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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. If a < b and b < c
A binary relation R over a set X is symmetric
operation
transitive
then a < c
2. Is the claim that two expressions have the same value and are equal.
Identity
Equations
The relation of inequality (<) has this property
value - result - or output
3. 0 - which preserves numbers: a + 0 = a
identity element of Exponentiation
identity element of addition
commutative law of Addition
equation
4. Applies abstract algebra to the problems of geometry
Conditional equations
value - result - or output
Algebraic geometry
Addition
5. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Algebraic number theory
Reflexive relation
Number line or real line
Identity
6. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
Quadratic equations
Difference of two squares - or the difference of perfect squares
Conditional equations
7. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
An operation ?
identity element of addition
commutative law of Multiplication
8. 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.
(k+1)-ary relation that is functional on its first k domains
Operations on functions
The relation of equality (=) has the property
Order of Operations
9. The operation of exponentiation means ________________: a^n = a
scalar
Algebraic number theory
Repeated multiplication
Solving the Equation
10. Is called the codomain of the operation
Quadratic equations can also be solved
Elementary algebra
the set Y
A differential equation
11. Is an equation where the unknowns are required to be integers.
Number line or real line
A Diophantine equation
Associative law of Exponentiation
commutative law of Multiplication
12. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
k-ary operation
The operation of exponentiation
Multiplication
Unknowns
13. 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.
inverse operation of Exponentiation
The central technique to linear equations
Properties of equality
system of linear equations
14. 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)
when b > 0
The operation of addition
Exponentiation
nullary operation
15. The values for which an operation is defined form a set called its
Operations
Elimination method
domain
Quadratic equations can also be solved
16. Can be added and subtracted.
Vectors
when b > 0
The relation of inequality (<) has this property
A Diophantine equation
17. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
nonnegative numbers
when b > 0
Variables
18. 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).
Elementary algebra
Reunion of broken parts
A Diophantine equation
Quadratic equations
19. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
A linear equation
The method of equating the coefficients
Algebraic number theory
the fixed non-negative integer k (the number of arguments)
20. Is Written as ab or a^b
Exponentiation
two inputs
Reflexive relation
The relation of equality (=) has the property
21. 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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22. Referring to the finite number of arguments (the value k)
Expressions
substitution
finitary operation
logarithmic equation
23. Involve only one value - such as negation and trigonometric functions.
Unary operations
identity element of Exponentiation
range
Equation Solving
24. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Identity element of Multiplication
Categories of Algebra
Rotations
has arity one
25. Division ( / )
A solution or root of the equation
inverse operation of 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.
Quadratic equations
26. (a + b) + c = a + (b + c)
Expressions
associative law of addition
then ac < bc
the fixed non-negative integer k (the number of arguments)
27. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
A Diophantine equation
Expressions
nonnegative numbers
The simplest equations to solve
28. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
reflexive
Variables
Difference of two squares - or the difference of perfect squares
Elementary algebra
29. k-ary operation is a
then bc < ac
Identity element of Multiplication
A polynomial equation
(k+1)-ary relation that is functional on its first k domains
30. Is Written as a
Number line or real line
then ac < bc
Constants
Multiplication
31. If a = b then b = a
inverse operation of Multiplication
when b > 0
transitive
symmetric
32. The value produced is called
Identity
The sets Xk
value - result - or output
The purpose of using variables
33. If an equation in algebra is known to be true - the following operations may be used to produce another true 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.
unary and binary
Equations
value - result - or output
34. A binary operation
has arity two
commutative law of Multiplication
Real number
operands - arguments - or inputs
35. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
operation
The operation of exponentiation
A transcendental equation
36. Are true for only some values of the involved variables: x2 - 1 = 4.
Quadratic equations
Identities
Conditional equations
Elimination method
37. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.
Variables
an operation
Algebra
system of linear equations
38. Not commutative a^b?b^a
commutative law of Exponentiation
The relation of equality (=)
Operations on sets
commutative law of Multiplication
39. An operation of arity k is called a
Operations on functions
The simplest equations to solve
k-ary operation
Repeated multiplication
40. Is an equation of the form log`a^X = b for a > 0 - which has solution
Change of variables
unary and binary
logarithmic equation
Reflexive relation
41. 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)
The relation of inequality (<) has this property
Repeated multiplication
The real number system
operation
42. 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)
Identity
Vectors
The operation of exponentiation
two inputs
43. A + b = b + a
commutative law of Addition
substitution
The simplest equations to solve
equation
44. There are two common types of operations:
unary and binary
Linear algebra
finitary operation
Vectors
45. 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.
Pure mathematics
A transcendental equation
symmetric
The central technique to linear equations
46. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Equation Solving
Exponentiation
The purpose of using variables
Reflexive relation
47. Is an equation involving a transcendental function of one of its variables.
range
A transcendental equation
then ac < bc
Polynomials
48. 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
Exponentiation
The operation of addition
has arity one
Real number
49. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
then a + c < b + d
(k+1)-ary relation that is functional on its first k domains
The relation of equality (=) has the property
Order of Operations
50. b = b
A Diophantine equation
nonnegative numbers
reflexive
range