SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
Search
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
Operations on sets
nullary operation
Difference of two squares - or the difference of perfect squares
Quadratic equations can also be solved
2. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Knowns
A solution or root of the equation
then bc < ac
Operations can involve dissimilar objects
3. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Repeated addition
nonnegative numbers
identity element of addition
Abstract algebra
4. 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)
Solving the Equation
The operation of exponentiation
Operations on functions
The relation of equality (=) has the property
5. 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).
equation
Quadratic equations
has arity two
finitary operation
6. If a < b and b < c
An operation ?
A binary relation R over a set X is symmetric
Number line or real line
then a < c
7. Is Written as a
has arity one
when b > 0
finitary operation
Multiplication
8. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
Solving the Equation
has arity one
Categories of Algebra
9. The squaring operation only produces
(k+1)-ary relation that is functional on its first k domains
Repeated multiplication
nonnegative numbers
Quadratic equations can also be solved
10. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
Operations can involve dissimilar objects
nullary operation
The operation of addition
11. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Difference of two squares - or the difference of perfect squares
Reflexive relation
has arity two
Operations on sets
12. 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
Quadratic equations can also be solved
Elementary algebra
Equation Solving
Repeated addition
13. The values for which an operation is defined form a set called its
domain
The relation of equality (=) has the property
The logical values true and false
Solution to the system
14. Is an equation involving derivatives.
A differential equation
value - result - or output
A transcendental equation
operands - arguments - or inputs
15. 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
Rotations
An operation ?
substitution
then ac < bc
16. The operation of multiplication means _______________: a
Repeated 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.
Equation Solving
has arity one
17. 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).
Categories of Algebra
then ac < bc
Repeated addition
operation
18. Not associative
Associative law of Exponentiation
Algebraic combinatorics
commutative law of Exponentiation
The relation of equality (=)'s property
19. 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
exponential equation
The central technique to linear equations
two inputs
Reunion of broken parts
20. 0 - which preserves numbers: a + 0 = a
A functional equation
identity element of addition
The real number system
Identity element of Multiplication
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)
domain
operation
The logical values true and false
Equation Solving
22. Is an action or procedure which produces a new value from one or more input values.
Knowns
Algebraic number theory
an operation
then bc < ac
23. 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.
Order of Operations
The central technique to linear equations
Unknowns
then bc < ac
24. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
then ac < bc
Abstract algebra
substitution
25. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Binary operations
The purpose of using variables
Rotations
transitive
26. The values combined are called
Polynomials
operands - arguments - or inputs
Number line or real line
finitary operation
27. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
Reunion of broken parts
Reflexive relation
identity element of Exponentiation
28. k-ary operation is a
(k+1)-ary relation that is functional on its first k domains
Equations
A polynomial equation
Expressions
29. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
A transcendental equation
Change of variables
Pure mathematics
then ac < bc
30. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Addition
Knowns
Exponentiation
equation
31. Include composition and convolution
(k+1)-ary relation that is functional on its first k domains
Operations on functions
The operation of addition
A functional equation
32. In which abstract algebraic methods are used to study combinatorial questions.
Unary operations
Algebraic combinatorics
A differential equation
the fixed non-negative integer k (the number of arguments)
33. 1 - which preserves numbers: a
the set Y
Identity element of Multiplication
Operations on functions
Operations can involve dissimilar objects
34. Is an equation of the form X^m/n = a - for m - n integers - which has solution
has arity two
A polynomial equation
radical equation
A solution or root of the equation
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.
Real number
Change of variables
Variables
Linear algebra
36. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebraic equation
domain
The simplest equations to solve
Algebraic number theory
37. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
A Diophantine equation
Number line or real line
(k+1)-ary relation that is functional on its first k domains
A solution or root of the equation
38. If a < b and c < d
commutative law of Multiplication
unary and binary
inverse operation of Multiplication
then a + c < b + d
39. If a < b and c > 0
The purpose of using variables
Identity
Linear algebra
then ac < bc
40. Subtraction ( - )
The operation of addition
Linear algebra
An operation ?
inverse operation of addition
41. A
The method of equating the coefficients
An operation ?
A Diophantine equation
commutative law of Multiplication
42. Is a function of the form ? : V ? Y - where V ? X1
operation
exponential equation
Variables
An operation ?
43. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Elementary algebra
The relation of equality (=)
range
Associative law of Exponentiation
44. A + b = b + a
Variables
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.
nonnegative numbers
commutative law of Addition
45. If a = b and b = c then a = c
A integral equation
transitive
Repeated multiplication
The purpose of using variables
46. Is the claim that two expressions have the same value and are equal.
Equations
nullary operation
The operation of exponentiation
operands - arguments - or inputs
47. The codomain is the set of real numbers but the range is the
Solving the Equation
Elimination method
finitary operation
nonnegative numbers
48. Is an algebraic 'sentence' containing an unknown quantity.
scalar
finitary operation
Polynomials
inverse operation of addition
49. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
The simplest equations to solve
Variables
A functional equation
50. Not commutative a^b?b^a
Universal algebra
commutative law of Exponentiation
A functional equation
Conditional equations