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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. A unary operation
has arity one
Conditional equations
identity element of addition
inverse operation of Multiplication
2. Is called the codomain of the operation
Number line or real line
Order of Operations
the set Y
The operation of addition
3. The value produced is called
Rotations
value - result - or output
nullary operation
Categories of Algebra
4. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Operations on sets
A transcendental equation
A linear equation
Unknowns
5. In which properties common to all algebraic structures are studied
Elementary algebra
k-ary operation
The relation of equality (=)'s property
Universal algebra
6. 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.
logarithmic equation
The relation of inequality (<) has this property
Operations can involve dissimilar objects
Conditional equations
7. (a
then a + c < b + d
A functional equation
Associative law of Multiplication
the fixed non-negative integer k (the number of arguments)
8. A vector can be multiplied by a scalar to form another vector
transitive
The operation of addition
Operations can involve dissimilar objects
the fixed non-negative integer k (the number of arguments)
9. 0 - which preserves numbers: a + 0 = a
Vectors
operation
identity element of addition
Unary operations
10. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po
Elimination method
operands - arguments - or inputs
the set Y
Vectors
11. Is the claim that two expressions have the same value and are equal.
Equations
finitary operation
The relation of equality (=)'s property
scalar
12. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Quadratic equations can also be solved
Algebraic geometry
Pure mathematics
scalar
13. 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
An operation ?
The relation of equality (=)
Rotations
Elementary algebra
14. Are called the domains of the operation
identity element of addition
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.
The sets Xk
Repeated multiplication
15. Letters from the beginning of the alphabet like a - b - c... often denote
Repeated addition
Binary operations
Conditional equations
Constants
16. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
Repeated addition
equation
has arity one
17. In an equation with a single unknown - a value of that unknown for which the equation is true is called
The relation of equality (=)
A linear equation
Algebraic number theory
A solution or root of the equation
18. A binary operation
identity element of addition
All quadratic equations
Linear algebra
has arity two
19. Applies abstract algebra to the problems of geometry
Algebraic geometry
Solving the Equation
Abstract algebra
All quadratic equations
20. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
symmetric
Identity
scalar
reflexive
21. Is an equation where the unknowns are required to be integers.
commutative law of Exponentiation
Multiplication
A Diophantine equation
Unknowns
22. If a < b and c < 0
Repeated addition
Elimination method
then bc < ac
A Diophantine equation
23. If a < b and c > 0
Expressions
then ac < bc
A Diophantine equation
operands - arguments - or inputs
24. Not commutative a^b?b^a
identity element of addition
scalar
then ac < bc
commutative law of Exponentiation
25. If it holds for all a and b in X that if a is related to b then b is related to a.
Associative law of Multiplication
system of linear equations
range
A binary relation R over a set X is symmetric
26. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
Unary operations
The central technique to linear equations
Elementary algebra
27. The squaring operation only produces
nonnegative numbers
The method of equating the coefficients
Number line or real line
an operation
28. 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).
Quadratic equations
Knowns
nullary operation
then bc < ac
29. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
The real number system
nonnegative numbers
value - result - or output
system of linear equations
30. Are true for only some values of the involved variables: x2 - 1 = 4.
Equations
Polynomials
Exponentiation
Conditional equations
31. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
Reunion of broken parts
The operation of addition
Exponentiation
32. An operation of arity k is called a
Elimination method
Associative law of Exponentiation
k-ary operation
equation
33. The inner product operation on two vectors produces a
The method of equating the coefficients
scalar
range
radical equation
34. The process of expressing the unknowns in terms of the knowns is called
Real number
nullary operation
Solving the Equation
reflexive
35. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
Reflexive relation
Rotations
logarithmic equation
36. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Conditional equations
Difference of two squares - or the difference of perfect squares
Operations on sets
when b > 0
37. The codomain is the set of real numbers but the range is the
reflexive
nonnegative numbers
logarithmic equation
Algebraic equation
38. A + b = b + a
A functional equation
Abstract algebra
Reflexive relation
commutative law of Addition
39. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
radical equation
Universal algebra
Algebraic equation
identity element of Exponentiation
40. Referring to the finite number of arguments (the value k)
Operations can involve dissimilar objects
then ac < bc
the set Y
finitary operation
41. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
A functional equation
The relation of equality (=)
Reflexive relation
the set Y
42. The values combined are called
operands - arguments - or inputs
value - result - or output
scalar
symmetric
43. 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.
Operations on functions
Reflexive relation
Knowns
Change of variables
44. 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'.
Associative law of Exponentiation
nonnegative numbers
Reflexive relation
A binary relation R over a set X is symmetric
45. Is an action or procedure which produces a new value from one or more input values.
commutative law of Exponentiation
Algebra
an operation
substitution
46. Is Written as a + b
Categories of Algebra
The simplest equations to solve
Addition
range
47. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
A Diophantine equation
Order of Operations
Constants
associative law of addition
48. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Conditional equations
A binary relation R over a set X is symmetric
The simplest equations to solve
Real number
49. If a = b then b = a
symmetric
operation
The relation of equality (=)
Abstract algebra
50. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
All quadratic equations
Algebraic number theory
Addition
An operation ?