Name: ____________________________________
Date: __________
Algebra I Common Core
Real Number System – Modeling Data with appropriate set
1
2
3
4
5
6
Which of the following sets best represents a
person’s bowling scores?
Mixed Practice
7 The product of two rational numbers is:
(1)
Set of integers
(1)
non-zero
(2)
Set of positive real numbers
(2)
an irrational number
(3)
Set of non-negative integers
(3)
a rational number
(4)
Set of negative integers
(4)
a non-repeating decimal
Which of the following sets best represents
the daily news reported temperatures?
(1)
Set of integers
(2)
Set of positive real numbers
(3)
Set of non-negative integers
(4)
Set of negative integers
Which of the following sets best represents
the lengths the number of household onlinedevices in terms of the number of people in
the household?
(1)
integers
(2)
whole numbers
(3)
irrational numbers
(4)
rational numbers
Which of the following sets best represents a
student’s report card grades?
(1)
Set of integers
(2)
Set of positive real numbers
(3)
Set of non-negative integers
(4)
Set of negative integers
Which of the following sets best represents
all of the possible numbers of spectators at
Carey’s first football game?
(1)
the set of real numbers
(2)
the set of positive numbers
(3)
the set of integers
(4)
the set of non-negative integers
Which of the following situations would best
be modeled using the set of integers?
Sheet #01 -03
8
9
Which of the following sets of numbers could
be used to model students in a math class?
(1)
imaginary numbers
(2)
irrational numbers
(3)
integers
(4)
counting/natural numbers
The set {1, 2, 3, 4} is equivalent to
(1)
{𝑥|1 < 𝑥 < 4, where 𝑥 is a whole #}
(2)
{𝑥|0 < 𝑥 < 4, where 𝑥 is a whole #}
(3)
{𝑥|0 < 𝑥 ≤ 4, where 𝑥 is a whole #}
(4)
{𝑥|1 < 𝑥 ≤ 4, where 𝑥 is a whole #}
10 Which interval notation represents the set of
all numbers greater than or equal to 5 and less
than 12?
(1)
[5, 12)
(3)
(5, 12)
(2)
[5, 12]
(4)
(5, 12]
11 Which statement is not always true?
(1)
The sum of two rational numbers is
rational.
(2)
The product of two irrational numbers is
rational.
(3)
The sum of a rational number and an
irrational number is irrational.
(4)
The product of a nonzero rational
number and an irrational number is
irrational.
12 For which value of P and W is P + W a
rational number?
(1)
(1)
county populations
(2)
number of homes
(3)
city temperatures
(3)
(4)
areas of towns in square miles
(4)
(2)
𝑃=
𝑃=
𝑃=
𝑃=
1
√3
1
√4
1
√6
1
and 𝑊 =
and 𝑊 =
and 𝑊 =
√25
1
√6
1
√9
1
√10
1
and 𝑊 =
√2
13 Given the inequality below, express the set of
numbers in both set-builder notation and
interval notation.
Set-builder notation ___________________________
16 Given:
Y = 4√3
W = √5
Z = √1
X= √36
Determine whether the following expressions result
in a rational or irrational number.
(A)
W+X
(B)
Y+W
(C)
X+Z
Interval Notation __________
14 Given the inequality below, express the set of
numbers in both set-builder notation and
interval notation.
17 Give a counterexample to the statement
below:
The product of a rational number and an
irrational number is always irrational.
Set-builder notation ___________________________
Interval Notation __________
15 Ms. Scarpati asked her class “Is the sum of
18 Give a counterexample to the statement
below:
The product of two irrational numbers is
always irrational.
4.2 and √2 rational or irrational?”
Patrick answered that the sum would be
irrational. State whether Patrick is correct or
incorrect. Justify your reasoning.
19 Given the equation 𝑦 = √16𝑏, state all
whole numbers from the interval 0 < 𝑏 < 10
that make y rational.
20 Check all the number sets that the number belongs to.
Number
A. .67
B. .12345…
C. 8.1414…
D. 0
3
E. − 4
F. 4𝜋
G. √35
Real #
Irrational #
Rational #
Integer
Whole #
Counting/Natural
#