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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. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
The simplest equations to solve
Equations
Operations on sets
Reflexive relation
2. 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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3. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Properties of equality
Order of Operations
range
A differential equation
4. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Equations
The simplest equations to solve
Order of Operations
Reflexive relation
5. Is an equation involving integrals.
associative law of addition
The operation of exponentiation
the fixed non-negative integer k (the number of arguments)
A integral equation
6. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
identity element of addition
reflexive
nonnegative numbers
7. 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.
Solution to the system
two inputs
equation
Properties of equality
8. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Associative law of Multiplication
Quadratic equations can also be solved
k-ary operation
scalar
9. Is an algebraic 'sentence' containing an unknown quantity.
has arity one
Polynomials
Elementary algebra
Binary operations
10. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
equation
nonnegative numbers
k-ary operation
11. Is called the codomain of the operation
The logical values true and false
Unknowns
The relation of equality (=)'s property
the set Y
12. The values of the variables which make the equation true are the solutions of the equation and can be found through
Change of variables
system of linear equations
Elementary algebra
Equation Solving
13. The operation of exponentiation means ________________: a^n = a
Unary operations
radical equation
Repeated multiplication
The operation of exponentiation
14. 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
Real number
then ac < bc
radical equation
inverse operation of Exponentiation
15. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Equations
Rotations
Abstract algebra
inverse operation of addition
16. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
The relation of equality (=) has the property
A polynomial equation
Identity
Elementary algebra
17. If a < b and b < c
has arity one
Associative law of Multiplication
value - result - or output
then a < c
18. Include the binary operations union and intersection and the unary operation of complementation.
A polynomial equation
A binary relation R over a set X is symmetric
The operation of exponentiation
Operations on sets
19. If a < b and c > 0
then ac < bc
identity element of addition
equation
Algebra
20. If a = b and b = c then a = c
commutative law of Multiplication
transitive
Exponentiation
Operations can involve dissimilar objects
21. (a
Associative law of Multiplication
range
identity element of Exponentiation
An operation ?
22. 1 - which preserves numbers: a
Vectors
Identity element of Multiplication
identity element of addition
Algebraic number theory
23. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
then bc < ac
A functional equation
A differential equation
24. Not associative
Associative law of Exponentiation
value - result - or output
A solution or root of the equation
The operation of addition
25. Is an equation where the unknowns are required to be integers.
A Diophantine equation
inverse operation of Exponentiation
when b > 0
Solution to the system
26. A unary operation
has arity one
then a + c < b + d
Universal algebra
The purpose of using variables
27. Can be defined axiomatically up to an isomorphism
Equation Solving
The real number system
commutative law of Addition
Knowns
28. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
Algebra
commutative law of Multiplication
Operations can involve dissimilar objects
29. Letters from the beginning of the alphabet like a - b - c... often denote
inverse operation of Exponentiation
inverse operation of Multiplication
A Diophantine equation
Constants
30. Is the claim that two expressions have the same value and are equal.
A solution or root of the equation
The method of equating the coefficients
when b > 0
Equations
31. 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)
two inputs
The operation of exponentiation
nonnegative numbers
logarithmic equation
32. Is an equation in which a polynomial is set equal to another polynomial.
reflexive
A polynomial equation
Unknowns
Repeated multiplication
33. 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).
Constants
unary and binary
Quadratic equations
The purpose of using variables
34. 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
symmetric
A integral equation
Quadratic equations
The method of equating the coefficients
35. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
the fixed non-negative integer k (the number of arguments)
nonnegative numbers
Elimination method
Identities
36. If a < b and c < d
Change of variables
then a + c < b + d
k-ary operation
The relation of equality (=)
37. 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
Properties of equality
Elementary algebra
Elimination method
Algebraic number theory
38. 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
Equations
value - result - or output
when b > 0
substitution
39. Is an equation involving derivatives.
nonnegative numbers
A differential equation
Algebraic combinatorics
value - result - or output
40. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Polynomials
A solution or root of the equation
has arity two
operation
41. May not be defined for every possible value.
The sets Xk
Order of Operations
Repeated addition
Operations
42. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
Multiplication
(k+1)-ary relation that is functional on its first k domains
Algebraic number theory
43. In which properties common to all algebraic structures are studied
operation
Universal algebra
Knowns
Identity element of Multiplication
44. 0 - which preserves numbers: a + 0 = a
The purpose of using variables
Reflexive relation
identity element of addition
Equation Solving
45. Subtraction ( - )
then a < c
inverse operation of addition
Knowns
then a + c < b + d
46. Involve only one value - such as negation and trigonometric functions.
when b > 0
A linear equation
has arity two
Unary operations
47. 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
Elementary algebra
Repeated multiplication
inverse operation of Multiplication
The purpose of using variables
48. Division ( / )
domain
system of linear equations
Identity element of Multiplication
inverse operation of Multiplication
49. 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)
A functional equation
Variables
range
operation
50. Is a function of the form ? : V ? Y - where V ? X1
operation
An operation ?
Categories of Algebra
Number line or real line