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.
Reuse / Edit
x

Collection:

Module:

Add to a lens
x

Add collection to:

Add module to:

Add to Favorites
x

Add collection to:

Add module to:

 

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 symbols, notations, and properties of numbers that form the basis of algebra, as well as exponents and the rules of exponents, are introduced in this chapter. Each property of real numbers and the rules of exponents are expressed both symbolically and literally. Literal explanations are included because symbolic explanations alone may be difficult for a student to interpret. This module contains the proficiency for the chapter "Basic Properties of Real Numbers".

Proficiency Exam

For the following problems, simplify each of the expressions.

Exercise 1

((Reference)) 8(6−3)−5⋅4+3(8)(2)÷4⋅3 8(6−3)−5⋅4+3(8)(2)÷4⋅3

[ Show Solution ]

Exercise 2

((Reference)) { 2 (1+7) 2 } 0 { 2 (1+7) 2 } 0

[ Show Solution ]

Exercise 3

((Reference)) 1 8 + 4 0 + 3 3 (1+4) 2 2 (2+15) 1 8 + 4 0 + 3 3 (1+4) 2 2 (2+15)

[ Show Solution ]

Exercise 4

((Reference)) 2⋅ 3 4 − 10 2 4−3 + 5( 2 2 + 3 2 ) 11−6 2⋅ 3 4 − 10 2 4−3 + 5( 2 2 + 3 2 ) 11−6

[ Show Solution ]

Exercise 5

((Reference)) Write the appropriate relation symbol (>,<) (>,<) in place of the * * .
 5(2+11)∗2(8−3)−2 5(2+11)∗2(8−3)−2

[ Show Solution ]

For the following problems, use algebraic notation.

Exercise 6

((Reference)) (x−1) (x−1) times (3x plus 2) (3x plus 2) .

[ Show Solution ]

Exercise 7

((Reference)) A number divided by twelve is less than or equal to the same number plus four.

[ Show Solution ]

Exercise 8

((Reference)) Locate the approximate position of −1.6 −1.6 on the number line.

A real number line with arrow on each end, labeled from negative three to three in increments of one.

[ Show Solution ]

Exercise 9

((Reference)) Is 0 a positive number, a negative number, neither, or both?

[ Show Solution ]

Exercise 10

((Reference)) Draw a portion of the number line and place points at all even integers strictly between 14 and 20.

[ Show Solution ]

Exercise 11

((Reference)) Draw a portion of the number line and place points at all real numbers strictly greater than −1 −1 but less than or equal to 4.

[ Show Solution ]

Exercise 12

((Reference)) What whole numbers can replace x x so that the following statement is true? −4≤x≤5 −4≤x≤5 .

[ Show Solution ]

Exercise 13

((Reference)) Is there a largest real number between and including 6 and 10? If so, what is it?

[ Show Solution ]

Exercise 14

((Reference)) Use the commutative property of multiplication to write m(a+3) m(a+3) in an equivalent form.

[ Show Solution ]

Exercise 15

((Reference)) Use the commutative properties to simplify 3a4b8cd 3a4b8cd .

[ Show Solution ]

Exercise 16

((Reference)) Use the commutative properties to simplify 4(x−9)2y(x−9)3y 4(x−9)2y(x−9)3y .

[ Show Solution ]

Exercise 17

((Reference)) Simplify 4 squared times x x cubed times y y to the fifth.

[ Show Solution ]

Exercise 18

((Reference)) Simplify (3)(3)(3)aabbbbabba(3)a (3)(3)(3)aabbbbabba(3)a .

[ Show Solution ]

For the following problems, use the rules of exponents to simplify each of the expressions.

Exercise 19

((Reference), (Reference)) (3a b 2 ) 2 (2 a 3 b) 3 (3a b 2 ) 2 (2 a 3 b) 3

[ Show Solution ]

Exercise 20

((Reference), (Reference)) x 10 y 12 x 2 y 5 x 10 y 12 x 2 y 5

[ Show Solution ]

Exercise 21

((Reference), (Reference)) 52 x 7 y 10 (y− x 4 ) 12 (y+x) 5 4 y 6 (y− x 4 ) 10 (y+x) 52 x 7 y 10 (y− x 4 ) 12 (y+x) 5 4 y 6 (y− x 4 ) 10 (y+x)

[ Show Solution ]

Exercise 22

((Reference), (Reference)) ( x n y 3m z 2p ) 4 ( x n y 3m z 2p ) 4

[ Show Solution ]

Exercise 23

(5x+4) 0 (3 x 2 −1) 0 (5x+4) 0 (3 x 2 −1) 0

[ Show Solution ]

Exercise 24

x ∇ x □ y Δ x Δ y ∇ x ∇ x □ y Δ x Δ y ∇

[ Show Solution ]

Exercise 25

((Reference), (Reference)) What word is used to describe the letter or symbol that represents an unspecified member of a particular collection of two or more numbers that are clearly defined?

[ Show Solution ]

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

Reuse / Edit:

Reuse or edit collection (?)

Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.

| Reuse or edit module (?)

Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.