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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. Applies abstract algebra to the problems of geometry
Operations on functions
Rotations
then bc < ac
Algebraic geometry
2. Can be defined axiomatically up to an isomorphism
Conditional equations
A polynomial equation
Unknowns
The real number system
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.
The central technique to linear equations
operation
then ac < bc
The purpose of using variables
4. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
Order of Operations
the set Y
then bc < ac
5. 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
Operations can involve dissimilar objects
Identity
domain
6. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Number line or real line
reflexive
Vectors
radical equation
7. 1 - which preserves numbers: a
The logical values true and false
Equations
A linear equation
Identity element of Multiplication
8. 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
logarithmic equation
Elementary algebra
An operation ?
(k+1)-ary relation that is functional on its first k domains
9. Include composition and convolution
commutative law of Addition
logarithmic equation
Operations on functions
Associative law of Multiplication
10. Subtraction ( - )
inverse operation of addition
Constants
symmetric
when b > 0
11. Include the binary operations union and intersection and the unary operation of complementation.
A polynomial equation
Equations
Operations on sets
when b > 0
12. If a < b and c < 0
Identities
then bc < ac
Exponentiation
Operations
13. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
the fixed non-negative integer k (the number of arguments)
The operation of addition
The relation of inequality (<) has this property
14. If a < b and b < c
the set Y
Algebraic equation
then a < c
inverse operation of addition
15. Can be combined using the function composition operation - performing the first rotation and then the second.
Multiplication
Rotations
Elimination method
Exponentiation
16. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Real number
Identities
The relation of equality (=) has the property
A linear equation
17. Is the claim that two expressions have the same value and are equal.
Unknowns
Equations
Expressions
the fixed non-negative integer k (the number of arguments)
18. A unary operation
An operation ?
Real number
has arity one
Difference of two squares - or the difference of perfect squares
19. Will have two solutions in the complex number system - but need not have any in the real number system.
A transcendental equation
All quadratic equations
Associative law of Multiplication
Unknowns
20. In which properties common to all algebraic structures are studied
Operations
Universal algebra
the set Y
range
21. In which the specific properties of vector spaces are studied (including matrices)
The simplest equations to solve
Operations can involve dissimilar objects
Linear algebra
system of linear equations
22. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
nullary operation
The sets Xk
Operations
23. A vector can be multiplied by a scalar to form another vector
The simplest equations to solve
Repeated addition
A binary relation R over a set X is symmetric
Operations can involve dissimilar objects
24. Is an equation involving derivatives.
Conditional equations
A differential equation
associative law of addition
Multiplication
25. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
The relation of equality (=) has the property
reflexive
Equations
nullary operation
26. If a < b and c > 0
A linear equation
then ac < bc
Operations on functions
Repeated multiplication
27. An operation of arity zero is simply an element of the codomain Y - called a
The method of equating the coefficients
nullary operation
A Diophantine equation
has arity one
28. Is Written as ab or a^b
Exponentiation
commutative law of Multiplication
Multiplication
nonnegative numbers
29. 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
substitution
then ac < bc
Algebraic geometry
The simplest equations to solve
30. 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).
Linear algebra
Repeated multiplication
Multiplication
operation
31. Referring to the finite number of arguments (the value k)
logarithmic equation
finitary operation
radical equation
A polynomial equation
32. An operation of arity k is called a
Conditional equations
Elimination method
k-ary operation
Properties of equality
33. Are true for only some values of the involved variables: x2 - 1 = 4.
The relation of equality (=)
Unknowns
The real number system
Conditional equations
34. Division ( / )
Number line or real line
inverse operation of Multiplication
symmetric
Repeated addition
35. Not commutative a^b?b^a
Algebra
commutative law of Addition
unary and binary
commutative law of Exponentiation
36. Is called the codomain of the operation
the set Y
Operations on functions
The relation of inequality (<) has this property
Identity element of Multiplication
37. b = b
Identity
reflexive
Exponentiation
A integral equation
38. The squaring operation only produces
All quadratic equations
equation
nonnegative numbers
The logical values true and false
39. (a
value - result - or output
Operations on functions
The relation of equality (=)
Associative law of Multiplication
40. Is an equation involving a transcendental function of one of its variables.
Identity element of Multiplication
Repeated multiplication
A transcendental equation
value - result - or output
41. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Vectors
Algebraic number theory
The relation of equality (=)'s property
Quadratic equations
42. () 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.
Associative law of Exponentiation
Algebraic geometry
Algebra
Operations can involve dissimilar objects
43. If a < b and c < d
Equation Solving
the set Y
then a + c < b + d
Binary operations
44. Is an action or procedure which produces a new value from one or more input values.
an operation
Unknowns
Quadratic equations can also be solved
Operations can involve dissimilar objects
45. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
Associative law of Exponentiation
The sets Xk
The purpose of using variables
46. Is Written as a
An operation ?
inverse operation of Exponentiation
nonnegative numbers
Multiplication
47. 0 - which preserves numbers: a + 0 = a
symmetric
Categories of Algebra
identity element of addition
A differential equation
48. 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.
Solving the Equation
the fixed non-negative integer k (the number of arguments)
operation
Change of variables
49. 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
Equations
two inputs
Equation Solving
50. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Operations on functions
Variables
has arity two
unary and binary