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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. The values for which an operation is defined form a set called its
Reunion of broken parts
an operation
Order of Operations
domain
2. Applies abstract algebra to the problems of geometry
inverse operation of addition
Equation Solving
Algebraic geometry
Quadratic equations can also be solved
3. Referring to the finite number of arguments (the value k)
Solution to the system
when b > 0
finitary operation
Expressions
4. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Equation Solving
equation
The relation of equality (=)
finitary operation
5. Is algebraic equation of degree one
commutative law of Exponentiation
A integral equation
range
A linear equation
6. A binary operation
has arity two
Operations
then a < c
The operation of addition
7. Is an equation in which a polynomial is set equal to another polynomial.
symmetric
Properties of equality
A polynomial equation
Knowns
8. Is called the codomain of the operation
nonnegative numbers
Multiplication
the set Y
Operations on sets
9. The operation of exponentiation means ________________: a^n = a
Unknowns
A linear equation
Repeated multiplication
An operation ?
10. Not associative
The simplest equations to solve
The sets Xk
Associative law of Exponentiation
Real number
11. 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).
inverse operation of addition
The real number system
Operations can involve dissimilar objects
operation
12. There are two common types of operations:
(k+1)-ary relation that is functional on its first k domains
The logical values true and false
operands - arguments - or inputs
unary and binary
13. If it holds for all a and b in X that if a is related to b then b is related to a.
The logical values true and false
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.
Repeated multiplication
A binary relation R over a set X is symmetric
14. Will have two solutions in the complex number system - but need not have any in the real number system.
Linear algebra
The relation of equality (=) has the property
All quadratic equations
Associative law of Exponentiation
15. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
The relation of equality (=)'s property
radical equation
finitary operation
16. Is called the type or arity of the operation
A transcendental equation
system of linear equations
has arity two
the fixed non-negative integer k (the number of arguments)
17. The inner product operation on two vectors produces a
the set Y
scalar
A functional equation
Operations can involve dissimilar objects
18. If a = b and b = c then a = c
the fixed non-negative integer k (the number of arguments)
transitive
Abstract algebra
Exponentiation
19. Is an algebraic 'sentence' containing an unknown quantity.
The relation of equality (=) has the property
inverse operation of Multiplication
Polynomials
The central technique to linear equations
20. Is an action or procedure which produces a new value from one or more input values.
when b > 0
Polynomials
unary and binary
an operation
21. 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'.
Quadratic equations
The operation of exponentiation
Algebraic combinatorics
Reflexive relation
22. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
A linear equation
Associative law of Exponentiation
Polynomials
23. 0 - which preserves numbers: a + 0 = a
identity element of addition
Linear algebra
Elementary algebra
has arity one
24. 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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25. 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
commutative law of Multiplication
Order of Operations
Elimination method
substitution
26. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
Equations
Identity element of Multiplication
Expressions
27. The value produced is called
value - result - or output
Operations
Identity
operation
28. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Universal algebra
A transcendental equation
then bc < ac
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.
29. Is an equation of the form log`a^X = b for a > 0 - which has solution
The sets Xk
value - result - or output
logarithmic equation
inverse operation of Multiplication
30. The process of expressing the unknowns in terms of the knowns is called
Order of Operations
Universal algebra
radical equation
Solving the Equation
31. 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.
The central technique to linear equations
Number line or real line
Repeated addition
Difference of two squares - or the difference of perfect squares
32. 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.
The operation of exponentiation
nullary operation
operands - arguments - or inputs
The relation of equality (=) has the property
33. 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
Polynomials
Reunion of broken parts
Real number
All quadratic equations
34. A unary operation
domain
equation
has arity one
Algebraic geometry
35. The squaring operation only produces
The relation of equality (=) has the property
The method of equating the coefficients
nonnegative numbers
an operation
36. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
associative law of addition
The operation of addition
The relation of equality (=)
37. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Universal algebra
Binary operations
Variables
A Diophantine equation
38. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Conditional equations
Number line or real line
system of linear equations
Linear algebra
39. 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
then a + c < b + d
reflexive
A linear equation
40. 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)
Binary operations
Algebraic equation
The operation of addition
A integral equation
41. 1 - which preserves numbers: a
when b > 0
operation
Identity element of Multiplication
The operation of exponentiation
42. Is a function of the form ? : V ? Y - where V ? X1
Elementary algebra
Number line or real line
domain
An operation ?
43. Is Written as a
inverse operation of Multiplication
Multiplication
the fixed non-negative integer k (the number of arguments)
operation
44. In an equation with a single unknown - a value of that unknown for which the equation is true is called
A solution or root of the equation
Expressions
the set Y
Change of variables
45. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
nonnegative numbers
A binary relation R over a set X is symmetric
Repeated multiplication
46. An operation of arity zero is simply an element of the codomain Y - called a
The relation of equality (=) has the property
A transcendental equation
nullary operation
Difference of two squares - or the difference of perfect squares
47. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Pure mathematics
Properties of equality
Knowns
Algebraic equation
48. May not be defined for every possible value.
Operations
The relation of equality (=)'s property
Addition
Constants
49. Operations can have fewer or more than
nullary operation
two inputs
Constants
A linear equation
50. Are called the domains of the operation
The sets Xk
The purpose of using variables
A integral equation
Solving the Equation