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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. Can be defined axiomatically up to an isomorphism
A transcendental equation
commutative law of Addition
The real number system
commutative law of Multiplication
2. If a < b and c < d
The sets Xk
Repeated multiplication
then a + c < b + d
Operations on functions
3. Is Written as a
A binary relation R over a set X is symmetric
Multiplication
radical equation
Polynomials
4. 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.
The relation of equality (=) has the property
Operations can involve dissimilar objects
Universal algebra
Algebra
5. Is called the codomain of the operation
unary and binary
operation
The logical values true and false
the set Y
6. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
Pure mathematics
Difference of two squares - or the difference of perfect squares
when b > 0
7. Not associative
Repeated multiplication
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 relation of equality (=)'s property
Associative law of Exponentiation
8. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
A binary relation R over a set X is symmetric
Associative law of Multiplication
Polynomials
range
9. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Vectors
Algebraic number theory
commutative law of Exponentiation
commutative law of Addition
10. Can be combined using the function composition operation - performing the first rotation and then the second.
an operation
Operations on sets
identity element of Exponentiation
Rotations
11. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
Pure mathematics
k-ary operation
A differential equation
12. Involve only one value - such as negation and trigonometric functions.
A functional equation
Binary operations
A binary relation R over a set X is symmetric
Unary operations
13. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
then ac < bc
Reunion of broken parts
A differential equation
14. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Algebraic geometry
radical equation
then ac < bc
logarithmic equation
15. Is the claim that two expressions have the same value and are equal.
The operation of addition
Equations
Order of Operations
Elementary algebra
16. Applies abstract algebra to the problems of geometry
commutative law of Addition
Solving the Equation
Algebraic geometry
Elementary algebra
17. A unary operation
then a + c < b + d
Unknowns
A transcendental equation
has arity one
18. 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 exponentiation
Abstract algebra
Polynomials
Reflexive relation
19. Is an algebraic 'sentence' containing an unknown quantity.
(k+1)-ary relation that is functional on its first k domains
operands - arguments - or inputs
Polynomials
Repeated multiplication
20. 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.
unary and binary
Polynomials
A linear equation
The relation of inequality (<) has this property
21. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Solution to the system
Conditional equations
operands - arguments - or inputs
Expressions
22. Is an equation involving derivatives.
when b > 0
A differential equation
Identity
The real number system
23. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
Solution to the system
transitive
domain
24. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
The logical values true and false
Number line or real line
A functional equation
Solution to the system
25. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Rotations
Solution to the system
Identity
domain
26. Subtraction ( - )
inverse operation of addition
Identity
when b > 0
has arity one
27. The values of the variables which make the equation true are the solutions of the equation and can be found through
A linear equation
A differential equation
nullary operation
Equation Solving
28. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
two inputs
A linear equation
Linear algebra
29. Is an equation involving a transcendental function of one of its variables.
radical equation
The logical values true and false
A transcendental equation
Binary operations
30. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Order of Operations
Categories of Algebra
Unary operations
associative law of addition
31. If a < b and c < 0
A binary relation R over a set X is symmetric
The relation of equality (=)'s property
then bc < ac
commutative law of Exponentiation
32. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that
Real number
inverse operation of Multiplication
operands - arguments - or inputs
commutative law of Addition
33. In an equation with a single unknown - a value of that unknown for which the equation is true is called
A integral equation
Operations on functions
scalar
A solution or root of the equation
34. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Exponentiation
The simplest equations to solve
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.
35. In which abstract algebraic methods are used to study combinatorial questions.
system of linear equations
Algebraic combinatorics
finitary operation
inverse operation of addition
36. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
The simplest equations to solve
Vectors
nullary operation
two inputs
37. 0 - which preserves numbers: a + 0 = a
The simplest equations to solve
Properties of equality
identity element of addition
Variables
38. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
Abstract algebra
A transcendental equation
scalar
39. Are denoted by letters at the beginning - a - b - c - d - ...
Identity
symmetric
Knowns
Expressions
40. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
value - result - or output
The sets Xk
The purpose of using variables
41. A binary operation
has arity one
Unary operations
nonnegative numbers
has arity two
42. The inner product operation on two vectors produces a
Polynomials
Difference of two squares - or the difference of perfect squares
scalar
operands - arguments - or inputs
43. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The relation of equality (=)
identity element of addition
operation
Solution to the system
44. The operation of multiplication means _______________: a
A Diophantine equation
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.
value - result - or output
45. 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)
finitary operation
identity element of Exponentiation
The operation of addition
Binary operations
46. Is an equation of the form aX = b for a > 0 - which has solution
system of linear equations
Categories of Algebra
Order of Operations
exponential equation
47. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Addition
Equations
equation
Associative law of Exponentiation
48. 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).
Quadratic equations
All quadratic equations
A solution or root of the equation
operation
49. If a = b then b = a
Linear algebra
symmetric
Unary operations
Quadratic equations
50. If a < b and b < c
The relation of equality (=) has the property
operation
Properties of equality
then a < c