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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. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
equation
value - result - or output
Variables
Operations can involve dissimilar objects
2. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Exponentiation
inverse operation of addition
Pure mathematics
The central technique to linear equations
3. 1 - which preserves numbers: a
operation
Identity element of Multiplication
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.
an operation
4. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
The method of equating the coefficients
Binary operations
k-ary operation
5. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
transitive
Categories of Algebra
identity element of Exponentiation
The purpose of using variables
6. The values for which an operation is defined form a set called its
inverse operation of Multiplication
domain
Algebraic geometry
Change of variables
7. Is the claim that two expressions have the same value and are equal.
The operation of addition
the set Y
Identity
Equations
8. In an equation with a single unknown - a value of that unknown for which the equation is true is called
commutative law of Addition
A solution or root of the equation
Change of variables
Algebraic combinatorics
9. Can be defined axiomatically up to an isomorphism
Solving the Equation
The real number system
Vectors
A linear equation
10. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
Elementary algebra
Identity element of Multiplication
has arity one
11. In which the specific properties of vector spaces are studied (including matrices)
Conditional equations
Linear algebra
The real number system
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.
12. The operation of exponentiation means ________________: a^n = a
The sets Xk
Repeated multiplication
Reunion of broken parts
Exponentiation
13. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
unary and binary
Difference of two squares - or the difference of perfect squares
The sets Xk
then ac < bc
14. The value produced is called
inverse operation of addition
value - result - or output
A integral equation
then bc < ac
15. 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
A solution or root of the equation
operands - arguments - or inputs
reflexive
16. Is an equation where the unknowns are required to be integers.
Associative law of Multiplication
Pure mathematics
A Diophantine equation
inverse operation of Exponentiation
17. Is Written as a + b
Rotations
Real number
the set Y
Addition
18. 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
Real number
has arity two
operation
The method of equating the coefficients
19. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
Linear algebra
inverse operation of Multiplication
commutative law of Exponentiation
20. 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
Reunion of broken parts
Equations
A integral equation
nonnegative numbers
21. Is an action or procedure which produces a new value from one or more input values.
Associative law of Multiplication
when b > 0
an operation
A differential equation
22. 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'.
Reflexive relation
The simplest equations to solve
Algebraic combinatorics
symmetric
23. In which properties common to all algebraic structures are studied
Universal algebra
A solution or root of the equation
the fixed non-negative integer k (the number of arguments)
range
24. An operation of arity zero is simply an element of the codomain Y - called a
An operation ?
Order of Operations
Quadratic equations
nullary operation
25. A unary operation
Knowns
has arity one
finitary operation
Difference of two squares - or the difference of perfect squares
26. A + b = b + a
commutative law of Addition
Equation Solving
radical equation
Identities
27. Involve only one value - such as negation and trigonometric functions.
Reflexive relation
Unary operations
commutative law of Exponentiation
Order of Operations
28. 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)
Solving the Equation
operation
commutative law of Multiplication
associative law of addition
29. Subtraction ( - )
Elementary algebra
inverse operation of addition
The relation of equality (=)'s property
The central technique to linear equations
30. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
operation
transitive
radical equation
31. 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.
(k+1)-ary relation that is functional on its first k domains
Polynomials
commutative law of Addition
Change of variables
32. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
The simplest equations to solve
then a + c < b + d
Associative law of Multiplication
Algebraic combinatorics
33. If a < b and c > 0
Quadratic equations
Repeated addition
The logical values true and false
then ac < bc
34. The values of the variables which make the equation true are the solutions of the equation and can be found through
has arity two
Equation Solving
Operations on sets
The method of equating the coefficients
35. k-ary operation is a
then a < c
(k+1)-ary relation that is functional on its first k domains
nullary operation
Equations
36. In which abstract algebraic methods are used to study combinatorial questions.
k-ary operation
nullary operation
scalar
Algebraic combinatorics
37. Applies abstract algebra to the problems of geometry
Quadratic equations can also be solved
Algebraic geometry
A differential equation
Vectors
38. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
A integral equation
Associative law of Multiplication
Reflexive relation
39. Is an equation involving integrals.
A integral equation
substitution
Change of variables
Identities
40. If a < b and b < c
Reflexive relation
operation
Solution to the system
then a < c
41. The operation of multiplication means _______________: a
Repeated addition
the set Y
Quadratic equations can also be solved
Unknowns
42. An operation of arity k is called a
when b > 0
range
k-ary operation
The real number system
43. If a < b and c < 0
exponential equation
then bc < ac
Rotations
Identity element of Multiplication
44. The values combined are called
operands - arguments - or inputs
Polynomials
range
The operation of addition
45. 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.
Algebra
The relation of equality (=) has the property
Operations on sets
A solution or root of the equation
46. Referring to the finite number of arguments (the value k)
Identity
Solution to the system
Multiplication
finitary operation
47. 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 exponentiation
Repeated addition
Equation Solving
then ac < bc
48. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
the fixed non-negative integer k (the number of arguments)
Algebraic equation
Quadratic equations
nonnegative numbers
49. May not be defined for every possible value.
Properties of equality
The simplest equations to solve
Operations
Linear algebra
50. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Quadratic equations can also be solved
Unary operations
Abstract algebra
Multiplication