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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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Study First
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. Are called the domains of the operation
The operation of addition
The sets Xk
Algebraic number theory
Equation Solving
2. In which abstract algebraic methods are used to study combinatorial questions.
Constants
A transcendental equation
k-ary operation
Algebraic combinatorics
3. If it holds for all a and b in X that if a is related to b then b is related to a.
A binary relation R over a set X is symmetric
Universal algebra
Quadratic equations
Identity element of Multiplication
4. Will have two solutions in the complex number system - but need not have any in the real number system.
symmetric
then a < c
The central technique to linear equations
All quadratic equations
5. May not be defined for every possible value.
Operations
nullary operation
commutative law of Exponentiation
commutative law of Multiplication
6. The operation of exponentiation means ________________: a^n = a
Number line or real line
has arity two
unary and binary
Repeated multiplication
7. If a = b and b = c then a = c
The central technique to linear equations
transitive
has arity one
k-ary operation
8. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Identity element of Multiplication
Elementary algebra
Quadratic equations can also be solved
two inputs
9. 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
Operations
Expressions
has arity two
Elimination method
10. 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.
A polynomial equation
The relation of equality (=) has the property
commutative law of Exponentiation
Solution to the system
11. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Number line or real line
Identity element of Multiplication
inverse operation of addition
The relation of equality (=) has the property
12. k-ary operation is a
inverse operation of Multiplication
A functional equation
The simplest equations to solve
(k+1)-ary relation that is functional on its first k domains
13. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
k-ary operation
The operation of exponentiation
The relation of inequality (<) has this property
14. If a < b and c < 0
then bc < ac
The method of equating the coefficients
Algebraic geometry
The central technique to linear equations
15. In which properties common to all algebraic structures are studied
Equation Solving
Universal algebra
then ac < bc
A functional equation
16. (a + b) + c = a + (b + c)
domain
associative law of addition
Algebraic combinatorics
transitive
17. If a < b and c < d
then a + c < b + d
commutative law of Exponentiation
reflexive
Quadratic equations can also be solved
18. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
A binary relation R over a set X is symmetric
Categories of Algebra
inverse operation of Multiplication
The simplest equations to solve
19. The values for which an operation is defined form a set called its
domain
Repeated addition
logarithmic equation
The simplest equations to solve
20. Can be defined axiomatically up to an isomorphism
The real number system
A integral equation
Operations on functions
commutative law of Multiplication
21. () 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.
Equations
Algebra
two inputs
Difference of two squares - or the difference of perfect squares
22. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Solution to the system
Variables
Expressions
Abstract algebra
23. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
commutative law of Exponentiation
an operation
Identities
value - result - or output
24. Division ( / )
has arity two
inverse operation of Multiplication
value - result - or output
The simplest equations to solve
25. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
Solution to the system
Change of variables
inverse operation of addition
26. 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.
An operation ?
A linear equation
The relation of inequality (<) has this property
exponential equation
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'.
Binary operations
Reflexive relation
Categories of Algebra
The relation of inequality (<) has this property
28. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
exponential equation
Solving the Equation
Expressions
Operations on sets
29. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
k-ary operation
A polynomial equation
Binary operations
30. 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 relation of inequality (<) has this property
The operation of addition
operation
A transcendental equation
31. 0 - which preserves numbers: a + 0 = a
(k+1)-ary relation that is functional on its first k domains
The relation of equality (=)'s property
identity element of addition
The relation of equality (=)
32. 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)
Properties of equality
The operation of exponentiation
A functional equation
Repeated multiplication
33. In which the specific properties of vector spaces are studied (including matrices)
Operations on sets
inverse operation of addition
Equation Solving
Linear algebra
34. Involve only one value - such as negation and trigonometric functions.
Unary operations
an operation
Linear algebra
The simplest equations to solve
35. Is called the codomain of the operation
A integral equation
Equation Solving
Binary operations
the set Y
36. 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
Repeated multiplication
The real number system
substitution
A integral equation
37. Can be added and subtracted.
reflexive
The relation of equality (=) has the property
Vectors
unary and binary
38. Not commutative a^b?b^a
commutative law of Exponentiation
the set Y
A polynomial equation
operation
39. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
exponential equation
Rotations
when b > 0
The relation of equality (=)
40. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
unary and binary
the fixed non-negative integer k (the number of arguments)
Knowns
Order of Operations
41. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
The purpose of using variables
Algebraic equation
when b > 0
A functional equation
42. 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.
Pure mathematics
Solving the Equation
The relation of equality (=)
43. Is an action or procedure which produces a new value from one or more input values.
Variables
Knowns
commutative law of Exponentiation
an operation
44. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
Change of variables
inverse operation of Exponentiation
Real number
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.
The central technique to linear equations
the set Y
Identities
Multiplication
46. Are true for only some values of the involved variables: x2 - 1 = 4.
nonnegative numbers
value - result - or output
Multiplication
Conditional equations
47. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
A linear equation
exponential equation
The method of equating the coefficients
48. Include the binary operations union and intersection and the unary operation of complementation.
identity element of Exponentiation
scalar
Operations on sets
then a < c
49. 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
identity element of addition
the fixed non-negative integer k (the number of arguments)
associative law of addition
when b > 0
50. Letters from the beginning of the alphabet like a - b - c... often denote
value - result - or output
Equation Solving
Constants
The purpose of using variables