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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. Is an algebraic 'sentence' containing an unknown quantity.
An operation ?
Polynomials
Equation Solving
unary and binary
2. Is algebraic equation of degree one
A linear equation
transitive
symmetric
The relation of equality (=) has the property
3. 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
the set Y
operands - arguments - or inputs
A transcendental equation
4. 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
A functional equation
The operation of addition
Unknowns
5. Is the claim that two expressions have the same value and are equal.
Linear algebra
when b > 0
then a + c < b + d
Equations
6. (a + b) + c = a + (b + c)
The relation of inequality (<) has this property
then a < c
associative law of addition
when b > 0
7. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
commutative law of Addition
system of linear equations
The operation of addition
then ac < bc
8. 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).
The operation of addition
The logical values true and false
operation
nonnegative numbers
9. 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
Operations
Universal algebra
substitution
Associative law of Exponentiation
10. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
has arity one
range
Order of Operations
Solution to the system
11. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Operations can involve dissimilar objects
Algebraic equation
when b > 0
Unknowns
12. In which the specific properties of vector spaces are studied (including matrices)
operation
operands - arguments - or inputs
domain
Linear algebra
13. Will have two solutions in the complex number system - but need not have any in the real number system.
Algebra
substitution
All quadratic equations
commutative law of Multiplication
14. If a < b and b < c
then a < c
scalar
A transcendental equation
Associative law of Exponentiation
15. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Properties of equality
An operation ?
Pure mathematics
A transcendental equation
16. 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.
Repeated addition
The operation of addition
Number line or real line
Properties of equality
17. The value produced is called
Multiplication
value - result - or output
The real number system
Polynomials
18. Include the binary operations union and intersection and the unary operation of complementation.
logarithmic equation
Elimination method
Reflexive relation
Operations on sets
19. Is Written as a + b
Addition
A Diophantine equation
Abstract algebra
domain
20. There are two common types of operations:
inverse operation of Exponentiation
scalar
transitive
unary and binary
21. Include composition and convolution
Algebraic number theory
an operation
Operations on functions
(k+1)-ary relation that is functional on its first k domains
22. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Associative law of Exponentiation
value - result - or output
radical equation
an operation
23. Can be combined using the function composition operation - performing the first rotation and then the second.
Multiplication
Rotations
two inputs
Quadratic equations
24. Involve only one value - such as negation and trigonometric functions.
Identities
scalar
Unary operations
then bc < ac
25. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Equations
The purpose of using variables
commutative law of Addition
Operations on functions
26. b = b
nullary operation
reflexive
the fixed non-negative integer k (the number of arguments)
Operations
27. Logarithm (Log)
inverse operation of Exponentiation
Polynomials
Algebraic number theory
Solution to the system
28. () 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.
A functional equation
operands - arguments - or inputs
substitution
Algebra
29. The values of the variables which make the equation true are the solutions of the equation and can be found through
Operations can involve dissimilar objects
value - result - or output
nonnegative numbers
Equation Solving
30. Operations can have fewer or more than
Algebra
two inputs
logarithmic equation
Real number
31. 1 - which preserves numbers: a
identity element of Exponentiation
Elementary algebra
Pure mathematics
Identity element of Multiplication
32. Can be added and subtracted.
A solution or root of the equation
(k+1)-ary relation that is functional on its first k domains
associative law of addition
Vectors
33. The operation of multiplication means _______________: a
Repeated addition
Operations
then a + c < b + d
value - result - or output
34. k-ary operation is a
(k+1)-ary relation that is functional on its first k domains
A polynomial equation
Knowns
nonnegative numbers
35. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
(k+1)-ary relation that is functional on its first k domains
reflexive
Identity
Operations can involve dissimilar objects
36. 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)
The operation of exponentiation
Equations
nonnegative numbers
operands - arguments - or inputs
37. 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
scalar
nullary operation
The central technique to linear equations
38. If a < b and c < 0
then bc < ac
A solution or root of the equation
identity element of Exponentiation
A transcendental equation
39. 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.
Knowns
Equations
Algebraic equation
The relation of equality (=) has the property
40. 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
Abstract algebra
Quadratic equations
logarithmic equation
41. Letters from the beginning of the alphabet like a - b - c... often denote
k-ary operation
reflexive
system of linear equations
Constants
42. If a < b and c > 0
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.
Variables
Constants
then ac < bc
43. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
A functional equation
Operations can involve dissimilar objects
Associative law of Multiplication
The relation of equality (=)
44. Is called the type or arity of the operation
Associative law of Exponentiation
Addition
the fixed non-negative integer k (the number of arguments)
Unknowns
45. Is Written as ab or a^b
associative law of addition
reflexive
The relation of inequality (<) has this property
Exponentiation
46. May not be defined for every possible value.
Unknowns
Linear algebra
Operations
Solution to the system
47. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
The central technique to linear equations
Difference of two squares - or the difference of perfect squares
inverse operation of Exponentiation
commutative law of Multiplication
48. 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
inverse operation of Exponentiation
then a + c < b + d
Change of variables
49. Division ( / )
equation
the set Y
inverse operation of Multiplication
commutative law of Exponentiation
50. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
scalar
Number line or real line
A functional equation