Question 1

Complete the magic (addition)square.
-Use each number 24, 25, 26, 27, 28, 29, 30, 31, and 32 once. $\begin{array}{|l|l|l|}
\hline 27 & & 25 \
\hline & 28 & 30 \
\hline & 24 & \
\hline
\end{array}$

Accepted Answer

A) 
$\begin{array}{|l|l|l|}
\hline 27 & 29 & 25 \
\hline 26 & 28 & 30 \
\hline 31 & 24 & 32 \
\hline
\end{array}$ 
B) 
$\begin{array}{|l|l|l|}
\hline 27 & 31 & 25 \
\hline 26 & 28 & 30 \
\hline 29 & 24 & 32 \
\hline
\end{array}$ 
C) 
$\begin{array}{|l|l|l|}
\hline 27 & 32 & 25 \
\hline 26 & 28 & 30 \
\hline 29 & 24 & 31 \
\hline
\end{array}$ 
D) 
$\begin{array}{|l|l|l|}
\hline 27 & 32 & 25 \
\hline 26 & 28 & 30 \
\hline 31 & 24 & 29 \
\hline
\end{array}$

Question 2

Provide an appropriate response.
-The first difference of a sequence is 3, 6, 9, 12, 15, . . . Find the first six terms of the original sequence if the sum of the first two terms is 17.

Accepted Answer

A) 7, 10, 16, 25, 37, 52 
B) 17, 20, 26, 35, 47, 62 
C) 17, 20, 23, 26, 29, 32 
D) 7, 10, 13, 16, 19, 22

Question 3

Provide an appropriate response.
-The first difference of a sequence is 2, 4, 6, 8, 10, . . . Find the first six terms of the original sequence if the first term in the original sequence is 8.

Accepted Answer

A) 10, 14, 20, 28, 38, 50 
B) 8, 10, 14, 20, 28, 38 
C) 8, 16, 32, 48, 64, 80 
D) 8, 10, 12, 14, 16, 18

Question 4

Solve the problem.
-How many different ways can you make change for a 25-cent coin using dimes, nickels, and pennies?

Accepted Answer

A) 11 
B) 12 
C) 10 
D) 13

Question 5

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
-6, 15, 18, 21, 24, . . .

Accepted Answer

A) Neither; 27; 30 
B) Arithmetic; 24; 27 
C) Geometric; 33; 30

Question 6

Solve the problem.
-A man earned $ 3000 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 15 th year?

Accepted Answer

A) $ 9000 
B) None of these 
C) $ 8600 
D) $ 5600

Question 7

Solve the problem.
-How many different amounts of money can you pay if you use two coins including only nickels, dimes, and quarters?

Accepted Answer

A) 6 
B) 4 
C) 7 
D) 5

Question 8

Solve the problem.
-The temperature rose 7 degrees from 10:00 A.M. to noon. By 3:00 P.M. the temperature had doubled. From 3:00 P.M. to 6:00 P.M. the temperature rose 6 degrees to 94 degrees. What was the
Temperature at 10:00 A.M. that morning?

Accepted Answer

A) 51 degrees 
B) 43 degrees 
C) 37 degrees 
D) 81 degrees

Question 9

Provide an appropriate response.
-Use a traditional clock face to determine the next three terms in the following sequence: 1, 11, 9, 7, 5, . . .

Accepted Answer

A) 3, 1, 11 
B) 3, 3, 10 
C) 2, 2, 11 
D) 4, 2, 12

Question 10

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
-15, 75, 375, 1875, 9375, . . .

Accepted Answer

A) Geometric; 46,875; 234,375 
B) Neither; 93,750; 468,750 
C) Arithmetic; 468,750; 703,125

Question 11

Find the number of terms in the sequence or the sum of the sequence as requested.
-Find the following sum: 5 + 405 + 805 + . . . + 4005

Accepted Answer

A) 22,050 
B) 22,055 
C) 18,045 
D) 22,060

Question 12

Solve the problem.
-How many different ways can you make change for a 50-cent coin using quarters, dimes, and nickels?

Accepted Answer

A) 11 
B) 10 
C) 9 
D) 8

Question 13

Solve the problem.
-If a person puts 1¢ in a piggy bank on the first day, 2¢ on the second day, 3¢ on the third day, and so forth, how much money will be in the bank after 30 days?

Accepted Answer

A) $ 9.30 
B) $ 2.33 
C) $ 4.65 
D) $ 0.30

Question 14

Which terms, n and m, in the arithmetic sequence 175, 250, 325, . . . and the geometric sequence 1, 10, 100, . . ., respectively, have the same value? What is the value?

Accepted Answer

The answer of Which terms, n and m, in the...

Question 15

Complete the magic (addition)square.
-Use each number 47, 48, 49, 50, 51, 52, 53, 54, and 55 once. $\begin{array}{|c|l|l|}
\hline 48 & & 52 \
\hline & & 47 \
\hline 50 & 49 & \
\hline
\end{array}$

Accepted Answer

A) 
$\begin{array}{|l|l|l|}
\hline 48 & 53 & 52 \
\hline 54 & 51 & 47 \
\hline 50 & 49 & 55 \
\hline
\end{array}$ 
B) 
$\begin{array}{|l|l|l|}
\hline 48 & 54 & 52 \
\hline 55 & 53 & 47 \
\hline 50 & 49 & 51 \
\hline
\end{array}$ 
C) 
$\begin{array}{|l|l|l|}
\hline 48 & 53 & 52 \
\hline 55 & 51 & 47 \
\hline 50 & 49 & 54 \
\hline
\end{array}$ 
D)

$\begin{array}{|l|l|l|}
\hline 48 & 54 & 52 \
\hline 55 & 51 & 47 \
\hline 50 & 49 & 53 \
\hline
\end{array}$

Question 16

Solve the problem.
-How many different ways can you make change for a 50-cent coin using nickels and dimes?

Accepted Answer

A) 4 
B) 5 
C) 7 
D) 6

Question 17

Find the number of terms in the sequence or the sum of the sequence as requested.
-Find the sum of the following arithmetic sequence. 11 + 13 + . . . + 601

Accepted Answer

A) 89,975 
B) 90,601 
C) 90,576 
D) 76,176

Question 18

Provide an appropriate response.
-What is the sum of three consecutive integers in terms of the middle number x? What would the sum be in terms of the middle number for five and seven consecutive integers? What can you generalize about the sum of n consecutive integers where n is odd?

Accepted Answer

The answer of Provide an appropriate response.
-What is the sum...

Question 19

Find the number of terms in the sequence or the sum of the sequence as requested.
-How many terms are there in the sequence $1,3,3 ^ { 2 } , 3 ^ { 3 } , \ldots , 3 ^ { 25 }$ ?

Accepted Answer

A)  25 
B)  26 
C)  24 
D)  27

Question 20

Determine how many of the indicated shape there are in the figure.
-Squares (of any size)

Accepted Answer

A)  11 
B)  8 
C)  9 
D)  12

Exam 1: An Introduction to Problem Solving

Complete the magic (addition) square. -Use each number 24, 25, 26, 27, 28, 29, 30, 31, and 32 once. $\begin{array}{|l|l|l|}\hline 27 & & 25 \\\hline & 28 & 30 \\\hline & 24 & \\\hline\end{array}$

Provide an appropriate response. -The first difference of a sequence is 3, 6, 9, 12, 15, . . . Find the first six terms of the original sequence if the sum of the first two terms is 17.

Provide an appropriate response. -The first difference of a sequence is 2, 4, 6, 8, 10, . . . Find the first six terms of the original sequence if the first term in the original sequence is 8.

Solve the problem. -How many different ways can you make change for a 25-cent coin using dimes, nickels, and pennies?

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence. -6, 15, 18, 21, 24, . . .

Solve the problem. -A man earned $ 3000 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 15 th year?

Solve the problem. -How many different amounts of money can you pay if you use two coins including only nickels, dimes, and quarters?

Solve the problem. -The temperature rose 7 degrees from 10:00 A.M. to noon. By 3:00 P.M. the temperature had doubled. From 3:00 P.M. to 6:00 P.M. the temperature rose 6 degrees to 94 degrees. What was the Temperature at 10:00 A.M. that morning?

Provide an appropriate response. -Use a traditional clock face to determine the next three terms in the following sequence: 1, 11, 9, 7, 5, . . .

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence. -15, 75, 375, 1875, 9375, . . .

Find the number of terms in the sequence or the sum of the sequence as requested. -Find the following sum: 5 + 405 + 805 + . . . + 4005

Solve the problem. -How many different ways can you make change for a 50-cent coin using quarters, dimes, and nickels?

Solve the problem. -If a person puts 1¢ in a piggy bank on the first day, 2¢ on the second day, 3¢ on the third day, and so forth, how much money will be in the bank after 30 days?

Which terms, n and m, in the arithmetic sequence 175, 250, 325, . . . and the geometric sequence 1, 10, 100, . . ., respectively, have the same value? What is the value?

Complete the magic (addition) square. -Use each number 47, 48, 49, 50, 51, 52, 53, 54, and 55 once. $\begin{array}{|c|l|l|}\hline 48 & & 52 \\\hline & & 47 \\\hline 50 & 49 & \\\hline\end{array}$

Solve the problem. -How many different ways can you make change for a 50-cent coin using nickels and dimes?

Find the number of terms in the sequence or the sum of the sequence as requested. -Find the sum of the following arithmetic sequence. 11 + 13 + . . . + 601

Provide an appropriate response. -What is the sum of three consecutive integers in terms of the middle number x? What would the sum be in terms of the middle number for five and seven consecutive integers? What can you generalize about the sum of n consecutive integers where n is odd?

Find the number of terms in the sequence or the sum of the sequence as requested. -How many terms are there in the sequence $1,3,3 ^ { 2 } , 3 ^ { 3 } , \ldots , 3 ^ { 25 }$ ?

Determine how many of the indicated shape there are in the figure. -Squares (of any size)

Exam 1: An Introduction to Problem Solving

Complete the magic (addition) square. -Use each number 24, 25, 26, 27, 28, 29, 30, 31, and 32 once. 2725283024\begin{array}{|l|l|l|}\hline 27 & & 25 \\\hline & 28 & 30 \\\hline & 24 & \\\hline\end{array}27​2824​2530​​

Provide an appropriate response. -The first difference of a sequence is 3, 6, 9, 12, 15, . . . Find the first six terms of the original sequence if the sum of the first two terms is 17.

Provide an appropriate response. -The first difference of a sequence is 2, 4, 6, 8, 10, . . . Find the first six terms of the original sequence if the first term in the original sequence is 8.

Solve the problem. -How many different ways can you make change for a 25-cent coin using dimes, nickels, and pennies?

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence. -6, 15, 18, 21, 24, . . .

Solve the problem. -A man earned $ 3000 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 15 th year?

Solve the problem. -How many different amounts of money can you pay if you use two coins including only nickels, dimes, and quarters?

Solve the problem. -The temperature rose 7 degrees from 10:00 A.M. to noon. By 3:00 P.M. the temperature had doubled. From 3:00 P.M. to 6:00 P.M. the temperature rose 6 degrees to 94 degrees. What was the Temperature at 10:00 A.M. that morning?

Provide an appropriate response. -Use a traditional clock face to determine the next three terms in the following sequence: 1, 11, 9, 7, 5, . . .

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence. -15, 75, 375, 1875, 9375, . . .

Find the number of terms in the sequence or the sum of the sequence as requested. -Find the following sum: 5 + 405 + 805 + . . . + 4005

Solve the problem. -How many different ways can you make change for a 50-cent coin using quarters, dimes, and nickels?

Solve the problem. -If a person puts 1¢ in a piggy bank on the first day, 2¢ on the second day, 3¢ on the third day, and so forth, how much money will be in the bank after 30 days?

Which terms, n and m, in the arithmetic sequence 175, 250, 325, . . . and the geometric sequence 1, 10, 100, . . ., respectively, have the same value? What is the value?

Complete the magic (addition) square. -Use each number 47, 48, 49, 50, 51, 52, 53, 54, and 55 once. 4852475049\begin{array}{|c|l|l|}\hline 48 & & 52 \\\hline & & 47 \\\hline 50 & 49 & \\\hline\end{array}4850​49​5247​​

Solve the problem. -How many different ways can you make change for a 50-cent coin using nickels and dimes?

Find the number of terms in the sequence or the sum of the sequence as requested. -Find the sum of the following arithmetic sequence. 11 + 13 + . . . + 601

Provide an appropriate response. -What is the sum of three consecutive integers in terms of the middle number x? What would the sum be in terms of the middle number for five and seven consecutive integers? What can you generalize about the sum of n consecutive integers where n is odd?

Find the number of terms in the sequence or the sum of the sequence as requested. -How many terms are there in the sequence 1,3,32,33,…,3251,3,3 ^ { 2 } , 3 ^ { 3 } , \ldots , 3 ^ { 25 }1,3,32,33,…,325 ?

Determine how many of the indicated shape there are in the figure. -Squares (of any size)

Complete the magic (addition) square. -Use each number 24, 25, 26, 27, 28, 29, 30, 31, and 32 once. $\begin{array}{|l|l|l|}\hline 27 & & 25 \\\hline & 28 & 30 \\\hline & 24 & \\\hline\end{array}$

Complete the magic (addition) square. -Use each number 47, 48, 49, 50, 51, 52, 53, 54, and 55 once. $\begin{array}{|c|l|l|}\hline 48 & & 52 \\\hline & & 47 \\\hline 50 & 49 & \\\hline\end{array}$

Find the number of terms in the sequence or the sum of the sequence as requested. -How many terms are there in the sequence $1,3,3 ^ { 2 } , 3 ^ { 3 } , \ldots , 3 ^ { 25 }$ ?