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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. Is an equation where the unknowns are required to be integers.
Addition
A Diophantine equation
Conditional equations
Change of variables
2. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
A functional equation
then a < c
Equations
Reunion of broken parts
3. There are two common types of operations:
Algebraic equation
finitary operation
unary and binary
Associative law of Exponentiation
4. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic number theory
Equation Solving
Operations can involve dissimilar objects
inverse operation of addition
5. 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
substitution
Operations on sets
the fixed non-negative integer k (the number of arguments)
then a < c
6. 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)
A integral equation
Quadratic equations
Addition
The operation of addition
7. An operation of arity zero is simply an element of the codomain Y - called a
A linear equation
inverse operation of addition
nullary operation
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.
8. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Operations on functions
Solution to the system
The simplest equations to solve
equation
9. 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.
A linear equation
The method of equating the coefficients
Properties of equality
Exponentiation
10. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
identity element of Exponentiation
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.
11. Include composition and convolution
Identity
Categories of Algebra
Operations on functions
operation
12. An operation of arity k is called a
Change of variables
The real number system
Reflexive relation
k-ary operation
13. Is algebraic equation of degree one
A linear equation
Elementary algebra
The purpose of using variables
Linear algebra
14. 1 - which preserves numbers: a
Identity element of Multiplication
An operation ?
reflexive
The relation of inequality (<) has this property
15. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Linear algebra
The relation of equality (=)'s property
Abstract algebra
Change of variables
16. Logarithm (Log)
inverse operation of Exponentiation
Algebraic number theory
Associative law of Exponentiation
Algebraic geometry
17. 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.
The relation of equality (=) has the property
unary and binary
system of linear equations
operation
18. Is an equation involving derivatives.
The relation of equality (=)'s property
substitution
equation
A differential equation
19. Is an equation of the form aX = b for a > 0 - which has solution
Solution to the system
associative law of addition
exponential equation
Identities
20. The values of the variables which make the equation true are the solutions of the equation and can be found through
the set Y
Equation Solving
then a < c
The relation of equality (=) has the property
21. Will have two solutions in the complex number system - but need not have any in the real number system.
Repeated multiplication
All quadratic equations
Associative law of Exponentiation
The central technique to linear equations
22. Are denoted by letters at the beginning - a - b - c - d - ...
An operation ?
Knowns
Algebraic equation
Real number
23. k-ary operation is a
A transcendental equation
(k+1)-ary relation that is functional on its first k domains
The simplest equations to solve
Difference of two squares - or the difference of perfect squares
24. A
commutative law of Exponentiation
Binary operations
commutative law of Multiplication
Equations
25. Division ( / )
The sets Xk
Operations on functions
range
inverse operation of Multiplication
26. Is Written as a + b
Real number
Constants
A functional equation
Addition
27. 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 addition
Algebraic number theory
Repeated multiplication
The operation of exponentiation
28. If a < b and b < c
Linear algebra
then a < c
Number line or real line
The relation of equality (=) has the property
29. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
when b > 0
Properties of equality
Categories of Algebra
Algebraic equation
30. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Linear algebra
Change of variables
Identity element of Multiplication
Unknowns
31. If a = b then b = a
then ac < bc
commutative law of Multiplication
symmetric
The sets Xk
32. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
The operation of exponentiation
A differential equation
commutative law of Addition
33. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Addition
inverse operation of Multiplication
system of linear equations
Quadratic equations can also be solved
34. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
Operations can involve dissimilar objects
Equation Solving
Variables
35. b = b
k-ary operation
The operation of exponentiation
All quadratic equations
reflexive
36. Is called the type or arity of the operation
transitive
Real number
the fixed non-negative integer k (the number of arguments)
Algebraic equation
37. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
scalar
A differential equation
Unknowns
38. A vector can be multiplied by a scalar to form another vector
Order of Operations
Operations can involve dissimilar objects
Equation Solving
The operation of addition
39. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
commutative law of Exponentiation
Associative law of Multiplication
Order of Operations
transitive
40. 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).
unary and binary
Categories of Algebra
operation
then a + c < b + d
41. 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
Expressions
when b > 0
Polynomials
Change of variables
42. The values for which an operation is defined form a set called its
The relation of inequality (<) has this property
inverse operation of Multiplication
commutative law of Exponentiation
domain
43. 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)
Elementary algebra
operation
A solution or root of the equation
inverse operation of addition
44. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Elimination method
operands - arguments - or inputs
Variables
A functional equation
45. If a < b and c > 0
The central technique to linear equations
The real number system
then ac < bc
scalar
46. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
symmetric
Algebraic equation
Multiplication
Properties of equality
47. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi
finitary operation
has arity one
commutative law of Addition
Elementary algebra
48. If a = b and b = c then a = c
A functional equation
transitive
Algebraic equation
Constants
49. 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).
Identity
operands - arguments - or inputs
Quadratic equations
Repeated multiplication
50. Is an equation of the form X^m/n = a - for m - n integers - which has solution
unary and binary
A transcendental equation
radical equation
Repeated addition