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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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. Letters from the beginning of the alphabet like a - b - c... often denote
then bc < ac
Constants
Elimination method
commutative law of Exponentiation
2. b = b
Polynomials
(k+1)-ary relation that is functional on its first k domains
reflexive
domain
3. 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)
the set Y
exponential equation
unary and binary
operation
4. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
commutative law of Exponentiation
Abstract algebra
Repeated addition
A polynomial equation
5. Is Written as a + b
Addition
Equation Solving
All quadratic equations
A functional equation
6. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Expressions
The method of equating the coefficients
Unknowns
system of linear equations
7. The values combined are called
Real number
has arity one
The logical values true and false
operands - arguments - or inputs
8. The operation of multiplication means _______________: a
The operation of exponentiation
Elementary algebra
the fixed non-negative integer k (the number of arguments)
Repeated addition
9. Referring to the finite number of arguments (the value k)
finitary operation
The operation of exponentiation
Operations on functions
operation
10. Is called the codomain of the operation
the set Y
finitary operation
transitive
Algebraic number theory
11. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
logarithmic equation
A linear equation
Elementary algebra
12. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
The sets Xk
operands - arguments - or inputs
Difference of two squares - or the difference of perfect squares
13. 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
Difference of two squares - or the difference of perfect squares
operation
Reunion of broken parts
commutative law of Multiplication
14. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
A differential equation
system of linear equations
Identity element of Multiplication
Difference of two squares - or the difference of perfect squares
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.
Multiplication
The relation of inequality (<) has this property
domain
The relation of equality (=) has the property
16. k-ary operation is a
commutative law of Multiplication
(k+1)-ary relation that is functional on its first k domains
Algebraic equation
Associative law of Multiplication
17. (a
A differential equation
A binary relation R over a set X is symmetric
two inputs
Associative law of Multiplication
18. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Binary operations
A functional equation
A binary relation R over a set X is symmetric
Variables
19. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
Rotations
Elementary algebra
The operation of exponentiation
20. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The method of equating the coefficients
then a < c
The purpose of using variables
system of linear equations
21. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Algebraic combinatorics
The method of equating the coefficients
k-ary operation
radical equation
22. The value produced is called
value - result - or output
Algebraic number theory
A Diophantine equation
Operations on functions
23. 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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24. Is an action or procedure which produces a new value from one or more input values.
an operation
The method of equating the coefficients
Expressions
substitution
25. 0 - which preserves numbers: a + 0 = a
The simplest equations to solve
Elimination method
The operation of exponentiation
identity element of addition
26. If a < b and c < d
then a + c < b + d
Rotations
has arity two
Reunion of broken parts
27. Is Written as ab or a^b
Exponentiation
Associative law of Multiplication
associative law of addition
The method of equating the coefficients
28. Is an equation involving a transcendental function of one of its variables.
Variables
exponential equation
The central technique to linear equations
A transcendental equation
29. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
equation
Rotations
The method of equating the coefficients
inverse operation of Multiplication
30. The values for which an operation is defined form a set called its
The relation of equality (=) has the property
has arity one
exponential equation
domain
31. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Variables
Algebraic equation
Algebraic number theory
identity element of addition
32. Division ( / )
A differential equation
inverse operation of Multiplication
operation
Universal algebra
33. If a < b and c < 0
then bc < ac
Reflexive relation
(k+1)-ary relation that is functional on its first k domains
then a < c
34. 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.
The central technique to linear equations
Associative law of Exponentiation
Change of variables
Conditional equations
35. Is Written as a
Polynomials
Multiplication
the set Y
Linear algebra
36. Not commutative a^b?b^a
Identity
commutative law of Exponentiation
system of linear equations
Rotations
37. Include composition and convolution
Operations on functions
has arity one
An operation ?
inverse operation of addition
38. Is an equation involving derivatives.
Identity
Change of variables
Equation Solving
A differential equation
39. The process of expressing the unknowns in terms of the knowns is called
A linear equation
nonnegative numbers
then ac < bc
Solving the Equation
40. Is an equation involving integrals.
radical equation
Solution to the system
A integral equation
Expressions
41. Can be combined using logic operations - such as and - or - and not.
Categories of Algebra
Associative law of Exponentiation
Reunion of broken parts
The logical values true and false
42. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
reflexive
system of linear equations
two inputs
Quadratic equations can also be solved
43. If a = b and b = c then a = c
Multiplication
Constants
Linear algebra
transitive
44. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
A differential equation
Addition
A binary relation R over a set X is symmetric
45. Include the binary operations union and intersection and the unary operation of complementation.
The logical values true and false
identity element of addition
Operations on sets
Linear algebra
46. May not be defined for every possible value.
Associative law of Exponentiation
A integral equation
Operations
nullary operation
47. Is algebraic equation of degree one
inverse operation of addition
Algebra
A linear equation
operation
48. The codomain is the set of real numbers but the range is the
Linear algebra
Algebraic geometry
then a < c
nonnegative numbers
49. 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.
range
Properties of equality
Quadratic equations
has arity one
50. A binary operation
The purpose of using variables
has arity two
then ac < bc
Operations on functions