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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
Change of variables
A functional equation
The relation of equality (=) has the property
2. The operation of exponentiation means ________________: a^n = a
has arity two
Rotations
commutative law of Multiplication
Repeated multiplication
3. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Number line or real line
Categories of Algebra
Unary operations
Variables
4. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Associative law of Multiplication
Operations
Unknowns
Reflexive relation
5. 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
A polynomial equation
Algebraic combinatorics
exponential equation
substitution
6. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Algebraic equation
then a < c
Properties of equality
Identities
7. In which abstract algebraic methods are used to study combinatorial questions.
Exponentiation
Algebraic combinatorics
A linear equation
Knowns
8. Are true for only some values of the involved variables: x2 - 1 = 4.
A functional equation
operands - arguments - or inputs
Conditional equations
The logical values true and false
9. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
The relation of equality (=) has the property
Unary operations
Quadratic equations can also be solved
an operation
10. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Difference of two squares - or the difference of perfect squares
Constants
Algebraic equation
All quadratic equations
11. (a + b) + c = a + (b + c)
radical equation
Polynomials
associative law of addition
Difference of two squares - or the difference of perfect squares
12. 0 - which preserves numbers: a + 0 = a
The relation of inequality (<) has this property
then ac < bc
Universal algebra
identity element of addition
13. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Categories of Algebra
The operation of addition
Abstract algebra
Repeated multiplication
14. Logarithm (Log)
nonnegative numbers
(k+1)-ary relation that is functional on its first k domains
Unknowns
inverse operation of Exponentiation
15. Applies abstract algebra to the problems of geometry
Algebraic geometry
Algebra
Number line or real line
the set Y
16. The values of the variables which make the equation true are the solutions of the equation and can be found through
The relation of equality (=)
Number line or real line
Equation Solving
Real number
17. Can be combined using logic operations - such as and - or - and not.
Algebra
The simplest equations to solve
Unary operations
The logical values true and false
18. A + b = b + a
Variables
Quadratic equations can also be solved
Operations on functions
commutative law of Addition
19. Is an equation involving integrals.
A integral equation
A binary relation R over a set X is symmetric
operation
Algebraic equation
20. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
value - result - or output
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.
two inputs
21. 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
Elimination method
Unknowns
The operation of exponentiation
22. Is Written as a + b
Addition
The central technique to linear equations
operands - arguments - or inputs
Operations on sets
23. Can be defined axiomatically up to an isomorphism
The real number system
operation
Quadratic equations
A polynomial equation
24. The operation of multiplication means _______________: a
Repeated addition
Algebraic equation
The purpose of using variables
Solution to the system
25. Subtraction ( - )
inverse operation of addition
Elementary algebra
Reunion of broken parts
Identity element of Multiplication
26. Is an action or procedure which produces a new value from one or more input values.
an operation
Algebraic combinatorics
Difference of two squares - or the difference of perfect squares
Multiplication
27. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
the set Y
The relation of equality (=) has the property
unary and binary
28. If a < b and c < d
Equations
commutative law of Exponentiation
then a + c < b + d
then bc < ac
29. 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 relation of equality (=)
The method of equating the coefficients
Elimination method
The central technique to linear equations
30. () 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.
Algebra
The operation of exponentiation
(k+1)-ary relation that is functional on its first k domains
associative law of addition
31. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
A transcendental equation
The simplest equations to solve
Operations can involve dissimilar objects
nonnegative numbers
32. An operation of arity k is called a
The relation of equality (=)'s property
k-ary operation
Polynomials
Pure mathematics
33. A vector can be multiplied by a scalar to form another vector
operation
Operations can involve dissimilar objects
has arity one
Solution to the system
34. Include the binary operations union and intersection and the unary operation of complementation.
commutative law of Addition
then ac < bc
Operations on sets
identity element of Exponentiation
35. Include composition and convolution
Identity
Operations on functions
Exponentiation
An operation ?
36. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym
substitution
Reunion of broken parts
k-ary operation
Variables
37. Are called the domains of the operation
The sets Xk
unary and binary
The operation of addition
two inputs
38. Is an equation involving a transcendental function of one of its variables.
The relation of inequality (<) has this property
A transcendental equation
symmetric
scalar
39. 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)
Number line or real line
The operation of addition
nonnegative numbers
Categories of Algebra
40. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
A solution or root of the equation
then bc < ac
The real number system
Identity
41. 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
Real number
commutative law of Addition
The central technique to linear equations
A integral equation
42. 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
unary and binary
A integral equation
Elimination method
Pure mathematics
43. If a < b and c < 0
The real number system
then bc < ac
scalar
Algebraic number theory
44. Can be expressed in the form ax^2 + bx + c = 0 - where a is not zero (if it were zero - then the equation would not be quadratic but linear).
Identities
range
then ac < bc
Quadratic equations
45. Will have two solutions in the complex number system - but need not have any in the real number system.
operation
Change of variables
inverse operation of Exponentiation
All quadratic equations
46. Is the claim that two expressions have the same value and are equal.
logarithmic equation
Associative law of Multiplication
k-ary operation
Equations
47. Is called the codomain of the operation
symmetric
the set Y
Vectors
Quadratic equations
48. Are denoted by letters at the beginning - a - b - c - d - ...
Elimination method
Knowns
Difference of two squares - or the difference of perfect squares
inverse operation of Exponentiation
49. b = b
exponential equation
unary and binary
reflexive
A solution or root of the equation
50. Is an equation where the unknowns are required to be integers.
The logical values true and false
Quadratic equations can also be solved
Linear algebra
A Diophantine equation