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Test your basic knowledge |
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. Is an algebraic 'sentence' containing an unknown quantity.
A functional equation
operation
system of linear equations
Polynomials
2. Is an equation in which a polynomial is set equal to another polynomial.
Associative law of Multiplication
A polynomial equation
Properties of equality
identity element of Exponentiation
3. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
Identities
The central technique to linear equations
Expressions
4. Can be combined using the function composition operation - performing the first rotation and then the second.
Difference of two squares - or the difference of perfect squares
Rotations
inverse operation of Exponentiation
The operation of exponentiation
5. If a < b and c < d
A binary relation R over a set X is symmetric
A integral equation
then a + c < b + d
Number line or real line
6. Applies abstract algebra to the problems of geometry
Algebraic geometry
Abstract algebra
nonnegative numbers
Vectors
7. Is Written as a
(k+1)-ary relation that is functional on its first k domains
The operation of exponentiation
Exponentiation
Multiplication
8. Can be combined using logic operations - such as and - or - and not.
then ac < bc
Categories of Algebra
An operation ?
The logical values true and false
9. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
The method of equating the coefficients
Expressions
then a < c
10. An operation of arity zero is simply an element of the codomain Y - called a
Rotations
All quadratic equations
Multiplication
nullary operation
11. May not be defined for every possible value.
Operations
Operations on functions
exponential equation
Real number
12. Is Written as ab or a^b
The relation of equality (=)'s property
Constants
Elementary algebra
Exponentiation
13. 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
A functional equation
exponential equation
Operations on functions
Reunion of broken parts
14. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Algebraic geometry
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.
radical equation
Repeated addition
15. The value produced is called
logarithmic equation
symmetric
value - result - or output
Vectors
16. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Pure mathematics
equation
k-ary operation
two inputs
17. Not commutative a^b?b^a
commutative law of Exponentiation
(k+1)-ary relation that is functional on its first k domains
range
Pure mathematics
18. () 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.
the set Y
Exponentiation
Algebra
The operation of addition
19. Is called the codomain of the operation
Reunion of broken parts
the set Y
k-ary operation
The relation of inequality (<) has this property
20. The squaring operation only produces
symmetric
transitive
an operation
nonnegative numbers
21. The values for which an operation is defined form a set called its
Elementary algebra
reflexive
domain
The real number system
22. Are true for only some values of the involved variables: x2 - 1 = 4.
Algebraic equation
Unknowns
Conditional equations
Polynomials
23. Involve only one value - such as negation and trigonometric functions.
A polynomial equation
Linear algebra
Identities
Unary operations
24. Can be defined axiomatically up to an isomorphism
radical equation
The real number system
Categories of Algebra
Quadratic equations
25. A binary operation
has arity one
Rotations
Solving the Equation
has arity two
26. If a = b and c = d then a + c = b + d and ac = bd; that if a = b then a + c = b + c; that if two symbols are equal - then one can be substituted for the other.
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27. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
Reflexive relation
Multiplication
scalar
28. 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.
The relation of inequality (<) has this property
A functional equation
Linear algebra
domain
29. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
when b > 0
Difference of two squares - or the difference of perfect squares
Associative law of Exponentiation
30. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic number theory
Algebraic combinatorics
Operations on sets
transitive
31. In which properties common to all algebraic structures are studied
inverse operation of Exponentiation
then ac < bc
Universal algebra
nonnegative numbers
32. 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
value - result - or output
The central technique to linear equations
inverse operation of addition
substitution
33. Is an equation of the form aX = b for a > 0 - which has solution
Identity element of Multiplication
Vectors
reflexive
exponential equation
34. Subtraction ( - )
A binary relation R over a set X is symmetric
Unknowns
inverse operation of addition
Equation Solving
35. Include the binary operations union and intersection and the unary operation of complementation.
A functional equation
Operations on sets
Number line or real line
The method of equating the coefficients
36. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
Algebraic geometry
Polynomials
finitary operation
37. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
has arity one
then a + c < b + d
A binary relation R over a set X is symmetric
Variables
38. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
inverse operation of Exponentiation
Operations on sets
All quadratic equations
39. Is an action or procedure which produces a new value from one or more input values.
range
Binary operations
an operation
the set Y
40. A
The sets Xk
commutative law of Addition
Associative law of Exponentiation
commutative law of Multiplication
41. The values combined are called
operands - arguments - or inputs
Order of Operations
Linear algebra
A functional equation
42. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Algebraic number theory
radical equation
Solution to the system
A functional equation
43. (a + b) + c = a + (b + c)
k-ary operation
associative law of addition
an operation
system of linear equations
44. Is an equation involving integrals.
The purpose of using variables
A integral equation
operands - arguments - or inputs
then ac < bc
45. Include composition and convolution
commutative law of Addition
Operations on functions
Knowns
finitary operation
46. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
nonnegative numbers
Algebraic equation
Change of variables
has arity two
47. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Pure mathematics
Repeated addition
The simplest equations to solve
The relation of equality (=)'s property
48. If a < b and c < 0
The method of equating the coefficients
Algebraic number theory
then bc < ac
Operations on sets
49. Is called the type or arity of the operation
commutative law of Multiplication
substitution
the fixed non-negative integer k (the number of arguments)
Universal algebra
50. Is an equation involving derivatives.
transitive
The logical values true and false
A differential equation
Algebraic number theory