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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. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
the fixed non-negative integer k (the number of arguments)
then a + c < b + d
Exponentiation
Algebraic number theory
2. Can be added and subtracted.
The sets Xk
A differential equation
Multiplication
Vectors
3. There are two common types of operations:
Real number
unary and binary
Repeated addition
Equations
4. Applies abstract algebra to the problems of geometry
inverse operation of Multiplication
Algebraic geometry
The relation of equality (=)
unary and binary
5. The squaring operation only produces
The relation of equality (=) has the property
Operations can involve dissimilar objects
Algebra
nonnegative numbers
6. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
All quadratic equations
has arity two
scalar
Identities
7. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
Quadratic equations
Operations on sets
Associative law of Exponentiation
8. If a < b and c > 0
Exponentiation
A solution or root of the equation
then ac < bc
Operations
9. Can be defined axiomatically up to an isomorphism
The real number system
identity element of Exponentiation
Algebraic equation
A differential equation
10. 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.
11. Subtraction ( - )
value - result - or output
inverse operation of addition
A integral equation
has arity two
12. 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
transitive
Solution to the system
identity element of Exponentiation
The method of equating the coefficients
13. () 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.
Algebraic number theory
Algebra
exponential equation
Operations can involve dissimilar objects
14. The values for which an operation is defined form a set called its
domain
Operations on sets
The central technique to linear equations
symmetric
15. 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)
operation
an operation
Rotations
Change of variables
16. In which the specific properties of vector spaces are studied (including matrices)
Exponentiation
Linear algebra
Pure mathematics
Elimination method
17. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Abstract algebra
Quadratic equations can also be solved
The relation of equality (=)
Operations on sets
18. If a < b and c < 0
then bc < ac
commutative law of Exponentiation
scalar
Equations
19. In which abstract algebraic methods are used to study combinatorial questions.
A differential equation
operation
Algebraic combinatorics
Binary operations
20. That 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.
radical equation
The relation of equality (=) has the property
Knowns
Variables
21. The operation of exponentiation means ________________: a^n = a
Properties of equality
Repeated multiplication
Operations
exponential equation
22. In an equation with a single unknown - a value of that unknown for which the equation is true is called
A solution or root of the equation
Identity element of Multiplication
An operation ?
Quadratic equations
23. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
A linear equation
inverse operation of Multiplication
Reflexive relation
24. Is an equation involving derivatives.
nullary operation
two inputs
The relation of inequality (<) has this property
A differential equation
25. The codomain is the set of real numbers but the range is the
nonnegative numbers
Identity
The relation of equality (=) has the property
Algebraic equation
26. If a = b then b = a
has arity one
symmetric
Reunion of broken parts
Variables
27. 0 - which preserves numbers: a + 0 = a
A binary relation R over a set X is symmetric
identity element of addition
Vectors
Equations
28. 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
An operation ?
operands - arguments - or inputs
inverse operation of addition
29. A + b = b + a
inverse operation of Exponentiation
then ac < bc
Operations
commutative law of Addition
30. Are true for only some values of the involved variables: x2 - 1 = 4.
nonnegative numbers
inverse operation of addition
Elimination method
Conditional equations
31. 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'.
Real number
An operation ?
Reflexive relation
finitary operation
32. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
inverse operation of addition
value - result - or output
Identity element of Multiplication
Difference of two squares - or the difference of perfect squares
33. 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 linear equation
Associative law of Exponentiation
Reunion of broken parts
Quadratic equations
34. Division ( / )
Solution to the system
Conditional equations
inverse operation of Exponentiation
inverse operation of Multiplication
35. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
radical equation
Binary operations
Identity
equation
36. Can be combined using the function composition operation - performing the first rotation and then the second.
A Diophantine equation
Rotations
(k+1)-ary relation that is functional on its first k domains
k-ary operation
37. Is called the type or arity of the operation
The operation of exponentiation
scalar
the fixed non-negative integer k (the number of arguments)
operands - arguments - or inputs
38. Can be combined using logic operations - such as and - or - and not.
Algebraic 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.
Addition
The logical values true and false
39. Are called the domains of the operation
The sets Xk
A polynomial equation
unary and binary
A binary relation R over a set X is symmetric
40. Include the binary operations union and intersection and the unary operation of complementation.
nonnegative numbers
Abstract algebra
equation
Operations on sets
41. If it holds for all a and b in X that if a is related to b then b is related to a.
The relation of equality (=)
when b > 0
A binary relation R over a set X is symmetric
then a < c
42. Not associative
Elimination method
inverse operation of addition
Associative law of Exponentiation
Operations on functions
43. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
The relation of inequality (<) has this property
operation
commutative law of Multiplication
Abstract algebra
44. Are denoted by letters at the beginning - a - b - c - d - ...
Pure mathematics
Knowns
Elementary algebra
Unary operations
45. Is the claim that two expressions have the same value and are equal.
Variables
Polynomials
Equation Solving
Equations
46. Is an equation in which the unknowns are functions rather than simple quantities.
Solution to the system
Binary operations
identity element of addition
A functional equation
47. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
The relation of equality (=) has the property
equation
The simplest equations to solve
Variables
48. The operation of multiplication means _______________: a
the set Y
Repeated addition
Change of variables
radical equation
49. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
Quadratic equations
Operations
Reunion of broken parts
50. k-ary operation is a
(k+1)-ary relation that is functional on its first k domains
operands - arguments - or inputs
The method of equating the coefficients
Operations can involve dissimilar objects