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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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
A Diophantine equation
range
The relation of equality (=)'s property
then a + c < b + d
2. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Variables
radical equation
Unknowns
equation
3. A unary operation
A functional equation
Identities
has arity one
The operation of addition
4. Referring to the finite number of arguments (the value k)
unary and binary
Operations on sets
then a + c < b + d
finitary operation
5. Operations can have fewer or more than
Quadratic equations can also be solved
inverse operation of Exponentiation
two inputs
Pure mathematics
6. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Associative law of Exponentiation
has arity one
commutative law of Addition
A solution or root of the equation
7. Is Written as a
Vectors
Multiplication
Identity
Identity element of Multiplication
8. 0 - which preserves numbers: a + 0 = a
associative law of addition
inverse operation of Multiplication
value - result - or output
identity element of addition
9. 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).
exponential equation
Conditional equations
operation
Reflexive relation
10. Will have two solutions in the complex number system - but need not have any in the real number system.
Categories of Algebra
All quadratic equations
Unary operations
Identity
11. 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
k-ary operation
two inputs
Unary operations
substitution
12. 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.
Operations
Change of variables
The relation of equality (=) has the property
Algebraic combinatorics
13. 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'.
The operation of addition
Reflexive relation
The real number system
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.
14. Is Written as ab or a^b
Algebra
reflexive
inverse operation of Multiplication
Exponentiation
15. Is an equation of the form log`a^X = b for a > 0 - which has solution
two inputs
Associative law of Exponentiation
logarithmic equation
the fixed non-negative integer k (the number of arguments)
16. In which the specific properties of vector spaces are studied (including matrices)
Variables
Linear algebra
Operations can involve dissimilar objects
value - result - or output
17. Applies abstract algebra to the problems of geometry
substitution
Algebra
then a + c < b + d
Algebraic geometry
18. If a = b then b = a
Exponentiation
Universal algebra
symmetric
Real number
19. Is Written as a + b
Identity
Associative law of Multiplication
Addition
Number line or real line
20. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
Knowns
A binary relation R over a set X is symmetric
A linear equation
21. In which abstract algebraic methods are used to study combinatorial questions.
reflexive
Algebraic combinatorics
inverse operation of Exponentiation
identity element of addition
22. The value produced is called
The central technique to linear equations
The relation of inequality (<) has this property
system of linear equations
value - result - or output
23. Is an equation involving a transcendental function of one of its variables.
Elimination method
A transcendental equation
nonnegative numbers
Binary operations
24. The values for which an operation is defined form a set called its
Equation Solving
The operation of addition
identity element of Exponentiation
domain
25. Is an equation in which a polynomial is set equal to another polynomial.
the set Y
inverse operation of Exponentiation
Quadratic equations
A polynomial equation
26. 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
Elementary algebra
logarithmic equation
the fixed non-negative integer k (the number of arguments)
operation
27. 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)
inverse operation of addition
The operation of addition
Elimination method
unary and binary
28. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
scalar
Algebraic number theory
domain
substitution
29. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
inverse operation of Multiplication
Algebraic geometry
value - result - or output
30. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
has arity two
The relation of equality (=)
Quadratic equations can also be solved
operands - arguments - or inputs
31. Not associative
Number line or real line
Equation Solving
Associative law of Exponentiation
The relation of equality (=)
32. Is an equation involving derivatives.
A differential equation
Identity element of Multiplication
Number line or real line
Properties of equality
33. The values combined are called
operands - arguments - or inputs
Reflexive relation
operation
The logical values true and false
34. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
the set Y
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.
Solving the Equation
A polynomial equation
35. The squaring operation only produces
nonnegative numbers
Operations on functions
Order of Operations
commutative law of Multiplication
36. In which properties common to all algebraic structures are studied
Linear algebra
nonnegative numbers
Universal algebra
A Diophantine equation
37. A binary operation
The relation of equality (=)
has arity two
Repeated addition
Knowns
38. May not be defined for every possible value.
Difference of two squares - or the difference of perfect squares
Unknowns
Repeated addition
Operations
39. Involve only one value - such as negation and trigonometric functions.
Unary operations
The relation of equality (=)'s property
identity element of Exponentiation
A integral equation
40. Is an equation in which the unknowns are functions rather than simple quantities.
Pure mathematics
A functional equation
Repeated addition
The purpose of using variables
41. A
range
has arity one
an operation
commutative law of Multiplication
42. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The relation of inequality (<) has this property
The purpose of using variables
Pure mathematics
A transcendental equation
43. Is an equation where the unknowns are required to be integers.
operands - arguments - or inputs
A integral equation
Equations
A Diophantine equation
44. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
The operation of exponentiation
Categories of Algebra
Operations on sets
substitution
45. There are two common types of operations:
Associative law of Multiplication
Knowns
Algebraic combinatorics
unary and binary
46. k-ary operation is a
identity element of Exponentiation
The real number system
The logical values true and false
(k+1)-ary relation that is functional on its first k domains
47. 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 operation of addition
Reflexive relation
The central technique to linear equations
then a < c
48. Can be added and subtracted.
Vectors
an operation
then a + c < b + d
Order of Operations
49. Is an equation involving integrals.
A integral equation
identity element of addition
Abstract algebra
Conditional equations
50. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
Identity element of Multiplication
Polynomials
value - result - or output