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CLEP College Algebra: Algebra Principles
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Subjects
:
clep
,
math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
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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 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.
an operation
Quadratic equations
A differential equation
Change of variables
2. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
Solution to the system
identity element of addition
The relation of equality (=) has the property
3. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
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.
operation
The operation of addition
Abstract algebra
4. Are true for only some values of the involved variables: x2 - 1 = 4.
A polynomial equation
The relation of equality (=)'s property
Conditional equations
equation
5. 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 exponentiation
The operation of addition
symmetric
Number line or real line
6. 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).
then ac < bc
Algebra
Quadratic equations
reflexive
7. Is Written as ab or a^b
Exponentiation
Knowns
Universal algebra
Pure mathematics
8. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Unknowns
then ac < bc
The simplest equations to solve
All quadratic equations
9. Referring to the finite number of arguments (the value k)
The operation of addition
A solution or root of the equation
finitary operation
has arity two
10. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Constants
The operation of addition
Operations can involve dissimilar objects
Number line or real line
11. The inner product operation on two vectors produces a
Rotations
radical equation
scalar
Operations can involve dissimilar objects
12. Is an equation in which a polynomial is set equal to another polynomial.
Repeated multiplication
A polynomial equation
k-ary operation
Identity
13. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
The operation of addition
Change of variables
finitary operation
14. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
(k+1)-ary relation that is functional on its first k domains
Algebraic equation
inverse operation of Multiplication
Knowns
15. A unary operation
Operations on sets
has arity one
A solution or root of the equation
Unknowns
16. A binary operation
The relation of equality (=)'s property
Vectors
two inputs
has arity two
17. Is a function of the form ? : V ? Y - where V ? X1
nullary operation
A polynomial equation
The purpose of using variables
An operation ?
18. Is an algebraic 'sentence' containing an unknown quantity.
Polynomials
Algebraic combinatorics
Linear algebra
two inputs
19. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Unknowns
Difference of two squares - or the difference of perfect squares
Polynomials
Binary operations
20. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
when b > 0
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.
A binary relation R over a set X is symmetric
Equations
21. In which abstract algebraic methods are used to study combinatorial questions.
Unary operations
Identity element of Multiplication
A binary relation R over a set X is symmetric
Algebraic combinatorics
22. Are denoted by letters at the beginning - a - b - c - d - ...
then a < c
Knowns
Identity element of Multiplication
range
23. 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).
operation
A functional equation
Operations on functions
system of linear equations
24. If a < b and c > 0
substitution
then ac < bc
Change of variables
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. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Constants
Identities
The relation of equality (=)
26. The process of expressing the unknowns in terms of the knowns is called
k-ary operation
has arity one
Solving the Equation
The operation of addition
27. If a = b and b = c then a = c
(k+1)-ary relation that is functional on its first k domains
The relation of inequality (<) has this property
Operations
transitive
28. (a
Associative law of Multiplication
inverse operation of addition
The logical values true and false
Quadratic equations
29. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
Addition
Algebraic geometry
The purpose of using variables
30. 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.
A transcendental equation
The real number system
The central technique to linear equations
nonnegative numbers
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
A differential equation
The sets Xk
when b > 0
reflexive
32. Is an equation of the form X^m/n = a - for m - n integers - which has solution
A binary relation R over a set X is symmetric
Pure mathematics
radical equation
The purpose of using variables
33. An operation of arity zero is simply an element of the codomain Y - called a
substitution
nullary operation
unary and binary
Equations
34. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
A linear equation
The relation of equality (=)
Identities
35. Is an action or procedure which produces a new value from one or more input values.
Elimination method
exponential equation
identity element of Exponentiation
an operation
36. 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
logarithmic equation
The sets Xk
The relation of equality (=)
37. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic number theory
identity element of Exponentiation
Equations
The method of equating the coefficients
38. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
Properties of equality
range
the fixed non-negative integer k (the number of arguments)
39. The operation of exponentiation means ________________: a^n = a
equation
the fixed non-negative integer k (the number of arguments)
Repeated multiplication
Repeated addition
40. Can be added and subtracted.
Equations
associative law of addition
Solving the Equation
Vectors
41. b = b
inverse operation of Exponentiation
Operations can involve dissimilar objects
two inputs
reflexive
42. In which the specific properties of vector spaces are studied (including matrices)
(k+1)-ary relation that is functional on its first k domains
Linear algebra
Order of Operations
identity element of Exponentiation
43. If a < b and c < 0
the fixed non-negative integer k (the number of arguments)
then bc < ac
then ac < bc
nonnegative numbers
44. 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.
Properties of equality
Identity element of Multiplication
The relation of equality (=) has the property
Solving the Equation
45. A + b = b + a
Equation Solving
Expressions
Operations can involve dissimilar objects
commutative law of Addition
46. 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
inverse operation of addition
Elimination method
A differential equation
commutative law of Addition
47. Not associative
Equations
Quadratic equations
The operation of addition
Associative law of Exponentiation
48. Is the claim that two expressions have the same value and are equal.
Identity
A Diophantine equation
Elimination method
Equations
49. Is an equation involving a transcendental function of one of its variables.
A polynomial equation
Abstract algebra
A transcendental equation
Identity element of Multiplication
50. 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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