SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
Search
Test your basic knowledge |
CLEP College Algebra: Algebra Principles
Start Test
Study First
Subjects
:
clep
,
math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The operation of exponentiation means ________________: a^n = a
operation
Repeated multiplication
Expressions
Quadratic equations
2. k-ary operation is a
(k+1)-ary relation that is functional on its first k domains
transitive
associative law of addition
Elimination method
3. 1 - which preserves numbers: a
Identity element of Multiplication
Vectors
Algebraic combinatorics
Conditional equations
4. Is called the type or arity of the operation
Rotations
Knowns
Real number
the fixed non-negative integer k (the number of arguments)
5. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
Categories of Algebra
equation
Constants
6. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
then bc < ac
A binary relation R over a set X is symmetric
An operation ?
Categories of Algebra
7. Will have two solutions in the complex number system - but need not have any in the real number system.
exponential equation
All quadratic equations
Linear algebra
Elementary algebra
8. In which the specific properties of vector spaces are studied (including matrices)
reflexive
Linear algebra
A linear equation
Any real number can be added to both sides. Any real number can be subtracted from both sides. Any real number can be multiplied to both sides. Any non-zero real number can divide both sides. Some functions can be applied to both sides.
9. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
The logical values true and false
Any real number can be added to both sides. Any real number can be subtracted from both sides. Any real number can be multiplied to both sides. Any non-zero real number can divide both sides. Some functions can be applied to both sides.
Variables
Categories of Algebra
10. 0 - which preserves numbers: a + 0 = a
nonnegative numbers
Equations
identity element of addition
the fixed non-negative integer k (the number of arguments)
11. Not commutative a^b?b^a
Repeated multiplication
commutative law of Exponentiation
(k+1)-ary relation that is functional on its first k domains
Elimination method
12. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in
Operations on sets
Repeated addition
The method of equating the coefficients
Variables
13. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Solution to the system
Properties of equality
Expressions
The operation of exponentiation
14. The codomain is the set of real numbers but the range is the
The relation of inequality (<) has this property
nonnegative numbers
Order of Operations
A integral equation
15. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym
then a < c
inverse operation of addition
Reunion of broken parts
A integral equation
16. Is an algebraic 'sentence' containing an unknown quantity.
Operations on functions
operation
Polynomials
Identity
17. In an equation with a single unknown - a value of that unknown for which the equation is true is called
the fixed non-negative integer k (the number of arguments)
domain
A solution or root of the equation
operation
18. A + b = b + a
A binary relation R over a set X is symmetric
operands - arguments - or inputs
commutative law of Addition
A integral equation
19. Is an equation involving derivatives.
A integral equation
A differential equation
Real number
Abstract algebra
20. Involve only one value - such as negation and trigonometric functions.
inverse operation of Exponentiation
Expressions
Rotations
Unary operations
21. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Properties of equality
Operations on functions
nonnegative numbers
Equations
22. A vector can be multiplied by a scalar to form another vector
Number line or real line
Properties of equality
Operations can involve dissimilar objects
Variables
23. 1 - which preserves numbers: a^1 = a
Associative law of Exponentiation
domain
Reflexive relation
identity element of Exponentiation
24. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
inverse operation of Exponentiation
radical equation
Variables
then a + c < b + d
25. If a = b then b = a
symmetric
Repeated addition
Categories of Algebra
The relation of equality (=)'s property
26. Include composition and convolution
Operations on functions
reflexive
radical equation
Difference of two squares - or the difference of perfect squares
27. The values for which an operation is defined form a set called its
domain
nonnegative numbers
an operation
Knowns
28. The relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Operations can involve dissimilar objects
Elimination method
has arity one
Properties of equality
29. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.
k-ary operation
the set Y
Operations
The relation of inequality (<) has this property
30. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po
inverse operation of Exponentiation
The central technique to linear equations
Elimination method
A functional equation
31. If a < b and c < d
The sets Xk
then a + c < b + d
The real number system
The relation of equality (=) has the property
32. Is Written as a + b
Associative law of Multiplication
Operations on sets
The logical values true and false
Addition
33. An operation of arity zero is simply an element of the codomain Y - called a
The sets Xk
an operation
Operations on sets
nullary operation
34. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that
Knowns
Real number
Exponentiation
Operations
35. b = b
reflexive
Operations
The operation of exponentiation
Polynomials
36. If a = b and b = c then a = c
nonnegative numbers
Variables
Reunion of broken parts
transitive
37. Can be combined using logic operations - such as and - or - and not.
An operation ?
The logical values true and false
The purpose of using variables
finitary operation
38. Is a function of the form ? : V ? Y - where V ? X1
then bc < ac
The central technique to linear equations
The relation of equality (=)
An operation ?
39. Is an equation where the unknowns are required to be integers.
A Diophantine equation
The relation of equality (=)'s property
Unary operations
Linear algebra
40. An operation of arity k is called a
k-ary operation
Repeated addition
The logical values true and false
Quadratic equations can also be solved
41. The values combined are called
Rotations
Reunion of broken parts
domain
operands - arguments - or inputs
42. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
nonnegative numbers
Operations can involve dissimilar objects
Algebraic combinatorics
43. Is an equation in which the unknowns are functions rather than simple quantities.
transitive
A functional equation
A transcendental equation
Change of variables
44. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)
A integral equation
has arity one
then bc < ac
The operation of exponentiation
45. The process of expressing the unknowns in terms of the knowns is called
Universal algebra
The method of equating the coefficients
The logical values true and false
Solving the Equation
46. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
substitution
Pure mathematics
system of linear equations
Any real number can be added to both sides. Any real number can be subtracted from both sides. Any real number can be multiplied to both sides. Any non-zero real number can divide both sides. Some functions can be applied to both sides.
47. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Properties of equality
Any real number can be added to both sides. Any real number can be subtracted from both sides. Any real number can be multiplied to both sides. Any non-zero real number can divide both sides. Some functions can be applied to both sides.
Solution to the system
An operation ?
48. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Difference of two squares - or the difference of perfect squares
Algebraic equation
Real number
The relation of equality (=)
49. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi
Elementary algebra
The operation of exponentiation
Algebra
A solution or root of the equation
50. Include the binary operations union and intersection and the unary operation of complementation.
Quadratic equations can also be solved
the fixed non-negative integer k (the number of arguments)
Operations on sets
identity element of addition