SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
Search
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. Division ( / )
the fixed non-negative integer k (the number of arguments)
inverse operation of Multiplication
Repeated multiplication
system of linear equations
2. 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.
Categories of Algebra
The central technique to linear equations
Algebraic equation
Equation Solving
3. In which properties common to all algebraic structures are studied
(k+1)-ary relation that is functional on its first k domains
the fixed non-negative integer k (the number of arguments)
Unary operations
Universal algebra
4. Is Written as a
Multiplication
Elimination method
operands - arguments - or inputs
Order of Operations
5. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
commutative law of Addition
The relation of equality (=)
Algebra
The sets Xk
6. The codomain is the set of real numbers but the range is the
A transcendental equation
Algebraic combinatorics
nonnegative numbers
A solution or root of the equation
7. Is an equation where the unknowns are required to be integers.
finitary operation
A Diophantine equation
Rotations
range
8. 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
the fixed non-negative integer k (the number of arguments)
range
when b > 0
commutative law of Addition
9. Is an equation involving derivatives.
has arity one
Algebraic geometry
A differential equation
range
10. A
A differential equation
Binary operations
commutative law of Multiplication
Repeated addition
11. Are true for only some values of the involved variables: x2 - 1 = 4.
Addition
Conditional equations
Multiplication
inverse operation of addition
12. Is called the type or arity of the operation
The relation of inequality (<) has this property
associative law of addition
Properties of equality
the fixed non-negative integer k (the number of arguments)
13. 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.
Algebraic equation
The relation of equality (=) has the property
nonnegative numbers
A transcendental equation
14. There are two common types of operations:
A functional equation
All quadratic equations
unary and binary
The relation of inequality (<) has this property
15. The value produced is called
Repeated multiplication
the set Y
Operations
value - result - or output
16. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
The simplest equations to solve
nullary operation
Expressions
Linear algebra
17. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.
Change of variables
nonnegative numbers
system of linear equations
Reunion of broken parts
18. If a < b and c > 0
Elementary algebra
then ac < bc
commutative law of Exponentiation
then a + c < b + d
19. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
unary and binary
An operation ?
radical equation
20. Is an equation involving a transcendental function of one of its variables.
finitary operation
Operations on functions
A transcendental equation
Expressions
21. In an equation with a single unknown - a value of that unknown for which the equation is true is called
commutative law of Addition
then a < c
A solution or root of the equation
when b > 0
22. Include the binary operations union and intersection and the unary operation of complementation.
Number line or real line
Algebraic equation
Operations on sets
unary and binary
23. 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)
Identities
nullary operation
Solving the Equation
The operation of exponentiation
24. 0 - which preserves numbers: a + 0 = a
identity element of addition
Binary operations
Unary operations
Difference of two squares - or the difference of perfect squares
25. 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
has arity one
Multiplication
substitution
Pure mathematics
26. The inner product operation on two vectors produces a
A Diophantine equation
radical equation
Associative law of Exponentiation
scalar
27. The squaring operation only produces
Unknowns
nonnegative numbers
Difference of two squares - or the difference of perfect squares
All quadratic equations
28. Is Written as ab or a^b
range
Identities
Exponentiation
reflexive
29. 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.
30. 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'.
Identity
(k+1)-ary relation that is functional on its first k domains
Reflexive relation
substitution
31. (a
an operation
Associative law of Multiplication
commutative law of Addition
Algebraic geometry
32. Are called the domains of the operation
domain
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 sets Xk
(k+1)-ary relation that is functional on its first k domains
33. 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).
Knowns
Unknowns
Quadratic equations
Operations on sets
34. Is an equation involving integrals.
nullary operation
Quadratic equations can also be solved
then bc < ac
A integral equation
35. Is an equation of the form X^m/n = a - for m - n integers - which has solution
An operation ?
radical equation
Difference of two squares - or the difference of perfect squares
nonnegative numbers
36. k-ary operation is a
Identity
An operation ?
Real number
(k+1)-ary relation that is functional on its first k domains
37. A binary operation
Associative law of Multiplication
has arity two
operands - arguments - or inputs
Equations
38. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
equation
range
Elimination method
39. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
Knowns
The real number system
The purpose of using variables
40. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
value - result - or output
Variables
Equations
The real number system
41. Not associative
Associative law of Exponentiation
range
A linear equation
Quadratic equations can also be solved
42. A unary operation
Associative law of Multiplication
has arity one
Polynomials
The relation of equality (=)
43. 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
range
Elementary algebra
Real number
The relation of equality (=)
44. 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
Associative law of Multiplication
Algebraic combinatorics
Elimination method
then bc < ac
45. Is an equation in which a polynomial is set equal to another polynomial.
Quadratic equations
A polynomial equation
The central technique to linear equations
Binary operations
46. 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.
Properties of equality
Operations
Elementary algebra
operation
47. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Rotations
All quadratic equations
Algebraic number theory
Identity
48. () 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.
equation
Algebra
operation
inverse operation of Multiplication
49. Is called the codomain of the operation
the set Y
Algebraic number theory
Real number
Number line or real line
50. 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
nullary operation
(k+1)-ary relation that is functional on its first k domains
Solution to the system