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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. () 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.
Algebra
scalar
inverse operation of addition
A integral equation
2. Not associative
Polynomials
Elimination method
Algebraic combinatorics
Associative law of Exponentiation
3. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Solving the Equation
Categories of Algebra
operation
logarithmic equation
4. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
The real number system
Algebraic number theory
commutative law of Multiplication
A functional equation
5. 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
Reflexive relation
Unknowns
Difference of two squares - or the difference of perfect squares
6. 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
logarithmic equation
scalar
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.
7. Is Written as a + b
has arity one
Addition
Reunion of broken parts
A solution or root of the equation
8. Is a function of the form ? : V ? Y - where V ? X1
A transcendental equation
An operation ?
A linear equation
the fixed non-negative integer k (the number of arguments)
9. In which properties common to all algebraic structures are studied
Universal algebra
Associative law of Multiplication
Polynomials
The real number system
10. Will have two solutions in the complex number system - but need not have any in the real number system.
nonnegative numbers
All quadratic equations
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.
Unknowns
11. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
Equation Solving
range
A polynomial equation
12. A unary operation
has arity one
inverse operation of Exponentiation
Vectors
Linear algebra
13. The operation of exponentiation means ________________: a^n = a
Equations
range
Repeated multiplication
Knowns
14. The codomain is the set of real numbers but the range is the
Repeated multiplication
Algebraic geometry
nonnegative numbers
transitive
15. 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
A functional equation
Equation Solving
operation
16. Is an algebraic 'sentence' containing an unknown quantity.
The sets Xk
Polynomials
Universal algebra
operands - arguments - or inputs
17. A
radical equation
then ac < bc
commutative law of Multiplication
Repeated addition
18. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Binary operations
exponential equation
range
commutative law of Multiplication
19. In which the specific properties of vector spaces are studied (including matrices)
inverse operation of Exponentiation
associative law of addition
Linear algebra
Associative law of Exponentiation
20. Is an action or procedure which produces a new value from one or more input values.
an operation
Operations can involve dissimilar objects
A functional equation
Real number
21. 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)
Abstract algebra
exponential equation
Operations on functions
operation
22. Division ( / )
Quadratic equations can also be solved
Associative law of Multiplication
inverse operation of Multiplication
then a + c < b + d
23. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Difference of two squares - or the difference of perfect squares
then ac < bc
range
Abstract algebra
24. Is an equation where the unknowns are required to be integers.
An operation ?
A Diophantine equation
operands - arguments - or inputs
Universal algebra
25. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
logarithmic equation
Vectors
Algebraic equation
26. If a < b and c > 0
then ac < bc
Identity element of Multiplication
Operations on sets
an operation
27. Is the claim that two expressions have the same value and are equal.
Pure mathematics
A functional equation
Equations
All quadratic equations
28. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.
Algebraic number theory
The relation of inequality (<) has this property
then bc < ac
Reflexive relation
29. Can be combined using logic operations - such as and - or - and not.
Real number
Elimination method
The logical values true and false
The operation of addition
30. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
equation
identity element of addition
The simplest equations to solve
31. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
The purpose of using variables
Operations
Repeated multiplication
Identity
32. 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).
Solution to the system
A integral equation
operation
Equation Solving
33. The squaring operation only produces
nonnegative numbers
has arity one
scalar
range
34. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Variables
Expressions
Algebraic geometry
Elementary algebra
35. 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.
Associative law of Exponentiation
commutative law of Addition
Multiplication
Change of variables
36. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
Multiplication
associative law of addition
Vectors
37. Letters from the beginning of the alphabet like a - b - c... often denote
Expressions
Identities
Pure mathematics
Constants
38. Is an equation in which the unknowns are functions rather than simple quantities.
All quadratic equations
A functional equation
Pure mathematics
scalar
39. The values of the variables which make the equation true are the solutions of the equation and can be found through
Repeated addition
Repeated multiplication
The real number system
Equation Solving
40. The values for which an operation is defined form a set called its
range
Unknowns
domain
Quadratic equations
41. 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
Associative law of Multiplication
Reunion of broken parts
Algebraic equation
42. The inner product operation on two vectors produces a
A solution or root of the equation
an operation
Operations can involve dissimilar objects
scalar
43. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
nonnegative numbers
system of linear equations
Real number
commutative law of Addition
44. Is an equation involving integrals.
then ac < bc
Unknowns
A integral equation
finitary operation
45. 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
Equation Solving
value - result - or output
substitution
Linear algebra
46. 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
radical equation
Unary operations
Exponentiation
47. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
A Diophantine equation
Repeated addition
The relation of inequality (<) has this property
48. 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
Exponentiation
Real number
operation
then a < c
49. 1 - which preserves numbers: a^1 = a
radical equation
identity element of Exponentiation
The sets Xk
inverse operation of Exponentiation
50. May not be defined for every possible value.
value - result - or output
Variables
Operations
range
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