Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Basic Mathematics Review » Proficiency Exam

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • College Open Textbooks display tagshide tags

    This module is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook CollaborativeAs a part of collection: "Elementary Algebra"

    Comments:

    "Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • OrangeGrove display tagshide tags

    This module is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange GroveAs a part of collection: "Elementary Algebra"

    Click the "OrangeGrove" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Elementary Algebra"

    Comments:

    "Elementary Algebra covers traditional topics studied in a modern elementary algebra course. Written by Denny Burzynski and Wade Ellis, it is intended for both first-time students and those […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Proficiency Exam

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples. This module provides a proficiency exam for the chapter "Basic Operations with Real Numbers".

Proficiency Exam

Simplify the expressions for the following problems.

Exercise 1

((Reference)) −{−[(−6)]} −{−[(−6)]}

Solution

−6 −6

Exercise 2

((Reference)) −|−15|−|−15|

Solution

−15 −15

Exercise 3

((Reference)) − [ | −12 |−10 ] 2 − [ | −12 |−10 ] 2

Solution

−4 −4

Exercise 4

((Reference)) −5(−6)+4(−8)−| −5 | −5(−6)+4(−8)−| −5 |

Solution

−7 −7

Exercise 5

((Reference)) 3(−8)−(−2)(−4−5) (−2)(−3) 3(−8)−(−2)(−4−5) (−2)(−3)

Solution

−7 −7

Exercise 6

((Reference)) −| 7 |− (2) 2 + (−2) 2 −| 7 |− (2) 2 + (−2) 2

Solution

−7 −7

Exercise 7

((Reference)) −6(2)(−2) −(−5−3) −6(2)(−2) −(−5−3)

Solution

3

Exercise 8

((Reference)) −3{ [ ( −2−3 ) ][ −2 ] } −3( 4−2 ) −3{ [ ( −2−3 ) ][ −2 ] } −3( 4−2 )

Solution

5

Exercise 9

((Reference)) Ifz=x−usz=x−us, find zz if x=14x=14, u=20u=20, and s=2s=2.

Solution

−3 −3

When simplifying the terms for the following problems, write each so that only positive exponents appear.

Exercise 10

((Reference)) 1 − ( −5 ) −3 1 − ( −5 ) −3

Solution

125

Exercise 11

((Reference)) 5 x 3 y −2 z −4 5 x 3 y −2 z −4

Solution

5 x 3 z 4 y 2 5 x 3 z 4 y 2

Exercise 12

((Reference)) 2 −2 m 6 (n−4) −3 2 −2 m 6 (n−4) −3

Solution

m 6 4 ( n−4 ) 3 m 6 4 ( n−4 ) 3

Exercise 13

((Reference)) 4 a −6 (2 a −5 ) 4 a −6 (2 a −5 )

Solution

8 a 11 8 a 11

Exercise 14

((Reference)) 6 −1 x 3 y −5 x −3 y −5 6 −1 x 3 y −5 x −3 y −5

Solution

1 6 1 6

Exercise 15

((Reference)) (k−6) 2 (k−6) −4 (k−6) 3 (k−6) 2 (k−6) −4 (k−6) 3

Solution

1 ( k−6 ) 5 1 ( k−6 ) 5

Exercise 16

((Reference))(y+1)3(y−3)4(y+1)5(y−3)−8(y+1)3(y−3)4(y+1)5(y−3)−8

Solution

( y−3 ) 12 ( y+1 ) 2 ( y−3 ) 12 ( y+1 ) 2

Exercise 17

((Reference)) ( 3 −6 )( 3 2 )( 3 −10 ) ( 3 −5 )( 3 −9 ) ( 3 −6 )( 3 2 )( 3 −10 ) ( 3 −5 )( 3 −9 )

Solution

1

Exercise 18

((Reference)) (a4)−3(a4)−3

Solution

1 a 12 1 a 12

Exercise 19

((Reference)) [ r 6 s −2 m −5 n 4 ] −4 [ r 6 s −2 m −5 n 4 ] −4

Solution

n 16 s 8 m 20 r 24 n 16 s 8 m 20 r 24

Exercise 20

((Reference)) ( c 0 ) −2 , c≠0 ( c 0 ) −2 , c≠0

Solution

1

Exercise 21

((Reference)) Write 0.000271 0.000271 using scientific notation.

Solution

2.71× 10 −4 2.71× 10 −4

Exercise 22

((Reference)) Write 8.90× 10 5 8.90× 10 5 in standard form.

Solution

890,000 890,000

Exercise 23

((Reference)) Find the value of (3× 10 5 )(2× 10 −2 ) (3× 10 5 )(2× 10 −2 ) .

Solution

6000 6000

Exercise 24

((Reference)) Find the value of (4× 10 −16 ) 2 (4× 10 −16 ) 2 .

Solution

1.6× 10 −31 1.6× 10 −31

Exercise 25

((Reference)) If k k is a negative integer, is −k −k a positive or negative integer?

Solution

a positive integer

Collection Navigation

Content actions

Download module as:

PDF | More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks