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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. 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
exponential equation
an operation
inverse operation of Multiplication
The method of equating the coefficients
2. Is the claim that two expressions have the same value and are equal.
commutative law of Addition
transitive
The relation of equality (=)'s property
Equations
3. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Categories of Algebra
Algebraic number theory
radical equation
Identity
4. Can be defined axiomatically up to an isomorphism
The real number system
has arity two
identity element of Exponentiation
The relation of equality (=)
5. 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
Real number
operation
domain
6. 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.
two inputs
The relation of inequality (<) has this property
Equations
Equation Solving
7. Is called the type or arity of the operation
unary and binary
The real number system
the fixed non-negative integer k (the number of arguments)
Unary operations
8. 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
operands - arguments - or inputs
transitive
Reunion of broken parts
Operations
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'.
Binary operations
The operation of exponentiation
Reflexive relation
Algebraic geometry
10. If it holds for all a and b in X that if a is related to b then b is related to a.
identity element of Exponentiation
symmetric
then a < c
A binary relation R over a set X is symmetric
11. 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.
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12. Is an algebraic 'sentence' containing an unknown quantity.
inverse operation of Exponentiation
Elimination method
Identities
Polynomials
13. Subtraction ( - )
then ac < bc
Equations
inverse operation of addition
Operations on functions
14. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
operands - arguments - or inputs
Universal algebra
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.
Equations
15. Will have two solutions in the complex number system - but need not have any in the real number system.
nonnegative numbers
Elementary algebra
All quadratic equations
Quadratic equations can also be solved
16. Is Written as a + b
Addition
commutative law of Exponentiation
an operation
The central technique to linear equations
17. The squaring operation only produces
The operation of exponentiation
Associative law of Exponentiation
Algebraic geometry
nonnegative numbers
18. Is Written as ab or a^b
Properties of equality
Algebraic geometry
nonnegative numbers
Exponentiation
19. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
equation
Identity
Solving the Equation
A solution or root of the equation
20. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
associative law of addition
Expressions
the fixed non-negative integer k (the number of arguments)
A integral equation
21. May not be defined for every possible value.
Operations
The real number system
the fixed non-negative integer k (the number of arguments)
The relation of inequality (<) has this property
22. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po
Elimination method
Equations
Exponentiation
Unary operations
23. 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
Quadratic equations
Operations
inverse operation of addition
24. A + b = b + a
substitution
then bc < ac
nullary operation
commutative law of Addition
25. There are two common types of operations:
then bc < ac
A transcendental equation
unary and binary
Universal algebra
26. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Real number
The relation of equality (=)'s property
A solution or root of the equation
two inputs
27. Symbols that denote numbers - is to allow the making of generalizations in mathematics
logarithmic equation
Operations on functions
The purpose of using variables
Equations
28. Is an equation involving derivatives.
Rotations
Reflexive relation
A Diophantine equation
A differential equation
29. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Addition
Categories of Algebra
transitive
then bc < ac
30. Is a function of the form ? : V ? Y - where V ? X1
commutative law of Exponentiation
An operation ?
Quadratic equations
symmetric
31. Is an equation involving a transcendental function of one of its variables.
unary and binary
scalar
A transcendental equation
symmetric
32. Referring to the finite number of arguments (the value k)
finitary operation
nullary operation
Repeated addition
Associative law of Multiplication
33. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebraic equation
has arity two
associative law of addition
The relation of equality (=)
34. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
nonnegative numbers
The purpose of using variables
Equations
value - result - or output
35. Is an equation of the form aX = b for a > 0 - which has solution
Constants
Properties of equality
Solving the Equation
exponential equation
36. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
then ac < bc
The simplest equations to solve
The method of equating the coefficients
37. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Algebraic equation
range
Equations
transitive
38. An operation of arity zero is simply an element of the codomain Y - called a
Associative law of Exponentiation
Exponentiation
nullary operation
the fixed non-negative integer k (the number of arguments)
39. Is an action or procedure which produces a new value from one or more input values.
an operation
The real number system
transitive
Properties of equality
40. Division ( / )
Abstract algebra
then ac < bc
inverse operation of Exponentiation
inverse operation of Multiplication
41. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
Unary operations
value - result - or output
inverse operation of Multiplication
42. Not associative
domain
Associative law of Exponentiation
the fixed non-negative integer k (the number of arguments)
exponential equation
43. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Binary operations
commutative law of Exponentiation
Change of variables
Repeated multiplication
44. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
reflexive
Pure mathematics
two inputs
Unknowns
45. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
system of linear equations
Equation Solving
commutative law of Addition
Solution to the system
46. Are denoted by letters at the beginning - a - b - c - d - ...
operands - arguments - or inputs
Vectors
Knowns
Polynomials
47. 1 - which preserves numbers: a^1 = a
The method of equating the coefficients
The logical values true and false
A integral equation
identity element of Exponentiation
48. 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.
(k+1)-ary relation that is functional on its first k domains
The central technique to linear equations
Binary operations
Reunion of broken parts
49. Include the binary operations union and intersection and the unary operation of complementation.
operands - arguments - or inputs
then bc < ac
Operations on sets
Difference of two squares - or the difference of perfect squares
50. Is an equation in which the unknowns are functions rather than simple quantities.
The simplest equations to solve
A functional equation
equation
Conditional equations