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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. The codomain is the set of real numbers but the range is the
The sets Xk
Solving the Equation
nonnegative numbers
All quadratic equations
2. An operation of arity zero is simply an element of the codomain Y - called a
The relation of inequality (<) has this property
nullary operation
The operation of exponentiation
Real number
3. Is called the type or arity of the operation
Pure mathematics
the fixed non-negative integer k (the number of arguments)
All quadratic equations
Difference of two squares - or the difference of perfect squares
4. Are called the domains of the operation
radical equation
Operations
The sets Xk
Solving the Equation
5. 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
(k+1)-ary relation that is functional on its first k domains
The operation of addition
Quadratic equations can also be solved
6. Logarithm (Log)
The method of equating the coefficients
A solution or root of the equation
inverse operation of Exponentiation
exponential equation
7. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
A binary relation R over a set X is symmetric
Difference of two squares - or the difference of perfect squares
The operation of exponentiation
Categories of Algebra
8. Can be combined using the function composition operation - performing the first rotation and then the second.
Unary operations
Difference of two squares - or the difference of perfect squares
Reunion of broken parts
Rotations
9. 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.
The central technique to linear equations
Number line or real line
Unknowns
Identity
10. Can be defined axiomatically up to an isomorphism
logarithmic equation
Equations
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.
The real number system
11. () 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.
an operation
A differential equation
Algebra
Rotations
12. An operation of arity k is called a
Identities
k-ary operation
Operations on functions
Operations on sets
13. Is algebraic equation of degree one
A linear equation
An operation ?
has arity one
Operations can involve dissimilar objects
14. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
operation
Algebraic geometry
Algebraic equation
The relation of inequality (<) has this property
15. 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
Identity
Identity element of Multiplication
when b > 0
A functional equation
16. May not be defined for every possible value.
Knowns
the set Y
Difference of two squares - or the difference of perfect squares
Operations
17. Is an algebraic 'sentence' containing an unknown quantity.
associative law of addition
Quadratic equations
inverse operation of addition
Polynomials
18. Applies abstract algebra to the problems of geometry
Algebraic geometry
has arity one
Linear algebra
(k+1)-ary relation that is functional on its first k domains
19. If a < b and b < c
reflexive
Equations
inverse operation of addition
then a < c
20. If a = b then b = a
domain
symmetric
Algebra
Equation Solving
21. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
Variables
Elementary algebra
has arity two
22. Is an action or procedure which produces a new value from one or more input values.
A integral equation
Solution to the system
The relation of inequality (<) has this property
an operation
23. 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).
symmetric
inverse operation of addition
Binary operations
operation
24. Can be added and subtracted.
inverse operation of Exponentiation
Vectors
Categories of Algebra
inverse operation of Multiplication
25. If it holds for all a and b in X that if a is related to b then b is related to a.
A binary relation R over a set X is symmetric
radical equation
Multiplication
Algebraic equation
26. 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)
operation
when b > 0
The relation of equality (=)
Knowns
27. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
value - result - or output
unary and binary
The sets Xk
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.
28. 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)
associative law of addition
Operations on sets
The operation of exponentiation
A integral equation
29. Is an equation in which a polynomial is set equal to another polynomial.
the set Y
A polynomial equation
Knowns
Operations on sets
30. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
Rotations
The relation of equality (=)
nonnegative numbers
31. If a = b and b = c then a = c
Equation Solving
Real number
transitive
The relation of equality (=) has the property
32. 1 - which preserves numbers: a^1 = a
scalar
identity element of Exponentiation
The relation of inequality (<) has this property
k-ary operation
33. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Conditional equations
Order of Operations
then ac < bc
Equation Solving
34. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
then bc < ac
Linear algebra
system of linear equations
A functional equation
35. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
The sets Xk
A binary relation R over a set X is symmetric
equation
An operation ?
36. 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
The method of equating the coefficients
Quadratic equations can also be solved
The logical values true and false
Abstract algebra
37. A + b = b + a
nonnegative numbers
The relation of equality (=)
commutative law of Addition
Operations
38. A binary operation
Elementary algebra
Associative law of Multiplication
has arity two
Reunion of broken parts
39. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
has arity one
Algebra
Solution to the system
The simplest equations to solve
40. Is an equation involving integrals.
Equations
A integral equation
(k+1)-ary relation that is functional on its first k domains
exponential equation
41. There are two common types of operations:
Operations on functions
unary and binary
Equation Solving
Conditional equations
42. Involve only one value - such as negation and trigonometric functions.
Quadratic equations can also be solved
The central technique to linear equations
operands - arguments - or inputs
Unary operations
43. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
nonnegative numbers
A polynomial equation
Variables
Number line or real line
44. Subtraction ( - )
inverse operation of addition
Elimination method
Identities
inverse operation of Multiplication
45. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
operands - arguments - or inputs
The relation of equality (=) has the property
Identity
Binary operations
46. 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
Algebraic equation
Rotations
Elementary algebra
identity element of addition
47. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
has arity one
Equation Solving
Unary operations
48. A
The relation of inequality (<) has this property
The real number system
commutative law of Multiplication
The central technique to linear equations
49. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Variables
Difference of two squares - or the difference of perfect squares
Unknowns
nonnegative numbers
50. Is called the codomain of the operation
then a + c < b + d
Polynomials
the set Y
The relation of equality (=)