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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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
Identities
Repeated addition
Expressions
Elementary algebra
2. Are called the domains of the operation
The sets Xk
Universal algebra
Associative law of Exponentiation
The relation of equality (=) has the property
3. 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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4. Not commutative a^b?b^a
The logical values true and false
Reflexive relation
Operations on functions
commutative law of Exponentiation
5. Is Written as a
Multiplication
Constants
finitary operation
Solving the Equation
6. k-ary operation is a
radical equation
logarithmic equation
(k+1)-ary relation that is functional on its first k domains
domain
7. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
The real number system
range
A integral equation
8. 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.
Properties of equality
Universal algebra
A solution or root of the equation
Operations on sets
9. 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.
The logical values true and false
Number line or real line
The relation of equality (=)'s property
The relation of inequality (<) has this property
10. Can be combined using the function composition operation - performing the first rotation and then the second.
Algebraic combinatorics
Rotations
The operation of addition
reflexive
11. If a = b then b = a
symmetric
Operations on functions
A differential equation
A solution or root of the equation
12. 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)
The sets Xk
nonnegative numbers
operation
has arity two
13. b = b
The operation of addition
reflexive
commutative law of Multiplication
A linear equation
14. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Addition
associative law of addition
Algebraic number theory
Solution to the system
15. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
A transcendental equation
The real number system
Binary operations
two inputs
16. Is an action or procedure which produces a new value from one or more input values.
an operation
Vectors
Polynomials
finitary operation
17. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
unary and binary
k-ary operation
identity element of Exponentiation
18. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.
Algebra
associative law of addition
Elementary algebra
two inputs
19. Is an equation in which a polynomial is set equal to another polynomial.
transitive
finitary operation
nullary operation
A polynomial equation
20. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
A integral equation
has arity one
has arity two
21. If a = b and b = c then a = c
transitive
Vectors
Order of Operations
Unknowns
22. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.
then a < c
commutative law of Addition
nonnegative numbers
Change of variables
23. A
exponential 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.
commutative law of Multiplication
Difference of two squares - or the difference of perfect squares
24. 1 - which preserves numbers: a
Solving the Equation
Identity element of Multiplication
Categories of Algebra
All quadratic equations
25. Can be combined using logic operations - such as and - or - and not.
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.
the set Y
Equations
26. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Constants
Difference of two squares - or the difference of perfect squares
Variables
Algebra
27. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Associative law of Multiplication
Pure mathematics
the fixed non-negative integer k (the number of arguments)
Multiplication
28. Is algebraic equation of degree one
an operation
A linear equation
The operation of addition
reflexive
29. The values for which an operation is defined form a set called its
scalar
Expressions
domain
reflexive
30. Can be defined axiomatically up to an isomorphism
operands - arguments - or inputs
Variables
The real number system
Algebraic combinatorics
31. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Difference of two squares - or the difference of perfect squares
Constants
unary and binary
Solving the Equation
32. 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).
Operations can involve dissimilar objects
Algebraic number theory
operation
then a + c < b + d
33. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
Rotations
Real number
All quadratic equations
34. The inner product operation on two vectors produces a
then bc < ac
Rotations
The relation of equality (=)'s property
scalar
35. 0 - which preserves numbers: a + 0 = a
Order of Operations
Algebraic geometry
operation
identity element of addition
36. Is a function of the form ? : V ? Y - where V ? X1
Algebraic geometry
The logical values true and false
Repeated multiplication
An operation ?
37. Is Written as a + b
Addition
The sets Xk
range
Identity element of Multiplication
38. In which properties common to all algebraic structures are studied
value - result - or output
Associative law of Multiplication
The relation of equality (=) has the property
Universal algebra
39. A + b = b + a
Categories of Algebra
Multiplication
commutative law of Addition
Elementary algebra
40. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s
substitution
The relation of equality (=)
inverse operation of addition
identity element of addition
41. 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)
Real number
The operation of exponentiation
Categories of Algebra
Change of variables
42. 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'.
The operation of addition
Identities
Solution to the system
Reflexive relation
43. 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
Real number
A Diophantine equation
Vectors
k-ary operation
44. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Number line or real line
nullary operation
Expressions
Reflexive relation
45. An operation of arity zero is simply an element of the codomain Y - called a
Properties of equality
Unknowns
nullary operation
Operations on sets
46. If a < b and c > 0
then a < c
Algebraic combinatorics
then ac < bc
The operation of exponentiation
47. A unary operation
k-ary operation
has arity one
then a < c
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.
48. Is called the codomain of the operation
the set Y
two inputs
A polynomial equation
Operations on sets
49. Subtraction ( - )
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.
Knowns
The relation of equality (=)'s property
inverse operation of addition
50. Operations can have fewer or more than
Identity
identity element of Exponentiation
Linear algebra
two inputs