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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. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
logarithmic equation
Categories of Algebra
Identity element of Multiplication
then bc < ac
2. Operations can have fewer or more than
symmetric
Equations
Elementary algebra
two inputs
3. 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.
then a < c
Order of Operations
Properties of equality
Difference of two squares - or the difference of perfect squares
4. Subtraction ( - )
inverse operation of addition
operation
All quadratic equations
Repeated multiplication
5. May not be defined for every possible value.
Operations
Knowns
Reflexive relation
Quadratic equations
6. In which properties common to all algebraic structures are studied
Universal algebra
Operations can involve dissimilar objects
A differential equation
Algebraic combinatorics
7. Is an algebraic 'sentence' containing an unknown quantity.
The purpose of using variables
Unary operations
then ac < bc
Polynomials
8. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Operations on functions
The relation of equality (=)
radical equation
Vectors
9. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Algebra
Identity element of Multiplication
Unknowns
A polynomial equation
10. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
Reunion of broken parts
Categories of Algebra
The central technique to linear equations
11. There are two common types of operations:
unary and binary
Real number
the set Y
Universal algebra
12. 1 - which preserves numbers: a^1 = a
A linear equation
Repeated addition
identity element of Exponentiation
Unary operations
13. Involve only one value - such as negation and trigonometric functions.
identity element of addition
associative law of addition
Unary operations
has arity one
14. (a + b) + c = a + (b + c)
has arity two
associative law of addition
inverse operation of addition
system of linear equations
15. k-ary operation is a
A Diophantine equation
The relation of equality (=)'s property
(k+1)-ary relation that is functional on its first k domains
inverse operation of Exponentiation
16. Is an equation of the form log`a^X = b for a > 0 - which has solution
commutative law of Exponentiation
Multiplication
logarithmic equation
Number line or real line
17. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)
A integral equation
Equations
the fixed non-negative integer k (the number of arguments)
The operation of exponentiation
18. Include composition and convolution
Associative law of Multiplication
Addition
An operation ?
Operations on functions
19. Is the claim that two expressions have the same value and are equal.
radical equation
Change of variables
commutative law of Multiplication
Equations
20. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
Equations
Unknowns
associative law of addition
21. 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
Linear algebra
The relation of equality (=)'s property
Expressions
Reunion of broken parts
22. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
Identity element of Multiplication
inverse operation of Exponentiation
A transcendental equation
23. If a < b and b < c
Multiplication
Equation Solving
then a < c
Solving the Equation
24. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
then a + c < b + d
The simplest equations to solve
The sets Xk
A solution or root of the equation
25. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
A binary relation R over a set X is symmetric
Real number
Categories of Algebra
Pure mathematics
26. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
Properties of equality
the fixed non-negative integer k (the number of arguments)
A binary relation R over a set X is symmetric
27. The values combined are called
A Diophantine equation
operands - arguments - or inputs
Algebraic geometry
Equations
28. In an equation with a single unknown - a value of that unknown for which the equation is true is called
A binary relation R over a set X is symmetric
unary and binary
A solution or root of the equation
Conditional equations
29. Are denoted by letters at the beginning - a - b - c - d - ...
system of linear equations
value - result - or output
Knowns
identity element of addition
30. Is an equation where the unknowns are required to be integers.
Algebraic number theory
A Diophantine equation
has arity two
commutative law of Multiplication
31. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Abstract algebra
then a + c < b + d
Operations can involve dissimilar objects
The relation of equality (=)
32. 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).
commutative law of Exponentiation
Quadratic equations
All quadratic equations
The logical values true and false
33. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Associative law of Multiplication
Universal algebra
Operations can involve dissimilar objects
Algebraic number theory
34. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Linear algebra
The logical values true and false
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.
commutative law of Addition
35. In which the specific properties of vector spaces are studied (including matrices)
Operations on sets
Linear algebra
then a + c < b + d
Abstract algebra
36. 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
then a < c
Real number
nullary operation
unary and binary
37. An operation of arity zero is simply an element of the codomain Y - called a
Real number
system of linear equations
nullary operation
value - result - or output
38. Division ( / )
k-ary operation
Operations can involve dissimilar objects
Solving the Equation
inverse operation of Multiplication
39. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Algebraic number theory
Associative law of Exponentiation
Equations
nonnegative numbers
40. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
nullary operation
All quadratic equations
Quadratic equations can also be solved
A integral equation
41. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
identity element of addition
A functional equation
Order of Operations
42. 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.
symmetric
operation
Universal algebra
The central technique to linear equations
43. Is called the type or arity of the operation
Real number
the fixed non-negative integer k (the number of arguments)
associative law of addition
All quadratic equations
44. A
Properties of equality
commutative law of Multiplication
Associative law of Multiplication
Conditional equations
45. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Categories of Algebra
A transcendental equation
finitary operation
Binary operations
46. Applies abstract algebra to the problems of geometry
value - result - or output
Algebraic geometry
the fixed non-negative integer k (the number of arguments)
logarithmic equation
47. 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).
Abstract algebra
associative law of addition
operation
Rotations
48. Are called the domains of the operation
The sets Xk
Quadratic equations can also be solved
scalar
The relation of equality (=)'s property
49. Referring to the finite number of arguments (the value k)
The operation of exponentiation
finitary operation
Associative law of Multiplication
Unary operations
50. Can be defined axiomatically up to an isomorphism
The real number system
when b > 0
A functional equation
Equations