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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. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Order of Operations
The purpose of using variables
inverse operation of Exponentiation
Identity
2. Can be added and subtracted.
(k+1)-ary relation that is functional on its first k domains
Vectors
A polynomial equation
The relation of inequality (<) has this property
3. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Exponentiation
commutative law of Exponentiation
Quadratic equations can also be solved
Real number
4. If an equation in algebra is known to be true - the following operations may be used to produce another true 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.
Expressions
Algebraic combinatorics
operation
5. Can be expressed in the form ax^2 + bx + c = 0 - where a is not zero (if it were zero - then the equation would not be quadratic but linear).
operation
Quadratic equations
A Diophantine equation
system of linear equations
6. Is an action or procedure which produces a new value from one or more input values.
Variables
Solution to the system
an operation
Exponentiation
7. Is an equation in which the unknowns are functions rather than simple quantities.
substitution
has arity one
Elementary algebra
A functional equation
8. Is Written as ab or a^b
Identity element of Multiplication
Repeated addition
operation
Exponentiation
9. 0 - which preserves numbers: a + 0 = a
identity element of addition
commutative law of Multiplication
Elimination method
Operations on functions
10. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
system of linear equations
The operation of addition
Associative law of Exponentiation
11. () 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.
Categories of Algebra
Algebra
Difference of two squares - or the difference of perfect squares
logarithmic equation
12. Is algebraic equation of degree one
finitary operation
A linear equation
has arity one
Categories of Algebra
13. Not commutative a^b?b^a
The purpose of using variables
An operation ?
Quadratic equations
commutative law of Exponentiation
14. Is an equation in which a polynomial is set equal to another polynomial.
Conditional equations
transitive
A polynomial equation
two inputs
15. The squaring operation only produces
nonnegative numbers
Order of Operations
system of linear equations
inverse operation of Multiplication
16. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
The operation of exponentiation
Reflexive relation
Identity
nonnegative numbers
17. (a + b) + c = a + (b + c)
identity element of Exponentiation
associative law of addition
Solving the Equation
reflexive
18. Is the claim that two expressions have the same value and are equal.
A integral equation
domain
Equations
Operations
19. 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.
inverse operation of addition
Elementary algebra
transitive
The relation of equality (=) has the property
20. Is called the codomain of the operation
Repeated multiplication
the set Y
transitive
equation
21. The inner product operation on two vectors produces a
associative law of addition
range
reflexive
scalar
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'.
Identity element of Multiplication
Reflexive relation
Linear algebra
Elimination method
23. In which the specific properties of vector spaces are studied (including matrices)
Identities
Linear algebra
has arity one
Associative law of Multiplication
24. A + b = b + a
commutative law of Addition
Exponentiation
then bc < ac
Constants
25. A vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
transitive
has arity one
Rotations
26. 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
Identities
substitution
Categories of Algebra
Identity
27. If a < b and c < 0
then bc < ac
A transcendental equation
exponential equation
A differential equation
28. In which abstract algebraic methods are used to study combinatorial questions.
exponential equation
Algebraic combinatorics
k-ary operation
Order of Operations
29. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
the set Y
Multiplication
when b > 0
30. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Conditional equations
Associative law of Multiplication
Pure mathematics
has arity one
31. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
inverse operation of Exponentiation
Unary operations
k-ary operation
32. The values combined are called
operands - arguments - or inputs
symmetric
The logical values true and false
Solving the Equation
33. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Order of Operations
A polynomial equation
Repeated addition
Binary operations
34. Letters from the beginning of the alphabet like a - b - c... often denote
Equations
k-ary operation
Constants
radical equation
35. 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
Equations
exponential equation
Unknowns
36. 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
substitution
identity element of Exponentiation
inverse operation of Exponentiation
37. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
Polynomials
Multiplication
Identity element of Multiplication
38. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Difference of two squares - or the difference of perfect squares
two inputs
inverse operation of Multiplication
The relation of equality (=)'s property
39. The codomain is the set of real numbers but the range is the
nonnegative numbers
unary and binary
Solving the Equation
Real number
40. 1 - which preserves numbers: a
Equations
Expressions
The relation of equality (=) has the property
Identity element of Multiplication
41. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Reflexive relation
value - result - or output
Expressions
Elementary algebra
42. The values for which an operation is defined form a set called its
operation
domain
Unknowns
Associative law of Multiplication
43. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
the set Y
Equations
A linear equation
The relation of inequality (<) has this property
44. Can be combined using the function composition operation - performing the first rotation and then the second.
Linear algebra
Rotations
Identities
The central technique to linear equations
45. 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.
Change of variables
(k+1)-ary relation that is functional on its first k domains
then bc < ac
The central technique to linear equations
46. Not associative
The method of equating the coefficients
Associative law of Exponentiation
Expressions
an operation
47. Applies abstract algebra to the problems of geometry
(k+1)-ary relation that is functional on its first k domains
has arity one
Repeated multiplication
Algebraic geometry
48. Is an equation involving derivatives.
Linear algebra
when b > 0
A differential equation
Identity element of Multiplication
49. (a
Associative law of Multiplication
substitution
domain
Solving the Equation
50. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Operations
The central technique to linear equations
Order of Operations
range
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