Download Gr 8 - Sets - Review - 12-13

HW#_______
Name: ____________________________
Mr. Art
Date: ______________
Section: ____________
Review #______
Real Numbers, Sets & Inequalities
Part I – Rational vs. Irrational - Date: ______________________
Real Number
1)
Rational or
Irrational?
Explanation
16
100
2) 12.77
3) – 123. 4
4)
81
5)
83
6) 0.121221222…
7)

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Part II – Converting Rational Decimals to Fractions - Date: ______________________
1) 0. 48
2) 9.3
1) 0. 48
2) 9. 3
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Part III – Set Vocabulary - Date: ______________________
o Define the following sets using your notes and examples.
o True of False. The words true and false must be written out.
1) ____________
4 is an element of {1, 2, 4, 7}.
2) ____________
{1, 4} is a subset of {1, 2, 4, 7}.
3) ____________
4 is an element of {a | a is a whole number}
4) ____________
{3, 4, 7} is equivalent to {3, 4, 6}
5) ____________
{3, 5, 7} is equal to {x | x is a natural number 3, 4, 6}
6) ____________
{consonants} is equivalent to {p, q, s, t, v}
7) ____________
{2, 4, 5, 6} is equal to {even numbers from 2 to 6, inclusive}
8) ____________
{counting numbers} is a finite set
9) ____________
{irrational numbers} is an infinite set
10) ____________
{real numbers} and {rational numbers} are disjoint sets
11) ____________
{seasons that begin with the letter p} is a null set
Part IV – Operations with Sets - Date: ______________________
Directions: Write an appropriate set for each of the following problems AND explain how you
determined which elements belong.
1) Given:
Q = {0, 2, 4, 6}
W = {0, 1, 2, 3, 5}
Z = {1, 2, 3, 4}
a) Universe =
b) Intersection of sets Q, W, and Z =
c) Union of sets Q and Z =
d) Complement of set W =
2
2) Maureen tracks the range of outdoor temperatures over three days. She records the following
information.
a) Express the intersection of the three sets as an inequality in terms of temperature, t.
b) Express the intersection of the three sets using interval notation.
Part V – Roster Form, Interval Notation, and Set-Builder Notation - Date: _____________________
1) _______ The set {11, 12} is equivalent to
(1) {x | 11 < x < 12, where x is an integer}
(2) {x | 11 < x  12, where x is an integer }
(3) {x | 10  x < 12, where x is an integer }
(4) {x | 10 < x  12, where x is an integer }
2) _______Which interval notation represents the set of all numbers from 2 through 7, inclusive?
(1) (2, 7]
(2) (2, 7)
(3) [2, 7)
(4) [2, 7]
Part VI – Closure Property - Date: ______________________
Directions: Determine if the following examples are closed or not closed. If you determine an example is
not closed, provide your counterexample as proof.
1) Counting Numbers are closed under Subtraction.
2) Integers Numbers are closed under Multiplication.
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Part VII – Solving Inequality Word Problems - Date: ____________________________
1) An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the
sale of each DVD player (d) and a $30 profit on the sale of each cordless telephone (c). The store
wants to make a profit of at least $255 from its sales of DVD players and cordless phones. Which
inequality describes this situation?
(1) 75d  30c  255
(2) 75d  30c  255
(3) 75d  30c  255
(4) 75d  30c  255
2) Which value of x is in the solution set of the inequality  2x  5  17 ?
(1)  2
(2)  6
(3)  4
(4)  8
Part VIII – Graphing Inequalities - Date: ______________________
Directions: Write the inequality that is shown in both set-builder & interval notation.
Set-Builder Notation
Interval Notation
1)
_______________________
______________________
2)
_______________________
______________________
3)
_______________________
______________________
4)
_______________________
______________________
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Part IX – Solving Compound Inequalities - Date: ______________________
Directions: For each inequality, solve if necessary, box the solution & finally graph the solution on a
number line.
1) b – 2 > 18 or 3b < 54
2) 1 < x < 10
3) 3f > 15 U 2f ≤ - 4
4) - 6 ≤ 9 + 3y < 6
5) t + 5 ≤ 2 U 3t + 1 ≤ 10
6) 9 ≤ - x + 2 ≤ 11
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