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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. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Number line or real line
The purpose of using variables
Multiplication
Solving the Equation
2. Is an equation involving integrals.
transitive
A integral equation
A binary relation R over a set X is symmetric
then a < c
3. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
then a + c < b + d
A integral equation
an operation
Identity
4. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
operation
Vectors
identity element of addition
5. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
Exponentiation
An operation ?
Elimination method
6. The inner product operation on two vectors produces a
scalar
Addition
operation
All quadratic equations
7. The values for which an operation is defined form a set called its
domain
identity element of Exponentiation
Real number
scalar
8. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
The real number system
The relation of equality (=) has the property
A polynomial equation
Number line or real line
9. The value produced is called
A polynomial equation
Order of Operations
commutative law of Addition
value - result - or output
10. Referring to the finite number of arguments (the value k)
finitary operation
Associative law of Exponentiation
Identities
system of linear equations
11. 0 - which preserves numbers: a + 0 = a
identity element of addition
then bc < ac
equation
commutative law of Addition
12. Not associative
Associative law of Exponentiation
A linear equation
inverse operation of addition
inverse operation of Exponentiation
13. Is algebraic equation of degree one
Elementary algebra
exponential equation
Equation Solving
A linear equation
14. The squaring operation only produces
range
Difference of two squares - or the difference of perfect squares
two inputs
nonnegative numbers
15. 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
operation
Operations can involve dissimilar objects
Elimination method
the set Y
16. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
Identities
Algebraic combinatorics
range
17. Are denoted by letters at the beginning - a - b - c - d - ...
Knowns
Expressions
Solution to the system
reflexive
18. In which the specific properties of vector spaces are studied (including matrices)
inverse operation of Multiplication
Linear algebra
A functional equation
Equations
19. 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 exponentiation
A functional equation
operation
Equation Solving
20. () 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 transcendental equation
logarithmic equation
the fixed non-negative integer k (the number of arguments)
Algebra
21. 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 relation of inequality (<) has this property
The operation of exponentiation
A Diophantine equation
equation
22. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Algebraic geometry
Abstract algebra
substitution
Properties of equality
23. The process of expressing the unknowns in terms of the knowns is called
Multiplication
Constants
Solving the Equation
Quadratic equations
24. In which properties common to all algebraic structures are studied
Identities
scalar
Operations on functions
Universal algebra
25. Is the claim that two expressions have the same value and are equal.
Categories of Algebra
Change of variables
The method of equating the coefficients
Equations
26. Is an equation in which the unknowns are functions rather than simple quantities.
A solution or root of the equation
Categories of Algebra
A functional equation
The operation of addition
27. 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
Algebraic equation
Elementary algebra
A transcendental equation
Order of Operations
28. 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
The central technique to linear equations
reflexive
Properties of equality
substitution
29. The values combined are called
Polynomials
operands - arguments - or inputs
scalar
Change of variables
30. 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.
Repeated multiplication
commutative law of Addition
has arity two
The central technique to linear equations
31. An operation of arity k is called a
the fixed non-negative integer k (the number of arguments)
then a < c
k-ary operation
The relation of equality (=)
32. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
A polynomial equation
Expressions
Quadratic equations can also be solved
Addition
33. Is Written as a + b
Binary operations
Addition
The purpose of using variables
Operations
34. Is called the type or arity of the operation
has arity two
the fixed non-negative integer k (the number of arguments)
Unary operations
The method of equating the coefficients
35. 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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36. Is an equation where the unknowns are required to be integers.
A Diophantine equation
Abstract algebra
Equation Solving
commutative law of Multiplication
37. Are true for only some values of the involved variables: x2 - 1 = 4.
The central technique to linear equations
Conditional equations
Vectors
the set Y
38. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
Associative law of Exponentiation
inverse operation of addition
Unary operations
39. A vector can be multiplied by a scalar to form another vector
Rotations
Operations can involve dissimilar objects
Expressions
A functional equation
40. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
A functional equation
The relation of equality (=) has the property
Order of Operations
inverse operation of Multiplication
41. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Quadratic equations can also be solved
The relation of equality (=)
Difference of two squares - or the difference of perfect squares
substitution
42. Is an equation involving a transcendental function of one of its variables.
Pure mathematics
All quadratic equations
A transcendental equation
Algebraic geometry
43. Means repeated addition of ones: a + n = a + 1 + 1 +...+ 1 (n number of times) - has an inverse operation called subtraction: (a + b) - b = a - which is the same as adding a negative number - a - b = a + (-b)
Variables
Repeated addition
Operations
The operation of addition
44. There are two common types of operations:
The logical values true and false
finitary operation
unary and binary
reflexive
45. Involve only one value - such as negation and trigonometric functions.
Unary operations
Identities
The simplest equations to solve
radical equation
46. b = b
the fixed non-negative integer k (the number of arguments)
Number line or real line
Operations on sets
reflexive
47. Division ( / )
operands - arguments - or inputs
A differential equation
inverse operation of addition
inverse operation of Multiplication
48. Is an algebraic 'sentence' containing an unknown quantity.
k-ary operation
The real number system
Polynomials
then a + c < b + d
49. Letters from the beginning of the alphabet like a - b - c... often denote
Algebraic combinatorics
reflexive
Constants
when b > 0
50. 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
Algebraic number theory
Binary operations
Algebraic combinatorics