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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. If a < b and b < c
then bc < ac
The sets Xk
then a < c
substitution
2. In which abstract algebraic methods are used to study combinatorial questions.
then a + c < b + d
Algebraic combinatorics
A functional equation
The simplest equations to solve
3. () 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.
A linear equation
The simplest equations to solve
Algebra
then bc < ac
4. Is called the codomain of the operation
Polynomials
Properties of equality
the set Y
operation
5. 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
the set Y
Elementary algebra
then a + c < b + d
Solving the Equation
6. In an equation with a single unknown - a value of that unknown for which the equation is true is called
radical equation
A functional equation
Equations
A solution or root of the equation
7. Is the claim that two expressions have the same value and are equal.
A linear equation
Equations
the set Y
The relation of equality (=)'s property
8. (a + b) + c = a + (b + c)
radical equation
A solution or root of the equation
then a + c < b + d
associative law of addition
9. A vector can be multiplied by a scalar to form another vector
Equations
Equations
An operation ?
Operations can involve dissimilar objects
10. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Exponentiation
Number line or real line
then bc < ac
k-ary operation
11. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
logarithmic equation
Difference of two squares - or the difference of perfect squares
Unary operations
A solution or root of the equation
12. In which properties common to all algebraic structures are studied
Solving the Equation
Universal algebra
substitution
Quadratic equations can also be solved
13. If a = b then b = a
symmetric
Equation Solving
Linear algebra
The sets Xk
14. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
An operation ?
system of linear equations
(k+1)-ary relation that is functional on its first k domains
commutative law of Exponentiation
15. Involve only one value - such as negation and trigonometric functions.
radical equation
Elementary algebra
substitution
Unary operations
16. 0 - which preserves numbers: a + 0 = a
identity element of addition
scalar
Addition
two inputs
17. Applies abstract algebra to the problems of geometry
Reflexive relation
Algebraic geometry
The method of equating the coefficients
finitary operation
18. 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
nullary operation
A polynomial equation
The method of equating the coefficients
range
19. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
Repeated multiplication
Operations
Categories of Algebra
20. Are true for only some values of the involved variables: x2 - 1 = 4.
Equations
the set Y
Conditional equations
The simplest equations to solve
21. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
system of linear equations
A linear equation
Addition
range
22. Can be defined axiomatically up to an isomorphism
The central technique to linear equations
The real number system
Operations on sets
All quadratic equations
23. A binary operation
radical equation
Repeated multiplication
symmetric
has arity two
24. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
k-ary operation
Vectors
Knowns
Unknowns
25. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
operation
A polynomial equation
Equations
26. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
then bc < ac
nullary operation
An operation ?
27. The inner product operation on two vectors produces a
Identity element of Multiplication
scalar
Change of variables
finitary operation
28. Not commutative a^b?b^a
commutative law of Exponentiation
Real number
The simplest equations to solve
The relation of equality (=)'s property
29. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Equation Solving
Pure mathematics
Order of Operations
identity element of addition
30. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
(k+1)-ary relation that is functional on its first k domains
Abstract algebra
Real number
Solution to the system
31. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
Algebraic equation
Identity
inverse operation of addition
32. Division ( / )
inverse operation of Multiplication
Solution to the system
Order of Operations
The purpose of using variables
33. 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.
Operations can involve dissimilar objects
Properties of equality
The relation of equality (=)
Unknowns
34. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
An operation ?
Number line or real line
exponential equation
Identities
35. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Solving the Equation
nullary operation
A solution or root of the 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.
36. 1 - which preserves numbers: a
operation
Identity element of Multiplication
an operation
Categories of Algebra
37. Referring to the finite number of arguments (the value k)
finitary operation
identity element of addition
Multiplication
inverse operation of Multiplication
38. The operation of multiplication means _______________: a
The purpose of using variables
then bc < ac
an operation
Repeated addition
39. 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
The purpose of using variables
the fixed non-negative integer k (the number of arguments)
Repeated addition
40. Are denoted by letters at the beginning - a - b - c - d - ...
A integral equation
The logical values true and false
Reflexive relation
Knowns
41. An operation of arity k is called a
A solution or root of the equation
k-ary operation
A functional equation
Addition
42. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Algebraic equation
k-ary operation
Equation Solving
Quadratic equations can also be solved
43. The codomain is the set of real numbers but the range is the
operands - arguments - or inputs
nonnegative numbers
then bc < ac
Algebraic combinatorics
44. Is called the type or arity of the operation
inverse operation of addition
Expressions
the fixed non-negative integer k (the number of arguments)
radical equation
45. 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
operands - arguments - or inputs
Real number
system of linear equations
Variables
46. (a
Associative law of Multiplication
The relation of equality (=)
A polynomial equation
identity element of addition
47. A + b = b + a
Repeated multiplication
Quadratic equations can also be solved
domain
commutative law of Addition
48. Is Written as ab or a^b
Exponentiation
symmetric
Algebraic combinatorics
(k+1)-ary relation that is functional on its first k domains
49. 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.
when b > 0
nonnegative numbers
operation
The relation of equality (=) has the property
50. Subtraction ( - )
inverse operation of addition
an operation
All quadratic equations
symmetric
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