SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
Search
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. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
A binary relation R over a set X is symmetric
identity element of Exponentiation
Equations
2. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
exponential equation
Identities
Order of Operations
Quadratic equations
3. Symbols that denote numbers - is to allow the making of generalizations in mathematics
inverse operation of addition
The purpose of using variables
The sets Xk
scalar
4. If a = b then b = a
Quadratic equations can also be solved
associative law of addition
symmetric
Algebra
5. An operation of arity k is called a
Quadratic equations can also be solved
k-ary operation
the set Y
Real number
6. Is called the codomain of the operation
Equations
the set Y
nullary operation
value - result - or output
7. The inner product operation on two vectors produces a
has arity two
scalar
Constants
identity element of Exponentiation
8. Is called the type or arity of the operation
Binary operations
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.
the fixed non-negative integer k (the number of arguments)
Universal algebra
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
two inputs
Difference of two squares - or the difference of perfect squares
Polynomials
10. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Solving the Equation
finitary 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.
unary and binary
11. Is Written as a
The simplest equations to solve
Multiplication
Variables
Solving the Equation
12. A
A integral equation
logarithmic equation
Operations on functions
commutative law of Multiplication
13. May not be defined for every possible value.
Operations
range
Identity
Polynomials
14. Subtraction ( - )
Solving the Equation
equation
inverse operation of addition
Algebra
15. If a = b and b = c then a = c
Order of Operations
Addition
transitive
Operations on sets
16. 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
Operations on sets
k-ary operation
the set Y
Elimination method
17. 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
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.
Real number
Equations
reflexive
18. 0 - which preserves numbers: a + 0 = a
identity element of addition
Expressions
Repeated addition
Identities
19. (a
Reunion of broken parts
k-ary operation
Associative law of Multiplication
transitive
20. Is an equation in which the unknowns are functions rather than simple quantities.
Pure mathematics
Expressions
A functional equation
Number line or real line
21. () 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 polynomial equation
Algebra
radical equation
Associative law of Multiplication
22. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
Algebraic number theory
Equations
Linear algebra
23. 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
nullary operation
A transcendental equation
Categories of Algebra
24. A unary operation
an operation
Algebraic equation
has arity one
A binary relation R over a set X is symmetric
25. A + b = b + a
equation
commutative law of Addition
Order of Operations
Difference of two squares - or the difference of perfect squares
26. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
value - result - or output
The purpose of using variables
Equations
equation
27. If a < b and c > 0
Operations on functions
scalar
then ac < bc
Elimination method
28. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
substitution
Quadratic equations
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.
29. Not commutative a^b?b^a
nullary operation
Change of variables
commutative law of Exponentiation
Repeated multiplication
30. The squaring operation only produces
nonnegative numbers
nullary operation
Identities
The operation of addition
31. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
scalar
A Diophantine equation
system of linear equations
Unary operations
32. Operations can have fewer or more than
identity element of addition
exponential equation
Unary operations
two inputs
33. Logarithm (Log)
inverse operation of Exponentiation
Identity element of Multiplication
The method of equating the coefficients
Rotations
34. Involve only one value - such as negation and trigonometric functions.
Reunion of broken parts
operation
Unary operations
nonnegative numbers
35. 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
Quadratic equations can also be solved
The method of equating the coefficients
Identity element of Multiplication
36. 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.
Properties of equality
Addition
Unary operations
equation
37. Referring to the finite number of arguments (the value k)
finitary operation
Associative law of Exponentiation
Operations can involve dissimilar objects
Algebraic combinatorics
38. There are two common types of operations:
unary and binary
Repeated addition
Elementary algebra
Constants
39. 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
A Diophantine equation
Polynomials
Elementary algebra
commutative law of Exponentiation
40. If a < b and c < 0
Identity
The operation of exponentiation
then bc < ac
radical equation
41. 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.
then ac < bc
commutative law of Exponentiation
The central technique to linear equations
inverse operation of Exponentiation
42. Include composition and convolution
the set Y
unary and binary
Operations on functions
finitary operation
43. The operation of exponentiation means ________________: a^n = a
Unary operations
Repeated multiplication
Equation Solving
Difference of two squares - or the difference of perfect squares
44. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
finitary operation
The purpose of using variables
the set Y
45. Can be combined using the function composition operation - performing the first rotation and then the second.
commutative law of Addition
Order of Operations
Algebraic number theory
Rotations
46. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
Algebra
Polynomials
commutative law of Addition
47. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Identity
finitary operation
Variables
Identities
48. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
Operations can involve dissimilar objects
Vectors
A binary relation R over a set X is symmetric
49. 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)
k-ary operation
A binary relation R over a set X is symmetric
logarithmic equation
The operation of exponentiation
50. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
then bc < ac
operation
value - result - or output