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CLEP College Algebra: Algebra Principles
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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. Applies abstract algebra to the problems of geometry
Binary operations
Algebraic geometry
The purpose of using variables
Number line or real line
2. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
Addition
operation
finitary operation
3. The values for which an operation is defined form a set called its
A functional equation
has arity one
Pure mathematics
domain
4. () 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.
Constants
radical equation
The sets Xk
Algebra
5. Is the claim that two expressions have the same value and are equal.
Equations
Number line or real line
nonnegative numbers
two inputs
6. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
The real number system
Number line or real line
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.
Properties of equality
7. If a < b and c < d
then a + c < b + d
A linear equation
Elementary algebra
A integral equation
8. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Algebraic number theory
(k+1)-ary relation that is functional on its first k domains
The relation of equality (=)
Rotations
9. Not commutative a^b?b^a
Polynomials
Universal algebra
transitive
commutative law of Exponentiation
10. The operation of exponentiation means ________________: a^n = a
Identities
Repeated multiplication
Universal algebra
the set Y
11. Is an equation involving a transcendental function of one of its variables.
Multiplication
inverse operation of Exponentiation
Quadratic equations
A transcendental equation
12. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Algebraic combinatorics
logarithmic equation
A solution or root of the equation
The relation of equality (=)
13. Include composition and convolution
Operations on functions
scalar
radical equation
then a + c < b + d
14. Operations can have fewer or more than
operands - arguments - or inputs
Identities
two inputs
Operations
15. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
operation
Abstract algebra
The method of equating the coefficients
16. If a = b and b = c then a = c
operands - arguments - or inputs
transitive
operation
Equation Solving
17. 1 - which preserves numbers: a
Identity element of Multiplication
value - result - or output
Equations
Expressions
18. If it holds for all a and b in X that if a is related to b then b is related to a.
A binary relation R over a set X is symmetric
nullary operation
Change of variables
Algebraic number theory
19. A unary operation
The operation of addition
The relation of inequality (<) has this property
has arity one
nonnegative numbers
20. 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
Universal algebra
substitution
finitary operation
Algebraic combinatorics
21. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
The relation of equality (=) has the property
The operation of addition
Exponentiation
22. Is an equation of the form aX = b for a > 0 - which has solution
The operation of addition
exponential equation
Equations
identity element of Exponentiation
23. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
A transcendental equation
when b > 0
Algebraic number theory
24. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
two inputs
Abstract algebra
Associative law of Exponentiation
The logical values true and false
25. The values combined are called
operands - arguments - or inputs
Solution to the system
Conditional equations
radical equation
26. A vector can be multiplied by a scalar to form another vector
commutative law of Addition
Algebra
Knowns
Operations can involve dissimilar objects
27. 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
Elementary algebra
Expressions
scalar
Constants
28. Referring to the finite number of arguments (the value k)
Variables
Repeated multiplication
finitary operation
The operation of addition
29. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Associative law of Exponentiation
Quadratic equations can also be solved
Operations
inverse operation of addition
30. b = b
Quadratic equations can also be solved
reflexive
The real number system
Universal algebra
31. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Algebraic combinatorics
The simplest equations to solve
Repeated addition
substitution
32. Involve only one value - such as negation and trigonometric functions.
The simplest equations to solve
domain
Equations
Unary operations
33. k-ary operation is a
Reflexive relation
The relation of equality (=)'s property
(k+1)-ary relation that is functional on its first k domains
logarithmic equation
34. Is an equation in which a polynomial is set equal to another polynomial.
the fixed non-negative integer k (the number of arguments)
A polynomial equation
commutative law of Exponentiation
Change of variables
35. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Rotations
Knowns
Pure mathematics
Algebra
36. Is an equation involving integrals.
The relation of inequality (<) has this property
Order of Operations
A integral equation
Unary operations
37. May not be defined for every possible value.
Operations
has arity two
Multiplication
scalar
38. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
associative law of addition
then ac < bc
when b > 0
range
39. 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.
identity element of Exponentiation
A functional equation
A binary relation R over a set X is symmetric
Properties of equality
40. Symbols that denote numbers - is to allow the making of generalizations in mathematics
operation
The operation of addition
The purpose of using variables
nullary operation
41. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
Variables
finitary operation
equation
42. Is an algebraic 'sentence' containing an unknown quantity.
nonnegative numbers
Identities
Unknowns
Polynomials
43. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The operation of exponentiation
Solution to the system
Repeated multiplication
The relation of equality (=)'s property
44. 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).
Properties of equality
Quadratic equations
operation
Quadratic equations can also be solved
45. The squaring operation only produces
A integral equation
symmetric
Equations
nonnegative numbers
46. A
when b > 0
commutative law of Multiplication
Conditional equations
Vectors
47. The values of the variables which make the equation true are the solutions of the equation and can be found through
Algebra
The simplest equations to solve
The sets Xk
Equation Solving
48. 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).
Linear algebra
The method of equating the coefficients
operation
nonnegative numbers
49. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
operands - arguments - or inputs
Identity
A differential equation
50. The value produced is called
Operations
Rotations
when b > 0
value - result - or output
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