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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. An operation of arity zero is simply an element of the codomain Y - called a
A linear equation
Binary operations
identity element of Exponentiation
nullary operation
2. If a < b and b < c
Order of Operations
The logical values true and false
then a < c
Knowns
3. 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)
Algebraic equation
The operation of exponentiation
nonnegative numbers
Rotations
4. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.
Reflexive relation
the set Y
Repeated multiplication
An operation ?
5. Is called the codomain of the operation
the set Y
Equations
k-ary operation
(k+1)-ary relation that is functional on its first k domains
6. If a = b then b = a
symmetric
The relation of equality (=)
Operations on functions
inverse operation of addition
7. In which abstract algebraic methods are used to study combinatorial questions.
two inputs
Algebraic combinatorics
Universal algebra
identity element of Exponentiation
8. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Difference of two squares - or the difference of perfect squares
Universal algebra
Categories of Algebra
Identities
9. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
The simplest equations to solve
range
The logical values true and false
Quadratic equations
10. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Quadratic equations
Operations on functions
A solution or root of the equation
Difference of two squares - or the difference of perfect squares
11. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
A linear equation
an operation
Polynomials
Binary operations
12. The values combined are called
operands - arguments - or inputs
A integral equation
has arity one
A Diophantine equation
13. A unary operation
Order of Operations
inverse operation of Multiplication
has arity one
identity element of addition
14. Is an equation of the form X^m/n = a - for m - n integers - which has solution
unary and binary
radical equation
Properties of equality
substitution
15. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Reflexive relation
Unknowns
system of linear equations
A integral equation
16. Can be combined using logic operations - such as and - or - and not.
Change of variables
radical equation
The logical values true and false
inverse operation of Exponentiation
17. Can be combined using the function composition operation - performing the first rotation and then the second.
The central technique to linear equations
Unary operations
Rotations
Operations
18. A vector can be multiplied by a scalar to form another vector
Algebra
Associative law of Multiplication
commutative law of Addition
Operations can involve dissimilar objects
19. Is the claim that two expressions have the same value and are equal.
The logical values true and false
Abstract algebra
Equations
inverse operation of Multiplication
20. An operation of arity k is called a
equation
k-ary operation
A binary relation R over a set X is symmetric
Elimination method
21. Can be defined axiomatically up to an isomorphism
Linear algebra
The logical values true and false
The real number system
Operations can involve dissimilar objects
22. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
inverse operation of Exponentiation
Rotations
identity element of addition
Categories of Algebra
23. 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
Order of Operations
The method of equating the coefficients
The central technique to linear equations
The logical values true and false
24. A + b = b + a
commutative law of Addition
Variables
The operation of exponentiation
nonnegative numbers
25. Is Written as ab or a^b
Associative law of Exponentiation
then a < c
Exponentiation
operands - arguments - or inputs
26. 1 - which preserves numbers: a
Order of Operations
Identity element of Multiplication
unary and binary
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.
27. Is an action or procedure which produces a new value from one or more input values.
an operation
A binary relation R over a set X is symmetric
Real number
nonnegative numbers
28. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Constants
nonnegative numbers
Algebraic equation
the set Y
29. Is Written as a
Multiplication
has arity two
Algebraic number theory
Repeated addition
30. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
operation
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.
then ac < bc
The relation of equality (=)
31. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain
then a + c < b + d
A integral equation
when b > 0
identity element of Exponentiation
32. 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
then a + c < b + d
The method of equating the coefficients
identity element of Exponentiation
Real number
33. Is called the type or arity of the operation
Linear algebra
the fixed non-negative integer k (the number of arguments)
Number line or real line
Difference of two squares - or the difference of perfect squares
34. 0 - which preserves numbers: a + 0 = a
Universal algebra
identity element of addition
Operations
system of linear equations
35. Is an equation involving derivatives.
exponential equation
range
operation
A differential equation
36. 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
Algebraic combinatorics
operation
k-ary operation
Elimination method
37. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
The method of equating the coefficients
Expressions
The logical values true and false
38. 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)
Identity
scalar
The operation of addition
Algebraic equation
39. Is algebraic equation of degree one
Identities
A linear equation
transitive
The operation of addition
40. Can be added and subtracted.
Vectors
commutative law of Multiplication
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.
(k+1)-ary relation that is functional on its first k domains
41. 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.
Vectors
A transcendental equation
Algebraic equation
The relation of equality (=) has the property
42. The codomain is the set of real numbers but the range is the
Equation Solving
two inputs
A Diophantine equation
nonnegative numbers
43. Symbols that denote numbers - is to allow the making of generalizations in mathematics
exponential equation
The purpose of using variables
The central technique to linear equations
The method of equating the coefficients
44. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
value - result - or output
The relation of equality (=)'s property
then a < c
Expressions
45. 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.
transitive
Equations
operation
The central technique to linear equations
46. The value produced is called
Solution to the system
Equations
value - result - or output
Categories of Algebra
47. Referring to the finite number of arguments (the value k)
then bc < ac
Abstract algebra
Difference of two squares - or the difference of perfect squares
finitary operation
48. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
The operation of addition
Linear algebra
Constants
Identity
49. Applies abstract algebra to the problems of geometry
k-ary operation
unary and binary
Algebraic geometry
Number line or real line
50. Are denoted by letters at the beginning - a - b - c - d - ...
Knowns
then a < c
Reunion of broken parts
then ac < bc