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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. 0 - which preserves numbers: a + 0 = a
identity element of addition
Unknowns
value - result - or output
The method of equating the coefficients
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)
value - result - or output
The operation of exponentiation
commutative law of Multiplication
identity element of Exponentiation
3. Is an equation of the form aX = b for a > 0 - which has solution
then a + c < b + d
operation
Associative law of Exponentiation
exponential equation
4. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Solution to the system
(k+1)-ary relation that is functional on its first k domains
Algebraic geometry
two inputs
5. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity element of Multiplication
Order of Operations
Identity
Quadratic equations
6. Subtraction ( - )
inverse operation of addition
identity element of addition
Equations
Identity element of Multiplication
7. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
commutative law of Multiplication
then a < c
Rotations
8. Not commutative a^b?b^a
Unary operations
commutative law of Exponentiation
Binary operations
A polynomial equation
9. Is an action or procedure which produces a new value from one or more input values.
an operation
All quadratic equations
Operations can involve dissimilar objects
Unknowns
10. Is called the codomain of the operation
the set Y
A transcendental equation
associative law of addition
has arity two
11. Include composition and convolution
logarithmic equation
identity element of addition
unary and binary
Operations on functions
12. () 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.
Algebra
Identity
then ac < bc
inverse operation of addition
13. Referring to the finite number of arguments (the value k)
symmetric
finitary operation
operation
Operations on sets
14. 1 - which preserves numbers: a
Identity element of Multiplication
Linear algebra
Universal algebra
The simplest equations to solve
15. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
Repeated addition
the set Y
value - result - or output
16. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
A transcendental equation
Reflexive relation
Unknowns
The logical values true and false
17. If a = b and b = c then a = c
logarithmic equation
transitive
Change of variables
The central technique to linear equations
18. If a < b and c < 0
then bc < ac
range
unary and binary
the fixed non-negative integer k (the number of arguments)
19. The value produced is called
value - result - or output
Equation Solving
Pure mathematics
Algebraic equation
20. 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.
equation
Universal algebra
The central technique to linear equations
the set Y
21. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Elimination method
Exponentiation
Rotations
Difference of two squares - or the difference of perfect squares
22. 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
commutative law of Multiplication
Constants
Real number
A binary relation R over a set X is symmetric
23. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
range
two inputs
operation
24. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
reflexive
The operation of addition
Variables
inverse operation of Exponentiation
25. Is an equation involving a transcendental function of one of its variables.
The relation of equality (=)
Vectors
Identity element of Multiplication
A transcendental equation
26. Is Written as a
The method of equating the coefficients
Identity
Constants
Multiplication
27. There are two common types of operations:
unary and binary
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.
symmetric
Unary operations
28. Applies abstract algebra to the problems of geometry
range
commutative law of Addition
Algebraic geometry
Properties of equality
29. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
range
The real number system
Identities
30. 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
Algebraic equation
The real number system
inverse operation of Exponentiation
31. The squaring operation only produces
Knowns
Quadratic equations can also be solved
nonnegative numbers
Variables
32. The codomain is the set of real numbers but the range is the
nonnegative numbers
The simplest equations to solve
The operation of exponentiation
transitive
33. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Abstract algebra
then bc < ac
The relation of equality (=)
Constants
34. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
The sets Xk
Number line or real line
an operation
A solution or root of the equation
35. Logarithm (Log)
Vectors
Pure mathematics
inverse operation of Exponentiation
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.
36. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
when b > 0
Equations
Multiplication
37. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
Change of variables
symmetric
A solution or root of the equation
38. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
Operations can involve dissimilar objects
Identity
Elimination method
39. If a = b then b = a
reflexive
The central technique to linear equations
symmetric
A solution or root of the equation
40. 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.
then a < c
The relation of inequality (<) has this property
The operation of addition
identity element of addition
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).
Quadratic 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.
nonnegative numbers
operation
42. 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
All quadratic equations
Elementary algebra
The method of equating the coefficients
Algebraic equation
43. k-ary operation is a
Binary operations
nullary operation
(k+1)-ary relation that is functional on its first k domains
commutative law of Addition
44. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Equation Solving
Solving the Equation
then bc < ac
45. 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'.
Associative law of Multiplication
Reflexive relation
The real number system
The simplest equations to solve
46. Is algebraic equation of degree one
A linear equation
Categories of Algebra
commutative law of Exponentiation
Reflexive relation
47. 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
All quadratic equations
Elimination method
logarithmic equation
Equations
48. Are true for only some values of the involved variables: x2 - 1 = 4.
associative law of addition
Conditional equations
The relation of equality (=)
transitive
49. Is the claim that two expressions have the same value and are equal.
substitution
the fixed non-negative integer k (the number of arguments)
Expressions
Equations
50. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
k-ary operation
Algebra
Algebraic equation
Repeated addition