Name: ______Date______
Mr. Art Period______
Review Packet #______- Number Sense
Real Number System, Sets & Inequalities
Part I – Subsets of the Real Number System - Date: ______
Directions: Define the following sets using your notes and examples.
1) Counting/Natural Numbers:
2) Whole Numbers:
3) Integers:
4) Rational Numbers:
5) Irrational Numbers:
Part II – Rational vs. Irrational - Date: ______
Real Number / Rational or Irrational? / Explanation1)
2)
3) –
4)
5)
6) 0.121221222…
7)
Part III – Perfect Squares & Square Roots - Date: ______
* You should have the entire "cheat sheet" memorized*
Square RootPerfect Square
Practice Examples:
1) = / 2) 72 = / 3) 122 =4) = / 5) = / 6) =
Part IV – Estimating Radicals - Date: ______
Directions: Between which two consecutive integers does each lie?
1) is between ______and ______.
2) is between ______and ______.
Part V - Placing Real Numbers on a Number Line - Date: ______
Directions: Use your estimation skills to place each of the following real numbers on the number line below.
1) – 5
2)
3)
4) – 2.75
5)
6)
7)
Part VI – Set Vocabulary - Date: ______
o Define the following sets using your notes and examples.
1) Finite Set vs. Infinite Set:
2) Universal Set:
3) Equal Sets vs. Equivalent Sets:
4) Subset:
5) Disjoint Sets:
6) Empty/Null Set:
7) Counterexample:
------
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 VII – Operations with Sets - Date: ______
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) 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 VIII – 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] (3) [2, 7)
(2) (2, 7) (4) [2, 7]
Part IX – Solving Inequality Word Problems - Date: ______
Help with word problems:
At Least / At MostMinimum / Maximum
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) (3)
(2) (4)
2) ______Which value of x is in the solution set of the inequality ?
(1) (3)
(2) (4)
Part X – Graphing Inequalities - Date: ______
Directions: Write the inequality that is shown on the line to the right of each graph.
1)
2)
3)
4)
Part XI – Solving Compound Inequalities - Date: ______
Directions: For each inequality, solve if necessary, box the solution & finally graph the solution on a number line.
Union (OR) "" / Intersection (AND) " "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
6