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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. A binary operation
An operation ?
has arity two
Variables
Addition
2. 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 polynomial equation
operation
nullary operation
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.
3. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
nonnegative numbers
then bc < ac
Unknowns
4. A
Universal algebra
k-ary operation
The relation of inequality (<) has this property
commutative law of Multiplication
5. The values for which an operation is defined form a set called its
exponential equation
A Diophantine equation
domain
Quadratic equations
6. If a < b and b < c
Repeated multiplication
then a < c
when b > 0
finitary operation
7. A vector can be multiplied by a scalar to form another vector
commutative law of Multiplication
Operations on sets
Operations can involve dissimilar objects
Identity element of Multiplication
8. May not be defined for every possible value.
The operation of addition
scalar
Exponentiation
Operations
9. A + b = b + a
A integral equation
Operations on sets
commutative law of Addition
(k+1)-ary relation that is functional on its first k domains
10. 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
unary and binary
Reunion of broken parts
The purpose of using variables
operands - arguments - or inputs
11. Is Written as a + b
Addition
Algebraic combinatorics
Algebraic equation
substitution
12. (a + b) + c = a + (b + c)
Algebraic equation
associative law of addition
The relation of equality (=)'s property
commutative law of Multiplication
13. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
commutative law of Exponentiation
The operation of exponentiation
Order of Operations
The relation of equality (=) has the property
14. Include composition and convolution
Operations on functions
substitution
A differential equation
The relation of inequality (<) has this property
15. 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.
identity element of Exponentiation
Associative law of Multiplication
Unknowns
Change of variables
16. Logarithm (Log)
then a + c < b + d
The operation of addition
inverse operation of Exponentiation
range
17. Include the binary operations union and intersection and the unary operation of complementation.
Knowns
Operations on sets
Pure mathematics
The relation of inequality (<) has this property
18. Involve only one value - such as negation and trigonometric functions.
range
Unary operations
when b > 0
Repeated addition
19. Can be combined using the function composition operation - performing the first rotation and then the second.
commutative law of Multiplication
has arity one
Vectors
Rotations
20. Operations can have fewer or more than
Repeated multiplication
two inputs
(k+1)-ary relation that is functional on its first k domains
Solving the Equation
21. In which the specific properties of vector spaces are studied (including matrices)
equation
then a + c < b + d
has arity one
Linear algebra
22. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
range
Operations
The real number system
23. The codomain is the set of real numbers but the range is the
identity element of Exponentiation
nonnegative numbers
A binary relation R over a set X is symmetric
Constants
24. 0 - which preserves numbers: a + 0 = a
Variables
identity element of addition
inverse operation of addition
identity element of Exponentiation
25. 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)
A Diophantine equation
substitution
operation
The relation of equality (=)
26. Is an equation where the unknowns are required to be integers.
Repeated addition
inverse operation of Multiplication
A Diophantine 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.
27. Is called the codomain of the operation
reflexive
k-ary operation
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.
the set Y
28. An operation of arity zero is simply an element of the codomain Y - called a
Properties of equality
scalar
commutative law of Exponentiation
nullary operation
29. If a < b and c > 0
value - result - or output
Identity element of Multiplication
then ac < bc
then a + c < b + d
30. Not associative
Associative law of Exponentiation
associative law of addition
The method of equating the coefficients
finitary operation
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
Universal algebra
The relation of equality (=)
Associative law of Multiplication
32. The process of expressing the unknowns in terms of the knowns is called
The logical values true and false
All quadratic equations
Solving the Equation
Constants
33. 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
logarithmic equation
Identities
Repeated addition
substitution
34. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Binary operations
The sets Xk
Variables
Pure mathematics
35. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
Elementary algebra
Abstract algebra
then a < c
36. 1 - which preserves numbers: a
The simplest equations to solve
Identity element of Multiplication
Unary operations
Real number
37. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
The relation of inequality (<) has this property
Identities
k-ary operation
commutative law of Addition
38. Is an action or procedure which produces a new value from one or more input values.
the fixed non-negative integer k (the number of arguments)
an operation
operation
when b > 0
39. k-ary operation is a
A polynomial equation
(k+1)-ary relation that is functional on its first k domains
Addition
commutative law of Addition
40. 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
Conditional equations
Algebraic combinatorics
Vectors
The method of equating the coefficients
41. Are called the domains of the operation
The sets Xk
Identity
inverse operation of addition
inverse operation of Multiplication
42. Division ( / )
Algebraic combinatorics
identity element of Exponentiation
inverse operation of Multiplication
inverse operation of addition
43. 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
has arity one
equation
Elementary algebra
Operations can involve dissimilar objects
44. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
The purpose of using variables
substitution
Binary operations
45. Is an equation of the form aX = b for a > 0 - which has solution
Quadratic equations can also be solved
exponential equation
The logical values true and false
The relation of inequality (<) has this property
46. 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).
The relation of inequality (<) has this property
Multiplication
commutative law of Addition
Quadratic equations
47. Not commutative a^b?b^a
commutative law of Exponentiation
an operation
has arity two
Universal algebra
48. If a = b and b = c then a = c
A integral equation
scalar
transitive
Algebraic geometry
49. The values combined are called
identity element of addition
operands - arguments - or inputs
The simplest equations to solve
All quadratic equations
50. In which properties common to all algebraic structures are studied
two inputs
Universal algebra
Repeated addition
system of linear equations