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CLEP College Algebra: Algebra Principles
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Subjects
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clep
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math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
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study here
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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. 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
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.
Operations on sets
A linear equation
2. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
exponential equation
Number line or real line
the set Y
associative law of addition
3. 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)
domain
operation
commutative law of Exponentiation
The logical values true and false
4. 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.
Equation Solving
Algebraic geometry
scalar
Properties of equality
5. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
The operation of addition
The method of equating the coefficients
Pure mathematics
operation
6. Not associative
commutative law of Addition
The operation of exponentiation
Associative law of Exponentiation
The sets Xk
7. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Operations can involve dissimilar objects
then a < c
A differential equation
Categories of Algebra
8. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
two inputs
Order of Operations
commutative law of Exponentiation
operation
9. May not be defined for every possible value.
operation
An operation ?
commutative law of Exponentiation
Operations
10. The codomain is the set of real numbers but the range is the
Properties of equality
nonnegative numbers
the fixed non-negative integer k (the number of arguments)
unary and binary
11. 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
commutative law of Multiplication
Elimination method
The relation of inequality (<) has this property
Reflexive relation
12. 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
A solution or root of the equation
Repeated multiplication
Reunion of broken parts
substitution
13. 1 - which preserves numbers: a
Difference of two squares - or the difference of perfect squares
Identity
Identity element of Multiplication
operation
14. Applies abstract algebra to the problems of geometry
Algebraic geometry
The sets Xk
Algebraic number theory
Number line or real line
15. Can be defined axiomatically up to an isomorphism
commutative law of Addition
the set Y
The real number system
Operations on functions
16. Referring to the finite number of arguments (the value k)
finitary operation
nonnegative numbers
identity element of Exponentiation
Abstract algebra
17. Logarithm (Log)
inverse operation of Exponentiation
domain
k-ary operation
symmetric
18. If it holds for all a and b in X that if a is related to b then b is related to a.
nonnegative numbers
when b > 0
inverse operation of Multiplication
A binary relation R over a set X is symmetric
19. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
Expressions
Operations on functions
Identity
20. Is called the codomain of the operation
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.
Operations on functions
the set Y
The central technique to linear equations
21. Is Written as a + b
substitution
Associative law of Multiplication
The logical values true and false
Addition
22. b = b
reflexive
Polynomials
finitary operation
two inputs
23. () 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.
The logical values true and false
All quadratic equations
Algebra
has arity two
24. Is an action or procedure which produces a new value from one or more input values.
logarithmic equation
A polynomial equation
Exponentiation
an operation
25. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
A Diophantine equation
Constants
The relation of equality (=)
nonnegative numbers
26. 1 - which preserves numbers: a^1 = a
Change of variables
Addition
inverse operation of addition
identity element of Exponentiation
27. 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
Knowns
when b > 0
A integral equation
value - result - or output
28. Division ( / )
The relation of inequality (<) has this property
Identity element of Multiplication
inverse operation of Multiplication
has arity two
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)
The operation of exponentiation
nonnegative numbers
The simplest equations to solve
inverse operation of Exponentiation
30. Is an equation involving derivatives.
an operation
Operations
identity element of addition
A differential equation
31. Is an equation of the form log`a^X = b for a > 0 - which has solution
The relation of equality (=) has the property
Categories of Algebra
logarithmic equation
A transcendental equation
32. 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
Algebraic equation
Real number
equation
system of linear equations
33. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic number theory
Identity
inverse operation of Multiplication
A differential equation
34. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
exponential equation
Solution to the system
Elimination method
A solution or root of the equation
35. 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 equality (=)
unary and binary
commutative law of Exponentiation
The relation of inequality (<) has this property
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 (=).
The purpose of using variables
inverse operation of Exponentiation
commutative law of Exponentiation
equation
37. A binary operation
A polynomial equation
Addition
scalar
has arity two
38. Is an equation of the form aX = b for a > 0 - which has solution
value - result - or output
Operations on functions
exponential equation
(k+1)-ary relation that is functional on its first k domains
39. Subtraction ( - )
value - result - or output
inverse operation of addition
An operation ?
two inputs
40. The inner product operation on two vectors produces a
The relation of equality (=)
Difference of two squares - or the difference of perfect squares
then a < c
scalar
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
the set Y
The method of equating the coefficients
Addition
Quadratic equations can also be solved
42. Is an algebraic 'sentence' containing an unknown quantity.
A binary relation R over a set X is symmetric
A Diophantine equation
when b > 0
Polynomials
43. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Operations on functions
Algebraic equation
A functional equation
transitive
44. Is the claim that two expressions have the same value and are equal.
Polynomials
Repeated addition
Operations
Equations
45. If a = b then b = a
(k+1)-ary relation that is functional on its first k domains
transitive
symmetric
Operations
46. 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
Equations
Conditional equations
The operation of exponentiation
Elementary algebra
47. Is an equation in which a polynomial is set equal to another polynomial.
nullary operation
Unary operations
A polynomial equation
operation
48. If a = b and b = c then a = c
A integral equation
transitive
Reunion of broken parts
operation
49. Can be added and subtracted.
Multiplication
Vectors
Elimination method
Knowns
50. Will have two solutions in the complex number system - but need not have any in the real number system.
system of linear equations
All quadratic equations
inverse operation of addition
operands - arguments - or inputs
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