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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. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Algebraic equation
A differential equation
Solution to the system
(k+1)-ary relation that is functional on its first k domains
2. Can be combined using the function composition operation - performing the first rotation and then the second.
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.
two inputs
Rotations
inverse operation of addition
3. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
The relation of equality (=)
Identities
Elementary algebra
operands - arguments - or inputs
4. Is Written as ab or a^b
Exponentiation
A binary relation R over a set X is symmetric
Reunion of broken parts
Universal algebra
5. Applies abstract algebra to the problems of geometry
then bc < ac
Order of Operations
symmetric
Algebraic geometry
6. A + b = b + a
Solving the Equation
commutative law of Addition
Unknowns
nullary operation
7. In which abstract algebraic methods are used to study combinatorial questions.
The relation of inequality (<) has this property
An operation ?
Algebraic geometry
Algebraic combinatorics
8. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
system of linear equations
operation
The relation of equality (=)'s property
Abstract algebra
9. Subtraction ( - )
Addition
logarithmic equation
Properties of equality
inverse operation of addition
10. 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.
operation
operands - arguments - or inputs
The relation of inequality (<) has this property
Algebraic equation
11. Division ( / )
inverse operation of Multiplication
Constants
identity element of Exponentiation
Change of variables
12. The value produced is called
value - result - or output
Quadratic equations can also be solved
Binary operations
Operations can involve dissimilar objects
13. Are called the domains of the operation
A differential equation
The logical values true and false
The sets Xk
Algebraic combinatorics
14. Operations can have fewer or more than
Elimination method
Associative law of Multiplication
two inputs
Quadratic equations can also be solved
15. (a
Equations
Associative law of Multiplication
two inputs
Variables
16. Is an equation involving integrals.
associative law of addition
A integral equation
when b > 0
Binary operations
17. 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
Reunion of broken parts
Operations on sets
when b > 0
inverse operation of addition
18. k-ary operation is a
Reflexive relation
Vectors
(k+1)-ary relation that is functional on its first k domains
operands - arguments - or inputs
19. A vector can be multiplied by a scalar to form another vector
value - result - or output
Operations can involve dissimilar objects
Equation Solving
range
20. Is Written as a
Multiplication
Equations
Order of Operations
Real number
21. There are two common types of operations:
unary and binary
Addition
Identity element of Multiplication
The relation of equality (=) has the property
22. Is an equation in which the unknowns are functions rather than simple quantities.
Elementary algebra
Elimination method
Conditional equations
A functional equation
23. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
an operation
then a < c
The simplest equations to solve
24. Means repeated addition of ones: a + n = a + 1 + 1 +...+ 1 (n number of times) - has an inverse operation called subtraction: (a + b) - b = a - which is the same as adding a negative number - a - b = a + (-b)
Solving the Equation
commutative law of Multiplication
The operation of addition
inverse operation of Multiplication
25. Will have two solutions in the complex number system - but need not have any in the real number system.
A transcendental equation
An operation ?
substitution
All quadratic equations
26. Not associative
Associative law of Exponentiation
The operation of addition
then bc < ac
k-ary operation
27. The operation of multiplication means _______________: a
range
operation
scalar
Repeated addition
28. Is an action or procedure which produces a new value from one or more input values.
an operation
Quadratic equations
Knowns
range
29. 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)
Vectors
Unknowns
The operation of exponentiation
Associative law of Exponentiation
30. If a < b and c > 0
Universal algebra
Equations
Unknowns
then ac < bc
31. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
then ac < bc
A functional equation
Algebraic combinatorics
32. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
Elementary algebra
value - result - or output
Addition
33. Is an algebraic 'sentence' containing an unknown quantity.
domain
Universal algebra
finitary operation
Polynomials
34. Involve only one value - such as negation and trigonometric functions.
Unary operations
reflexive
the fixed non-negative integer k (the number of arguments)
A Diophantine equation
35. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Linear algebra
domain
The central technique to linear equations
system of linear equations
36. b = b
The logical values true and false
A polynomial equation
Conditional equations
reflexive
37. Symbols that denote numbers - is to allow the making of generalizations in mathematics
then a < c
The purpose of using variables
scalar
Categories of Algebra
38. Are true for only some values of the involved variables: x2 - 1 = 4.
Exponentiation
The simplest equations to solve
Conditional equations
Associative law of Multiplication
39. Is called the type or arity of the operation
logarithmic equation
Solution to the system
the fixed non-negative integer k (the number of arguments)
operation
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
substitution
A differential equation
associative law of addition
Quadratic equations can also be solved
41. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
An operation ?
Order of Operations
Variables
A Diophantine equation
42. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
two inputs
substitution
identity element of Exponentiation
Algebraic equation
43. Referring to the finite number of arguments (the value k)
Rotations
A solution or root of the equation
finitary operation
Identities
44. 0 - which preserves numbers: a + 0 = a
Operations can involve dissimilar objects
Real number
A polynomial equation
identity element of addition
45. 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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46. If a = b and b = c then a = c
equation
transitive
The real number system
nonnegative numbers
47. If a < b and c < 0
Categories of Algebra
Linear algebra
then bc < ac
The relation of inequality (<) has this property
48. 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
radical equation
Universal algebra
k-ary operation
Real number
49. 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).
nonnegative numbers
The method of equating the coefficients
Change of variables
operation
50. If a = b then b = a
symmetric
exponential equation
Algebraic number theory
Expressions
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