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. k-ary operation is a
associative law of addition
Abstract algebra
exponential equation
(k+1)-ary relation that is functional on its first k domains
2. 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).
Variables
Quadratic equations
Unary operations
Rotations
3. Is Written as ab or a^b
Algebra
Exponentiation
Algebraic combinatorics
Equations
4. 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.
Equation Solving
The logical values true and false
The relation of inequality (<) has this property
then bc < ac
5. If a < b and b < c
then a < c
Equations
A differential equation
inverse operation of addition
6. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
commutative law of Exponentiation
Reflexive relation
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.
value - result - or output
7. If a < b and c < d
Equations
An operation ?
Reunion of broken parts
then a + c < b + d
8. The codomain is the set of real numbers but the range is the
Equations
finitary operation
k-ary operation
nonnegative numbers
9. Is an equation in which the unknowns are functions rather than simple quantities.
range
finitary operation
Constants
A functional equation
10. 0 - which preserves numbers: a + 0 = a
identity element of addition
The relation of equality (=) has the property
Equations
The relation of inequality (<) has this property
11. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
Addition
nonnegative numbers
Equations
12. Are denoted by letters at the beginning - a - b - c - d - ...
Operations on sets
Reunion of broken parts
range
Knowns
13. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
The relation of equality (=)'s property
Expressions
A solution or root of the equation
The central technique to linear equations
14. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
Vectors
The real number system
Equations
15. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
associative law of addition
Quadratic equations
Algebraic number theory
exponential equation
16. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
the set Y
Knowns
symmetric
17. Are true for only some values of the involved variables: x2 - 1 = 4.
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.
Algebraic equation
Operations on sets
Conditional equations
18. Is an equation in which a polynomial is set equal to another polynomial.
The relation of equality (=)'s property
Operations
transitive
A polynomial equation
19. If it holds for all a and b in X that if a is related to b then b is related to a.
The sets Xk
A binary relation R over a set X is symmetric
Addition
domain
20. Division ( / )
equation
scalar
inverse operation of Multiplication
Operations on functions
21. Subtraction ( - )
domain
Rotations
Number line or real line
inverse operation of addition
22. 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.
Warning
: Invalid argument supplied for foreach() in
/var/www/html/basicversity.com/show_quiz.php
on line
183
23. Applies abstract algebra to the problems of geometry
Expressions
Algebraic geometry
Algebra
Elementary algebra
24. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
The central technique to linear equations
Unknowns
Operations on sets
then a + c < b + d
25. 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.
identity element of addition
transitive
Properties of equality
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)
radical equation
operation
Constants
Abstract algebra
27. If a < b and c > 0
Equation Solving
Addition
Associative law of Multiplication
then ac < bc
28. In an equation with a single unknown - a value of that unknown for which the equation is true is called
inverse operation of Multiplication
A solution or root of the equation
A polynomial equation
Difference of two squares - or the difference of perfect squares
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
Variables
equation
Number line or real line
The method of equating the coefficients
30. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
logarithmic equation
the set Y
A differential equation
The relation of equality (=)
31. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
the set Y
All quadratic equations
A transcendental equation
32. 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
scalar
range
Change of variables
substitution
33. Is the claim that two expressions have the same value and are equal.
Equations
A transcendental equation
A binary relation R over a set X is symmetric
Universal algebra
34. May not be defined for every possible value.
two inputs
commutative law of Exponentiation
Quadratic equations
Operations
35. Are called the domains of the operation
Identity
The relation of inequality (<) has this property
The sets Xk
associative law of addition
36. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Solving the Equation
Number line or real line
Unknowns
radical equation
37. 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'.
commutative law of Addition
The method of equating the coefficients
the fixed non-negative integer k (the number of arguments)
Reflexive relation
38. 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
Knowns
system of linear equations
The sets Xk
Elimination method
39. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Universal algebra
inverse operation of Exponentiation
A differential equation
Categories of Algebra
40. If a = b and b = c then a = c
commutative law of Exponentiation
Abstract algebra
The purpose of using variables
transitive
41. Is an algebraic 'sentence' containing an unknown quantity.
nonnegative numbers
A binary relation R over a set X is symmetric
Polynomials
operation
42. Is called the codomain of the operation
(k+1)-ary relation that is functional on its first k domains
Order of Operations
Variables
the set Y
43. A vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
A transcendental equation
Addition
has arity two
44. 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.
operands - arguments - or inputs
(k+1)-ary relation that is functional on its first k domains
The relation of equality (=) has the property
nonnegative numbers
45. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Multiplication
inverse operation of addition
A polynomial equation
Solution to the system
46. (a + b) + c = a + (b + c)
The relation of equality (=)
associative law of addition
Operations
nullary operation
47. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Algebraic equation
symmetric
radical equation
exponential equation
48. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
The purpose of using variables
All quadratic equations
range
The relation of inequality (<) has this property
49. An operation of arity k is called a
k-ary operation
Pure mathematics
Real number
Equation Solving
50. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym
Algebra
A linear equation
Elimination method
Reunion of broken parts