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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. Is an equation involving integrals.
then a + c < b + d
A integral equation
A differential equation
The operation of addition
2. There are two common types of operations:
Reunion of broken parts
unary and binary
identity element of Exponentiation
The relation of equality (=)
3. Referring to the finite number of arguments (the value k)
Multiplication
finitary operation
The real number system
Rotations
4. 1 - which preserves numbers: a
system of linear equations
Identity element of Multiplication
Solving the Equation
Algebra
5. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
The simplest equations to solve
All 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.
identity element of addition
6. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Equations
Identity element of Multiplication
Identity
The method of equating the coefficients
7. 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
Multiplication
then a < c
The method of equating the coefficients
finitary operation
8. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
commutative law of Addition
The real number system
Reflexive relation
9. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
Equations
Difference of two squares - or the difference of perfect squares
Variables
10. If a < b and c < d
then a + c < b + d
nonnegative numbers
inverse operation of Exponentiation
The relation of equality (=) has the property
11. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Exponentiation
system of linear equations
operands - arguments - or inputs
Change of variables
12. If a = b then b = a
A functional equation
then a + c < b + d
symmetric
The relation of inequality (<) has this property
13. b = b
Properties of equality
reflexive
operation
logarithmic equation
14. Is an equation involving derivatives.
k-ary operation
A differential equation
two inputs
exponential equation
15. The values combined are called
symmetric
operands - arguments - or inputs
Order of Operations
All quadratic equations
16. A
then bc < ac
commutative law of Multiplication
The purpose of using variables
The relation of equality (=) has the property
17. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
then bc < ac
The relation of equality (=)
transitive
A solution or root of the equation
18. 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
radical equation
Number line or real line
A solution or root of the equation
19. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic number theory
two inputs
The method of equating the coefficients
Operations on sets
20. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Quadratic equations
operation
has arity one
21. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
operands - arguments - or inputs
Constants
Binary operations
A differential equation
22. If a = b and b = c then a = c
The relation of equality (=)
transitive
domain
The central technique to linear equations
23. Is an equation in which the unknowns are functions rather than simple quantities.
equation
Pure mathematics
A functional equation
The logical values true and false
24. Division ( / )
The simplest equations to solve
then a < c
inverse operation of addition
inverse operation of Multiplication
25. Is the claim that two expressions have the same value and are equal.
Abstract algebra
Equations
A integral equation
operands - arguments - or inputs
26. 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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27. 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
Addition
Categories of Algebra
commutative law of Multiplication
28. A binary operation
Operations on functions
A functional equation
has arity two
Operations can involve dissimilar objects
29. The squaring operation only produces
nonnegative numbers
when b > 0
Abstract algebra
domain
30. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
All quadratic equations
reflexive
nonnegative numbers
31. 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
A solution or root of the equation
Real number
nonnegative numbers
32. Subtraction ( - )
inverse operation of addition
The operation of exponentiation
The simplest equations to solve
The relation of equality (=) has the property
33. The process of expressing the unknowns in terms of the knowns is called
Associative law of Exponentiation
then a < c
Solving the Equation
then a + c < b + d
34. 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
An operation ?
when b > 0
Reflexive relation
Difference of two squares - or the difference of perfect squares
35. Involve only one value - such as negation and trigonometric functions.
symmetric
The operation of addition
Unary operations
identity element of addition
36. 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.
Pure mathematics
A Diophantine equation
when b > 0
The central technique to linear equations
37. Operations can have fewer or more than
then a < c
All quadratic equations
then ac < bc
two inputs
38. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
the set Y
Conditional equations
Identities
then ac < bc
39. The operation of exponentiation means ________________: a^n = a
Polynomials
Repeated multiplication
A solution or root of the equation
Binary operations
40. 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
the fixed non-negative integer k (the number of arguments)
operation
Reunion of broken parts
reflexive
41. 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
scalar
operands - arguments - or inputs
then ac < bc
42. An operation of arity zero is simply an element of the codomain Y - called a
finitary operation
The operation of exponentiation
A transcendental equation
nullary operation
43. Is a function of the form ? : V ? Y - where V ? X1
commutative law of Addition
reflexive
The method of equating the coefficients
An operation ?
44. The value produced is called
Quadratic equations can also be solved
A functional equation
value - result - or output
Reflexive relation
45. If a < b and c < 0
inverse operation of addition
Algebraic geometry
operands - arguments - or inputs
then bc < ac
46. 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'.
Addition
value - result - or output
Reflexive relation
Polynomials
47. 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)
when b > 0
Algebraic combinatorics
Elimination method
The operation of exponentiation
48. The operation of multiplication means _______________: a
A functional equation
then bc < ac
Repeated addition
A solution or root of the equation
49. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
The central technique to linear equations
Algebraic equation
Multiplication
when b > 0
50. Can be added and subtracted.
Linear 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.
Unknowns
Vectors