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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 relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Universal algebra
Repeated multiplication
Properties of equality
Repeated addition
2. 1 - which preserves numbers: a^1 = a
system of linear equations
has arity one
identity element of Exponentiation
commutative law of Addition
3. If it holds for all a and b in X that if a is related to b then b is related to a.
Associative law of Multiplication
The logical values true and false
operation
A binary relation R over a set X is symmetric
4. 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.
The relation of inequality (<) has this property
then a < c
Algebraic combinatorics
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.
5. The operation of exponentiation means ________________: a^n = a
logarithmic equation
Repeated multiplication
commutative law of Multiplication
value - result - or output
6. A + b = b + a
Quadratic equations can also be solved
Identity
commutative law of Addition
system of linear equations
7. The operation of multiplication means _______________: a
Repeated 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.
Algebraic equation
Elementary algebra
8. 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)
Real number
The operation of addition
Solving the Equation
scalar
9. 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'.
Reflexive relation
Operations can involve dissimilar objects
Vectors
scalar
10. Is Written as a + b
Addition
Expressions
A transcendental equation
the set Y
11. Applies abstract algebra to the problems of geometry
A linear 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.
then a + c < b + d
Algebraic geometry
12. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
commutative law of Addition
reflexive
Identities
Algebraic number theory
13. Not commutative a^b?b^a
equation
Constants
commutative law of Exponentiation
then bc < ac
14. The inner product operation on two vectors produces a
finitary operation
operands - arguments - or inputs
Rotations
scalar
15. An operation of arity k is called a
Number line or real line
k-ary operation
inverse operation of Multiplication
Algebra
16. Are denoted by letters at the beginning - a - b - c - d - ...
Operations on functions
The central technique to linear equations
range
Knowns
17. Letters from the beginning of the alphabet like a - b - c... often denote
The logical values true and false
radical equation
operation
Constants
18. In which abstract algebraic methods are used to study combinatorial questions.
Equations
Algebraic combinatorics
Binary operations
the fixed non-negative integer k (the number of arguments)
19. Can be defined axiomatically up to an isomorphism
The real number system
Pure mathematics
Reunion of broken parts
Abstract algebra
20. Are true for only some values of the involved variables: x2 - 1 = 4.
Difference of two squares - or the difference of perfect squares
operation
Change of variables
Conditional equations
21. 1 - which preserves numbers: a
Identity element of Multiplication
when b > 0
associative law of addition
Algebraic equation
22. 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
Unary operations
Exponentiation
Variables
23. Involve only one value - such as negation and trigonometric functions.
commutative law of Multiplication
Variables
A polynomial equation
Unary operations
24. The value produced is called
Polynomials
Addition
Knowns
value - result - or output
25. Is Written as ab or a^b
Operations can involve dissimilar objects
(k+1)-ary relation that is functional on its first k domains
Exponentiation
Reunion of broken parts
26. Include composition and convolution
The sets Xk
Reunion of broken parts
Operations on functions
The simplest equations to solve
27. If a < b and c > 0
Abstract algebra
k-ary operation
A differential equation
then ac < bc
28. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Rotations
Vectors
then a < c
Unknowns
29. Is an action or procedure which produces a new value from one or more input values.
(k+1)-ary relation that is functional on its first k domains
nullary operation
an operation
has arity one
30. A vector can be multiplied by a scalar to form another vector
Universal algebra
Operations can involve dissimilar objects
commutative law of Addition
A Diophantine equation
31. 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)
when b > 0
then bc < ac
operation
Abstract algebra
32. The squaring operation only produces
Solution to the system
Algebraic geometry
Pure mathematics
nonnegative numbers
33. A
The real number system
has arity two
commutative law of Multiplication
unary and binary
34. 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
All quadratic equations
substitution
Operations can involve dissimilar objects
Linear algebra
35. 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
Unary operations
Elimination method
The method of equating the coefficients
36. Division ( / )
transitive
commutative law of Exponentiation
inverse operation of Multiplication
Algebraic combinatorics
37. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Multiplication
Change of variables
Constants
38. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Pure mathematics
Number line or real line
Associative law of Exponentiation
an operation
39. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
Change of variables
Categories of Algebra
domain
40. Symbols that denote numbers - is to allow the making of generalizations in mathematics
has arity two
Difference of two squares - or the difference of perfect squares
The purpose of using variables
Operations on functions
41. If a < b and b < c
then a < c
nullary operation
Difference of two squares - or the difference of perfect squares
Vectors
42. There are two common types of operations:
unary and binary
All quadratic equations
Equations
symmetric
43. 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
inverse operation of Multiplication
Order of Operations
Reunion of broken parts
nonnegative numbers
44. 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 logical values true and false
Universal algebra
The central technique to linear equations
logarithmic equation
45. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
The relation of equality (=) has the property
Identity
operands - arguments - or inputs
operation
46. Logarithm (Log)
inverse operation of Exponentiation
Reunion of broken parts
Elimination method
domain
47. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
reflexive
Solution to the system
the fixed non-negative integer k (the number of arguments)
Identities
48. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Operations
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.
nonnegative numbers
Reflexive relation
49. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
has arity two
Expressions
Pure mathematics
Equation Solving
50. The codomain is the set of real numbers but the range is the
transitive
reflexive
Difference of two squares - or the difference of perfect squares
nonnegative numbers