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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
Start Test
Study First
Subjects
:
clep
,
math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
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. An operation of arity zero is simply an element of the codomain Y - called a
operation
nullary operation
Difference of two squares - or the difference of perfect squares
Order of Operations
2. 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)
Exponentiation
Algebraic equation
operation
Number line or real line
3. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Repeated addition
Algebraic number theory
The relation of equality (=)'s property
The purpose of using variables
4. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Repeated addition
Algebra
Unknowns
Change of variables
5. 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
substitution
Categories of Algebra
inverse operation of Exponentiation
Algebraic number theory
6. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
finitary operation
range
inverse operation of addition
The relation of equality (=)
7. Is an algebraic 'sentence' containing an unknown quantity.
operands - arguments - or inputs
unary and binary
then ac < bc
Polynomials
8. May not be defined for every possible value.
Operations
operation
Universal algebra
Real number
9. 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).
Change of variables
Quadratic equations
operation
The relation of equality (=)
10. The values combined are called
Order of Operations
The sets Xk
operands - arguments - or inputs
Conditional equations
11. Can be defined axiomatically up to an isomorphism
the fixed non-negative integer k (the number of arguments)
A functional equation
The real number system
Operations can involve dissimilar objects
12. If it holds for all a and b in X that if a is related to b then b is related to a.
Pure mathematics
A binary relation R over a set X is symmetric
The relation of equality (=)'s property
Rotations
13. 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
Identity element of Multiplication
The operation of addition
has arity one
14. Is an equation involving a transcendental function of one of its variables.
Algebraic geometry
transitive
domain
A transcendental equation
15. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Repeated addition
The simplest equations to solve
two inputs
equation
16. Is an equation in which a polynomial is set equal to another polynomial.
Real number
A polynomial equation
Operations on functions
Change of variables
17. 0 - which preserves numbers: a + 0 = a
commutative law of Exponentiation
radical equation
system of linear equations
identity element of addition
18. If a = b and b = c then a = c
An operation ?
transitive
nonnegative numbers
Rotations
19. The value produced is called
The method of equating the coefficients
symmetric
Multiplication
value - result - or output
20. Is Written as a
Categories of Algebra
Operations
Multiplication
Equations
21. A
A differential equation
Real number
commutative law of Multiplication
Identities
22. If a < b and b < c
Algebra
A differential equation
then a < c
operation
23. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Linear algebra
inverse operation of Exponentiation
The relation of equality (=)
the set Y
24. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
value - result - or output
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.
Binary operations
system of linear equations
25. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
The central technique to linear equations
A Diophantine equation
nonnegative numbers
Equations
26. 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
The relation of inequality (<) has this property
identity element of Exponentiation
finitary operation
Real number
27. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
Reflexive relation
transitive
Reunion of broken parts
28. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
then bc < ac
Difference of two squares - or the difference of perfect squares
Universal algebra
operation
29. If a < b and c < d
finitary operation
Elimination method
Properties of equality
then a + c < b + d
30. The values for which an operation is defined form a set called its
finitary operation
domain
scalar
Quadratic equations
31. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
Unary operations
Constants
identity element of Exponentiation
32. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Identities
A solution or root of the equation
All quadratic equations
The simplest equations to solve
33. b = b
then bc < ac
Unary operations
reflexive
Algebraic number theory
34. Is Written as a + b
Addition
The relation of equality (=)'s property
Multiplication
Exponentiation
35. () 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
value - result - or output
scalar
Conditional equations
36. 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.
k-ary operation
Change of variables
value - result - or output
Vectors
37. Applies abstract algebra to the problems of geometry
Associative law of Exponentiation
Algebraic geometry
Repeated addition
The relation of equality (=)
38. Is called the codomain of the operation
the set Y
A binary relation R over a set X is symmetric
Universal algebra
A integral equation
39. Letters from the beginning of the alphabet like a - b - c... often denote
Algebra
Repeated multiplication
Constants
two inputs
40. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
The method of equating the coefficients
An operation ?
Polynomials
41. 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
The real number system
exponential equation
The method of equating the coefficients
Rotations
42. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Algebraic equation
Pure mathematics
Exponentiation
Reflexive relation
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
All quadratic equations
Reunion of broken parts
Algebraic geometry
Associative law of Exponentiation
44. Is an equation where the unknowns are required to be integers.
system of linear equations
then a < c
A Diophantine equation
The central technique to linear equations
45. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
commutative law of Addition
Abstract algebra
two inputs
Equation Solving
46. k-ary operation is a
The relation of equality (=)
nonnegative numbers
then bc < ac
(k+1)-ary relation that is functional on its first k domains
47. The codomain is the set of real numbers but the range is the
nonnegative numbers
operation
The simplest equations to solve
Number line or real line
48. (a
radical equation
nullary operation
Algebra
Associative law of Multiplication
49. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
A functional equation
The relation of equality (=) has the property
Algebraic geometry
50. Is an equation of the form aX = b for a > 0 - which has solution
nonnegative numbers
inverse operation of Exponentiation
exponential equation
nullary operation