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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. Logarithm (Log)
A differential equation
A linear equation
Identity element of Multiplication
inverse operation of Exponentiation
2. Is an equation of the form log`a^X = b for a > 0 - which has solution
Repeated addition
nullary operation
nonnegative numbers
logarithmic equation
3. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
Operations
The operation of exponentiation
Knowns
4. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
associative law of addition
Difference of two squares - or the difference of perfect squares
domain
5. Is Written as a + b
Associative law of Multiplication
finitary operation
The simplest equations to solve
Addition
6. The value produced is called
value - result - or output
Equations
nonnegative numbers
Repeated addition
7. If a = b and b = c then a = c
Elementary algebra
The simplest equations to solve
Repeated addition
transitive
8. Is called the type or arity of the operation
The purpose of using variables
the fixed non-negative integer k (the number of arguments)
Rotations
Order of Operations
9. Not associative
two inputs
Real number
Associative law of Exponentiation
Universal algebra
10. b = b
identity element of Exponentiation
commutative law of Multiplication
Exponentiation
reflexive
11. 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)
The operation of exponentiation
operation
commutative law of Addition
Variables
12. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
Knowns
associative law of addition
Expressions
13. A + b = b + a
(k+1)-ary relation that is functional on its first k domains
commutative law of Addition
has arity one
Properties of equality
14. A vector can be multiplied by a scalar to form another vector
Associative law of Multiplication
Elimination method
Operations can involve dissimilar objects
A differential equation
15. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
exponential equation
an operation
Polynomials
16. 1 - which preserves numbers: a
Linear algebra
value - result - or output
Algebraic combinatorics
Identity element of Multiplication
17. Is called the codomain of the operation
k-ary operation
Conditional equations
scalar
the set Y
18. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Unary operations
nonnegative numbers
Variables
Quadratic equations can also be solved
19. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Elimination method
Reflexive relation
Algebraic number theory
Equations
20. If a < b and b < c
then a < c
The real number system
Equations
A functional equation
21. k-ary operation is a
Equation Solving
Unknowns
(k+1)-ary relation that is functional on its first k domains
scalar
22. Is an equation where the unknowns are required to be integers.
operands - arguments - or inputs
A solution or root of the equation
Operations can involve dissimilar objects
A Diophantine equation
23. A binary operation
The method of equating the coefficients
has arity two
The relation of inequality (<) has this property
All quadratic equations
24. 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
The method of equating the coefficients
Operations can involve dissimilar objects
operands - arguments - or inputs
Real number
25. Include the binary operations union and intersection and the unary operation of complementation.
A binary relation R over a set X is symmetric
inverse operation of addition
Operations on sets
then ac < bc
26. If it holds for all a and b in X that if a is related to b then b is related to a.
then ac < bc
Equations
A binary relation R over a set X is symmetric
exponential equation
27. 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 purpose of using variables
Quadratic equations
then ac < bc
Equation Solving
28. 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
when b > 0
Polynomials
Multiplication
range
29. An operation of arity zero is simply an element of the codomain Y - called a
Difference of two squares - or the difference of perfect squares
Real number
Multiplication
nullary operation
30. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
then bc < ac
commutative law of Addition
Number line or real line
two inputs
31. Is Written as a
Categories of Algebra
Multiplication
reflexive
A binary relation R over a set X is symmetric
32. Is the claim that two expressions have the same value and are equal.
Elementary algebra
Equations
Linear algebra
Identities
33. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
k-ary operation
the fixed non-negative integer k (the number of arguments)
Binary operations
Expressions
34. 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
Reunion of broken parts
Algebraic number theory
Solving the Equation
Unary operations
35. (a
radical equation
A solution or root of the equation
Associative law of Multiplication
system of linear equations
36. Is an equation of the form X^m/n = a - for m - n integers - which has solution
k-ary operation
Expressions
radical equation
symmetric
37. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Properties of equality
Expressions
identity element of Exponentiation
The operation of exponentiation
38. 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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39. 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.
unary and binary
Unary operations
The central technique to linear equations
radical equation
40. Not commutative a^b?b^a
inverse operation of addition
A transcendental equation
commutative law of Exponentiation
then ac < bc
41. In an equation with a single unknown - a value of that unknown for which the equation is true is called
A solution or root of the equation
then a < c
Algebra
operands - arguments - or inputs
42. Referring to the finite number of arguments (the value k)
Associative law of Exponentiation
Variables
finitary operation
Quadratic equations
43. (a + b) + c = a + (b + c)
radical equation
associative law of addition
Equations
Pure mathematics
44. Operations can have fewer or more than
Properties of equality
Knowns
two inputs
Polynomials
45. Is an algebraic 'sentence' containing an unknown quantity.
The logical values true and false
Polynomials
Operations on sets
Conditional equations
46. If a < b and c < 0
then bc < ac
unary and binary
The relation of inequality (<) has this property
the fixed non-negative integer k (the number of arguments)
47. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
Operations on sets
Constants
operation
48. 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
Conditional equations
The method of equating the coefficients
two inputs
Equations
49. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Algebraic number theory
Identity
inverse operation of Multiplication
50. The squaring operation only produces
nonnegative numbers
Elimination method
The relation of equality (=)
Vectors