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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. 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
A differential equation
Order of Operations
then bc < ac
2. Is Written as a
Equation Solving
operation
Vectors
Multiplication
3. 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
Associative law of Multiplication
An operation ?
Elementary algebra
commutative law of Multiplication
4. A vector can be multiplied by a scalar to form another vector
reflexive
Equations
Operations can involve dissimilar objects
Solving the Equation
5. Is a function of the form ? : V ? Y - where V ? X1
an operation
has arity two
Pure mathematics
An operation ?
6. 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)
substitution
Associative law of Multiplication
operation
Change of variables
7. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Equation Solving
The logical values true and false
radical equation
A polynomial equation
8. Is an algebraic 'sentence' containing an unknown quantity.
operation
Properties of equality
Difference of two squares - or the difference of perfect squares
Polynomials
9. Applies abstract algebra to the problems of geometry
range
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.
Algebraic geometry
A solution or root of the equation
10. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
(k+1)-ary relation that is functional on its first k domains
two inputs
has arity one
11. A + b = b + a
exponential equation
Properties of equality
Algebraic geometry
commutative law of Addition
12. 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)
The operation of addition
The simplest equations to solve
associative law of addition
nonnegative numbers
13. 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.
Properties of equality
Solving the Equation
substitution
14. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Polynomials
Number line or real line
Algebraic equation
An operation ?
15. A
commutative law of Multiplication
Operations on functions
An operation ?
Vectors
16. The operation of multiplication means _______________: a
domain
Repeated addition
A linear 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.
17. The inner product operation on two vectors produces a
A transcendental equation
scalar
The relation of inequality (<) has this property
Change of variables
18. If a < b and b < c
then a < c
Equation Solving
Abstract algebra
two inputs
19. Can be added and subtracted.
Knowns
the set Y
Vectors
(k+1)-ary relation that is functional on its first k domains
20. The values for which an operation is defined form a set called its
Associative law of Exponentiation
Solution to the system
The simplest equations to solve
domain
21. Not associative
Associative law of Exponentiation
A linear equation
Algebra
The operation of addition
22. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
A integral equation
then a + c < b + d
Number line or real line
The real number system
23. Is an equation of the form aX = b for a > 0 - which has solution
Associative law of Exponentiation
exponential equation
The relation of inequality (<) has this property
The simplest equations to solve
24. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po
A Diophantine equation
An operation ?
A differential equation
Elimination method
25. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Algebraic geometry
Pure mathematics
domain
symmetric
26. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
has arity two
The simplest equations to solve
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.
27. 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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28. A unary operation
has arity one
Identity
Elimination method
Operations on sets
29. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The purpose of using variables
finitary operation
The relation of equality (=)
Operations can involve dissimilar objects
30. Is Written as a + b
Addition
Equations
radical equation
Properties of equality
31. 1 - which preserves numbers: a^1 = a
The real number system
The simplest equations to solve
identity element of Exponentiation
Operations
32. 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
The method of equating the coefficients
Operations on functions
inverse operation of Exponentiation
Algebraic combinatorics
33. Are true for only some values of the involved variables: x2 - 1 = 4.
radical equation
Associative law of Exponentiation
Conditional equations
operation
34. The squaring operation only produces
Identity
then bc < ac
nonnegative numbers
The relation of equality (=) has the property
35. Is an equation involving a transcendental function of one of its variables.
Binary operations
A transcendental equation
Abstract algebra
Real number
36. 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
transitive
Reunion of broken parts
Real number
Properties of equality
37. 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.
Constants
The logical values true and false
Properties of equality
finitary operation
38. There are two common types of operations:
unary and binary
Algebraic geometry
A integral equation
Vectors
39. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
equation
Difference of two squares - or the difference of perfect squares
an operation
Variables
40. Is an equation involving derivatives.
the set Y
A linear equation
Constants
A differential equation
41. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
an operation
The simplest equations to solve
A integral equation
range
42. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
Reunion of broken parts
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.
has arity two
43. 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
logarithmic equation
All quadratic equations
The relation of inequality (<) has this property
44. The values combined are called
Reunion of broken parts
operands - arguments - or inputs
scalar
then bc < ac
45. The codomain is the set of real numbers but the range is the
Equations
The real number system
commutative law of Addition
nonnegative numbers
46. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Equation Solving
Algebra
The relation of inequality (<) has this property
The simplest equations to solve
47. Will have two solutions in the complex number system - but need not have any in the real number system.
A Diophantine equation
All quadratic equations
A linear equation
Quadratic equations
48. Include composition and convolution
the set Y
Operations on functions
Associative law of Exponentiation
Properties of equality
49. In which abstract algebraic methods are used to study combinatorial questions.
All quadratic equations
A solution or root of the equation
Algebraic combinatorics
Equations
50. In which properties common to all algebraic structures are studied
A polynomial equation
A functional equation
an operation
Universal algebra
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