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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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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 set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
A integral equation
nonnegative numbers
range
domain
2. An operation of arity k is called a
Solution to the system
domain
scalar
k-ary operation
3. A unary operation
A Diophantine equation
A polynomial equation
Constants
has arity one
4. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
two inputs
Pure mathematics
nonnegative numbers
The simplest equations to solve
5. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The central technique to linear equations
Solution to the system
The simplest equations to solve
transitive
6. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
The method of equating the coefficients
Properties of equality
The sets Xk
7. 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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8. 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.
A transcendental equation
Difference of two squares - or the difference of perfect squares
A polynomial equation
Change of variables
9. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
nonnegative numbers
Categories of Algebra
A solution or root of the equation
10. Is Written as a + b
Addition
operands - arguments - or inputs
inverse operation of Exponentiation
Equation Solving
11. If a = b and b = c then a = c
then a < c
The purpose of using variables
transitive
A polynomial equation
12. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
Quadratic equations can also be solved
Reunion of broken parts
Algebra
13. Involve only one value - such as negation and trigonometric functions.
Elementary algebra
unary and binary
Binary operations
Unary operations
14. Not commutative a^b?b^a
commutative law of Exponentiation
substitution
Solving the Equation
finitary operation
15. In which properties common to all algebraic structures are studied
nonnegative numbers
Algebraic combinatorics
then ac < bc
Universal algebra
16. 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
Elimination method
radical equation
an operation
17. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Equations
A Diophantine equation
nonnegative numbers
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.
18. Can be expressed in the form ax^2 + bx + c = 0 - where a is not zero (if it were zero - then the equation would not be quadratic but linear).
Reunion of broken parts
(k+1)-ary relation that is functional on its first k domains
Quadratic equations
Conditional equations
19. Is an equation involving a transcendental function of one of its variables.
Conditional equations
Universal algebra
Identity
A transcendental equation
20. Can be combined using logic operations - such as and - or - and not.
Elementary algebra
The logical values true and false
Elimination method
Number line or real line
21. b = b
The relation of equality (=) has the property
reflexive
Operations on functions
Algebra
22. 1 - which preserves numbers: a
Associative law of Exponentiation
domain
Identity element of Multiplication
A differential equation
23. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Pure mathematics
Identity
radical equation
Difference of two squares - or the difference of perfect squares
24. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic number theory
Operations on functions
The relation of inequality (<) has this property
transitive
25. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Number line or real line
nonnegative numbers
Solving the Equation
Variables
26. 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 purpose of using variables
k-ary operation
operation
Categories of Algebra
27. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Equations
Identity
Associative law of Exponentiation
domain
28. Is the claim that two expressions have the same value and are equal.
Equations
The real number system
nullary operation
The operation of exponentiation
29. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebraic equation
(k+1)-ary relation that is functional on its first k domains
Elementary algebra
Conditional equations
30. Is an equation of the form aX = b for a > 0 - which has solution
The relation of equality (=)'s property
A polynomial equation
exponential equation
Difference of two squares - or the difference of perfect squares
31. Are denoted by letters at the beginning - a - b - c - d - ...
A transcendental equation
Pure mathematics
The relation of inequality (<) has this property
Knowns
32. 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
an operation
Algebraic number theory
Algebra
The method of equating the coefficients
33. A vector can be multiplied by a scalar to form another vector
The operation of addition
Operations can involve dissimilar objects
finitary operation
Operations on functions
34. Is an action or procedure which produces a new value from one or more input values.
Solution to the system
Identities
Pure mathematics
an operation
35. Subtraction ( - )
identity element of Exponentiation
inverse operation of addition
Algebra
Conditional equations
36. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The method of equating the coefficients
The purpose of using variables
Vectors
Identity
37. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Quadratic equations can also be solved
A integral equation
finitary operation
Difference of two squares - or the difference of perfect squares
38. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Binary operations
two inputs
The sets Xk
nonnegative numbers
39. If a < b and b < c
Operations can involve dissimilar objects
Binary operations
then a < c
Elimination method
40. Is Written as a
commutative law of Addition
Pure mathematics
Multiplication
Solving the Equation
41. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
Associative law of Exponentiation
Operations on functions
Repeated addition
42. 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
when b > 0
k-ary operation
operation
identity element of Exponentiation
43. 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
A binary relation R over a set X is symmetric
identity element of addition
Elementary algebra
Operations on sets
44. If a = b then b = a
symmetric
Elementary algebra
commutative law of Addition
scalar
45. 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.
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.
(k+1)-ary relation that is functional on its first k domains
The central technique to linear equations
Operations can involve dissimilar objects
46. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
value - result - or output
Equations
nonnegative numbers
k-ary operation
47. Is algebraic equation of degree one
A linear equation
A binary relation R over a set X is symmetric
The relation of equality (=)'s property
Exponentiation
48. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
radical equation
The operation of addition
Operations
49. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
Binary operations
exponential equation
an operation
50. There are two common types of operations:
Unknowns
Linear algebra
Polynomials
unary and binary
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