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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. Is an algebraic 'sentence' containing an unknown quantity.
Universal algebra
Polynomials
Solving the Equation
then bc < ac
2. Is an equation where the unknowns are required to be integers.
then ac < bc
Number line or real line
The method of equating the coefficients
A Diophantine equation
3. The inner product operation on two vectors produces a
scalar
A integral equation
The central technique to linear equations
then ac < bc
4. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.
Change of variables
Equations
Algebraic number theory
commutative law of Multiplication
5. () 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.
unary and binary
identity element of addition
Algebra
The relation of equality (=)
6. Not associative
The purpose of using variables
then ac < bc
substitution
Associative law of Exponentiation
7. Are called the domains of the operation
The central technique to linear equations
Repeated multiplication
commutative law of Exponentiation
The sets Xk
8. Is Written as a + b
Identities
then a < c
Addition
(k+1)-ary relation that is functional on its first k domains
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
commutative law of Exponentiation
(k+1)-ary relation that is functional on its first k domains
Elimination method
Pure mathematics
10. Not commutative a^b?b^a
commutative law of Exponentiation
Reflexive relation
Operations on functions
reflexive
11. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
The method of equating the coefficients
scalar
Pure mathematics
has arity two
12. Is called the codomain of the operation
Universal algebra
inverse operation of addition
inverse operation of Exponentiation
the set Y
13. 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.
identity element of Exponentiation
The central technique to linear equations
scalar
A transcendental equation
14. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
Solving the Equation
transitive
Elementary algebra
15. A vector can be multiplied by a scalar to form another vector
transitive
then a < c
inverse operation of Multiplication
Operations can involve dissimilar objects
16. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
operation
Real number
Expressions
Repeated multiplication
17. (a + b) + c = a + (b + c)
associative law of addition
Algebraic combinatorics
Linear algebra
Reflexive relation
18. The values for which an operation is defined form a set called its
Algebraic number theory
domain
symmetric
has arity one
19. Is an equation involving a transcendental function of one of its variables.
nullary operation
A transcendental equation
A integral equation
Algebraic equation
20. 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.
Abstract algebra
identity element of addition
Properties of equality
value - result - or output
21. 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 polynomial equation
commutative law of Exponentiation
identity element of addition
operation
22. Can be combined using logic operations - such as and - or - and not.
inverse operation of Exponentiation
The logical values true and false
inverse operation of addition
The simplest equations to solve
23. Involve only one value - such as negation and trigonometric functions.
The sets Xk
Algebra
Real number
Unary operations
24. The process of expressing the unknowns in terms of the knowns is called
system of linear equations
Solving the Equation
Exponentiation
the set Y
25. An operation of arity zero is simply an element of the codomain Y - called a
when b > 0
scalar
nullary operation
Polynomials
26. Subtraction ( - )
finitary operation
range
inverse operation of addition
Conditional equations
27. A unary operation
Properties of equality
Expressions
Repeated multiplication
has arity one
28. Is Written as a
Rotations
Multiplication
A functional equation
Operations can involve dissimilar objects
29. If a < b and c < d
A polynomial equation
then a + c < b + d
unary and binary
equation
30. (a
Associative law of Multiplication
The relation of equality (=)'s property
Polynomials
Multiplication
31. In which properties common to all algebraic structures are studied
Universal algebra
exponential equation
Constants
Difference of two squares - or the difference of perfect squares
32. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
A binary relation R over a set X is symmetric
equation
The purpose of using variables
then ac < bc
33. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
The method of equating the coefficients
nonnegative numbers
finitary operation
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
Identities
Number line or real line
The method of equating the coefficients
Pure mathematics
35. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
the set Y
Change of variables
Quadratic equations can also be solved
36. 0 - which preserves numbers: a + 0 = a
associative law of addition
identity element of addition
Knowns
then bc < ac
37. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
(k+1)-ary relation that is functional on its first k domains
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.
Number line or real line
radical equation
38. If it holds for all a and b in X that if a is related to b then b is related to a.
Equation Solving
Change of variables
A binary relation R over a set X is symmetric
Associative law of Exponentiation
39. Include composition and convolution
Number line or real line
Constants
Operations on functions
The operation of addition
40. Is an action or procedure which produces a new value from one or more input values.
an operation
Solving the Equation
Reflexive relation
Reunion of broken parts
41. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
A integral equation
domain
exponential equation
Quadratic equations can also be solved
42. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
Identity
Unknowns
Properties of equality
43. 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)
Identities
A integral equation
operation
The operation of exponentiation
44. Can be defined axiomatically up to an isomorphism
Properties of equality
operands - arguments - or inputs
The real number system
nonnegative numbers
45. Can be added and subtracted.
The logical values true and false
Vectors
Algebra
Unary operations
46. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Order of Operations
Algebraic equation
Elimination method
operands - arguments - or inputs
47. 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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48. May not be defined for every possible value.
A solution or root of the equation
Number line or real line
Polynomials
Operations
49. If a = b then b = a
symmetric
transitive
The sets Xk
operands - arguments - or inputs
50. Can be combined using the function composition operation - performing the first rotation and then the second.
Algebra
Rotations
Elimination method
inverse operation of addition