Question 1

Determine what the next equation would be, and verify that it is indeed a true statement.
-(1 × 9)- 8 = 1 
(21 × 9)- 8 = 81
(321 × 9)- 8 = 2881

Accepted Answer

A) (4,321 × 9)- 8 = 38,881 
B) (432 × 9)- 8 = 38,881 
C) (4,321 × 9)- 8 = 28,881 
D) (4,321 × 9)- 8 = 3880 
A) (4,321 × 9)- 8 = 38,881 
B) (432 × 9)- 8 = 38,881 
C) (4,321 × 9)- 8 = 28,881 
D) (4,321 × 9)- 8 = 3880

Question 2

Determine the number of figures (of any size)in the design.
-Triangles (of any size)

Accepted Answer

A)  14 
B)  10 
C)  12 
D)  9 
A)  14 
B)  10 
C)  12 
D)  9

Question 3

Determine the indicated term in the given sequence.
-The 6 th term of $15,5 , \frac { 5 } { 3 } , \ldots$

Accepted Answer

A)  $\frac { 5 } { 243 }$ 
B)  $\frac { 5 } { 729 }$ 
C)  $\frac { 5 } { 81 }$ 
D)  $\frac { 5 } { 27 }$ 
A)  $\frac { 5 } { 243 }$ 
B)  $\frac { 5 } { 729 }$ 
C)  $\frac { 5 } { 81 }$ 
D)  $\frac { 5 } { 27 }$

Question 4

Draw the next figure in the pattern.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 5

Use this graph to answer the question.  
-What month in 2010 had the lowest sales?

Accepted Answer

A) Month 5 
B) Month 12 
C) Month 2 
D) Month 3 
A) Month 5 
B) Month 12 
C) Month 2 
D) Month 3

Question 6

Give the appropriate counting number answer to the problem.
-A particular freight elevator can safely carry 1036 pounds. How many 122-pound bundles of wood can be safely carried by this elevator?

Accepted Answer

A) 7 
B) 4 
C) 8 
D) 5 
A) 7 
B) 4 
C) 8 
D) 5

Question 7

Use inductive reasoning to predict the next equation.
-$\begin{array} { r } 
\frac { 1 } { 3 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 3 } \right) \
\frac { 1 } { 3 } + \frac { 1 } { 9 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 9 } \right) \
\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 27 } \right) \
\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 81 } \right)
\end{array}$

Accepted Answer

A)  $\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 243 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 243 } \right)$ 
B)  $\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 729 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 729 } \right)$ 
C)  $\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 162 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 162 } \right)$ 
D)  $\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 243 } = \frac { 1 } { 3 } \left( 1 - \frac { 1 } { 243 } \right)$ 
A)  $\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 243 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 243 } \right)$ 
B)  $\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 729 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 729 } \right)$ 
C)  $\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 162 } = \frac { 1 } { 2 } \left( 1 - \frac { 1 } { 162 } \right)$ 
D)  $\frac { 1 } { 3 } + \frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 243 } = \frac { 1 } { 3 } \left( 1 - \frac { 1 } { 243 } \right)$

Question 8

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true.
-$\sqrt { - 13 } ; \sqrt [ 4 ] { - 2 } ; \sqrt [ 6 ] { - 1.8 } ; \sqrt [ 8 ] { - 278 }$

Accepted Answer

A) An even root of a negative number is negative. 
B) An even root of a negative number is undefined. 
C) An even root of a negative number is positive. 
D) An even root of a negative number can be either positive or negative. 
A) An even root of a negative number is negative. 
B) An even root of a negative number is undefined. 
C) An even root of a negative number is positive. 
D) An even root of a negative number can be either positive or negative.

Question 9

Give the appropriate counting number answer to the problem.
-David's company has to ship 3752 boxes of sprinklers. If a truck can hold 550 boxes, how many trucks does he need to ship all the boxes?

Accepted Answer

A) 8 
B) 7 
C) 6 
D) 5 
A) 8 
B) 7 
C) 6 
D) 5

Question 10

In a school survey, students showed these preferences for instructional materials. Answer the question.  
-About how many students would you expect to prefer computers in a school of 650 students?

Accepted Answer

A) About 130 students 
B) About 117 students 
C) About 36 students 
D) About 234 students 
A) About 130 students 
B) About 117 students 
C) About 36 students 
D) About 234 students

Question 11

Solve the problem.
-Mr. Smith's salary last year was a palindromic, 7 -digit amount, say $\$ \mathrm { a }$, bcd,efg, satisfying these conditions:
$\mathrm { a } + \mathrm { b } \neq \mathrm { e } + \mathrm { f } ; \mathrm { a } = ( \mathrm { b } + \mathrm { e } ) - 8$;
if $c$ were decreased by 2 , the difference would equal the sum of $f$ and $d$; $d = 2$;
and all of the numbers are multiples of $2 .$
What was Mr. Smith's salary last year?

Accepted Answer

A)  $\$ 4,482,844$ 
B)  $\$ 2,462,642$ 
C)  $\$ 4,462,644$ 
D)  $\$ 6,642,466$ 
A)  $\$ 4,482,844$ 
B)  $\$ 2,462,642$ 
C)  $\$ 4,462,644$ 
D)  $\$ 6,642,466$

Question 12

Use problem solving strategies to solve the problem.
-There is a number between 100 and 115, such that if you find the sum of the cubes of the digits, subtract this sum from 99, divide the result by 3, and add the digits once more, you get 2. What is
The number?

Accepted Answer

A) 113 
B) 100 
C) 102 
D) 114 
A) 113 
B) 100 
C) 102 
D) 114

Question 13

Decide whether the argument is an example of inductive or deductive reasoning.
-If $( - p ) ^ { 2 } = p ^ { 2 }$, then $( - 7 ) ^ { 2 } = 49$

Accepted Answer

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

Question 14

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true.
-$\frac { - 3 } { - 8 } ; \frac { - 96 } { - 7 } ; \frac { - 5 } { - 291 } ; \frac { - 1.7 } { - 6.1 }$

Accepted Answer

A) Dividing a negative number by a negative number gives a positive result. 
B) Dividing a negative number by a negative number gives an error message on a calculator. 
C) Dividing a negative number by a negative number gives a negative result. 
D) Dividing a negative number by a negative number can give either a positive or negative result. 
A) Dividing a negative number by a negative number gives a positive result. 
B) Dividing a negative number by a negative number gives an error message on a calculator. 
C) Dividing a negative number by a negative number gives a negative result. 
D) Dividing a negative number by a negative number can give either a positive or negative result.

Question 15

Give the appropriate counting number answer to the problem.
-One cook can make enough food for 350 people a night. How many cooks are needed to feed 1326 people a night?

Accepted Answer

A) 3 
B) 5 
C) 2 
D) 4 
A) 3 
B) 5 
C) 2 
D) 4

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.
-10, 13, 16, 19, 22, . . .

Accepted Answer

A) neither 
B) arithmetic; 25 
C) geometric; 25 
A) neither 
B) arithmetic; 25 
C) geometric; 25

Question 17

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true.
-$( - 11 ) ^ { 3 } ; ( - 4 ) ^ { 5 } ; ( - 1.3 ) ^ { 7 } ; ( - 0.96 ) ^ { 9 }$

Accepted Answer

A) Raising a negative number to an odd power gives an error message on a calculator. 
B) Raising a negative number to an odd power gives a positive result. 
C) Raising a negative number to an odd power can give either a positive or negative result. 
D) Raising a negative number to an odd power gives a negative result. 
A) Raising a negative number to an odd power gives an error message on a calculator. 
B) Raising a negative number to an odd power gives a positive result. 
C) Raising a negative number to an odd power can give either a positive or negative result. 
D) Raising a negative number to an odd power gives a negative result.

Question 18

Use the method of Gauss to find the sum.
-1 + 2 + 3 + . . . + 375

Accepted Answer

A) 35,156.25 
B) 141,376 
C) 70,312.5 
D) 70,500 
A) 35,156.25 
B) 141,376 
C) 70,312.5 
D) 70,500

Question 19

Use problem solving strategies to solve the problem.
-A rabbit grows so that every 2 months it doubles in weight. However, the rabbit will never go over 75 pounds. If a bunny is born on July 15th, weighing 2 pounds, in which month will it weigh 46 Pounds?

Accepted Answer

A) July 
B) June 
C) April 
D) February 
A) July 
B) June 
C) April 
D) February

Question 20

Solve the problem using inductive reasoning.
-Write the next three "square" figurate numbers.

Accepted Answer

None

Determine what the next equation would be, and verify that it is indeed a true statement. -(1 × 9)- 8 = 1 (21 × 9)- 8 = 81 (321 × 9)- 8 = 2881

Determine the number of figures (of any size)in the design. -Triangles (of any size)

Determine the indicated term in the given sequence. -The 6 th term of $15,5 , \frac { 5 } { 3 } , \ldots$

Draw the next figure in the pattern.

Use this graph to answer the question. -What month in 2010 had the lowest sales?

Give the appropriate counting number answer to the problem. -A particular freight elevator can safely carry 1036 pounds. How many 122-pound bundles of wood can be safely carried by this elevator?

Use inductive reasoning to predict the next equation. - = 1- += 1- ++= 1- +++= 1-

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true. - $\sqrt { - 13 } ; \sqrt [ 4 ] { - 2 } ; \sqrt [ 6 ] { - 1.8 } ; \sqrt [ 8 ] { - 278 }$

Give the appropriate counting number answer to the problem. -David's company has to ship 3752 boxes of sprinklers. If a truck can hold 550 boxes, how many trucks does he need to ship all the boxes?

In a school survey, students showed these preferences for instructional materials. Answer the question. -About how many students would you expect to prefer computers in a school of 650 students?

Use problem solving strategies to solve the problem. -There is a number between 100 and 115, such that if you find the sum of the cubes of the digits, subtract this sum from 99, divide the result by 3, and add the digits once more, you get 2. What is The number?

Decide whether the argument is an example of inductive or deductive reasoning. -If $( - p ) ^ { 2 } = p ^ { 2 }$ , then $( - 7 ) ^ { 2 } = 49$

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true. - $\frac { - 3 } { - 8 } ; \frac { - 96 } { - 7 } ; \frac { - 5 } { - 291 } ; \frac { - 1.7 } { - 6.1 }$

Give the appropriate counting number answer to the problem. -One cook can make enough food for 350 people a night. How many cooks are needed to feed 1326 people a night?

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. -10, 13, 16, 19, 22, . . .

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true. - $( - 11 ) ^ { 3 } ; ( - 4 ) ^ { 5 } ; ( - 1.3 ) ^ { 7 } ; ( - 0.96 ) ^ { 9 }$

Use the method of Gauss to find the sum. -1 + 2 + 3 + . . . + 375

Use problem solving strategies to solve the problem. -A rabbit grows so that every 2 months it doubles in weight. However, the rabbit will never go over 75 pounds. If a bunny is born on July 15th, weighing 2 pounds, in which month will it weigh 46 Pounds?

Solve the problem using inductive reasoning. -Write the next three "square" figurate numbers.

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

Determine what the next equation would be, and verify that it is indeed a true statement. -(1 × 9)- 8 = 1 (21 × 9)- 8 = 81 (321 × 9)- 8 = 2881

Determine the number of figures (of any size)in the design. -Triangles (of any size)

Determine the indicated term in the given sequence. -The 6 th term of 15,5,53,…15,5 , \frac { 5 } { 3 } , \ldots15,5,35​,…

Draw the next figure in the pattern.

Use this graph to answer the question. -What month in 2010 had the lowest sales?

Give the appropriate counting number answer to the problem. -A particular freight elevator can safely carry 1036 pounds. How many 122-pound bundles of wood can be safely carried by this elevator?

Use inductive reasoning to predict the next equation. - = 1- += 1- ++= 1- +++= 1-

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true. - −13;−24;−1.86;−2788\sqrt { - 13 } ; \sqrt [ 4 ] { - 2 } ; \sqrt [ 6 ] { - 1.8 } ; \sqrt [ 8 ] { - 278 }−13​;4−2​;6−1.8​;8−278​

Give the appropriate counting number answer to the problem. -David's company has to ship 3752 boxes of sprinklers. If a truck can hold 550 boxes, how many trucks does he need to ship all the boxes?

In a school survey, students showed these preferences for instructional materials. Answer the question. -About how many students would you expect to prefer computers in a school of 650 students?

Use problem solving strategies to solve the problem. -There is a number between 100 and 115, such that if you find the sum of the cubes of the digits, subtract this sum from 99, divide the result by 3, and add the digits once more, you get 2. What is The number?

Decide whether the argument is an example of inductive or deductive reasoning. -If (−p)2=p2( - p ) ^ { 2 } = p ^ { 2 }(−p)2=p2 , then (−7)2=49( - 7 ) ^ { 2 } = 49(−7)2=49

Give the appropriate counting number answer to the problem. -One cook can make enough food for 350 people a night. How many cooks are needed to feed 1326 people a night?

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. -10, 13, 16, 19, 22, . . .

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true. - (−11)3;(−4)5;(−1.3)7;(−0.96)9( - 11 ) ^ { 3 } ; ( - 4 ) ^ { 5 } ; ( - 1.3 ) ^ { 7 } ; ( - 0.96 ) ^ { 9 }(−11)3;(−4)5;(−1.3)7;(−0.96)9

Use the method of Gauss to find the sum. -1 + 2 + 3 + . . . + 375

Use problem solving strategies to solve the problem. -A rabbit grows so that every 2 months it doubles in weight. However, the rabbit will never go over 75 pounds. If a bunny is born on July 15th, weighing 2 pounds, in which month will it weigh 46 Pounds?

Solve the problem using inductive reasoning. -Write the next three "square" figurate numbers.

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

Determine the indicated term in the given sequence. -The 6 th term of $15,5 , \frac { 5 } { 3 } , \ldots$

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true. - $\sqrt { - 13 } ; \sqrt [ 4 ] { - 2 } ; \sqrt [ 6 ] { - 1.8 } ; \sqrt [ 8 ] { - 278 }$

Decide whether the argument is an example of inductive or deductive reasoning. -If $( - p ) ^ { 2 } = p ^ { 2 }$ , then $( - 7 ) ^ { 2 } = 49$

Use your calculator to perform each calculation and observe the answers. Use inductive reasoning to determine which statement is true. - $( - 11 ) ^ { 3 } ; ( - 4 ) ^ { 5 } ; ( - 1.3 ) ^ { 7 } ; ( - 0.96 ) ^ { 9 }$