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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
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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. 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).
Equations
Quadratic equations
associative law of addition
inverse operation of Exponentiation
2. 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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3. 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
Order of Operations
Elimination method
A polynomial equation
commutative law of Addition
4. If a < b and c > 0
then ac < bc
then bc < ac
range
Algebraic equation
5. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in
The method of equating the coefficients
Quadratic equations can also be solved
The operation of addition
Associative law of Multiplication
6. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Equations
inverse operation of Multiplication
Categories of Algebra
A differential equation
7. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
associative law of addition
Difference of two squares - or the difference of perfect squares
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.
Algebraic number theory
8. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Solution to the system
Quadratic equations can also be solved
then a + c < b + d
Knowns
9. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
A integral equation
value - result - or output
nonnegative numbers
10. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Equations
Expressions
The relation of inequality (<) has this property
A transcendental equation
11. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebraic equation
Order of Operations
commutative law of Addition
the set Y
12. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
radical equation
A integral equation
The relation of equality (=)
The operation of exponentiation
13. Is an equation involving integrals.
A transcendental equation
Abstract algebra
The central technique to linear equations
A integral equation
14. A vector can be multiplied by a scalar to form another vector
associative law of addition
commutative law of Multiplication
Universal algebra
Operations can involve dissimilar objects
15. 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.
Repeated multiplication
Change of variables
then a + c < b + d
Exponentiation
16. Letters from the beginning of the alphabet like a - b - c... often denote
Identity element of Multiplication
Algebraic number theory
system of linear equations
Constants
17. 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'.
commutative law of Multiplication
The relation of equality (=) has the property
Reflexive relation
k-ary operation
18. Is algebraic equation of degree one
A linear equation
A functional equation
equation
Identity element of Multiplication
19. A unary operation
Algebraic combinatorics
has arity one
Identities
Quadratic equations can also be solved
20. Division ( / )
Rotations
Categories of Algebra
inverse operation of Multiplication
system of linear equations
21. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
A transcendental equation
Order of Operations
The central technique to linear equations
22. Is Written as a + b
then a < c
commutative law of Addition
Addition
Unknowns
23. Logarithm (Log)
inverse operation of Exponentiation
nonnegative numbers
then a + c < b + d
logarithmic equation
24. Are called the domains of the operation
The sets Xk
scalar
The central technique to linear equations
Solving the Equation
25. In which properties common to all algebraic structures are studied
Equations
unary and binary
logarithmic equation
Universal algebra
26. The operation of exponentiation means ________________: a^n = a
Operations on sets
unary and binary
identity element of Exponentiation
Repeated multiplication
27. In which abstract algebraic methods are used to study combinatorial questions.
Number line or real line
Algebraic combinatorics
inverse operation of Multiplication
Rotations
28. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
The relation of equality (=)
equation
nullary operation
nonnegative numbers
29. The codomain is the set of real numbers but the range is the
nonnegative numbers
Unknowns
commutative law of Addition
A linear equation
30. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Unknowns
system of linear equations
Order of Operations
logarithmic equation
31. Is the claim that two expressions have the same value and are equal.
an operation
radical equation
Equations
Conditional equations
32. Referring to the finite number of arguments (the value k)
two inputs
The relation of inequality (<) has this property
unary and binary
finitary operation
33. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Variables
Categories of Algebra
Equations
The logical values true and false
34. 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.
commutative law of Multiplication
The relation of equality (=) has the property
Change of variables
operation
35. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
Number line or real line
symmetric
A linear equation
36. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Difference of two squares - or the difference of perfect squares
The operation of addition
Quadratic equations
Linear algebra
37. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
The logical values true and false
Binary operations
The real number system
value - result - or output
38. () 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
operation
then ac < bc
A transcendental equation
39. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Equations
A binary relation R over a set X is symmetric
A polynomial equation
Identity
40. Include composition and convolution
Repeated multiplication
Elimination method
Operations on functions
the set Y
41. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
k-ary operation
Abstract algebra
then a < c
then ac < bc
42. The values of the variables which make the equation true are the solutions of the equation and can be found through
then ac < bc
Equation Solving
The relation of inequality (<) has this property
the set Y
43. b = b
range
reflexive
Identity element of Multiplication
Polynomials
44. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Properties of equality
inverse operation of Exponentiation
The simplest equations to solve
Unary operations
45. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Change of variables
Solving the Equation
Number line or real line
then a < c
46. If a = b then b = a
symmetric
inverse operation of addition
Solving the Equation
A transcendental equation
47. 0 - which preserves numbers: a + 0 = a
Unary operations
Repeated addition
then bc < ac
identity element of addition
48. Applies abstract algebra to the problems of geometry
scalar
when b > 0
The relation of equality (=)
Algebraic geometry
49. The value produced is called
A differential equation
value - result - or output
commutative law of Addition
substitution
50. 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
Linear algebra
Elementary algebra
Reunion of broken parts
A functional equation
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