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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. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
A Diophantine equation
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 equality (=)
nonnegative numbers
2. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
radical equation
an operation
Equation Solving
3. In which abstract algebraic methods are used to study combinatorial questions.
finitary operation
radical equation
Constants
Algebraic combinatorics
4. May not be defined for every possible value.
The relation of equality (=)
Rotations
operation
Operations
5. 1 - which preserves numbers: a
identity element of Exponentiation
The logical values true and false
Reflexive relation
Identity element of Multiplication
6. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
nullary operation
Equations
range
7. 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
Order of Operations
range
Real number
The sets Xk
8. Is an equation in which a polynomial is set equal to another polynomial.
Polynomials
A polynomial equation
Operations
domain
9. 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
domain
Elimination method
Categories of Algebra
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.
10. Is an action or procedure which produces a new value from one or more input values.
A polynomial equation
Reflexive relation
unary and binary
an operation
11. 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
operands - arguments - or inputs
Reunion of broken parts
Order of Operations
Repeated multiplication
12. (a
The central technique to linear equations
Associative law of Multiplication
inverse operation of Multiplication
Reflexive relation
13. 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
Multiplication
when b > 0
has arity two
Addition
14. Is called the type or arity of the operation
then bc < ac
operation
the fixed non-negative integer k (the number of arguments)
Vectors
15. Subtraction ( - )
Operations on functions
identity element of addition
inverse operation of addition
Order of Operations
16. k-ary operation is a
(k+1)-ary relation that is functional on its first k domains
Equation Solving
Algebraic geometry
then ac < bc
17. Operations can have fewer or more than
Abstract algebra
Elimination method
two inputs
A functional equation
18. Are called the domains of the operation
domain
The sets Xk
Expressions
operation
19. In an equation with a single unknown - a value of that unknown for which the equation is true is called
The logical values true and false
Multiplication
A solution or root of the equation
Quadratic equations can also be solved
20. The codomain is the set of real numbers but the range is the
commutative law of Multiplication
nonnegative numbers
Elementary algebra
The operation of addition
21. Is an equation involving derivatives.
A differential equation
Elementary algebra
The operation of addition
Algebraic combinatorics
22. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Reunion of broken parts
system of linear equations
Exponentiation
Rotations
23. A + b = b + a
Solving the Equation
The simplest equations to solve
commutative law of Addition
Repeated addition
24. An operation of arity k is called a
k-ary operation
when b > 0
nonnegative numbers
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.
25. 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)
A solution or root of the equation
A linear equation
The operation of exponentiation
nonnegative numbers
26. 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.
Exponentiation
Change of variables
Order of Operations
an operation
27. The values for which an operation is defined form a set called its
nonnegative numbers
The method of equating the coefficients
Constants
domain
28. 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).
equation
Pure mathematics
then a < c
Quadratic equations
29. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Equations
Rotations
Pure mathematics
Quadratic equations
30. Is an equation involving a transcendental function of one of its variables.
k-ary operation
A transcendental equation
two inputs
Solving the Equation
31. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
finitary operation
Unknowns
range
Variables
32. If a < b and c < 0
the set Y
The sets Xk
then ac < bc
then bc < ac
33. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
commutative law of Multiplication
Algebraic combinatorics
Operations can involve dissimilar objects
Identities
34. Can be combined using the function composition operation - performing the first rotation and then the second.
operation
Rotations
the set Y
Multiplication
35. 1 - which preserves numbers: a^1 = a
Quadratic equations
Operations on functions
identity element of Exponentiation
transitive
36. 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)
An operation ?
The simplest equations to solve
The operation of addition
nonnegative numbers
37. Is an algebraic 'sentence' containing an unknown quantity.
Equations
Operations
A solution or root of the equation
Polynomials
38. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
The operation of exponentiation
Identities
The purpose of using variables
Identity
39. In which the specific properties of vector spaces are studied (including matrices)
Quadratic equations can also be solved
Linear algebra
Conditional equations
substitution
40. The process of expressing the unknowns in terms of the knowns is called
commutative law of Addition
The operation of exponentiation
value - result - or output
Solving the Equation
41. 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'.
range
Reflexive relation
Repeated addition
then bc < ac
42. The values combined are called
has arity one
operands - arguments - or inputs
then ac < bc
Solution to the system
43. 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).
Knowns
operation
inverse operation of addition
Equations
44. Is an equation of the form log`a^X = b for a > 0 - which has solution
identity element of addition
logarithmic equation
scalar
Repeated multiplication
45. A vector can be multiplied by a scalar to form another vector
operands - arguments - or inputs
Operations can involve dissimilar objects
range
Reflexive relation
46. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
The relation of equality (=) has the property
The relation of equality (=)
inverse operation of addition
Unknowns
47. 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.
The method of equating the coefficients
The central technique to linear equations
Identity
The relation of inequality (<) has this property
48. 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
A Diophantine equation
identity element of addition
Solution to the system
49. Can be added and subtracted.
Categories of Algebra
A polynomial equation
Vectors
system of linear equations
50. Can be defined axiomatically up to an isomorphism
An operation ?
A binary relation R over a set X is symmetric
The real number system
radical equation