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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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 it holds for all a and b in X that if a is related to b then b is related to a.
Algebraic geometry
substitution
commutative law of Multiplication
A binary relation R over a set X is symmetric
2. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Multiplication
An operation ?
Unary operations
range
3. There are two common types of operations:
Conditional equations
Repeated addition
exponential equation
unary and binary
4. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain
when b > 0
nonnegative numbers
The relation of equality (=)
Categories of Algebra
5. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
reflexive
A solution or root of the equation
Operations on sets
Quadratic equations can also be solved
6. 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)
Abstract algebra
Binary operations
operation
The relation of equality (=) has the property
7. In an equation with a single unknown - a value of that unknown for which the equation is true is called
two inputs
A polynomial equation
A solution or root of the equation
A functional equation
8. Are true for only some values of the involved variables: x2 - 1 = 4.
The simplest equations to solve
The purpose of using variables
Conditional equations
Identity
9. The inner product operation on two vectors produces a
The simplest equations to solve
substitution
scalar
when b > 0
10. 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).
operation
Algebraic combinatorics
Algebraic geometry
Vectors
11. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Equation Solving
Difference of two squares - or the difference of perfect squares
inverse operation of addition
Addition
12. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebraic equation
an operation
commutative law of Multiplication
has arity two
13. Logarithm (Log)
inverse operation of Exponentiation
Algebraic combinatorics
All quadratic equations
Unknowns
14. 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).
Quadratic equations
Properties of equality
Equations
inverse operation of Multiplication
15. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Repeated addition
Real number
The purpose of using variables
domain
16. 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.
Exponentiation
A solution or root of the equation
Properties of equality
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.
17. b = b
reflexive
operands - arguments - or inputs
operation
inverse operation of Exponentiation
18. The operation of exponentiation means ________________: a^n = a
commutative law of Multiplication
Number line or real line
Repeated multiplication
nonnegative numbers
19. 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)
Expressions
commutative law of Exponentiation
The operation of addition
Identity element of Multiplication
20. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
A polynomial equation
A integral equation
has arity one
Expressions
21. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
The operation of exponentiation
Algebraic geometry
Real number
Variables
22. 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)
An operation ?
Operations can involve dissimilar objects
Conditional equations
The operation of exponentiation
23. Is an equation of the form log`a^X = b for a > 0 - which has solution
Number line or real line
logarithmic equation
Identities
(k+1)-ary relation that is functional on its first k domains
24. Letters from the beginning of the alphabet like a - b - c... often denote
then a < c
Operations on sets
Constants
associative law of addition
25. If a = b and b = c then a = c
then bc < ac
The relation of equality (=) has the property
transitive
inverse operation of addition
26. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
Universal algebra
Identity element of Multiplication
A solution or root of the equation
27. Can be added and subtracted.
Variables
Vectors
Pure mathematics
Binary operations
28. 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
Elimination method
value - result - or output
Reunion of broken parts
reflexive
29. 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'.
equation
Elimination method
Reflexive relation
commutative law of Multiplication
30. 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.
The sets Xk
Abstract algebra
The relation of inequality (<) has this property
finitary operation
31. If a < b and b < c
The relation of equality (=) has the property
The relation of equality (=)
Algebraic geometry
then a < c
32. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Binary operations
Equations
The operation of exponentiation
the set Y
33. The value produced is called
value - result - or output
The relation of equality (=)
Identity element of Multiplication
Reflexive relation
34. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
commutative law of Addition
k-ary operation
transitive
35. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Associative law of Multiplication
Solution to the system
Unary operations
Identity
36. 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.
inverse operation of Multiplication
has arity one
Change of variables
Addition
37. If a < b and c < 0
Categories of Algebra
A linear equation
then bc < ac
Variables
38. Not associative
exponential equation
Quadratic equations
Algebra
Associative law of Exponentiation
39. An operation of arity k is called a
k-ary operation
Equation Solving
has arity two
The relation of equality (=)
40. Is an equation involving a transcendental function of one of its variables.
A linear equation
A transcendental equation
Quadratic equations can also be solved
The relation of equality (=) has the property
41. The values combined are called
operands - arguments - or inputs
Algebraic number theory
Solution to the system
associative law of addition
42. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
equation
Rotations
Properties of equality
Expressions
43. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
operands - arguments - or inputs
Real number
inverse operation of Multiplication
44. (a + b) + c = a + (b + c)
associative law of addition
radical equation
commutative law of Multiplication
identity element of Exponentiation
45. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
(k+1)-ary relation that is functional on its first k domains
Unknowns
The relation of equality (=)
k-ary operation
46. If a = b then b = a
then bc < ac
The sets Xk
Binary operations
symmetric
47. Operations can have fewer or more than
equation
A functional equation
commutative law of Exponentiation
two inputs
48. Is an equation of the form aX = b for a > 0 - which has solution
symmetric
commutative law of Multiplication
exponential equation
Knowns
49. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Repeated addition
Abstract algebra
the fixed non-negative integer k (the number of arguments)
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.
50. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
The relation of equality (=)'s property
Categories of Algebra
Vectors
Rotations