MATH 110 Exam 2 Complete Review
(2026) | 100% Verified Responses | A+
• Problem Solving -✓✓Open ended stretegies
Non-routine Problems
• Reasoning and Proof -✓✓Discuss the WHY!!
Make theories and think about it!
• Communication -✓✓Student discussion
Think-pair-share
Math Journals
• Connections -✓✓Where does Math show up in the real world
• Representation -✓✓How you can show math in other ways
• Cardinality -✓✓the number of elements in a set
• Natural Numbers (N) -✓✓Counting Numbers {1,2,3,4,...}
• Whole Numbers (W) -✓✓{0,1,2,3,4,...}
INCLUDES ZERO
• Integers (J) -✓✓{-3,-2,-1,0,1,2,3}
no fractions
• Rationals (Q) -✓✓{x|x can be written (a/b) where a and b are both integers}
(integer/integer)
ex) 1/4
ex) 0.13 (13/100)
ex) 5 (5/1)
• Irrationals (I or R/Q) -✓✓Real Numbers that aren't rationals
ex) pi
ex) e
ex) sqrt3
ex) 0.262262226...
• Real Numbers (R) -✓✓The set of all rational and irrational numbers
, • Math 110 happens in all? -✓✓REAL NUMBERS (R)
• Complex Numbers (C) -✓✓All numbers, a combination of a real and an imaginary
numbers
• Subtraction Breaks out... -✓✓of the natural numbers, out of the whole numbers (e.g. 2
- 4)
• Division breaks out... -✓✓of the integers (e.g. 1÷4)
• Square root breaks out... -✓✓of the rational numbers (e.g sqrt 3)
• Square root (of negatives) breaks out... -✓✓of the real numbers (e.g. sqrt -4)
• Venn Diagram of N,W,Q,I,R -✓✓
• Does Q u I = R -✓✓Yes, this is a fact.
(look in notes for venn diagram)
• Terminating Decimals -✓✓Only 2's and/or 5's in the P.F. of the denominators
• 1/7 equals? -✓✓0.142857 rep.
• 2/7 equals? -✓✓0.285714 rep.
• 3/7 equals? -✓✓0.428571 rep.
• 4/7 equals? -✓✓0.571428 rep.
• 5/7 equals? -✓✓0.714285 rep.
• 6/7 equals? -✓✓0.857142 rep.
• 7/7 equals? -✓✓1
• Convert a fraction to a decimal -✓✓Divide numerator by denominator
• Converting a terminal decimal to a fraction -✓✓ex) 0.83 = 83/100
ex) 0.109 = 109/1000
• Convert a repeating decimal to a fraction -✓✓9's trick
(2026) | 100% Verified Responses | A+
• Problem Solving -✓✓Open ended stretegies
Non-routine Problems
• Reasoning and Proof -✓✓Discuss the WHY!!
Make theories and think about it!
• Communication -✓✓Student discussion
Think-pair-share
Math Journals
• Connections -✓✓Where does Math show up in the real world
• Representation -✓✓How you can show math in other ways
• Cardinality -✓✓the number of elements in a set
• Natural Numbers (N) -✓✓Counting Numbers {1,2,3,4,...}
• Whole Numbers (W) -✓✓{0,1,2,3,4,...}
INCLUDES ZERO
• Integers (J) -✓✓{-3,-2,-1,0,1,2,3}
no fractions
• Rationals (Q) -✓✓{x|x can be written (a/b) where a and b are both integers}
(integer/integer)
ex) 1/4
ex) 0.13 (13/100)
ex) 5 (5/1)
• Irrationals (I or R/Q) -✓✓Real Numbers that aren't rationals
ex) pi
ex) e
ex) sqrt3
ex) 0.262262226...
• Real Numbers (R) -✓✓The set of all rational and irrational numbers
, • Math 110 happens in all? -✓✓REAL NUMBERS (R)
• Complex Numbers (C) -✓✓All numbers, a combination of a real and an imaginary
numbers
• Subtraction Breaks out... -✓✓of the natural numbers, out of the whole numbers (e.g. 2
- 4)
• Division breaks out... -✓✓of the integers (e.g. 1÷4)
• Square root breaks out... -✓✓of the rational numbers (e.g sqrt 3)
• Square root (of negatives) breaks out... -✓✓of the real numbers (e.g. sqrt -4)
• Venn Diagram of N,W,Q,I,R -✓✓
• Does Q u I = R -✓✓Yes, this is a fact.
(look in notes for venn diagram)
• Terminating Decimals -✓✓Only 2's and/or 5's in the P.F. of the denominators
• 1/7 equals? -✓✓0.142857 rep.
• 2/7 equals? -✓✓0.285714 rep.
• 3/7 equals? -✓✓0.428571 rep.
• 4/7 equals? -✓✓0.571428 rep.
• 5/7 equals? -✓✓0.714285 rep.
• 6/7 equals? -✓✓0.857142 rep.
• 7/7 equals? -✓✓1
• Convert a fraction to a decimal -✓✓Divide numerator by denominator
• Converting a terminal decimal to a fraction -✓✓ex) 0.83 = 83/100
ex) 0.109 = 109/1000
• Convert a repeating decimal to a fraction -✓✓9's trick
