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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
Start Test
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. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The real number system
The relation of equality (=)
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.
then a + c < b + d
2. In which properties common to all algebraic structures are studied
Expressions
Reunion of broken parts
The operation of addition
Universal algebra
3. 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.
radical equation
Equations
nonnegative numbers
The central technique to linear equations
4. 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
the fixed non-negative integer k (the number of arguments)
Exponentiation
range
Elimination method
5. The codomain is the set of real numbers but the range is the
The method of equating the coefficients
A polynomial equation
nonnegative numbers
Algebraic number theory
6. The process of expressing the unknowns in terms of the knowns is called
Universal algebra
Associative law of Exponentiation
Solving the Equation
nonnegative numbers
7. 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
Solution to the system
Binary operations
Equations
8. 0 - which preserves numbers: a + 0 = a
associative law of addition
Operations can involve dissimilar objects
transitive
identity element of addition
9. Is algebraic equation of degree one
The method of equating the coefficients
A linear equation
Elimination method
nonnegative numbers
10. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).
transitive
operation
Equations
Quadratic equations can also be solved
11. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic number theory
Change of variables
The relation of inequality (<) has this property
has arity one
12. 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).
Change of variables
The relation of equality (=)
Solving the Equation
Quadratic equations
13. The operation of multiplication means _______________: a
Operations on sets
Repeated addition
identity element of Exponentiation
A functional equation
14. () 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.
substitution
Operations can involve dissimilar objects
A binary relation R over a set X is symmetric
Algebra
15. A binary operation
has arity two
Addition
A polynomial equation
Conditional equations
16. Will have two solutions in the complex number system - but need not have any in the real number system.
Equation Solving
The relation of equality (=) has the property
Constants
All quadratic equations
17. Operations can have fewer or more than
two inputs
Real number
the fixed non-negative integer k (the number of arguments)
the set Y
18. Is an equation involving derivatives.
then a + c < b + d
A differential equation
A Diophantine equation
Equations
19. 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)
Equation Solving
Number line or real line
operation
the fixed non-negative integer k (the number of arguments)
20. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
Operations on sets
The simplest equations to solve
Constants
21. Not commutative a^b?b^a
Linear algebra
Rotations
operation
commutative law of Exponentiation
22. May not be defined for every possible value.
Categories of Algebra
Polynomials
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
23. 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
operands - arguments - or inputs
Reunion of broken parts
(k+1)-ary relation that is functional on its first k domains
Order of Operations
24. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
nullary 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.
then bc < ac
Unary operations
25. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Operations on functions
Exponentiation
Identities
The simplest equations to solve
26. The values combined are called
A transcendental equation
Associative law of Exponentiation
then ac < bc
operands - arguments - or inputs
27. Can be added and subtracted.
A transcendental equation
Vectors
Operations can involve dissimilar objects
associative law of addition
28. (a
A solution or root of the equation
Associative law of Multiplication
Real number
Identity
29. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
An operation ?
Pure mathematics
has arity one
30. A
system of linear equations
The relation of equality (=) has the property
Difference of two squares - or the difference of perfect squares
commutative law of Multiplication
31. 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
Addition
Real number
The purpose of using variables
Equation Solving
32. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
an operation
The simplest equations to solve
Algebraic geometry
Unknowns
33. Referring to the finite number of arguments (the value k)
Operations on functions
Difference of two squares - or the difference of perfect squares
Algebraic combinatorics
finitary operation
34. Is an equation of the form aX = b for a > 0 - which has solution
Operations can involve dissimilar objects
Algebraic combinatorics
exponential equation
scalar
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 inequality (<) has this property
The operation of exponentiation
commutative law of Addition
equation
36. Letters from the beginning of the alphabet like a - b - c... often denote
then ac < bc
Equations
Constants
The simplest equations to solve
37. Not associative
Algebraic combinatorics
Associative law of Exponentiation
inverse operation of Multiplication
equation
38. If a = b then b = a
identity element of addition
symmetric
range
Associative law of Multiplication
39. The values for which an operation is defined form a set called its
The method of equating the coefficients
commutative law of Exponentiation
domain
Polynomials
40. In which the specific properties of vector spaces are studied (including matrices)
Solving the Equation
A transcendental equation
Categories of Algebra
Linear algebra
41. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Exponentiation
The simplest equations to solve
A transcendental equation
Pure mathematics
42. If a < b and c > 0
then ac < bc
An operation ?
commutative law of Addition
The method of equating the coefficients
43. (a + b) + c = a + (b + c)
The simplest equations to solve
associative law of addition
Algebraic number theory
scalar
44. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
an operation
Algebraic equation
Solving the Equation
Addition
45. Is an equation where the unknowns are required to be integers.
Algebraic equation
The logical values true and false
A Diophantine equation
Algebraic combinatorics
46. Is an equation involving integrals.
The method of equating the coefficients
operation
A integral equation
then ac < bc
47. Can be defined axiomatically up to an isomorphism
Identity
The real number system
Vectors
system of linear equations
48. Subtraction ( - )
nullary operation
Number line or real line
Abstract algebra
inverse operation of addition
49. There are two common types of operations:
The relation of equality (=) has the property
unary and binary
The operation of addition
reflexive
50. k-ary operation is a
Elimination method
then a + c < b + d
(k+1)-ary relation that is functional on its first k domains
transitive