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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. 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)
The operation of exponentiation
radical equation
Exponentiation
Solution to the system
2. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Multiplication
inverse operation of Multiplication
Constants
3. Include composition and convolution
Operations on functions
Repeated multiplication
Quadratic equations
operation
4. Operations can have fewer or more than
two inputs
A integral equation
an operation
Elimination method
5. Are true for only some values of the involved variables: x2 - 1 = 4.
Solution to the system
then bc < ac
nonnegative numbers
Conditional equations
6. Are denoted by letters at the beginning - a - b - c - d - ...
commutative law of Multiplication
Knowns
Identities
Addition
7. Involve only one value - such as negation and trigonometric functions.
Binary operations
Algebraic number theory
equation
Unary operations
8. If a < b and c < 0
identity element of Exponentiation
The sets Xk
Universal algebra
then bc < ac
9. Are called the domains of the operation
The purpose of using variables
The sets Xk
The simplest equations to solve
Constants
10. In which the specific properties of vector spaces are studied (including matrices)
Universal algebra
(k+1)-ary relation that is functional on its first k domains
Linear algebra
Associative law of Multiplication
11. 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
Order of Operations
Expressions
Real number
The method of equating the coefficients
12. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
A integral equation
when b > 0
Solving the Equation
13. Is Written as a
operands - arguments - or inputs
Multiplication
Constants
substitution
14. In which properties common to all algebraic structures are studied
Universal algebra
inverse operation of addition
operands - arguments - or inputs
then a + c < b + d
15. Can be added and subtracted.
Vectors
has arity one
the set Y
A integral equation
16. Symbols that denote numbers - is to allow the making of generalizations in mathematics
finitary operation
The purpose of using variables
A integral equation
Solution to the system
17. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
The logical values true and false
The operation of addition
A Diophantine equation
18. 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
The simplest equations to solve
Number line or real line
substitution
the fixed non-negative integer k (the number of arguments)
19. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Linear algebra
The method of equating the coefficients
Rotations
Quadratic equations can also be solved
20. Is an equation involving integrals.
A functional equation
then a < c
operation
A integral equation
21. (a + b) + c = a + (b + c)
when b > 0
associative law of addition
Variables
Identity element of Multiplication
22. 1 - which preserves numbers: a^1 = a
Constants
A transcendental equation
Knowns
identity element of Exponentiation
23. Is a function of the form ? : V ? Y - where V ? X1
The logical values true and false
An operation ?
inverse operation of addition
The relation of equality (=)
24. If a = b and b = c then a = c
Polynomials
system of linear equations
transitive
Algebraic number theory
25. Include the binary operations union and intersection and the unary operation of complementation.
The operation of exponentiation
commutative law of Addition
Operations on sets
A integral equation
26. The squaring operation only produces
The relation of equality (=) has the property
Repeated addition
Algebraic combinatorics
nonnegative numbers
27. An operation of arity k is called a
Properties of equality
Elimination method
A Diophantine equation
k-ary operation
28. The value produced is called
two inputs
Conditional equations
identity element of addition
value - result - or output
29. The operation of exponentiation means ________________: a^n = a
The relation of equality (=)'s property
Algebraic number theory
Equations
Repeated multiplication
30. The codomain is the set of real numbers but the range is the
exponential equation
commutative law of Addition
nonnegative numbers
The relation of equality (=)
31. Is an equation where the unknowns are required to be integers.
Algebraic equation
Unary operations
The operation of exponentiation
A Diophantine equation
32. The values of the variables which make the equation true are the solutions of the equation and can be found through
The sets Xk
Repeated addition
Algebra
Equation Solving
33. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Elementary algebra
Solution to the system
The sets Xk
Exponentiation
34. 1 - which preserves numbers: a
Identity element of Multiplication
A binary relation R over a set X is symmetric
Algebraic equation
Order of Operations
35. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
A differential equation
reflexive
transitive
36. May not be defined for every possible value.
Operations
Expressions
Knowns
Rotations
37. 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
radical equation
Operations
logarithmic equation
when b > 0
38. Can be combined using logic operations - such as and - or - and not.
finitary operation
Operations on sets
associative law of addition
The logical values true and false
39. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Constants
Equations
A linear equation
Knowns
40. 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
Solving the Equation
inverse operation of Exponentiation
Abstract algebra
Elimination method
41. If a < b and b < c
Associative law of Exponentiation
The operation of exponentiation
operation
then a < c
42. If it holds for all a and b in X that if a is related to b then b is related to a.
Identities
A binary relation R over a set X is symmetric
reflexive
Order of Operations
43. A + b = b + a
Reunion of broken parts
commutative law of Addition
The method of equating the coefficients
Constants
44. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic number theory
Algebraic combinatorics
exponential equation
inverse operation of addition
45. 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
The relation of inequality (<) has this property
Change of variables
then ac < bc
46. Is Written as ab or a^b
Exponentiation
The relation of equality (=)'s property
The logical values true and false
nullary operation
47. A
Operations can involve dissimilar objects
commutative law of Multiplication
Rotations
nonnegative numbers
48. 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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49. 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
radical equation
All quadratic equations
Elementary algebra
scalar
50. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
A linear equation
associative law of addition
Number line or real line
Algebraic equation
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