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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. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Vectors
radical equation
All quadratic equations
range
2. Division ( / )
A integral equation
scalar
inverse operation of Multiplication
substitution
3. 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
Algebraic equation
system of linear equations
The method of equating the coefficients
Equations
4. Is an equation involving a transcendental function of one of its variables.
operation
A transcendental equation
Unknowns
The central technique to linear equations
5. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Expressions
commutative law of Multiplication
Solution to the system
A Diophantine equation
6. Is Written as a + b
Operations on sets
Addition
A polynomial equation
nonnegative numbers
7. Is an equation involving derivatives.
A integral equation
Solution to the system
A differential equation
logarithmic equation
8. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
A functional equation
Operations on sets
the set Y
Number line or real line
9. Not associative
Associative law of Exponentiation
An operation ?
A binary relation R over a set X is symmetric
Repeated addition
10. 1 - which preserves numbers: a
Linear algebra
equation
Identity element of Multiplication
The simplest equations to solve
11. 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.
Binary operations
Properties of equality
Categories of Algebra
system of linear equations
12. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Reunion of broken parts
radical equation
Associative law of Multiplication
system of linear equations
13. Not commutative a^b?b^a
A functional equation
Algebraic combinatorics
Universal algebra
commutative law of Exponentiation
14. (a
All quadratic equations
Solving the Equation
has arity one
Associative law of Multiplication
15. 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
scalar
Equations
Conditional equations
Elementary algebra
16. May not be defined for every possible value.
Knowns
Operations
then bc < ac
Algebraic equation
17. The process of expressing the unknowns in terms of the knowns is called
Pure mathematics
Solving the Equation
A functional equation
symmetric
18. The squaring operation only produces
Operations
An operation ?
nonnegative numbers
radical equation
19. A unary operation
Elimination method
has arity one
Operations
Identity
20. A
commutative law of Multiplication
The relation of equality (=)'s property
A differential equation
range
21. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
Repeated multiplication
equation
value - result - or output
22. 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.
commutative law of Multiplication
Identities
A polynomial equation
The relation of inequality (<) has this property
23. In which abstract algebraic methods are used to study combinatorial questions.
Quadratic equations
Algebraic combinatorics
Solving the Equation
nonnegative numbers
24. The inner product operation on two vectors produces a
scalar
Repeated multiplication
symmetric
inverse operation of addition
25. Is an action or procedure which produces a new value from one or more input values.
The simplest equations to solve
Algebraic equation
Exponentiation
an operation
26. Is an equation in which the unknowns are functions rather than simple quantities.
Vectors
A functional equation
Algebra
The real number system
27. Is called the codomain of the operation
Operations on sets
Quadratic equations
Properties of equality
the set Y
28. Can be added and subtracted.
Reunion of broken parts
Vectors
Variables
two inputs
29. () 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.
Reunion of broken parts
Algebra
The relation of equality (=)'s property
then a + c < b + d
30. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
has arity two
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.
Reflexive relation
Abstract algebra
31. The values for which an operation is defined form a set called its
Associative law of Exponentiation
transitive
domain
The method of equating the coefficients
32. Is an equation in which a polynomial is set equal to another polynomial.
Addition
Number line or real line
Solving the Equation
A polynomial equation
33. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Equations
nonnegative numbers
equation
k-ary operation
34. Can be defined axiomatically up to an isomorphism
identity element of Exponentiation
The real number system
operation
unary and binary
35. An operation of arity k is called a
Exponentiation
A binary relation R over a set X is symmetric
Equations
k-ary operation
36. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
The operation of exponentiation
Abstract algebra
A binary relation R over a set X is symmetric
37. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Associative law of Exponentiation
Change of variables
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.
38. Can be combined using the function composition operation - performing the first rotation and then the second.
system of linear equations
Conditional equations
A binary relation R over a set X is symmetric
Rotations
39. 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.
Variables
The central technique to linear equations
equation
A integral equation
40. 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.
associative law of addition
Change of variables
Reflexive relation
Solving the Equation
41. Involve only one value - such as negation and trigonometric functions.
Conditional equations
nullary operation
A binary relation R over a set X is symmetric
Unary operations
42. If a < b and c < d
Quadratic equations can also be solved
Associative law of Exponentiation
then a + c < b + d
The method of equating the coefficients
43. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
Operations on functions
associative law of addition
An operation ?
44. Are denoted by letters at the beginning - a - b - c - d - ...
inverse operation of addition
Knowns
Repeated multiplication
All quadratic equations
45. 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).
A transcendental equation
operation
Abstract algebra
finitary operation
46. 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
Algebraic equation
Reunion of broken parts
scalar
Multiplication
47. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
All quadratic equations
k-ary operation
Pure mathematics
operation
48. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Reunion of broken parts
range
Operations can involve dissimilar objects
Algebraic number theory
49. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
Algebraic equation
operation
Associative law of Exponentiation
50. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
identity element of addition
Equations
scalar