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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. The process of expressing the unknowns in terms of the knowns is called
Identities
Solving the Equation
system of linear equations
The relation of equality (=)'s property
2. 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
A Diophantine equation
Quadratic equations
A solution or root of the equation
The method of equating the coefficients
3. Is Written as ab or a^b
commutative law of Addition
Exponentiation
Universal algebra
The simplest equations to solve
4. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Expressions
system of linear equations
The method of equating the coefficients
Quadratic equations can also be solved
5. 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 central technique to linear equations
(k+1)-ary relation that is functional on its first k domains
Vectors
Algebraic geometry
6. A + b = b + a
commutative law of Addition
identity element of addition
operation
The method of equating the coefficients
7. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
operation
k-ary operation
associative law of addition
8. 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
Quadratic equations
has arity two
The operation of addition
9. If a < b and c > 0
Repeated addition
value - result - or output
Operations on sets
then ac < bc
10. Is an algebraic 'sentence' containing an unknown quantity.
Polynomials
Linear algebra
commutative law of Multiplication
Properties of equality
11. A binary operation
The logical values true and false
The purpose of using variables
has arity two
Rotations
12. Is an equation involving integrals.
operands - arguments - or inputs
Associative law of Exponentiation
A integral equation
nonnegative numbers
13. The operation of multiplication means _______________: a
Quadratic equations
Repeated addition
Operations can involve dissimilar objects
Solution to the system
14. Applies abstract algebra to the problems of geometry
Exponentiation
Knowns
the set Y
Algebraic geometry
15. Not associative
Operations
Rotations
value - result - or output
Associative law of Exponentiation
16. Is algebraic equation of degree one
inverse operation of Exponentiation
Conditional equations
A linear equation
Identity
17. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
system of linear equations
A solution or root of the equation
Associative law of Exponentiation
range
18. In which the specific properties of vector spaces are studied (including matrices)
Polynomials
Algebraic equation
identity element of addition
Linear algebra
19. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
then a < c
Algebra
A differential equation
20. Is an equation of the form aX = b for a > 0 - which has solution
Knowns
has arity one
exponential equation
Reflexive relation
21. b = b
an operation
reflexive
symmetric
A differential equation
22. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
The simplest equations to solve
Algebraic equation
k-ary operation
Binary operations
23. Is an action or procedure which produces a new value from one or more input values.
equation
an operation
then ac < bc
range
24. In which properties common to all algebraic structures are studied
Universal algebra
A linear equation
Knowns
The sets Xk
25. There are two common types of operations:
unary and binary
An operation ?
The simplest equations to solve
A polynomial equation
26. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Multiplication
Binary operations
The simplest equations to solve
Operations on sets
27. 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
A linear equation
transitive
The operation of addition
28. A
inverse operation of addition
commutative law of Multiplication
An operation ?
then a + c < b + d
29. Include the binary operations union and intersection and the unary operation of complementation.
A transcendental equation
when b > 0
Operations on sets
reflexive
30. Operations can have fewer or more than
two inputs
The relation of equality (=)'s property
Operations on functions
value - result - or output
31. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
Knowns
logarithmic equation
exponential equation
32. Can be added and subtracted.
Vectors
domain
A binary relation R over a set X is symmetric
associative law of addition
33. 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
Change of variables
transitive
Order of Operations
Real number
34. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)
domain
The operation of exponentiation
The relation of equality (=)
Constants
35. Is the claim that two expressions have the same value and are equal.
substitution
Equations
transitive
nonnegative numbers
36. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
then bc < ac
Expressions
Algebraic number theory
commutative law of Addition
37. Not commutative a^b?b^a
commutative law of Exponentiation
nonnegative numbers
(k+1)-ary relation that is functional on its first k domains
The relation of equality (=) has the property
38. Will have two solutions in the complex number system - but need not have any in the real number system.
The method of equating the coefficients
Identity
The central technique to linear equations
All quadratic equations
39. 1 - which preserves numbers: a
Abstract algebra
associative law of addition
an operation
Identity element of Multiplication
40. If a = b and b = c then a = c
operation
Unknowns
(k+1)-ary relation that is functional on its first k domains
transitive
41. Can be defined axiomatically up to an isomorphism
An operation ?
exponential equation
The real number system
Difference of two squares - or the difference of perfect squares
42. The values for which an operation is defined form a set called its
Linear algebra
domain
Algebraic geometry
Exponentiation
43. If a < b and c < 0
Variables
Pure mathematics
Operations
then bc < ac
44. 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'.
Multiplication
Reflexive relation
when b > 0
then a < c
45. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Algebra
Identities
Associative law of Exponentiation
Pure mathematics
46. The operation of exponentiation means ________________: a^n = a
identity element of addition
value - result - or output
Constants
Repeated multiplication
47. 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.
commutative law of Multiplication
scalar
The relation of equality (=) has the property
The real number system
48. 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
A polynomial equation
system of linear equations
inverse operation of Exponentiation
Elementary algebra
49. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Number line or real line
Difference of two squares - or the difference of perfect squares
nonnegative numbers
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.
50. (a + b) + c = a + (b + c)
A solution or root of the equation
Algebraic geometry
associative law of addition
inverse operation of addition