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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. If a < b and b < c
scalar
Multiplication
then a < c
A functional equation
2. In which abstract algebraic methods are used to study combinatorial questions.
Polynomials
Addition
Algebraic combinatorics
commutative law of Exponentiation
3. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Operations on sets
radical equation
inverse operation of Multiplication
The operation of addition
4. In an equation with a single unknown - a value of that unknown for which the equation is true is called
the fixed non-negative integer k (the number of arguments)
reflexive
A solution or root of the equation
has arity one
5. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
radical equation
Categories of Algebra
Linear algebra
6. The values combined are called
identity element of addition
Vectors
operands - arguments - or inputs
domain
7. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Unary operations
equation
Expressions
unary and binary
8. Operations can have fewer or more than
two inputs
Linear algebra
Identity element of Multiplication
Order of Operations
9. A vector can be multiplied by a scalar to form another vector
inverse operation of Exponentiation
logarithmic equation
Operations can involve dissimilar objects
A differential equation
10. If a = b then b = a
k-ary operation
substitution
symmetric
then bc < ac
11. An operation of arity zero is simply an element of the codomain Y - called a
inverse operation of Exponentiation
inverse operation of Multiplication
commutative law of Multiplication
nullary operation
12. Is an action or procedure which produces a new value from one or more input values.
then ac < bc
an operation
Algebraic number theory
equation
13. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
identity element of addition
Algebraic equation
Properties of equality
exponential equation
14. 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.
Properties of equality
equation
Associative law of Exponentiation
commutative law of Addition
15. Are true for only some values of the involved variables: x2 - 1 = 4.
Pure mathematics
Conditional equations
The logical values true and false
scalar
16. Include composition and convolution
The real number system
Unknowns
Operations on functions
Pure mathematics
17. Is Written as a
operation
A functional equation
Multiplication
unary and binary
18. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
The relation of inequality (<) has this property
Associative law of Exponentiation
A functional equation
19. A
commutative law of Multiplication
Identity
system of linear equations
Order of Operations
20. The codomain is the set of real numbers but the range is the
Associative law of Multiplication
then ac < bc
nonnegative numbers
value - result - or output
21. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
then ac < bc
A binary relation R over a set X is symmetric
Quadratic equations can also be solved
Elimination method
22. There are two common types of operations:
reflexive
Knowns
All quadratic equations
unary and binary
23. Subtraction ( - )
inverse operation of addition
Quadratic equations can also be solved
Algebraic equation
k-ary operation
24. 1 - which preserves numbers: a
Identity element of Multiplication
Categories of Algebra
The method of equating the coefficients
Algebraic combinatorics
25. Is an equation of the form aX = b for a > 0 - which has solution
Identity element of Multiplication
A polynomial equation
Exponentiation
exponential equation
26. The operation of multiplication means _______________: a
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.
Pure mathematics
Identity element of Multiplication
Repeated addition
27. 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 (=)
A Diophantine equation
The relation of inequality (<) has this property
28. Are denoted by letters at the beginning - a - b - c - d - ...
scalar
symmetric
commutative law of Multiplication
Knowns
29. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
equation
Variables
Equations
Algebra
30. Not associative
Categories of Algebra
Associative law of Exponentiation
Equations
A Diophantine equation
31. If it holds for all a and b in X that if a is related to b then b is related to a.
Constants
radical equation
symmetric
A binary relation R over a set X is symmetric
32. 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).
operation
A linear equation
Pure mathematics
unary and binary
33. Is an equation in which the unknowns are functions rather than simple quantities.
operation
A functional equation
Universal algebra
A integral equation
34. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Associative law of Exponentiation
Quadratic equations
Pure mathematics
Associative law of Multiplication
35. Is an equation of the form log`a^X = b for a > 0 - which has solution
A integral equation
Categories of Algebra
The purpose of using variables
logarithmic equation
36. In which the specific properties of vector spaces are studied (including matrices)
the set Y
Linear algebra
reflexive
operation
37. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
All quadratic equations
The logical values true and false
Associative law of Multiplication
Categories of Algebra
38. 1 - which preserves numbers: a^1 = a
A differential equation
identity element of Exponentiation
The relation of inequality (<) has this property
A binary relation R over a set X is symmetric
39. Is an equation where the unknowns are required to be integers.
Associative law of Multiplication
Rotations
Associative law of Exponentiation
A Diophantine equation
40. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that
equation
Real number
The relation of inequality (<) has this property
The sets Xk
41. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
Knowns
Exponentiation
Identity element of Multiplication
42. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
inverse operation of Exponentiation
Identities
Difference of two squares - or the difference of perfect squares
43. Is called the codomain of the operation
The relation of equality (=)'s property
the set Y
Identities
(k+1)-ary relation that is functional on its first k domains
44. Is Written as ab or a^b
Exponentiation
Equations
then a < c
nonnegative numbers
45. Is an equation involving derivatives.
A differential equation
Variables
Identities
Solution to the system
46. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
nonnegative numbers
Real number
A Diophantine equation
system of linear equations
47. In which properties common to all algebraic structures are studied
Algebraic number theory
A differential equation
Equation Solving
Universal algebra
48. (a
A solution or root of the equation
Associative law of Multiplication
The logical values true and false
commutative law of Addition
49. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
(k+1)-ary relation that is functional on its first k domains
finitary operation
range
50. Is a function of the form ? : V ? Y - where V ? X1
then a + c < b + d
k-ary operation
An operation ?
The relation of inequality (<) has this property