SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
Search
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. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
commutative law of Exponentiation
equation
Identity
Equations
2. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Equations
Binary operations
The real number system
Categories of Algebra
3. The inner product operation on two vectors produces a
A functional equation
scalar
Operations on functions
operation
4. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
Repeated multiplication
A functional equation
when b > 0
5. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Unary operations
Solution to the system
commutative law of Exponentiation
when b > 0
6. (a
nonnegative numbers
transitive
The sets Xk
Associative law of Multiplication
7. If a < b and c < 0
The central technique to linear equations
then bc < ac
then ac < bc
unary and binary
8. In an equation with a single unknown - a value of that unknown for which the equation is true is called
then ac < bc
then a + c < b + d
A solution or root of the equation
nullary operation
9. Letters from the beginning of the alphabet like a - b - c... often denote
commutative law of Exponentiation
Constants
two inputs
Solving the Equation
10. If a < b and c > 0
Operations can involve dissimilar objects
The central technique to linear equations
then ac < bc
Linear algebra
11. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
has arity two
Algebraic geometry
associative law of addition
12. If a < b and c < d
then a + c < b + d
associative law of addition
The relation of inequality (<) has this property
commutative law of Addition
13. Are true for only some values of the involved variables: x2 - 1 = 4.
radical equation
commutative law of Addition
The logical values true and false
Conditional equations
14. If a < b and b < c
commutative law of Multiplication
then a < c
Polynomials
A differential equation
15. 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)
The operation of addition
commutative law of Multiplication
inverse operation of Exponentiation
Expressions
16. If a = b and b = c then a = c
operands - arguments - or inputs
transitive
Algebraic equation
range
17. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
Solution to the system
A integral equation
then bc < ac
18. 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.
substitution
inverse operation of Exponentiation
Properties of equality
Algebraic equation
19. Is an equation involving integrals.
A integral equation
Order of Operations
commutative law of Exponentiation
Difference of two squares - or the difference of perfect squares
20. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
system of linear equations
Change of variables
Unknowns
Operations
21. 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.
Operations on sets
Change of variables
has arity two
Equation Solving
22. A + b = b + a
Reunion of broken parts
Properties of equality
commutative law of Addition
identity element of addition
23. k-ary operation is a
(k+1)-ary relation that is functional on its first k domains
A functional equation
The method of equating the coefficients
Algebra
24. A vector can be multiplied by a scalar to form another vector
The relation of equality (=)'s property
Operations can involve dissimilar objects
Associative law of Multiplication
Multiplication
25. 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).
Quadratic equations
A transcendental equation
The sets Xk
Operations
26. 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
Linear algebra
substitution
Algebraic geometry
Identities
27. The operation of exponentiation means ________________: a^n = a
identity element of Exponentiation
Repeated multiplication
Identities
commutative law of Exponentiation
28. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
nonnegative numbers
Repeated multiplication
Exponentiation
29. Is an action or procedure which produces a new value from one or more input values.
an operation
then ac < bc
identity element of Exponentiation
Categories of Algebra
30. 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
identity element of Exponentiation
Elementary algebra
Operations on sets
has arity one
31. 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
when b > 0
Quadratic equations
Elimination method
Repeated multiplication
32. 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'.
Reflexive relation
The relation of equality (=) has the property
Categories of Algebra
An operation ?
33. Operations can have fewer or more than
A Diophantine equation
A differential equation
Elimination method
two inputs
34. Division ( / )
inverse operation of Multiplication
Multiplication
(k+1)-ary relation that is functional on its first k domains
The relation of inequality (<) has this property
35. Logarithm (Log)
inverse operation of Exponentiation
The relation of equality (=) has the property
Elementary algebra
(k+1)-ary relation that is functional on its first k domains
36. 0 - which preserves numbers: a + 0 = a
identity element of addition
finitary operation
has arity one
Expressions
37. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
inverse operation of addition
A linear equation
Unary operations
38. 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 simplest equations to solve
A differential equation
Multiplication
Real number
39. 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
The sets Xk
when b > 0
nonnegative numbers
The relation of equality (=)
40. 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)
operation
Abstract algebra
Solution to the system
Elementary algebra
41. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Binary operations
has arity one
Pure mathematics
Equations
42. Can be defined axiomatically up to an isomorphism
range
Elimination method
Conditional equations
The real number system
43. Is algebraic equation of degree one
Change of variables
Elementary algebra
A linear equation
A functional equation
44. Is an equation of the form aX = b for a > 0 - which has solution
operands - arguments - or inputs
Exponentiation
exponential equation
Repeated addition
45. Is an equation where the unknowns are required to be integers.
A Diophantine equation
Associative law of Exponentiation
Polynomials
identity element of Exponentiation
46. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Algebraic number theory
The relation of equality (=) has the property
The operation of exponentiation
Quadratic equations can also be solved
47. Is an equation in which a polynomial is set equal to another polynomial.
A Diophantine equation
unary and binary
A polynomial equation
Vectors
48. Is called the codomain of the operation
reflexive
the set Y
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.
The relation of inequality (<) has this property
49. Is an equation involving derivatives.
radical equation
A differential equation
The relation of equality (=)'s property
Conditional equations
50. May not be defined for every possible value.
operation
unary and binary
Operations
identity element of addition