how much the jackpot would increase, using the incorrect formula 75n .
D-Determined by how much the jackpot would increase.
2.
Find S n for the arithmetic series described by a1  2, an  68, n  12 .
A. 420
B. 4,512
C. 82
D. 880
2,A,12.P.2,Algebra,Arithmetic Series,Identify the sum of an arithmetic series,Glencoe Algebra
2,11.2,16
Student:
A-Correctly utilized the formula S n 
n
(a1  an ) .
2
n
B-Used the incorrect formula Sn  [2a1  (n  1)d ] , for the given information using an as d.
2
C-Found the sum of a1, an , and n .
n
D-Incorrectly utilized the formula S n  (a1  an ) as Sn  n(a1  an ) .
2
Page 1 of 5
Boston Public Schools
Assessment: Course 456 – End Module Chapter 11
3.
2007-2008
Which of the following geometric sequences has a common ratio of
A. 20, 5,
5 5
, ,...
4 16
B. 28, 8,
16 32
,
,...
7 49
C. 16, 12, 9,
27
,...
4
1
?
6
5 5
D. 30, 5, , ,...
6 36
3,D,12.P.2,Algebra,Geometric Sequences,Determine which geometric sequence has a given common
ratio,Glencoe Algebra 2,11.3,30
Student:
1
.
4
2
B-Chosen a geometric sequence having a common ratio of .
7
3
C-Chosen a geometric sequence having a common ratio of .
4
D-Correct Answer
A-Chosen a geometric sequence having a common ratio of
4.
Find S n for the geometric series described by a1  12, r  2, n  6 .
A. 420
B. 144
C. 756
D. 20
4,C,12.P.2,Algebra,Geometric Series,Calculate the sum of a geometric series,Glencoe Algebra
2,11.4,23
Student:
A-Confused r with n and n with r in r n .
B-Found the product of a1, r , and n .
C-Correctly utilized the formula Sn 
a1 (1  r n )
.
1 r
D-Found the sum of a1, r , and n .
Page 2 of 5
Boston Public Schools
Assessment: Course 456 – End Module Chapter 11
5.
2007-2008
Find the sum of the following infinite geometric series, if it exists: 12  9  6.75  ....
A.
48
7
B. 48
C. 9.75
D. Does Not Exist
5,A,12.P.2,Algebra,Infinite Geometric Series,Determine the sum of an infinite geometric
series,Glencoe Algebra 2,11.5,17
Student:
A-Correctly utilized the formula S 
a1
.
1 r
3
.
4
C-Found the sum of the series’ elements that appear in the given geometric series.
D-Did not recognize the series as having a defined limit.
B-Incorrectly determined the common ratio to be
6.
Jonathan deposited $750 in a bank account. At the end of each year, the bank posts interest to
his account in the amount of 3% of the balance; but then takes out a $15 annual fee. Find the balance
in the account after five years.
A. $871.38
B. $781.38
C. $2,649.05
D. $789.82
6,D,12.P.2,Algebra,Recursion and Special Sequences,Determine the value of a term of a recursive
formula in application,Glencoe Algebra 2,11.6,6
Student:
A-Used a formula that compounds interest continuously, B  Pe rt .
B-Mistakenly included the initial deposit as a year.
C-Incorrectly changed 3% into a decimal as .3.
D-Correctly set up and applied the formula bn  1.03bn1  15 .
7. Ms. Donohue is giving a seven-question true-false quiz. How many ways could a student answer
the questions with three true answers and four false answers?
A. 21
B. 35
C. 1
D. 15
7,B,12.P.3,Algebra,Binomial Theorem,Solve using the binomial theorem in app.,Glencoe Algebra
2,11.7,26
Page 3 of 5
Boston Public Schools
Assessment: Course 456 – End Module Chapter 11
2007-2008
Student:
A-Correctly used the binomial theorem, but used the coefficient of x5 y 2 .
B-Correct Answer
C-Mistakenly determined that there is only a single way to obtain the desired result.
D-Assigned the first layer of Pascal’s Triangle with an exponent of 1, rather than 0, yielding
x7  6 x6 y  15x5 y 2  20 x 4 y3  15x3 y 4  6 x 2 y5  xy 6 .
8,12.P.3,Algebra,The Binomial Theorem,Expand a power using the binomial theorem,Glencoe
Algebra 2,11.7,12
8.
Expand (m  n)6 .
Answer:
Using Pascal’s Triangle we obtain,
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
Using Pascal’s Triangle we write m6  6m5n  15m4n 2  20m3n3  15m2 n4  6mn5  n6 .
Page 4 of 5
Boston Public Schools
Assessment: Course 456 – End Module Chapter 11
2007-2008
9,12.P.2,Algebra,Recursion and Special Sequences,Calculate the first five terms of a recursive
sequence,Glencoe Algebra 2,11.6,10
9.
Find the first five terms of the sequence defined by a1  6, an1  2an  4 .
Answer:
a1  6
a2  2(6)  4  8
a3  2(8)  4  12
a4  2(12)  4  20
a5  2(20)  4  36
Therefore, the first five terms of the sequence are 6, 8, 12, 20, 36 .
10,12.P.2,Algebra,Infinite Geometric Series,Calculate the sum of an infinite geometric
series,Glencoe Algebra 2,11.5,1
10.
Find the sum of the infinite geometric series defined by a1  24, r 
1
.
4
Answer:
Using the formula for the sum of an infinite geometric series, S 
S
24
24

 32
1
3
1
4 4
Page 5 of 5
a1
24
as S 
.
1
1 r
1
4