SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
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. 1 - which preserves numbers: a^1 = a
Properties of equality
identity element of Exponentiation
A transcendental equation
then bc < ac
2. Are true for only some values of the involved variables: x2 - 1 = 4.
exponential equation
the fixed non-negative integer k (the number of arguments)
Conditional equations
then a < c
3. 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
the set Y
when b > 0
Rotations
4. The operation of multiplication means _______________: a
Conditional equations
Repeated addition
Equations
Algebraic geometry
5. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Operations on sets
Rotations
the fixed non-negative integer k (the number of arguments)
The relation of equality (=)
6. 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'.
Algebra
substitution
Algebraic geometry
Reflexive relation
7. (a + b) + c = a + (b + c)
radical equation
Elimination method
associative law of addition
system of linear equations
8. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)
operation
commutative law of Exponentiation
has arity one
Exponentiation
9. 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
Universal algebra
The method of equating the coefficients
Identities
domain
10. Include composition and convolution
Unknowns
transitive
Operations on functions
Pure mathematics
11. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Polynomials
the fixed non-negative integer k (the number of arguments)
transitive
Number line or real line
12. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Elementary algebra
nonnegative numbers
operands - arguments - or inputs
Variables
13. 0 - which preserves numbers: a + 0 = a
has arity two
then bc < ac
Order of Operations
identity element of addition
14. Are called the domains of the operation
Quadratic equations can also be solved
A solution or root of the equation
The sets Xk
Algebraic number theory
15. An operation of arity k is called a
commutative law of Exponentiation
k-ary operation
A solution or root of the equation
Unknowns
16. A unary operation
Equations
equation
operation
has arity one
17. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Algebraic geometry
Identities
Categories of Algebra
substitution
18. 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.
Conditional equations
A functional equation
The central technique to linear equations
Operations on sets
19. Is Written as ab or a^b
Knowns
Vectors
Exponentiation
Repeated multiplication
20. 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
domain
Exponentiation
substitution
Repeated addition
21. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Difference of two squares - or the difference of perfect squares
A binary relation R over a set X is symmetric
operands - arguments - or inputs
A solution or root of the equation
22. Applies abstract algebra to the problems of geometry
Algebraic geometry
Repeated addition
The central technique to linear equations
Properties of equality
23. If a < b and b < c
Reunion of broken parts
The method of equating the coefficients
Repeated addition
then a < c
24. Is the claim that two expressions have the same value and are equal.
Change of variables
logarithmic equation
Equations
The relation of equality (=)
25. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
equation
radical equation
The logical values true and false
A polynomial equation
26. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
A linear equation
A binary relation R over a set X is symmetric
Operations can involve dissimilar objects
27. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
A linear equation
Operations
A polynomial equation
28. Is algebraic equation of degree one
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 relation of inequality (<) has this property
A linear equation
A transcendental equation
29. Not commutative a^b?b^a
operands - arguments - or inputs
commutative law of Exponentiation
identity element of addition
k-ary operation
30. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
then a < c
A solution or root of the equation
Rotations
Expressions
31. 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.
inverse operation of addition
Pure mathematics
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.
Change of variables
32. The inner product operation on two vectors produces a
scalar
Categories of Algebra
Solving the Equation
Difference of two squares - or the difference of perfect squares
33. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
radical equation
Pure mathematics
Properties of equality
The relation of inequality (<) has this property
34. The process of expressing the unknowns in terms of the knowns is called
Identity element of Multiplication
Associative law of Multiplication
the set Y
Solving the Equation
35. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Linear algebra
unary and binary
A differential equation
The simplest equations to solve
36. Can be combined using the function composition operation - performing the first rotation and then the second.
Polynomials
Equation Solving
Algebraic number theory
Rotations
37. Letters from the beginning of the alphabet like a - b - c... often denote
Associative law of Exponentiation
Knowns
Reunion of broken parts
Constants
38. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Vectors
the set Y
Unknowns
nullary operation
39. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
A polynomial equation
The logical values true and false
The sets Xk
Abstract algebra
40. There are two common types of operations:
Variables
unary and binary
Constants
Operations
41. The values for which an operation is defined form a set called its
Difference of two squares - or the difference of perfect squares
Real number
domain
operation
42. Subtraction ( - )
finitary operation
operands - arguments - or inputs
inverse operation of addition
Linear algebra
43. 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
Elimination method
Constants
system of linear equations
The operation of addition
44. Will have two solutions in the complex number system - but need not have any in the real number system.
A transcendental equation
A solution or root of the equation
substitution
All quadratic equations
45. A binary operation
The central technique to linear equations
has arity two
Conditional equations
radical equation
46. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
(k+1)-ary relation that is functional on its first k domains
Reunion of broken parts
the fixed non-negative integer k (the number of arguments)
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.
47. 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 purpose of using variables
Constants
Addition
operation
48. Is an equation involving integrals.
Linear algebra
Difference of two squares - or the difference of perfect squares
Operations
A integral equation
49. Is an equation of the form aX = b for a > 0 - which has solution
Real number
The sets Xk
exponential equation
domain
50. Operations can have fewer or more than
two inputs
an operation
Expressions
Properties of equality