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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. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
identity element of Exponentiation
Solving the Equation
Equation Solving
2. Is Written as a
Addition
domain
commutative law of Addition
Multiplication
3. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
Reflexive relation
A differential equation
logarithmic equation
4. 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
reflexive
An operation ?
Elementary algebra
range
5. The operation of multiplication means _______________: a
Order of Operations
Variables
Repeated addition
Multiplication
6. k-ary operation is a
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.
(k+1)-ary relation that is functional on its first k domains
radical equation
the set Y
7. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
The operation of addition
Properties of equality
A differential equation
Pure mathematics
8. Subtraction ( - )
Identity element of Multiplication
inverse operation of addition
then bc < ac
The operation of addition
9. Can be combined using the function composition operation - performing the first rotation and then the second.
The operation of addition
Algebraic geometry
Associative law of Exponentiation
Rotations
10. If a < b and c < d
Elementary algebra
scalar
identity element of addition
then a + c < b + d
11. 0 - which preserves numbers: a + 0 = a
range
identity element of addition
Equations
(k+1)-ary relation that is functional on its first k domains
12. Is an equation in which a polynomial is set equal to another polynomial.
operands - arguments - or inputs
A polynomial equation
substitution
Linear algebra
13. Is an equation of the form aX = b for a > 0 - which has solution
Identities
inverse operation of Exponentiation
the set Y
exponential equation
14. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
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.
operation
A integral equation
15. 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).
Quadratic equations
substitution
Conditional equations
nonnegative numbers
16. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
(k+1)-ary relation that is functional on its first k domains
radical equation
then bc < ac
Variables
17. Division ( / )
then a + c < b + d
Algebra
A integral equation
inverse operation of Multiplication
18. If a = b then b = a
identity element of Exponentiation
Equation Solving
The relation of equality (=)
symmetric
19. Logarithm (Log)
Linear algebra
inverse operation of Exponentiation
Identity
Operations
20. Is an equation involving derivatives.
Algebra
commutative law of Exponentiation
A differential equation
An operation ?
21. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain
domain
then a < c
when b > 0
exponential equation
22. Is an equation where the unknowns are required to be integers.
domain
A Diophantine equation
The central technique to linear equations
Elimination method
23. 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
substitution
has arity one
The relation of equality (=)
scalar
24. A binary operation
the set Y
has arity two
Unknowns
then ac < bc
25. Can be combined using logic operations - such as and - or - and not.
The purpose of using variables
Operations
Expressions
The logical values true and false
26. The inner product operation on two vectors produces a
when b > 0
Elimination method
unary and binary
scalar
27. The values combined are called
Equations
unary and binary
Identity
operands - arguments - or inputs
28. If a < b and c < 0
Knowns
Linear algebra
Exponentiation
then bc < ac
29. Not commutative a^b?b^a
Quadratic equations can also be solved
Algebraic equation
then a < c
commutative law of Exponentiation
30. Applies abstract algebra to the problems of geometry
domain
Algebraic geometry
inverse operation of Exponentiation
then a < c
31. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
Elementary algebra
A integral equation
Operations can involve dissimilar objects
32. If a < b and b < c
Identities
Multiplication
then a < c
The relation of equality (=)'s property
33. An operation of arity k is called a
an operation
The operation of addition
k-ary operation
has arity two
34. Involve only one value - such as negation and trigonometric functions.
Unary operations
A solution or root of the equation
Constants
Elementary algebra
35. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
inverse operation of Multiplication
The method of equating the coefficients
Categories of Algebra
36. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
two inputs
equation
Pure mathematics
Conditional equations
37. The values for which an operation is defined form a set called its
an operation
domain
A integral equation
nonnegative numbers
38. b = b
the fixed non-negative integer k (the number of arguments)
domain
An operation ?
reflexive
39. 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.
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40. If it holds for all a and b in X that if a is related to b then b is related to a.
A binary relation R over a set X is symmetric
reflexive
Pure mathematics
The sets Xk
41. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Operations on functions
Equations
A binary relation R over a set X is symmetric
Associative law of Multiplication
42. Operations can have fewer or more than
range
two inputs
Equation Solving
Vectors
43. Is the claim that two expressions have the same value and are equal.
nonnegative numbers
Linear algebra
Equations
The relation of equality (=) has the property
44. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
Change of variables
operation
Algebra
45. Can be defined axiomatically up to an isomorphism
Polynomials
Operations on sets
The real number system
has arity two
46. The value produced is called
operation
Binary operations
value - result - or output
A Diophantine equation
47. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Identity
Order of Operations
The logical values true and false
Abstract algebra
48. () 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.
Identity element of Multiplication
Quadratic equations can also be solved
Algebraic geometry
Algebra
49. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
The relation of equality (=)
value - result - or output
Algebraic number theory
k-ary operation
50. Are called the domains of the operation
Algebraic number theory
domain
The sets Xk
A integral equation