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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.
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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. The operation of multiplication means _______________: a
A integral equation
radical equation
A transcendental equation
Repeated addition
2. If a < b and c > 0
an operation
Difference of two squares - or the difference of perfect squares
then ac < bc
Binary operations
3. If a < b and c < 0
then bc < ac
Equation Solving
Identities
Algebra
4. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
the set Y
logarithmic equation
system of linear equations
A polynomial equation
5. If a = b and b = c then a = c
transitive
has arity one
radical equation
Algebraic number theory
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).
associative law of addition
Reflexive relation
Quadratic equations
Number line or real line
7. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
The simplest equations to solve
Quadratic equations
associative law of addition
Order of Operations
8. 0 - which preserves numbers: a + 0 = a
Solving the Equation
identity element of addition
Conditional equations
A transcendental equation
9. The inner product operation on two vectors produces a
Algebraic combinatorics
equation
scalar
domain
10. 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.
The relation of equality (=)'s property
The operation of exponentiation
Change of variables
nullary operation
11. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
The operation of addition
Quadratic equations
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.
12. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
Identities
Algebra
The simplest equations to solve
13. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
The operation of exponentiation
A Diophantine equation
Equations
Reflexive relation
14. May not be defined for every possible value.
the fixed non-negative integer k (the number of arguments)
An operation ?
Constants
Operations
15. b = b
value - result - or output
reflexive
A binary relation R over a set X is symmetric
the set Y
16. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
commutative law of Multiplication
Number line or real line
exponential equation
the fixed non-negative integer k (the number of arguments)
17. Involve only one value - such as negation and trigonometric functions.
Unary operations
The operation of exponentiation
The relation of inequality (<) has this property
two inputs
18. 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
Algebraic number theory
exponential equation
Elementary algebra
19. Is an action or procedure which produces a new value from one or more input values.
the fixed non-negative integer k (the number of arguments)
A linear equation
range
an operation
20. Can be added and subtracted.
Linear algebra
Vectors
Difference of two squares - or the difference of perfect squares
The sets Xk
21. Are true for only some values of the involved variables: x2 - 1 = 4.
associative law of addition
Reflexive relation
Algebraic combinatorics
Conditional equations
22. Is Written as a + b
Addition
The simplest equations to solve
Unknowns
Difference of two squares - or the difference of perfect squares
23. Is an algebraic 'sentence' containing an unknown quantity.
Polynomials
All quadratic equations
Algebraic geometry
an operation
24. A + b = b + a
Algebraic combinatorics
commutative law of Addition
commutative law of Exponentiation
symmetric
25. Will have two solutions in the complex number system - but need not have any in the real number system.
Identities
The simplest equations to solve
then ac < bc
All quadratic equations
26. The codomain is the set of real numbers but the range is the
nonnegative numbers
Elimination method
commutative law of Addition
A integral equation
27. k-ary operation is a
(k+1)-ary relation that is functional on its first k domains
The simplest equations to solve
range
Rotations
28. Is an equation in which the unknowns are functions rather than simple quantities.
has arity two
Algebraic number theory
A differential equation
A functional equation
29. 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
nonnegative numbers
Change of variables
Reunion of broken parts
Operations can involve dissimilar objects
30. Not commutative a^b?b^a
inverse operation of addition
Equations
Identity
commutative law of Exponentiation
31. In which abstract algebraic methods are used to study combinatorial questions.
transitive
identity element of Exponentiation
Multiplication
Algebraic combinatorics
32. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
equation
Operations
commutative law of Exponentiation
unary and binary
33. 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.
when b > 0
The central technique to linear equations
Algebraic combinatorics
Elimination method
34. Is an equation in which a polynomial is set equal to another polynomial.
A Diophantine equation
then a < c
A polynomial 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.
35. Is called the codomain of the operation
Algebraic equation
Categories of Algebra
the set Y
the fixed non-negative integer k (the number of arguments)
36. Can be combined using logic operations - such as and - or - and not.
Properties of equality
The logical values true and false
A solution or root of the equation
A transcendental equation
37. If a < b and b < c
associative law of addition
Algebraic combinatorics
Operations on sets
then a < c
38. If a = b then b = a
Exponentiation
substitution
The method of equating the coefficients
symmetric
39. Include the binary operations union and intersection and the unary operation of complementation.
A solution or root of the equation
The logical values true and false
Unary operations
Operations on sets
40. Is an equation involving derivatives.
exponential equation
then a + c < b + d
A differential equation
Quadratic equations can also be solved
41. There are two common types of operations:
The purpose of using variables
The operation of exponentiation
unary and binary
inverse operation of addition
42. The operation of exponentiation means ________________: a^n = a
Binary operations
has arity two
Repeated multiplication
Number line or real line
43. Operations can have fewer or more than
Reflexive relation
Linear algebra
Elementary algebra
two inputs
44. Is an equation where the unknowns are required to be integers.
Equation Solving
The sets Xk
Operations
A Diophantine equation
45. 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.
logarithmic equation
The relation of equality (=) has the property
Repeated multiplication
Constants
46. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
Exponentiation
Equations
has arity two
47. 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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48. If a < b and c < d
system of linear equations
then a + c < b + d
range
A polynomial equation
49. 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
reflexive
Quadratic equations
A Diophantine equation
50. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Solution to the system
Algebraic combinatorics
The purpose of using 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.
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