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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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 multiplication means _______________: a
commutative law of Addition
transitive
Repeated addition
k-ary operation
2. 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
operation
Real number
Solution to the system
3. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
The logical values true and false
Rotations
Difference of two squares - or the difference of perfect squares
then ac < bc
4. Can be added and subtracted.
Vectors
Algebraic equation
All quadratic equations
Solving the Equation
5. May not be defined for every possible value.
Properties of equality
Universal algebra
Equations
Operations
6. The values for which an operation is defined form a set called its
Solution to the system
associative law of addition
domain
A integral equation
7. Is called the codomain of the operation
the set Y
Identity element of Multiplication
then a < c
Expressions
8. That if a = b and c = d then a + c = b + d and ac = bd;that if a = b then a + c = b + c; that if two symbols are equal - then one can be substituted for the other.
commutative law of Addition
Addition
associative law of addition
The relation of equality (=) has the property
9. Is a function of the form ? : V ? Y - where V ? X1
A binary relation R over a set X is symmetric
operation
An operation ?
commutative law of Addition
10. Are denoted by letters at the beginning - a - b - c - d - ...
scalar
The real number system
Knowns
Elementary algebra
11. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
The central technique to linear equations
Identity element of Multiplication
range
The relation of inequality (<) has this property
12. (a
The relation of equality (=)'s property
Rotations
Quadratic equations can also be solved
Associative law of Multiplication
13. 0 - which preserves numbers: a + 0 = a
Number line or real line
the set Y
identity element of addition
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.
14. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).
Conditional equations
Elimination method
operation
Pure mathematics
15. Is an equation involving a transcendental function of one of its variables.
value - result - or output
then a < c
Associative law of Exponentiation
A transcendental equation
16. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
commutative law of Multiplication
Universal algebra
Categories of Algebra
Change of variables
17. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Equation Solving
symmetric
Conditional equations
Algebraic equation
18. Can be combined using the function composition operation - performing the first rotation and then the second.
An operation ?
Rotations
Reflexive relation
Polynomials
19. 1 - which preserves numbers: a
Repeated multiplication
The relation of inequality (<) has this property
operation
Identity element of Multiplication
20. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Rotations
Binary operations
The relation of inequality (<) has this property
Universal algebra
21. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
has arity one
when b > 0
then a + c < b + d
22. Is an equation of the form X^m/n = a - for m - n integers - which has solution
commutative law of Addition
Solution to the system
an operation
radical equation
23. Letters from the beginning of the alphabet like a - b - c... often denote
domain
A binary relation R over a set X is symmetric
Algebraic geometry
Constants
24. If an equation in algebra is known to be true - the following operations may be used to produce another true 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.
A polynomial equation
the fixed non-negative integer k (the number of arguments)
Identities
25. If a < b and c < 0
then bc < ac
Algebra
All quadratic equations
Real number
26. The value produced is called
value - result - or output
identity element of Exponentiation
Multiplication
Constants
27. 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.
has arity two
unary and binary
The relation of inequality (<) has this property
Pure mathematics
28. Is the claim that two expressions have the same value and are equal.
Vectors
Equations
Identities
then bc < ac
29. A unary operation
has arity one
(k+1)-ary relation that is functional on its first k domains
Number line or real line
Vectors
30. Can be defined axiomatically up to an isomorphism
The relation of inequality (<) has this property
The real number system
Change of variables
has arity two
31. If a < b and b < c
Identities
commutative law of Exponentiation
range
then a < c
32. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
The relation of equality (=)'s property
inverse operation of Multiplication
The simplest equations to solve
33. Is an equation involving derivatives.
Universal algebra
A differential equation
The logical values true and false
value - result - or output
34. Is an algebraic 'sentence' containing an unknown quantity.
Polynomials
two inputs
A solution or root of the 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.
35. If a = b and b = c then a = c
transitive
finitary operation
The logical values true and false
A differential equation
36. Can be combined using logic operations - such as and - or - and not.
Variables
The logical values true and false
All quadratic equations
inverse operation of Exponentiation
37. The operation of exponentiation means ________________: a^n = a
A binary relation R over a set X is symmetric
equation
Repeated multiplication
The operation of exponentiation
38. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)
Operations
(k+1)-ary relation that is functional on its first k domains
operation
Identity
39. A vector can be multiplied by a scalar to form another vector
Algebraic combinatorics
Number line or real line
Operations can involve dissimilar objects
The real number system
40. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
finitary operation
system of linear equations
Elementary algebra
Identities
41. 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
Equations
identity element of addition
The purpose of using variables
The method of equating the coefficients
42. The squaring operation only produces
Unary operations
nonnegative numbers
Categories of Algebra
The relation of inequality (<) has this property
43. Is Written as a
Multiplication
operation
Unary operations
Vectors
44. Is Written as a + b
radical equation
The real number system
Addition
commutative law of Addition
45. If a < b and c > 0
then ac < bc
Change of variables
The central technique to linear equations
nullary operation
46. b = b
when b > 0
reflexive
A solution or root of the equation
then a < c
47. Are called the domains of the operation
operands - arguments - or inputs
The sets Xk
Identity
Associative law of Multiplication
48. 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
Reunion of broken parts
A functional equation
Exponentiation
operation
49. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.
two inputs
Reflexive relation
domain
identity element of Exponentiation
50. A
Identity element of Multiplication
A solution or root of the equation
Constants
commutative law of Multiplication