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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. Will have two solutions in the complex number system - but need not have any in the real number system.
Linear algebra
All quadratic equations
finitary operation
inverse operation of Multiplication
2. The value produced is called
Operations on functions
an operation
Algebraic number theory
value - result - or output
3. Is an equation involving integrals.
A integral 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.
inverse operation of addition
Solving the Equation
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
domain
Difference of two squares - or the difference of perfect squares
A Diophantine equation
Elimination method
5. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Constants
A polynomial equation
Order of Operations
A solution or root of the equation
6. 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
reflexive
Reflexive relation
Elementary algebra
Expressions
7. The codomain is the set of real numbers but the range is the
Change of variables
A Diophantine equation
nonnegative numbers
The operation of addition
8. 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)
system of linear equations
The sets Xk
two inputs
The operation of exponentiation
9. The values of the variables which make the equation true are the solutions of the equation and can be found through
the fixed non-negative integer k (the number of arguments)
an operation
commutative law of Addition
Equation Solving
10. The process of expressing the unknowns in terms of the knowns is called
exponential equation
then a < c
Solving the Equation
(k+1)-ary relation that is functional on its first k domains
11. The operation of exponentiation means ________________: a^n = a
operation
Repeated multiplication
Associative law of Multiplication
unary and binary
12. Can be added and subtracted.
(k+1)-ary relation that is functional on its first k domains
Algebraic geometry
Vectors
Conditional equations
13. 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
Identity
(k+1)-ary relation that is functional on its first k domains
A polynomial equation
14. The values combined are called
inverse operation of Exponentiation
Difference of two squares - or the difference of perfect squares
Abstract algebra
operands - arguments - or inputs
15. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
The simplest equations to solve
Real number
system of linear equations
Solution to the system
16. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
k-ary operation
Variables
Algebraic number theory
equation
17. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
Unary operations
An operation ?
unary and binary
18. 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).
an operation
nonnegative numbers
Categories of Algebra
operation
19. A vector can be multiplied by a scalar to form another vector
Unknowns
Operations can involve dissimilar objects
identity element of addition
A linear equation
20. If a < b and c < 0
Multiplication
Number line or real line
then bc < ac
Knowns
21. 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).
Elimination method
Quadratic equations
the fixed non-negative integer k (the number of arguments)
exponential equation
22. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
commutative law of Multiplication
The relation of equality (=)
Reflexive relation
inverse operation of Exponentiation
23. Involve only one value - such as negation and trigonometric functions.
k-ary operation
Unary operations
A binary relation R over a set X is symmetric
Pure mathematics
24. Division ( / )
Algebraic combinatorics
Addition
Unknowns
inverse operation of Multiplication
25. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
Algebra
Real number
Binary operations
26. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
The real number system
Polynomials
Elementary algebra
27. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
symmetric
The sets Xk
Algebraic equation
28. A + b = b + a
Abstract algebra
Algebraic number theory
commutative law of Addition
The relation of inequality (<) has this property
29. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Algebra
radical equation
A polynomial equation
commutative law of Exponentiation
30. Referring to the finite number of arguments (the value k)
(k+1)-ary relation that is functional on its first k domains
finitary operation
symmetric
The logical values true and false
31. k-ary operation is a
(k+1)-ary relation that is functional on its first k domains
then bc < ac
The simplest equations to solve
The central technique to linear equations
32. Is called the codomain of the operation
Unknowns
The central technique to linear equations
nonnegative numbers
the set Y
33. 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
operation
inverse operation of addition
Real number
Multiplication
34. May not be defined for every possible value.
nonnegative numbers
Operations
A integral equation
Algebraic combinatorics
35. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Reflexive relation
A polynomial equation
The method of equating the coefficients
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.
36. Is an equation in which the unknowns are functions rather than simple quantities.
The relation of inequality (<) has this property
unary and binary
Elimination method
A functional equation
37. An operation of arity k is called a
k-ary operation
A differential equation
Solution to the system
The operation of exponentiation
38. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
The method of equating the coefficients
substitution
nonnegative numbers
Abstract algebra
39. Not commutative a^b?b^a
nonnegative numbers
commutative law of Exponentiation
Identity
Operations on functions
40. 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.
Equations
Identities
the fixed non-negative integer k (the number of arguments)
The central technique to linear equations
41. Is an equation where the unknowns are required to be integers.
identity element of addition
A Diophantine equation
Algebraic equation
Polynomials
42. Not associative
Categories of Algebra
Associative law of Exponentiation
An operation ?
The relation of equality (=) has the property
43. Are denoted by letters at the beginning - a - b - c - d - ...
an operation
Abstract algebra
Knowns
Linear algebra
44. 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)
Algebraic equation
The operation of exponentiation
The operation of addition
operation
45. Is Written as ab or a^b
identity element of addition
A integral equation
when b > 0
Exponentiation
46. An operation of arity zero is simply an element of the codomain Y - called a
(k+1)-ary relation that is functional on its first k domains
scalar
nullary operation
associative law of addition
47. The values for which an operation is defined form a set called its
A binary relation R over a set X is symmetric
an operation
domain
Quadratic equations
48. Is an algebraic 'sentence' containing an unknown quantity.
Knowns
Elimination method
two inputs
Polynomials
49. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic equation
Algebraic number theory
Solution to the system
Linear algebra
50. b = b
Reunion of broken parts
inverse operation of Multiplication
inverse operation of Exponentiation
reflexive