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Real Number System Worksheet

Real Number System Worksheet
  • Page 1
 1.  
Convert interval notation [- 2, 4) to inequality notation.
a.
2 ≤ x ≤ 4
b.
- 2 ≤ x < 4
c.
- 2 < x < 4
d.
- 2 ≤ x ≤ 4


Solution:

The interval [- 2, 4) corresponds to - 2 ≤ x < 4.


Correct answer : (2)
 2.  
Convert interval notation [- 2, 2] to inequality notation.
a.
- 2 ≤ x ≤ 2
b.
- 2 < x < 2
c.
- 2 > x > 2
d.
- 2 ≤ x < 2


Solution:

The interval [- 2, 2] corresponds to - 2 ≤ x ≤ 2.


Correct answer : (1)
 3.  
Find the end points of the interval [- 4, 3).
a.
- 4 & 3
b.
- 3 & ∞
c.
- ∞, ∞
d.
- ∞ & 4


Solution:

The end points of the interval [- 4, 3) are - 4 & 3.


Correct answer : (1)
 4.  
Convert the inequality - 3 ≤ x ≤ 3 to interval notation.
a.
[- 3, 3]
b.
(- 3, 3)
c.
[3, 3]
d.
[3, 3)


Solution:

The corresponding interval notation for the given inequality is [- 3, 3].


Correct answer : (1)
 5.  
Convert the inequality - 3 ≤ x < 6 to interval notation.
a.
[3, 6)
b.
(3, 6)
c.
(- 3, 6)
d.
[- 3, 6)


Solution:

The interval notation for the given inequality is [- 3, 6).


Correct answer : (4)
 6.  
Write the expanded form of (c + x)z.
a.
xzc
b.
cz + xz
c.
cx - xz
d.
cx + xz


Solution:

(c + x)z = cz + xz
[Use distributive property.]


Correct answer : (2)
 7.  
Write the expanded form of 3(x - 2).
a.
3x - 6
b.
3x + 6
c.
3x
d.
3x - 2


Solution:

3(x - 2) = 3x - 6
[Use distributive property.]


Correct answer : (1)
 8.  
The base of the exponential expression (8)45 is ____.
a.
53
b.
45
c.
8
d.
37


Solution:

The base of the exponential expression (8)45 is 8.


Correct answer : (3)
 9.  
The exponent of the exponential expression (3)-3 is
a.
3
b.
- 3
c.
10
d.
6


Solution:

The exponent of the exponential expression (3)-3 is - 3.


Correct answer : (2)
 10.  
Simplify: 5yz10y4z5
a.
5yz
b.
5 yz
c.
5 z5y3
d.
5 y5z3


Solution:

5yz10y4z5 = 5 (y1 - 4)(z10 - 5)
[Use aman=am-n.]

= 5 (y -3)(z 5)

= 5 z5y3


Correct answer : (3)

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