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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. Referring to the finite number of arguments (the value k)
finitary operation
A solution or root of the equation
Identities
All quadratic equations
2. Can be defined axiomatically up to an isomorphism
equation
then bc < ac
The real number system
Reunion of broken parts
3. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
scalar
has arity one
A linear equation
system of linear equations
4. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Equations
Algebraic equation
commutative law of Exponentiation
The simplest equations to solve
5. Can be combined using logic operations - such as and - or - and not.
inverse operation of Exponentiation
Associative law of Multiplication
The logical values true and false
Equation Solving
6. 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
Algebraic combinatorics
Solution to the system
Reunion of broken parts
A differential equation
7. If a = b and b = c then a = c
Associative law of Multiplication
Repeated multiplication
transitive
commutative law of Multiplication
8. 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
logarithmic equation
Identities
commutative law of Exponentiation
9. Is an action or procedure which produces a new value from one or more input values.
operation
an operation
Algebra
Elimination method
10. 0 - which preserves numbers: a + 0 = a
Reunion of broken parts
Equation Solving
Binary operations
identity element of addition
11. Operations can have fewer or more than
domain
Associative law of Exponentiation
two inputs
A functional equation
12. Applies abstract algebra to the problems of geometry
nullary operation
Algebraic geometry
Associative law of Multiplication
Order of Operations
13. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain
inverse operation of addition
A functional equation
The method of equating the coefficients
when b > 0
14. Will have two solutions in the complex number system - but need not have any in the real number system.
operands - arguments - or inputs
range
All quadratic equations
Repeated addition
15. A + b = b + a
operation
Algebraic equation
commutative law of Addition
Multiplication
16. If a < b and c < 0
The operation of addition
then bc < ac
Operations on functions
Elimination method
17. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
Elimination method
Associative law of Multiplication
Operations can involve dissimilar objects
18. If a < b and c < d
Identity element of Multiplication
then a + c < b + d
Operations can involve dissimilar objects
A differential equation
19. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
The logical values true and false
Change of variables
Binary operations
Real number
20. 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
Operations can involve dissimilar objects
inverse operation of Multiplication
logarithmic equation
21. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
operation
The method of equating the coefficients
The simplest equations to solve
22. 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
Multiplication
value - result - or output
Operations can involve dissimilar objects
23. Is the claim that two expressions have the same value and are equal.
Equations
Operations on functions
The sets Xk
commutative law of Addition
24. Is an equation involving derivatives.
exponential equation
A differential equation
Algebra
A functional equation
25. Logarithm (Log)
The relation of equality (=)'s property
Addition
domain
inverse operation of Exponentiation
26. Involve only one value - such as negation and trigonometric functions.
nonnegative numbers
associative law of addition
value - result - or output
Unary operations
27. 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
then bc < ac
Categories of Algebra
Algebra
28. Is Written as a + b
commutative law of Addition
Quadratic equations can also be solved
Addition
Operations
29. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
then bc < ac
Solving the Equation
Pure mathematics
30. The values for which an operation is defined form a set called its
domain
inverse operation of addition
Elimination method
A integral equation
31. The values combined are called
inverse operation of Multiplication
Algebraic equation
two inputs
operands - arguments - or inputs
32. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
Identity
The relation of equality (=)'s property
The purpose of using variables
33. Is an equation where the unknowns are required to be integers.
commutative law of Exponentiation
A Diophantine equation
exponential equation
Categories of Algebra
34. Is an equation of the form aX = b for a > 0 - which has solution
Abstract algebra
The simplest equations to solve
Algebra
exponential equation
35. Is an algebraic 'sentence' containing an unknown quantity.
then a < c
Polynomials
A integral equation
The real number system
36. There are two common types of operations:
unary and binary
Identities
an operation
Algebraic combinatorics
37. In which properties common to all algebraic structures are studied
Universal algebra
Conditional equations
finitary operation
Associative law of Exponentiation
38. The process of expressing the unknowns in terms of the knowns is called
symmetric
Reunion of broken parts
Solving the Equation
Repeated multiplication
39. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Change of variables
A solution or root of the equation
A integral equation
A transcendental equation
40. 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
The sets Xk
Change of variables
Solution to the system
substitution
41. Is an equation involving integrals.
A integral equation
nonnegative numbers
Equations
commutative law of Multiplication
42. The codomain is the set of real numbers but the range is the
then ac < bc
nullary operation
exponential equation
nonnegative numbers
43. The squaring operation only produces
An operation ?
Equation Solving
nonnegative numbers
commutative law of Exponentiation
44. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
Algebraic combinatorics
Properties of equality
identity element of addition
45. Are called the domains of the operation
The simplest equations to solve
The sets Xk
A transcendental equation
equation
46. Is called the type or arity of the operation
commutative law of Multiplication
Algebraic equation
the fixed non-negative integer k (the number of arguments)
has arity one
47. Is Written as ab or a^b
Unknowns
Algebraic combinatorics
Solving the Equation
Exponentiation
48. A unary operation
an operation
has arity one
Algebraic combinatorics
the fixed non-negative integer k (the number of arguments)
49. 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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50. 1 - which preserves numbers: a^1 = a
substitution
Associative law of Exponentiation
A transcendental equation
identity element of Exponentiation
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