Question 1

Use the method of successive differences to determine the next term in the sequence.
-8, 25, 79, 170, 298, . . .

Accepted Answer

A) 499 
B) 426 
C) 500 
D) 463 
A) 499 
B) 426 
C) 500 
D) 463

Question 2

Find a pattern and use it to solve the problem.
-Find the next term: 5, 10, 15, 25

Accepted Answer

A) 30 
B) 35 
C) 50 
D) 55 
A) 30 
B) 35 
C) 50 
D) 55

Question 3

Determine what the next equation would be, and verify that it is indeed a true statement.
-32 + 10 = 42 
43 + 21 = 64
54 + 32 = 86

Accepted Answer

A) 56 + 43 = 99 
B) 64 + 53 = 117 
C) 65 + 43 = 108 
D) 65 + 32 = 97 
A) 56 + 43 = 99 
B) 64 + 53 = 117 
C) 65 + 43 = 108 
D) 65 + 32 = 97

Question 4

Use this graph to answer the question.  
-Which month in 2009 had the lowest sales?

Accepted Answer

A) Month 6 
B) Month 3 
C) Month 2 
D) Month 8 
A) Month 6 
B) Month 3 
C) Month 2 
D) Month 8

Question 5

How many triangles are in the next figure?

Accepted Answer

A)  18 
B)  12 
C)  16 
D)  36 
A)  18 
B)  12 
C)  16 
D)  36

Question 6

Complete the magic (addition)square. A magic square has the property that the sum of the numbers in any row, column,
or diagonal is the same.
-Use each number 12, 13, 14, 15, 16, 17, 18, 19, and 20 once. $\begin{array}{|l|l|l|}
\hline 15 & & \
\hline 14 & 16 & \
\hline 19 & 12 & 17 \
\hline
\end{array}$

Accepted Answer

A) 
$\begin{array}{|l|l|l|}
\hline 15 & 20 & 18 \
\hline 14 & 16 & 13 \
\hline 19 & 12 & 17 \
\hline
\end{array}$ 
B) 
$\begin{array}{|l|l|l|}
\hline 15 & 20 & 13 \
\hline 14 & 16 & 18 \
\hline 19 & 12 & 17 \
\hline
\end{array}$ 
C) 
$\begin{array}{|l|l|l|}
\hline 15 & 18 & 13 \
\hline 14 & 16 & 20 \
\hline 19 & 12 & 17 \
\hline
\end{array}$ 
D) 
$\begin{array}{|c|c|c|}
\hline 15 & 18 & 20 \
\hline 14 & 16 & 13 \
\hline 19 & 12 & 17 \
\hline
\end{array}$ 
A) 
$\begin{array}{|l|l|l|}
\hline 15 & 20 & 18 \
\hline 14 & 16 & 13 \
\hline 19 & 12 & 17 \
\hline
\end{array}$ 
B) 
$\begin{array}{|l|l|l|}
\hline 15 & 20 & 13 \
\hline 14 & 16 & 18 \
\hline 19 & 12 & 17 \
\hline
\end{array}$ 
C) 
$\begin{array}{|l|l|l|}
\hline 15 & 18 & 13 \
\hline 14 & 16 & 20 \
\hline 19 & 12 & 17 \
\hline
\end{array}$ 
D) 
$\begin{array}{|c|c|c|}
\hline 15 & 18 & 20 \
\hline 14 & 16 & 13 \
\hline 19 & 12 & 17 \
\hline
\end{array}$

Question 7

Solve the problem.
-Rose's work ID is based on her last name, Smith, and her code number is $19 - 13 - 9 - 20 - 8$, written as 19139208. If Jen's ID is an 8-digit palindrome, say a - b - cd - e - $\mathrm { f } - \mathrm { gh }$, which satisfies the given conditions, what is Jen's last name?
$\begin{array} { l } 
2 ( a + h ) = d + e ; \
a \times b \times h = d ; \
b + c = a ; \
a \neq b \neq d ;
\end{array}$
the sum of the digits is 16 ;
$c = b ; e = 4 \text {; }$
Jen's last name starts with a letter in the first half of the alphabet.

Accepted Answer

A)  Andal 
B)  Rundal 
C)  Mandal 
D)  Bandal 
A)  Andal 
B)  Rundal 
C)  Mandal 
D)  Bandal

Question 8

Use inductive reasoning to predict the next equation.
-9 × 9 = 81 
99 × 99 = 9801
999 × 999 = 998,001

Accepted Answer

A) 9999 × 9999 = 999,001 
B) 999 × 9999 = 99,980,001 
C) 9999 × 9999 = 1,000,001 
D) 9999 × 9999 = 99,980,001 
A) 9999 × 9999 = 999,001 
B) 999 × 9999 = 99,980,001 
C) 9999 × 9999 = 1,000,001 
D) 9999 × 9999 = 99,980,001

Question 9

Use problem solving strategies to solve the problem.
-What's the easiest way to heat a pan of water for 9 minutes when you have only a 6-minute hour-glass timer and a 21-minute hour-glass timer?

Accepted Answer

A) Start both timers. When the 6-min one runs out, turn it over. When it runs out again, start heating the water until the 21-min timer runs out. 
B) Start the 6-min timer. When it's halfway through start heating the water. When it runs out turn it over and heat the water until it runs out again. 
C) Can't be done. 
D) Start both timers. When the 6-min timer runs out, start heating the water. Continue until the 21-min timer runs out. 
A) Start both timers. When the 6-min one runs out, turn it over. When it runs out again, start heating the water until the 21-min timer runs out. 
B) Start the 6-min timer. When it's halfway through start heating the water. When it runs out turn it over and heat the water until it runs out again. 
C) Can't be done. 
D) Start both timers. When the 6-min timer runs out, start heating the water. Continue until the 21-min timer runs out.

Question 10

Decide whether the argument is an example of inductive or deductive reasoning.
-$| - p | = p$, therefore $| - 46 | = 46$

Accepted Answer

A)  Inductive 
B)  Deductive 
A)  Inductive 
B)  Deductive

Question 11

Use inductive reasoning to predict the next equation.
-9 × 10 = 11 × 12 - (9 + 10 + 11 + 12) 
10 × 11 = 12 × 13 - (10 + 11 + 12 + 13)

Accepted Answer

A) 12 × 13 = 14 × 15 - (11 + 10 + 9 + 8) 
B) 12 × 13 = 14 × 15 - (12 + 13 + 14 + 15) 
C) 11 × 12 = 13 × 14 - (9 + 10 + 11 + 12 + 13 + 14) 
D) 11 × 12 = 13 × 14 - (11 + 12 + 13 + 14) 
A) 12 × 13 = 14 × 15 - (11 + 10 + 9 + 8) 
B) 12 × 13 = 14 × 15 - (12 + 13 + 14 + 15) 
C) 11 × 12 = 13 × 14 - (9 + 10 + 11 + 12 + 13 + 14) 
D) 11 × 12 = 13 × 14 - (11 + 12 + 13 + 14)

Question 12

Determine the most probable next term in the sequence.
-34, 28, 22, 16, 10

Accepted Answer

A) 4 
B) 0 
C) 2 
D) 6 
A) 4 
B) 0 
C) 2 
D) 6

Question 13

Use the method of successive differences to determine the next term in the sequence.
-4, 18, 90, 264, 605, 1199, . . .

Accepted Answer

A) 2143 
B) 2132 
C) 2174 
D) 2153 
A) 2143 
B) 2132 
C) 2174 
D) 2153

Question 14

Solve the problem.
-A girl asks her father how many ties he has and he answers with a riddle: "Seven-eighths of my ties plus five." How many ties does her father have?

Accepted Answer

A) 40 
B) 45 
C) 50 
D) 35 
A) 40 
B) 45 
C) 50 
D) 35

Question 15

Determine what the next equation would be, and verify that it is indeed a true statement.
-40 - 9 = 31 
400 - 89 = 311
4000 - 789 = 3211

Accepted Answer

A) 400,000 - 6,789 = 33,211 
B) 40,000 - 6,789 = 393,211 
C) 4000 - 6,789 = 33,211 
D) 40,000 - 6,789 = 33,211 
A) 400,000 - 6,789 = 33,211 
B) 40,000 - 6,789 = 393,211 
C) 4000 - 6,789 = 33,211 
D) 40,000 - 6,789 = 33,211

Question 16

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or geometric, give the next term in the sequence.
-4, 12, 36, 108, 324, . . .

Accepted Answer

A) arithmetic; 972 
B) geometric; 972 
C) neither 
A) arithmetic; 972 
B) geometric; 972 
C) neither

Question 17

Use the method of Gauss to find the sum.
-2 + 4 + 6 + . . . + 400

Accepted Answer

A) 161,604 
B) 40,200 
C) 40,000 
D) 10,000 
A) 161,604 
B) 40,200 
C) 40,000 
D) 10,000

Question 18

In a school survey, students showed these preferences for instructional materials. Answer the question.  
-About how many students would you expect to prefer lectures in a school of 750 students?

Accepted Answer

A) About 18 students 
B) About 270 students 
C) About 135 students 
D) About 150 students 
A) About 18 students 
B) About 270 students 
C) About 135 students 
D) About 150 students

Question 19

Give the appropriate counting number answer to the problem.
-Each gallon of shingle stain covers 120 square feet. How many gallons should you buy to cover 686 square feet?

Accepted Answer

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

Question 20

How many line segments are used in the next figure?

Accepted Answer

A)  36 
B)  30 
C)  24 
D)  27 
A)  36 
B)  30 
C)  24 
D)  27

Use the method of successive differences to determine the next term in the sequence. -8, 25, 79, 170, 298, . . .

Find a pattern and use it to solve the problem. -Find the next term: 5, 10, 15, 25

Determine what the next equation would be, and verify that it is indeed a true statement. -32 + 10 = 42 43 + 21 = 64 54 + 32 = 86

Use this graph to answer the question. -Which month in 2009 had the lowest sales?

How many triangles are in the next figure?

Complete the magic (addition)square. A magic square has the property that the sum of the numbers in any row, column, or diagonal is the same. -Use each number 12, 13, 14, 15, 16, 17, 18, 19, and 20 once. 15 14 16 19 12 17

Use inductive reasoning to predict the next equation. -9 × 9 = 81 99 × 99 = 9801 999 × 999 = 998,001

Use problem solving strategies to solve the problem. -What's the easiest way to heat a pan of water for 9 minutes when you have only a 6-minute hour-glass timer and a 21-minute hour-glass timer?

Decide whether the argument is an example of inductive or deductive reasoning. - $| - p | = p$ , therefore $| - 46 | = 46$

Use inductive reasoning to predict the next equation. -9 × 10 = 11 × 12 - (9 + 10 + 11 + 12) 10 × 11 = 12 × 13 - (10 + 11 + 12 + 13)

Determine the most probable next term in the sequence. -34, 28, 22, 16, 10

Use the method of successive differences to determine the next term in the sequence. -4, 18, 90, 264, 605, 1199, . . .

Solve the problem. -A girl asks her father how many ties he has and he answers with a riddle: "Seven-eighths of my ties plus five." How many ties does her father have?

Determine what the next equation would be, and verify that it is indeed a true statement. -40 - 9 = 31 400 - 89 = 311 4000 - 789 = 3211

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or geometric, give the next term in the sequence. -4, 12, 36, 108, 324, . . .

Use the method of Gauss to find the sum. -2 + 4 + 6 + . . . + 400

In a school survey, students showed these preferences for instructional materials. Answer the question. -About how many students would you expect to prefer lectures in a school of 750 students?

Give the appropriate counting number answer to the problem. -Each gallon of shingle stain covers 120 square feet. How many gallons should you buy to cover 686 square feet?

How many line segments are used in the next figure?

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 1: The Art of Problem Solving

Use the method of successive differences to determine the next term in the sequence. -8, 25, 79, 170, 298, . . .

Find a pattern and use it to solve the problem. -Find the next term: 5, 10, 15, 25

Determine what the next equation would be, and verify that it is indeed a true statement. -32 + 10 = 42 43 + 21 = 64 54 + 32 = 86

Use this graph to answer the question. -Which month in 2009 had the lowest sales?

How many triangles are in the next figure?

Complete the magic (addition)square. A magic square has the property that the sum of the numbers in any row, column, or diagonal is the same. -Use each number 12, 13, 14, 15, 16, 17, 18, 19, and 20 once. 15 14 16 19 12 17

Use inductive reasoning to predict the next equation. -9 × 9 = 81 99 × 99 = 9801 999 × 999 = 998,001

Use problem solving strategies to solve the problem. -What's the easiest way to heat a pan of water for 9 minutes when you have only a 6-minute hour-glass timer and a 21-minute hour-glass timer?

Decide whether the argument is an example of inductive or deductive reasoning. - ∣−p∣=p| - p | = p∣−p∣=p , therefore ∣−46∣=46| - 46 | = 46∣−46∣=46

Use inductive reasoning to predict the next equation. -9 × 10 = 11 × 12 - (9 + 10 + 11 + 12) 10 × 11 = 12 × 13 - (10 + 11 + 12 + 13)

Determine the most probable next term in the sequence. -34, 28, 22, 16, 10

Use the method of successive differences to determine the next term in the sequence. -4, 18, 90, 264, 605, 1199, . . .

Solve the problem. -A girl asks her father how many ties he has and he answers with a riddle: "Seven-eighths of my ties plus five." How many ties does her father have?

Determine what the next equation would be, and verify that it is indeed a true statement. -40 - 9 = 31 400 - 89 = 311 4000 - 789 = 3211

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or geometric, give the next term in the sequence. -4, 12, 36, 108, 324, . . .

Use the method of Gauss to find the sum. -2 + 4 + 6 + . . . + 400

In a school survey, students showed these preferences for instructional materials. Answer the question. -About how many students would you expect to prefer lectures in a school of 750 students?

Give the appropriate counting number answer to the problem. -Each gallon of shingle stain covers 120 square feet. How many gallons should you buy to cover 686 square feet?

How many line segments are used in the next figure?

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Decide whether the argument is an example of inductive or deductive reasoning. - $| - p | = p$ , therefore $| - 46 | = 46$