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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. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
Operations can involve dissimilar objects
Reunion of broken parts
Properties of equality
2. A unary operation
Universal algebra
Multiplication
has arity one
Rotations
3. k-ary operation is a
The operation of exponentiation
Vectors
The logical values true and false
(k+1)-ary relation that is functional on its first k domains
4. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
equation
an operation
Elimination method
inverse operation of addition
5. The inner product operation on two vectors produces a
Linear algebra
scalar
inverse operation of addition
exponential equation
6. Is called the codomain of the operation
an operation
the set Y
Identities
inverse operation of addition
7. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebraic equation
Equations
identity element of Exponentiation
Solution to the system
8. 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'.
commutative law of Addition
reflexive
The relation of inequality (<) has this property
Reflexive relation
9. Include composition and convolution
Number line or real line
Operations on functions
The relation of equality (=) has the property
The relation of equality (=)'s property
10. A + b = b + a
reflexive
then ac < bc
k-ary operation
commutative law of Addition
11. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The method of equating the coefficients
Equations
The relation of equality (=)
operation
12. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
finitary operation
Algebraic number theory
has arity one
Constants
13. 0 - which preserves numbers: a + 0 = a
an operation
The relation of inequality (<) has this property
identity element of addition
the fixed non-negative integer k (the number of arguments)
14. The process of expressing the unknowns in terms of the knowns is called
commutative law of Addition
Algebraic geometry
Solving the Equation
Real number
15. Will have two solutions in the complex number system - but need not have any in the real number system.
inverse operation of Exponentiation
scalar
All quadratic equations
Addition
16. If a < b and c < d
then a + c < b + d
A polynomial equation
The operation of exponentiation
operands - arguments - or inputs
17. Are denoted by letters at the beginning - a - b - c - d - ...
A polynomial equation
Knowns
substitution
logarithmic equation
18. If a < b and c > 0
logarithmic equation
then ac < bc
Operations on sets
The operation of exponentiation
19. Division ( / )
radical equation
finitary operation
inverse operation of Multiplication
The relation of equality (=)'s property
20. 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
Elementary algebra
The simplest equations to solve
unary and binary
Reunion of broken parts
21. Include the binary operations union and intersection and the unary operation of complementation.
A functional equation
Operations on sets
finitary operation
commutative law of Addition
22. The operation of exponentiation means ________________: a^n = a
(k+1)-ary relation that is functional on its first k domains
Number line or real line
Repeated multiplication
operands - arguments - or inputs
23. (a
Associative law of Multiplication
A differential equation
The operation of addition
Polynomials
24. If a < b and b < c
then a < c
Elementary algebra
operation
Real number
25. In an equation with a single unknown - a value of that unknown for which the equation is true is called
system of linear equations
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.
substitution
26. 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.
Variables
Equations
The relation of equality (=) has the property
substitution
27. If it holds for all a and b in X that if a is related to b then b is related to a.
A binary relation R over a set X is symmetric
Vectors
inverse operation of Multiplication
Algebra
28. There are two common types of operations:
A functional equation
Exponentiation
The simplest equations to solve
unary and binary
29. Operations can have fewer or more than
then a + c < b + d
transitive
Associative law of Multiplication
two inputs
30. Is an equation of the form aX = b for a > 0 - which has solution
Variables
Operations
exponential equation
identity element of Exponentiation
31. The codomain is the set of real numbers but the range is the
Reunion of broken parts
Associative law of Exponentiation
The relation of equality (=)'s property
nonnegative numbers
32. Is an algebraic 'sentence' containing an unknown quantity.
transitive
Addition
Polynomials
A solution or root of the equation
33. Is an equation involving a transcendental function of one of its variables.
The logical values true and false
A functional equation
The relation of inequality (<) has this property
A transcendental equation
34. Is Written as a + b
Operations
(k+1)-ary relation that is functional on its first k domains
Addition
Associative law of Exponentiation
35. 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.
Expressions
Properties of equality
nullary operation
Real number
36. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Vectors
nullary operation
The simplest equations to solve
Polynomials
37. 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
range
value - result - or output
Elementary algebra
All quadratic equations
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)
Number line or real line
logarithmic equation
Reflexive relation
operation
39. If a < b and c < 0
logarithmic equation
then bc < ac
A functional equation
then a < c
40. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
The logical values true and false
Algebraic combinatorics
then bc < ac
41. Is an equation in which the unknowns are functions rather than simple quantities.
nonnegative numbers
Order of Operations
k-ary operation
A functional equation
42. The values combined are called
then bc < ac
The relation of equality (=)'s property
operands - arguments - or inputs
Repeated addition
43. The operation of multiplication means _______________: a
system of linear equations
Repeated addition
Solution to the system
Constants
44. Not associative
nonnegative numbers
Real number
Associative law of Exponentiation
The real number system
45. 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.
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46. Logarithm (Log)
nonnegative numbers
inverse operation of Exponentiation
Unary operations
Pure mathematics
47. 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).
Reflexive relation
system of linear equations
Knowns
operation
48. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Number line or real line
radical equation
The relation of inequality (<) has this property
Exponentiation
49. Not commutative a^b?b^a
commutative law of Exponentiation
Operations on sets
The operation of exponentiation
then ac < bc
50. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
when b > 0
has arity two
Pure mathematics