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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. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
The sets Xk
then ac < bc
Addition
2. (a + b) + c = a + (b + c)
identity element of Exponentiation
Unknowns
associative law of addition
reflexive
3. Can be added and subtracted.
Equation Solving
A integral equation
Vectors
inverse operation of Multiplication
4. 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).
The operation of addition
Quadratic equations
A binary relation R over a set X is symmetric
Categories of Algebra
5. A
when b > 0
All quadratic equations
The relation of equality (=) has the property
commutative law of Multiplication
6. Are called the domains of the operation
nonnegative numbers
The sets Xk
Conditional equations
Associative law of Multiplication
7. Is an equation of the form log`a^X = b for a > 0 - which has solution
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.
Reflexive relation
Conditional equations
logarithmic equation
8. 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.
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9. Is an equation involving integrals.
A integral equation
Equations
value - result - or output
Associative law of Multiplication
10. 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'.
A transcendental equation
Reflexive relation
commutative law of Exponentiation
Multiplication
11. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
has arity two
Operations on functions
A polynomial equation
12. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
Identity element of Multiplication
Universal algebra
Constants
13. A unary operation
scalar
has arity one
system of linear equations
The real number system
14. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
The logical values true and false
Equations
Vectors
15. A + b = b + a
commutative law of Addition
range
Polynomials
the fixed non-negative integer k (the number of arguments)
16. 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
Universal algebra
Elimination method
Quadratic equations
value - result - or output
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.
Properties of equality
The relation of equality (=)'s property
when b > 0
equation
18. Can be combined using the function composition operation - performing the first rotation and then the second.
A polynomial equation
Rotations
The central technique to linear equations
then a < c
19. Division ( / )
scalar
Reunion of broken parts
inverse operation of Multiplication
then a + c < b + d
20. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
two inputs
A solution or root of the equation
Abstract algebra
Solving the Equation
21. 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
Unknowns
when b > 0
commutative law of Exponentiation
A integral equation
22. The squaring operation only produces
Operations can involve dissimilar objects
two inputs
nonnegative numbers
The sets Xk
23. (a
All quadratic equations
Associative law of Multiplication
nullary operation
Expressions
24. Is called the codomain of the operation
nullary operation
Multiplication
A functional equation
the set Y
25. The inner product operation on two vectors produces a
Repeated addition
Multiplication
scalar
Change of variables
26. The values of the variables which make the equation true are the solutions of the equation and can be found through
then ac < bc
Expressions
Unknowns
Equation Solving
27. Is an action or procedure which produces a new value from one or more input values.
an operation
The relation of equality (=)
inverse operation of addition
Elimination method
28. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
when b > 0
Quadratic equations
unary and binary
Binary operations
29. Applies abstract algebra to the problems of geometry
The logical values true and false
Binary operations
domain
Algebraic geometry
30. Is an equation of the form aX = b for a > 0 - which has solution
scalar
exponential equation
radical equation
A linear equation
31. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Identity
Solution to the system
has arity one
A polynomial equation
32. Involve only one value - such as negation and trigonometric functions.
Unary operations
value - result - or output
identity element of Exponentiation
A functional equation
33. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
has arity one
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.
domain
Conditional equations
34. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
commutative law of Addition
the set Y
nonnegative numbers
35. Are true for only some values of the involved variables: x2 - 1 = 4.
Algebraic equation
The relation of inequality (<) has this property
commutative law of Exponentiation
Conditional equations
36. Is an equation in which the unknowns are functions rather than simple quantities.
Knowns
A functional equation
an operation
Multiplication
37. 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)
Elimination method
operation
equation
A solution or root of the equation
38. If a < b and c > 0
Unknowns
then ac < bc
Operations can involve dissimilar objects
identity element of Exponentiation
39. Not commutative a^b?b^a
Quadratic equations
Equation Solving
Operations can involve dissimilar objects
commutative law of Exponentiation
40. 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)
Identity
Equations
A differential equation
The operation of addition
41. May not be defined for every possible value.
Equations
Operations
The purpose of using variables
The operation of addition
42. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
Repeated addition
exponential equation
Equations
43. In which properties common to all algebraic structures are studied
A polynomial equation
Algebraic geometry
Universal algebra
Algebraic number theory
44. If a < b and c < d
operation
then a + c < b + d
A transcendental equation
An operation ?
45. 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.
A differential equation
The relation of inequality (<) has this property
Change of variables
exponential equation
46. Logarithm (Log)
Abstract algebra
Equations
nonnegative numbers
inverse operation of Exponentiation
47. There are two common types of operations:
unary and binary
Elementary algebra
Binary operations
The operation of addition
48. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
A solution or root of the equation
an operation
operands - arguments - or inputs
49. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Algebra
nullary operation
Algebraic equation
Pure mathematics
50. Is the claim that two expressions have the same value and are equal.
Repeated addition
Polynomials
when b > 0
Equations