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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 process of expressing the unknowns in terms of the knowns is called
Solving the Equation
Equations
Order of Operations
Addition
2. Is an equation in which a polynomial is set equal to another polynomial.
Equations
Repeated addition
The operation of exponentiation
A polynomial equation
3. A + b = b + a
Rotations
commutative law of Addition
Algebraic combinatorics
The purpose of using variables
4. Is Written as ab or a^b
Algebra
The simplest equations to solve
Algebraic equation
Exponentiation
5. In which abstract algebraic methods are used to study combinatorial questions.
has arity one
Properties of equality
Algebraic combinatorics
The operation of exponentiation
6. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
Algebraic geometry
then ac < bc
inverse operation of Multiplication
7. Is the claim that two expressions have the same value and are equal.
Equations
when b > 0
commutative law of Addition
Identity
8. 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).
an operation
A integral equation
then ac < bc
Quadratic equations
9. 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.
An operation ?
Change of variables
nullary operation
Variables
10. 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.
scalar
A integral equation
commutative law of Addition
The relation of inequality (<) has this property
11. Applies abstract algebra to the problems of geometry
Properties of equality
The method of equating the coefficients
The logical values true and false
Algebraic geometry
12. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
Reflexive relation
Identity element of Multiplication
Associative law of Exponentiation
13. Is an equation where the unknowns are required to be integers.
A Diophantine equation
domain
Associative law of Multiplication
an operation
14. The values combined are called
Knowns
operands - arguments - or inputs
The logical values true and false
operation
15. Not commutative a^b?b^a
commutative law of Exponentiation
Number line or real line
when b > 0
Associative law of Multiplication
16. Is called the type or arity of the operation
Operations
the fixed non-negative integer k (the number of arguments)
Equations
symmetric
17. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
commutative law of Addition
associative law of addition
nonnegative numbers
range
18. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
substitution
associative law of addition
Order of Operations
Algebraic number theory
19. Can be combined using the function composition operation - performing the first rotation and then the second.
then bc < ac
Expressions
Binary operations
Rotations
20. The values of the variables which make the equation true are the solutions of the equation and can be found through
then a < c
nonnegative numbers
Equation Solving
The logical values true and false
21. Is called the codomain of the operation
The relation of equality (=)'s property
the set Y
Knowns
nullary operation
22. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
The method of equating the coefficients
The simplest equations to solve
Solution to the system
Quadratic equations can also be solved
23. The operation of multiplication means _______________: a
Addition
The operation of addition
Repeated addition
inverse operation of Exponentiation
24. A unary operation
Binary operations
Linear algebra
An operation ?
has arity one
25. Involve only one value - such as negation and trigonometric functions.
Unary operations
inverse operation of Exponentiation
The logical values true and false
Categories of Algebra
26. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Operations
radical equation
Algebra
A functional equation
27. Can be defined axiomatically up to an isomorphism
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.
Change of variables
The real number system
Operations on sets
28. k-ary operation is a
Elimination method
(k+1)-ary relation that is functional on its first k domains
operands - arguments - or inputs
Solution to the system
29. In an equation with a single unknown - a value of that unknown for which the equation is true is called
domain
Difference of two squares - or the difference of perfect squares
A solution or root of the equation
Algebraic geometry
30. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
Repeated addition
identity element of Exponentiation
commutative law of Addition
31. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
when b > 0
The simplest equations to solve
Order of Operations
Vectors
32. Include the binary operations union and intersection and the unary operation of complementation.
associative law of addition
Operations on sets
Linear algebra
Algebraic geometry
33. Division ( / )
finitary operation
inverse operation of Multiplication
(k+1)-ary relation that is functional on its first k domains
inverse operation of addition
34. 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
The method of equating the coefficients
then ac < bc
commutative law of Exponentiation
Exponentiation
35. The codomain is the set of real numbers but the range is the
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
radical equation
commutative law of Exponentiation
36. An operation of arity k is called a
k-ary operation
The logical values true and false
inverse operation of Exponentiation
has arity two
37. 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
Real number
Order of Operations
the fixed non-negative integer k (the number of arguments)
Reunion of broken parts
38. Is an equation involving derivatives.
A differential equation
Variables
Solution to the system
Algebraic geometry
39. The squaring operation only produces
unary and binary
The relation of equality (=) has the property
nonnegative numbers
Universal algebra
40. 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
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.
unary and binary
A polynomial equation
Elementary algebra
41. Is a function of the form ? : V ? Y - where V ? X1
Change of variables
The relation of equality (=) has the property
Identity element of Multiplication
An operation ?
42. Is an algebraic 'sentence' containing an unknown quantity.
Order of Operations
A differential equation
The method of equating the coefficients
Polynomials
43. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Knowns
Identities
The purpose of using variables
commutative law of Exponentiation
44. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
unary and binary
equation
Categories of Algebra
Algebraic number theory
45. If a < b and c < 0
Constants
Identity element of Multiplication
then bc < ac
All quadratic equations
46. Operations can have fewer or more than
two inputs
operation
Addition
Change of variables
47. Letters from the beginning of the alphabet like a - b - c... often denote
Identity
Constants
The logical values true and false
an operation
48. Is an equation involving integrals.
A Diophantine equation
A integral equation
nonnegative numbers
logarithmic equation
49. 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'.
Expressions
Reflexive relation
The method of equating the coefficients
range
50. 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).
Algebraic combinatorics
Addition
A functional equation
operation