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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. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Operations
Unknowns
Algebraic number theory
A linear equation
2. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
A functional equation
Algebraic equation
Equation Solving
The purpose of using variables
3. Is an equation where the unknowns are required to be integers.
A Diophantine equation
Solving the Equation
Order of Operations
reflexive
4. Is Written as ab or a^b
Pure mathematics
Exponentiation
Equations
nullary operation
5. 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
Operations can involve dissimilar objects
Order of Operations
Elimination method
Equations
6. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
Identity element of Multiplication
inverse operation of Multiplication
Equations
7. Is called the codomain of the operation
has arity one
Universal algebra
A solution or root of the equation
the set Y
8. Logarithm (Log)
Solving the Equation
symmetric
inverse operation of Exponentiation
range
9. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
the set Y
Solution to the system
Order of Operations
Operations on sets
10. In which the specific properties of vector spaces are studied (including matrices)
A polynomial equation
A Diophantine equation
Operations
Linear algebra
11. 1 - which preserves numbers: a
Associative law of Multiplication
Binary operations
Expressions
Identity element of Multiplication
12. Include the binary operations union and intersection and the unary operation of complementation.
the set Y
Operations on sets
Equation Solving
nonnegative numbers
13. 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)
Reflexive relation
inverse operation of Multiplication
Constants
The operation of exponentiation
14. () 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
The purpose of using variables
inverse operation of Exponentiation
has arity one
15. Include composition and convolution
Pure mathematics
Exponentiation
Operations on functions
The central technique to linear equations
16. Can be combined using the function composition operation - performing the first rotation and then the second.
reflexive
radical equation
Difference of two squares - or the difference of perfect squares
Rotations
17. If a < b and b < c
then a < c
commutative law of Addition
The relation of equality (=)'s property
The sets Xk
18. Is the claim that two expressions have the same value and are equal.
Equations
The relation of equality (=)
Elementary algebra
The operation of addition
19. The value produced is called
value - result - or output
The operation of exponentiation
operation
Algebra
20. Is an equation in which the unknowns are functions rather than simple quantities.
The operation of exponentiation
A functional equation
A polynomial equation
The relation of equality (=) has the property
21. Is an equation involving a transcendental function of one of its variables.
k-ary operation
Associative law of Exponentiation
A transcendental equation
Order of Operations
22. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Identity
value - result - or output
Algebraic equation
Variables
23. A
the fixed non-negative integer k (the number of arguments)
commutative law of Multiplication
exponential equation
Repeated addition
24. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
Identities
Solving the Equation
Repeated multiplication
25. Is Written as a + b
then bc < ac
has arity one
Addition
A linear equation
26. Can be added and subtracted.
Vectors
The central technique to linear equations
A linear equation
Operations
27. Are denoted by letters at the beginning - a - b - c - d - ...
inverse operation of Exponentiation
Vectors
Knowns
Reunion of broken parts
28. Is an equation involving integrals.
range
when b > 0
nonnegative numbers
A integral equation
29. Is an equation of the form X^m/n = a - for m - n integers - which has solution
A integral equation
domain
radical equation
A differential equation
30. If a < b and c < 0
Pure mathematics
Associative law of Multiplication
Algebraic combinatorics
then bc < ac
31. 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
has arity one
scalar
when b > 0
A functional equation
32. Division ( / )
Equations
Reflexive relation
Operations can involve dissimilar objects
inverse operation of Multiplication
33. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
identity element of addition
Abstract algebra
The purpose of using variables
Solving the Equation
34. If a = b then b = a
Solving the Equation
Knowns
Repeated multiplication
symmetric
35. 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
The relation of equality (=) has the property
Multiplication
Polynomials
Elementary algebra
36. The operation of exponentiation means ________________: a^n = a
Unary operations
Equation Solving
Unknowns
Repeated multiplication
37. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
Binary operations
Reunion of broken parts
Operations on functions
38. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Constants
Quadratic equations can also be solved
Categories of Algebra
then ac < bc
39. The values for which an operation is defined form a set called its
Order of Operations
scalar
Unary operations
domain
40. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
radical equation
has arity one
Number line or real line
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.
41. 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
Variables
A solution or root of the equation
Equation Solving
42. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Real number
Quadratic equations
Pure mathematics
then ac < bc
43. May not be defined for every possible value.
Associative law of Exponentiation
Elimination method
Operations
Linear algebra
44. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Order of Operations
then a < c
Associative law of Exponentiation
Number line or real line
45. Is an equation involving derivatives.
Binary operations
A differential equation
exponential equation
inverse operation of Multiplication
46. Is an equation of the form aX = b for a > 0 - which has solution
two inputs
exponential equation
A polynomial equation
identity element of Exponentiation
47. Not commutative a^b?b^a
commutative law of Exponentiation
Algebraic geometry
Binary operations
system of linear equations
48. Operations can have fewer or more than
identity element of Exponentiation
Operations can involve dissimilar objects
Algebraic equation
two inputs
49. 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
The sets Xk
Reunion of broken parts
An operation ?
The relation of inequality (<) has this property
50. Is a function of the form ? : V ? Y - where V ? X1
Operations
operation
An operation ?
The sets Xk