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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.
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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. 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).
operation
commutative law of Addition
The real number system
nonnegative numbers
2. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Order of Operations
Algebraic equation
has arity one
Equation Solving
3. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
The purpose of using variables
Real number
Repeated addition
4. 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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5. Can be combined using logic operations - such as and - or - and not.
transitive
Properties of equality
Algebraic number theory
The logical values true and false
6. (a
scalar
commutative law of Addition
Conditional equations
Associative law of Multiplication
7. Can be defined axiomatically up to an isomorphism
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.
Rotations
The real number system
8. 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
A differential equation
Real number
Algebra
9. Subtraction ( - )
(k+1)-ary relation that is functional on its first k domains
The method of equating the coefficients
Properties of equality
inverse operation of addition
10. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
associative law 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.
A integral equation
Operations can involve dissimilar objects
11. Is to add - subtract - multiply - or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated - the other side of the equation is the value of the variable.
The relation of equality (=) has the property
The central technique to linear equations
then a + c < b + d
Repeated multiplication
12. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain
Operations can involve dissimilar objects
Categories of Algebra
The sets Xk
when b > 0
13. Is an equation involving integrals.
Algebraic combinatorics
A integral equation
The logical values true and false
Change of variables
14. May not be defined for every possible value.
Equations
Operations
A functional equation
has arity one
15. The inner product operation on two vectors produces a
Multiplication
Operations on functions
scalar
Identity
16. Is a function of the form ? : V ? Y - where V ? X1
A transcendental equation
transitive
An operation ?
All quadratic equations
17. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
Identity element of Multiplication
A Diophantine equation
logarithmic equation
18. If a < b and c < d
then a + c < b + d
identity element of Exponentiation
Algebra
the set Y
19. An operation of arity k is called a
k-ary operation
Algebraic equation
Reunion of broken parts
Algebraic geometry
20. The process of expressing the unknowns in terms of the knowns is called
Associative law of Exponentiation
Solving the Equation
substitution
The operation of exponentiation
21. Are called the domains of the operation
the set Y
The sets Xk
scalar
Elementary algebra
22. 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
Vectors
Algebraic number theory
operands - arguments - or inputs
23. 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'.
Reflexive relation
equation
inverse operation of addition
then ac < bc
24. 0 - which preserves numbers: a + 0 = a
Reflexive relation
inverse operation of addition
Linear algebra
identity element of addition
25. Is an equation involving derivatives.
A differential equation
Unknowns
Operations
has arity two
26. Division ( / )
Difference of two squares - or the difference of perfect squares
Operations on sets
Binary operations
inverse operation of Multiplication
27. Is an algebraic 'sentence' containing an unknown quantity.
Reflexive relation
A transcendental equation
The relation of equality (=)'s property
Polynomials
28. The values for which an operation is defined form a set called its
Exponentiation
then ac < bc
Linear algebra
domain
29. In which properties common to all algebraic structures are studied
Elementary algebra
Equations
Universal algebra
k-ary operation
30. Involve only one value - such as negation and trigonometric functions.
Operations
Unary operations
Multiplication
All quadratic equations
31. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Variables
nullary operation
Pure mathematics
A solution or root of the equation
32. If a < b and c > 0
then ac < bc
commutative law of Exponentiation
Algebra
Unknowns
33. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
Associative law of Multiplication
Algebraic equation
transitive
34. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
has arity one
operation
Algebraic number theory
substitution
35. If a = b and b = c then a = c
Multiplication
Unknowns
range
transitive
36. 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.
Change of variables
Repeated addition
operation
Algebraic number theory
37. Is an equation in which the unknowns are functions rather than simple quantities.
Identity element of Multiplication
Vectors
All quadratic equations
A functional equation
38. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
The logical values true and false
symmetric
unary and binary
39. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The method of equating the coefficients
Solution to the system
Quadratic equations
Algebraic number theory
40. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
range
Difference of two squares - or the difference of perfect squares
An operation ?
The operation of exponentiation
41. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Variables
Elementary algebra
system of linear equations
Algebraic combinatorics
42. The codomain is the set of real numbers but the range is the
scalar
nonnegative numbers
Operations on sets
The relation of equality (=)'s property
43. Can be added and subtracted.
Vectors
Identity
radical equation
A transcendental equation
44. 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
operands - arguments - or inputs
Quadratic equations can also be solved
Elimination method
Repeated multiplication
45. The squaring operation only produces
Vectors
(k+1)-ary relation that is functional on its first k domains
nonnegative numbers
A polynomial equation
46. () 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.
transitive
The operation of addition
then a < c
Algebra
47. The operation of exponentiation means ________________: a^n = a
Identity
system of linear equations
Repeated multiplication
inverse operation of Exponentiation
48. Not commutative a^b?b^a
Unary operations
commutative law of Exponentiation
identity element of Exponentiation
A differential equation
49. Is Written as ab or a^b
radical equation
Algebra
Associative law of Exponentiation
Exponentiation
50. b = b
Operations can involve dissimilar objects
Rotations
A differential equation
reflexive
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