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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
the fixed non-negative integer k (the number of arguments)
Equation Solving
range
2. Is Written as ab or a^b
Operations
when b > 0
then ac < bc
Exponentiation
3. Is called the codomain of the operation
the set Y
Exponentiation
value - result - or output
nullary operation
4. Can be combined using the function composition operation - performing the first rotation and then the second.
All quadratic equations
equation
nonnegative numbers
Rotations
5. There are two common types of operations:
nonnegative numbers
unary and binary
Elimination method
Operations on functions
6. Not commutative a^b?b^a
then ac < bc
commutative law of Exponentiation
Operations can involve dissimilar objects
Multiplication
7. A vector can be multiplied by a scalar to form another vector
A solution or root of the equation
Operations can involve dissimilar objects
domain
Rotations
8. Referring to the finite number of arguments (the value k)
finitary operation
domain
Reflexive relation
Expressions
9. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Rotations
Constants
radical equation
identity element of Exponentiation
10. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
Operations on functions
Expressions
identity element of addition
11. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
radical equation
Operations
system of linear equations
Rotations
12. May not be defined for every possible value.
Operations
Linear algebra
Real number
identity element of addition
13. The values of the variables which make the equation true are the solutions of the equation and can be found through
substitution
Equation Solving
commutative law of Multiplication
transitive
14. 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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15. 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.
Categories of Algebra
The relation of inequality (<) has this property
scalar
A Diophantine equation
16. () 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
All quadratic equations
An operation ?
symmetric
17. Can be defined axiomatically up to an isomorphism
The operation of exponentiation
The real number system
Equation Solving
an operation
18. 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).
operation
Rotations
Pure mathematics
A transcendental equation
19. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
The relation of inequality (<) has this property
reflexive
Difference of two squares - or the difference of perfect squares
The logical values true and false
20. 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
Real number
Reunion of broken parts
The relation of inequality (<) has this property
Multiplication
21. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Operations on sets
Variables
symmetric
Unknowns
22. Not associative
An operation ?
logarithmic equation
nonnegative numbers
Associative law of Exponentiation
23. 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
A binary relation R over a set X is symmetric
Change of variables
Real number
An operation ?
24. Are true for only some values of the involved variables: x2 - 1 = 4.
Algebraic geometry
Conditional equations
scalar
A functional equation
25. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
value - result - or output
Linear algebra
nonnegative numbers
26. Can be combined using logic operations - such as and - or - and not.
A integral equation
A polynomial equation
Real number
The logical values true and false
27. An operation of arity zero is simply an element of the codomain Y - called a
identity element of Exponentiation
nullary operation
the fixed non-negative integer k (the number of arguments)
has arity two
28. 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
then a < c
Operations
commutative law of Exponentiation
29. Letters from the beginning of the alphabet like a - b - c... often denote
Real number
domain
has arity one
Constants
30. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Unary operations
Operations
Expressions
Operations can involve dissimilar objects
31. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Variables
inverse operation of Multiplication
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
32. Is Written as a
Categories of Algebra
has arity two
Reunion of broken parts
Multiplication
33. 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 relation of equality (=) has the property
The method of equating the coefficients
A solution or root of the equation
operation
34. A unary operation
has arity one
Difference of two squares - or the difference of perfect squares
Equation Solving
The sets Xk
35. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Reflexive relation
Equation Solving
range
operands - arguments - or inputs
36. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
reflexive
Identity element of Multiplication
The sets Xk
37. A + b = b + a
nonnegative numbers
An operation ?
Identity element of Multiplication
commutative law of Addition
38. The values for which an operation is defined form a set called its
the fixed non-negative integer k (the number of arguments)
domain
logarithmic equation
The relation of equality (=) has the property
39. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
identity element of addition
Identity
A polynomial equation
A differential equation
40. If a = b and b = c then a = c
commutative law of Addition
transitive
Difference of two squares - or the difference of perfect squares
radical equation
41. If a = b then b = a
scalar
has arity two
symmetric
substitution
42. Is the claim that two expressions have the same value and are equal.
nonnegative numbers
Algebra
The logical values true and false
Equations
43. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
logarithmic equation
symmetric
then ac < bc
44. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
then bc < ac
the set Y
Order of Operations
A Diophantine equation
45. 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).
Reunion of broken parts
Order of Operations
Quadratic equations
exponential equation
46. Is an equation involving integrals.
A transcendental equation
The operation of exponentiation
A integral equation
Universal algebra
47. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Knowns
Equations
finitary operation
Binary operations
48. Include composition and convolution
associative law of addition
operands - arguments - or inputs
Operations on functions
The relation of equality (=)
49. 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.
Exponentiation
A binary relation R over a set X is symmetric
The central technique to linear equations
The relation of inequality (<) has this property
50. Are called the domains of the operation
The sets Xk
the fixed non-negative integer k (the number of arguments)
Algebra
Real number