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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
equation
finitary operation
A binary relation R over a set X is symmetric
Algebraic number theory
2. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
Algebraic equation
the fixed non-negative integer k (the number of arguments)
Number line or real line
3. 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 addition
Difference of two squares - or the difference of perfect squares
The operation of exponentiation
Properties of equality
4. 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 relation of equality (=) has the property
Elementary algebra
then bc < ac
Expressions
5. May not be defined for every possible value.
Constants
Reunion of broken parts
Repeated addition
Operations
6. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
identity element of Exponentiation
Linear algebra
Elimination method
7. Applies abstract algebra to the problems of geometry
Algebraic geometry
Reunion of broken parts
The relation of equality (=) has the property
k-ary operation
8. The operation of multiplication means _______________: a
Repeated addition
A transcendental equation
The relation of equality (=) has the property
Knowns
9. Is Written as a + b
The relation of equality (=)
Addition
Identity
A functional equation
10. There are two common types of operations:
The simplest equations to solve
inverse operation of addition
when b > 0
unary and binary
11. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
The operation of exponentiation
Multiplication
Solving the Equation
12. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Identity
Difference of two squares - or the difference of perfect squares
Algebraic combinatorics
The logical values true and false
13. 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
Exponentiation
transitive
identity element of Exponentiation
The method of equating the coefficients
14. Means repeated addition of ones: a + n = a + 1 + 1 +...+ 1 (n number of times) - has an inverse operation called subtraction: (a + b) - b = a - which is the same as adding a negative number - a - b = a + (-b)
The operation of addition
has arity two
The logical values true and false
Addition
15. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Operations on functions
Unknowns
Pure mathematics
when b > 0
16. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
Algebraic equation
(k+1)-ary relation that is functional on its first k domains
Equations
17. If a = b and b = c then a = c
(k+1)-ary relation that is functional on its first k domains
reflexive
transitive
Solution to the system
18. A unary operation
an operation
Equations
The relation of inequality (<) has this property
has arity one
19. Is an equation of the form log`a^X = b for a > 0 - which has solution
then a < c
All quadratic equations
Operations can involve dissimilar objects
logarithmic equation
20. Is an action or procedure which produces a new value from one or more input values.
Knowns
(k+1)-ary relation that is functional on its first k domains
an operation
unary and binary
21. If a < b and c < d
Addition
logarithmic equation
then a + c < b + d
Quadratic equations can also be solved
22. Are true for only some values of the involved variables: x2 - 1 = 4.
An operation ?
A polynomial equation
Reunion of broken parts
Conditional equations
23. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Expressions
value - result - or output
Equations
A differential equation
24. Is an equation involving derivatives.
inverse operation of addition
The relation of inequality (<) has this property
Repeated multiplication
A differential equation
25. The values of the variables which make the equation true are the solutions of the equation and can be found through
transitive
Equation Solving
Elementary algebra
Quadratic equations can also be solved
26. Is to add - subtract - multiply - or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated - the other side of the equation is the value of the variable.
The central technique to linear equations
reflexive
Constants
value - result - or output
27. () 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.
Knowns
The relation of equality (=)
The sets Xk
Algebra
28. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
The operation of addition
exponential equation
Pure mathematics
29. Not commutative a^b?b^a
A integral equation
The purpose of using variables
system of linear equations
commutative law of Exponentiation
30. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
two inputs
Identity
range
A functional equation
31. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Solution to the system
The relation of equality (=)
Binary operations
has arity two
32. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Constants
A differential equation
A solution or root of the equation
unary and binary
33. In which abstract algebraic methods are used to study combinatorial questions.
then a + c < b + d
Algebraic combinatorics
The operation of addition
reflexive
34. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Reflexive relation
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 relation of equality (=)
two inputs
35. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
nonnegative numbers
The relation of equality (=)
identity element of Exponentiation
36. If a < b and c > 0
then ac < bc
scalar
two inputs
The simplest equations to solve
37. Subtraction ( - )
inverse operation of addition
Difference of two squares - or the difference of perfect squares
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.
Operations on functions
38. If it holds for all a and b in X that if a is related to b then b is related to a.
symmetric
Unknowns
A binary relation R over a set X is symmetric
commutative law of Exponentiation
39. Will have two solutions in the complex number system - but need not have any in the real number system.
Real number
Reflexive relation
transitive
All quadratic equations
40. A vector can be multiplied by a scalar to form another vector
Algebraic geometry
symmetric
Operations can involve dissimilar objects
A binary relation R over a set X is symmetric
41. 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
k-ary operation
Reunion of broken parts
Quadratic equations
Categories of Algebra
42. Is an equation where the unknowns are required to be integers.
logarithmic 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.
The method of equating the coefficients
A Diophantine equation
43. 1 - which preserves numbers: a^1 = a
Reunion of broken parts
The simplest equations to solve
identity element of Exponentiation
The central technique to linear equations
44. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Change of variables
value - result - or output
Quadratic equations can also be solved
range
45. An operation of arity zero is simply an element of the codomain Y - called a
the fixed non-negative integer k (the number of arguments)
associative law of addition
operation
nullary operation
46. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Identity
nonnegative numbers
finitary operation
equation
47. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Knowns
Linear algebra
Algebraic equation
Expressions
48. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
The central technique to linear equations
An operation ?
The simplest equations to solve
Elementary algebra
49. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
then bc < ac
scalar
range
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.
50. 1 - which preserves numbers: a
Identity element of Multiplication
Rotations
Associative law of Multiplication
The relation of equality (=)'s property