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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. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
The real number system
Reflexive relation
The method of equating the coefficients
2. Can be combined using the function composition operation - performing the first rotation and then the second.
Difference of two squares - or the difference of perfect squares
Rotations
nonnegative numbers
then a < c
3. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Reunion of broken parts
Multiplication
commutative law of Addition
Algebraic equation
4. If a < b and c < 0
A integral equation
then bc < ac
Identities
commutative law of Addition
5. Is an equation in which the unknowns are functions rather than simple quantities.
Equation Solving
an operation
A transcendental equation
A functional equation
6. Operations can have fewer or more than
has arity two
Unknowns
A linear equation
two inputs
7. Is Written as a
A polynomial equation
Multiplication
Conditional equations
Pure mathematics
8. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Categories of Algebra
A solution or root of the equation
the set Y
The central technique to linear equations
9. If a = b and b = c then a = c
Reflexive relation
transitive
k-ary operation
then a + c < b + d
10. The operation of multiplication means _______________: a
Unknowns
substitution
Repeated addition
inverse operation of Exponentiation
11. A
reflexive
nullary operation
Variables
commutative law of Multiplication
12. The values for which an operation is defined form a set called its
domain
Equation Solving
Algebraic geometry
Properties of equality
13. b = b
two inputs
Pure mathematics
reflexive
Algebraic geometry
14. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Operations
Identity
(k+1)-ary relation that is functional on its first k domains
Constants
15. 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
Variables
then bc < ac
Quadratic equations can also be solved
16. Is the claim that two expressions have the same value and are equal.
has arity two
Solution to the system
Equations
The relation of equality (=) has the property
17. 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.
Equations
Binary operations
An operation ?
Properties of equality
18. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
the set Y
Algebraic number theory
Equation Solving
Equations
19. Is called the type or arity of the operation
inverse operation of Exponentiation
The simplest equations to solve
the fixed non-negative integer k (the number of arguments)
A polynomial equation
20. Not commutative a^b?b^a
The logical values true and false
commutative law of Exponentiation
range
value - result - or output
21. Logarithm (Log)
inverse operation of Exponentiation
Change of variables
Equations
A solution or root of the equation
22. A unary operation
A functional equation
symmetric
has arity one
Real number
23. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
Equation Solving
Addition
Polynomials
24. 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)
finitary operation
commutative law of Addition
Polynomials
The operation of exponentiation
25. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
when b > 0
then bc < ac
Repeated multiplication
26. Include composition and convolution
nullary operation
Operations on functions
Expressions
value - result - or output
27. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
A polynomial equation
Binary operations
system of linear equations
Reflexive relation
28. (a
has arity two
Associative law of Multiplication
Quadratic equations
The relation of equality (=)'s property
29. An operation of arity k is called a
Expressions
Identities
k-ary operation
(k+1)-ary relation that is functional on its first k domains
30. () 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.
(k+1)-ary relation that is functional on its first k domains
A integral equation
Algebra
Quadratic equations can also be solved
31. Division ( / )
logarithmic equation
Associative law of Multiplication
The operation of exponentiation
inverse operation of Multiplication
32. Are denoted by letters at the beginning - a - b - c - d - ...
Constants
Knowns
Operations on functions
inverse operation of Exponentiation
33. The codomain is the set of real numbers but the range is the
Algebraic geometry
Universal algebra
nonnegative numbers
reflexive
34. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
operands - arguments - or inputs
An operation ?
has arity one
35. There are two common types of operations:
unary and binary
commutative law of Multiplication
The relation of equality (=)
Knowns
36. If a = b then b = a
Equation Solving
symmetric
Identity element of Multiplication
unary and binary
37. (a + b) + c = a + (b + c)
The operation of exponentiation
associative law of addition
Unary operations
The relation of equality (=) has the property
38. A binary operation
has arity two
The central technique to linear equations
the fixed non-negative integer k (the number of arguments)
value - result - or output
39. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
Unary operations
Elimination method
A Diophantine equation
40. 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
The purpose of using variables
Reflexive relation
Solving the Equation
Elimination method
41. 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)
Reflexive relation
(k+1)-ary relation that is functional on its first k domains
The operation of addition
The sets Xk
42. The inner product operation on two vectors produces a
A Diophantine equation
scalar
transitive
Repeated addition
43. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
operands - arguments - or inputs
inverse operation of Exponentiation
Order of Operations
inverse operation of addition
44. Referring to the finite number of arguments (the value k)
exponential equation
k-ary operation
Reflexive relation
finitary operation
45. May not be defined for every possible value.
operation
Operations
Quadratic equations can also be solved
The central technique to linear equations
46. If it holds for all a and b in X that if a is related to b then b is related to a.
unary and binary
Algebraic number theory
Quadratic equations
A binary relation R over a set X is symmetric
47. 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
Elimination method
exponential equation
Constants
Real number
48. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
domain
Difference of two squares - or the difference of perfect squares
Change of variables
A solution or root of the equation
49. The values combined are called
scalar
operands - arguments - or inputs
A Diophantine equation
Change of variables
50. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
A Diophantine equation
Expressions
transitive
scalar