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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
.
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. 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.
inverse operation of Exponentiation
The relation of equality (=) has the property
The method of equating the coefficients
Operations on sets
2. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Difference of two squares - or the difference of perfect squares
The purpose of using variables
the fixed non-negative integer k (the number of arguments)
logarithmic equation
3. Letters from the beginning of the alphabet like a - b - c... often denote
Repeated multiplication
an operation
Reunion of broken parts
Constants
4. 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
All quadratic equations
Algebraic number theory
A functional equation
5. 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)
identity element of addition
The operation of exponentiation
commutative law of Exponentiation
A transcendental equation
6. 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
Algebraic equation
Real number
A functional equation
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 set Y
k-ary operation
Algebraic geometry
Algebra
8. The values for which an operation is defined form a set called its
domain
finitary operation
Number line or real line
Vectors
9. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Elementary algebra
Algebra
Equations
Expressions
10. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Algebra
an operation
Difference of two squares - or the difference of perfect squares
radical equation
11. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
Equations
associative law of addition
Polynomials
12. (a + b) + c = a + (b + c)
A polynomial equation
Identity element of Multiplication
inverse operation of Multiplication
associative law of addition
13. (a
Associative law of Multiplication
Reflexive relation
symmetric
Solving the Equation
14. An operation of arity k is called a
domain
All quadratic equations
k-ary operation
Elementary algebra
15. Can be combined using the function composition operation - performing the first rotation and then the second.
Variables
inverse operation of Exponentiation
Difference of two squares - or the difference of perfect squares
Rotations
16. Is an equation of the form log`a^X = b for a > 0 - which has solution
The method of equating the coefficients
the set Y
A linear equation
logarithmic equation
17. Is an equation where the unknowns are required to be integers.
A Diophantine equation
substitution
Equations
The relation of inequality (<) has this property
18. 1 - which preserves numbers: a
An operation ?
Algebraic geometry
Reflexive relation
Identity element of Multiplication
19. A
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
Operations on sets
inverse operation of addition
20. 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
transitive
The method of equating the coefficients
Operations on functions
(k+1)-ary relation that is functional on its first k domains
21. Is Written as ab or a^b
Pure mathematics
The central technique to linear equations
when b > 0
Exponentiation
22. Logarithm (Log)
inverse operation of Exponentiation
Operations
has arity two
Universal algebra
23. The squaring operation only produces
has arity two
Unknowns
then ac < bc
nonnegative numbers
24. Is Written as a
Operations can involve dissimilar objects
Multiplication
A functional equation
Identity element of Multiplication
25. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Rotations
Elimination method
system of linear equations
then a + c < b + d
26. The process of expressing the unknowns in terms of the knowns is called
A functional equation
Polynomials
Solving the Equation
Operations on functions
27. The values combined are called
Operations can involve dissimilar objects
Algebraic combinatorics
operands - arguments - or inputs
Multiplication
28. May not be defined for every possible value.
Polynomials
Multiplication
Operations
commutative law of Addition
29. If a < b and c < 0
The simplest equations to solve
then bc < ac
inverse operation of addition
Categories of Algebra
30. Involve only one value - such as negation and trigonometric functions.
Unary operations
Quadratic equations
The method of equating the coefficients
when b > 0
31. The values of the variables which make the equation true are the solutions of the equation and can be found through
domain
Equation Solving
transitive
identity element of Exponentiation
32. If a < b and c < d
then a + c < b + d
Categories of Algebra
Multiplication
Associative law of Exponentiation
33. Will have two solutions in the complex number system - but need not have any in the real number system.
nonnegative numbers
All quadratic equations
The relation of equality (=)'s property
Difference of two squares - or the difference of perfect squares
34. Is Written as a + b
range
The central technique to linear equations
Addition
Repeated multiplication
35. Is called the codomain of the operation
Abstract algebra
Identity element of Multiplication
the set Y
Algebraic geometry
36. Is an equation involving integrals.
The relation of equality (=)'s property
Polynomials
All quadratic equations
A integral equation
37. Is an equation in which a polynomial is set equal to another polynomial.
A binary relation R over a set X is symmetric
operation
A polynomial equation
Operations
38. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Real number
logarithmic equation
Equations
finitary operation
39. In which the specific properties of vector spaces are studied (including matrices)
Operations
Equations
Linear algebra
k-ary operation
40. 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
Vectors
operands - arguments - or inputs
A polynomial equation
41. Can be defined axiomatically up to an isomorphism
The real number system
Quadratic equations can also be solved
Reunion of broken parts
A functional equation
42. Division ( / )
Addition
commutative law of Multiplication
inverse operation of Multiplication
Equations
43. 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
nullary operation
Reunion of broken parts
substitution
The central technique to linear equations
44. There are two common types of operations:
Quadratic equations can also be solved
unary and binary
Algebraic combinatorics
commutative law of Multiplication
45. Can be combined using logic operations - such as and - or - and not.
inverse operation of addition
nonnegative numbers
The logical values true and false
the set Y
46. 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
an operation
reflexive
substitution
Associative law of Multiplication
47. 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
Identity
Quadratic equations can also be solved
Conditional equations
48. Is an equation in which the unknowns are functions rather than simple quantities.
The purpose of using variables
k-ary operation
A functional equation
value - result - or output
49. The value produced is called
inverse operation of Exponentiation
Linear algebra
value - result - or output
Conditional equations
50. Are called the domains of the operation
All quadratic equations
Multiplication
Operations on functions
The sets Xk
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