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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. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
inverse operation of Exponentiation
The operation of exponentiation
operation
2. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Equations
Order of Operations
associative law of addition
system of linear equations
3. 0 - which preserves numbers: a + 0 = a
system of linear equations
Identities
identity element of addition
Unary operations
4. 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.
The operation of addition
The relation of equality (=) has the property
Equations
then ac < bc
5. A + b = b + a
commutative law of Addition
The logical values true and false
Equations
Expressions
6. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Addition
A differential equation
Expressions
Variables
7. Not associative
Associative law of Exponentiation
Equations
Algebraic geometry
Change of variables
8. Is Written as a
Operations on sets
identity element of Exponentiation
Multiplication
The central technique to linear equations
9. 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 (=) has the property
Rotations
Equation Solving
The operation of exponentiation
10. Not commutative a^b?b^a
commutative law of Exponentiation
when b > 0
Reunion of broken parts
operation
11. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
A integral equation
Solution to the system
then bc < ac
The method of equating the coefficients
12. Applies abstract algebra to the problems of geometry
A binary relation R over a set X is symmetric
Algebraic geometry
The relation of inequality (<) has this property
the fixed non-negative integer k (the number of arguments)
13. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
Vectors
nullary operation
Exponentiation
14. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Pure mathematics
Vectors
Binary operations
The central technique to linear equations
15. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Algebraic combinatorics
equation
commutative law of Exponentiation
reflexive
16. Is Written as ab or a^b
A transcendental equation
Exponentiation
A linear equation
Algebraic combinatorics
17. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
Solution to the system
Vectors
Reunion of broken parts
18. Include composition and convolution
Addition
Identities
Elementary algebra
Operations on functions
19. In which properties common to all algebraic structures are studied
Universal algebra
system of linear equations
Equations
The purpose of using variables
20. The operation of exponentiation means ________________: a^n = a
Quadratic equations can also be solved
All quadratic equations
exponential equation
Repeated multiplication
21. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
Difference of two squares - or the difference of perfect squares
The purpose of using variables
Unknowns
22. If a < b and c > 0
reflexive
A transcendental equation
then ac < bc
Linear algebra
23. Letters from the beginning of the alphabet like a - b - c... often denote
operands - arguments - or inputs
The sets Xk
Constants
The real number system
24. The inner product operation on two vectors produces a
The operation of addition
scalar
Rotations
operands - arguments - or inputs
25. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
unary and binary
Unknowns
reflexive
domain
26. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
(k+1)-ary relation that is functional on its first k domains
then a + c < b + d
Universal algebra
27. 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
The sets Xk
substitution
Unary operations
The relation of equality (=)'s property
28. b = b
Associative law of Exponentiation
has arity two
Number line or real line
reflexive
29. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
domain
has arity two
All quadratic equations
Difference of two squares - or the difference of perfect squares
30. Are true for only some values of the involved variables: x2 - 1 = 4.
Operations
Binary operations
Conditional equations
inverse operation of Multiplication
31. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
k-ary operation
Operations can involve dissimilar objects
Pure mathematics
range
32. Are called the domains of the 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.
system of linear equations
The sets Xk
Number line or real line
33. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Knowns
Number line or real line
unary and binary
radical equation
34. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
identity element of Exponentiation
Algebraic number theory
symmetric
35. Logarithm (Log)
Difference of two squares - or the difference of perfect squares
Order of Operations
A solution or root of the equation
inverse operation of Exponentiation
36. 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'.
The relation of equality (=) has the property
Reflexive relation
Quadratic equations
Identity
37. If a < b and c < 0
then bc < ac
Unknowns
The operation of addition
associative law of addition
38. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
scalar
Elementary algebra
nullary operation
Equations
39. An operation of arity zero is simply an element of the codomain Y - called a
The simplest equations to solve
nullary operation
substitution
reflexive
40. () 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.
Properties of equality
transitive
Algebraic geometry
Algebra
41. 1 - which preserves numbers: a
Solving the Equation
inverse operation of Exponentiation
unary and binary
Identity element of Multiplication
42. Operations can have fewer or more than
two inputs
Order of Operations
A polynomial equation
Reflexive relation
43. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
Algebraic geometry
has arity two
Unknowns
44. Is called the codomain of the operation
Identity
the set Y
Operations can involve dissimilar objects
Associative law of Exponentiation
45. k-ary operation is a
operation
Order of Operations
(k+1)-ary relation that is functional on its first k domains
Polynomials
46. The values for which an operation is defined form a set called its
Equations
reflexive
The logical values true and false
domain
47. Is an equation involving a transcendental function of one of its variables.
Operations
Algebraic combinatorics
A transcendental equation
Solving the Equation
48. Is an equation involving derivatives.
A transcendental equation
operation
A solution or root of the equation
A differential equation
49. 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).
Identity
Multiplication
Quadratic equations
An operation ?
50. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
The relation of equality (=) has the property
system of linear equations
Reunion of broken parts