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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. In an equation with a single unknown - a value of that unknown for which the equation is true is called
A integral equation
Operations can involve dissimilar objects
has arity one
A solution or root of the equation
2. 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.
Expressions
The central technique to linear equations
commutative law of Addition
Addition
3. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
logarithmic equation
Identity
Difference of two squares - or the difference of perfect squares
4. In which abstract algebraic methods are used to study combinatorial questions.
Binary operations
identity element of Exponentiation
Algebraic combinatorics
Repeated multiplication
5. Can be combined using the function composition operation - performing the first rotation and then the second.
The operation of addition
Associative law of Multiplication
A integral equation
Rotations
6. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
operation
Expressions
The simplest equations to solve
finitary operation
7. Applies abstract algebra to the problems of geometry
Algebraic geometry
associative law of addition
exponential equation
All quadratic equations
8. Is an equation in which the unknowns are functions rather than simple quantities.
operation
Real number
A functional equation
Reunion of broken parts
9. The values of the variables which make the equation true are the solutions of the equation and can be found through
Algebra
Solution to the system
commutative law of Addition
Equation Solving
10. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
then a + c < b + d
Binary operations
Algebraic number theory
symmetric
11. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
A linear equation
equation
identity element of Exponentiation
nonnegative numbers
12. Can be combined using logic operations - such as and - or - and not.
Algebraic number theory
Addition
The purpose of using variables
The logical values true and false
13. A
commutative law of Multiplication
A solution or root of the equation
Change of variables
(k+1)-ary relation that is functional on its first k domains
14. b = b
reflexive
Number line or real line
inverse operation of addition
then a < c
15. In which properties common to all algebraic structures are studied
Universal algebra
Exponentiation
Repeated multiplication
A differential equation
16. The inner product operation on two vectors produces a
Elimination method
Order of Operations
scalar
Number line or real line
17. If a < b and c < d
operands - arguments - or inputs
then a + c < b + d
Associative law of Exponentiation
Addition
18. Is Written as a + b
domain
Addition
Identity element of Multiplication
A integral equation
19. (a + b) + c = a + (b + c)
associative law of addition
A polynomial equation
The real number system
Linear algebra
20. 0 - which preserves numbers: a + 0 = a
Order of Operations
Identity
equation
identity element of addition
21. Is an action or procedure which produces a new value from one or more input values.
A Diophantine equation
an operation
A differential equation
Operations can involve dissimilar objects
22. 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)
Unary operations
system of linear equations
A Diophantine equation
The operation of addition
23. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
has arity one
range
identity element of addition
nonnegative numbers
24. In which the specific properties of vector spaces are studied (including matrices)
Polynomials
finitary operation
inverse operation of Multiplication
Linear algebra
25. The values for which an operation is defined form a set called its
symmetric
Operations on functions
domain
A binary relation R over a set X is symmetric
26. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
symmetric
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.
Operations on functions
The sets Xk
27. If a < b and c > 0
unary and binary
nullary operation
Elimination method
then ac < bc
28. 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.
(k+1)-ary relation that is functional on its first k domains
Multiplication
Change of variables
Number line or real line
29. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=) has the property
The relation of equality (=)
Elimination method
A integral equation
30. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
The relation of equality (=)'s property
Quadratic equations can also be solved
Solving the Equation
Reflexive relation
31. Are denoted by letters at the beginning - a - b - c - d - ...
nonnegative numbers
Quadratic equations
Knowns
when b > 0
32. Is Written as ab or a^b
Exponentiation
Order of Operations
The relation of equality (=)
The operation of addition
33. 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
k-ary operation
The method of equating the coefficients
Vectors
Equations
34. () 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.
The relation of equality (=) has the property
Algebra
A polynomial equation
The central technique to linear equations
35. Is called the codomain of the operation
Properties of equality
A Diophantine equation
nonnegative numbers
the set Y
36. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
Abstract algebra
The operation of addition
Unknowns
37. A binary operation
Properties of equality
An operation ?
operation
has arity two
38. 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.
Equations
The relation of equality (=) has the property
nonnegative numbers
substitution
39. The values combined are called
Variables
Elimination method
Algebraic equation
operands - arguments - or inputs
40. The squaring operation only produces
equation
Identity element of Multiplication
Abstract algebra
nonnegative numbers
41. Subtraction ( - )
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.
inverse operation of addition
Equation Solving
Elimination method
42. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The sets Xk
unary and binary
commutative law of Multiplication
Solution to the system
43. Is algebraic equation of degree one
A linear equation
(k+1)-ary relation that is functional on its first k domains
Change of variables
Universal algebra
44. 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
nonnegative numbers
Addition
A integral equation
45. 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.
then a + c < b + d
The operation of exponentiation
The relation of inequality (<) has this property
inverse operation of Exponentiation
46. Is the claim that two expressions have the same value and are equal.
Conditional equations
A functional equation
Equations
Rotations
47. Letters from the beginning of the alphabet like a - b - c... often denote
operation
Algebraic number theory
Constants
The simplest equations to solve
48. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
The relation of inequality (<) has this property
A polynomial equation
A solution or root of the equation
49. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
the set Y
identity element of Exponentiation
Identity element of Multiplication
50. There are two common types of operations:
unary and binary
The real number system
Constants
Change of variables