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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
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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).
commutative law of Multiplication
Quadratic equations
operation
Reflexive relation
2. 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
then a + c < b + d
Repeated multiplication
Real number
Equation Solving
3. Applies abstract algebra to the problems of geometry
has arity two
A polynomial equation
Algebraic geometry
Expressions
4. Is an algebraic 'sentence' containing an unknown quantity.
then a + c < b + d
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.
has arity one
Polynomials
5. Not associative
Identity
commutative law of Exponentiation
Associative law of Exponentiation
inverse operation of Multiplication
6. Can be combined using logic operations - such as and - or - and not.
Abstract algebra
Equation Solving
Algebraic geometry
The logical values true and false
7. () 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.
the fixed non-negative integer k (the number of arguments)
reflexive
Operations on functions
Algebra
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'.
system of linear equations
Reflexive relation
Exponentiation
Operations
9. Is algebraic equation of degree one
Conditional equations
A linear equation
Change of variables
commutative law of Multiplication
10. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
The simplest equations to solve
Identities
then bc < ac
Algebra
11. Logarithm (Log)
Polynomials
finitary operation
inverse operation of Exponentiation
has arity two
12. A unary operation
the fixed non-negative integer k (the number of arguments)
commutative law of Multiplication
has arity one
A polynomial equation
13. 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
Number line or real line
Elimination method
the fixed non-negative integer k (the number of arguments)
scalar
14. Is an equation in which the unknowns are functions rather than simple quantities.
Elementary algebra
A functional equation
two inputs
The relation of equality (=)
15. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
Equations
The operation of exponentiation
exponential equation
16. Is an equation involving a transcendental function of one of its variables.
The relation of equality (=)'s property
A transcendental equation
symmetric
Algebraic combinatorics
17. An operation of arity k is called a
The method of equating the coefficients
an operation
k-ary operation
then ac < bc
18. Include composition and convolution
The real number system
Difference of two squares - or the difference of perfect squares
equation
Operations on functions
19. If a = b and b = c then a = c
transitive
The relation of equality (=)
has arity two
Solving the Equation
20. Is an equation involving derivatives.
Algebraic equation
The operation of exponentiation
A differential equation
Real number
21. The values of the variables which make the equation true are the solutions of the equation and can be found through
operands - arguments - or inputs
Operations on functions
Linear algebra
Equation Solving
22. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Elimination method
Unknowns
Pure mathematics
A solution or root of the equation
23. If it holds for all a and b in X that if a is related to b then b is related to a.
Vectors
The real number system
Operations on functions
A binary relation R over a set X is symmetric
24. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Difference of two squares - or the difference of perfect squares
A solution or root of the equation
identity element of Exponentiation
operands - arguments - or inputs
25. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
Unary operations
Reunion of broken parts
value - result - or output
26. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
operation
Associative law of Exponentiation
The logical values true and false
Expressions
27. Is an equation of the form log`a^X = b for a > 0 - which has solution
Difference of two squares - or the difference of perfect squares
logarithmic equation
A transcendental equation
substitution
28. Subtraction ( - )
Abstract algebra
Unary operations
The relation of equality (=) has the property
inverse operation of addition
29. The squaring operation only produces
the set Y
The sets Xk
nonnegative numbers
Algebraic number theory
30. Is an equation of the form aX = b for a > 0 - which has solution
inverse operation of Exponentiation
Algebraic equation
exponential equation
The operation of addition
31. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Number line or real line
equation
Algebraic equation
Binary operations
32. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Number line or real line
inverse operation of Exponentiation
two inputs
Unknowns
33. The values combined are called
Reunion of broken parts
operands - arguments - or inputs
then ac < bc
Variables
34. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Vectors
Universal algebra
inverse operation of addition
35. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
Algebraic combinatorics
radical equation
Equations
36. Is called the type or arity of the operation
Identities
the fixed non-negative integer k (the number of arguments)
Algebraic combinatorics
value - result - or output
37. In which abstract algebraic methods are used to study combinatorial questions.
then a + c < b + d
Equation Solving
Algebraic combinatorics
Operations on functions
38. Can be added and subtracted.
has arity two
Vectors
Algebraic equation
(k+1)-ary relation that is functional on its first k domains
39. Division ( / )
inverse operation of Multiplication
Equations
Identities
Algebraic combinatorics
40. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Order of Operations
Addition
Identity
Algebraic equation
41. Is Written as a + b
Equations
Identity
inverse operation of Exponentiation
Addition
42. Is an equation where the unknowns are required to be integers.
A Diophantine equation
unary and binary
operation
A binary relation R over a set X is symmetric
43. 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.
Variables
radical equation
Operations can involve dissimilar objects
44. Is the claim that two expressions have the same value and are equal.
transitive
Algebraic combinatorics
operands - arguments - or inputs
Equations
45. 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
Reflexive relation
The method of equating the coefficients
Expressions
46. The values for which an operation is defined form a set called its
Constants
domain
when b > 0
symmetric
47. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
two inputs
Solution to the system
value - result - or output
A solution or root of the equation
48. k-ary operation is a
Quadratic equations
A transcendental equation
(k+1)-ary relation that is functional on its first k domains
All quadratic equations
49. 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.
equation
Reunion of broken parts
Equations
Change of variables
50. 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
symmetric
Elementary algebra
Constants
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