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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. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
A functional equation
The relation of equality (=)
A linear equation
then a < c
2. 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)
The operation of exponentiation
Constants
inverse operation of addition
Equations
3. An operation of arity k is called a
k-ary operation
Identities
commutative law of Addition
The relation of equality (=)
4. If a = b then b = a
An operation ?
Algebraic geometry
A linear equation
symmetric
5. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
The simplest equations to solve
The method of equating the coefficients
range
Associative law of Multiplication
6. The codomain is the set of real numbers but the range is the
Associative law of Multiplication
nullary operation
Expressions
nonnegative numbers
7. Not associative
Rotations
operands - arguments - or inputs
The operation of addition
Associative law of Exponentiation
8. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Change of variables
Identities
Algebraic number theory
nonnegative numbers
9. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Repeated addition
transitive
equation
Order of Operations
10. The operation of multiplication means _______________: a
Repeated addition
Categories of Algebra
Binary operations
Multiplication
11. 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
has arity two
system of linear equations
Elimination method
The operation of addition
12. Is an equation where the unknowns are required to be integers.
has arity one
Categories of Algebra
A Diophantine equation
inverse operation of addition
13. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
Equation Solving
Knowns
Identity element of Multiplication
14. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Associative law of Exponentiation
the set Y
exponential equation
Algebraic number theory
15. 0 - which preserves numbers: a + 0 = a
Addition
logarithmic equation
Identity element of Multiplication
identity element of addition
16. Is an equation of the form log`a^X = b for a > 0 - which has solution
Expressions
logarithmic equation
The sets Xk
A linear equation
17. Is an action or procedure which produces a new value from one or more input values.
commutative law of Addition
an operation
Polynomials
then a < c
18. Is Written as ab or a^b
Exponentiation
commutative law of Multiplication
the set Y
The relation of equality (=)
19. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
A binary relation R over a set X is symmetric
The operation of addition
Operations on functions
20. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
Constants
The operation of exponentiation
(k+1)-ary relation that is functional on its first k domains
21. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
commutative law of Multiplication
Operations
Pure mathematics
A linear equation
22. The values for which an operation is defined form a set called its
Associative law of Exponentiation
domain
symmetric
operation
23. Letters from the beginning of the alphabet like a - b - c... often denote
inverse operation of Exponentiation
Constants
The central technique to linear equations
Elimination method
24. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
A solution or root of the equation
The central technique to linear equations
Number line or real line
inverse operation of addition
25. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
associative law of addition
inverse operation of Exponentiation
Solution to the system
Repeated multiplication
26. Can be defined axiomatically up to an isomorphism
The real number system
reflexive
Algebraic equation
the fixed non-negative integer k (the number of arguments)
27. In which the specific properties of vector spaces are studied (including matrices)
Algebra
nullary operation
radical equation
Linear algebra
28. Is Written as a + b
nonnegative numbers
Addition
inverse operation of Multiplication
operation
29. 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
commutative law of Addition
Categories of Algebra
Reflexive relation
30. Include the binary operations union and intersection and the unary operation of complementation.
Quadratic equations
Operations on sets
range
Equations
31. A binary operation
operation
Operations can involve dissimilar objects
Algebraic geometry
has arity two
32. May not be defined for every possible value.
A Diophantine equation
Reflexive relation
Operations
Multiplication
33. Applies abstract algebra to the problems of geometry
system of linear equations
Exponentiation
has arity two
Algebraic geometry
34. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
inverse operation of Multiplication
Constants
Categories of Algebra
The sets Xk
35. Is a function of the form ? : V ? Y - where V ? X1
Rotations
An operation ?
then ac < bc
Multiplication
36. 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.
Exponentiation
nullary operation
when b > 0
The relation of equality (=) has the property
37. The values of the variables which make the equation true are the solutions of the equation and can be found through
range
Change of variables
(k+1)-ary relation that is functional on its first k domains
Equation Solving
38. Division ( / )
commutative law of Multiplication
Repeated multiplication
Expressions
inverse operation of Multiplication
39. Are called the domains of the operation
nonnegative numbers
The sets Xk
inverse operation of Exponentiation
Algebraic number theory
40. A vector can be multiplied by a scalar to form another vector
when b > 0
Addition
The operation of exponentiation
Operations can involve dissimilar objects
41. Will have two solutions in the complex number system - but need not have any in the real number system.
Properties of equality
All quadratic equations
logarithmic equation
has arity one
42. Subtraction ( - )
inverse operation of addition
A functional equation
k-ary operation
equation
43. 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
Operations
Conditional equations
A transcendental equation
when b > 0
44. Is Written as a
Multiplication
then ac < bc
unary and binary
Operations on sets
45. 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
Elementary algebra
Addition
Identity element of Multiplication
The relation of equality (=) has the property
46. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
Linear algebra
An operation ?
Rotations
47. If a < b and c < d
Algebraic combinatorics
then a + c < b + d
Quadratic equations
Knowns
48. If a < b and c > 0
then ac < bc
Conditional equations
Operations
k-ary operation
49. Include composition and convolution
equation
commutative law of Addition
The relation of inequality (<) has this property
Operations on functions
50. 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'.
two inputs
Order of Operations
A functional equation
Reflexive relation