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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. A + b = b + a
commutative law of Addition
has arity one
A differential equation
inverse operation of Multiplication
2. The inner product operation on two vectors produces a
Quadratic equations can also be solved
the set Y
scalar
Number line or real line
3. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
commutative law of Multiplication
The purpose of using variables
Number line or real line
Expressions
4. 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.
A polynomial equation
An operation ?
the set Y
The relation of equality (=) has the property
5. Is an equation of the form log`a^X = b for a > 0 - which has solution
nonnegative numbers
radical equation
logarithmic equation
Algebraic combinatorics
6. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
logarithmic equation
Multiplication
A solution or root of the 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.
7. If a = b and b = c then a = c
transitive
The purpose of using variables
A differential equation
Identity
8. The codomain is the set of real numbers but the range is the
nonnegative numbers
Algebraic equation
associative law of addition
unary and binary
9. There are two common types of operations:
domain
Associative law of Multiplication
unary and binary
Algebraic combinatorics
10. Is an equation involving derivatives.
The purpose of using variables
A differential equation
A solution or root of the equation
Constants
11. k-ary operation is a
identity element of Exponentiation
(k+1)-ary relation that is functional on its first k domains
The central technique to linear equations
Identity
12. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Number line or real line
Order of Operations
finitary operation
two inputs
13. Is an equation involving integrals.
Identities
A integral equation
A differential equation
k-ary operation
14. 1 - which preserves numbers: a^1 = a
Pure mathematics
Unknowns
identity element of Exponentiation
A binary relation R over a set X is symmetric
15. Is an equation in which the unknowns are functions rather than simple quantities.
Quadratic equations
Reunion of broken parts
The relation of equality (=)
A functional equation
16. The process of expressing the unknowns in terms of the knowns is called
Binary operations
Expressions
unary and binary
Solving the Equation
17. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
logarithmic equation
Algebraic equation
Abstract algebra
commutative law of Exponentiation
18. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
value - result - or output
Algebraic equation
domain
19. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Expressions
Exponentiation
The operation of addition
A solution or root of the equation
20. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
commutative law of Multiplication
Expressions
then a + c < b + d
21. Are denoted by letters at the beginning - a - b - c - d - ...
Elementary algebra
Operations on sets
A binary relation R over a set X is symmetric
Knowns
22. Is an action or procedure which produces a new value from one or more input values.
system of linear equations
an operation
radical equation
inverse operation of Multiplication
23. Are true for only some values of the involved variables: x2 - 1 = 4.
symmetric
Addition
The purpose of using variables
Conditional equations
24. If it holds for all a and b in X that if a is related to b then b is related to a.
commutative law of Multiplication
identity element of Exponentiation
A binary relation R over a set X is symmetric
Algebraic equation
25. The squaring operation only produces
nonnegative numbers
A linear equation
Operations
Algebraic geometry
26. Is an equation where the unknowns are required to be integers.
A integral equation
A Diophantine equation
domain
commutative law of Addition
27. Is Written as ab or a^b
two inputs
Exponentiation
The relation of equality (=) has the property
Abstract algebra
28. Is an equation of the form X^m/n = a - for m - n integers - which has solution
nonnegative numbers
radical equation
Algebra
then a + c < b + d
29. 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
A functional equation
The relation of equality (=) has the property
The operation of exponentiation
The method of equating the coefficients
30. Will have two solutions in the complex number system - but need not have any in the real number system.
Reunion of broken parts
Addition
All quadratic equations
transitive
31. Include composition and convolution
Equation Solving
Operations on functions
Constants
Exponentiation
32. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
identity element of Exponentiation
Multiplication
Properties of equality
33. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
Repeated multiplication
Equations
Number line or real line
34. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s
Identity element of Multiplication
domain
substitution
Unary operations
35. Is Written as a + b
Addition
identity element of addition
has arity two
the fixed non-negative integer k (the number of arguments)
36. Can be defined axiomatically up to an isomorphism
The operation of exponentiation
Equations
Unknowns
The real number system
37. Logarithm (Log)
Algebra
Solving the Equation
inverse operation of Exponentiation
equation
38. A
Difference of two squares - or the difference of perfect squares
commutative law of Multiplication
exponential equation
Constants
39. 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'.
Unary operations
A differential equation
The relation of inequality (<) has this property
Reflexive relation
40. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
range
The operation of exponentiation
Solution to the system
Unary operations
41. 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).
Repeated multiplication
Universal algebra
nullary operation
Quadratic equations
42. Subtraction ( - )
Equation Solving
inverse operation of addition
Repeated multiplication
Categories of Algebra
43. 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
Elimination method
unary and binary
domain
finitary operation
44. If a < b and c > 0
Identity
finitary operation
Equation Solving
then ac < bc
45. 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
Elimination method
equation
Algebraic number theory
46. Is an equation of the form aX = b for a > 0 - which has solution
Unknowns
A polynomial equation
exponential equation
Difference of two squares - or the difference of perfect squares
47. Is called the codomain of the operation
Properties of equality
the set Y
commutative law of Exponentiation
Repeated addition
48. Is called the type or arity of the operation
has arity two
logarithmic equation
the fixed non-negative integer k (the number of arguments)
Order of Operations
49. If a < b and c < 0
Real number
Knowns
Algebraic number theory
then bc < ac
50. The values of the variables which make the equation true are the solutions of the equation and can be found through
Change of variables
Equation Solving
k-ary operation
Difference of two squares - or the difference of perfect squares