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CLEP College Algebra: Algebra Principles
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Subjects
:
clep
,
math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
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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. 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
inverse operation of addition
value - result - or output
has arity one
2. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
A transcendental equation
Operations on functions
Properties of equality
3. 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.
Quadratic equations
Identity
Associative law of Multiplication
The central technique to linear equations
4. Is the claim that two expressions have the same value and are equal.
operands - arguments - or inputs
Equations
Algebraic combinatorics
The operation of addition
5. The squaring operation only produces
nonnegative numbers
Associative law of Exponentiation
Universal algebra
Vectors
6. If a = b and b = c then a = c
transitive
reflexive
Order of Operations
associative law of addition
7. Are denoted by letters at the beginning - a - b - c - d - ...
Elementary algebra
Knowns
Unary operations
when b > 0
8. 1 - which preserves numbers: a^1 = a
unary and binary
identity element of Exponentiation
Number line or real line
Algebraic combinatorics
9. Can be combined using the function composition operation - performing the first rotation and then the second.
Algebraic equation
Rotations
A Diophantine equation
An operation ?
10. If a < b and c < 0
has arity one
Identities
system of linear equations
then bc < ac
11. Is algebraic equation of degree one
identity element of addition
logarithmic equation
Identity
A linear equation
12. In which properties common to all algebraic structures are studied
Associative law of Exponentiation
Elementary algebra
Universal algebra
operation
13. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
The central technique to linear equations
k-ary operation
Expressions
14. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
equation
Properties of equality
unary and binary
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
Equations
commutative law of Addition
Algebraic combinatorics
substitution
16. In an equation with a single unknown - a value of that unknown for which the equation is true is called
has arity one
the fixed non-negative integer k (the number of arguments)
A solution or root of the equation
Categories of Algebra
17. The values for which an operation is defined form a set called its
nonnegative numbers
the set Y
system of linear equations
domain
18. Is an equation involving derivatives.
A differential equation
Abstract algebra
The method of equating the coefficients
All quadratic equations
19. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
A differential equation
Associative law of Exponentiation
Solution to the system
Number line or real line
20. A + b = b + a
commutative law of Addition
Algebra
Order of Operations
The purpose of using variables
21. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
the fixed non-negative integer k (the number of arguments)
Order of Operations
range
Expressions
22. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
Unary operations
Variables
Equation Solving
23. 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
then bc < ac
symmetric
inverse operation of Multiplication
24. 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
Identity element of Multiplication
inverse operation of Multiplication
reflexive
25. If a < b and b < c
Equation Solving
then a < c
The relation of inequality (<) has this property
Linear algebra
26. Subtraction ( - )
Order of Operations
Identity element of Multiplication
logarithmic equation
inverse operation of addition
27. Operations can have fewer or more than
an operation
two inputs
system of linear equations
Binary operations
28. Is an algebraic 'sentence' containing an unknown quantity.
has arity two
nullary operation
Polynomials
A Diophantine equation
29. A vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
The relation of inequality (<) has this property
A binary relation R over a set X is symmetric
Order of Operations
30. b = b
The simplest equations to solve
reflexive
A solution or root of the equation
logarithmic 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.
finitary operation
Change of variables
The operation of addition
Algebraic combinatorics
32. Not associative
inverse operation of Exponentiation
Reflexive relation
Algebraic number theory
Associative law of Exponentiation
33. If it holds for all a and b in X that if a is related to b then b is related to a.
Reflexive relation
The operation of addition
The purpose of using variables
A binary relation R over a set X is symmetric
34. Is an equation in which the unknowns are functions rather than simple quantities.
an operation
operands - arguments - or inputs
Variables
A functional equation
35. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
The operation of addition
Number line or real line
has arity two
Operations on sets
36. 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.
The relation of equality (=) has the property
A binary relation R over a set X is symmetric
then ac < bc
The operation of addition
37. 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
Operations
identity element of addition
Elementary algebra
value - result - or output
38. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
nonnegative numbers
nullary operation
Quadratic equations can also be solved
39. Is Written as a + b
Addition
operation
Variables
The logical values true and false
40. Involve only one value - such as negation and trigonometric functions.
A transcendental equation
The relation of inequality (<) has this property
Unary operations
Operations on functions
41. 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
Quadratic equations
The logical values true and false
A transcendental equation
The method of equating the coefficients
42. In which abstract algebraic methods are used to study combinatorial questions.
Quadratic equations
A polynomial equation
Pure mathematics
Algebraic combinatorics
43. k-ary operation is a
then a < c
substitution
(k+1)-ary relation that is functional on its first k domains
The method of equating the coefficients
44. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
Multiplication
Associative law of Multiplication
The sets Xk
45. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Quadratic equations
Exponentiation
Universal algebra
Identity
46. Not commutative a^b?b^a
Equations
Equations
commutative law of Exponentiation
transitive
47. 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
k-ary operation
exponential equation
Conditional equations
48. Is an equation where the unknowns are required to be integers.
The central technique to linear equations
Solution to the system
A Diophantine equation
two inputs
49. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Categories of Algebra
Algebra
associative law of addition
The relation of equality (=)
50. An operation of arity k is called a
nullary operation
commutative law of Multiplication
k-ary operation
A binary relation R over a set X is symmetric
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