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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. Letters from the beginning of the alphabet like a - b - c... often denote
The method of equating the coefficients
Constants
All quadratic equations
Categories of Algebra
2. 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)
The operation of addition
A integral equation
operands - arguments - or inputs
Operations
3. Symbols that denote numbers - is to allow the making of generalizations in mathematics
inverse operation of addition
The purpose of using variables
substitution
All quadratic equations
4. Is an equation where the unknowns are required to be integers.
A Diophantine equation
the set Y
Polynomials
The purpose of using variables
5. 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
nullary operation
The relation of inequality (<) has this property
Equation Solving
6. If a < b and b < c
Linear algebra
Elementary algebra
Knowns
then a < c
7. 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
The method of equating the coefficients
Algebraic equation
Associative law of Exponentiation
The relation of equality (=)
8. Is called the type or arity of the operation
The simplest equations to solve
the fixed non-negative integer k (the number of arguments)
Associative law of Exponentiation
commutative law of Addition
9. 1 - which preserves numbers: a
Identity element of Multiplication
Algebra
The sets Xk
Elimination method
10. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
exponential equation
Addition
Associative law of Multiplication
Algebraic number theory
11. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Linear algebra
Properties of equality
The relation of equality (=)
then a < c
12. Is an equation involving a transcendental function of one of its variables.
The relation of equality (=)'s property
Reunion of broken parts
A transcendental equation
symmetric
13. A binary operation
has arity two
Reunion of broken parts
has arity one
The operation of exponentiation
14. Is an equation involving derivatives.
A differential equation
The central technique to linear equations
has arity one
Operations on functions
15. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Elimination method
radical equation
Vectors
Polynomials
16. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Order of Operations
Binary operations
The real number system
Algebraic equation
17. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
finitary operation
Categories of Algebra
Identity
inverse operation of addition
18. The process of expressing the unknowns in terms of the knowns is called
A transcendental equation
Solving the Equation
reflexive
Reunion of broken parts
19. An operation of arity k is called a
Equation Solving
commutative law of Multiplication
k-ary operation
operands - arguments - or inputs
20. If a < b and c < d
scalar
then a + c < b + d
then ac < bc
transitive
21. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
commutative law of Addition
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.
commutative law of Multiplication
nonnegative numbers
22. 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
logarithmic equation
A differential equation
Identities
23. Is an equation of the form aX = b for a > 0 - which has solution
inverse operation of Multiplication
exponential equation
Quadratic equations can also be solved
Operations on functions
24. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Elimination method
A solution or root of the equation
Constants
finitary operation
25. Is an equation in which a polynomial is set equal to another polynomial.
Addition
Quadratic equations
Pure mathematics
A polynomial equation
26. 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.
value - result - or output
Quadratic equations can also be solved
Universal algebra
Properties of equality
27. A vector can be multiplied by a scalar to form another vector
Number line or real line
then a + c < b + d
Operations can involve dissimilar objects
Operations on functions
28. A
commutative law of Multiplication
Identity
Elimination method
Identity element of Multiplication
29. There are two common types of operations:
has arity two
then a + c < b + d
The operation of exponentiation
unary and binary
30. The operation of exponentiation means ________________: a^n = a
The relation of equality (=)'s property
The relation of inequality (<) has this property
Repeated multiplication
range
31. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
Properties of equality
equation
Operations on sets
32. b = b
reflexive
The operation of exponentiation
Algebraic number theory
the fixed non-negative integer k (the number of arguments)
33. Is called the codomain of the operation
A Diophantine equation
the set Y
Properties of equality
nonnegative numbers
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.
Algebra
operands - arguments - or inputs
operation
inverse operation of addition
35. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Exponentiation
Expressions
Identities
The purpose of using variables
36. Referring to the finite number of arguments (the value k)
Operations
The real number system
Universal algebra
finitary operation
37. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)
Knowns
Vectors
identity element of Exponentiation
operation
38. 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
The operation of exponentiation
range
then a < c
39. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Rotations
Associative law of Exponentiation
Repeated addition
40. Is an action or procedure which produces a new value from one or more input values.
Variables
The operation of exponentiation
inverse operation of Exponentiation
an operation
41. If it holds for all a and b in X that if a is related to b then b is related to a.
A solution or root of the equation
The simplest equations to solve
A binary relation R over a set X is symmetric
The sets Xk
42. Involve only one value - such as negation and trigonometric functions.
Polynomials
operands - arguments - or inputs
Real number
Unary operations
43. Is algebraic equation of degree one
A linear equation
system of linear equations
Rotations
has arity one
44. Can be added and subtracted.
Vectors
Real number
has arity two
Operations on functions
45. Applies abstract algebra to the problems of geometry
substitution
Algebraic geometry
An operation ?
range
46. k-ary operation is a
then a + c < b + d
two inputs
Properties of equality
(k+1)-ary relation that is functional on its first k domains
47. The value produced is called
A solution or root of the equation
A functional equation
value - result - or output
then ac < bc
48. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Knowns
range
Categories of Algebra
Binary operations
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).
An operation ?
Constants
Quadratic equations
Equations
50. In which properties common to all algebraic structures are studied
when b > 0
Algebra
k-ary operation
Universal algebra